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Guide

ANSI/AIAAG-034-1998

Guide to Reference and StandardIonosphere Models

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ANSI/AIAAG-034-1998

American National Standard

Guide to Reference and StandardIonosphere Models

Sponsor

American Institute of Aeronautics and Astronautics

Approved July 15, 1999

American National Standards Institute

Abstract

This standard provides guidelines for selecting ionospheric models for engineering design or scientificresearch. The Guide describes the content of the models, uncertainties and limitations, technical basis,databases from which the models are formed, publication references, and sources of computer codes forapproximately 30 ionospheric models. The models cover the altitude range from the Earth’s surface toapproximately 10,000 kilometers. This Guide is intended to assist communication (C

3I) and space sys-

tem designers and developers, geophysicists, space physicists, and climatologists in understandingavailable models and comparing sources of data and interpreting engineering and scientific results basedon different ionospheric models.

ANSI/AIAA G-034-1998

ii

AmericanNationalStandard

Approval of an American National Standard requires verification by ANSI that the require-ments for due process, consensus, and other criteria have been met by the standards devel-oper.

Consensus is established when, in the judgment of the ANSI Board of Standards Review,substantial agreement has been reached by directly and materially affected interests. Sub-stantial agreement means much more than a simple majority, but not necessarily unanimity.Consensus requires that all views and objections be considered, and that a concerted effortbe made toward their resolution.

The use of American National Standards is completely voluntary; their existence does not inany respect preclude anyone, whether he has approved the standards or not, from manufac-turing, marketing, purchasing, or using products, processes, or procedures not conforming tothe standards.

The American National Standards Institute does not develop standards and will in no circum-stances give an interpretation of any American National Standard. Moreover, no person shallhave the right or authority to issue an interpretation of an American National Standard in thename of the American National Standards Institute. Requests for interpretations should beaddressed to the secretariat or sponsor whose name appears on the title page of this stan-dard.

CAUTION NOTICE: This American National Standard may be revised or withdrawn at anytime. The procedures of the American National Standards Institute require that action betaken to affirm, revise, or withdraw this standard no later than five years from the date of ap-proval. Purchasers of American National Standards may receive current information on allstandards by calling or writing the American National Standards Institute.

Guide to reference and standard ionosphere models/sponsor, American Institute of Aeronautics and Astronautics.

p. cm."ANSI/AIAA G-034-1998"

Includes bibliographical references. ISBN 1-56347-347-X 1. Ionosphere--Mathematical models. I. American Institute of Aeronautics andAstronautics.QC881.2.I6G85 1999551.51'45'05118--dc21 99-23533 CIP

Published byAmerican Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344

Copyright © 1999 American Institute of Aeronautics and Astronautics, Inc.All rights reserved.

No part of this publication may be reproduced in any form, in an electronicretrieval system or otherwise, without prior written permission of the publisher.

Printed in the United States of America


iii

ContentsForeword .................................................................................................................................................vSummary of Reference and Standard Ionospheres................................................................................ vii

GLOBAL IONOSPHERE MODELS

USU Time-Dependent Model of the Global Ionosphere,R.W. Schunk and J.J. Sojka........................................................................................................1

NCAR Thermosphere-Ionosphere-Electrodynamics General Circulation Model,1993, R. G. Roble .......................................................................................................................3

Coupled Thermosphere-Ionosphere Model (CTIM), T. J. Fuller-Rowell ....................................................5Coupled Thermosphere-Ionosphere-Plasmasphere Model (CTIP),

T. J. Fuller-Rowell .......................................................................................................................7AFRL Global Theoretical Ionospheric Model (GTIM), D. N. Anderson ......................................................8Parameterized Ionospheric Model (PIM), D. N. Anderson, R. E. Daniell................................................. 10International Reference Ionosphere (IRI), 1996, D. Bilitza...................................................................... 12Empirical Model of the Ionosphere, W. Kohnlein.................................................................................... 15The Sheffield University Plasmashphere-Ionsophere Model (SUPIM), G.J. Bailey ................................. 17The Field Line Interhemispheric Plasma Model, P. Richards.................................................................. 19

LOWER IONOSPHERE

D Region:Algebraic Model, W. Swider................................................................................................................... 21Numerical Model of D-Region Ion Chemistry, 1995, E. Turunen ............................................................ 23

E Region:Solar EUV and Chemistry Model, W. Swider ......................................................................................... 26AFRL Bolzmann-Fokker-Planck Model for the Daytime Lower Ionosphere,

J. Jasperse................................................................................................................................ 28AFRL Transport Model for the Electron-Proton-Hydrogen Atom Aurora, J. Jasperse.............................. 30

KEY RELATED PROPERTIES

Electric Fields:Two-Cell Ionospheric Convection Model, R.A. Heelis............................................................................. 33Heppner-Maynard Electric Field Models, J.P. Heppner and N.C. Maynard............................................. 35Millstone Hill Empirical Electric Field Model, 1986, J.C. Foster.............................................................. 37APL High-Latitude Convection Model, M. Ruohoniemi........................................................................... 39

Neutral Winds:HWM Empirical Wind Model, A. Hedin .................................................................................................. 41

Temperature:Global Empirical Models of Te, L.H. Brace............................................................................................. 43Empirical Model of the Ionospheric Electron and Ion Temperatures, W. Kohnlein.................................. 45Photochemical Equilibrium Model for Ionospheric Conductivity, C.E. Rasmussen ................................. 47Empirical Model of Conductivities, D. Brautigam ................................................................................... 48

Particles and Currents:Auroral Electron and Ion Fluxes, D. Brautigam ...................................................................................... 50


iv

IONOSPHERIC EFFECTS

Scintillation—C3I/Navigation Outage:WBMOD Ionospheric Scintillation Model (NWRA), 1995,

E.J. Fremouw and S. Basu .............................................................................................................. 52

Clutter and Trough—HF/VHF Loss:Model of the Trough in the High-Latitude F Layer, J.A. Whalen ............................................................. 55

TEC—Navigation Errors:GPS Eight-Coefficient TEC Model, R.E. Daniell .................................................................................... 56The CPI TEC Model, R.E. Daniell .......................................................................................................... 57


v

ForewordThis Guide to Reference and Standard Iono-sphere Models has been sponsored by theAmerican Institute of Aeronautics and Astronau-tics (AIAA) as part of its Standards Program.

The proliferation of ionospheric models and thelack of documentation have hindered generalknowledge of their availability as well as theirrelative strengths, weaknesses, and limitations.The intent of this guide is to compile in one ref-erence practical information about known andavailable ionospheric models—those that de-scribe the physical properties and practical ef-fects of the ionosphere as a function of altitude,latitude, and other key parameters. At this writ-ing, the included models are those intended forgeneral-purpose, scientific, or aerospace appli-cations and therefore extend to heights rangingfrom 50 to 10,000 km. Dynamical models of theionosphere are included in this guide, as the dy-namics are essential to many applications.

The guide summarizes the principal features ofthe models:

• model content• model uncertainties and limitations• basis of the model• database or model input parameters• publication references• dates of development, authors, and

sponsors• model codes and sources

The models are grouped according to whetherthey describe primarily global, regional, or spe-cial properties.

There is limited information on standard devia-tions from the mean values or frequencies ofoccurrence of some of the variables describedby these models. This limits quantitative as-sessments of uncertainties. Correlation dis-tances for electron densities, and statistics onscintillation are well defined. These and otherstatistics are discussed in the body of the guide.Candidates for inclusion in this guide have beensolicited by means of advertisements in publica-tions including: announcements at national andinternational meetings of URSI, IAGA, AGU,COSPAR, AIAA, and scientific communitynewsletters. This collection of models is not ex-haustive. It is hoped that future editions will in-

clude additional models from the internationalcommunity.

The AIAA Standards Procedures provide that allapproved Standards, Recommended Practices,and Guides are advisory only. Their use byanyone engaged in industry or trade is entirelyvoluntary. There is no agreement to adhere toany AIAA standards publication and no commit-ment to conform to or be guided by any stan-dards report. In formulating, revising, and ap-proving standards publications, the Committeeson Standards will not consider patents, whichmay apply to the subject matter. Prospectiveusers of the publications are responsible forprotecting themselves against liability for in-fringement of patents or copyrights, or both.

We are indebted to those authors who submittedtheir models for inclusion, to those who offeredvaluable advice, to Robert S. Skrivanek for no-table assistance, and to the reviewers/editors:Drs. Herbert C. Carlson (Chair), David N. An-derson, Santi Basu, Edward J. Fremouw,Roderic A. Heelis, and Robert W. Schunk.

The AIAA Atmospheric & Space EnvironmentsCommittee on Standards (Shu T. Lai, Chair-man) approved the document in April 1999.

The members of this consensus body at thetime of voting on the document are:Dana A. Brewer (NASA Headquarters)Herbert C Carlson (Air Force Office of Scientific

Research)Adarsh Deepak (Science & Technology Corp.)Gerald Dittberner (NOAA/NEDIS)L. J. Ehernberger (NASA Ames-Dryden Facil-

ity)Jeffrey M. Forbes (University of Colorado)Henry B. Garrett (Jet Propulsion Lab.)G. Barry Hillard (NASA Lewis Research Center)Stuart L. Huston (Boeing Space & Defense)JoAnn Joselyn (NOAA Space Environment

Lab.)Neil D. Kelley (National Renewable Energy

Lab.)O. Kenneth Moe (USAF Space & Missile

Systems Center)Jerry Owens (NASA Marshall Space Flight

Center)Robert Sears (Jamieson Science & Engineering)Robert A. Skrivanek (Visidyne Inc.)Guy F. Spitale (Jet Propulsion Laboratory)Walther Spjeldvik (Weber State University)


vi

Robert M. Suggs (NASA Marshall Space FlightCenter)

Gopal D. Tejwani (Lockheed Martin SpaceOperations.)

Alfred Vampola (Consultant)

William W. Vaughan (UAH Research Center)

The AIAA Standards Executive Council ac-cepted the document for publication in April1999.


vii

SUMMARY OF REFERENCE AND STANDARD IONOSPHERES

Model Geographic Altitude Parameters Species Temporal Output Principal(Page #) Region Range Included Variation Data Pre- Application

(km) sentation

USU global 90–1000 Ne, Ni, Te, NO+, O2+, N2

+ 10–100 sec tables, scientific(1) T i||, T i⊥, ue N+, O+, He+ plots studies

ui

NCAR/ global 70–600 Ne, Ni, Nn, all ion and 60 sec tables, scientificTIEGCM Te, T i, Tn, neutral plots studies(3) Ue, Ui, Un

CTIM global 80–10,000 Ne, Ni O+, H+, NO+, 1–6 min tables, scientific(5) neutrals O2 N2

+, N+, plots studiesU, V, W O, O2

+, N2, NO,Tn, Te, T i N(2D), N(4S)

CTIP global 80–10,000 Ne, Ni O+, H+, NO+, 1–15 min tables, scientific(7) neutrals O2

+, N2+, N+, plots studies

U, V, W O, O2, N2, NO,Tn, Te, T i, Te N(2D), N(4S)

GTIM global 90–22,000 Ne, Ni NO+, O2+, O+, diurnal with tables, theoretical

(8) H+, He+ resolution plots climatologyof 15 min and develop-

ment ofparametricmodels suchas PIM

PIM global 90–22,000 Ne, TEC O+, NO+, diurnal with tables theoretical(10) foF2, hmF2 O2

+ resolution climatology,foE, hmE of 30 min systems

design

IRI global Ne: 50–2000 Ne, Te, O-, H+, diurnal tables, spacecraft(12) T: 120–3000 T i, Ni He-, NO-, (LT, UT, interactive instrument

Ni: 100–2000 O2-, N2

- solar zenith on WWW design,cluster angle), satellite

seasonal tracking,solar cycle radio wave

propagation,altimeterdata analysisray-tracing,education,etc.

EMI global 50–4000 H+, He+ N+, O+, diurnal figures, scientific

(15) coverage N2+, NO+ O2

+, Ne seasonal tables studies(lat) solar activity

SUPIM global 90–22,000 Ne, Ni O+, O2+ diurnal tables theoretical

(17) Te, T i NO+, H+ with studies andHe+ resolution climatology

of x hr

FLIP mid-lat 90–22,000 Ne, Ni H+, He+, O+, N+ diurnal tables, mid-latitude(19) Te, T i NO+, O2

+, O+(2D) 1–30 min plots ionosphere-O+(2P), N(2D), resolution plasma-N(S4), N0, 0(1D), sphere singleN2(vib) ground

comparison

ALGEBRAIC global 60–90 21 positive ions diurnal tables, scientific(21) 8 negative ions plots studies

NUMERICAL global 60–90 36 positive ions diurnal tables, scientificCHEM 19 negative ions plots studies(23)


viii



(km) sentation

SOLAR EUV global 90–120 Ni+, Ni- 5 negative ions diurnal tables, scientific

(26) Ne, neutrals 4 positive ions plots studies

SOLAR mid-lat 100–250 Ne, Ni, Te O+, N2+, steady tables, mid-latitude

PHOTO O2 O, N2 state plots daytime ECHEM ,O2, NO and F1 re-(28) gions of iono

sphere

PROTON high lat 90–600 Ne, Ni, H+, H steady tables, auroralELECTRON >60 deg N2

+ (3914Å), O, N2, O2 state plots ionosphere:AURORAL N2(3371Å), ionization of(30) LBH (1325,1354 emission

1383,1493Å), yieldsOI (1356Å),Lα (1216Å),Hβ (4861Å),Hα (6563Å)

UTD high lat 150–2000 electrostatic N/A directly IMF tables ionosphere(32) potential input driven convection

flowapplications

HEPPNER high lat 100–150 electric N/A statistical point values, modelingMAYNARD >45 deg potential kp-dependent plots studies,(35) geomagnetic comparison

to other data

MILL- high lat 150–2000 electrostatic N/A either of 3 tables ionosphereSTONE potential indices: convectionHILL precipitation, flow(37) Kp or IMF By/Bz applications

APL global 100–500 Vi (electric N/A 2 min velocity scientific(39) potential) maps modeling

studies

HWM global 7–500 neutral total diurnal tables wind(41) atm wind density seasonal solar climatology

and magneticactivity

EMPIRICAL global 140–4000 Te (Ne dependent) Te, Ne latitude local tables climatologicalTe time model testing(43)

EMPRICAL global 50–4000 Te, T i Te, T i diurnal figures, scientificTe, T i coverage seasonal tables studies(44) (lat) solar activity

PEMIC high lat 85–220 Ne, Ni, σp, NO+, O2+, sec tables, scientific

(45) σH, Σp, N2+, O+ plots studies

ΣH

EMC high-lat 110 Σp, ΣH e-, ions hr tables, input to(48) >50 deg figures ionospheric

geomagnetic models,scientificstudies


ix



(km) sentation

AEIF high-lat 110 Σp, ΣH e-, ions hr tables, input to(50) >50 deg figures ionospheric

geomagnetic odels,scientificstudies

WBMOD global 150–1000 plasma Ne diurnal tables, eng specs,(52) irregularity seasonal plots climatology of

strength & solar cycle scintillation atspectrum VHF and above

HF/VHF high lat F-layer foF2 Ne 15 min to graphs, input to(55) maximum MLAT/MLT several hr formulae global

boundaries ionosphericmodels

GPS global N/A TEC, N/A diurnal tables singleTEC ionospheric frequency(56) delay at GPS GPS users

frequencies

CPI global N/A TEC, O+, H+, He+ diurnal tables singleTEC ionosphere NO+, O2

+ frequency(57) delay at GPS GPS users,

frequencies TECclimatology,TEC variabilitystudies


1

USU TIME-DEPENDENT MODEL OF THEGLOBAL IONOSPHERE

1. Model content

The USU ionospheric model describes thethree-dimensional time-dependent evolution ofthe global ionosphere at altitudes between 90and 1000 km. The numerical model yields den-sity distributions for electrons and six ion spe-cies (NO+, O2

+, N2+, O+, N+, He+) as a function of

latitude, longitude, and altitude on a prespeci-fied spatial grid. The model also calculates theisotropic electron temperature and the ion tem-peratures both parallel and perpendicular to thegeomagnetic field on the same spatial grid. Themodel outputs the global density and tempera-ture distributions at specified times.

Numerous physical and chemical processes arecontained in the model, including field-aligneddiffusion, cross-field electrodynamic drifts,thermospheric winds, polar wind escape, en-ergy-dependent chemical reactions, neutralcomposition changes, ion production due toEUV radiation and auroral electron precipitation,thermal conduction, diffusion-thermal heat flow,and a host of local heating and cooling mecha-nisms. The model also takes account of the off-set between the geomagnetic and geographicpoles.

Depending on the inputs, the global ionosphericmodel can describe different solar cycle, sea-sonal, and daily variations. It can describe dif-ferent levels of sustained geomagnetic activityas well as storm and substorm dynamics.

2. Model uncertainties and limitations

2.1 To a large extent, the reliability of the cal-culated ionospheric parameters depends on theaccuracy to which the global inputs can bespecified. The ionospheric model is most sensi-tive to the magnetospheric electric field andparticle precipitation inputs at high latitudes, thethermospheric winds at mid-latitudes, and theequatorial (dynamo) electric fields at low lati-tudes.

2.2 The topside plasma scale heights can besignificantly affected by the downward electronheat flux through the upper boundary, but thisinput is virtually unknown on a global scale.

2.3 Steep spatial gradients can lead to plasmainstabilities and scintillations, but the iono-

spheric model does not take instabilities intoaccount.

2.4 A supercomputer is needed for globalsimulations.

3. Basis of the model

3.1 The USU model of the global ionosphereis based on an Euler-Lagrange hybrid numericalscheme. For the mid-high latitude region, theion continuity, momentum, and energy equa-tions are solved as a function of altitude using afixed spatial grid, whereas for the equatorial re-gion the ion equations are solved along themagnetic field (B) from one hemisphere to theconjugate hemisphere on a fixed spatial grid. Inall latitudinal domains, the plasma flux tubes areallowed to convect through a moving neutralatmosphere in a direction perpendicular to Bdue to magnetospheric, corotational, and dy-namo electric fields. The three-dimensional na-ture of the model is obtained by following manyflux tubes of plasma while keeping track of theirpositions at all times. This approach has theadvantage over a purely Eulerian scheme,which requires fixed grid points in latitude andlongitude, because more flux tubes can beplaced in the high-latitude regions where sharphorizontal gradients are expected, such as nearthe auroral oval and main trough.

3.2 The continuity, momentum, and energyequations correspond to a set of nonlinear, sec-ond-order, partial differential equations. Theequations are first linearized in time, and thenfinite differences are used for the spatial andtemporal derivatives. The resulting coupled al-gebraic equations are solved with standard ma-trix inversion techniques.

3.3 At the lower boundary (90 km), the differ-ent ion species are assumed to be in chemicalequilibrium, and hence the boundary ion densi-ties are obtained simply by equating localsources and sinks. Likewise, the ion and elec-tron temperatures at the lower boundary areobtained by equating local heating and coolingrates.

3.4 At the upper boundary (1000 km), a proto-nospheric exchange flux is specified for O+, andthe fluxes of the other ion species are assumedto be negligibly small. The upper boundary con-ditions on the ion and electron temperatures arespecifications of the downward heat fluxesthrough this boundary.


2

3.5 A 4-km spatial step is used in the verticaldirection, and the time step typically varies from10 to 100 sec as a given flux tube follows aspecified trajectory. The high-latitude regionabove 500 North is usually modeled with 500flux tubes of plasma if empirical plasma con-vection and particle precipitation patterns areused (climatology modeling). For storm andhigh-resolution studies, 1000–3000 flux tubesare used.

4. Model Input Parameters

The ionospheric model requires several inputs.The main global inputs are the neutral densities,temperatures, and winds; the magnetosphericand equatorial electric field distributions; theauroral electron precipitation pattern; the down-ward electron heat flux through the upperboundary; and the protonospheric exchangeflux. Typically, empirical or statistical modelsare used for the required atmospheric and mag-netospheric inputs, but in this case the calcu-lated ionospheric parameters pertain to the cli-matology of the region. For storm and substormsimulations, the temporal variation of the mag-netospheric and atmospheric inputs must bespecified.

5. Publication References

5.1 Schunk, R.W. (1988), “A MathematicalModel of the Middle and High Latitude Iono-sphere,” Pure Appl. Geophys. 127, 255–303.

5.2 Sojka, J.J. (1989), “Global Scale, PhysicalModels of the F Region Ionosphere,” Rev. Geo-phys. 27, 371–403.

6. Dates of Development:

1973 Original one-dimensional, mid-latitude,multi-ion (NO+, O2

+, N2+, O+) model.

1975 High-latitude effects due to plasma con-vection and particle precipitation added for sin-gle plasma flux tubes.

1980 Updated chemical scheme and new ions(N+ and He+) are added.

1981 Plasma convection and particle pre-cipitation patterns added so that multiple fluxtubes can be followed.

1982 A more complete ion energy equation isadded.

1983 Time-dependent plasma convection andparticle precipitation patterns are included sothat geomagnetic storms and substorms can bemodeled.

1985 An equatorial ionospheric model isadded so that the entire globe can be modeled.

1986 The complete electron energy equationis added.

1992 A grid system that allows for a highspatial resolution in a specified region is devel-oped.

7. Model Codes and Sources

The model is in the form of a large Fortrancode, but it is not user friendly and is not avail-able. However, the authors frequently run themodel in collaborative studies with both experi-mentalists and other modelers.


3

NCAR THERMOSPHERE-IONOSPHERE-ELECTRODYNAMICSGENERAL CIRCULATION MODEL,1993

1. Model content

The National Center for Atmospheric ResearchThermosphere-Ionosphere-ElectrodynamicsGeneral Circulation Model (TIE-GCM) is a nu-merical model of the thermosphere and iono-sphere that is coupled through self-consistentelectrodynamics. The global model is on an ef-fective 5-deg latitude-longitude grid in geo-graphic coordinates and extends in altitude be-tween 95 and 500 km. The model time step is 5min, and the model runs on the NCAR CRAY Y-MP8-64. The model calculates the global distri-butions of neutral temperature and winds andalso solves for global distributions of the majorneutral gas density. The ionospheric portion ofthe model calculates global distributions ofelectron density, electron and ion temperatureand the number densities of O+(2P), O+(2D),O+(4S), NO+, N2, N+, and O2

+. The model alsocalculates the global distribution of electricfields, currents, and ground magnetic perturba-tions at each model time step.

The model requires as input a specification ofthe time-dependent solar EUV and UV flux be-tween 1 and 200 nm, the hemispheric powerinput of precipitating auroral particles, and thepotential drop across magnetic polar caps. Italso requires a specification of the amplitudeand phase of the diurnal and semi-diurnal com-ponents of upward propagating tides from themiddle atmosphere. With these time-dependentinputs, the model takes 20 min of NCAR CRAYY-MP8-64 to simulate one day of coupled ther-mosphere-ionosphere dynamics.


2.1 The model requires an accurate specifica-tion of the solar EUV and UV output and itstemporal variation, as well as inputs of auroralparticle precipitation and cross polar cap poten-tial drop. Various parameterizations of theseinputs have been generated and related to solarF107 and F107A indices, as well as Kp and Apgeomagnetic indices. The model auroral inputscan also be specified using the AssimilativeMapping of Ionospheric Electrodynamics inputprocedure (AMIE) that has been developed atNCAR (Richmond and Kamide, 1988).

2.2 The model has been used in various satel-lite track studies, and the accuracy is roughly10% for total mass density and 5% for tem-perature.

2.3 The model is also influenced by tides,gravity waves, and planetary waves that propa-gate upward from the middle atmosphere andintroduce considerable variability into the lowerthermosphere. A good description of these fea-tures must be specified at the lower boundary ofthe model.

2.4 The model requires a specification of ini-tial conditions for time-dependent simulations.

2.5 This large model has been designed to runonly on the NCAR CRAY computer and utilizesthe NCAR mass store system to record massivehistory volumes. Post processors are then usedto obtain the desired information such as densityalong a satellite track or time variations of den-sity and temperature over a given station.

2.6 The model development is essentiallycomplete, but it is in a constant state of refine-ment as the details of physical and chemicalprocesses become clearer by existing research.


3.1 The NCAR TIE-GCM is a first-principlesmodel based on nearly 15 years of model de-velopment. It does not use any empirical mod-els for the specifications of thermosphere andionosphere variables but calculates these prop-erties self-consistently. The model solves theprimitive equations of dynamic meteorology, butthe physical and chemical processes have beenadapted to thermospheric heights.

3.2 The model uses a self-consistent aero-nomic scheme based on our current knowledgeof the aeronomy of the upper atmosphere andionosphere.

3.3 The model is similar to the lower atmos-phere general circulation models used to predictmeteorology of the lower atmosphere. The nu-merical procedures are similar, but the TIE-GCM predicts the weather in the upper atmos-phere and ionosphere.

4. Database

4.1 There is a set of standard history files forequinox and solstice conditions for solar mini-


4

mum, solar medium, and solar maximum condi-tions that are used by the research communityfor various studies.

4.2 Most model runs are made on request fora specific geophysical condition. The results arethen processed for the specific application usingour variety of post processors that have beendeveloped to support the model.

4.3 The model is being developed as a com-munity model for scientific research but couldbe developed into an operational model if thereis a need.

5. Publication references

5.1 Dickinson, R.E., E.C. Ridley, and R.G.Roble (1981), “A Three-Dimensional GeneralCirculation Model of the Thermosphere,” J.Geophys. Res. 86, 1499–1512.

5.2 Dickinson, R.E., E.C. Ridley, and R.G.Roble (1984), “Thermospheric General Circula-tion with Coupled Dynamics and Composition,”J. Atmos. Sci. 41, 205–219.

5.3 Fesen, C.G., R.E. Dickinson, and R.G.Roble (1986), “Simulation of ThermosphericTides at Equinox with the National Center forAtmospheric Research Thermospheric GeneralCirculation Model,” J. Geophys. Res. 91, 4471–4489.

5.4 Richmond, A.D., and R.G. Roble (1987),“Electrodynamic Effects of ThermosphericWinds form the NCAR Thermospheric GeneralCirculation Model,” J. Geophys. Res. 92,12,365–12,376.

5.5 Richmond, A.D., and Y. Kamide (1988),“Mapping Electrodynamic Features of the High-Latitude Ionosphere form Localized Observa-tions: Technique,” J. Geophys. Res. 93, 5741–5759.

5.6 Richmond, A.D., E.C. Ridley, and R.G.Roble (1992), “A Thermosphere/IonosphereGeneral Circulation Model with Coupled Electro-dynamics,” Geophys. Res. Letters19, 601-604.

5.7 Roble, R.G., E.C. Ridley, and R.E. Dickin-son (1987), “On the Global Mean Structure of

the Thermosphere,” J. Geophys. Res. 92, 8745-8758.

5.8 Roble, R.G., E.C. Ridley, and R.E. Dickin-son (1987), “An Auroral Model for the NCARThermospheric General Circulation Model(TGCM),“ Ann. Geophys. 5A (6), 369-382.

5.9 Roble, R.G., E.C. Ridley, and R.E. Dickin-son (1982), “Global Circulation and Tempera-ture Structure of the Thermosphere with HighLatitude Convection,” J. Geophys. Res. 87,1599-1614.

6. Dates of development, authors, andsponsors

6.1 Dates:

1979 Thermosphere General Circulation Model(TGCM)

1987 Thermosphere-Ionosphere General Cir-culation Model (TIGCM)

1992 Thermosphere – Ionosphere - Electro-dynamics General Circulation Model (TIME-GCM)

1993 Thermosphere–Ionosphere–Mesophere-Electrodynamics General Circulation Model(TIME-GCM)

6.2 Authors: R.G. Roble, E.C. Ridley, A.D.Richmond, and R.E. Dickinson

6.3 Sponsors: The National Science Founda-tion, National Aerosnautics and Space Admini-stration, U.S. Air Force, U.S. Navy.

7. Model codes and sources

This research model has been specially de-signed to run on the NCAR CRAY Y-MPs, and itis not transferable to other machines. Time maybe purchased from NCAR to run the model, andthe results can be transferred to the requestor’sinstitution for analysis.


5

COUPLED THERMOSPHERE-IONOSPHERE MODEL (CTIM)

The coupled thermosphere-ionosphere model(CTIM) has evolved from an integration of a neu-tral thermospheric code and a high- and mid-latitude ionosphere model. The neutral thermos-pheric model was originally developed by Fuller-Rowell and Rees (1980) at University CollegeLondon (UCL); the ionospheric model originatedfrom Sheffield University (Quegan et al., 1982). Acomplete description is provided in Fuller-Rowellet al. (1996). A recent upgrade of this model, in-cluding a self-consistent plasmasphere and low-latitude ionosphere, is described in the section onCTIP.

1. Thermosphere model

The thermospheric code simulates the time-dependent structure of the wind vector, tempera-ture, and density of the neutral thermosphere bynumerically solving the non-linear primitive equa-tions of momentum, energy, and continuity. Theglobal atmosphere is divided into a series of ele-ments in geographic latitude, longitude, and pres-sure. Each grid point rotates with Earth to define anoninertial frame of reference in a spherical polarcoordinate system. Latitude resolution is 2 deg,and longitude is 18 deg. Each longitude slicesweeps through local time with a 1-min time step.In the vertical direction the atmosphere is dividedinto 15 levels, in logarithm of pressure, from alower boundary of 1 Pa at 80 km altitude, to analtitude above 500 km.

The momentum equation is nonlinear, and thesolution describes the horizontal and vertical ad-vection, curvature and Coriolis effects, pressuregradients, horizontal and vertical viscosity, andion drag. The nonlinear energy equation is solvedself-consistently with the momentum equation; itdescribes three-dimensional advection and theexchange between internal, kinetic, and potentialenergy. The solutions also describe horizontaland vertical heat conduction by both molecularand turbulent diffusion, heating by solar UV andEUV radiation, cooling by infrared radiation, andJoule heating.

Time-dependent major species compositionequations are solved including the evolution of O,O2, and N2, under chemistry, transport and mutualdiffusion (Fuller-Rowell et al., 1994). The time-dependent variables of southward and eastwardwind, total energy density, and concentrations of

O, O2, and N2 are evaluated at each grid point byan explicit, time-stepping numerical technique.After each iteration the vertical wind, the tem-perature, the density, and the heights of pressuresurfaces are derived. The parameters can be in-terpolated to fixed heights for comparison withexperimental data.

2. Ionosphere model

The equations for the neutral thermosphere aresolved self-consistently with a high- and mid-latitude ionospheric convection model (Quegan etal., 1982). The ionosphere is computed self-consistently with the thermosphere poleward of23-deg latitude in both hemispheres. In this cou-pled model the ionospheric Lagrangian frame hasbeen modified to be more compatible with theEulerian frame by the use of semi-Lagrangiantechnique (Fuller-Rowell et al. 1987, 1988).

Transport under the influence of the magneto-spheric electric field is explicitly treated, assum-ing E × B drifts and collisions with the neutral par-ticles. The densities of atomic ions H+ and O+ andthe ion temperature are evaluated over the heightrange from 100 to 10,000 km, including horizontaltransport, vertical diffusion, and the ion-ion andion-neutral chemical processes. Below 400 km,the additional contribution from the molecular ionspecies N2

+, O2+, and NO+ and atomic ion N+ are

included. The ion temperature is calculated underthe assumption of thermal balance between heatgained from the electron gas and from ion-neutralfrictional heating, and heat lost to the neutral gas.

3. Common inputs

The magnetospheric input to the model is basedon the statistical models of auroral precipitationand electric fields described by Fuller-Rowell andEvans (1987) and Foster et al. (1986), respec-tively. Both inputs are keyed to a hemisphericpower index (PI), based on the TIROS/NOAAauroral particle measurements, and are mutuallyconsistent in this respect. The PI index runs from1 to 10 to cover very quiet to storm levels ofgeomagnetic activity; the relationship between PIand Kp can be found in Foster et al. (1986). Alter-native electric field and auroral precipitation mod-els can easily be incorporated into the model.

The (2,2), (2,3), (2,4), (2,5), and (1,1,) propagat-ing tidal modes are imposed at 97 km altitude(Fuller-Rowell et al. 1991); amplitude and phasecan be prescribed. Ionization rates from the EUVflux are evaluated from reference spectra for high


6

and low solar activity on the basis of the Atmos-pheric Explorer (AE) measurements.


4.1 Foster, J.C., J.M. Holt, R.G. Musgrove, andD.S. Evans (1986), Geophys. Res. Letters 13,656–659.

4.2 Fuller-Rowell, T.J., and D.S. Evans (1987),J. Geophys. Res. 92, 7606–7618.

4.3 Fuller-Rowell, T.J., and D. Rees (1980), J.Atmos. Sci. 37, 2545–2567.

4.4 Fuller-Rowell, T.J., S. Quegan, D. Rees,R.J. Moffett, and G.J. Bailey, J. Geophys. Res.92, 7744-7748, 1987.

4.5 Fuller-Rowell, T.J., S. Quegan, D. Rees,R.J. Moffett, and G.J. Bailey (1988), Pure Appl.Geophys. 127, 189–217.

4.6 Fuller-Rowell, T.J., D. Rees, H.F. Parish,T.S. Virdi, P.J.S. Williams, and R.G. Johnson(1991), J. Geophys. Res. 96, 1181–1202.

4.7 Fuller-Rowell, T.J., M.V. Codrescu, R.J.Moffett, and S. Quegan (1994), J. Geophys. Res,99, 3893–3914.

4.8 Fuller-Rowell, T.J., D. Rees, S. Quegan,R.J. Moffett, M.V. Codrescu, and G.H. Millward(1996), STEP Handbook of Ionospheric Models,edited by R.W. Schunk, Utah State Univ.

4.9 Quegan, S., G.J. Bailey, R.J. Moffett, R.A.Heelis, T.J. Fuller-Rowell, D. Rees, and R.W.Spiro (1982), J. Atmos. Terr. Phys. 44, 619–640.

5. Contacts

The model is available for collaborations. Pleasecontact Tim Fuller-Rowell, Space EnvironmentCenter, 325 Broadway, Boulder, CO 80303, tel.303/497-5764 (e-mail [email protected]); or Mi-hail Codrescu, same address, tel. 303/497-6763(e-mail [email protected]).


7

COUPLED THERMOSPHERE-IONOSPHERE-PLASMASPHEREMODEL (CTIP)

1. Model content

The Coupled Thermosphere-Ionosphere-Plasma-sphere model (CTIP) is an enhanced version ofthe CTIM model described elsewhere in thisguide. The new enhanced version is identical toCTIM but includes a fully coupled model of theEarth’s mid- and low-latitude ionosphere andplasmasphere, where CTIM relies on an empiricaldescription.


The new ionosphere-plasmasphere component ofCTIP solves the coupled equations of continuity,momentum and energy to calculate the densities,field-aligned velocities and temperatures of theions O+ and H+ and the electrons, along a total of800 independent flux-tubes arranged in magneticlongitude and L value (20 longitudes and 40 Lvalues). The effects of E × B drift at lower lati-tudes are incorporated by the inclusion of an em-pirical low-latitude electric field model. Full three-dimensional routines are used to interpolate pa-rameters between the thermosphere and iono-sphere-plasmasphere grids.

Recent developments of the CTIP model haveincluded changing the mid- and low-latitude iono-sphere/plasmasphere component such that thebasic equations are now solved in a Eulerian(rather than Lagrangian) framework. This is asubtle change that allows ionospheric E × B con-vection to take any form (previous incarnationsrequired flux-tubes to return to their geographicstarting positions during a 24-hr simulation). Inaddition the resolution of the ionosphere, in theheight-latitude plane, has been significantly in-

creased such that the equatorial ionosphere, be-tween altitudes of 200 and 1300 km, is modeledwith a vertical resolution of 20 km. The newresolution represents a threefold increase in thenumber of individual flux-tubes solved within themodel, necessary in order to correctly simulate (inparticular) the dusk sector ionospheric responseto the “pre-reversal enhancement” low-latitudeelectric field.

The CTIP model is thus a fully dynamic coupledmodel of the global thermosphere and ionosphereand has recently been used to study the mid-latitude ionospheric F2-layer annual and semi-annual variations (Millward et al., 1996a). A fulldescription of the mathematical basis of themodel has been given by Millward et al. (1996b).


3.1 Millward, G.H., H. Rishbeth, T.J. Fuller-Rowell, A.D. Aylward, S. Quegan, and R.J. Mof-fett (1996a), “Ionospheric F2-Layer Annual andSemi-Annual Variations,” J. Geophys. Res. 101(3).

3.2 Millward, G.H., R.J. Moffett, S. Quegan, andT.J. Fuller-Rowell (1996b), “A Coupled Thermo-sphere-Ionosphere-Plasmasphere Model, CTIP,”STEP Handbook of Ionospheric Models, edited byR.W. Schunk, Utah State Univ.


The model consists of a large and tortuousFORTRAN code, requires a powerful workstationor supercomputer to run, and is not particularlyuser-friendly. However, it is suitable for collabora-tive studies. Contact either Tim Fuller-Rowell (atthe address given in the CTIM report) or GeorgeMillward, Space Environment Center, 325 Broad-way, Boulder, CO 80303, tel. 303/497-7754 (e-mail [email protected]).


8

AFRL GLOBAL THEORETICALIONOSPHERIC MODEL (GTIM)

1. Model content

The Air Force Research Laboratory (AFRL)Global Theoretical Ionospheric Model (GTIM) is atime-dependent, ionospheric model that calcu-lates ion (NO+, O2

+, O+, He+, H+) densities as afunction of altitude, latitude, longitude and localtime, globally. The output from GTIM covers theheight range from 90 to 1600 km on a prespeci-fied grid of latitudes and longitudes, depending onthe scale of the phenomenon under investigation.Nominally, the output ion and electron densitiesare calculated every 2 deg dip latitude, every 5deg longitude, and every 0.5 hr local time.

The model calculates O+, He+, and H+ densitiesby solving the coupled ion momentum and conti-nuity equations numerically using a Crank-Nicholson implicit finite differencing technique.The model includes the effects of production bysolar EUV radiation and energetic particle pre-cipitation, loss through charge exchange with theneutral atmosphere and transport by E × B drift,ambipolar diffusion, and collisions with neutralatmosphere. The offset between the geographicpoles and geomagnetic poles is taken into ac-count. The molecular ions NO+ and O2

+ are cal-culated under the chemical equilibrium assump-tion that production equals loss, and no transporteffects are included.


In calculating global ion and electron density dis-tributions, the model uncertainties relate to howwell the required inputs to GTIM can be specified.A number of studies have established that, ifthese can be realistically specified, then excellentagreement between calculated and observedelectron density profiles is achieved. At low andhigh latitudes, the most important transportmechanism is E × B drift whereas at mid lati-tudes, it is neutral winds that are critical in deter-mining realistic ion and electron densities.

The major limitation of the model is that it is notcoupled to the neutral atmosphere, the electrody-namics, or the energetics of the plasma so thatneither temperatures nor electric fields are self-consistently calculated.


GTIM solves the coupled ion (O+, He+, and H+)momentum and continuity equations in a frame ofreference that drifts with the E × B drift velocity(Eulerian frame of reference) of the ion and elec-trons. The r, θ, φ coordinate system is trans-formed to an α, β, γ coordinate system, where αand β are perpendicular to the geomagnetic fieldline direction, and γ is parallel to B. A number oftransformations are carried out which facilitate thesolving of the linear, second-order partial differ-ential equation. At low and mid latitudes the solu-tion is carried out along the entire field line formone hemisphere (90 km N) to the other (90 km S),and the boundary conditions at both ends assume[O+] = 0. At high latitudes (above about ± 60 degdip latitude), the upper boundary condition at1600 km provides flux values (Nvγ) parallel to B.

4. Model input parameters

Inputs to GTIM include a neutral atmospheremodel, a solar production rate model, E × B driftpattern, a model for precipitating energetic elec-trons and protons, a horizontal neutral windmodel, and a model for electron and ion tem-peratures. All of these inputs come from well es-tablished references and observations and will notbe detailed here.


5.1 Anderson, D.N. (1973), “A Theoretical Studyof the Ionospheric F Region Equatorial Anomaly,I; Theory,” Planetary Space Sci. 21, 409–420.

5.2 Decker, D.T., C.E. Valladares, R. Sheehan,S. Basu, D.N. Anderson, and R.A. Heelis (1994),“Modeling Daytime F Layer Patches over Sonder-strom,” Radio Sci. 29, 249–268.


6.1 Dates:

1973 Development of the low-latitude portion ofGTIM).

1976 Development of the mid-latitude portionof GTIM).


9

1994 Development of the high-latitude portionof GTIM).

1995–97 Addition of light ions (He+ and H+) tolow- and mid-latitude portion of GTIM.

6.2 Authors: D.N. Anderson, D.T. Decker, M.W.Fox, R.E. Daniell, and R.W. Simon.


The model consists of a large number of Fortrancoded subroutines that provide the GTIM output,but in no way is it well documented, user-friendly,or available to outside users. However, manycollaborative studies have been carried out usingGTIM.


10

PARAMETERIZED IONOSPHERICMODEL (PIM)

1. Model content

The Parameterized Ionospheric Model (PIM) is aglobal model of the theoretical climatology of theionosphere. That is, PIM is a parameterization ofthe output from an amalgamation of theoreticalionospheric models, including the USU Time De-pendent Ionospheric Model (TDIM) for high lati-tudes and the Global Theoretical IonosphericModel (GTIM) for low and mid latitudes, aug-mented by the empirical plasmasphere model ofGallagher (1988). An earlier version of PIM hasbeen described by Daniell et al. (1995).

The output from all of these models has been pa-rameterized in terms of solar activity (F10.7), geo-magnetic activity (Kp), and season (Equinox, JuneSolstice, December Solstice). The format of theoutput of PIM is user selectable, and includeselectron density profiles and/or profile parameters(TEC, NmF2, hmF2, NmE, hmE, etc.) on user-specified grids in latitude/longitude/altitude (geo-graphic or geomagnetic) or azimuth/elevation/range.


PIM is a climatological model based on diurnallyreproducible runs of physics-based models. Assuch, it cannot accurately reproduce specificsituations, especially the storm-time ionosphere.It is intended to represent “typical” (rather than“average”) ionospheric conditions.

Because the model is based on seasonal runs, itdoes not represent the complete annual variationof the ionosphere and is most inaccurate betweenequinoxes and solstices.


PIM consists of two major components: (1) alarge set of coefficient files, from which the elec-tron density profile may be derived at any speci-fied latitude, longitude, season, and solar geo-physical condition, and (2) an algorithm for recon-structing the electron density profiles from thesecoefficients.

PIM is based on diurnally reproducible runs of itsparent physics-based models for specified so-lar/geophysical conditions and seasons. That is,the physics-based models are run with constant or

steady-state forcing functions until the steady-state response of the ionosphere is obtained.(This usually occurs after a few hours of solar il-lumination.) The output of the physics-basedmodels consists of altitude profiles of the densi-ties of the three dominant ions of the E and F re-gions (O+, N2

+, and O2+) on a latitude/longitude

grid at regular intervals of local time or UT, de-pending on the model.

The ion density profiles are then represented aslinear combinations of Empirical OrthonormalFunctions (EOFs), which are derived from thecomplete set of profiles for a given set of so-lar/geophysical conditions. Depending on latituderegion, the coefficients of the EOFs are fit by or-thogonal functions in latitude, longitude, and/orUT.

The resulting coefficients are stored in files andconstitute one of the two major constituents ofPIM. The other component, the FORTRAN codeitself, reconstructs the ion density profiles at thetimes and places specified by the user and sumsthe ion densities to obtain the electron density. Ifthe user has asked for profile parameters, theheight and density of the E- and F-layer peaks arefound, and the profile is integrated to produceTEC.

The structure of the coefficient files differs for thevarious ionospheric regions. Merging betweenregions is accomplished by averaging betweenprofiles in overlapping regions. Interpolation forsolar/geophysical conditions between the valuesof the model runs is also accomplished by oper-ating on profiles (rather than coefficients). This isbecause the EOFs were derived separately fromeach block of runs; that is, the basis functions aredifferent for different sets of solar/geophysicalconditions and different ionospheric regions.

This will probably change in PIM version 2, whichwill be based on a “universal” set of EOFs so thatall interpolation can be done in “coefficientspace.” It will also be based on a single, unifiedionospheric model, GTIM.


The user inputs are the date and time (UT) of therun, the solar/geophysical conditions (F10.7 andKp), choice of coordinates (geomagnetic or geo-graphic), choice of output grid (latitude/longitude/altitude or azimuth/elevation/ range), and thespecifics of the output grid.


11

5. Publications references

5.1 Daniell, R.E., L.D. Brown, D.N. Anderson,M.W. Fox, P.H. Doherty, D.T. Decker, J.J. Sojka,and R.W. Schunk (1995), “Parameterized Iono-spheric Model: A Global Ionospheric Parameter-ization Based on First Principles Models,” RadioSci. 30, 1499–1510.

5.2 Gallagher, D.L., P.D. Craven, and R.H.Comfort (1988), “An Empirical Model of theEarth’s Plasmasphere,” Adv. Space Res. 8, 15–24.

6. Dates of development, authors, and spon-sors

6.1 Dates:

1987–90 Development of the high-latitude por-tion of the model.

1990 Development of the low- and mid-latitudeportion.

1993 Version 1 of PIM.

1997 Most recent version of the code (1.6).

6.2 Authors: R.E. Daniell, L.D. Brown, W.G.Whartenby, J.J. Sojka, P.H. Doherty, D.T.Decker, and D.N. Anderson.

6.3 Sponsor: Air Force Research Laboratory.


The model may be obtained by contacting LincolnBrown at CPI, tel. 781/487-2250 (e-mail [email protected]). The source code and associatedcoefficient files are available free of charge fromeither of two ftp sites on the Internet. They arealso available on CD-ROM for a nominal charge.(Contact Mr. Brown for specific information.) Thesource code is FORTRAN, and each version isverified to run under MS-DOS, DEC-VMS, andSun-UNIX operating systems. (With minor modifi-cations, the code has been successfully run underother UNIX “flavors.”) There are approximately40–50 registered PIM users around the world.


12

INTERNATIONAL REFERENCEIONOSPHERE (IRI), 1996

1. Model content

The International Reference Ionosphere is thestandard ionospheric model recommend for inter-national use by the scientific unions Committeeon Space Research (COSPAR) and InternationalUnion of Radio Science (URSI). A joint WorkingGroup of COSPAR and URSI is in charge of de-veloping and improving the model. By charter IRI,like other international standard models (e.g.,CIRA, MSIS, IGRF), is an empirical model, thusavoiding the uncertainties of the evolving theo-retical understanding. Annual IRI Workshops arethe forum for progress/status reports of ongoingIRI projects, for comparisons with new datasources, for resolving issues of conflicting datasources, and for decisions about improvementsand additions for the next release of the model.The presentations from these workshops are pub-lished in Advances in Space Research, Vols.(Nos.) 4 (1), 5 (7), 5 (10), 7 (6), 8 (4), 10 (8), 10(11), 11 (10), 13 (3), 14 (12), 15 (2), 16 (1).

IRI provides monthly averages of the electrondensity, the ion composition (O+, H+, He+, NO+,O2

+, N2+, cluster ions), the electron temperature,

and the ion temperature for magnetically quietconditions. Efforts are underway to include mod-els for ionospheric storm effects and models forthe ion drift and spread-F.

The IRI model, its background, database, andmathematical formulas are explained in detail inspecial reports published by URSI (Rawer et al.,1978), by the WDC-A-STP (Rawer et al., 1981),and by the NSSDC (Bilitza, 1990).


Like any empirical model, IRI is as good and rep-resentative as the data that are available for de-veloping/improving the model. Since most of theionospheric data have been accumulated atEuropean and North American latitudes, theseregions are also the ones that are best repre-sented in IRI. The Northern hemisphere and thecontinents in general are better represented thanthe Southern hemisphere and the oceans, againbecause of obvious differences in data volume.The IRI model should be primarily used for sub-auroral latitudes. At auroral and polar latitudes,the model has to rely on data from just a few sta-

tion and satellites, clearly not enough to fully de-scribe this highly variable region. At these highlatitudes, IRI should be considered as a first esti-mate for describing the background ionosphere.

The uncertainties are typically as follows:

Peak Peak Temp- Ionheight density eratures comp.

F region ±15% ±30% ±20% ±50%E region ± 5% ±10% ±10% ±50%D region ±10% ±70%

Improvements in the accuracy of the electrondensity values can be obtained by introducingmeasured values for the F peak height and den-sity; IRI supports this option. In addition, IRI pro-vides an option to use measured electron densi-ties to obtain more accurate electron tempera-tures by employing the well known anti-correlationbetween electron temperature and density.


The IRI electron density model uses the CCIRworld maps for the F and E peak parameters. Aspecial formula was developed by the IRI team toconvert the CCIR-given M3000 propagation factorto the F peak height. For the F peak density anadditional choice is given with the URSI-88 maps.These were developed by a special URSI Work-ing Group (C. Rush, Chair) and have shown bet-ter results than CCIR in the ocean areas. In addi-tion, a user can also enter measured peak pa-rameters into IRI, if available. The CCIR formulasfor the F1 ledge and the E peak densities weremodified for IRI to better agree with more recentmeasurements. The IRI topside is based on ananalytical representation of Bent's compilation ofAlouette and ISIS topside sounder data. Incoher-ent scatter data from Jicamarca and Arecibo andAEROS and AE-C in situ measurements havebeen used to improve the formula at low latitudes.The representation of the region between E and Fpeaks is based on ionosonde real-height profilesand on incoherent scatter data (valley). The D-region model assumes an inflection point at 80 to88 km; this height is correlated to the transitionfrom molecular to cluster ions. The global andtemporal variation of the density at that point wasmodeled with the help of all available (reliable)rocket data.

The electron and ion temperature models arebased largely on AEROS RPA and AE-C, ISIS-1,ISIS-2 Langmuir probe data. These data providea global mapping of temperatures at several alti-


13

tudes. The whole profile was than established withthe help of incoherent scatter data from Ji-camarca, Arecibo, and Millstone Hill. At 120 km,the plasma temperatures coincide with the valuegiven by the COSPAR International ReferenceAtmosphere (CIRA); this was one of the COSPARrequirements. Through all altitudes the tempera-tures are such that Tn < Ti < Te.

The IRI ion composition model assumes chargeneutrality. IRI primarily models the global andtemporal variation of atomic and molecular oxy-gen ions (O+, O2

+) and then fills up to 100% withlight ions (H+, He+) above the F peak and withNO+ ions below. The model is based on a compi-lation of rocket and satellite RPA and IMS data.The rather limited database makes the ion com-position model the weakest part of the IRI. Prob-lems with instrument calibrations have made itdifficult to use IMS data from several of the earlysatellites. Discrepancies were also found betweensatellite and incoherent scatter measurements.Efforts are now focussing on using the transitionheights (light ions to O+, O+ to molecular ions,molecular to cluster, cluster to negative ions) asthe characteristic parameters of the compositionprofiles.

4. Database

Electron density: ionosonde (E,F peak, bottom-side), incoherent scatter radar (hmF2, E-valley,topside), absorption (D-region), rockets (D-, E-region), Alouette, ISIS topside sounder (topside),AEROS, AE-C, DE-2 in situ (topside); ion compo-sition: RPA and IMS measurements from satel-lites (AE-C, AEROS-B, S3-1, OGO-6, Electron 2,4, Cosmos 274, Sputnik 3) and rockets; tem-peratures: Langmuir probe and RPA measure-ments from AEROS-A,B, ISIS-1,-2, AE-C, -E, DE-2, incoherent scatter data from Jicamarca, Are-cibo, Millstone Hill, St. Santin, Malvern.


5.1 Bilitza, D. (1990), “International ReferenceIonosphere 1990,” NSSDC/WDC-A-R&S 90-22,Greenbelt, MD.

5.2 Bilitza, D.,K., and E.G. Rawer, eds. (1994),“Ionospheric Models,” Adv. Space Res. 14 (12).

5.3 Rawer, K., S. Ramakrishnan, and D. Bilitza

(1978), “International Reference Ionosphere1978,” URSI Special Rept., Brussels, Belgium.

5.4 Rawer, K., D. Bilitza, and S. Ramakrishnan(1978), “Goals and Status of the InternationalReference Ionosphere,” Rev. Geophys. 16, 177–181.

5.5 Rawer, K., J.V. Lincoln, and R.O. Conkright(1981), “International Reference Ionosphere IRI-79,” WDC-A-STP Rept. UAG-82, Boulder, CO.

5.6 Rawer, K., and W.R. Piggott (1990), “De-velopment of IRI-90,” Adv. Space Res. 10 (11).

5.7 Rawer, K., and W.R. Piggott (1991), “En-larged Space and Ground Data Base for Iono-spheric Modelling,” Adv. Space Res. 11 (10).

5.8 Rawer, K., W.R. Piggott, and A.K. Paul(1993), “Advances in Global/Regional Descrip-tions of Ionospheric Parameters,” Adv. SpaceRes. 13 (3).

5.9 Rawer, K., W.R. Piggott, and A.K. Paul,eds. (1995), “Off Median Phenomena and IRI,”Adv. Space Res. 15 (2).

5.10 Rawer, K., D. Bilitza, and W. Singer, eds.(1995), “The High Latitudes in the IRI,” Adv.Space Res. 16 (1).

5.11 Rawer, K., D. Bilitza, K. Mahajan, and A.Mitra, eds. (1996), “ÒLow and Equatorial Lati-tudes in the IRI,” Adv. Space Res. 18 (6).


6.1 Dates:

1968 Working Group established.

1972 First set of preliminary tables.

1978 IRI-78, URSI Special Report.

1981 IRI-80, WDC-A-STP Report UAG-82.

1986 IRI-86 (also on diskette for use on PCs).

1990 IRI-90, NSSDC Report 90-22.

1995 IRI-95, anonymous ftp and WWW.

6.2 Authors: COSPAR/URSI Working Group(K. Rawer, L. Bossy, and D. Bilitza, Chairs).



14

The model codes can be retrieved from theanonymous ftp site at nssdca.gsfc.nasa.gov indirectory pub/models/IRI; an ASCII version of themodel coefficients can be found in directorypub/models/IRI90ASCII. The software packagecan be also obtained on diskette from NSSDC'srequest coordination office (CRUSO), NationalSpace Science Data Center, NASA/GSFC, Code

633.4, Greenbelt, MD 20771, tel. 301/286-6695,FAX 301/286-1771 (e-mail [email protected]). The model can also be accessed andrun interactively on the World Wide Web at http://nssdc.gsfc.nasa.gov/space/model. There are alsoWWW pages describing the model and listing theWorking Group composition and the IRI Work-shops that have been held so far.


15

EMPIRICAL MODEL OF THEIONOSPHERE

1. Model content

The empirical model of the ionosphere providesnumber densities (cm-3) of

Atomic ions: H+, He+, N+, O+

Molecular ions: N2+, NO+, O2

+

Electrons: Ne

as a function of

Altitude: 50–4000 kmLatitude: dipole latitude, N2, O2, O, NOTime: day count d (annual variation)

magnetic local time τSolar activity: solar flux F10.7

for quiet geophysical conditions(Kp ≤ 3)

The number densities n of the ion species and theelectrons are obtained from the appropriate fig-ures (Köhnlein, 1989a and 1989b). At F10.7 = 84 ×10-22 Wm-2 Hz-1 and Kp ≤ 3:

Average density (time independent):see Köhnlein (1989a and 1989b, Figs. 3–6),

log10n vs altitude;

Time-independent density (latitudinal):see Köhnlein (1989a and 1989b, Figs. 7–18),

log10n vs altitude at φ = 90°, 45°, 0°, -90°;

log10n vs dipole latitude at discrete heights;

Annual variation:see Köhnlein (1989a and 1989b, Figs. 19–30),

log10n vs altitude at equinox and solsticeconditions (d = 80, 173, 266, 356);comparison with data:log10n vs day count at discrete heights;

∆ log10n(relative):dipole latitude vs day count at discreteheights;

Diurnal variation:see Köhnlein (1989a, Figs. 31–46), andKöhnlein (1989b, Figs. 31–48),

log10n vs altitude at φ = 0°, 45°, andτ =0h, 6h, 12h, 18h;comparison with data:

log10n vs magnetic local time at discreteheights and φ = 0°, 45°;

∆ log10n(relative):dipole latitude vs magnetic local time at dis-crete heights;

And superpositions thereof, i.e.,diurnal variation + relative annual variation⇒ diurnal variation at a selected day of theyear;annual variation + relative diurnal variation⇒ diurnal variation at a selected magneticlocal time.


The discrepancies between the model and theobservations (used) are shown for the annual anddiurnal variations in Köhnlein (1989a and 1989b,Figs. 20, 23, 26, 29, 32, 33, 36, 37, 40, 41, 44,45), and in Köhnlein (1989b, Figs. 46 and 47). Ingeneral, the model agrees well with the observa-tions.

The uncertainties of the model are mainly due tothe uneven data coverage and the simplicity ofthe analytical approach (e.g., linearity, no longitu-dinal terms, no disturbed conditions).

Data from epochs not used in the database mayshow greater deviations from the model. This isespecially true for disturbed geophysical condi-tions that are not considered in the model (alsosee Köhnlein, 1993).


The vertical and horizontal structures of themodel are treated on an equal footing.

The plasma parameters are expanded intospherical harmonics (Köhnlein, 1989a, Eqs. 2.1–2.10) wherein the model coefficients depend onaltitude, solar flux F10.7, and the geomagnetic in-dex Kp.

Restricting the model to quiet geophysical condi-tions (Kp ≤ 3), the above coefficients dependlinearly on F10.7, whereas their height variationsare expressed by cubic spline functions.

4. Database

The database of the model consists of observa-tions by satellites, incoherent scatter stations, androcket profiles covering the time interval 1964–1979 (Köhnlein, 1989a, Table1; and Köhnlein,


16

79 (Köhnlein, 1989a, Table1; and Köhnlein,1989b, Table1 and Figs.1 and 2).


5.1 Köhnlein, W. (1989a), “A Model of the Ter-restrial Ionosphere in the Altitude Interval 50–4000 km: I. Atomic Ions (H+, He+, N+, O+),” Earth,Moon, and Planets 45, 53–100.

5.2 Köhnlein, W. (1989b), “A Model of the Ter-restrial Ionosphere in the Altitude Interval 50–4000 km: II. Molecular Ions (N2

+, NO+, O2+) and

Electron Density,” Earth, Moon, and Planets 47,109–163.

5.3 Köhnlein, W. (1993), “Comparison of the IonComposition Data with Empirical Models (Com-ment),” Advances in Space Research 13 (3), 85–86, 125–132.


6.1 Date: 1983.

6.2 Author: W. Köhnlein.

6.3 Sponsors: Deutsche Forschungsgemein-schaft and University of Bonn.


The model was developed in FORTRAN codespecifically adapted to a CDC computer.

Because of the detailed graphical representation,Köhnlein (1989a and 1989b) can be used as aquick reference for ion and electron densities atlow solar fluxes (F10.7 ≈ 84) and quiet geophysicalconditions (Kp ≤ 3) in the altitude interval 50–4000km.


17

THE SHEFFIELD UNIVERSITYPLASMASPHERE-IONOSPHEREMODEL (SUPIM)

1. Model content

The Sheffield University Plasmasphere-Iono-sphere Model (SUPIM) is a mathematical modelthat describes the distribution of ionization withinthe Earth’s mid and equatorial latitude iono-sphere. In the model, time-dependent equationsof continuity, momentum, and energy balance forthe O+, H+, He+, N2

+, O2+ and NO+ ions, and the

electrons, are solved along magnetic field linesfor the ion and electron concentrations, field-aligned velocities, and temperatures. The mag-netic field is an eccentric-dipole representation ofthe Earth’s magnetic field, the offset between themagnetic and geographic poles being determinedfrom the first eight non-zero terms of the usualspherical harmonic expansion of the geomagneticscalar potential used in the International Geo-magnetic Reference Field (IGRF). Particularlycases of the eccentric dipole are the tilted-centered dipole and the axial-centered dipole.These cases are obtained by truncating thespherical harmonic expansion after the first threenonzero terms and the first term, respectively.

Included in the model are numerous physical andchemical processes. The principal processes in-clude ion production due to solar EUV radiation,ion production and loss due to chemical reactionsbetween the constituent ions and with the neutralgases, ambipolar and thermal diffusion, ion-ionand ion-neutral collisions, thermospheric meridi-onal and zonal winds, electrodynamic drift, ther-mal conduction, photoelectron heating, frictionalheating, and a host of local heating and coolingmechanisms.

Enhancements/modifications have been made tothe “standard” model for specific studies. For ex-ample, inclusion of sub-auroral ion drifts (SAIDs),a self-consistent low-latitude atmospheric dynamomodel, anisotropic ion temperatures, vibrationalexcitation of N2, the separation of O+ into its 4S,2D and 2P states, and vertical neutral winds.

Depending upon the inputs the model can de-scribe different solar cycle, seasonal, daily, andmagnetic activity variations. It can also providedescriptions of the diurnal, altitude, latitude, andlongitudinal variations.


2.1 To a large extent, the reliability of the cal-culated ionospheric parameters depends upon theaccuracy to which the model inputs can be speci-fied.

2.2 Except for a few locations, the model inputsof thermospheric wind and the vertical E × B driftare poorly known. Some adjustments to theseparameters may be needed.


3.1 The model is a mathematical formulation ofthe known physical and chemical processes of theEarth’s ionosphere and plasmasphere. The mo-tion of the plasma is considered to be due to am-bipolar diffusion parallel to the magnetic field withan additional E × B drift perpendicular to themagnetic field.

3.2 The model equations are solved at a dis-crete set of points along an eccentric dipole mag-netic field line from a base altitude of around 120km in the northern hemisphere to a base altitudeof around 120 km in the southern hemisphere.There are switches in the model code to make themagnetic field a tilted-centered or axial-centereddipole.

3.3 At mid latitudes, the vertical E × B drift ve-locity has little effect on the model results and isusually taken to be zero. For many applications,only one field line needs to be considered.

3.4 At equatorial latitudes, inclusion of the verti-cal E × B drift is essential as this drift gives rise tothe equatorial anomaly. Under the influence of avertical E × B drift the plasma associated with aparticular magnetic field line is associated with adifferent magnetic field line at later times. Thus,in order to provide reasonable 24-hr coverage ofthe modeled parameters within a specified alti-tude and latitude region, the model equationshave to be solved for many magnetic field lines.

3.5 The continuity, momentum, and energy bal-ance equations for each constituent ion and theelectrons form a set of highly nonlinear, second-order partial parabolic equations. The equationsare first linearized in them, and then finite differ-ences are used for the spatial and temporal de-rivatives. The resulting coupled tri-diagonal sys-


18

tems of linear algebraic equations are solved by astandard technique.

3.6 At the lower boundary of each hemisphere( ∪120 km), the ions and electrons are taken tobe in chemical equilibrium, and the densities areobtained by equating the local sources and sinks.Likewise, the ion and electron temperatures areobtained by equating local heating and coolingrates.

3.7 The time step is usually taken to be 15 min.The spatial step along the magnetic field linevaries along the field line, and the number ofpoints increases with increasing apex altitude. Amathematical formulation is used to give the pointdistribution. The points are arranged to give aspatial step of about 5 km at F-region altitudes.


4.1 Latitude and longitude of ground station,day, and year.

4.2 An IGRF (presently IGRF85) for the deter-mination of the magnetic field.

4.3 A solar EUV flux spectrum (presently fromEUV94).

4.4 A thermosphere model (presently MSIS86)for the determination of the neutral densities andtemperatures.

4.5 A thermospheric wind model (presentlyHWM90) for the determination of the meridionaland zonal winds.

4.6 A vertical E × B drift model.

The model inputs described in Sec. 4.1 are readinto the model from an input file. The model in-puts described in Secs. 4.2–4.6 are incorporatedinto the model code as sets of subroutines. Thesubroutines permit easy modification as improvedvalues become available and for the modifica-tions/ changes made in applications of the modelto particular studies.


5.1 Bailey, G.J., and R. Sellek (1990), “AMathematical Model of the Earth’s Plasmasphereand Its Application in a Study of He+ at L=3.0,”Ann. Geophys. 8, 171–190.

5.2 Bailey, G.J., R. Sellek, and Y. Rippeth(1993), “A Modeling Study of the Equatorial Top-side Ionosphere,” Ann. Geophys. 11, 263–272.


6.1 Dates:

1975 One-hemisphere model—ions O+ and H+.

1978 Extended to two hemispheres.

1979 He+ added to one-hemisphere model.

1980 Major revision—two-hemisphere model,axial-centered dipole magnetic field, energy bal-ance equations, new numerical procedures forsolving model equations, ions O+ and H+.

1983 E × B drift added.

1990 Major revision—the ions He+, N2+, O2

+,and NO+ added.

1993 Major revision—magnetic field represen-ted by an eccentric dipole.

1994 Two-stream approximation method usedto determine photoelectron heating rates.

1995 Changes made to numerical proceduresto improve numerical stability.

6.2 Author (principal): Graham J. Bailey,School of Mathematics and Statistics, AppliedMathematics Section, The University of Sheffield,Sheffield S3 7RH, UK.

6.3 Sponsors: Plasma Physics and AstronomyResearch Council (PPARC), UK.


The model is not user-friendly, and collaboration,in the first instance, is required between the userand the author (Graham Bailey). The authorwould be happy to discuss collaborations with in-terested groups. The author would consider en-hancing/ modifying the model and model codes tomeet specific requests. The model codes arewritten in FORTRAN and have been developedfor use on a high-performance PC. It is straight-forward to modify the codes for use on worksta-tions and mainframes.


19

THE FIELD LINE INTER-HEMISPHERIC PLASMA MODEL

1. Model content

The field line interhemispheric plasma (FLIP)model is a first-principles, one-dimensional, time-dependent chemical and physical model of theionosphere and plasmasphere. It couples the lo-cal ionosphere to the overlying plasmasphere andconjugate ionosphere by solving the ion continuityand momentum, ion and electron energy, andphotoelectron equations along entire magneticflux tubes. The interhemispheric solutions yielddensities and fluxes of H+, O+, He+, and N+ as wellas the electron and ion temperatures. In addition,continuity and momentum equations are solved toprovide the densities of minor neutral species[N(2D), N(4S), NO] and the first six vibrationallevels of N2 in both hemispheres. A large numberof other minor ion and neutral densities are cal-culated from chemical equilibrium between 80and 600 km in the northern and southern hemi-spheres. Other outputs from the model includeparticle and heat fluxes, electron heating andcooling rates, photoelectron fluxes, chemical pro-duction and loss rates, and most significant air-glow emission rates. Major neutral densities aresupplied by the MSIS model. A three-dimensionalversion of the model is obtained by simulatingseveral hundred corotating flux tubes.


2.1 In several recent studies, the FLIP modeltypically produces F2 peak electron densitieswithin 30% of the measured densities during thedaytime despite the potential for large errors inseveral key inputs. At night, discrepancies be-tween measured and modeled densities can oftenbe as much as a factor of 2.

2.2 During quiet times the error in the inputs forthe solar EUV flux, MSIS neutral densities, reac-tion rates, and cross sections are typically about20%. During magnetic storms uncertainties in theMSIS neutral densities may be much larger, re-sulting in similar errors in calculated electron den-sities.

2.3 The largest uncertainty for ionosphericmodeling at mid latitudes is the neutral windmagnitude. However, when measurements ofhmF2 are available, the uncertainty is reduced toabout 20% by using the algorithm that we havedeveloped.

2.4 The current FLIP model is basically a mid-latitude model because it neglects convectionelectric fields, which are important at equatorialand auroral latitudes.

2.5 The uncertainty of the plasma content ofplasmaspheric flux tubes is not important duringthe daytime but can produce about a 50% error incalculated NmF2 at night.

2.6 The FLIP model is a low-speed model thatis not applicable in the plasmasphere for ion den-sities below about 100 cm-3.


3.1 The FLIP model calculates the plasma den-sities and temperatures along complete magneticflux tubes from 80 km in the northern hemispherethrough the plasmasphere to 80 km in the south-ern hemisphere as a function of time. A tilted di-pole approximation is used for the Earth's mag-netic field.

3.2 The set of nonlinear, second-order, partialdifferential equations for continuity, momentum,and energy is transformed into finite differenceequations and solved by a Newton-Raphson it-erative scheme. The scheme is stable, and timesteps are generally 0.5 hr except near twilight,where 10 min or less are used.

3.3 A variable spatial grid is set up along themagnetic field line. There are approximately 200grid points distributed in such a way as to give agrid spacing of less than 10 km in the ionosphereand less than one scale height of H+ in the plas-masphere.

3.4 The boundary conditions imposed at thefeet of the flux tube near 100 km are chemicalequilibrium for ions and thermal equilibrium fortemperatures. The initial plasmaspheric H+ den-sity must also be specified.

3.5 A unique feature of the FLIP model is theoption to employ measurements of hmF2, NmF2 ,and topside Te as additional constraints for differ-ent types of studies.


4.1 The standard model can be run by simplyspecifying the date and the geographic location,but there are a large number of other options.


20

4.2 Activity indices Kp, daily F10.7, and averageF10.7 for the MSIS neutral density, HWM93 wind,and solar EUV flux models are read from a filebut can also be specified.

4.3 Measured hmF2, NmF2, and topside Te canbe input from a file. The hmF2 is automaticallyturned into a neutral wind so that the model hmF2

follows the observed values.

4.4 There are a large number of adjustable pa-rameters, such as time step and length of the run,which control the action of the model.


5.1 Torr, M. R., D. G. Torr, P. G. Richards, andS. P. Yung (1990), “Mid- and Low-Latitude Modelof Thermospheric Emissions, 1, O+(2P) 7320 •and N2 (

2P) 3371 •,” J. Geophys. Res. 95 (21),147.

5.2 Richards, P. G. (1991), “An Improved Algo-rithm for Determining Neutral Winds from theHeight of the F2 Peak Electron Density,” J. Geo-phys. Res. 96 (17), 839.

5.3 Richards, P. G., D. G. Torr, B. W. Reinisch,R. R. Gamache, and P. J. Wilkinson (1994), “F2Peak Electron Density at Millstone Hill andHobart: Comparison of Theory and Measurementat Solar Maximum,” J. Geophys. Res. 99 (15), 5.

5.4 Richards, P. G., D. G. Torr, M. J. Buon-santo, and D. P. Sipler (1994), “Ionospheric Ef-fects of the March 1990 Magnetic Storm: Com-parison of Theory and Measurement,” J. Geo-phys. Res. 99 (23), 359.

5.5 Richards, P. G., J. A. Fennelly, and D. G.Torr (1994), “EUVAC: A Solar EUV Flux Modelfor Aeronomic Calculations,” J. Geophys. Res.99, 8981.

5.6 Richards, P. G., D. G. Torr, M. E. Hagan,and M. J. Buonsanto (1995), “A New Algorithm forImproved Ionospheric Electron Density Modeling,”Geophys. Res. Letters 22, 1385.

5.7 Richards, P. G. (1996), “The Field Line In-terhemispheric Plasma Model,” Solar-TerrestrialEnergy Program: Handbook of Ionospheric Mod-els, edited by R.W. Schunk, p. 207.


6.1 Dates:

1979 Development of interhemispheric solu-tions for [O+], [H+], Te, and Ti..

1980 Interhemispheric solutions for photoelec-tron flux and solutions for minor ion and neutraldensities added.

1981 Diffusion equations for vibrationally ex-cited N2 effects included.

1982 Improvements to the photoelectron fluxmodel to reproduce observed flux.

1986 Developed original algorithm for obtainingwinds from hmF2.

1991 Improved algorithm for getting winds fromhmF2.

1992 Added energetic electron precipitation forauroral studies.

1993 Developed algorithm to cause model toreproduce both hmF2 and NmF2.

1994 Developed EUVAC solar EUV flux model.

1995 Developed algorithm to reproduce ob-served topside ionosphere.

6.2 Author (principal): Phil Richards, Com-puter Science Department, The University of Ala-bama in Huntsville, Huntsville, AL 35899, USA.

6.3 Sponsors: National Aeronautics and SpaceAgency, National Science Foundation.


A VAX version of the model is available to be in-stalled at the user's institution. A UNIX version isalso under development. The model runs fromDEC command files that are well documented.There is also an interface that helps the user un-derstand the model and aids in the setting up ofthe DEC command files. Some previous userswith a good knowledge of the ionosphere havebeen able to run the model with little additionalhelp. The author also runs the model for collabo-rative studies. Contact person: Phil Richards,Computer Science Department, The University ofAlabama in Huntsville, Huntsville, AL 35899, USA(e-mail [email protected]).


21

ALGEBRAIC MODEL

1. Model content

The D region has the most complex chemistry ofany ionospheric region by far, and, to this day, itschemistry has not been elucidated fully. Never-theless, there has been success in modeling theD region, especially the electron concentrations ofthe disturbed D region. This achievement hasbeen made possible largely because ion-ion re-combination (neutralization) coefficients all ap-pear to be near 10-7 cm-3 s-1 (Smith et al., 1976)regardless of the type of ions involved. Hence,even though the negative ion chemistry is stillunsatisfactory as to the concentrations of thevarious individual ions, the electron concentrationcan be determined with some confidence, as seenin Fig. 1 of Smith (1976), where the model to bediscussed is shown to match well the upleg datafor a Solar Proton Event (SPE) or Polar Cap Ab-sorption (PCA) event.

The formation of the model is purely a sequenceof algebraic expressions that yield solutions, aftersufficient iterations, for the electron concentration[e] and all the individual ions currently in themodel: 21 positive ions and 8 negative ions. Es-pecially for disturbed events, but even for quietconditions, D-region processes are sufficientlyrapid, compared with the complexity of thechemistry, that steady-state conditions are appro-priate, except during twilight.

Transport is ignored. Collision frequencies maybe included for calculating the absorption of elec-tromagnetic waves (Swider and Chidsey, 1977).


The model has been fitted well to the November1969 PCA event (Swider and Foley, 1978;Swider, 1988). Indeed, for electron concentrationsunder disturbed condition, the day and night em-pirical expressions given above for initial [e] maybe sufficiently accurate (Swider, 1988). For quietconditions, the accuracy of the outputs is lesscertain, in part because D-region data for quietconditions are also of low accuracy.

3. Basis of model

An iterative scheme was developed to solve forall species concentrations. Using initial concen-trations for electrons [e] and the positive ion sumSP, the individual negative ion concentrations are

first determined and summed, NSUM. Then thepositive ions are individually calculated andsummed, PSUM. A new

[e] = {previous [e] + PSUM/(1+λ)}/2 (1)

where λ = NSUM/previous [e], and a new

SP = {previous [e] + NSUM + PSUM}/2 (2)

are then determined. This sequence is repeateduntil PSUM = NSUM + [e] within a specified pre-cision. For the November 1969 SPE, not morethan nine iterations were required to reach +1%for altitudes 40–90 km.

Initial daytime concentrations were derived from[e] - (q/Ψ)_, where the effective recombinationcoefficient Ψ is that derived from the Nov. 2–5,1969, SPE (Swider and Dean, 1975). The valuesdetermined (in cm-3 s-1) were 3.4 × 10-7 (85 km),4.8 × 10-7 (80 km), 1.1 × 10-6 (75 km), 1.8 × 10-6

(70 km), 4 × 10-6 (65 km), 8.8 × 10-6 (60 km), 5.5× 10-5 (55 km), 5.1 × 10-4 (50 km), and 3.5 × 10-2

(45 km).

Initial nighttime electron concentrations were de-rived from (Swider et al., 1975)

[e] = {(L(A)/2αD)2+q/αD}_ -L(A)/2αD (3)

where the mean (ion-electron) recombination co-efficient αD is 4 × 10-7 cm-3 s-1, and where

L(A) = k61{O2]2+k62[O2][N2] (4)

is the loss rate (s-1) for electrons through attach-ment to O2, with kxx a specific reaction rate.

Initial total positive ion concentrations were de-termined from

SP = {q(5[O]/αD+[O3]/αi)/(5[O]+[O3](}_ (5)

with αi the mean ion-ion recombination coeffi-cient, 6 × 10-8 cm-3 s-1.

Concentrations of electrons, 21 positive ions and8 negative ions, are determined to two significantfigures. Also printed are q, λ, Ψ, L(A), PSUM,NSUM + [e], initial [e], and initial SP.



22

The following neutral concentrations are required:O, O2, O3, O2(

1∆), N2, CO2, H2O, NO, NO2, tem-perature T, and total neutral concentration M. Therelationships [N2] = 0.7808[M], [O2] = 0.2095[M],CO2 = 3 × 10-4[M] may be used. Values for totalionization production q must be provided. Forquiet conditions in the daytime, q may be derivedfrom the photoionization of NO by H Lyα, nomi-nally (Swider, 1978)

q(NO+) = 6 × 10-7[NO] exp{-10-20[O2]H} (6)

where H is the scale height of the atmosphere.

Processes and rate coefficients are listed in Ta-bles 1 and 2 of Swider (1978). Photodissociationrates were multiplied by unity for daytime andzero for nighttime. Choices for αi and αD weregiven above.


5.1 Smith, D., N.G. Adams, and M.J. Church(1976), Planetary Space Sci. 24, 697–703.

5.2 Swider, W. (1978), J. Geophys. Res. 83,4407–4410.

5.3 Swider, W. (1988), PAGEOPH 127, 403–414.

5.4 Swider, W., and I.L. Chidsey Jr. (1977), J.Geophys. Res. 82, 1617–1619.

5.5 Swider, W., and W.A. Dean (1975), J. Geo-phys. Res. 80,1815–1819.

5.6 Swider, W., and C.I. Foley (1978), AFGL-TR-78-0155.

5.7 Swider, W., R.S. Narcisi, T.J. Keneshea,and J.C. Ulwick (1971), J. Geophys. Res. 76,4691– 4694.


The model (Swider and Foley, 1978) may be or-dered from National Technical Information Serv-ice.


23

NUMERICAL MODEL OFD-REGION ION CHEMISTRY, 1995

1. Model content

The numerical model Sodankyla Ion Chemistry(SIC) was developed as an alternative approachto those D-region ion-chemistry models that com-bine the more doubtful chemical reactions to ef-fective parameters, the values of which are setagainst experimental data. A detailed chemicalscheme, in a conceptually simple model, was builtto be a tool for interpretation of D-region incoher-ent scatter experiments and cosmic radio-noiseabsorption measurements, both of which form thebasis of D-region research done at SodankylaGeophysical Observatory. The number of differ-ent ions in the current version is 55, of which 36are positive and 19 are negative. The model wasfirst applied by Burns et al. (1991) in a study ofincoherent scatter measurements. A detailed de-scription of the first version of the model is givenby Turunen et al. (1992, 1996). The SIC modelcan be run either as a steady-state model or atime-dependent model. The model solves for ionand electron concentrations in ionospheric D andlower E regions. Local chemical equilibrium canbe calculated in the altitude range from 50 to 100km at 1-km steps. The solution for the steadystate can be advanced in time to solve for re-sponse of the ion concentrations to a sudden dis-turbance, e.g., in ion production rates or in neu-tral-gas properties. Originally the model was de-veloped for applications during geophysicallyquiet conditions. Consequently, as ionizationsources acting on five primary neutral compo-nents N2, O2, O, NO, and O2(

1∆g), the solar radia-tion at wavelength range 5–134 nm and galacticcosmic rays were considered. At present, how-ever, the model is extended to include electronprecipitation as an ionization source. A similarextension was made to use the model during so-lar-proton events, as in the application of the SICmodel by Turunen (1993).


A detailed ion-chemical scheme with many reac-tions is subject to the uncertainties and inaccura-cies in the reaction rate constants. Neutral chem-istry and ion chemistry are not coupled in thismodel. The neutral atmosphere is taken only as astatic background. If the effect of particle fluxes isconsidered in detail, one should care about thedissociation of neutral minor constituents. Forinvestigations around sunset and sunrise, the ef-

fects of neutral photochemistry should be in-cluded in detail. Hard x rays and scattered radia-tion at night are not included as ionizationsources. In addition to the presently includedcomponents, heavier cluster ions, heavier clus-ters of negative ions, and more metallic ions areknown to exist in the D region. The assumptionson which the model is based are as follows:

1) The neutral atmosphere is described by thesemi-empirical model MSIS-90 (Hedin, 1991).

2) The ionospheric D region is sunlit. This re-stricts the range of the solar zenith angle to bebelow 95 deg.

3) Ionization during quiet time is primarilycaused by photoionization and galactic cosmicrays. Ionization by solar protons and precipitatingelectrons is calculated using measured particle-energy deposition rates in air.

4) We neglect any transport effects. Chemicallifetimes of the ions are assumed to be short withrespect to transport processes.

5) The concentrations of neutral species aremuch higher than those of ions and thus assumedto be unaffected by ion chemistry.

6) An overall charge neutrality prevails.


In addition to the above-mentioned neutrals, Ar,He, and CO2 also are included in photoionizationcalculations, because they absorb the solar radia-tion at the relevant wavelength range. To accountfor important ion-chemical reactions we need toinclude also H2O, N, H, O3, OH, NO2, HO2, NO3,HNO2, CO3, H2, HCl, HNO3, Cl, ClO, CH4, andCH3 in the list of the neutral components of themodel.

Continuity equation for ion i (transport effectsneglected):

∂ n i

∂ t= P i − n i ⋅ L i

where

P i = p improduction processes m

∑,

L i = limloss processes m

∑

Consider reaction

A + + B → C + + D


24

for

C +:

and for

A+: lA + m = k[ A + ][ B]

Assume constant neutral concentrations:

p C +m = Π C + m A +[ ] , lA + m= Λ

A + mA +[ ]

Continuity equation in matrix form:

( ) ( ) ( )NQNNNF

N+Γ==

t

ˆ

δδ

Γ is a 55 × 55 matrix. Elements Π and Λ describethe production and loss rates of each ion.

r N is a

vector containing the 55 unknown ion concentra-tions.

r Q is a vector that contains the constant

primary ionization rates. Chemical equilibriummay be solved by setting

∂ n i

∂ t= 0

Starting from the equilibrium solution of the ionconcentrations, we advance the concentrations intime by taking small time steps according to theexpression

( ) ( )

−⋅+∆+= +

=

+ nn

NN

nnn NNN

FNFtNN

n

11δ

δ

where the elements φ ij of the matrix

nNNN

F

=δ

δ

are the partial derivatives

nNN

ijN

F

=

=δ

δφ

The expression above is a set of linear equations,

which has to be solved for each time step.

4. Database and input to the model

As input to the neutral atmosphere model, MSIS-90, one gives time, location, and informationabout solar and geomagnetic activity. The result-ing neutral constituent concentrations are thenused to calculate ion production rates and chemi-cal reaction rates. For those neutral constituentsthat are not covered by the MSIS-90 model, fixedreference profiles may be selected. Also fixedmixing ratios of 3 × 104 and 1 × 106 for CO2 andH2O, respectively, can be used. Some applica-tions may require that a set of the neutral minorconstituent profiles is kept fixed while selectedconcentrations are varied.

Absorption cross sections for N2, O2, O, and Heare from Torr et al. (1979); for NO and Ar, theconstants from the tables of Ohshio et al. (1966)are used; and for CO2, the data are from McEwanand Phillips (1975). Photoionization efficienciescome from the same references as the absorptioncross sections.

A reference solar spectrum was collected fromthe spectrum by Torr et al. (1979) and from spec-trum R74113 by Heroux and Hinteregger (1978).The intensities for wavelengths 103.76 nm and110.8 nm were taken from the paper of Huffmanet al. (1971). For our reference spectrum, Ly-αline was chosen from Lean and Skumanich(1983). The intensities can be varied according tothe chosen level of solar activity. Heaps (1978)has derived a convenient parametrization of theempirical rate of ion-pair production by cosmicrays, Qcr, as a function of latitude, altitude, andsolar activity.

The spectrum of precipitating electrons can begiven in a parameterized form of the differentialenergy spectrum. Alternatively, a precise form ofthe spectrum can be given, e.g., in the form offluxes at selected energy channels. Input of theproton flux is formulated to correspond to meas-urements at predefined energy channels, as, e.g.,those used by the satellite GOES-7.

For the chemical schemes, the main contributionswere taken from the works by Chakrabarty et al.(1978), Dymek (1980), Wisemberg and Kockarts(1980), Torkar and Friedrich (1983), and Thomasand Bowman (1985). The reaction rate constantswere updated from several sources.


25


5.1 Burns, C.J., E. Turunen, and H. Matveinen(1991), J. Atmos. Terr. Phys. 53, 115.

5.2 Chakrabarty, D.K., P. Chakrabarty, and G.Witt (1978), J. Atmos. Terr. Phys. 40, 437.

5.3 Dymek M.K. (1980), Low Latitude Aero-nomical Processes, edited by A.P. Mitra,COSPAR Symposium Series, Pergamon Press,Oxford and New York, Vol. 8, p. 118.

5.4 Heaps, M.G. (1978), Planetary Space Sci.26, 513.

5.5 Hedin A.E. (1991), J. Geophys. Res. 96,1159.

5.6 Heroux, L., and H.E. Hinteregger (1978),J. Geophys. Res. 83, 5305.

5.7 Huffman, R.E., D.E. Paulsen, and J.C.Larrabee (1971), J. Geophys. Res. 76, 1028.

5.8 Lean, J.L., and A. Shumanich (1983), J.Geophys. Res. 88, 5751.

5.9 McEwan, M.J., and L.F. Phillips (1975),Chemistry of the Atmosphere, Edward ArnoldLtd., London.

5.10 Ohshio, M., R. Maeda, and H. Saka-gami(1966), J. Radio Res. Lab. 13, 245.

5.11 Thomas, L., and M.R. Bowman (1985), J.Atmos. Terr. Phys. 47, 547.

5.12 Torkar, K.M., and M. Friedrich (1983), J.Atmos. Terr. Phys. 45, 369.

5.13 Torr, M.R., D.G. Torr, R.A. Ong, and H.E.Hinteregger (1979), Geophys. Res. Letters 6,771.

5.14 Turunen E. (1993), J. Atmos. Terr. Phys.55, 767–781.

5.15 Turunen, E., H. Matveinen, and H. Ranta(1992), “Sodankyla Ion Chemistry (SIC) Model,”Sodankyla Geophysical Observatory, Rept. 49,

Sodankyla, Finland.

5.16 Turunen, E., J. Tolvanen, H. Matveinen,and H. Ranta (1996), “D Region Ion ChemistryModel,” STEP Handbook of Ionospheric Models,edited by R.W. Schunk.

5.17 Wisemberg, J., and G. Kockarts (1980), J.Geophys. Res. 85, 4642.


6.1 Dates:

1989 Version 1.0, 35 ions.

1991 Version 1.1, reaction rates updated.

1994 Version 2.0, adding and removing reac-tions.

1995 Version 2.1, 55 ions.

1995 Version 3.0, time-dependent code.

6.2 Author (principal): Esa Turunen, Head ofthe Ionospheric Station, SGO; Helena Matveinen,Scientist, SGO.

6.3 Sponsor: Finnish Academy of Science andLetters, Geophysical Observatory, Sodankyla,Finland.


The early versions of the model were based onFORTRAN code, which we no longer support.The present version of the model is coded inMATLAB language, which makes the model user-friendly, easy to adapt, and easy to tailor to spe-cific needs. The current version is written usingMATLAB 4.2c. The code runs on computers thatcan run MATLAB. The code is not optimized forspeed, but this could be done by any user. Thelatest version will be made available to anyoneinterested. Contact person: Esa Turunen, Sodan-kyla Geophysical Observatory, FIN-99600 So-dankyla, Finland (e-mail: Esa.Turunen@ sgo.fi).


26

SOLAR EUV AND CHEMISTRY MODEL

1. Model content

A modeling technique of Keneshea (1967) wasapplied by Keneshea et al. (1970) to the E regionfor detailed comparisons with ionic compositionsmeasured at twilight (two at sunset and two atsunrise). The experiments were conducted undernormal (quiet) conditions at mid latitudes, nearEglin Air Force Base, Florida, during April 1967.This month was one of moderate solar activity,with a mean sunspot number of 69.5.


It is our experience that [NO] appears generally tobe greater in the E region than many models as-sume. Thus some models yield O2

+>>NO+ near95–100 km, whereas the observational data, withperhaps one exception, do not support this result(Swider, 1994). The values of [NO] used here arein the higher range of those determined fromgamma-band data. However, these values haveworked well. Again, our use of a somewhat higherx-ray flux appears justified by the model’s favor-able comparison with the observational ionic data.There have been suggestions that there is insuffi-cient ionization produced near 95–100 km, im-plying a missing source of ionization. However,none have offered any specific details, and ourmodel agrees quite well with incoherent scatterdata in the lower E region (Trost, 1979).

3. Basis of model

The model was set up to simultaneously solve aset of coupled partial differential equations

∂ni

∂t= Qi − Li (1)

where ni is the number density of the i species,with Qi and Li the respective production and lossterms for that species, which terms commonlyinclude other species concentrations.

Concentrations were calculated for negative ionsO-, O2

-, O3-, NO2

-, NO3-, and CO3

-; positive ionsO+, O2

+, N2+, and NO+; and electrons e. In addi-

tion, differential equations were solved for thefollowing neutral species: NO, N, NO2, O, N2O,O3, CO2, H2, H, OH, HO2, H2O, H2O2, O2, and N2.However, in applying the code to the E region,NO and N were held fixed. The major gaseschanged very little over the course of the run:about one day commencing at noon, when the

solar zenith angle was 21.6 deg. The major spe-cies (O2, N2) changed imperceptibly over this pe-riod, and negative ions were negligible. As wewere not focusing on the chemistry of the minorneutrals but rather on the major positive ions andelectrons, we list only their relevant chemistry(Summary of Reference and Standard Iono-spheres), which has changed little over the inter-vening years.

Transport was ignored in this model. However,because one sunset observation was quite dis-torted, a special calculation was performed (Ke-neshea and MacLeod, 1970), which comparedwell with the data. This model variation includedtransport terms using the full continuity equations.The velocities required for the divergence termwere derived from the measured neutral windprofiles for an earlier flight and used in a colli-sion–geomagnetic equilibrium expression

vi =1

1 + ρ 2i

[ρ 2

i u + ρiu × Γ + (u ⋅ Γ)Γ],(2)

where ρi is the ratio of neutral-ion collision fre-quency to gyrofrequency, Γ a unit vector in thegeomagnetic field direction, and u the neutralwind (MacLeod, 1966).

The method of solution for the partial differentialequations uses a fourth-order Runge Kutta inte-gration with a variable mesh. When a speciesenters its quasi-equilibrium state, its differentialequation is removed from the set, and its equilib-rium equation is inserted into the simultaneousalgebraic set, which is solved by the methods ofsuccessive substitutions. The overall solution isobtained by iteration between the differential andalgebraic sets.

A numerical solution to this problem that requiresthe use of a high-speed digital computer has beendiscussed (Keneshea, 1962). The computer pro-gram resulting from that study, although it devel-oped satisfactory solutions within a minimum ofcomputer time, can be used only at E-region alti-tudes. One reason for this restriction is that thenumber density of NO+ ions is always computedfrom the requirement of balance of charge. (Thesum of the positive ions equals the sum of theelectrons and the negative ions.) This method isapplicable, however, only if NO+ is the mostabundant ion. Although this appears to be true inthe E region, it will not be the case at lower alti-tudes, in the D region. Because the system issolved on a digital computer, it is not possible to


27

accurately determine the concentration of a minorspecies through conservation of charge. The re-quired number density is located in the least sig-nificant bits of the computer word, and, dependingupon the amount of accumulated round-off error,the result could be erroneous.


Solar fluxes and absorption cross sections weretaken from Watanabe and Hinteregger (1962)above about 100A. Below this wavelength, thevalues listed by Nicolet and Aiken (1960) for quietsolar conditions were adopted. The solar flux inthe range 10–170A was increased by a factor of 4over the values cited above in order to bestmatch the data. The proper x-ray flux for the Eregion is still of concern in more recent codeswhich aim to determine minor odd nitrogen spe-cies, particularly N and NO. An H Lyα flux of 4egs com-2 sec-1 was adopted, and the ionizationeffects of the scattered H Lyα and H Lyβ radia-tions were approximated by setting their fluxes at1% and 0.4%, respectively, of their noontimeheight-dependent direct flux profiles. The paperby Strobel et al. (1980) should be consulted for adetailed analysis of nighttime ionization sourcesand their intensities. The declination of the sunwas fixed at 8.62 deg for comparison with thespecific experimental data, with the noontime so-lar zenith angle χ being 21.63 deg. Atmosphericconcentrations and temperatures were taken fromthe mean 1965 COSPAR International ReferenceAtmosphere (CIRA). All particles were assumedto have the same temperature distribution. In cal-culating the optical depth, appropriate CIRA con-centrations were integrated along the various so-lar zenith angles. The nitric oxide concentrationsessentially were a smooth version of Barth’s(1966) results, but lower at 85 km, the lowest al-titude of the calculation. Atomic nitrogen concen-trations were effectively negligible, [N] = 10-2[NO].Both species were held constant throughout thetime-dependent solutions of the charged constitu-ents.

The specific nitric oxide concentrations used were(in 106 cm-3) 3 (140 km), 5.4 (130 km), 11 (120km), 25 (110 km), 34 (105 km), 40 (100 km), 38(95 km), 25 (90 km), and 10 (85 km). Calculationswere performed only at these altitudes. Nitric ox-ide plays two major roles. First, it converts O2

+

ions into NO+ ions via the charge transfer reaction(#9 in Summary of Reference and Standard Iono-spheres). However, it is the product k9 [NO] that is

important. Thus, as k9 is now about 25% lowerthan the value in Summary of Reference andStandard Ionospheres, the [NO] used is effec-tively 4/3 the values cited. More significant is that,near a solar zenith angle of 90 deg, the attenua-tion of H Lyα near 100–110 km is negligible, andthe main ionization source is therefore H Lyα +NO → NO+ + e. If [NO] is enhanced, as is oftenthe case for the auroral region (discussed below),E-region concentrations [e] at sunrise increase,too, as [e]2 is proportional (numerically) to [NO](Swider and Keneshea, 1993).

5. Publications references

5.1 Barth, C.A. (1966), Ann. Geophys. 22,198–207.

5.2 Keneshea, T.J. (1967), AFCRL-67-0221.

5.3 Keneshea, T.J., and M.A. MacLeod(1970), J. Atmos. Sci. 27, 981–984.

5.4 Keneshea, T.J., R.S. Narcisi, and W.Swider Jr. (1970), J. Geophys. Res. 75, 845–854.

5.5 Nicolet, M., and A.C. Aikin (1960), J. Geo-phys. Res. 65, 1469–1483.

5.6 Stobel, D.F., C.B. Opal, and R.R. Meier(1980), Planetary Space Sci. 28, 1027–1033.

5.7 Swider, W., and T.J. Keneshea (1993), J.Geophys. Res. 98, 1725–1728.

5.8 Swider, W. (1994), EOS 75, 246.

5.9 Trost, T.F. (1979), J. Geophys. Res. 84,2736–2742.

5.10 Watanabe, K., and H.E. Hinteregger(1962), J. Geophys. Res. 67, 999–1006.


A version of the model may be available (contactW. Swider), but it may not be worth running inview of the published outputs, especially becauseothers undoubtedly have codes much faster thanthe one discussed here. The original printout isavailable (W. Swider). The originator/writer of thecode (T.J. Keneshea) has expanded it to includetransport and IR emissions, but its availabilitythrough Visidyne Research, Inc., may be limited.


28

AFRL BOLTZMANN-FOKKER-PLANCKMODEL FOR THEDAYTIME LOWER IONOSPHERE

1. Model content

The Boltzmann-Fokker-Planck (BFP) model cal-culates the energy-dependent electron distributionfunction, the electron density, the electron tem-perature, and the densities of four ion species(O+, N2

+, O2+, N2

+) in the earth's daytime lowerionosphere. Electron and ion production rates perunit volume are also calculated. The model as-sumes a steady state and uses a local approxi-mation. Thus the above quantities are calculatedfor a given time, location, and altitude. To de-velop any spatial or temporal information requiresthat a series of calculations be made for the dif-ferent altitudes, locations, and times of interest.Past use has usually focused on several altitudesat a specific time and place.


One source of model inaccuracy lies in the un-certainties in our knowledge of various cross sec-tions and reaction rates needed for the calcula-tion. Fortunately, most of the cross sections andreaction rates have been measured so that thereis an empirical basis for the values that are used.Another limitation to the model accuracy occursbecause of the need to know the geophysicalconditions of the time and place being modeled.

As described earlier, the model is restricted to thelower ionosphere, which typically means the Eand F1 regions. In previous work, the model hasbeen used down to around 100 km. There is po-tential for going down to around 90 km. However,in any particular case, the appropriate lowerboundary is defined wherever processes normallyassociated with the D region can no longer beneglected. The upper boundary is typically slightlybelow the F2 peak and, for any particular case,should be determined by where electron and iontransport become important. At mid latitudes thisaltitude is typically 220 –250 km.

The model is strictly a daytime model, with thesolar flux acting as the primary source of ioniza-tion. As such, it is generally inappropriate for usein the auroral regions or any daytime location thatis undergoing significant particle precipitation.

The model calculates the zero-order state of thephotoelectron distribution function and does not

include any wave-particle or wave-wave plasmainteractions.


The BFP model produces a numerical solution ofa kinetic equation for the isotropic portion of thesteady-state electron distribution function (EDF)and of four ion continuity equations for the iondensities. The equations solved can be derived bybeginning with a system of one-particle plasmakinetic equations, where one equation appears foreach state of each kind of particle. By assumingthat the ion distribution functions are local Max-wellian functions and that transport effects can beneglected (local approximation), a steady-stateequation for each ion density can be derived. Forthe lower ionosphere, this results in four coupledequations for the ion densities. In these fourequations, there are terms that depend on theenergy-dependent EDF, which is considered un-known. An equation for this distribution function isderived by assuming a steady state, by neglectingthe anisotropic portion of the distribution function,and by integrating the kinetic equation for theEDF over angles in velocity space. The resultingequation contains a series of terms that describethe rates of change of the EDF due to photoioni-zation and collision processes. The name of themodel comes from the fact that the explicit ex-pressions for each of these terms come from us-ing either Boltzmann or Fokker-Planck methods.Finally, both the electron density and temperaturecan be found from their definitions once the EDFis known. The primary sources and sinks of ioni-zation are photoionization and recombination,respectively. The electron-neutral processes in-cluded are elastic collisions, excitation collisions,de-excitation collisions, and ionizing collisions.Also included are elastic electron-ion and elec-tron-electron collisions. These terms are nonlinearin the EDF and are formulated in terms of theRosenbluth potentials. Included are a variety ofchemical reactions that involve the above ionsand the three major neutral species (O, N2, O2) ofthe earth's atmosphere.

In solving the kinetic equation for the EDF, anonuniform grid of several hundred energy pointsis used that typically spans from 1 × 10-9 to 225eV. As mentioned, a single computer run of themodel performs the calculation for a specific alti-tude, time, and location.



29

The model requires geophysical inputs as well asa variety of cross sections and reaction rates. Thecross sections and rates are provided by a seriesof data files that can be updated whenever newvalues are available. The geophysical inputs arethe solar flux, neutral densities, neutral tempera-tures, and ion temperatures. These are generallysupplied by empirical or statistical models forthese quantities.


5.1 Jasperse, J.R. (1976), “Boltzmann-Fokker-Planck Model for the Electron DistributionFfunc-tion in the Earth's Ionosphere,” Planetary SpaceSci. 24, 33–40.

5.2 Jasperse, J.R. (1977), “Electron DistributionFunction and Ion Concentrations in the Earth'sLower Ionosphere from Boltzmann-Fokker-PlanckTheory,” Planetary Space Sci. 25, 743–756.

5.3 Jasperse, J.R. (1981), “The PhotoelectronDistribution Function in the Terrestrial Iono-sphere,” Physics of Space Plasmas, edited by T.Chang, B. Coppi, and J. R. Jasperse, SPI Con-ference Proceedings and Reprint Series, Scien-tific Publishers, Cambridge, MA, Vol. 4, p. 53.

5.4 Winningham, J.D., D.T. Decker, J.U. Ko-zyra, J.R. Jasperse, and A.F. Nagy (1989), “Ener-getic (> 60 eV) Atmospheric Photoelectrons,” J.Geophys. Res. 94, 15,335–15,348.


6.1 Dates:

1973 Coupled nonlinear equations for electrondistribution function in the earth's ionosphere arederived.

1976 Numerical solution of electron kineticequation and local ion continuity equations iscompleted.

1982 Low-energy electron and photon crosssections are updated.

1989 BFP model compared with other photo-electron models.

6.2 Authors: John R. Jasperse, Phillips Labo-ratory/GPIM; Neil J. Grossbard, Boston College;and Dwight T. Decker, Boston College.

6.3 Sponsors: Air Force Office of ScientificResearch and Phillips Laboratory of the U. S. AirForce Material Command.


The model is in the form of a large FORTRANcode, but it is not user friendly. Anyone interestedin results from this code should contact John R.Jasperse.


30

AFRL TRANSPORT MODEL FOR THEELECTRON-PROTON-HYDROGENATOM AURORA

1. Model content

The PL transport model for the combined elec-tron-proton-hydrogen atom aurora describes theenergy deposition, ionization, and excitation ofoptical emissions by the precipitating electrons,protons, and hydrogen atoms associated with theauroral zone for steady-state conditions. The nu-merical code solves a coupled set of three lineartransport equations for the three particle speciesto obtain the particle fluxes as functions of alti-tude, energy, and pitch angle. The altitude pro-files of the rates of energy deposition, ionization,and excitation of optical emissions are then cal-culated from the fluxes. The code also calculatesthe electron-density profile associated with thecombined aurora. Densities of the important ionspecies are calculated by using a detailed chem-istry model that solves a set of coupled rateequations. The electron density is then specifiedby requiring charge neutrality. The model canalso be used to study a pure electron aurora or apure proton-hydrogen-atom aurora by choosingthe appropriate boundary conditions. At presentthe model calculates volume emission rates forthe following optical features: N2

+ first negativegroup (3914 Å), N2 second positive group (3371Å), selected N2 Lyman-Birge-Hopfield bands(1325 Å, 1354 Å, 1383 Å, 1493 Å, and all bandsbetween 1700 and 1800 Å), OI (1356 Å), NI (1493Å), Lα (1216 Å), Hb (4861 Å), and Hα (6563 Å).More optical features will be added to the modelas their cross sections become available.

The transport model assumes steady-state condi-tions with no electric fields present, plane-parallelgeometry, and a uniform geomagnetic field(magnetic mirroring effects are neglected). Theeffect of the atmospheric lateral spreading of theincident proton stream due to charge-changingprocesses (charge exchange and stripping), whichis neglected in the plane-parallel geometry, canbe included, to a good approximation, by multi-plying the incident flux with an appropriate cor-rection factor (Jasperse and Basu, 1982).

The inputs for the model are (1) the cross sec-tions for the various collision processes involvingelectrons, protons, and hydrogen atoms; (2) ef-fective cross sections for selected emission fea-tures; (3) the neutral atmosphere; and (4) the in-

cident particle (electron and proton) fluxes at theupper boundary of the atmosphere.


2.1 The reliability of the calculated aurora-related quantities largely depends on the accu-racy with which the input quantities can be speci-fied.

2.2 The steep bottomside profile, which is thegeneral characteristic of the precipitating particlefluxes, requires fine altitude grid points to obtain adesired accuracy.

2.3 The model does not take into account theeffect of magnetic mirroring on the pitch-angledistribution of the particle fluxes.


The model is based on a coupled set of threetransport equations for the electrons, protons, andhydrogen (H) atoms that includes all the elasticand inelastic collision processes involving theseparticles and the neutral particles. The proton andH atom fluxes are coupled only to each other be-cause of the charge-changing collisions, whereasthe electron flux is coupled to both the proton andthe H atom fluxes through the secondary elec-trons that they generate. The equations for pro-tons and H atom fluxes are first converted intointegral equations and then solved on a two-dimensional grid of energy (E) points from Emin toEmax and altitude (z) points from zmin to zmax (fordetails, see Basu et al., 1990). These fluxes areused to calculate the secondary-electron sourceterms in the electron transport equation. Theelectron transport equation is then solved to ob-tain the degraded primary and secondary electronfluxes by using a discrete ordinate and eigen-value technique (for details, see Strickland et al.,1976; Basu et al., 1993). From the particle fluxesas a function of altitude, energy, and pitch angle,various quantities of interest are calculated byusing rigorous theoretical formulae (Basu et al.,1993).


4.1 The set of particle impact and effectiveemission cross sections used in the model andthe sources of these cross sections are given byBasu et al. (1990) and Strickland et al. (1993).

4.2 The model can use any neutral atmospherespecified by the user. Presently, it uses the MSIS-86 thermospheric model.


31

4.3 The incident electron and proton fluxes arespecified by analytic functions. Two commonlyused energy distributions for the incident electronflux are (1) a Maxwellian distribution with the op-tions of adding low- and high-energy tails and (2)a Gaussian distribution with the same options. Forthe protons, a Maxwellian or a Kappa distribution,or some combination of them, is used.


5.1 Basu, B., J.R. Jasperse, and N.J. Grossbard(1990), “A Numerical Solution of the CoupledProton-H Atom Transport Equations for the Pro-ton Aurora,” J. Geophys. Res. 95, 19,069.

5.2 Basu, B., J.R. Jasperse, R.M. Robinson,R.R. Vondrak, and D.S. Evans (1987), “LinearTransport Theory of Auroral Proton Precipitation:A Comparison with Observations,” J. Geophys.Res. 92, 5920.

5.3 Basu, B., J.R. Jasperse, D.J. Strickland andR.E. Daniell (1993), “Transport-Theoretic Modelfor the Electron-Proton-Hydrogen Atom Aurora, 1.Theory,” J. Geophys. Res. 98, 21,517.

5.4 Daniell, R.E., and D.J. Strickland (1986),“Dependence of Auroral Middle UV Emissions onthe Incident Electron Spectrum and Neutral At-mosphere,” J. Geophys. Res. 91, 321.

5.5 Decker, D.T., B. Basu, J.R. Jasperse, D.J.Strickland, J.R. Sharber, and J.D. Winningham(1995), “Upgoing Electrons in an Electron-Proton-Hydrogen Atom Aurora,” J. Geophys. Res. 100,21,409.

5.6 Jasperse, J.R., and B. Basu (1982), “Trans-port Theoretic Solutions for Auroral Proton and HAtom Fluxes and Related Quantities,” J. Geo-phys. Res. 87, 811.

5.7 Strickland, D.J., D.L. Book, T.P. Coffey, andJ.A. Fedder (1976), “Transport Equation Tech-niques for the Deposition of Auroral Electrons,” J.Geophys. Res. 81, 2755.

5.8 Strickland, D.J., J.R. Jasperse, and J.A.Whalen (1983), “Dependence of Auroral FUVEmissions on the Incident Electron Spectrum andNeutral Atmosphere,” J. Geophys. Res. 88, 8051.

5.9 Strickland, D.J., R.R. Meier, J.H. Hecht, andA.B. Christenson (1989), “Deducing Compositionand Incident Electron Spectra from Ground BasedAuroral Optical Measurements: Theory and ModelResults,” J. Geophys. Res. 94, 13,527.

5.10 Strickland, D.J., R.E. Daniell, J.R. Jas-perse, and B. Basu (1993), “Transport-TheoreticModel for the Electron-Proton-Hydrogen AtomAurora, 2. Model Results,” J. Geophys. Res. 98,21,533.


6.1 Dates:

1976 Original electron transport code for a one-constituent medium.

1982 Original proton-H-atom transport modeland its analytic solutions for a one-constituentmedium.

1983 Generalization of electron transport codeto a multiconstituent medium and application toan auroral study.

1987 Study of a pure proton aurora with theproton-H-atom transport model.

1989 Application of electron transport code toan auroral study.

1990 Numerical proton-H-atom transport codefor a multiconstituent medium.

1993 Electron-proton-H-atom transport code fora multiconstituent medium.

1995 Study of upgoing electrons in an electron-proton-hydrogen-atom aurora with transport code.

6.2 Authors: B. Basu and J. R. Jasperse, Phil-lips Laboratory/GPIM, Hanscom AFB, MA 01731;D. J. Strickland and R. E. Daniell, ComputationalPhysics, Inc., 2750 Prosperity Avenue, Suite 600,Fairfax, VA 22031; D. T. Decker, Institute for Sci-entific Research, Boston College, Newton, MA02159.

6.3 Sponsors: Air Force Office of ScientificResearch (AFOSR), Defense Nuclear Agency(DNA), Defense Meteorological Satellite Program(DMSP), National Science Foundation (NSF), andAir Force Phillips Laboratory (PL).


The model is in the form of a research-typeFORTRAN code and is not very user friendly.However, the authors frequently run the model incollaborative studies with experimentalists andother modelers. Anyone interested in such a studyshould contact J. R. Jasperse, Phillips Labora-tory/GPIM, 29 Randolph Road, Hanscom AFB,MA 01731 (e-mail [email protected]).


32

TWO-CELL IONOSPHERICCONVECTION MODEL

1. Model content

In the F-region ionosphere, the plasma drifts per-pendicular to the magnetic field under the influ-ence of the electric field such that V = E × B/B2.The electric field may be expressed in terms of ascalar electrostatic potential, and then electricequipotential lines indicate the instantaneous flowpaths of the plasma. The F-region plasma motionis highly dependent on conditions in the inter-planetary medium, particularly the interplanetarymagnetic field (IMF) and the solar wind velocity.When the IMF is directed southward, most in-situand remote sensing of the plasma motion at highlatitudes in the F-region ionosphere confirms theexistence of a two-cell circulation of the plasma,with antisunward flow at highest latitudes andsunward flow at lower latitudes largely confined tothe regions of the auroral zone. This model pro-vides an analytical expression for the electrostaticpotential that describes a two-cell convectionpattern and its first-order dependencies on theIMF. Specification of the potential distribution isachieved by defining a circular region (the polarcap) at high latitudes, within which the plasmaflow is antisunward. The radius of the polar capand the potential distribution across it determinethe magnitude of the antisunward plasma flow.These variables may be specified by the user, orsimple functional dependencies derived from ob-servations from the Dynamics Explorer spacecraftand residing within the model algorithm may beinvoked. Outside the polar cap, the sunward flowin the auroral region is determined by the distri-bution of the potential around the polar capboundary and by a specification of the effectivewidth of the auroral zone. These dependenciesmay also be fully specified by the user, or simplefunctional dependencies derived from DE-2 datamay be invoked.

2. Model uncertainties

This model does not represent a synthesis of datain any way. It simply provides a tool by whichmajor observed characteristics of the high-latitudeconvection pattern can be mimicked or by whichspecific observations of the electrostatic potentialcan be fit. The simple analytical functions that areemployed do not allow convection features withscale sizes less than 10 deg in latitude or 6 hr inlocal time to be reproduced. The simple functionaldependencies on the IMF presently provided by

the algorithms are based on a rather limited data-base from DE-2 and may differ significantly fromthose derived from other sources. Care shouldtherefore be exercised when comparing derivedresults utilizing different specifications of the con-vection pattern. The model may presently be ap-plied to conditions of southward IMF when confi-dence is high that a two-cell convection patternexists. It is not applicable to times of weaklysouthward IMF or northward IMF when significantvariations from the two-cell configuration arelikely.


Many studies of the high-latitude ionosphericconvection describe a two-cell circulation (e.g.,Foster, 1983; Heppner and Maynard, 1987). Anoriginal description of this convection configura-tion was given by Volland (1975). This model rep-resents extensions to the functional forms givenby Heelis et al. (1982) and dependencies of thedriving parameters on the IMF given by Hairstonand Heelis (1990). The model determines a distri-bution of electrostatic potential around a circularboundary defining the polar cap. This distributionis specified by a maximum and minimum poten-tial, each of which occupies a local time extentdependent on the y component of the IMF. Theselocal time regions are connected around theboundary using cubic splines through zero pointsthat are also dependent on the y component ofthe IMF. The potential distribution inside thisboundary is completed using a cubic spline thatconnects the specified boundary potentials withthe location of a zero potential dependent on they component of the IMF. Equatorward of the polarcap boundary, the electrostatic potential is speci-fied by the segment of a gaussian with a half-width dependent on local time only.

4. Database

The functional forms utilized in the model arethose that adapt most readily to the variety oftwo-cell convection patterns described by a num-ber of workers. The dependence of the majordriving parameters on the IMF was derived fromfits to the derived potential distributions availablefrom the DE-2 database.


5.1 Volland, H. (1975), “Models of the GlobalElectric Fields within the Magnetosphere,” Ann.Geophys. 31, 159.


33

5.2 Heelis, R.A., J.K. Lowell, and R.W. Spiro(1982), “A Model of the High-Latitude IonosphericConvection Pattern,” J. Geophys. Res. 87, 6339.

5.3 Foster, J.C. (1983), “An Empirical ElectricField Model Derived from Chatanika Radar Data,”J. Geophys. Res. 88, 981–987.

5.4 Heppner, J.P. and N.C. Maynard (1987),“Empirical High Latitude Electric Field Models,” J.Geophys. Res. 92, 4467–4489.

5.5 Hairston, M.R. and R.A. Heelis (1990), “AModel of the Ionospheric Convection Pattern for

Southward IMF Based on DE-2 Observations,” J.Geophys. Res. 95, 2333–2343.


Functional forms that constitute the model areavailable in the published literature. Source codesthat provide callable subroutines to provide thepotential at any given location are available fromR. A. Heelis, W. B. Hanson Center for Space Sci-ences, University of Texas at Dallas, Box 830688,Richardson, TX 75083-0688, USA (e-mail [email protected]).


34

HEPPNER-MAYNARD ELECTRICFIELD MODELS

1. Model content

The Heppner-Maynard electric field models ofhigh-latitude convection electric fields were de-rived from the DE-2 satellite electric field meas-urements using a pattern recognition technique(Heppner and Maynard, 1987). The models areempirically derived potential patterns for variousinterplanetary magnetic field (IMF) orientationsand for varying levels of Kp. The original patternswere presented for a nominal Kp level of 3+ withrules for changing size and potential strength asKp varied. These patterns were parameterizedusing fits to spherical harmonic functions by Richand Maynard (1989). The parameterized versioncovers Kp levels up through 7.

Convection patterns in the high-latitude iono-sphere are very variable; however, basic signa-tures in the data tend to repeat for similar IMFconditions (Heppner, 1973). The goal was to de-velop a minimum set of patterns that would berepresentative of most conditions. Three patternsfor IMF Bz south were derived. The BC pattern isrepresentative of convection in the northern(southern) hemisphere for BY negative (positive)conditions. In the BC and DE patterns, the polarcap convection is tilted to one side or the other.The A pattern is symmetric across the polar capand is more often found in the sunlit hemispherefor appropriate IMF conditions.

For northward IMF, two levels of distortion of thesouthward IMF patterns were proposed. Thesepatterns are qualitative but are conceptually use-ful. For pure Bz north, the pattern is more likely tobe a four-cell pattern rather than the distortedtwo-cell. Both the distorted two-cell and the four-cell patterns are seen in the empirical models ofRich and Hairston (1994), which are derived fromaveraging DMSP ion drift data.

The advantage of a pattern recognition techniqueis that features near noon and midnight, whichtend to shift back and forth in magnetic local time,retain their crispness of definition. A straight av-eraging technique tends to wash out detail inthese regions because of the dynamics of theseregions.

The Rich-Maynard parameterization of the Hepp-ner-Maynard patterns requires the IMF Bz and BY

polarities to specify the patterns type and the Kp

level. The output is a map of the potential. Allpatterns are given in magnetic-latitude/magnetic-local-time coordinates in a coordinate systemcorotating with the Earth. This is the natural sys-tem of the ionosphere. Conversion of these pat-terns into the inertial system, which is the naturalsystem of the magnetospheric source, can befound in Maynard et al. (1995).


The model is valid at all altitudes in the iono-sphere, assuming equipotential magnetic fieldlines. The projection of the electric fields alongthe magnetic field assumes that E × B = 0. Abovethe ionosphere, field aligned electric fields atauroral latitudes may distort the projection back tothe magnetospheric source.

The model is meant to represent the potentialpattern for typical conditions for given model in-puts. The model may or may not replicate the realconvection pattern in any individual circumstance.This is especially true in the noon and midnightportions of the pattern, where considerable shiftsin the pattern with magnetic local time are possi-ble. Local mesoscale processes that may existwithin the global system may distort areas ofthese global scale patterns.

The northward IMF patterns are conceptual only.The complexity of the patterns and the limiteddatabase do not provide the statistical signifi-cance that exists with the southward IMF patterns.For weakly northward IMF, the appropriate south-ward patterns for the given Kp conditions will ap-proximate actual conditions. As the IMF turnsmore northward, the patterns evolve to the mildlydistorted patterns and eventually toward thestrongly distorted patterns or into a four-cell pat-tern.

3. Basis of model

The Heppner-Maynard patterns have been fittedto a spherical harmonic function based on Legen-dre polynomials. The resulting equipotential con-tours describe the plasma flow directions basedon E × B = 0 and the convective flow E × B/B2 inan incompressible fluid.

The global scale validity of the southward IMFmodels is attested to by the field-aligned currentpatterns derived by Rich and Maynard (1989) us-ing the Heppner-Maynard patterns and the Hardyet al. (1987) conductivity patterns (averaging


35

patterns based on DMSP energetic electron pre-cipitation statistical patterns). The divergence ofthe perpendicular currents calculated from thesetwo empirical average patterns combines to pro-duce reasonable facsimiles of the Iijima and Po-temra (1976) average field-aligned current pat-terns based on Triad data.

4. Database

The Heppner-Maynard patterns were derivedfrom the double-probe electric field data from theDE-2 satellite covering the period from August1981 to February 1983. This is a solarmax data-base.


5.1 Hardy, D.A., M.S. Gussenhoven, R. Rais-trick, and W.J. McNeil (1987), “Statistical andFunctional Representations of the Patterns ofAuroral Energy Flux. Number Flux and Conduc-tivity,” J. Geophys. Res. 92, 12,275.

5.2 Heppner, J.P. (1972), “Polar Cap ElectricField Distributions Related to the InterplanetaryMagnetic Field,” J. Geophys. Res. 77, 4877.

5.3 Heppner, J.P., and N.C. Maynard (1987),“Empirical High-Latitude Electric Field Models,” J.Geophys. Res. 92, 4467.

5.4 Iijima, T., and T.A. Potemra (1976), “TheAmplitude Distribution of Field-Aligned Currentsat Northern High Latitudes Observed by Triad,” J.Geophys. Res. 81, 2165.

5.5 Maynard, N.C., W.F. Denig, and W.J. Burke(1995), “Mapping Ionospheric Convection Pat-terns to the Magnetosphere,” J. Geophys. Res.100, 1713.

5.6 Rich, F.J., and M. Hairston (1994), “Large-Scale Convection Patterns Observed by DMSP,”J. Geophys. Res. 99, 3827.

5.7 Rich, F.J., and N.C. Maynard (1989), “Con-sequences of Using Simple Analytical Functionsfor the High-Latitude Convection Electric Field,” J.Geophys. Res. 94, 3697.


6.1 Dates:

1976 Beginning of NASA Dynamics Explorerprogram.

1981 Satellites launched.

1987 Model completed and published.

1989 Parameterization of the models com-pleted and published.

6.2 Authors (principal): J. P. Heppner, NASAGoddard Space Flight Center (now at HughesSTX, Lanham, MD); N. C. Maynard, NASA God-dard Space Flight Center and Phillips Laboratory(now at Mission Research Corporation, Nashua,NH); and F. J. Rich, Phillips Laboratory.

6.3 Sponsors: NASA, Phillips Laboratory, andAir Force Office of Scientific Research.


The model is written in FORTRAN and is easilyrun on a workstation. It is available from F. J.Rich, Space Physics Division (Mail Code GPSG),Phillips Laboratory, 29 Randolph Road, HanscomAFB, MA 01731 (e-mail [email protected]).


36

MILLSTONE HILL EMPIRICALELECTRIC FIELD MODEL, 1986

1. Model content

The Millstone Hill empirical electric field modelsare average patterns of ionospheric electric fieldderived from Millstone Hill incoherent scatter ra-dar observations covering all local times at sub-auroral and auroral latitudes. Over 2.5 million ra-dar measurements of plasma convection velocity,taken over the six-year interval from 1978–1984,were used in a variety of models. Bin-averagedconvection models were generated from the radardata for each of the nine levels of an empiricalhigh-latitude particle precipitation model derivedfrom NOAA/ TIROS satellite observations (Fosteret al., 1986). Data were binned, and averagedvectors calculated, each 0.5 hr of local time in 2-deg steps between 55 and 75 deg apex magneticlatitude. (Apex latitude is nearly identical to in-variant latitude at Millstone Hill’s longitude.) Av-eraged velocity vectors were determined com-pletely independently in each cell. Assuming thatthe observed plasma velocities are the result of E× B drifts in a time-stationary electric field, ananalytical potential model with 12 (14) degrees offreedom in local time (latitude) was fit to each bin-averaged velocity pattern; these are available ascoefficients of the B-spline expansion of the iono-spheric electric field in magnetic latitude–localtime coordinates. The methodology followed inconstructing these empirical models accentuatesthe close relationship between electric field andconductances at ionospheric heights. The rela-tionship, as presented in these models, was dis-cussed by Kamide and Richmond (1987) and byFoster (1987). Averaged patterns of ionosphericconductances, derived in a similar fashion fromthe NOAA/TIROS database, were presented byFuller-Rowell and Evans (1987); these were com-bined with the Millstone Hill electric field modelsto provide quantitative patterns of field-alignedcurrents by Foster et al. (1989). IMF sector de-pendence of auroral-latitude convection is repre-sented by a set of models that binned the radarvelocity observations by the 1-hr averaged valuesof IMF By and Bz components (Foster et al.,1986b). These IMF-dependent models were ex-tended to polar latitudes through the inclusion offive years of data form the Sondrestrom incoher-ent scatter radar. The Millstone Hill empiricalelectric field models are used as electric field ba-sis functions in studies of high-latitude electrody-

namics using the KRM (Richmond et al., 1988)and AMIE (Knipp et al., 1989) techniques.


The electric fields presented in these models de-scribe average conditions on Millstone Hill’s lon-gitude (285°E), and electric field patterns deter-mined here may reflect the unique Northernhemisphere relationship between solar-producedand auroral conductivities found in this sector.These are numerically averaged models and, assuch, do not contain external biases due to dataselection or interpretation. However, averagingsmoothes boundaries (spatially) and reduces theextreme values in the patterns. The effects ofindividual substorms are not represented in thesemodels, which average over such tempo-ral/spatial effects.

3. Basis of model

Assume that the observed plasma velocities arethe result of E × B drifts in a time-stationary elec-tric field.

4. Input to the model

Either the precipitation activity index or its asso-ciated value of Kp (Foster et al., 1986a) deter-mines which averaged pattern is accessed. Alter-nately, models dependent on IMF By/Bz areavailable. The analytic subroutine provided withthe model coefficients outputs field componentsor potential value at a user-specified latitude andlocal time.


5.1 Evans, D.S., T.J. Fuller-Rowell, S. Maeda,and J. Foster (1987), “Specification of the HeatInput to the Thermosphere from MagnetosphericProcesses Using TIROS/NOAA Auroral ParticleObservations,” Adv. Astronaut. Sci. 65, 1649–1668.

5.2 Foster, J.C., J.M. Holt, R.E. Musgrove, andD.S. Evans (1986a), “Ionospheric Convection As-sociated with Discrete Levels of Particle Precipi-tation,” Geophys. Res. Letters 13, 656–659.

5.3 Foster, J.C. (1987a), “Radar-Deduced Mod-els of the Convection Electric Field,” QuantitativeModeling of Magnetosphere-Ionosphere CouplingProcesses, pp. 71–76, edited by Y. Kamide,Kyoto Sangyo Univ. Publishers, Kyoto.


37

5.4 Foster, J.C. (1987b), “Reply to Kamide andRichmond,” Geophys. Res. Letters 14, 160–161.

5.5 Foster, J.C., J.M. Holt, R.G. Musgrove, andD.S. Evans (1986b), “Solar Wind Dependenciesof High-Latitude Convection and Precipitation,”Proceedings of the Chapman Conference on So-lar Wind-Magnetosphere Coupling, edited by Y.Kamide and J. Slavin, pp. 477–494.

5.6 Foster, J.C., T. Fuller-Rowell, and D.S. Ev-ans (1989), “Quantitative Patterns of Large-ScaleField-Aligned Currents in the Auroral Ionosphere,”J. Geophys. Res. 94, 2555–2564.

5.7 Fuller-Rowell, T., and D.S. Evans (1987),“Height-Integrated Hall and Pedersen Conductiv-ity Patterns Inferred from the NOAA-TIROS Sat-ellite Data,” J. Geophys. Res. 92, 7606–7618.

5.8 Maeda, S., T.J. Fuller-Rowell, D.S. Evans,and J.C. Foster (1987), “Numerical Simulations ofThermospheric Disturbances Excited by Magne-tospheric Energy Input,” Quantitative Modeling ofMagnetosphere-Ionosphere Coupling Processes,pp. 22–27,edited by Y. Kamide, Kyoto SangyoUniv. Publishers, Kyoto.

5.9 Kamide, Y., and A.D. Richmond (1987),“Comment on ‘Ionospheric Convection Associatedwith Discrete Levels of Particle Precipitation,’”Geophys. Res. Letters 14, 158–159.

5.10 Knipp, D.J., A.D. Richmond, J.C. Foster,et al., Electrodynamic Patterns for September 19,1984, J. Geophys. Res., 94, 16913-16923, 1989.

5.11 Richmond, A.D., Y. Kamide, B.H. Ahn, S.I.Akasofu, D. Alcayde, M. Blanc, O. de la Beujardi-ere, D.S. Evans, J.C. Foster, E. Friis-Chris-tensen, T.J. Fuller-Rowell, J.M. Holt, D. Knipp,

H.W. Kroehl, R.P. Lepping, R.J. Pellinen, C.Senior, and A.N. Zaitzev (1988), “Mapping Elec-trodynamic Features of the High-Latitude Iono-sphere from Localized Observations: CombinedIncoherent-Scatter Radar and MagnetometerMeasurements for 1984 January 18–19,” J. Geo-phys. Res. 93, 5760–5776.


6.1 Dates:

1986 Precipitation index/Kp models.

1986 IMF By/Bz models.

1988 Millstone/Sondrestrom merged models.

6.2 Author (principal): John Foster, AssociateDirector, MIT Haystack Observatory, Westford,MA.

6.3 Sponsor: U.S. National Science Founda-tion.

7. Model code

FORTRAN codes to generate full LT/latitude pat-terns of electrostatic potential or electric fieldcomponents or magnitude have been distributedto the community or are available from theauthors. The model has been deposited in theNCAR/CE-DAR database for research-communityuse.


38

APL HIGH-LATITUDECONVECTION MODEL

1. Model content

The Atmospheric and Ionospheric Remote Sens-ing group of the Johns Hopkins University AppliedPhysics Laboratory (APL) has developed an em-pirical model of high-latitude magnetosphericplasma convection. The principal product is thedistribution of electrostatic potential in invariantlatitude and MLT coordinates above ~50°Λ. Thecontours of constant electrostatic potential deline-ate the plasma drift trajectories. The values of theelectric field and drift velocity at any position canbe directly inferred. The model is keyed to suchindices of geomagnetic conditions as the IMF andKp.

The model can be reduced to a set of coefficientsthat describe a series expansion of the potentialin spherical harmonics. Equipped with these co-efficients and the transformation formulas givenbelow, the user can generate all convection pa-rameters.

At the current stage of development, the mostcomplete modeling has been done for the primaryIMF dependencies, namely, IMF magnitude in they-z plane (three levels) and orientation (45-degstep in IMF y-z clock angle). There is also a de-tailed solution for the IMF y-z clock angle de-pendencies under moderately disturbed condi-tions, 2<Kp<3+.


2.1 The model is statistical in nature and hencecan only approximate real-time convection, whichis known to be highly variable. For example, thetransient effects associated with substorm phasescannot be reliably imaged.

2.2 Beyond the effective latitudinal limits of ra-dar coverage (65°–85°Λ), the convection is partlysolved by applying Laplace’s condition,

∇2Φ = 0

subject to boundary conditions that include theassumption that the region below a referencelatitude Λ0 is shielded from the convection electricfield. The model can be expected to be less reli-able outside the region of direct radar observa-tions.

2.3 The radar velocity coverage becomessparse for more restricted conditions, e.g., smallsteps in IMF clock angle or Kp disturbance level.The indicial sorting intervals are selected for reli-able mapping of the large-scale convection overas large a range of indicial variation as possible.Where the statistics are insufficient, a reduction inthe quality of the results may be apparent.

2.4 The geomagnetic field model of Baker andWing (1989) was applied in the analysis. The fieldmodels in common usage can differ in latitude byseveral degrees.


3.1 The model is based on observations carriedout with the coherent-scatter HF radar located atGoose Bay, Labrador, over the period September1987–July 1993. This instrument measures the E× B drift of F-region plasma at invariant latitudesgreater than 65°Λ.

3.2 To generate the model for a set of specifiedconditions, the line-of-sight velocity data are firstsorted and averaged in 12-min UT bins. Two-dimensional vectors are generated by examiningthe variation of the line-of-sight velocity withinMLT/latitude cells with UT. The vectors are thenfitted to a polynomial expansion of the electro-static potential distribution. The mapping of thepotential is extrapolated to the high polar cap andlower latitude regions. Finally, the potential distri-bution is expressed as a series expansion inspherical harmonics.

3.3 The product of the analysis is the set of co-efficients required to solve for the electrostaticpotential via the expression

Φ(θ,φ) = AlmYlm(θ,φ )− l

l

∑l =0

∞

∑

where the spherical harmonics are defined by

Ylm (θ ,φ ) =2l +1

4π(l − m)!

(l + m)!Pl

m(cosθ)e imϕ

and the effective colatitude is given by

θ =π

(π 2 − Λ0 )(π 2 − Λ)


39

where f is the MLT clock angle in radians meas-ured from 0 MLT, Λ is the invariant latitude in ra-dians, and Λ0 is a reference latitude in radiansthat is output by the model. The electric field andconvection velocity can be solved from the rela-tions

E = −∇Φ and v = ExB( ) / B2

3.4 The derivation of the model and the relatedanalysis were described by Ruohoniemi andGreenwald (1995, 1996).

4. Database

The primary measurements of convection velocitywere made with the Goose Bay HF radar. Thisinstrument is located at 299.5°E longitude and53.3°N latitude. It operates around the clock andcompletes an azimuthal scan of the F-regionionosphere north of the site every 2 min. TheGoose Bay radar is part of a network of HF radarsthat have recently been installed at high latitudesas part of the SuperDARN initiative (Greenwald etal., 1995). The IMF data were culled from the re-cords of the IMP8 spacecraft provided by severalsources of geophysical data.


5.1 Baker, K.B., and S. Wing (1989), “A NewMagnetic Coordinate System for ConjugateStudies of High Latitudes,” J. Geophys. Res. 94,9139–9143.

5.2 Greenwald, R.A., et al. (1995), “DARN/Su-perDARN: A Global View of High-Latitude Con-vection,” Space Sci. Rev. 71, 763–796.

5.3 Ruohoniemi, J.M., and R.A. Greenwald(1995), “Observations of IMF and Seasonal Ef-fects in High-Latitude Convection,” Geophys.Res. Letters 9, 1121–1124.

5.4 Ruohoniemi, J.M., and R.A. Greenwald(1996), “Statistical Patterns of High Latitude Con-vection Obtained from Goose Bay HF Radar Ob-servations,” J. Geophys. Res. 101, 21,743–21,763.


6.1 Date: 1995 Development of code to re-duce archival Goose Bay HF radar velocity datato maps of high-latitude convection.

6.2 Authors: J. Michael Ruohoniemi and Ray-mond A. Greenwald.

6.3 Sponsor: The National Science Founda-tion.


The model, or portions thereof, can be readilyacquired either in the form of global maps of theelectrostatic potential or as sets of coefficientsthat describe expansions of the potential patternsin terms of spherical harmonics. A small packageof IDL routines allows easy access to the outputsof the model in graphical or digital form. The in-ventory of currently available solutions was de-scribed in Sec. 1. Interested persons should con-tact the authors at [email protected] ray_ [email protected].


40

HWM EMPIRICAL WIND MODEL

1. Model content

The HWM (Horizontal Wind Model) provides anestimate of the climatological average meridionaland zonal components of the atmospheric windvector as a function of altitude, latitude, longitude,day of year, time of day, and solar and magneticactivity. Solar and magnetic activity variations areonly included for the thermosphere. Solar diurnaland semidiurnal tides are included in the strato-sphere and above, and annual and semiannualvariations at all altitudes. Longitude and UTvariations related to magnetic field control of en-ergy input and drag forces are included in thethermosphere and stationary wave longitudevariations in the lower atmosphere (7–90 km).


Solar activity variations are weak and not veryclearly delineated by the data. Because of thesparsity of data between 130 and 220 km andconcern with providing reasonable continuitythrough this region, a simplifying assumption ofproportionality to exospheric winds was intro-duced in this region. Rapid changes in winds athigh latitudes resulting from magnetic control arelikely underestimated by the small number ofharmonics used. Quasi-biennial variations in thelower atmosphere are not included. Longitudevariations in the lower atmosphere were only rep-resented by the nondivergent vector field and hadto be dependent on gradient wind derivations.Meridional winds are assumed to be zero below45 km. There appear to be unresolved discrepan-cies between measurement techniques in themeso-pause region, which are a difficulty formodel generation at these altitudes.

Overall root mean square differences betweendata and model values are on the order of 100–150 m/sec in the high-latitude thermosphere and50 m/sec or less at mid to low latitudes. Rootmean square differences are 15 m/sec in themesosphere and10 m/sec in the stratosphere forzonal winds, and 10 and 5 m/sec, respectively, formeridional winds.


The model represents spatial variations in thewind vector by an expansion in vector sphericalharmonics, with each expansion coefficient repre-sented by a Fourier series in universal timeand/or day of year as appropriate, and with sim-

plified supplemental equations for solar activityand magnetic activity variations. The expansioninvolves two orthogonal vector fields, the diver-gence B field and the rotational C field. Above200 km, the altitude variations of the wind com-ponents are each represented by an analog of theBates formula as used for thermospheric tem-perature profiles. Below 200 km, the wind profilesare represented by a cubic spline between speci-fied nodes, with first and second derivatives con-tinuous across interior nodes. The variation of thewind at each node is represented by an inde-pendent spherical harmonic/Fourier expansion.

4. Database and input to the model

The primary data incorporated in the model de-pend upon altitude. For the thermosphere (Hedinet al., 1991a), these are satellite mass spec-trometer (WATS on DE-2 and NATE on AE-E)and Fabry-Perot (FPI on DE-2) instruments,ground-based incoherent scatter radar, andground-based Fabry-Perot optical instrumenta-tion. In the esosphere/lower thermosphere (Hedinet al., 1996), data are included from a wide rangeof MF radar and meteor radar stations, rocket-sondes, rocket grenade soundings, gradient windsfrom MSISE-90 (Hedin et al., 1991b), CIRA-86,and earlier data tabulations. In the stratosphere,the data include rocketsondes and rocket grenadesoundings, CIRA-86, and some earlier data tabu-lations. In the troposphere, the model is essen-tially a recasting of CIRA-86. The influence ofgradient wind estimates was minimized in favor ofdirect wind measurements whenever possible. Inaddition to position and time coordinates, themodel (in the thermosphere) requires a three-month average and previous day value of the10.7-cm solar flux index (at the earth) and eitherthe daily Ap magnetic index or a prescribed his-tory of 3-hr Ap indices.


5.1 Hedin, A.E., N.W. Spencer, and T.L. Killeen(1988), “Empirical Global Model of Upper Ther-mosphere Winds Based on Atmosphere and Dy-namics Explorer Satellite Data,” J. Geophys. Res.93, 9959–9989.

5.2 Hedin, A.E., et al. (1991a), “Revised GlobalModel of Thermosphere Winds Using Satelliteand Ground-Based Observations,” J. Geophys.Res. 96, 7657–7688.


41

5.3 Hedin, A.E. , et al. (1991b), “Extension ofthe MSIS Thermosphere Model into the Middleand Lower Atmosphere,” J. Geophys. Res. 96,1159–1172.

5.4 Hedin A.E., et al. (1996), “Empirical WindModel for the Upper, Middle and Lower Atmos-phere,” J. Atmos. Terr. Phys. 58, 1421–1447.


6.1 Dates:

1988 HWM87 satellite-based thermosphere on-ly model.

1991 HWM90 satellite- and ground-based ther-mosphere model.

1996 HWM93 extension to lower atmosphere(no change in thermosphere).

6.2 Author (principal): Alan E. Hedin.

6.3 Sponsor: NASA.


FORTRAN subroutines are available from theNational Space Science Data Center RequestCoordinator Office, NSSDC, Code 633, NASAGoddard Space Flight Center, Greenbelt, MD20771, tel. 301/286-6695 (e-mail [email protected]. nasa.gov;http://nssdc.gsfc.nasa.gov).


42

GLOBAL EMPIRICAL MODELSOF Te

1. Model content

Satellite Langmuir probe measurements havebeen used extensively to devise global empiricalmodels of F-region Te, and sometimes Ne. Theuse of in situ measurements for this purpose of-fers many challenges, however, since orbitallimitations and the limited duration of the data-bases make it difficult to separate spatial andtemporal variations (altitude, latitude, local time,season, solar cycle, geomagnetic activity).Therefore, it is usually necessary to devise mod-els that describe limited aspects of ionospherestructure at specific times, such as the latitudinaland local time structure at a fixed altitude, or thelatitudinal structure at fixed local times and atspecific seasons. It is particularly difficult to re-solve the solar cycle variations, because satellitelifetimes are usually much shorter than a solarcycle, or even half of a cycle. One can sometimescombine two or three satellite databases to iden-tify the solar cycle effects, but differences in theinclinations and altitudes of the orbits can makethe task more difficult. The following describesseveral attempts to devise such models usingLangmuir probe measurements from the Atmos-phere Explorer (AE-C), ISIS-1, ISIS-2, and Dy-namic Explorer (DE-2) satellites.

2. Global models for fixed altitudes

Brace and Theis (1981) employed measurementsfrom Atmosphere Explorer-C, ISIS-1, and ISIS-2to define the coefficients of global models thatdescribed the variations of Te at several fixed al-titudes (300, 400, 1400, and 2000 km) as a func-tion of dip latitude and local time. CorrespondingNe models were not attempted because the muchlarger altitude and solar cycle variations of Ne

tended to hide or distort the geographical varia-tions. The circular orbit phase of AE-C provideddata at altitudes of 300 and 400 km at solarminimum (1975–77), which became the basis forglobal Te models for these altitudes. ISIS-2 pro-vided measurements from a circular, near-polarorbit at 1400 km at low to moderate levels of solaractivity in 1971–72. The Te data were used to de-fine the coefficients of a spherical harmonicmodel of Te that described the latitude and localtime variations at that altitude. The Langmuirprobes on ISIS-1 provided data over a range ofaltitudes between 600 and 3600 km during therelatively weak solar maximum of 1969–70. The

Te data obtained between 2000 and 3600 kmwere averaged to define the latitude and localtime variations at 3000 km.

3. Inverse relationship between Ne and Te inthe F region

During the elliptical orbit phase of the AE-C mis-sion (1973–74), when the perigee was beingmaintained deep in the lower thermosphere, Ne

and Te were measured frequently down to about130 km. Brace and Theis (1978) employed thesedata to investigate the relationship between Ne

and Te in the daytime ionosphere. (Actually, inthat mission, the total ion density Ni was meas-ured rather than Ne.) As expected, Ne and Te werefound to be inversely related, probably becausethe electron-ion cooling rate varies as the productof Ni and Ne, or Ne

2. This is the dominant processthat determines Te at altitudes near the F2 peak,whereas electron-neutral cooling becomes moreimportant in the lower F region and E region.Since the elliptical phase of the mission lastedonly through 1974 (low solar activity), the effect ofthe solar cycle on the inverse relationship be-tween Ne and Te could only be determined fromlater measurements in the circular orbit phase(1975–78) when the orbit was maintained be-tween 250 and 400 km.

The above study of the inverse behavior of Ne

and Te applied only to the daytime ionosphere atlatitudes below 50 deg. Higher latitudes wereavoided to eliminate high-latitude electron heatsources. In general, Ne and Te do not exhibit thisinverse behavior in regions where there is noelectron heat source (such as in the middle- andlow-latitude nighttime ionosphere), since Te and Ti

cool to the gas temperature when the heat sourceis removed. For example, the nightside does ex-hibit inverse variations in Ne and Te at geomag-netic latitudes between 40 and 60 deg. The elec-tron heating is understood to be caused by heatconduction from the overlying plasmasphere, thetime constant for cooling of which is longer thanone night. The plasmasphere is also heated bycollisions with magnetospheric ring current ions,and this heat causes an elevation of Te at theselatitudes, whereas the behavior of Ne is controlledby plasma and neutral gas transport processes.

4. Solar cycle effects on the relationshipbetween Ne and Te

The AE-C mission (altitudes between 300–400km) extended well into the period of rising solar


43

activity in 1977 and 1978, thus permitting the so-lar cycle variations of the F region to be investi-gated. Brace and Theis (1984) found little re-sponse of Te to the rising solar activity, althoughNe increased significantly. Apparently, increasedeffect of electron heating with increasing solaractivity was canceled by increased electron-ionand electron-neutral cooling that goes along withincreased ion and neutral gas densities.

The DE-2 Langmuir probe measurements allowedthe above AE-C study to be extended through thefollowing solar maximum (1981–83). Brace andTheis (1984) combined the AE-C and DE-2 datato study the effect of solar activity on the relation-ship between Ne and Te. Their equation gives theratio Te/Te model as a function of F10.7, where Te

represents individual measured values, and Te

model refers to the Brace and Theis (1978) solarminimum model discussed above. At solar maxi-mum, Te/Te model is enhanced by nearly a factor of2 relative to solar minimum values, although Te

itself did not change much during the solar cyclewhile Ne increased.

5. Te and Ne models at solar maximum

The DE-2 satellite also provided global Langmuirprobe measurements at solar maximum (1981–83). Brace and Theis (1990) used these data todevise an empirical model of the global variation(geomagnetic latitude and local time) of Ne and Te

at 400 km. Legendre polynomials through the fifthorder were retained. Their comparisons of theDE-2 and AE-C models with the IRI modelshowed that the two exhibited similar solar cyclevariations. They confirm the fact that Te does notvary greatly with solar activity, but the Ne variesby nearly an order of magnitude from solar mini-mum to solar maximum.

6. Models of the latitude variation of Ne andTe at fixed altitudes

An important limitation of the global models(Brace and Theis, 1990) is that the nature of theselected orbit provided insufficient coverage of allthe important spatial and temporal variations ofthe ionosphere. This means that many aspects of

the latitudinal and local time structure could notbe captured with high resolution; thus the 1990global model was limited to fifth-order polynomial.Brace and Theis (1991) attempted to improve thelatitudinal resolution by employing subsets of theDE-2 measurements that suppressed the localtime, latitude, and seasonal variations. This al-lowed them to define a seventeenth-order poly-nomial model of the latitudinal variation of Ne andTe at fixed altitudes and fixed local times thatwere allowed by the orbit. This was achieved bylimiting the database to narrow altitude slices andsingle sweeps of perigee from pole to pole. Com-parisons of the resulting high-resolution modelswith the corresponding Te and Ne measurementsthemselves showed that most of the latitudinalstructure that had previously been washed out inthe fifth-order global models (Brace and Theis,1990) was captured by the higher-order models.


7.1 Brace, L.H., and R.F. Theis (1981), “GlobalEmpirical Models of Ionospheric Electron Tem-perature in the Upper F-Region and Plasma-sphere Based on In Situ Measurements from theAtmosphere Explorer-C, ISIS-2 Satellites,” J. At-mos. Terr. Phys. 43, 1317–1343.

7.2 Brace, L.H. and R.F. Theis (1978), “An Em-pirical Model of the Interrelationship of ElectronTemperature and Density in the Daytime Ther-mosphere at Solar Minimum,” Geophys. Res.Letters 5, 275–278.

7.3 Brace, L.H. and R.F. Theis (1984), “SolarCycle Effects upon the Relationship of Ne and Te

in the F-Region,” Adv. Space Res. 4 (1), 89–91.

7.4 Brace, L.H. and R.F. Theis (1990), “GlobalModels of Ne and Te at Solar Maximum Based onDE-2 Measurements,” Adv. Space Res. 10 (11),39–45.

7.5 Brace, L.H. and R.F. Theis (1991), “Empiri-cal Models of the Latitudinal Variations of Te andNe in the Ionosphere at Solar Maximum,” Adv.Space Res. 11 (10), 159–166.


44

EMPIRICAL MODEL OF THEIONOSPHERIC ELECTRON AND IONTEMPERATURES

1. Model content

The empirical model provides electron tempera-tures Te [K] and ion temperatures Ti [K] as afunction of

Altitude: 50–4000 km

Attitude: dipole latitude, N2, O2, O, NO

Time: day count d (annual variation),magnetic local time τ

Solar activity: solar flux F10.7 for quiet geo-physical conditions (Kp ≤ 3)

The electron and ion temperatures are obtainedfrom the appropriate figures of Köhnlein (1986) atF10.7 = 84 × 10-22 Wm-2 H ∪-1 and Kp ≤ 3:

Average temperature (time-independent):see Köhnlein (1986, Figs. 4 and 5),

Te,i vs altitude

Time-independent temperature (latitudinal):see Köhnlein (1986, Figs. 6–11),

Te,i vs altitude at φ = 90°, 45°, 0°, -90°

Te,i vs dipole latitude at discrete heights

Annual variation:see Köhnlein (1986, Figs. 12– 17),

Te,i vs altitude at equinox and solstice condi-tions (d=80, 173, 266, 356)

Comparison with data: Te,i vs day count atdiscrete heights

∆ Te,i (relative): dipole latitude vs day countat discrete heights

Diurnal variation:see Köhnlein (1986, Figs. 18– 25),

Te,i vs altitude at φ = 0°, 45° andτ = 0h, 6h,12h, 18h

Comparison with data: Te,i vs magnetic localtime at discrete heights and φ = 0°, 45°

∆ Te,i(relative): dipole latitude vs magneticlocal time at discrete heights

and superpositions thereof, i.e.,

Diurnal variation + relative annual variation⇒

diurnal variation at a selected day of theyear

Annual variation + relative diurnal variation⇒

annual diurnal variation at a selectedmagnetic local time


The discrepancies between the model and theobservations (used) are shown for the annual anddiurnal variations in Köhnlein (1986, Figs. 13, 16,20, 21, 23, 24). In general, the model agrees wellwith the observations.

The uncertainties of the model are mainly due tothe uneven data coverage and the simplicity ofthe analytical approach (e.g., linearity, no longitu-dinal terms, no disturbed conditions).

Data from epochs not used in the database mayshow stronger deviations toward the model. Thisis especially true for disturbed geophysical condi-tions that are not considered in the model.


The vertical and horizontal structures of themodel are treated on an equal footing.

The electron and ion temperatures are expandedinto spherical harmonics (Köhnlein, 1986, Eqs. 1–12) wherein the model coefficients depend onaltitude, solar flux F10.7, and geomagnetic indexKp.

Restricting the model to quiet geophysical condi-tions (Kp ≤ 3), the above coefficients depend line-arly on F10.7, whereas their height variations areexpressed by cubic spline functions.

4. Database

The database of the model consists of observa-tions by satellites, incoherent scatter stations, androcket profiles covering the time interval 1964–1979 (Köhnlein, 1986, Table1; Brace and Theis,1981).


5.1 Brace, L.H., and Theis, R.F. (1981), “GlobalEmpirical Model of Ionospheric Electron Tem-perature in the Upper F-Region and Plas-masphere Based on In Situ Measurements fromthe Atmospheric Explorer-C, ISIS-1, and ISIS-2Satellites,” J. Atmos. Terr. Phys. 43, 1317.


45

5.2 Köhnlein, W. (1986), “A Model of the Elec-tron and Ion Temperatures in the Ionosphere,”Planetary Space Sci. 34 (7), 609–630.


6.1 Date: 1983.

6.2 Author: W. Köhnlein.

6.3 Sponsors: Deutsche Forschungsgemein-schaft and University of Bonn.


The model was developed in FORTRAN code,specifically adapted to a CDC-computer. Becauseof the detailed graphical representation, Köhnlein(1986) can be used as a quick reference for iono-spheric temperatures (Te, Ti) at low solar fluxes(F10.7 ≈ 84) and quiet geophysical conditions(Kp ≤ 3) in the altitude interval 50–4000 km.


46

PHOTOCHEMICAL EQUILIBRIUMMODEL FOR IONOSPHERICCONDUCTIVITY

1. Model content

The photochemical equilibrium model of the high-latitude ionosphere calculates density profiles forfour ions (N2

+, O2+, NO+, and O+) and electrons

over the altitude range from 85 to ~220 km. Thedensities are then used to calculate Pedersen andHall conductivities. The model takes account ofphotoionization, impact ionization due to ener-getic electron precipitation, and ionization due toresonantly scattered solar radiation, starlight, andrecombination radiation. The model outputs theion and electron density profiles, altitude profilesfor the Hall and Pedersen conductivities, andheight-integrated conductivities.


The model is based on the assumption of chemi-cal equilibrium and, therefore, is valid only at thealtitudes where transport processes are negligible.The model results are also sensitive to certaininputs, including the auroral electron energy fluxand characteristic energy, and the adopted ionand electron temperatures.


3.1 The model is based on a numerical solutionof the coupled continuity equations for the ionsNO+, O2

+, N2+, and O+, assuming chemical equi-

librium conditions prevail. The coupled nonlinearequations are solved with an iterative procedureat the specified altitudes and times.

3.2 The momentum equations are solved toobtain expressions for the Hall and Pedersenconductivities assuming steady-state conditionsand neglecting spatial gradients. In calculating theappropriate collision frequencies, account is takenof ion collisions with the neutrals N2, O2, O, N,and NO.

3.3 The height-integrated conductivities areobtained by using a trapezoidal rule to integrate inheight.


The model requires the electron energy flux andcharacteristic energy of the auroral precipitation,the neutral densities and temperature, and the ionand electron temperatures. These inputs are de-scribed by empirical models if they are not speci-fied.


5.1 C.E. Rasmussen, R.W. Schunk, and V.B.Wickwa (1988), “A Photochemical EquilibriumModel for Ionospheric Conductivity,” J. Geophys.Res. 93, 9831–9840.


6.1 Date: 1988 Developed this year, but noimprovements since then.


The model is in the form of a Fortran code, and itcan be obtained from the lead author of the refer-enced publication.


47

EMPIRICAL MODEL OFCONDUCTIVITIES

1. Model content

The global patterns of the integral energy flux andaverage energy of precipitating auroral electronsare used to determine height-integrated Hall andPedersen conductivities as a function of correctedgeomagnetic latitude (CGL) and magnetic localtime (MLT) for a range of magnetospheric condi-tions parameterized by either Kp or by IMF Bzand Vsw (see “Auroral Electron and Ion Fluxes”on page 49 of this report).


2.1 The individual statistical maps were con-structed from anywhere between 0.2 and 3.8 mil-lion spectra (depending on the magnetosphericactivity sort parameter), which were binned andaveraged into a spatial grid (CGL × MLT). By theirvery nature, statistical maps obscure the short-lived, small-scale-length precipitation features(Redus et al., 1988). Thus, these models are notexpected to track the ionospheric conductivities(as determined by electron precipitation) through-out individual (sub)storms with high precision, butthey do provide a reasonable measure of thegross variations in an average sense. Whetherthe Bz-Vsw maps resolve the short-lived, small-scale-length features more successfully than dothe Kp maps has never been investigated, al-though they are expected to because the sort pa-rameters are more directly tied to solar wind-magnetospheric coupling (hence electron pre-cipitation), and the parameter space has a finergrid (30 Bz-Vsw maps vs 7 Kp maps).

2.2 The steep gradient (with respect to CGL) inconductivity at the time-dependent equatorwardand poleward auroral boundary introduces an in-trinsic difficulty in predicting conductivities alonga specified orbit trajectory in proximity to suchboundaries (as is the case for auroral precipitationflux). An uncertainty of 2–4 deg in magnetic lati-tude in the boundary location can mean up to afactor of 2 difference in conductivity, dependingon whether the trajectory is cutting through theoval or just skimming it.


3.1 This model is based on a compilation ofstatistical hemispherical maps of auroral electronprecipitation derived from measurements madeby Air Force particle detectors flown primarily on

the DMSP (and, to a lesser extent, P78-1) satel-lites under a wide range of magnetospheric con-ditions.

3.2 These statistical maps were created fromelectron flux databases, which were separatedaccording to the magnetic activity index Kp(Hardy et al., 1985) and according to the z com-ponent of the interplanetary magnetic field (Bz)and the solar wind speed (Vsw) (Brautigam et al.,1991). For the Kp models, the separation resultedin seven intervals of Kp: Kp = 0, 0+, Kp = 1-, 1,1+, etc., up to Kp = 5-, 5, 5+, and for Kp ≥ 6-. Forthe Bz-Vsw models, each map was defined by adiscrete point in the parameter space defined byordered pairs of Bz = (-4.5, -2.2, -0.7, 0.7, 2.2, 4.5nT) and Vsw = (346, 408, 485, 572, and 677km/sec).

3.3 The various maps were all created using thesame spatial grid defined by CGL and MLT. Thehigh-latitude region was separated into 30 zonesin CGL between 50 and 90 deg and 48 0.5-hrzones in MLT. The zones in latitude are 2 degwide between 50 and 60 deg and between 80 and90 deg; they are 1 deg wide between 60 and 80deg latitude. Although the nominal altitude of theDMSP satellites is 840 km, particle fluxes aremapped down the magnetic field lines to 110 km(base of the ionospheric E layer) before con-structing the statistical maps.

3.4 In each spatial element, and at each level ofactivity, the average flux value in each of the en-ergy channels was determined. The resulting av-erage spectra were extrapolated to 100 keV. Thefinal spectra were integrated over energy (from0.5 to 100 keV) to determine the average integralnumber flux and the average integral energy fluxof the precipitating electrons in each spatial ele-ment. The average energy was calculated by di-viding the integral energy flux by the integralnumber flux. The Hall and Pedersen conductivi-ties were then determined from the average en-ergy and energy flux.

3.5 Finally, the conductivities were fit to Epsteinfunctions, with the function coefficients publishedas a representation of the statistical maps: (1) Kpmodels (Hardy et al., 1987); and (2) Bz-Vswmodels (McNeil and Brautigam, 1998).


There is a version of the conductivity models thatis driven by the magnetic activity index Kp, andone that is driven by a pair of parameters: the z


48

component of the interplanetary magnetic field(Bz) and solar wind speed (Vsw). One source forthese parameters is the World Wide Web sitehttp://nssdc.gsfc.nasa.gov/omniweb.


5.1 Brautigam, D.H., M.S. Gussenhoven, andD.A. Hardy (1991), “A Statistical Study on theEffects of IMF Bz and Solar Wind Speed on Auro-ral Ion and Electron Precipitation,” J. Geophys.Res. 96, 5525.

5.2 Hardy, D.A., M.S. Gussenhoven, R. Rais-trick, and W.J. McNeil (1987), “Statistical andFunctional Representations of the Pattern ofAuroral Energy Flux, Number Flux, and Conduc-tivity,” J. Geophys. Res. 92, 12,275.

5.3 Hardy, D.A., M.S. Gussenhoven, and E.Holeman (1985), “A Statistical Model of AuroralElectron Precipitation,” J. Geophys. Res. 90,4229.

5.4 Redus, R.H., M.S. Gussenhoven, D.A.Hardy, and D.H. Brautigam (1988), “Deviationsfrom the Average Patterns of Auroral Ion Pre-cipitation,” Physics of Space Plasmas (1987),Vol.7, edited by T. Chang, G.B. Crew, and J.R.Jasperse, Scientific Publishers, Inc.


6.1 Dates: 1985–1991 Development of con-ductivity models.

6.2 Authors: D.H. Brautigam, M.S. Gussen-hoven, D.A. Hardy, E. Holeman, W.J. McNeil, R.Raistrick, and R.H. Redus.

6.3 Sponsor: Air Force Research Laboratory/VSBS.


The model code for Hall and Pedersen conduc-tivities is identical to that described in the “AuroralElectron and Ion Fluxes” model.

7.1 The simplest package of models is a set ofFORTRAN subroutines for each species (elec-tron; ion) and for each parameterized model (Kp;Bz and Vsw) which contain the Epstein coeffi-cients for the functional forms of the variouscomputed quantities (integral number flux, inte-gral energy flux, average energy, and conductivi-ties). These subroutines return a specified aver-age quantity for a given model parameter andmagnetic coordinates (CGL, MLT). They areavailable on PC diskettes. Contact D.H. Brauti-gam, AFRL/VSBS, 29 Randolph Road, HanscomAFB, MA 10731 (e-mail [email protected]).

7.2 These subroutines (7.1) are embeddedwithin AF-Geospace, where they may be run inconjunction with a number of other options via aninteractively driven graphical interface. AF-Geospace currently runs on UNIX-based SiliconGraphics workstations but is being ported to aDec-Alpha workstation and will eventually run onMicrosoft NT workstations. Contact G.P. Ginet,AFRL/VSBS, 29 Randolph Road, Hanscom AFB,MA 10731 (e-mail [email protected]).


49

AURORAL ELECTRON AND IONFLUXES

1. Model content

Auroral particle (electron and ion) integral numberflux, integral energy flux, and average energy arespecified as a function of corrected geomagneticlatitude (CGL) and magnetic local time (MLT) fora range of magnetospheric conditions param-eterized by either Kp or by IMF Bz and Vsw. Fromthese statistical auroral flux maps, the numberand energy flux precipitating over the entire auro-ral oval can be estimated for periods spanningweak to strong magnetic activity.


2.1 The individual statistical maps were con-structed from anywhere between 0.2 and 3.8 mil-lion spectra (depending on the magnetosphericactivity sort parameter), which were binned andaveraged into a spatial grid (CGL × MLT). By theirvery nature, statistical maps obscure the short-lived, small-scale-length features (Redus et al.,1988). Thus, these models are not expected totrack the auroral particle precipitation throughoutindividual (sub)storms with high precision, butthey do provide a reasonable measure of thegross variations in the auroral oval in an averagesense. Whether the Bz-Vsw maps resolve theshort-lived, small-scale-length features more suc-cessfully than do the Kp maps has never beeninvestigated, although they are expected to be-cause the sort parameters are more directly tiedto solar wind-magnetospheric coupling, and theparameter space has a finer grid (30 Bz-Vswmaps vs 7 Kp maps).

2.2 The steep gradient (with respect to CGL) inauroral precipitation flux at the time-dependentequatorward and poleward auroral boundary in-troduces an intrinsic difficulty in predicting fluxesalong a specified orbit trajectory in proximity tosuch boundaries. Even though the hemisphericnumber and energy flux inputs may be well mod-eled, an uncertainty of 2–4 deg in magnetic lati-tude in the boundary location can mean up to anorder of magnitude difference in local flux, de-pending on whether the trajectory is cuttingthrough the oval or just skimming it.


3.1 This model is based on a compilation ofstatistical hemispherical maps of auroral ion andelectron precipitation derived from measurements

made by Air Force particle detectors flown pri-marily on the DMSP (and, to a lesser extent, P78-1) satellites under a wide range of magneto-spheric conditions.

3.2 These statistical maps were created fromparticle flux databases, which were separatedaccording to the magnetic activity index Kp forboth electrons (Hardy et al., 1985) and ions(Hardy et al., 1989) and according to the z com-ponent of the interplanetary magnetic field (Bz)and the solar wind speed (Vsw) for both electronsand ions([Brautigam et al., 1991). For the Kpmodels, the separation resulted in seven intervalsof Kp: Kp = 0, 0+, Kp = 1-, 1, 1+, etc., up to Kp =5-, 5, 5+, and for Kp ≥ 6-. For the Bz-Vsw models,each map was defined by a discrete point in theparameter space defined by ordered pairs of Bz =(-4.5, -2.2, -0.7, 0.7, 2.2, 4.5 nT) and Vsw = (346,408, 485, 572, and 677 km/sec).

3.3 The various maps were all created using thesame spatial grid defined by CGL and MLT. Thehigh-latitude region was separated into 30 zonesin CGL between 50 and 90 deg and 48 0.5-hrzones in MLT. The zones in latitude are 2 degwide between 50 and 60 deg and between 80 and90 deg; they are 1 deg wide between 60 and 80deg latitude. Although the nominal altitude of theDMSP satellites is 840 km, particle fluxes aremapped down the magnetic field lines to 110 km(base of the ionospheric E layer) before con-structing the statistical maps.

3.4 In each spatial element and at each level ofactivity, the average flux value in each of the en-ergy channels was determined. The resulting av-erage spectra were extrapolated to 100 keV. Thefinal spectra were integrated over energy to de-termine the average integral number flux and theaverage integral energy flux of the precipitatingelectrons and ions in each spatial element. Theaverage energy was calculated by dividing theintegral energy flux by the integral number flux.

3.5 Finally, these average quantities were fit toEpstein functions, with the tables of function co-efficients published as a representation of thestatistical maps. These quantities and the refer-ences defining their representations are as fol-lows: (1) Kp models (electrons): integral numberand energy flux (Hardy et al., 1987); (2) Kp mod-els (ions): average energy (McNeil and Brauti-gam, 1998), integral number, and energy flux(Hardy et al., 1987); and (3) Bz-Vsw models(electrons and ions): average energy, integral


50

number, and energy flux (McNeil and Brautigam,1998).


There is a version of the auroral model that isdriven by the magnetic activity index Kp, and onethat is driven by a pair of parameters: the IMF Bzand solar wind speed Vsw. One source for theseparameters is the World Wide Web sitehttp://nssdc.gsfc.nasa.gov/omniweb.


5.1 Brautigam, D.H., M.S. Gussenhoven, andD.A. Hardy (1991), “A Statistical Study on theEffects of IMF Bz and Solar Wind Speed on Auro-ral Ion and Electron Precipitation,” J. Geophys.Res. 96, 5525.

5.2 Hardy, D.A., W.J. McNeil, M. S. Gussenho-ven, and D. Brautigam (1991), “A StatisticalModel of Auroral Ion Precipitation: 2. FunctionalRepresentation of the Average Patterns,” J. Geo-phys. Res. 96, 5539.

5.3 Hardy, D.A., M.S. Gussenhoven, and D.Brautigam (1989), “A Statistical Model of AuroralIon Precipitation,” J. Geophys. Res. 94, 370.

5.4 Hardy, D.A., M.S. Gussenhoven, R. Rais-trick, and W. J. McNeil (1987), “Statistical andFunctional Representations of the Pattern ofAuroral Energy Flux, Number Flux, and Conduc-tivity,” J. Geophys. Res. 92, 12,275.

5.5 Hardy, D.A., M.S. Gussenhoven, and E.Holeman (1985), “A Statistical Model of AuroralElectron Precipitation,” J. Geophys. Res. 90,4229.

5.6 McNeil, W.J., and D.H. Brautigam (1998),AFRL Technical Report (to be published).

5.7 Redus, R.H., M.S. Gussenhoven, D.A.Hardy, and D.H. Brautigam (1988), “Deviations

from the Average Patterns of Auroral Ion Pre-cipitation,” Physics of Space Plasmas (1987),Vol.7, edited by T. Chang, G.B. Crew, and J.R.Jasperse, Scientific Publishers, Inc.


6.1 Dates: 1985–1998 Development ofauroral models.

6.2 Authors: D.H. Brautigam, M.S. Gussen-hoven, D.A. Hardy, E. Holeman, W.J. McNeil, R.Raistrick, and R.H. Redus.

6.3 Sponsor: Air Force Research Laboratory/VSBS.


7.1 The simplest package of models is a set ofFORTRAN subroutines for each species (elec-tron; ion) and for each parameterized model (Kp;Bz and Vsw) which contain the Epstein coeffi-cients for the functional forms of the variouscomputed quantities (integral number flux, inte-gral energy flux, average energy, and conductivi-ties). These subroutines will return a specifiedaverage quantity for a given model parameterand magnetic coordinates (CGL, MLT). They areavailable on PC diskettes. Contact D.H. Brauti-gam, AFRL/VSBS, 29 Randolph Road, HanscomAFB, MA 10731 (e-mail [email protected]).

7.2 These subroutines (7.1) are embeddedwithin AF-Geospace, where they may be run inconjunction with a number of other options via aninteractively driven graphical interface. AF-Geospace currently runs on UNIX-based SiliconGraphics workstations but is being ported to aDec-Alpha workstation and will eventually run onMicrosoft NT workstations. Contact G.P. Ginet,AFRL/VSBS, 29 Randolph Road, Hanscom AFB,MA 10731 (e-mail [email protected]).


51

WBMOD IONOSPHERICSCINTILLATION MODEL (NWRA), 1995

1. Model content

NorthWest Research Associates (NWRA) hasdeveloped an empirical model of the irregularitiesin F-layer plasma density which produce radio-wave scintillation. Based mainly on direct meas-urement of intensity and phase scintillation, pri-marily from the Defense Nuclear Agency (DNA)Wide-Band Satellite Experiment, the scintillationmodel is incorporated in a computer programcalled WBMOD. Development of the model ini-tially (Fremouw and Lansinger, 1981; Fremouwand Secan, 1984) was sponsored by DNA. Be-cause of Wide-Band's sun-synchronous orbit anda limited number of observing sites, the early ver-sion of WBMOD did not fully reproduce the ob-served temporal and spatial variations of scintilla-tion (Basu et al., 1988). Recently, the model wasupgraded by ingesting high-latitude scintillationdata from DNA's Hilat and Polar BEAR satellitesand the time-continuous equatorial scintillationdatabase of the Geophysics Directorate of PhillipsLaboratory (PL/GD). These model upgrades (Se-can and Bussey, 1994; Secan et al, 1995) havebeen executed by NWRA and were sponsored byPL/GD with the support of HQ Air Weather Serv-ice. In addition to scintillation observations,WBMOD incorporates a modified version of thephase-screen propagation theory of Rino (1979).For two-way propagation, the theory is aug-mented by the work of Fremouw and Ishimaru(1992). The irregularity model contains statisticaldescriptions of their anisotropy in geomagneticcoordinates and their spatial power spectrum, thelatter characterized by means of an outer scale, apower-law spectral index, and the height-integrated power spectral density (psd), CkL, at across-field scale size of 1 km/cycle. The occur-rence statistics of the most variable of these pa-rameters, CkL, are modeled by means of a prob-ability density function (pdf), the relevant mo-ments of which are expressed as functions ofgeomagnetic latitude, longitude, local time of day,season, solar-cycle epoch, and planetary geo-magnetic activity index. The irregularities aretaken to drift with the background F layer. For anoperating scenario (location, time, operating fre-quency, etc.) specified by the user, WBMOD out-puts signal-statistical parameters that quantifyphase and intensity scintillation. The phase spec-trum is characterized by its power-law spectralindex p and its psd T at a fluctuation frequency of1 Hz. The rms phase fluctuation σφ for a time in-

terval specified by the user is computed as thesquare root of the integral of the spectrum. Inten-sity scintillation is quantified by the normalized(by the mean) standard deviation S4 of power,which also is converted to a dB scintillation index.


2.1 The observations on which WBMOD isbased were carried out at VHF, UHF, and Lbands. The propagation theory that it incorporatesis valid down to about 100 MHz (somewhat less athigh elevation angles) and improves with in-creasing frequency.

2.2 The irregularities are characterized by asingle-regime power-law spatial spectrum, al-though spectra with at least two power-law re-gimes are known to exist at both auroral andequatorial latitudes.

2.3 The high-latitude portion of the model hasbeen well tested only at auroral latitudes, and de-ficiencies are likely in the polar cap. At aurorallatitudes, testing has been without benefit of datafrom the Russian sector.

2.4 The model's description of the coupled sea-sonal and longitudinal dependence of equatorialscintillation may suffer from sparse data and in-complete understanding of the relevant geophysi-cal drivers.

2.5 Versions 12, 13.00, and 13.01 output the SIindex of Whitney et al. (1969) as an auxilliary(dB) intensity scintillation index. Since SI dependsupon record length, the standard deviation of dBintensity is output instead of SI in Version 13.02.

2.6 WBMOD is a climatological model. In viewof the patchiness and day-to-day variability ofscintillation, its outputs may differ considerablyfrom measurements at a given place on a givenday.


3.1 The model is based on multi-frequencyscintillation measurements. The data were ac-quired at a variety of ground stations, which re-corded scintillation of radio signals from low-orbiting and geostationary satellites.

3.2 The scintillation data were translated to tur-bulence strengths of the irregularities by means ofthe phase-screen theory for weak scattering fromirregularities with a power-law spectrum (Rino,1979). The turbulence strength of the irregularitiesis characterized by the height-integrated psd at a


52

cross-field wave number corresponding to 1-kmscale size. The irregularity spectrum is defined byan outer scale and a power-law spectral index. Anempirical model of irregularity anisotropy and itsvariations is incorporated.

3.3 The global irregularity model is used tospecify scintillation parameters. Transformationfrom spatial to temporal statistics is based onscan of the line of sight and appropriate models ofionospheric drift.

4. Database

4.1 The primary data employed are intensityand phase scintillation measurements at VHF,UHF, and L band (with an S-band phase refer-ence) carried out at Poker Flat, AK; Stanford, CA;Ancon, Peru; and Kwajalein, Marshall Islands inthe WideBand experiment.

4.2 More recently, data from the DNA HiLat andPolar BEAR Satellite experiments have been em-ployed. Specifically, VHF and UHF phase (with anL-band reference) and intensity data recorded atBellevue, WA; Tromso, Norway; Ft. Churchill,Manitoba; and Sondre Stromfjord, Greenlandhave been used.

4.3 The foregoing have been augmented withintensity measurements performed by PL/GD at Lband on Ascension Island in the Atlantic and atVHF in Manila, Phillipines, and Huancayo, Peru.Similar VHF data from Narssarssuaq, Greenland(Basu, 1975), have been applied to the questionof seasonal variation at high latitudes.


5.1 Basu, Sa., E. MacKenzie, and Su. Basu(1988), “Ionospheric Constraints on VHF/UHFCommunications Links During Solar Maximumand Minimum Periods,” Radio Sci. 23, 363.

5.2 Basu, Su. (1975), “Universal-Time/SeasonalVariations of Auroral-Zone Magnetic Activity andVHF Scintillations,” J. Geophys. Res. 80, 4725–4728.

5.3 Fremouw, E.J., and A. Ishimaru (1992),“Intensity Scintillation Index and Mean ApparentRadar Cross Section on Monostatic and BistaticPaths,” Radio Sci. 27, 539–543.

5.4 Fremouw, E.J., and J.M. Lansinger (1981),“A Computer Model for High-Latitude PhaseScintillation Based on Wideband Satellite Datafrom Poker Flat,” Defense Nuclear Agency,Washington, DC, Rept. DNA5686F.

5.5 Fremouw, E.J., and J.A. Secan (1984),“Modeling and Scientific Application of Scintilla-tion Results,” Radio Sci.19, 87–694.

5.6 Rino, C.L. (1979), “A Power-law Phase-screen Model for Ionospheric Scintillation: 1,Weak Scatter,” Radio Sci. 14, 1135–1145.

5.7 Secan, J.A., and R.M. Bussey (1994), “AnImproved Model of High-latitude F-Region Scin-tillation (WBMOD Version 13),” Phillips Lab.,Hanscom AFB, MA, Rept. PL-TR-94-2254.

5.8 Secan, J.A., R.M Bussey, E.J. Fremouw,and Sa. Basu (1995), “An Improved Model ofEquatorial Scintillation,” Radio Sci. 30, 607–617.

5.9 Whitney, H.E., J. Aarons, and C. Malik(1969), “A Proposed Index for Measuring Iono-spheric Scintillations,” Planetary Space Sci. 17,1069–1073.


6.1 Dates:

1981 Original high-latitude WMOD.1984 Extension to equatorial latitudes.1986 Extension to middle latitudes.1994 Improvement at high latitudes.1994 Improvement at middle latitudes.1993, 1995 Improvements at equatorial lati-tudes.

6.2 Authors (principal): Edward J. Fremouw,NWRA President and Senior Research Scientist,and James A. Secan, NWRA Research Scientist.

6.3 Sponsors: Defense Nuclear Agency (nowDefense Special Weapons Agency) of the U.S.Department of Defense, and Phillips Laboratoryof the USAF Materiel Command.


The evolution of WBMOD traced herein refers tothe “research” versions developed by NWRA un-der contracts from DNA and Phillips Laboratory.Users interested in obtaining a copy should ad-dress requests to J.A. Secan (e-mail [email protected]) or E.J. Fremouw (e-mail [email protected]) atNWRA, P.O. Box 3027, Bellevue, WA 98009, tel.425/644-9660. NWRA has devised specializedversions for the USAF Air Weather Service. Par-ties interested in versions tailored for particularapplications should visit http://www.nwra.com, orcontact Mr. Secan or Dr. Fremouw.


53

MODEL OF THE TROUGH IN THEHIGH-LATITUDE F LAYER

1. Model content

MLAT/MLT boundaries occur in the high-latitudeionosphere that separates regions where thereare macroscopic changes in F-layer electron den-sity. These boundaries, which are often stable formany hours UT, are formed by the convectionpattern and the auroral oval.


The model describes only foF2, so that hmF2 andthe shape of the altitude profile must come fromthe parameterized USU model or from some em-pirical model. In addition, the model is uncertainabout the merging of the afternoon trough withthe mid-latitude ionosphere in the hours beforemidnight. A further uncertainty is the daytimetrough in the morning sector from ~0600 to 1100MLT, which is variable and poorly defined.

3. Basis of model

3.1 This is an empirical model derived fromdata from a dense network of ionospheric sound-ers during winter at solar maximum.

3.2 The first part is a daytime trough in the af-ternoon sector. The equatorward boundary of thistrough separates the high-density daytime F layerfrom the depleted and disturbed F-region plasma.This is nighttime plasma that is transported sun-ward by the convection pattern. This trough is welldefined and very persistent, extending as a spiralfrom about 1300 MLT until nearly midnight. Theequatorward edge is the boundary of the convec-tion pattern. At this edge, foF2 decreases expo-nentially with increasing MLAT over a nominalrange of 3 deg to a nominal minimum value 2.5times smaller than at the edge. However, foF2remains constant over a range of 2 deg MLAT,where it is terminated by the auroral F layer.

3.3 The second part is a post-midnight troughextending from midnight to dawn at nearly con-stant MLAT. This trough is defined by its mini-mum, which is the juncture between the normalnighttime mid-latitude F layer that decreases withlatitude, and the auroral F layer that increaseswith latitude to form the poleward trough wall. Asdefined from its minimum, the trough increases in

foF2 with increasing latitude as exp(Λ/3.7 deg). Itincreases equatorward from the minimum withdecreasing latitude as exp(Λ/16 deg) with themid-latitude F layer. The location and value of theminimum are determined by the intersection ofthese two regions, which vary independently. Ifnot measurable directly, they are given by theboundary of the auroral oval and of the mid-latitude F layer, the latter given by the URSI co-efficients.


4.1 If not measurable directly, the equatorwardedge of the afternoon trough is taken from theHeppner-Maynard model, and foF2 at the equa-torward edge, from the URSI coefficients.

4.2 If not measurable directly, the post-midnighttrough minimum is given by the boundary of theauroral oval and of the mid-latitude F layer by theURSI coefficients.


5.1 Whalen, J.A. (1987), “The Daytime F LayerTrough Observed on a Macroscopic Scale,” J.Geophys. Res. 92, 2571.

5.2 Whalen, J.A. (1989), “The Daytime F LayerTrough and Its Relation to Ionospheric-Mag-netospheric Convection,” J. Geophys. Res. 94,17,169.

5.3 Sojka, J.J., R.W. Schunk, and J.A. Whalen(1990), “The Longitude Dependence of the Day-side F-Region Trough: A Detailed Model-Ob-servation Comparison,” J. Geophys. Res. 95,15,275.


6.1 Dates: 1985–1990.

6.2 Author: J.A. Whalen.

6.3 Sponsor: Air Force Geophysics Laboratory.


This daytime trough is incorporated in the HighLatitude Ionospheric Specification Model.


54

GPS EIGHT-COEFFICENT TEC MODEL

1. Model content

The GPS (or Klobuchar) TEC model was origi-nally developed in the late 1970s to provide anestimate of the ionospheric range delay for single-frequency users of the Global Positioning System(GPS). Because of very severe restrictions on theamount of data that could be transmitted as partof the GPS navigation message, the model at-tempts to represent the global ionosphere usingonly eight coefficients. These coefficients werederived from the Bent model and are functions oftime of year and solar activity (represented byF10.7). Despite the model’s computational simplic-ity, it performs remarkably well, with a root meansquare (RMS) error of about 50%.

For a specified location, line of sight, time of day,day of the year, and solar activity level (F10.7), themodel provides the ionospheric slant TEC (interms of the group delay at 1.57542 GHz).


The most obvious limitation of the model is itsreliance on only eight coefficients to represent theglobal ionosphere. It makes no attempt to modelthe equatorial anomaly or the highly dynamichigh-latitude ionosphere.


The GPS Eight-Coefficient Model was obtainedby performing least-squares fits to vertical TECcomputed from the Bent model. Since the Bentmodel’s own coefficients are provided at 10-dayintervals throughout the year, the GPS model wasorganized in the same way. The diurnal variationis described as a half cosine (actually calculatedby its truncated Taylor series) for the daytimeTEC and a constant value for the nighttime TEC.The amplitude and period of the half cosine areeach described by a cubic equation in geomag-netic latitude (accounting for the eight coefficientsbroadcast in the GPS navigation message).

The conversion from vertical TEC to slant TEC isaccomplished by multiplication by an obliquityfactor that assumes a constant ionospheric heightof 350 km. Conversion from the geodetic coordi-nates of the ionospheric intersection point to thegeomagnetic coordinates required by the model isaccomplished using approximate formulae.


As implemented in a typical single-frequencyGPS receiver, the inputs are the universal time(UT), the user’s approximate location in geodeticcoordinates, the azimuth and elevation of the lineof sight, and the eight coefficients broadcast inthe GPS navigation message. When used as astand-alone model, it also requires the day of theyear and solar activity level (F10.7). The stand-alone model can provide vertical TEC and slantTEC, as well as vertical and slant group delay.


5.1 Klobuchar, J.A. (1986), “Design and Char-acteristics of the GPS Ionospheric Time DelayAlgorithm for Single Frequency Users,” Proceed-ings of PLANS ’86, Las Vegas, NV, pp. 280–286.

5.2 Klobuchar, J.A. (1987), “Ionospheric Time-Delay Algorithm for Single Frequency GPS Us-ers,” IEEE Transactions on Aerospace and Elec-tronic Systems AES-23 (3), 325–331.

5.3 Spilker, J.J. (1996), “GPS Navigation Data,”Global Positioning System: Theory and Applica-tions, Vol. I, edited by B.W. Parkinson and J.J.Spilker, AIAA, Reston, VA, pp. 121–176.


6.1 Date: Late 1970s.

6.2 Author: John R. Klobuchar.

6.3 Sponsor: Air Force Geophysics Laboratory(AFGL), which is now a part of the Air Force Re-search Laboratory (AFRL).


Although the mathematical formulae of the modelhave been published in the references citedabove, the tables of the eight coefficients for each10-day period and each level of solar activity arenot publicly available. A master set is maintainedat AFRL and at the GPS Control Segment, whichbroadcasts the appropriate coefficients as part ofthe GPS navigation message.


55

THE CPI TEC MODEL

1. Model content

The CPI TEC model for single-frequency GPSusers was developed to replace the GPS Eight-Coefficient Model (Klobuchar Model). The CPImodel is actually a three-dimensional model ofthe ionosphere similar to PIM but with additionalenvironmental parameters, specifically a set oflongitude-dependent parameters describing theequatorial vertical drift and thermospheric windsthat control much of the day-to-day variability ofthe ionosphere.

The model takes advantage of the enormouscomputing power available in even handheld de-vices now available. The model provides slantTEC (in terms of the group delay at 1.57542 GHz)along the lines of sight to GPS satellites.


Although capturing more of the spatial structure ofthe ionosphere than the GPS Eight-CoefficientModel, the accuracy of the model is dependent ontimely measurements of the equatorial verticaldrift (for low latitudes) and/or the thermosphericwinds (for mid latitudes). The model does not at-tempt to capture the dynamic state of the high-latitude ionosphere.


Like its cousin PIM, the CPI GPS model is a pa-rameterization of diurnally reproducible runs ofthe AFRL Global Theoretical Ionospheric Model(GTIM). Unlike PIM, however, the geophysicalparameters include not only solar activity but alsothe equatorial vertical drift (which drives the for-mation of the equatorial anomaly) and the ther-mospheric winds (which control much of the vari-ability of the mid-latitude ionosphere).

The output of GTIM is represented by an expan-sion in terms of Empirical Orthonormal Functions(EOFs) derived from a representative subset ofthe complete set of GIM runs. The coefficients ofthis orthonormal expansion are themselves repre-sented by simple functions of solar activity,equatorial drift, and thermospheric winds.

The conversion from vertical TEC to slant TEC isaccomplished by integrating model electron den-

sity along the line of sight rather than applying anobliquity factor to the vertical TEC. Although theobliquity factor works well at mid latitudes, it canbe very inaccurate in the equatorial anomaly oranywhere there are large spatial gradients.


The model requires the date and time (UT) andthe location of the observer, the solar activitylevel, and the equatorial drift and thermosphericwind parameters for the longitude of the user. Ifdrift and wind parameter values are not available,the model uses climatological estimates.


5.1 Daniell, R.E., L.D. Brown, and R.W. Simon(1996), “A New, Improved Ionospheric CorrectionAlgorithm for Single Frequency GPS Receivers,”Proceedings of ION GPS-96, Institute of Naviga-tion, Alexandria, VA, pp. 635–640.

5.2 Daniell, R.E., L.D. Brown, and R.W. Simon(1997), “Performance Comparisons Between theCurrent and a New Prototype Single FrequencyIonospheric Correction Algorithm,” Proceedings ofthe 53rd Annual Meeting, Institute of Navigation,Alexandria, VA, pp. 101–106.


6.1 Dates: 1996–1998.

6.2 Authors: R.E. Daniell, L.D. Brown, and R.W.Simon.

6.3 Sponsors: Computational Physics, Inc. (CPI)under a Small Business Innovation Research(SBIR) contract with the Air Force ResearchLaboratory.


Under the terms of the SBIR program, the modelis a proprietary product of CPI, although the gov-ernment retains certain rights to license the soft-ware. Others may contact CPI to obtain licensinginformation: Robert E. Daniell Jr., ComputationalPhysics, Inc., Suite 202A, 240 Bear Hill Road,Waltham, MA 02154-1026, tel. 781/487-2250,FAX 781/487-2290 (e-mail [email protected]).

American Institute ofAeronautics and Astronautics

1801 Alexander Bell Drive, Suite 500Reston, VA 20191-4344

ISBN 1-56347-347-X

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