The Integrated Terminal Weather System terminal winds product · 2019. 8. 30. · Surface Observing...

• COLE AND WILSONThe Integrated Terminal Weather System Terminal Winds Product

VOLUME 7, NUMBER 2, 1994 THE LINCOLN LABORATORY JOURNAL 475

The Integrated Terminal WeatherSystem Terminal Winds ProductRodney E. Cole and F. Wesley Wilson

■ The wind in the airspace around an airport impacts both airport safety andoperational efficiency. Knowledge of the wind helps controllers and automationsystems merge streams of traffic; it is also important for the prediction of stormgrowth and decay, burn-off of fog and lifting of low ceilings, and wake vortexhazards. This knowledge is provided by the Integrated Terminal WeatherSystem (ITWS) gridded wind product, or Terminal Winds. The TerminalWinds product combines data from a national numerical weather-predictionmodel, called the Rapid Update Cycle, with observations from ground stations,aircraft reports, and Doppler weather radars to provide estimates of thehorizontal wind field in the terminal area. The Terminal Winds analysis differsfrom previous real-time winds-analysis systems in that it is dominated byDoppler weather-radar data. Terminal Winds uses an analysis called cascade ofscales and a new winds-analysis technique based on least squares to take fulladvantage of the information contained in the diverse data set available in anITWS. The weather radars provide sufficiently fine-scale winds information tosupport a 2-km horizontal-resolution analysis and a five-minute update rate.

A prototype of the Terminal Winds analysis system was tested at OrlandoInternational Airport in 1992, 1993, and 1995, and at Memphis InternationalAirport in 1994. The field operations featured the first real-time winds analysiscombining data from the Federal Aviation Administration TDWR radar and theNational Weather Service NEXRAD radar. The evaluation plan is designed tocapture both the overall system performance and the performance duringconvective weather, when the fine-scale analysis is expected to show its greatestbenefit.

A in the terminalarea have a significant impact on airport op-erations and safety. A number of Federal Avi-

ation Administration (FAA) systems under develop-ment to improve airport safety and capacity requireknowledge of the wind and other atmospheric vari-ables. These systems include (1) the Center TRA-CON Advisory System (CTAS) to automate air traf-fic control to optimize fuel consumption, scheduling,and aircraft merging and separations [1]; (2) theWake Vortex Advisory System (WVAS) to reduce air-craft separations for wake vortex avoidance; (3) theIntegrated Terminal Weather System (ITWS) wind-

shift and runway-winds prediction systems to predictwind shifts—from gust fronts and other sources—that lead to runway reconfiguration; (4) the ITWSlow ceiling and visibility predictions [2]; and (5) theITWS convective storm growth-and-decay predic-tions. Figure 1 illustrates the different aviation sys-tems, and shows where in the terminal airspace eachsystem has the most impact and utility.

Currently in development by the FAA, ITWS willproduce a fully automated, integrated terminalweather information system to improve the safety, ef-ficiency, and capacity of terminal-area aviation opera-tions [3]. This system will acquire data from FAA and


476 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER 2, 1994

National Weather Service radar sensors as well asfrom aircraft in flight in the terminal area, and it willprovide air traffic control personnel with weather in-formation products that are immediately usable with-out further meteorological interpretation. Theseproducts include current terminal-area weather andshort term (zero to thirty minute) predictions of sig-nificant weather phenomena.

The ITWS gridded analysis system will providecurrent-time estimates and short-term forecasts ofwind, temperature, moisture, and atmospheric pres-sure at each point in a three-dimensional grid in theterminal area. Estimates of these quantities are cur-rently produced by national-scale forecast models atthe National Weather Service, although these nation-al-scale models are on coarse grids in space and time,relative to airport operations. To support the specialrequirements of aviation systems, the ITWS gridded

analysis system will improve the resolution and time-liness of the estimates from the national-scale modelsby incorporating additional information from termi-nal-area sensors.

We have concentrated our initial development ef-forts on gridded horizontal winds, with a griddedtemperature analysis to follow. There are three reasonsfor choosing this sequence of development: (1) hori-zontal winds and wind changes have a direct impacton aviation operations and in the automated aviationsystems mentioned above; (2) high-resolution hori-zontal wind data are provided by meteorologicalDoppler radars (each ITWS is expected to have datafrom at least one Doppler radar, and often two ormore, which makes winds analysis tractable in thenear term); and (3) horizontal winds are an importantfactor in many meteorological processes because theycontribute to the transport of momentum, heat, and

FIGURE 1. Aviation systems supported by the ITWS gridded horizontal winds product, or Terminal Winds. Systems re-quiring Terminal Winds information are being developed to automate air traffic control to optimize fuel consumption,scheduling, and aircraft separation (the Center TRACON Advisory System, or CTAS); reduce aircraft separation forwake vortex avoidance (the Wake Vortex Advisory System, or WVAS); predict wind shifts from gust fronts and othersources that would lead to runway reconfiguration (the ITWS wind-shift and runway-winds prediction systems); predictthe onset and dissipation of fog and low-ceiling conditions; and predict storm growth and decay.

Runway-winds predictions

FAAdisplays

Center TRACONAdvisory System

(CTAS)

Wake VortexAdvisory System

(WVAS)

Ceiling and visibilitypredictions

Wind-shift predictions

Storm growth-and-decay

predictions



Surface Observing System (ASOS) and Low LevelWind Shear Alert System (LLWAS) surface anemom-eters. The design of the Terminal Winds analysis sys-tem must take into account the weather phenomenato be captured, sensor characteristics, and nonuni-form and dynamic data distributions; the systemmust also be robust to sensor failures. Figure 2 illus-trates the location and variety of the data sources usedin the Terminal Winds analysis.

In the summer of 1992 an initial Terminal Windsprototype [4, 5] based on the Local Analysis and Pre-diction System (LAPS) developed at the NationalOceanic and Atmospheric Administration’s (NOAA)Forecast Systems Laboratory (FSL) [6, 7] was testedin the Lincoln Laboratory ITWS testbed in Orlando,Florida. This prototype featured the first real-time

humidity (in particular, the gridded temperatureanalysis and the gridded humidity analysis depend onthe gridded winds analysis).

The ITWS gridded horizontal winds product, orTerminal Winds, was developed to provide detailedknowledge of the winds in the terminal airspace toeach of the aviation systems illustrated in Figure 1.Terminal Winds obtains wind information from anumber of sources, including a national-scale forecastmodel called Rapid Update Cycle (RUC) provided bythe National Weather Service; meteorological Dop-pler radars, including the FAA’s Terminal DopplerWeather Radar (TDWR) and the National WeatherService WSR-88D (NEXRAD) radar; commercialaircraft using the Meteorological Data Collection andReporting System (MDCRS); and the Automated

FIGURE 2. Data sources for Terminal Winds. These sources are a national-scale forecast model called Rapid UpdateCycle (RUC) provided by the National Weather Service; meteorological Doppler radars including the Terminal DopplerWeather Radar (TDWR) and the National Weather Service WSR-88D (NEXRAD) radar; commercial aircraft using theMeteorological Data Collection and Reporting System (MDCRS); and Automated Surface Observing System (ASOS)and Low Level Wind Shear Alert System (LLWAS) surface anemometers.

NEXRAD

TDWR

ASOS ASOS

ASOS

MDCRS

MDCRS

LLWAS

RUC

ASOSASOS



winds analysis using data from the TDWR radar [8]and the NEXRAD radar [9].

Based on lessons learned from the 1992 test, a newanalysis technique was developed to extract the windinformation in the Doppler radar data more effective-ly. This new technique, called optimal estimation, usesa minimum-error-variance technique (least squares)and is closely related to both the state-of-the-art oper-ational non-Doppler winds-analysis technique, calledoptimal interpolation, and standard multiple-Dopplertechniques. The optimal-estimation technique wasevaluated on the 1992 Orlando data set, and demon-strated in real time in the Orlando testbed during thesummer of 1993, in Memphis during the spring andsummer of 1994, and in Orlando during the winterof 1995. The optimal-estimation-based analysis pro-vides a significant improvement over previous windsanalyses using Doppler radar data.

In the next section we discuss design consider-ations that motivated the development of the Termi-nal Winds system. Then we give an overview of theTerminal Winds system, and provide a description ofthe analysis with particular attention to Doppler dataanalysis and the optimal-estimation analysis. Finally,we give an overview of our product accuracy evalua-tion based on data collected in the Orlando testbed,and we discuss the direction of future work. The sec-tion entitled “Details of the Terminal Winds Analy-sis” can be omitted by readers interested only in anoverview of the Terminal Winds system.

Design Considerations

There are a number of design considerations for awinds-analysis system that will support the aviationsystems listed above and operate with informationfrom sensors in the terminal area. Ideally, users of thegridded winds analyses levy performance require-ments for resolution, accuracy, and timeliness. Theautomated aviation systems that rely on these analy-ses, however, are still under development, and finalperformance requirements are not yet completelydetermined. We have taken the approach of basingresolution, accuracy, and timeliness on expectedwind-field phenomenology and sensor characteristics,with the goal of minimizing the norm of the wind-vector error in the analyzed wind fields.

There are a variety of information sources availablefor the gridded winds analysis, including forecastmodels, surface observing systems, commercial air-craft, and meteorological Doppler radars. These datasources provide information of differing content, ac-curacy, and resolution. The gridded winds analysissystem must correctly resolve important wind-fieldfeatures by assembling this diverse information, andmust be robust when sensors unexpectedly go off lineor come back on line.

Wind-Field Phenomenology

The terminal airspace extends from the airport sur-face to 18,000 feet mean sea level (MSL). Meteoro-logically, this airspace is divided into two regimes.The portion of the atmosphere closest to the Earth’ssurface is referred to as the planetary boundary layer(PBL), and its dynamical structure is strongly influ-enced by surface effects. The atmosphere in the PBLis well mixed during daylight hours, and solar heatingof the Earth’s surface often expands the PBL to asmuch as 6000 feet above ground level. At night, whenthe air is relatively cool (and less well mixed), the PBLmay extend to less than 300 feet above ground level.A mixture of wind-field features can coexist in thePBL with a wide range of spatial and temporal scales.Features with spatial scales smaller than a few kilome-ters or temporal scales shorter than a few minutes,however, are not important to the users of the griddedwinds analysis. These small-scale features do not, forexample, affect time of flight.

The region above the PBL is referred to as the freeatmosphere because of its relative insulation from sur-face effects. The free atmosphere is usually composedof large-scale wind features, each with horizontal ex-tent of at least tens of kilometers and lasting tens ofminutes. Small-scale wind features can exist in thefree atmosphere—for example, within thunder-storms—but are rare.

Information Sources

The underpinning of the Terminal Winds system isprovided by the RUC, which is a numerical weather-prediction model run by the National MeteorologicalCenter of the National Weather Service. The RUC isbased on the Mesoscale Analysis and Prediction Sys-



tal resolution to 10 km and the update rate to onehour by the end of the decade). MDCRS-equippedaircraft measurements are available only at randompositions and times along flight paths of commercialaircraft, with a data latency of at least fifteen minutes.On average, approximately ten MDCRS reports arereceived per hour. Surface stations such as LLWASand ASOS anemometers vary in update rate betweenten seconds and twenty minutes, and Doppler radarsprovide only a single component of the wind. Com-bining these widely varying sources of information isa significant technical challenge.

Meteorological Doppler radars provide estimatesof the wind-velocity component along the radar beam(radial velocities) as well as measurements of returnintensity (reflectivity). These radars cannot directlymeasure the wind-velocity component perpendicularto the radar beam. The radial-velocity wind estimatesare derived from the phase shift in returns from air-borne reflectors such as bugs, water droplets, and re-fractive index inhomogeneities that are assumed to betraveling with the wind. Doppler radars provide accu-rate and dense measurements only in regions withsufficient reflectors.

Doppler radars provide high-resolution radial-ve-locity wind information throughout the PBL becauseatmospheric mixing tends to distribute the particlesthat serve as reflectors for the Doppler radars. Thisphenomenon allows the gridded analysis to providehigh-resolution wind information in the PBL, wheresmall-scale wind structures are expected. Because offewer reflectors in the free atmosphere above the PBL,

Table 1. Characteristics of Data Sources for Terminal Winds

Source Update Rate Horizontal Accuracy Information(min) Resolution (m/sec) Content

RUC 180 60 km 2–7 vector

TDWR 5 0.120 km x 0.5° 1–2 single component

NEXRAD 6 0.250 km x 1° 2–4 single component

MDCRS variable variable 4 vector

ASOS 20 ≈60 km 2 vector

LLWAS 0.16 (10 sec) 2–3 km 1 vector

tem (MAPS) developed at NOAA’s FSL [10]. Hori-zontal wind measurements are provided at the surfacenear an airport by LLWAS anemometers [11] and inoutlying regions by ASOS anemometers [12].MDCRS-equipped aircraft provide measurements ofthe horizontal winds aloft [13]. These aircraft are notwidely distributed but are typically located alongroutes of commercial air traffic, making them an im-portant source of information about winds in the freeatmosphere.

The ITWS will also have information from thetwo meteorological Doppler radars mentionedabove—the TDWR and the NEXRAD radar. Dop-pler radars provide measurements of a single compo-nent of the wind, the radial component directed to-ward the radar. These radars provide the vast majorityof the information coming into the Terminal Windssystem, although the other data sources also play animportant role, especially in the free atmosphere.

Table 1 shows that the information from the dif-ferent data sources differs widely in spatial and tem-poral resolution, as well as in content and accuracy.The accuracy listed is relative to an average wind overa disk with a 3-km radius in the horizontal during atime span on the order of a few minutes. For example,Doppler radars provide accurate information onwinds at specific points in space, but these values canreflect small-scale features that are considered noise inthe Terminal Winds system, which reduces their ef-fective accuracy. Because of the 60-km grid spacing,RUC cannot resolve most thunderstorm-scale weath-er phenomena (there are plans to reduce the horizon-



Doppler information is often available but sparse.The RUC and MDCRS information sources play animportant role at these altitudes. The lower-resolu-tion information available aloft from these two sourc-es, as well as from Doppler radars, is usually appropri-ate for the expected scales of the wind-field dynamicsabove the PBL. In regions of convective activitywhere small-scale wind structures are likely to existabove the PBL, the Doppler radars continue to pro-vide substantial amounts of information.

In regions with information from two or moreDoppler radars, a linear system of equations can besolved to estimate the horizontal winds [14]. The de-tails of this multiple-Doppler analysis are given in thenext section. The quality of the estimate derived fromthis linear system of equations varies depending onthe range of radar azimuth angles associated with theDoppler data and the separations between the loca-tions of the data in space and time. If Doppler dataare available for two independent directions at thesame location and time, the resulting estimate will beof high quality. If the Doppler data are all from nearlythe same direction or are widely separated, the result-ing estimate will be of lower quality.

Overview of the Terminal Winds Analysis

The Terminal Winds analysis is based on the follow-ing design goals related to the above considerations.The analysis should (1) respect the variety of spatialand temporal scales of wind-field features in the PBLand above the PBL, (2) respect the variety of spatialand temporal scales of the information from the dif-ferent data sources, (3) respect the differing quality ofinformation from the different sources, (4) properlymerge vector information with single-component in-formation, (5) properly interpolate nonuniformlydistributed information, (6) provide a smooth transi-tion from regions of dense data to regions of sparsedata, (7) take advantage of the information content ofa multiple-Doppler data set while respecting the vary-ing quality of that information, (8) handle fluctua-tions in data availability, and (9) minimize the magni-tude of the error in the wind-vector estimates.

The primary philosophy of the Terminal Windsanalysis is that the national-scale forecast model pro-vides an overall picture of the winds in the terminal

airspace, although painted in broad strokes. Informa-tion from the terminal sensors is then used to fill indetail and correct the broad-scale picture. Of course,the corrections and added detail can be provided onlyin those regions with nearby data. What constitutes“nearby” depends on the spatial and temporal scale ofthe feature to be captured in the analysis. The refine-ment of the broad-scale wind field is accomplished byaveraging the model forecasts with current data. Thisaveraging allows the analysis technique to producewind vectors that vary smoothly from regions with alarge number of observations to regions with few ob-servations or no observations at all, and enables theanalysis to cope gracefully with unexpected changesto the suite of available sensors.

To account for the different scales of wind featuresand the differing resolution of the information pro-vided from the various sensors, the Terminal Windsanalysis employs a cascade-of-scales analysis. This cas-cade-of-scales analysis uses nested grids, with an anal-ysis using a 2-km horizontal resolution and a 5-minupdate rate nested within an analysis using a 10-kmhorizontal resolution and 30-min update rate, whichin turn is nested within the RUC forecast using a 60-km horizontal resolution and 180-min update rate.All the data sources are used in the 10-km-resolutionanalysis, and data are allowed to be as old as ninetyminutes. Only the information from the Doppler ra-dars and the LLWAS anemometers, however, are suit-able for the 2-km-resolution analysis. The cascade-of-scales analysis is appropriate for the different scales ofwind-field features that need to be captured in theanalysis, as well as the different scales of informationprovided by the different data sources, and the cas-cade-of-scales analysis provides a uniform level of re-finement at each step of the cascade. An additionalbenefit is that the 10-km-resolution analysis acts as astand-in for the planned 10-km-resolution nationalforecast. When a 10-km national forecast becomesavailable, the 10-km ITWS analysis can be dropped.

An important goal is the minimization of the errorof the analyzed wind field. To achieve this goal theTerminal Winds analysis uses a least-squares tech-nique, which is designed to average vector quantitiesand single-component quantities jointly. Previousstate-of-the-art operational winds-analysis systems



have used statistical techniques to great advantage.None of these systems, however, have the ability toanalyze the data from Doppler radars directly. TheTerminal Winds analysis represents a substantial stepforward in winds analysis, which is especially impor-tant because increasing numbers of Doppler weatherradars are being deployed.

The least-squares technique used in the TerminalWinds analysis accounts for the variations in qualityof the information available to the Terminal Windsanalysis, as well as errors arising from data age and er-rors arising from estimating winds at locations re-moved from the observation location. The least-squares technique also corrects for correlated errors.Highly correlated errors arise frequently because ofthe nonuniform distribution of data from the Dop-pler radars. Often the Terminal Winds analysis esti-mates the wind at locations with many Doppler val-ues clumped together at a distance, and few datavalues elsewhere. Because of the nonhomogeneity ofthe wind field, the data values in the region of Dop-pler information contain highly correlated errors, rel-ative to the wind at the distant analysis point. If thiserror correlation is not accounted for, these data val-ues dominate the analysis to a greater degree thanwarranted by their information content. This situa-tion is illustrated by an example later.

Details of the Terminal Winds Analysis

The details of the cascade-of-scales analysis and statis-tical analysis are given in this section. The reader mayskip to the next section without losing the continuityof the exposition.

The Terminal Winds analysis system is designed toachieve the nine goals stated in the previous section.The next subsection describes the method used toachieve the goal of respecting the variety of spatialand temporal scales both within the PBL and in thefree atmosphere above the PBL, as well as the goal ofproperly merging information from data sources withdiffering spatial and temporal update rates. The fol-lowing subsections provide general background infor-mation on winds analysis from meteorological Dop-pler radar data. These subsections discuss the types oferrors found in Doppler data, the method used toproduce regionally representative wind estimates on a

Cartesian grid from point measurements in sphericalcoordinates, and the traditional method for estimat-ing horizontal winds from multiple-Doppler datasets. The last topic is especially germane to the devel-opment of the optimal-estimation technique. Finally,we present a subsection on the optimal-estimationtechnique, and conclude this section of the articlewith a subsection on illustrative examples.

Cascade-of-Scales Analysis

Within the PBL or inside regions of convectiveweather, the Terminal Winds analysis needs to be ableto resolve wind-field structures that have spatial scalesas small as a few kilometers, and that evolve on timescales as small as several minutes. Above the PBL andoutside regions of convective weather, the analysisneeds to be able to resolve wind-field structures withspatial scales and temporal scales that are about an or-der of magnitude larger. To capture the differingscales of wind structures while respecting the differ-ences in information content of the various sources,Terminal Winds uses a cascade-of-scales analysis.

The cascade-of-scales analysis starts with an RUCforecast having a 60-km horizontal-resolution gridand a 3-hr update rate. The RUC data are used to ini-tialize an analysis with a 10-km horizontal-resolutiongrid and a 30-min update rate. The 10-km-resolutionwind field is used in turn to initialize an analysis witha 2-km horizontal-resolution grid and a 5-min updaterate. Each analysis grid has a vertical resolution of 50millibars of atmospheric pressure; Table 2 gives thenominal altitudes for the analysis levels in both milli-bars and feet. All of the data sources are used in the10-km-resolution analysis, but only Doppler dataand LLWAS data are used in the 2-km-resolutionanalysis. The cascade-of-scales analysis matches theatmospheric dynamics and information content ofthe different data sources, and gives a uniform ratio ofrefinement as the analysis steps from coarser to finerresolution. Stepping down this cascade of scales, theratios for temporal resolution are both 6:1, and theratios for horizontal resolution are 6:1 and 5:1, asshown in Table 3. The nested cascade-of-scales analy-sis grids simplify the software implementation.

Ideally, the cascade-of-scales analysis would pro-vide a refinement of the vertical resolution from one



in space and time between the two RUC forecaststhat bracket the analysis time. All data used in the 10-km analysis must have collection times within ninetyminutes of the analysis time. The current 10-km anal-ysis is then used as the background wind field for ananalysis with a 2-km horizontal resolution, a 50-mbvertical resolution, and a 5-min update rate. OnlyDoppler radar data and LLWAS data are used in the2-km analysis. The MDCRS aircraft reports and oth-er surface data are not used in the 2-km analysis be-cause of data latency. On grid levels with no observa-tions, the 2-km analysis is simply the 10-km analysisinterpolated to the 2-km-resolution grid.

Wind-Field Analysis from MeteorologicalDoppler Radar Data

This subsection provides an overview of the basics ofwinds analysis using information from meteorologi-cal Doppler radars. We discuss three topics: (1) dataquality, (2) data resampling to produce regionally rep-resentative wind estimates on a Cartesian grid frompoint measurements in spherical coordinates, and (3)estimating horizontal winds from information pro-vided by two or more Doppler radars.

Doppler Radar Errors

Data-quality issues should be addressed before ananalysis of the wind field is performed. There arethree major types of error in meteorological Dopplerradar data:1. Returns from objects that are not moving with

the wind, such as the ground and objects on theground (ground clutter), or flocks of birds andaircraft (point targets).

2. Velocity values that are misrepresented by veloc-ity folding. These errors result from the insuffi-cient sampling rate in the Doppler velocity cal-culation. Given a sampling rate, or the pulserepetition frequency (PRF), the unambiguousvelocity range is determined by

vc

f= ± ⋅ PRF

4,

where ƒ is the radar frequency and c is the speedof light. When velocity falls outside this range,it is folded back into the range of representable

Table 2. Pressure Levels in Millibars in theCascade-of-Scales Analysis, and

Corresponding Altitudes in Feet (MSL)

Altitude in millibars Altitude in feet

1000 360

950 1770

900 3240

850 4780

800 6390

750 8090

700 9880

650 11,780

600 13,800

550 15,960

500 18,290

450 20,810

400 23,580

350 26,633

300 30,070

250 34,000

200 38,770

150 44,760

100 53,190

analysis scale to the next. A Doppler radar provideshigh-horizontal-resolution wind measurements, butdoes not provide high vertical resolution except nearthe radar. The current Terminal Winds system usesthe same 50-mb vertical resolution for the 10-kmanalysis as for the 2-km analysis. In the future we planto examine the need for a higher vertical resolutionover the airport, where the higher resolution can besupported by the data from the TDWR.

Figure 3 shows the data flow for the TerminalWinds cascade-of-scales analysis. First, an analysis isperformed with a 10-km horizontal resolution, a 50-mb vertical resolution, and a 30-min update rate uti-lizing all of the data sources. The 10-km-resolutionbackground field is produced by linear interpolation



Table 3. Scales of Analysis for Rapid Update Cycle and Terminal Winds

Update Rate Horizontal Resolution Domain Size

Rapid Update Cycle 180 min 60 km national

Terminal Winds above PBL 30 min 10 km 240 x 240 km

Terminal Winds in PBL 5 min 2 km 120 x 120 km

FIGURE 3. Data flow for the Terminal Winds cascade-of-scales analysis. The RUC data are used to initialize an analysiswith a 10-km horizontal-resolution grid and a 30-min update rate. The 10-km horizontal-resolution wind field is used inturn to initialize an analysis with a 2-km horizontal-resolution grid and a 5-min update rate. All of the data sources areused in the 10-km analysis, but only Doppler data and LLWAS data are used in the 2-km analysis.

to classify radar errors or correct for them. This errordetection and correction is performed by each radarsystem prior to providing data to the ITWS. The Ter-minal Winds analysis system does attempt to identifyincorrect or nonrepresentative wind estimates and re-move them during the resampling process.

Radar Data Resampling

Resampling is the process by which radial velocity in-formation is transformed from radar coordinates to

velocities (velocity folding). Both TDWR andNEXRAD have algorithms that attempt to cor-rect for velocity folding.

3. Returns from objects beyond the unambiguousrange of the radar. These errors are the result ofechoes from distant and bright reflectors, suchas large storms or topographic features that arereceived after a subsequent pulse has been trans-mitted (multiple trip or range folding).Currently, the Terminal Winds system does not try

Rapid Update Cycle 60-km-resolution grid180-min update rate

TDWR

NEXRAD

MDCRS

LLWAS

ASOS

TDWR

NEXRAD

LLWAS

10-km-resolution winds

240 x 240 km grid10-km-resolution grid19 levels (100 mb, 53,000 ft)30-min update rate

120 x 120 km grid2-km-resolution grid11 levels (500 mb, 18,000 ft)5-min update rate

2-km-resolution winds

10-km interpolation

2-km interpolation



the Cartesian coordinates used in the Terminal Windsanalysis. Spatial averaging is used to provide data val-ues that represent a regional average wind. Data-qual-ity tests are used to remove questionable data.

The radar reflectivity and radial velocity data arecollected in contiguous, equally spaced gates alongeach radar beam. Both radars scan sectors of the re-gion with a fixed elevation angle during the scan. Atilt is a maximal collection of beams that are contigu-ous in time and have the same elevation angle. Geo-metrically, a tilt is a section of a cone whose vertex isat the radar. All NEXRAD tilts are full cones, cover-ing full 360° sectors. NEXRAD has several differentscan strategies, each with its own set of tilt elevationangles. TDWR can scan either with 360° sectors(monitor mode), or with two 360° tilts near the sur-face and an intense pattern of approximately 120°sectors at various elevations over the airport (hazard-ous-weather mode). The TDWR tilt elevation anglesare preset for each airport installation, so there areonly two TDWR scan strategies for each airport.

Each radar also interrupts its standard velocityscanning to make long-range (low-PRF) scans thatare used to detect the possibility for range folding.The low-PRF data are not used in the winds analysis.They provide an artificial temporal partition of thetilts into volume scans. The Terminal Winds analysisdoes not make use of this volume structure. Instead,at each analysis time, it composes a volume scan outof the most recent tilts. This design also accommo-dates the fact that the scan strategies of the radars canchange during operations. By constructing its ownvolume scan from the most recent tilts, the TerminalWinds analysis uses the most current radar data andis able to continue processing during changes in theradar scan strategy.

The resampling of the Doppler radar data is a two-step process—tilt resampling and volume resampling.

Tilt Resampling. This process produces a regionallyrepresentative estimate of the radial component of thehorizontal wind velocity at each tilt position (x,y, z* )on an (x,y ) column of the analysis grid. The verticalheight z* is the height at which the tilt intersects the(x,y) column of the analysis grid, and does not neces-sarily correspond to an analysis height z . Each tilt isresampled immediately after its scan is completed, an

asynchronous process controlled by the radar scanstrategy. The resampled radial velocity for (x,y, z* ) isthe median of all tilt data that lie within approximate-ly 0.5 km of (x, y,z* ). A median filter is used insteadof a linear filter, because of the possibility of grossdata errors such as point targets. Therefore, this stepalso has a data-quality editing benefit. The radial ve-locities are corrected to account for elevation angle byassuming that the vertical velocity is zero. The magni-tude of the vertical velocity is usually very small ex-cept within strongly convective weather. This excep-tion is accounted for in the volume resampling step.

Volume resampling. This process produces a region-ally representative estimate of the radial componentof the horizontal wind velocity at each analysis posi-tion (x,y,z) from the resampled tilts by either linearinterpolation or extrapolation in the vertical. This is asynchronous process triggered by each winds-analysiscycle. Additional data-quality editing is provided by(1) a buddy check on each tilt of data to remove ques-tionable data values or data that may not be regionallyrepresentative, and (2) removal of data in regions ofhigh reflectivity, since winds within highly convectivestorms may not be regionally representative and thehorizontal wind estimates are likely to be contaminat-ed by a large vertical component.

Multiple-Doppler Techniques

Multiple-Doppler wind-field analysis provides a valu-able starting point in the discussion and developmentof winds-analysis techniques when information fromtwo or more Doppler radars is available. The use ofmultiple-Doppler radars is the only practical methodavailable for obtaining closely spaced measurementsof wind fields in a three-dimensional region. MultipleDoppler analysis can be applied only at points withDoppler information for two independent compo-nents of the wind. When Doppler analysis can be ap-plied, however, the resulting wind estimates are veryaccurate, as discussed below.

The horizontal wind at a point can be estimatedfrom two or more Doppler horizontal wind-compo-nent estimates at that location, if the difference in az-imuth angles is sufficiently large. Least-squares esti-mation is usually used for this purpose. This process isnumerically stable only if the difference in azimuth



angles is sufficiently large so that the radars have atleast two independent estimates of the wind field.Even when the difference in azimuth angles is small,this wind-retrieval process returns one high-qualitywind component, the radial component measured bythe radars; only the azimuthal component is unstable.Techniques are being developed to estimate the azi-muthal component from the motion of features inthe reflectivity field. Work in this area is under way atthe Cooperative Institute for Mesoscale Meteorologi-cal Studies [15] and at the National Center for Atmo-spheric Research (NCAR) [16]. These azimuthal-component analysis techniques are not used in thecurrent implementation. When these techniques aredeveloped to the point that they can be used opera-tionally, they will be included in the Terminal Windssystem as a new source of information.

Multiple-Doppler analysis is the process by whichthe best estimate of the horizontal wind-velocity vec-tor is computed at an analysis position (x, y,z), on thebasis of estimates of the radial velocity produced byresampling the data from two or more Doppler ra-dars. We represent the horizontal wind as a vector(u,v ), where u is the component in the east directionand v is the component in the north direction; how-ever, any orthogonal coordinate system can be used.For an azimuth angle θ, with east at 0° and north at90°, the radar measures a radial velocity r given by

r u v= +cos sin .θ θ

Given two or more Doppler wind component esti-mates, we can write a system of equations with (u,v)as the wind vector to be determined. The system ofequations for two Doppler measurements is given by

cos sin

cos sin.

θ θ

θ θ1 1

2 2

1

2

=

u

v

r

r

To illustrate the mathematical behavior of the so-lution to the multiple-Doppler system of equations,we consider an example with two Doppler estimatesat a point, and simple geometry. Suppose we have tworadars, as shown in Figure 4. The radars make mea-surements r1 and r2, respectively, of the radial compo-nent of the wind at the intersection of the north and

FIGURE 4. Simple geometry for two Doppler radars. Eachradar makes a measurement of the wind at the intersec-tion of the north and east axes. For small values of θ, theu component is nearly the radial component, and the ra-dar measurement contains little information about v.

FIGURE 5. General geometry for two Doppler radars. Themeasurement geometry shown in Figure 4 can always becreated by performing a rotation of coordinates into asuitable coordinate system.

Radar 1

Radar 2

uEast

θ

θ

Northv

–r2

r1

Wind

θ–θ

east axes. For small values of θ, the u component ofthe wind is nearly the radial component and the vcomponent is nearly the azimuthal component. Theradar measurement contains little information aboutv. Similar geometry can always be arranged by using arotation of coordinates to choose a suitable coordi-nate system, as shown in Figure 5.

The dual-Doppler equations for the simple geome-try of Figure 4 are



cos sin

cos sin.

θ θ

θ θ−

=

u

v

r

r1

2(1)

The solution to Equation 1 is

u

v

r r

r r

=+−

( )/ cos

( )/ sin.

1 2

1 2

2

2

θ

θ

Let ueDD and veDD denote the error in the u and vcomponents of the dual-Doppler solution. Let σR

2

denote the average of the error variances for the tworadars. The dual-Doppler error variances, providedthat the radars have uncorrelated errors, are

var( )cos

ueDDR= σ

θ

2

22

and

var( )sin

.veDDR= σ

θ

2

22

As θ approaches zero, the error in the solution for vbecomes numerically unstable. To control this nu-

merical instability, the angle between radar beams,2θ, is generally constrained to be greater than 30°.Figure 6 shows the region where 2θ is greater than 30°for a TDWR/NEXRAD dual-Doppler analysis at theLincoln Laboratory testbed in Orlando.

We now consider the general case of multiple Dop-pler radars. Figure 7 shows an example of a situationin which a given location is covered by three Dopplerradars. In this case the Doppler equations are

cos sin

cos sin

cos sin

, .

θ θ

θ θ

θ θ

1 1

3 3

1

2

3

1

2

3

2 2

=

=

u

v

r

r

r

u

v

r

r

r

or A

The best-estimate solution is provided by leastsquares, given by

u

v

r

r

r

T T

=

−( ) .A A A11

2

3

Even though this system of equations is overdeter-mined, it is not numerically stable unless at least twoof the angles are significantly different.

In this formulation of the least-squares problem,each radar is treated as if it produced radial measure-ments of equal quality. However, many factors can in-troduce unequal errors in the data, such as radar sen-sitivity or the distance from the radar site to theanalysis location. In our wind-field analysis, unequalerrors are accounted for by means of the Gauss-Mar-kov theorem [17].

Terminal Winds Interpolation Technique:Optimal Estimation

The Local Analysis and Prediction System (LAPS),developed by NOAA/FSL, provided the basis for theinitial Terminal Winds prototype. In 1992, LAPS wasthe state-of-the-art operational 10-km-resolutionwinds-analysis system for fusing data from Dopplerradars as well as traditional wind-data sources, nu-merical models, anemometers, MDCRS, and othermeteorological data sources. However, while LAPScan utilize data from more than one Doppler radar, it

FIGURE 6. The shaded region depicts the numericallystable TDWR/NEXRAD dual-Doppler region for theOrlando airport overlaid on the 2-km-resolution analysisdomain.

60

40

20

0

–20

–40

–60–60 –40 –20 0 20 40 60

Distance from Orlando in km70

NEXRAD

Orlando

TDWR



was not designed to take advantage of the large multi-ple-Doppler data sets available in an ITWS. This ini-tial Terminal Winds prototype was demonstrated inreal time in the Lincoln Laboratory Orlando testbedin the summers of 1992 and 1993. The operation ofthis prototype, as well as numerous discussions withFSL, provided valuable insight into traditional winds-analysis techniques. The initial prototype has beensuperseded by the Terminal Winds analysis describedin this article.

The Terminal Winds analysis is dominated byDoppler radar data. In regions with coverage by twoor more radars, the Terminal Winds analysis systemshould provide information about winds with at leastthe quality of the information from the multiple-Doppler analysis discussed earlier. The state-of-the-art analysis technique for non-Doppler meteorologi-cal data analysis is optimal interpolation [18, 19],which is a statistical interpolation technique that un-der certain hypotheses gives an unbiased minimum-variance estimate. In other scientific fields, similarminimum-variance techniques have been used suc-cessfully. In geophysics a technique called Kriging,which is similar to optimal interpolation, is used [20],and in oceanography optimal interpolation is calledthe Gauss-Markov method [21]. We wish to build onthe foundation laid down by the multiple-Doppleranalysis and by these other statistical interpolationtechniques.

We have developed a minimum-variance tech-nique that utilizes Doppler measurements directly.We call this technique optimal estimation to distin-guish it from optimal interpolation. The initial focusis on analyzing horizontal wind data in a three-di-mensional grid; however, the method also applies toother weather variables such as temperature and hu-midity. The method is based on the Gauss-Markovtheorem, and under suitable conditions gives an un-biased minimum-variance estimate of the horizontalwinds. Optimal estimation is an extension of bothoptimal interpolation and multiple-Doppler analysis.The development of optimal estimation is motivatedby the ease with which it incorporates Doppler radardata. Because our software development lags behindour theoretical understanding of optimal estimation,we present only that part of optimal estimation whichhas been tested, leaving a full treatment to a latertime.

Optimal estimation has the following properties:(1) dual-Doppler-quality winds are automaticallyprovided in regions where dual Doppler is numerical-ly stable, (2) small gaps in dual-Doppler radar cover-age are filled to provide near dual-Doppler-qualitywinds in these gaps, and (3) the analysis produceswind vectors that vary smoothly between regions withdata from differing numbers of Doppler radars.

Throughout this section we use the following no-tation conventions: r denotes a radial wind compo-nent, u denotes an east wind component, v denotes anorth wind component, superscript a denotes an ana-lyzed quantity, superscript b denotes a backgroundquantity, superscript o denotes an observed quantity,and subscripts denote location (o denoting an analysislocation).

We seek a linear minimum-variance unbiased esti-mate, and we employ the Gauss-Markov theorem togenerate this estimate. To apply the Gauss-Markovtheorem we need to pose the problem in the form

Ax d= , (2)

where

x = ( )u va a T

0 0, ,

and the data vector

FIGURE 7. Radar geometry for the overdetermined caseof three Doppler radars.

Radar 1NEXRAD

Radar 2TDWR

Radar 3NEXRAD



d = ( )u v u v u v r rob

ob o o

mo

mo o

no T

, , , , , , , , ,1 1 1K K

contains the background estimate at the analysis loca-tion and observations in a data window centered onthe analysis location. The form of the matrix A de-pends on the type of data, vector, or radial to be ana-lyzed. The Gauss-Markov theorem states that the lin-ear minimum-variance unbiased estimate of x is givenby

x A C A A C d= ( ) = ( )− − −u va a T T T0 0

1 1 1, , (3)

if each element of d is unbiased, and C is the errorcovariance matrix for the elements of d. The error co-variance of the solution is

A C AT − −( )1 1. (4)

In the case of m vector observations and n Dopplerobservations, Equation 2 has the form

1 0

0 1

1 0

0 1

1 1 1

M M

M M

M

M

cos sin

cos sin

θ θ

θ θn n

oa

oa

ob

ob

mo

mo

o

no

u

v

u

v

u

v

r

r

=

Unlike the multiple-Doppler analysis, the optimal-estimation solution is always numerically stable be-cause of the inclusion of the background wind esti-mate. The inclusion of a ( , )u vo

bob data point provides

two component estimates at right angles, giving amaximum spread of azimuth angles. Since the errorvariances of the Doppler data are usually much small-er than the error variances of the other data, the opti-mal-estimation solution closely matches the multiple-Doppler solution at locations where the multiple-Doppler problem is well conditioned. Otherwise, theanalysis gives a solution that largely agrees with the

radar observations in the radial component measuredby the radars. The remaining component is derivedfrom the non-Doppler data sources. An example il-lustrating this feature is given in the next section.

In practice, the error covariance matrix C is notknown and must be estimated. There are two types oferrors to estimate. The first is the error that arisesfrom imperfect sensors. The second is the displace-ment error due to taking the measurement at somedistance, in space and time, from the analysis loca-tion. Our initial error models are based on the follow-ing simplifying assumptions: (1) observations are un-biased; (2) sensor errors from different observationsare uncorrelated; (3) errors in u and v components,measured or background, are uncorrelated; (4) dis-placement errors and sensor errors are uncorrelated;and (5) displacement errors are independent of thecomponent being measured.

With these assumptions, the error covariance ma-trix C decomposes into the sum of a sensor-error co-variance matrix and a displacement-error covariancematrix. The sensor-error covariance matrix is diago-nal, and the sensor-error variances are known. The re-maining task is the estimation of the displacement-er-ror covariance matrix.

The initial displacement-error variance model is alinear function of the displacement between the ob-servation location and the analysis location. The ini-tial displacement-error correlation model for two likecomponents is a decreasing exponential function ofthe displacement between two observation locations.The displacement-error covariance model for twononorthogonal, nonparallel components must takeinto account the angle between the two components.We denote the angle between the observed compo-nent and the u axis by θ, with east at 0° and north at90°, and the displacement error in observation i byδi

o . Then the displacement-error covariance for twoobservations is given by the following equation:

cov( , )

cos( ) var( ) var( ) , ,

δ δ

θ θ δ δ δ δ

1 2

1 2 1 2 1 2

o o

o o o o= − cor( )

where cor( )δ δ1 2o o, is the displacement-error correla-

tion model.



Let ρ σ σ= B R2 2/ denote the relative quality of the

radar observations versus the background observa-tions. Typically, ρ is on the order of 10. Then

C− =

12

1

1 0 0 0

0 1 0 0

0 0 0

0 0 0

σ ρ

ρB

.

With these assumptions, the optimal-estimationsolution is computed from Equation 3, giving:

u ur r

oa

ob

o o

= + −+

α αθ

( )cos

121 2

and

v vr r

oa

ob

o o

= + −−

β βθ

( )sin

,121 2

where

αρ θ

ρ ρ θ θ= +

+ +1 2

1 2 4

2

2 2 2

sin

cos sin

and

βρ θ

ρ ρ θ θ= +

+ +1 2

1 2 4

2

2 2 2

cos

cos sin.

The terms 1–α and 1– β represent the fraction ofthe optimal-estimation solution that is given by thesolution to the dual-Doppler equations for the u andv components. If α or β is zero, the correspondingcomponent of the optimal-estimation solution isequal to the dual-Doppler solution, and if α or β is 1,the corresponding component of the optimal-estima-tion solution is equal to the background estimate.

We see that if ρ is large (i.e., the radar error vari-ance is small relative to the error variance of the back-ground) and θ is not near zero, then α and β are nearzero, and the optimal-estimation solution is nearlydual Doppler. If θ = 0, then β = 1, and optimal esti-mation returns a v component equal to the back-ground. In this last case, the u component is the stan-

Illustrative Examples

We illustrate some benefits of optimal estimation byapplying it in two examples for which solutions areeasily computed. The first example demonstratessome advantages of the optimal estimation techniqueover the standard dual-Doppler technique. The sec-ond illustrates the benefit of accounting for correlatederrors that arise from nonuniform data distributions.The ability to account for correlated errors is especial-ly important for a system that utilizes Doppler infor-mation because the Doppler data are often not uni-formly distributed throughout the analysis domain.

For our first example, we compare optimal-estima-tion analysis to dual-Doppler analysis at those pointswith coverage from two radars. We restrict our discus-sion to the case in which we have only a backgroundwind estimate and two Doppler observations at afixed analysis location, as illustrated in Figure 4.

We use the assumptions listed above regarding theerror models. That is, we assume the errors in the uand v components of the background are not correlat-ed with each other or with the error in the radar mea-surements, and we assume that the errors in the radarmeasurements are not correlated. We also assume thatthe error variance is the same for each component ofthe background wind, and that the error variance isthe same for each radar. These are reasonable assump-tions if the Doppler values are average (or median)values over a fixed region surrounding the analysispoint, and the background is independent of theDoppler data. The background is independent of theDoppler data, for example, if the background comesfrom a forecast model or is derived from the radar re-flectivity fields. Let σB be the standard deviation ofthe error in the background components, and let σRbe the standard deviation of the error in the radarmeasurements. This gives the error correlation matrixC , where

C =

σ

σ

σ

σ

B

B

R

R

2

2

2

2

0 0 0

0 0 0

0 0 0

0 0 0

.



and

var( )sin

,veOEB=

+σ

ρ θ

2

21 2(6)

again demonstrating the numerical stability of themethod; the error variance of the optimal-estimationsolution is bounded above by the error variance of thebackground.

Substitution of ρ σ σ= B R2 2/ into Equations 5 and

6 gives

var( )cos

cos cos

ueOEB R

R B

B R

B

R

=+

≤ =

σ σ

σ σ θ

σ σ

σ θ

σ

θ

2 2

2 2 2

2 2

2 2

2

2

2

2 2

(7)

and

var( )sin

sin sin.

veOEB R

R B

B R

B

R

=+

≤ =

σ σ

σ σ θ

σ σ

σ θ

σ

θ

2 2

2 2 2

2 2

2 2

2

2

2

2 2

(8)

These equations show that the error variances of theoptimal-estimation solution are never greater thanthe error variances of the dual-Doppler solution.Combining Equations 5 through 8, we conclude that

var( ) min var( ), var( )u u ueOE eDD eB≤ { }and

var( ) min var( ), var( ) .v v veOE eDD eB≤ { }In the second example we look at an important

benefit of statistical methods such as optimal interpo-lation and optimal estimation—namely, their abilityto handle correctly situations with a significant spatialvariation in the density of observations, resulting inobservations with highly correlated displacement er-rors. For simplicity, we examine an example with asingle variable, and we omit a background estimate.Figure 9 shows an example with three observations.We assume that the sensor errors are equal and uncor-related. Observation 1 is located far from observa-

FIGURE 8. The fractional contribution of the dual-Dop-pler term in the optimal-estimation solution of the v com-ponent, as a function of the angle between radar beams(2θ) and the quantity ρ, which is a measure of the relativequality of the radar observations. If ρ is large and θ is notnear zero, the optimal-estimation solution for v is prima-rily the dual-Doppler solution. If θ is near zero, the dual-Doppler contribution drops to zero.

0 10 20 30 40 50 60 70 80 90

1.0

0.8

0.6

0.4

0.2

0

2 (deg)θ

1

= 50

20

10

1

–β

ρ

dard least-squares solution; the background and Dop-pler values are weighted inversely to their variances.Figure 8 shows how 1–β varies with the angle be-tween the two radar beams (2θ) for different values ofρ. When the angle is greater than about 30°, optimalestimation returns a value for v that is primarily thedual-Doppler solution. As the angle decreases below30°, the weight given to the v component of the dual-Doppler solution drops quickly to zero. In fact, as θdecreases to zero, the quantity

( )sin

121 2−

−β

θ

r ro o

goes to zero, removing the dual-Doppler instabilityfor small θ.

The error variances for the optimal-estimation so-lution, computed from Equation 4, are

var( )cos

ueOEB=

+σ

ρ θ

2

21 2(5)



tions 2 and 3; therefore, its displacement error is near-ly uncorrelated with the displacement errors in theother two observations. To simplify the example, weassume the displacement error in observation 1 is un-correlated with the displacement errors in observa-tions 2 and 3. Observations 2 and 3, on the otherhand, are located close together, so we assume thattheir displacement errors are highly correlated. Ob-servations 2 and 3 are nearly repeat observations, andas such they should not get twice the weight of a sin-gle independent observation, as is the case when errorcorrelations are not accounted for.

Because the observations are equidistant from theanalysis point, we assume that their displacement er-ror variances are equal, and without loss of generalitywe assume that the sum of the sensor-error varianceand the displacement-error variance is equal to onefor each observation. Since we have assumed that theerrors in observation 1 are uncorrelated with the er-rors in observations 2 and 3, the error covariance ma-trix C has the following form:

C =

1 0 0

0 1

0 123

23

c

c

,

where 0 ≤ c 23 < 1. The entry c 23 cannot equal one be-cause the sensor errors are uncorrelated.

To compute the optimal-estimation solution, weinvert C and apply Equation 3, with A = (1 1 1)T.Examination of the weight of each observation gives

wc

cw w

c123

232 3

23

1

3

1

3=

++

= =+

, .

We see that if the errors are assumed to be uncorrelat-ed (i.e., the error correlations are not accounted for),the observations each get weight 1/3. As c 23 increasestoward 1, the weight given to observation 1 increasestoward 1/2, and the weights given to observations 2and 3 decrease toward 1/4, or a combined weight of1/2. This is the desired weighting because if the errorsin observations 2 and 3 are completely correlated, ob-servations 2 and 3 contain the same information.

Operational Experience and Evaluation

Starting in 1992, Lincoln Laboratory has operated anITWS testbed at Orlando International Airport. Thistestbed is a continuation of the Lincoln LaboratoryTDWR testbed that was initiated in 1990. In thesummers of 1992 and 1993 the initial TerminalWinds prototype operated in real time, and in thesummer of 1993 the new optimal-estimation-basedTerminal Winds prototype operated in real time. Theevaluation results presented here are from data col-lected in 1992 and 1993 at the Orlando testbed.

The wind-data sources in the Orlando testbed arethe Mesoscale Analysis and Prediction System(MAPS), which is a prototype of the RUC system;the TDWR prototype Doppler radar at Kissimmee,Florida, 10 km south of Orlando; the NEXRADDoppler radar at Melbourne, Florida, 65 km south-east of Orlando; MDCRS-equipped aircraft observa-tions; the LLWAS anemometer network; the ASOSautomatic observing stations; and Surface AviationObservations (SAO) hourly observations.

The Doppler radars complete their volume scansevery five to six minutes. The ASOS stations provideupdates every twenty minutes, and the LLWAS ane-mometers provide updates every ten seconds. TheLLWAS network is located at the airport and containsfourteen sensors with a spacing of 2 to 3 km. TheSAOs are updated on the hour. The MDCRS reportsoccur with variable spacing, averaging about ten per

Analysis point

Observation 1

Observation 2

Observation 3

FIGURE 9. Nonuniform data distribution gives rise tocorrelation errors. Observation 1 is located far from ob-servations 2 and 3, so its displacement error is nearlyuncorrelated with the displacement errors in the othertwo observations, which are close together and arehighly correlated. The statistical analysis methods of op-timal interpolation and optimal estimation account forthe error correlations caused by this distribution.



chive. These days were chosen to include a variety ofweather, and good comparison data.

Statistics for a number of performance metricshave been compiled. We report statistics only for thenorm of the vector difference between the analysesand forecasts and the comparison observations. Threecomparison observation data sets were used—MDCRS reports, Cross-Loran Atmospheric Sound-ing System (CLASS) soundings, and TDWR andNEXRAD dual-Doppler wind fields. These compari-son data sets are discussed in detail below.

Results are presented for two analyses and oneforecast: Terminal Winds 2-km resolution, TerminalWinds 10-km resolution, and MAPS. Comparisonsbetween analyzed and forecast wind fields and ob-served winds were constrained to the 2-km grid toensure consistent evaluation data sets and becauseproduct accuracy is paramount in this region. Weused bilinear interpolation of the Terminal Winds 10-km analyses and MAPS forecasts to the 2-km grid.For each analysis, the observations were compared tothe wind vector from the 2-km grid point nearest theobservation.

Although each of the three comparison data sets istreated as a standard against which the analyzed windfields are judged, it is important to keep in mind thatno observation is perfect. The performance of eachalgorithm is referred to as “relative to MDCRS,” forexample, keeping explicit that any conclusions wedraw are subject to the error characteristics of thecomparison observations, as well as the error charac-teristics of the analysis. We cannot expect the com-parison with independent observations, on average,to be less than the average magnitude of the sensorerror. This limits the ability of the comparison to dis-cern product accuracy to the accuracy of the compar-ison observations.

The characterization of a “perfect” local windsanalysis has not been made. In particular, the desireddegree of smoothing of the wind field has not beenspecified. At any given instant, a wind field is a super-position of wind structures with a wide spectrum ofspatial and temporal scales. For a given application,some of these structures are at scales that are unim-portant, and other structures are too small or shortlived to be captured by the analysis. These subscale

hour during the hours of peak aircraft operation.Figure 10 shows the analysis domains and sensor

locations for the 1992 Orlando Terminal Winds anal-ysis. The 10-km and 2-km analysis regions are shownas squares centered on the airport. The dimensionsare 180 km × 180 km and 120 km × 120 km, respec-tively. In 1993 the 10-km analysis region was in-creased to 240 km × 240 km. The background fieldfor the 10-km analysis was derived from the wind es-timates on the 6 × 6 sub-domain of the MAPS gridthat contains the 10-km-resolution grid. The TDWRradar is located near the center of the 2-km domain,and the NEXRAD radar is located near the southeastcorner of the 2-km domain. Aircraft reports wereavailable primarily along arrival and departure routes,to the north and south of the airport.

The basis of the evaluation is the comparison ofobservations with analyzed and forecast winds atnearly coincident points. This amounts to spotchecks, since we cannot control the availability of ob-servations, except to select days on which they wereplentiful. Each algorithm was evaluated on a twenty-day subset of the 1992 and 1993 Orlando data ar-

FIGURE 10. Analysis domains and sensor locations forthe 1992 Orlando Terminal Winds analysis. The 180 x 180-km analysis region (10-km-resolution grid) and the 120 x120-km analysis region (2-km-resolution grid) are shownas squares centered on the airport.

Surface stationDoppler radarMAPS grid

10-km-resolution grid

2-km-resolution grid



features may influence an observation, however.When these observations are compared with the anal-ysis, the differences reflect errors in the analysis, errorsin the observation, and the structure of the subscalefeatures captured in the observations. Given the lim-ited set of observations used in the evaluation, wehave not attempted to separate the effects of the dif-ferent sources of error.

Comparison Observation Data Sets

There are three types of comparison observationsused in the evaluation. Two of these—MDCRS ob-servations and CLASS soundings—are independentof the associated analysis fields. The independence ofMDCRS is explained in the next paragraph. Thethird type of comparison observation—dual-Dopplerwinds based on TDWR and NEXRAD—is not inde-pendent of the analyzed wind fields because both theTerminal Winds analysis and the dual-Doppler analy-sis are derived from the same Doppler radar data, in-cluding similar data-quality editing.

Despite the fact that MDCRS observations are in-puts to the analysis, they are independent of the ana-lyzed wind fields to which they are compared. TheMDCRS observations are used as inputs to the 10-km analysis, but are always at least fifteen minutes oldby the time they are assimilated. MDCRS-observedwinds are compared with the corresponding analysiswinds at the analysis update time closest to theMDCRS measurement time, not the MDCRS assim-ilation time. This time delay results in comparing theMDCRS observation to an analysis computed beforethe MDCRS report was available to the TerminalWinds system. MDCRS observations are quite sparsein space and time (approximately five per hour in the2-km analysis domain in which the evaluation wasperformed). They offer the advantage that they are lo-cated where aircraft operate and thus are relevant toair traffic concerns. Preliminary results from a studyconducted by the NOAA FSL indicate that MDCRSobservations have an rms vector error of approximate-ly 4 m/sec.

Table 4. Height Distribution for the Three Observational Data Sets

Level Nominal Altitude MSL Observational Data Set(mb) (feet)

MDCRS CLASS Dual Doppler

500 18,290 4 9 0

550 15,960 79 7 29k

600 13,800 61 10 31k

Sample 650 11,780 87 9 27k

Size 700 9880 104 10 25k

per 750 8090 98 12 31k

Level 800 6390 52 12 30k

850 4780 63 10 22k

900 3240 91 10 77k

950 1770 96 11 337k

1000 360 0 4 3k

Totals 735 104 612k



The University of Massachusetts–Lowell launchedCLASS rawinsondes during August 1992 from theUniversity of North Dakota radar site located slightlyeast of the Orlando airport. Several soundings had tobe omitted because of poor data quality or because ofballoon position alignment errors. For the evaluation,seven CLASS soundings were judged acceptable, rep-resenting seven vertical profiles with a total effectivesample size of roughly one hundred data points. Theaccuracy of rawinsonde wind-speed observations,measured by rms error, is typically 3 m/sec. For winddirection, the accuracy is typically 14° when the truewind speed exceeds 5 m/sec [22].

When two Doppler measurements exist at a givenlocation, a wind vector can be reliably recovered fromthe two measured components, assuming certain geo-metrical constraints are satisfied. The dual-Dopplercomputations were performed only in regions wherethe angle between the TDWR and NEXRAD radarbeams is greater than 30° and less than 150° to avoidnumerical instability. Data from high-reflectivity re-gions were additionally eliminated, since wind-veloci-ty variations in convective weather make it difficult tocharacterize a 2-km cell by a single representative val-ue. Also, the interpolation and extrapolation limits in

FIGURE 11. Cumulative probability distribution for windspeeds in the MDCRS, CLASS soundings, and dual-Doppler analysis data sets.

the volume resampler were reduced by a factor of twoto reduce errors introduced during the transforma-tion from radar coordinates to Cartesian coordinates.Finally, no tilts with elevation angle above 20° wereused in order to limit the error from sampling the ver-tical component of the wind. We do not have a suffi-ciently accurate set of wind measurements to establishthe accuracy of our dual-Doppler winds empirically;however, theoretical arguments show that the rmsvector error is approximately 2.4 m/sec.

Table 4 shows the height distribution for theMDCRS, CLASS soundings, and dual-Doppler anal-ysis data sets. Both MDCRS and CLASS are fairlyuniformly distributed in altitude. The dual-Dopplerwind vectors are fairly uniformly distributed in alti-tude above 4000 feet, with a significant abundancecloser to the ground. Only a few dual-Doppler windvectors are at 1000 mb because of a very small regionof overlap in radar coverage at this altitude. Figure 11gives the cumulative probability distribution for windspeeds of the observations in the three comparisondata sets. For example, Figure 11 shows winds speedsof 5 m/sec or less for approximately 57% of theMDCRS data, 40% of the CLASS soundings data,and 45% of the dual-Doppler wind vectors.

FIGURE 12. Cumulative probability distribution for thenorm of the vector difference between the MDCRS re-ports and each of the three sets of wind fields.

Terminal WindsMAPS 10 km 2 km

0

100

Norm of the vector difference (m/sec)1 2 3 4 5 6 7 8 9 10 11 12 13

Per

cen

t

80

60

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MDCRSCLASS soundingsDual Doppler



Unlike dual Doppler, the presence of MDCRS andCLASS observations is not correlated with the type ofweather. These data sets are too small to be parti-tioned by weather type, so the results of the compari-son with MDCRS and CLASS represent an averageover all the weather situations occurring duringMDCRS and CLASS data collection.

Figures 12, 13, and 14 are plots of cumulativeprobability distributions for the norm of the vectordifference between each analysis and forecast, andeach of the three sets of comparison observation datasets. For example, Figure 12 shows that the vector dif-ference between MAPS forecasts and MDCRS is 5m/sec or less about 70% of the time. Table 5 gives theRMS and median values for the norm of the vectordifferences between the analyses and forecasts, andthe comparison observations.

Figures 12 and 13 provide the comparisons of theTerminal Winds analyses and the MAPS forecasts toMDCRS and CLASS observations, respectively.These comparisons (summarized in Table 5) indicatethat both the 2-km and 10-km analyses consistentlyhave better agreement with the observations than dothe MAPS forecasts. These comparisons do not indi-cate that the 2-km analysis provides an improvement

FIGURE 13. Cumulative probability distribution for thenorm of the vector difference between the CLASSsoundings and each of the three sets of wind fields.

FIGURE 14. Cumulative probability distribution for thenorm of the vector difference between the dual-Doppleranalysis and each of the three sets of wind fields.


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Evaluation Results

The statistical evaluation indicates how well the Ter-minal Winds algorithm matches the comparisonobservations over a large period of time. Statistics col-lected over a large period of time do not allow perfor-mance quantification for different weather situations.For example, when the winds are relatively uniform, a2-km analysis is not expected to perform better than a10-km analysis, since the wind field does not containstructures smaller than tens of kilometers. When thewind fields are more complex, we expect to see a vari-ation in performance.

The comparison with dual-Doppler observationsdid not target specific weather situations; however,the majority of the dual-Doppler observations are inthe PBL, and they are more numerous in regions ofmoderate reflectivity. Complex wind fields are expect-ed in the PBL and during convection, so the results ofthe comparison with dual Doppler are indicative ofalgorithm performance when small-scale wind fea-tures are present in the atmosphere. In addition, wediscuss an example in the next section that qualita-tively indicates the differences in the two scales ofanalysis during convection.

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observations in the PBL, and relatively more Dopplerreturns are available during and near convectiveweather than in weather with more clear air. Thus thedual-Doppler data set contains observations in re-gions where MAPS is not expected to perform well.The relationship between the optimal-estimation al-gorithm and the dual-Doppler algorithm is also inevidence. Because care was taken to ensure that dual-Doppler winds were produced only when good Dop-pler data were available, and only in regions where thedual-Doppler process is numerically stable, the abilityto match the dual-Doppler winds is important.

An Example

The bulk statistics reported above address the ques-tion of how the different analyses perform on average.However, there are differences in the analyses that arenot explored by this type of evaluation. In this sectionwe give an example that shows the ability of the dif-ferent winds analyses to capture important small-scalewind-field structures. We discuss the 2-km-resolutionand 10-km-resolution Terminal Winds analyses andMAPS forecast fields for two time periods on the af-ternoon of 20 August 1992. The behavior discussed istypical for convective weather situations.

Each figure discussed in this example shows an an-alyzed wind field at approximately 1800 feet MSL inthe region covered by the 2-km analysis. Each windfield is displayed on a 4-km-resolution grid to aid thecomparison. The 4-km grid was chosen to avoid visu-al clutter. The wind vectors are scaled to wind speed,with a 5-m/sec reference vector shown in the upperright corner. The Orlando airport is at the center ofthe wind field, the coast of Florida is shown along theright, and the outlines of four lakes are shown. Thecolored background indicates the radar reflectivity.

Figure 15 shows three wind fields for 22:10 Green-wich mean time (GMT). A gust front and its associat-ed reflectivity thin line can be seen to the east of theairport. This gust front was generated from a stormeast of the coast. A convergence pocket in the windfield exists southwest of the airport. Just after thisconvergence pocket developed, a storm began to format this location. The convergence strengthened alongwith the reflectivity associated with the growingstorm. This coupling of convergence and storm

Table 5. Root Mean Square and Median(in Parentheses) Values for the Norm of the

Vector Difference between the TerminalWinds Analyses and MAPS Forecasts, and

the Three Comparison Observations (m/sec)

2 km 10 km MAPS

MDCRS 4.1 (3.1) 3.8 (2.8) 4.6 (3.6)

CLASS 2.9 (2.2) 2.7 (2.2) 3.7 (3.0)

Dual Doppler 2.0 (1.0) 3.8 (2.6) 5.4 (4.1)

over the 10-km analysis. This result is not too surpris-ing, since these comparisons are over all weather situ-ations. The similarity in performance of the twoscales of analysis may also reflect that we have reachedthe limit of these data sets to discern algorithm per-formance. Against MDCRS, the two analyses haveapproximately a 4 m/sec rms error, and againstCLASS they have approximately a 3 m/sec rms error,which are the reported RMS accuracies of theMDCRS and CLASS observations. The wind fields,including MAPS forecasts, agree more closely withthe CLASS soundings than with the MDCRS re-ports. This closer agreement may be due to superioraccuracy of the CLASS sounding measurements, or itmay be due to the expected variation in the statisticswhen small data sets are used.

The comparison with the dual-Doppler windsanalysis provides greater distinction between the vari-ous analyses; the 2-km analysis matches the dual-Doppler winds more closely than the 10-km analysis.The rms vector difference between the 2-km analysisand the dual-Doppler wind vectors (as shown in Ta-ble 5) is less than the theoretical rms vector error ofthe dual-Doppler winds (2.4 m/sec), reflecting thestatistical dependence between the two estimates ofthe wind field. Both the 2-km and 10-km TerminalWinds analyses show a greater improvement overMAPS forecasts than they show in the comparisons toMDCRS. This improvement is expected. The dual-Doppler data set contains observations from morecomplex wind fields than the other two comparisondata sets, since the Doppler data are dominated by



(a) (b)

(c)

FIGURE 15. Wind-field analyses around Orlando on 20 August 1992 at22:10 Greenwich mean time (GMT). (a) The 2-km-resolution optimal-estimation wind field, (b) the 10-km-resolution optimal-estimationwind field, and (c) the MAPS wind field. Each of these wind fields isdisplayed on the same 4-km-resolution grid for comparison. OrlandoInternational Airport is at the center of each grid, and the east coastof Florida is shown at the right. The wind vectors are scaled to windspeed, with a 5-m/sec reference vector shown in the upper right cor-ner of part c.



(a) (b)

(c)

FIGURE 16. Wind-field analyses around Orlando on 20 August 1992 at23:10 GMT, one hour after the wind fields shown in Figure 15. (a) The2-km-resolution optimal-estimation wind field, (b) the 10-km-resolu-tion optimal-estimation wind field, and (c) the MAPS wind field. Eachof these wind fields is displayed on the same 4-km-resolution grid forcomparison. Orlando International Airport is at the center of eachgrid, and the east coast of Florida is shown at the right. The wind vec-tors are scaled to wind speed, with a 5-m/sec reference vector shownin the upper right corner of part c.



growth continued at various locations for the remain-der of the afternoon. The lifting of water vapor in theatmosphere, and the resulting release of heat as thewater vapor cools, is the driving force behind the for-mation of thunderstorms. Forecasting the formationof these storms requires that the wind-field conver-gence, and hence the vertical motion of the air, becorrectly analyzed.

The 2-km-resolution Terminal Winds analysisshown in Figure 15(a) provides an excellent resolu-tion of both the wind-field convergence associatedwith the gust front, and the convergence pocketsouthwest of the airport. The 10-km-resolution Ter-minal Winds analysis shown in Figure 15(b) capturesthese features, but underestimates the magnitude ofthe convergence and is missing the detail contained inthe finer-resolution analysis. The MAPS forecast fieldshown in Figure 15(c) is not well correlated with theTerminal Winds analyses.

Figure 16 shows wind fields for 23:10 GMT, anhour later than the wind fields shown in Figure 15.The storm system generated by the convergencepocket seen at 22:10 GMT has grown into a large,strong convective storm that has evolved to the north-east of its original position. The 2-km-resolution Ter-minal Winds analysis shown in Figure 16(a) showstwo regions of strong winds, northwest and southeastof the airport. The winds southeast of the airport be-gan with the convergence pocket that existed at 22:10GMT, and they started to die off after this time. Thewinds began to pick up in the region northwest of theairport at 22:40 GMT. These winds strengthened asthe region of surface-wind convergence moved northalong with the storm, and continued beyond the endof the day (24:00 GMT). The winds behind the gustfront remained, although the gust-front thin line dis-appeared when the gust front collided with the stormsystem. The convection continued to build in the re-gion of convergence that extends toward the northernboundary of the analysis. The 10-km-resolution Ter-minal Winds analysis shown in Figure 16(b) capturesthe general tendency of this convergence, but under-estimates the strength of the stronger winds and thestrength of the convergence. Again the MAPS fore-cast field shown in Figure 16(c) is not well correlatedwith the Terminal Winds–analyzed wind field.

Future Work

Two types of future work are discussed below. Thefirst is analysis enhancements, including improve-ments to Terminal Winds and the development of agridded temperature analysis. The second is real-timedemonstrations at selected airports.

Analysis Enhancements

The ITWS gridded analysis system will undergo con-tinued refinement and testing. A number of analysisupgrades are planned, including the use of the lastanalysis to refine the background wind field, the esti-mation and removal of errors arising from using anobservation at locations away from the observationlocation, and the use of ITWS gust-front detectionsto increase the wind-field accuracy by suppressing av-eraging across the gust-front boundaries. A major ef-fort will be undertaken to add surface forcing to re-fine the winds in the PBL, which is important forregions with coverage from only a single Doppler ra-dar or with significant topographical variation. Weare also assessing the ability of developing technolo-gies to derive wind information from time variationsin the radar reflectivity fields [15, 16]. When suffi-ciently developed, these technologies will be an im-portant new source of wind information.

Accurate error models are required to ensure thesuccess of any statistical technique. The volume ofdata at an ITWS site is not sufficient to estimate errormodels in real time; instead, we utilize a priori errormodels. Our current error models are qualitativelycorrect but can be refined on the basis of extensiveexamination of observed winds. A survey of the litera-ture shows that past studies were conducted to con-struct error models for analyses with national or glo-bal domains in which observation separations are onthe order of hundreds to thousands of kilometers.The results of these studies are not appropriate to er-ror models for the Terminal Winds scale of analysis.We now have an archive of data including data fromtwo summers and one winter in Orlando, and onesummer in Memphis. We will use these data to con-struct quantitatively correct error models.

Starting in the summer of 1995, we will begin todevelop a gridded temperature analysis. This analysis



will use a scalar version of the optimal-estimationwinds analysis. The initial temperature-analysis sys-tem will use information from the RUC, MDCRS,and surface reports. The information from thesesources will support a temperature analysis on theTerminal Winds 10-km-resolution grid. The temper-ature field and wind field are linked through physicalprocesses. In an ITWS the wind field is known moreprecisely than the temperature field, so the knowledgeof the wind field can be exploited to refine the tem-perature field. Current research at the University ofOklahoma and at NCAR provides techniques to re-trieve temperature fields from wind fields. After de-velopment of the initial temperature analysis, we willassess the ability of the temperature retrieval to refinethe temperature field.

Real-Time Demonstrations

A number of real-time demonstrations are planned.The ITWS had an FAA Demonstration and Evalua-tion at Memphis during the spring and summer of1994, and at Orlando during the winter of 1995. TheDemonstration and Evaluation continues at Dallas–Fort Worth in the summer of 1995 in conjunctionwith the Terminal Air Traffic Control Automation–Center TRACON Advisory System, which is the pri-mary initial customer of the Terminal Winds infor-mation, and at Memphis. These Demonstration andEvaluation exercises will provide valuable testing in avariety of meteorological environments.

Summary

The Terminal Winds analysis is an important compo-nent of the ITWS. The Terminal Winds provides anaccurate, high-resolution analysis of the horizontalwinds in a three-dimensional grid in the terminalarea. The wind information from this system is pro-vided to a number of users, including air traffic auto-mation systems and other ITWS algorithms. Termi-nal Winds combines wind information from anational-scale numerical-forecast model, meteorolog-ical Doppler radars, commercial aircraft, and ane-mometer networks. It is flexible enough to run reli-ably with any available subset of these data, addingvalue to the national winds forecast in the terminalarea as local sensors provide information. The Termi-

nal Winds system operated in the summers of 1992and 1993 and the winter of 1995 in the Lincoln Lab-oratory ITWS testbed at Orlando, Florida, and in thespring and summer of 1994 at Memphis. The Termi-nal Winds system has demonstrated that it is a reli-able operational system incorporating data from mul-tiple sources, including operational TDWR andNEXRAD Doppler radars.

The terminal airspace extends from the surface to18,000 feet above ground level, and is divided intotwo regimes. The planetary boundary layer (PBL)contains the atmosphere near the Earth’s surface, andoften contains wind structures with spatial scales onthe order of kilometers and temporal scales on the or-der of minutes. Above the PBL, wind structures typi-cally have spatial scales of at least tens of kilometersand temporal changes occur over at least tens of min-utes. Doppler radars provide high-resolution infor-mation in the PBL, where small-scale wind structuresare expected. Above the PBL, Doppler informationbecomes more sparse and the RUC and MDCRS areimportant sources of additional information. A cas-cade-of-scales analysis is used to capture these differ-ent scales of atmospheric activity.

A new winds-analysis technique, optimal estima-tion, was developed for the Terminal Winds product.This technique is an extension of both optimal inter-polation and multiple-Doppler analysis. Under cer-tain restrictive hypotheses, high-quality estimates ofthe horizontal winds can be derived from multiple-Doppler data sets. The ITWS will usually have datafrom at least two Doppler radars. Optimal interpola-tion, a statistical interpolation technique, is used inthe current state-of-the-art operational non-Dopplerwinds analysis. Optimal estimation provides wind es-timates that are of higher quality than multiple-Dop-pler analysis and does not suffer from the numericalinstabilities that arise in multiple-Doppler analysis.The optimal-estimation analysis also produces windvectors that vary smoothly between regions with cov-erage from differing numbers of Doppler radars.

The ITWS gridded analysis system will undergocontinued refinement and testing. A number of anal-ysis upgrades are planned, including the use of thelast analysis to refine the background wind field, theestimation and removal of errors arising from estimat-



ing winds at locations removed from the observationlocation, and the use of ITWS gust-front detectionsto increase the wind-field accuracy. A major effortwill be undertaken to add surface forcing to refine thewinds in the PBL. We are also assessing the ability ofdeveloping technologies to derive wind informationfrom radar reflectivity fields. When sufficiently devel-oped, these technologies will be an important newsource of wind information.

Acknowledgments

A number of people at NOAA/FSL provided impor-tant contributions to the Terminal Winds effort. Inparticular, we thank John McGinley and Steve Albersfor the generous use of their Local Analysis and Pre-diction System code to build our initial prototype,and their many comments and general support. Wealso thank Thomas Schlatter and Stan Benjamin forproviding wind forecasts from the Mesoscale Analysisand Prediction System. We thank the Melbourne Na-tional Weather Service Office for access to theNEXRAD base data. Providing this access was nomean feat. We also thank Russ Bolton and Jerry Starrat Computer Science–Raytheon for modifying theirdatabase to provide the off-airport ground-stationdata in our analysis region. Finally, we thank theLLWAS program office for expediting the installationof the LLWAS-3 anemometer network at the OrlandoInternational Airport.

The development of the Terminal Winds systemrepresents the combined efforts of a number of Lin-coln Laboratory employees. Significant contributionswere made by Steve Olson, Sue Yao, Cindy McLain,Russell Todd, Steve Kim, William Comery, Jim Cap-pucci, Gary Rasmussen, and Steve Finch.

R E F E R E N C E S1. Seagull Technology, Inc., “Center-TRACON Automation

System–Description to Support an Operational ConceptDocument,” 90112-03 (1990).

2. F.W. Wilson, J. Keller, R.G. Rasmussen, and P. Zwack, “ITWSCeiling and Visibility Products,” Fifth Int. Conf. on AviationWeather Syst., Vienna, VA, 2–6 Aug. 1993, p. 51.

3. J.E. Evans and E.R. Ducot, “The Integrated Terminal WeatherSystem (ITWS),” Linc. Lab. J., in this issue.

4. R. Cole, F.W. Wilson, J.A. McGinley and S.C. Albers, “ITWSGridded Analysis,” Fifth International Conference on AviationWeather Syst., Vienna, VA, 2–6 Aug. 1993, p. 56 (1993).

5. S.R. Finch, R.E. Cole, R.G. Rasmussen, F.W. Wilson, andS. Kim, “Summer 1992 Terminal Area—Local Analysis andPrediction System (T-LAPS) Evaluation,” ATC-218, MITLincoln Laboratory (7 Oct. 1994), DOT/FAA/RD-94/13.

6. S.C. Albers, “The LAPS Wind Analysis,” Fourth Workshop onOperational Meteorology, Whistler, BC, Canada (1992).

7. J. McGinley, S. Albers, and P. Stamus, “Validation of a Com-posite Convective Index as Defined by a Real-Time LocalAnalysis System,” Weather Forecast 6, 337 (1991).

8. M.W. Merritt, D. Klingle-Wilson, and S.D. Campbell, “WindShear Detection with Pencil-Beam Radars,” Linc. Lab. J. 2,483 (1989).

9. T.D. Crum, R.L. Alberty, and D.W. Burgess, “Recording,Archiving, and Using WSR-88D Data,” Bull. Amer. Meteor.Soc.. 74, 645 (1993).

10. S.G. Benjamin, K.A. Brewster, R. Brümmer, B.F. Jewett, T.W.Schlatter, T.L. Smith, and P.A. Stamus, “An Isentropic Three-Hourly Data Assimilation System Using ACARS AircraftObservations,” Mon. Weather Rev. 119, 888 (1991).

11. F.W. Wilson and R.H. Gramzow, “The Redesigned Low LevelWind Shear Alert System,” Fourth Int. Conf. on AviationWeather Syst., Paris, 24–28 June 1991, p. 370.

12. ASOS Program Office Staff, “Automated Surface ObservingSystem Users Guide–Preliminary,” National Weather ServiceASOS Program Office, 84 pp. (1991). [Available from NWSASOS Program Office, Silver Spring, MD 20910.]

13. K.A. Brewster, S.G. Benjamin, and R. Crawford, “QualityControl of ACARS Meteorological Observations—A Prelim-inary Data Survey,” Preprints, Third Int. Conf. on AviationWeather Syst., Anaheim, CA, 30 Jan.–3 Feb. 1989, p. 124.

14. L. Armijo, “A Theory for the Determination of Wind and Pre-cipitation Velocities with Doppler Radars,” J. Atmospheric Sci-ences 26, 570 (1969)

15. C.-J. Qui and Q. Xu, “A Simple Adjoint Method of WindAnalysis for Single-Doppler Data,” J. Atmos. Oceanic Technol.9, 588 (1992).

16. J.D. Tuttle and G.B. Foote, “Determination of the BoundaryLayer Airflow from a Single Doppler Radar,” J. Atmos. OceanicTechnol. 7, 218 (1990).

17. D.G. Luenberger, Optimization by Vector Space Methods(Wiley, New York, 1969).

18. L.S. Gandin, “Objective Analysis of Meteorological Fields,”Leningrad, translated by Israel Program for Scientific Transla-tions, Jerusalem, 1965 (1963).

19. R. Daley, “Atmospheric Data Analysis” (Cambridge UniversityPress, Cambridge, UK, 1991).

20. F.P. Bretherton and J.C. McWilliams, “Estimations from Irreg-ular Grids,” Reviews of Geophysics and Space Physics 18, 789(1980).

21. A.F. Bennett, “Inverse Methods in Physical Oceanography”(Cambridge University Press, Cambridge, UK, 1992).

22. M. Cairns et al., “A Preliminary Evaluation of Aviation-ImpactVariables Derived From Numerical Models,” NOAA Tech.Memo. ERL FSL-5 (1993).



. is a staff member in theWeather Sensing group. Hisresearch interests are in auto-mated weather analysis andforecast algorithms, and linearand nonlinear optimization.He received a B.S. degree witha double major in mathematicsand physics from the VirginiaPolytechnic Institute and StateUniversity (VPI), an M.S.degree in mathematics fromVPI, and a Ph.D. degree inmathematics from the Univer-sity of Colorado at Boulder.Before joining Lincoln Labora-tory in 1990, he worked at theNational Center for Atmo-spheric Research. His firstproject as a staff member atLincoln Laboratory was to leadthe integration of the TerminalDoppler Weather Radar(TDWR) system and the LowLevel Wind Shear Alert Sys-tem (LLWAS) III, which iscurrently being installed in thefield.

. is a staff member in theWeather Sensing group. Hisprimary focus of research is inthe development of weathernowcast algorithms. He re-ceived B.S. and Ph.D. degreesin mathematics from theUniversity of Maryland. Hewas an assistant professor ofmathematics at Brown Univer-sity in 1965 and the Universityof Michigan in 1966, and aprofessor of mathematics atthe University of Colorado atBoulder from 1967 to 1987.Before joining Lincoln Labora-tory in 1990 he worked at theNational Center for Atmo-spheric Research. In 1992 Wesreceived the Aviation WeekLauriat Award for his inven-tion of the Low Level WindShear Alert System (LLWAS)III, which was credited withsaving a commercial aircraftfrom a wind-shear crash inDenver on 8 July 1989.

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