A New Empirical Model for Ionospheric Total Electron Content
1
l Ionospheric Total Electron Content (TEC) fluctuates based on a number of factors, including solar flux, geomagnetic activity, and seasonal variability. Models of these changes are constructed with the intention of determining the nature of TEC fluctuations as a result of external parameters. This project presents preliminary results for a new model for ionospheric TEC with unprecedented spatial and temporal resolution and data reliability, applied to all longitudes at 45 degrees North latitude. Introduction Periodic recurrence of artificial data variability in TEC that is related to the sidereal motion of satellites is more severe at solar minimum, while regions of low GPS coverage offer less data than other locations. Several steps are taken to account for this, including (1) the application of a Hampel filter for outlier removal, (2) a cubic spline interpolant with low tolerance, and (3) “iterative model-building,” a method which removes points with excessively high differences between the model and data under the condition that geomagnetic activity and solar flux are relatively low. Data Preparation A New Empirical Model for Ionospheric Total Electron Content Cole Tamburri 1,2 , Larisa Goncharenko 2 , William Rideout 2 , Anthea Coster 2 The final selection of 36 input parameters includes a quadratic EUV term, EUV delays of 1 day, 8 days, 24 days, and 36 days, a quadratic Ap3 term, Ap3 delays of 3 hours, 24 hours, 48 hours (quadratic), and 72 hours, seasonal terms (annual, semiannual, four-monthly, three-monthly), modulation of the EUV linear term by annual, semiannual, and three-monthly terms, and modulation of the EUV quadratic term by all periodic terms. Input Parameters: Final Selection Solar Flux: Relative importance of EUV and the F10.7 radio flux was examined. While the latter captures the last solar cycle of data well, the EUV data are more comprehensive in capturing the solar spectral output. Modulation of the real-time EUV by seasonal terms is included, as are temporal delay terms. Unlike prior models, the parameter is not a moving average of solar flux. Input Parameters This work was funded by the National Science Foundation through its Research Experience for Undergraduates (REU) Program in cooperation with the MIT Haystack Observatory. Thanks are given to the development team of the CEDAR Madrigal Database and the TIMED SEE Mission. Acknowledgements Further study will include (1) expansion of the model to other latitudes beyond 45 degrees North, (2) expansion of the model to a longer time period, as it may be possible to expand the limiting dataset (TIMED SEE EUV) to the full extent of TEC data available (2000-2019), (3) investigation of additional drivers/independent variables, and ultimately, (4) identification of ionospheric anomalies using the final model. Future Work Geomagnetic Index: Relative significance of geomagnetic activity indices Ap3, Kp, and various delays was investigated. Ultimately it was found that integration of the Ap3 Index over the past 33 hours was unnecessary, but that several delays showed significance. Seasonal Variation: Besides the modulation of EUV by seasonal terms, terms corresponding to annual, semi-annual, four-monthly, and three-monthly terms are themselves included in the model. The annual term was deemed superior to a solar zenith angle input for reasons of practicality. Figure 2. Sample raw TEC data with 5 minute temporal resolution. The effect of sidereal motion of satellites is evident. Figure 3. The result of cleaning the data by application of a Hampel filter alongside a cubic spline interpolant with low tolerance. GNSS-based TEC, 10.7cm radio flux (f10.7), and geomagnetic activity data are provided by the CEDAR Madrigal Database. Extreme Ultraviolet (EUV) data are provided by the TIMED Solar Extreme Ultraviolet Experiment (SEE). Data Sources Model Description Figure 1. Sample gridded TEC data provided by the CEDAR Madrigal Database The new empirical linear regression model is constructed with TEC as the response variable and several parameters representing solar EUV flux, geomagnetic activity, and season as independent variables. The model is based on GNSS TEC data from the years 2002-2019. The model is constructed at 45 o N latitude in 3 o longitude bins with a 30 minute temporal resolution and shows an average RMS error of 1.78 TECu for this location. Figure 5. Sample coefficients and associated p-values at 45 o N latitude, 0 o E longitude corresponding to EUV (top), Ap3 (middle), and Ap3 with a 24 hour delay (bottom). A p-value of less than 0.05 indicates statistical significance. A positive storm effect is observed for the Ap3 data, while a negative storm effect is observed for the Ap3 input with a 24 hour delay. • Preliminary results are presented for an empirical model for ionospheric TEC that has been produced with unprecedented spatial (3 o ) and temporal (30 min) resolution. • The model is based on comprehensive global GPS data, allowing for less interpolation of original TEC data over areas of low coverage than prior models. • Emphasis is placed on including only parameters with physical meaning in model construction. • The model-to-data comparison shows small error values and good statistical agreement. Conclusions Figure 6. Sample statistical comparison of data to model, 45 o N latitude, 0 o E longitude. (a) Mean absolute percentage error. (b) Root mean squared error. (c) Root mean squared percentage error. Figure 7. Sample comparison of data to model, 2012, 45 o N latitude, 0 o E longitude. (a) TEC data. (b) Constructed model. (c) Absolute difference between data and model. (d) Percentage difference between data and model. Figure 4. Correlation coefficients associated with data organized into bins according to solar flux value for all local times at 45 o N latitude, 0 o E longitude. 1 Institute for Scientific Research at Boston College; 2 MIT Haystack Observatory
Transcript of A New Empirical Model for Ionospheric Total Electron Content
l
Ionospheric Total Electron Content (TEC) fluctuates based on a number of factors,including solar flux, geomagnetic activity, and seasonal variability. Models of thesechanges are constructed with the intention of determining the nature of TECfluctuations as a result of external parameters. This project presents preliminaryresults for a new model for ionospheric TEC with unprecedented spatial and temporalresolution and data reliability, applied to all longitudes at 45 degrees North latitude.
Introduction
Periodic recurrence of artificial data variability in TEC that is related to the siderealmotion of satellites is more severe at solar minimum, while regions of low GPScoverage offer less data than other locations. Several steps are taken to account forthis, including (1) the application of a Hampel filter for outlier removal, (2) a cubicspline interpolant with low tolerance, and (3) “iterative model-building,” a methodwhich removes points with excessively high differences between the model and dataunder the condition that geomagnetic activity and solar flux are relatively low.
Data Preparation
A New Empirical Model for Ionospheric Total Electron Content Cole Tamburri1,2, Larisa Goncharenko2, William Rideout2, Anthea Coster2
The final selection of 36 inputparameters includes a quadratic EUVterm, EUV delays of 1 day, 8 days, 24days, and 36 days, a quadratic Ap3term, Ap3 delays of 3 hours, 24 hours,48 hours (quadratic), and 72 hours,seasonal terms (annual, semiannual,four-monthly, three-monthly), modulationof the EUV linear term by annual,semiannual, and three-monthly terms,and modulation of the EUV quadraticterm by all periodic terms.
Input Parameters: Final Selection
Solar Flux: Relative importance of EUVand the F10.7 radio flux was examined.While the latter captures the last solarcycle of data well, the EUV data aremore comprehensive in capturing thesolar spectral output. Modulation ofthe real-time EUV by seasonal terms isincluded, as are temporal delay terms.Unlike prior models, the parameter isnot a moving average of solar flux.
Input Parameters
This work was funded by the National Science Foundation through its ResearchExperience for Undergraduates (REU) Program in cooperation with the MIT HaystackObservatory. Thanks are given to the development team of the CEDAR MadrigalDatabase and the TIMED SEE Mission.
Acknowledgements
Further study will include (1) expansion of the model to other latitudes beyond 45degrees North, (2) expansion of the model to a longer time period, as it may bepossible to expand the limiting dataset (TIMED SEE EUV) to the full extent of TEC dataavailable (2000-2019), (3) investigation of additional drivers/independent variables,and ultimately, (4) identification of ionospheric anomalies using the final model.
Future Work
Geomagnetic Index: Relativesignificance of geomagnetic activityindices Ap3, Kp, and various delayswas investigated. Ultimately it wasfound that integration of the Ap3Index over the past 33 hours wasunnecessary, but that several delaysshowed significance.Seasonal Variation: Besides themodulation of EUV by seasonalterms, terms corresponding toannual, semi-annual, four-monthly,and three-monthly terms arethemselves included in the model.The annual term was deemedsuperior to a solar zenith angle inputfor reasons of practicality.
Figure 2. Sample raw TEC data with 5 minutetemporal resolution. The effect of siderealmotion of satellites is evident.
Figure 3. The result of cleaning the data byapplication of a Hampel filter alongside acubic spline interpolant with low tolerance.
GNSS-based TEC, 10.7cm radio flux (f10.7), and geomagnetic activity data areprovided by the CEDAR Madrigal Database. Extreme Ultraviolet (EUV) data areprovided by the TIMED Solar Extreme Ultraviolet Experiment (SEE).
Data Sources
Model Description
Figure 1. Sample gridded TEC data provided by the CEDAR Madrigal Database
The new empirical linear regression model is constructed with TEC as the responsevariable and several parameters representing solar EUV flux, geomagnetic activity,and season as independent variables. The model is based on GNSS TEC data fromthe years 2002-2019. The model is constructed at 45oN latitude in 3o longitudebins with a 30 minute temporal resolution and shows an average RMS error of 1.78TECu for this location.
Figure 5. Sample coefficients and associated p-valuesat 45oN latitude, 0oE longitude corresponding to EUV(top), Ap3 (middle), and Ap3 with a 24 hour delay(bottom). A p-value of less than 0.05 indicates statisticalsignificance. A positive storm effect is observed for theAp3 data, while a negative storm effect is observed forthe Ap3 input with a 24 hour delay.
• Preliminary results are presented foran empirical model for ionosphericTEC that has been produced withunprecedented spatial (3o) andtemporal (30 min) resolution.
• The model is based oncomprehensive global GPS data,allowing for less interpolation oforiginal TEC data over areas of lowcoverage than prior models.
• Emphasis is placed on including onlyparameters with physical meaning inmodel construction.
• The model-to-data comparisonshows small error values and goodstatistical agreement.
Conclusions
Figure 6. Sample statistical comparison of datato model, 45oN latitude, 0oE longitude. (a) Meanabsolute percentage error. (b) Root meansquared error. (c) Root mean squaredpercentage error.
Figure 7. Sample comparison of data to model, 2012, 45oN latitude, 0oE longitude. (a) TEC data. (b) Constructed model. (c) Absolute difference between data and model. (d) Percentage difference between data and model.
Figure 4. Correlation coefficients associatedwith data organized into bins according tosolar flux value for all local times at 45oNlatitude, 0oE longitude.
1Institute for Scientific Research at Boston College; 2MIT Haystack Observatory
