Rodney E. Cole and F. Wesley Wilson

Transcription

1 The Integrated Terminal Weather System Terminal Winds Prduct Rdney E. Cle and F. Wesley Wilsn The wind in the airspace arund an airprt impacts bth airprt safety and peratinal efficiency. Knwledge f the wind helps cntrllers and autmatin systems merge streams f traffic; it is als imprtant fr the predictin f strm grwth and decay, burn-ff f fg and lifting f lw ceilings, and wake vrtex hazards. This knwledge is prvided by the Integrated Terminal Weather System (ITWS) gridded wind prduct, r Terminal Winds. The Terminal Winds prduct cmbines data frm a natinal numerical weather-predictin mdel, called the Rapid Update Cycle, with bservatins frm grund statins, aircraft reprts, and Dppler weather radars t prvide estimates f the hrizntal wind field in the terminal area. The Terminal Winds analysis differs frm previus real-time winds-analysis systems in that it is dminated by Dppler weather-radar data. Terminal Winds uses an analysis called cascade f scales and a new winds-analysis technique based n least squares t take full advantage f the infrmatin cntained in the diverse data set available in an ITWS. The weather radars prvide sufficiently fine-scale winds infrmatin t supprt a -km hrizntal-reslutin analysis and a five-minute update rate. A prttype f the Terminal Winds analysis system was tested at Orland Internatinal Airprt in 199, 1993, and 1995, and at Memphis Internatinal Airprt in The field peratins featured the first real-time winds analysis cmbining data frm the Federal Aviatin Administratin TDWR radar and the Natinal Weather Service NEXRAD radar. The evaluatin plan is designed t capture bth the verall system perfrmance and the perfrmance during cnvective weather, when the fine-scale analysis is expected t shw its greatest benefit. ATMOSPHERIC CONDITIONS in the terminal area have a significant impact n airprt peratins and safety. A number f Federal Aviatin Administratin (FAA) systems under develpment t imprve airprt safety and capacity require knwledge f the wind and ther atmspheric variables. These systems include (1) the Center TRA- CON Advisry System (CTAS) t autmate air traffic cntrl t ptimize fuel cnsumptin, scheduling, and aircraft merging and separatins [1]; () the Wake Vrtex Advisry System (WVAS) t reduce aircraft separatins fr wake vrtex avidance; (3) the Integrated Terminal Weather System (ITWS) windshift and runway-winds predictin systems t predict wind shifts frm gust frnts and ther surces that lead t runway recnfiguratin; (4) the ITWS lw ceiling and visibility predictins []; and (5) the ITWS cnvective strm grwth-and-decay predictins. Figure 1 illustrates the different aviatin systems, and shws where in the terminal airspace each system has the mst impact and utility. Currently in develpment by the FAA, ITWS will prduce a fully autmated, integrated terminal weather infrmatin system t imprve the safety, efficiency, and capacity f terminal-area aviatin peratins [3]. This system will acquire data frm FAA and VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 475

2 Natinal Weather Service radar sensrs as well as frm aircraft in flight in the terminal area, and it will prvide air traffic cntrl persnnel with weather infrmatin prducts that are immediately usable withut further meterlgical interpretatin. These prducts include current terminal-area weather and shrt term (zer t thirty minute) predictins f significant weather phenmena. The ITWS gridded analysis system will prvide current-time estimates and shrt-term frecasts f wind, temperature, misture, and atmspheric pressure at each pint in a three-dimensinal grid in the terminal area. Estimates f these quantities are currently prduced by natinal-scale frecast mdels at the Natinal Weather Service, althugh these natinal-scale mdels are n carse grids in space and time, relative t airprt peratins. T supprt the special requirements f aviatin systems, the ITWS gridded analysis system will imprve the reslutin and timeliness f the estimates frm the natinal-scale mdels by incrprating additinal infrmatin frm terminal-area sensrs. We have cncentrated ur initial develpment effrts n gridded hrizntal winds, with a gridded temperature analysis t fllw. There are three reasns fr chsing this sequence f develpment: (1) hrizntal winds and wind changes have a direct impact n aviatin peratins and in the autmated aviatin systems mentined abve; () high-reslutin hrizntal wind data are prvided by meterlgical Dppler radars (each ITWS is expected t have data frm at least ne Dppler radar, and ften tw r mre, which makes winds analysis tractable in the near term); and (3) hrizntal winds are an imprtant factr in many meterlgical prcesses because they cntribute t the transprt f mmentum, heat, and Strm grwth-and-decay predictins Ceiling and visibility predictins FAA displays Wind-shift predictins Wake Vrtex Advisry System (WVAS) Center TRACON Advisry System (CTAS) Runway-winds predictins FIGURE 1. Aviatin systems supprted by the ITWS gridded hrizntal winds prduct, r Terminal Winds. Systems requiring Terminal Winds infrmatin are being develped t autmate air traffic cntrl t ptimize fuel cnsumptin, scheduling, and aircraft separatin (the Center TRACON Advisry System, r CTAS); reduce aircraft separatin fr wake vrtex avidance (the Wake Vrtex Advisry System, r WVAS); predict wind shifts frm gust frnts and ther surces that wuld lead t runway recnfiguratin (the ITWS wind-shift and runway-winds predictin systems); predict the nset and dissipatin f fg and lw-ceiling cnditins; and predict strm grwth and decay. 476 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

3 RUC MDCRS ASOS ASOS MDCRS ASOS ASOS ASOS TDWR LLWAS NEXRAD FIGURE. Data surces fr Terminal Winds. These surces are a natinal-scale frecast mdel called Rapid Update Cycle (RUC) prvided by the Natinal Weather Service; meterlgical Dppler radars including the Terminal Dppler Weather Radar (TDWR) and the Natinal Weather Service WSR-88D (NEXRAD) radar; cmmercial aircraft using the Meterlgical Data Cllectin and Reprting System (MDCRS); and Autmated Surface Observing System (ASOS) and Lw Level Wind Shear Alert System (LLWAS) surface anemmeters. humidity (in particular, the gridded temperature analysis and the gridded humidity analysis depend n the gridded winds analysis). The ITWS gridded hrizntal winds prduct, r Terminal Winds, was develped t prvide detailed knwledge f the winds in the terminal airspace t each f the aviatin systems illustrated in Figure 1. Terminal Winds btains wind infrmatin frm a number f surces, including a natinal-scale frecast mdel called Rapid Update Cycle (RUC) prvided by the Natinal Weather Service; meterlgical Dppler radars, including the FAA s Terminal Dppler Weather Radar (TDWR) and the Natinal Weather Service WSR-88D (NEXRAD) radar; cmmercial aircraft using the Meterlgical Data Cllectin and Reprting System (MDCRS); and the Autmated Surface Observing System (ASOS) and Lw Level Wind Shear Alert System (LLWAS) surface anemmeters. The design f the Terminal Winds analysis system must take int accunt the weather phenmena t be captured, sensr characteristics, and nnunifrm and dynamic data distributins; the system must als be rbust t sensr failures. Figure illustrates the lcatin and variety f the data surces used in the Terminal Winds analysis. In the summer f 199 an initial Terminal Winds prttype [4, 5] based n the Lcal Analysis and Predictin System (LAPS) develped at the Natinal Oceanic and Atmspheric Administratin s (NOAA) Frecast Systems Labratry (FSL) [6, 7] was tested in the Lincln Labratry ITWS testbed in Orland, Flrida. This prttype featured the first real-time VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 477

4 winds analysis using data frm the TDWR radar [8] and the NEXRAD radar [9]. Based n lessns learned frm the 199 test, a new analysis technique was develped t extract the wind infrmatin in the Dppler radar data mre effectively. This new technique, called ptimal estimatin, uses a minimum-errr-variance technique (least squares) and is clsely related t bth the state-f-the-art peratinal nn-dppler winds-analysis technique, called ptimal interplatin, and standard multiple-dppler techniques. The ptimal-estimatin technique was evaluated n the 199 Orland data set, and demnstrated in real time in the Orland testbed during the summer f 1993, in Memphis during the spring and summer f 1994, and in Orland during the winter f The ptimal-estimatin-based analysis prvides a significant imprvement ver previus winds analyses using Dppler radar data. In the next sectin we discuss design cnsideratins that mtivated the develpment f the Terminal Winds system. Then we give an verview f the Terminal Winds system, and prvide a descriptin f the analysis with particular attentin t Dppler data analysis and the ptimal-estimatin analysis. Finally, we give an verview f ur prduct accuracy evaluatin based n data cllected in the Orland testbed, and we discuss the directin f future wrk. The sectin entitled Details f the Terminal Winds Analysis can be mitted by readers interested nly in an verview f the Terminal Winds system. Design Cnsideratins There are a number f design cnsideratins fr a winds-analysis system that will supprt the aviatin systems listed abve and perate with infrmatin frm sensrs in the terminal area. Ideally, users f the gridded winds analyses levy perfrmance requirements fr reslutin, accuracy, and timeliness. The autmated aviatin systems that rely n these analyses, hwever, are still under develpment, and final perfrmance requirements are nt yet cmpletely determined. We have taken the apprach f basing reslutin, accuracy, and timeliness n expected wind-field phenmenlgy and sensr characteristics, with the gal f minimizing the nrm f the windvectr errr in the analyzed wind fields. There are a variety f infrmatin surces available fr the gridded winds analysis, including frecast mdels, surface bserving systems, cmmercial aircraft, and meterlgical Dppler radars. These data surces prvide infrmatin f differing cntent, accuracy, and reslutin. The gridded winds analysis system must crrectly reslve imprtant wind-field features by assembling this diverse infrmatin, and must be rbust when sensrs unexpectedly g ff line r cme back n line. Wind-Field Phenmenlgy The terminal airspace extends frm the airprt surface t 18,000 feet mean sea level (MSL). Meterlgically, this airspace is divided int tw regimes. The prtin f the atmsphere clsest t the Earth s surface is referred t as the planetary bundary layer (PBL), and its dynamical structure is strngly influenced by surface effects. The atmsphere in the PBL is well mixed during daylight hurs, and slar heating f the Earth s surface ften expands the PBL t as much as 6000 feet abve grund level. At night, when the air is relatively cl (and less well mixed), the PBL may extend t less than 300 feet abve grund level. A mixture f wind-field features can cexist in the PBL with a wide range f spatial and tempral scales. Features with spatial scales smaller than a few kilmeters r tempral scales shrter than a few minutes, hwever, are nt imprtant t the users f the gridded winds analysis. These small-scale features d nt, fr example, affect time f flight. The regin abve the PBL is referred t as the free atmsphere because f its relative insulatin frm surface effects. The free atmsphere is usually cmpsed f large-scale wind features, each with hrizntal extent f at least tens f kilmeters and lasting tens f minutes. Small-scale wind features can exist in the free atmsphere fr example, within thunderstrms but are rare. Infrmatin Surces The underpinning f the Terminal Winds system is prvided by the RUC, which is a numerical weatherpredictin mdel run by the Natinal Meterlgical Center f the Natinal Weather Service. The RUC is based n the Messcale Analysis and Predictin Sys- 478 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

5 tem (MAPS) develped at NOAA s FSL [10]. Hrizntal wind measurements are prvided at the surface near an airprt by LLWAS anemmeters [11] and in utlying regins by ASOS anemmeters [1]. MDCRS-equipped aircraft prvide measurements f the hrizntal winds alft [13]. These aircraft are nt widely distributed but are typically lcated alng rutes f cmmercial air traffic, making them an imprtant surce f infrmatin abut winds in the free atmsphere. The ITWS will als have infrmatin frm the tw meterlgical Dppler radars mentined abve the TDWR and the NEXRAD radar. Dppler radars prvide measurements f a single cmpnent f the wind, the radial cmpnent directed tward the radar. These radars prvide the vast majrity f the infrmatin cming int the Terminal Winds system, althugh the ther data surces als play an imprtant rle, especially in the free atmsphere. Table 1 shws that the infrmatin frm the different data surces differs widely in spatial and tempral reslutin, as well as in cntent and accuracy. The accuracy listed is relative t an average wind ver a disk with a 3-km radius in the hrizntal during a time span n the rder f a few minutes. Fr example, Dppler radars prvide accurate infrmatin n winds at specific pints in space, but these values can reflect small-scale features that are cnsidered nise in the Terminal Winds system, which reduces their effective accuracy. Because f the 60-km grid spacing, RUC cannt reslve mst thunderstrm-scale weather phenmena (there are plans t reduce the hrizn- tal reslutin t 10 km and the update rate t ne hur by the end f the decade). MDCRS-equipped aircraft measurements are available nly at randm psitins and times alng flight paths f cmmercial aircraft, with a data latency f at least fifteen minutes. On average, apprximately ten MDCRS reprts are received per hur. Surface statins such as LLWAS and ASOS anemmeters vary in update rate between ten secnds and twenty minutes, and Dppler radars prvide nly a single cmpnent f the wind. Cmbining these widely varying surces f infrmatin is a significant technical challenge. Meterlgical Dppler radars prvide estimates f the wind-velcity cmpnent alng the radar beam (radial velcities) as well as measurements f return intensity (reflectivity). These radars cannt directly measure the wind-velcity cmpnent perpendicular t the radar beam. The radial-velcity wind estimates are derived frm the phase shift in returns frm airbrne reflectrs such as bugs, water drplets, and refractive index inhmgeneities that are assumed t be traveling with the wind. Dppler radars prvide accurate and dense measurements nly in regins with sufficient reflectrs. Dppler radars prvide high-reslutin radial-velcity wind infrmatin thrughut the PBL because atmspheric mixing tends t distribute the particles that serve as reflectrs fr the Dppler radars. This phenmenn allws the gridded analysis t prvide high-reslutin wind infrmatin in the PBL, where small-scale wind structures are expected. Because f fewer reflectrs in the free atmsphere abve the PBL, Table 1. Characteristics f Data Surces fr Terminal Winds Surce Update Rate Hrizntal Accuracy Infrmatin (min) Reslutin (m/sec) Cntent RUC km 7 vectr TDWR km x single cmpnent NEXRAD km x 1 4 single cmpnent MDCRS variable variable 4 vectr ASOS 0 60 km vectr LLWAS 0.16 (10 sec) 3 km 1 vectr VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 479

6 Dppler infrmatin is ften available but sparse. The RUC and MDCRS infrmatin surces play an imprtant rle at these altitudes. The lwer-reslutin infrmatin available alft frm these tw surces, as well as frm Dppler radars, is usually apprpriate fr the expected scales f the wind-field dynamics abve the PBL. In regins f cnvective activity where small-scale wind structures are likely t exist abve the PBL, the Dppler radars cntinue t prvide substantial amunts f infrmatin. In regins with infrmatin frm tw r mre Dppler radars, a linear system f equatins can be slved t estimate the hrizntal winds [14]. The details f this multiple-dppler analysis are given in the next sectin. The quality f the estimate derived frm this linear system f equatins varies depending n the range f radar azimuth angles assciated with the Dppler data and the separatins between the lcatins f the data in space and time. If Dppler data are available fr tw independent directins at the same lcatin and time, the resulting estimate will be f high quality. If the Dppler data are all frm nearly the same directin r are widely separated, the resulting estimate will be f lwer quality. Overview f the Terminal Winds Analysis The Terminal Winds analysis is based n the fllwing design gals related t the abve cnsideratins. The analysis shuld (1) respect the variety f spatial and tempral scales f wind-field features in the PBL and abve the PBL, () respect the variety f spatial and tempral scales f the infrmatin frm the different data surces, (3) respect the differing quality f infrmatin frm the different surces, (4) prperly merge vectr infrmatin with single-cmpnent infrmatin, (5) prperly interplate nnunifrmly distributed infrmatin, (6) prvide a smth transitin frm regins f dense data t regins f sparse data, (7) take advantage f the infrmatin cntent f a multiple-dppler data set while respecting the varying quality f that infrmatin, (8) handle fluctuatins in data availability, and (9) minimize the magnitude f the errr in the wind-vectr estimates. The primary philsphy f the Terminal Winds analysis is that the natinal-scale frecast mdel prvides an verall picture f the winds in the terminal airspace, althugh painted in brad strkes. Infrmatin frm the terminal sensrs is then used t fill in detail and crrect the brad-scale picture. Of curse, the crrectins and added detail can be prvided nly in thse regins with nearby data. What cnstitutes nearby depends n the spatial and tempral scale f the feature t be captured in the analysis. The refinement f the brad-scale wind field is accmplished by averaging the mdel frecasts with current data. This averaging allws the analysis technique t prduce wind vectrs that vary smthly frm regins with a large number f bservatins t regins with few bservatins r n bservatins at all, and enables the analysis t cpe gracefully with unexpected changes t the suite f available sensrs. T accunt fr the different scales f wind features and the differing reslutin f the infrmatin prvided frm the varius sensrs, the Terminal Winds analysis emplys a cascade-f-scales analysis. This cascade-f-scales analysis uses nested grids, with an analysis using a -km hrizntal reslutin and a 5-min update rate nested within an analysis using a 10-km hrizntal reslutin and 30-min update rate, which in turn is nested within the RUC frecast using a 60- km hrizntal reslutin and 180-min update rate. All the data surces are used in the 10-km-reslutin analysis, and data are allwed t be as ld as ninety minutes. Only the infrmatin frm the Dppler radars and the LLWAS anemmeters, hwever, are suitable fr the -km-reslutin analysis. The cascade-fscales analysis is apprpriate fr the different scales f wind-field features that need t be captured in the analysis, as well as the different scales f infrmatin prvided by the different data surces, and the cascade-f-scales analysis prvides a unifrm level f refinement at each step f the cascade. An additinal benefit is that the 10-km-reslutin analysis acts as a stand-in fr the planned 10-km-reslutin natinal frecast. When a 10-km natinal frecast becmes available, the 10-km ITWS analysis can be drpped. An imprtant gal is the minimizatin f the errr f the analyzed wind field. T achieve this gal the Terminal Winds analysis uses a least-squares technique, which is designed t average vectr quantities and single-cmpnent quantities jintly. Previus state-f-the-art peratinal winds-analysis systems 480 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

7 have used statistical techniques t great advantage. Nne f these systems, hwever, have the ability t analyze the data frm Dppler radars directly. The Terminal Winds analysis represents a substantial step frward in winds analysis, which is especially imprtant because increasing numbers f Dppler weather radars are being deplyed. The least-squares technique used in the Terminal Winds analysis accunts fr the variatins in quality f the infrmatin available t the Terminal Winds analysis, as well as errrs arising frm data age and errrs arising frm estimating winds at lcatins remved frm the bservatin lcatin. The leastsquares technique als crrects fr crrelated errrs. Highly crrelated errrs arise frequently because f the nnunifrm distributin f data frm the Dppler radars. Often the Terminal Winds analysis estimates the wind at lcatins with many Dppler values clumped tgether at a distance, and few data values elsewhere. Because f the nnhmgeneity f the wind field, the data values in the regin f Dppler infrmatin cntain highly crrelated errrs, relative t the wind at the distant analysis pint. If this errr crrelatin is nt accunted fr, these data values dminate the analysis t a greater degree than warranted by their infrmatin cntent. This situatin is illustrated by an example later. Details f the Terminal Winds Analysis The details f the cascade-f-scales analysis and statistical analysis are given in this sectin. The reader may skip t the next sectin withut lsing the cntinuity f the expsitin. The Terminal Winds analysis system is designed t achieve the nine gals stated in the previus sectin. The next subsectin describes the methd used t achieve the gal f respecting the variety f spatial and tempral scales bth within the PBL and in the free atmsphere abve the PBL, as well as the gal f prperly merging infrmatin frm data surces with differing spatial and tempral update rates. The fllwing subsectins prvide general backgrund infrmatin n winds analysis frm meterlgical Dppler radar data. These subsectins discuss the types f errrs fund in Dppler data, the methd used t prduce reginally representative wind estimates n a Cartesian grid frm pint measurements in spherical crdinates, and the traditinal methd fr estimating hrizntal winds frm multiple-dppler data sets. The last tpic is especially germane t the develpment f the ptimal-estimatin technique. Finally, we present a subsectin n the ptimal-estimatin technique, and cnclude this sectin f the article with a subsectin n illustrative examples. Cascade-f-Scales Analysis Within the PBL r inside regins f cnvective weather, the Terminal Winds analysis needs t be able t reslve wind-field structures that have spatial scales as small as a few kilmeters, and that evlve n time scales as small as several minutes. Abve the PBL and utside regins f cnvective weather, the analysis needs t be able t reslve wind-field structures with spatial scales and tempral scales that are abut an rder f magnitude larger. T capture the differing scales f wind structures while respecting the differences in infrmatin cntent f the varius surces, Terminal Winds uses a cascade-f-scales analysis. The cascade-f-scales analysis starts with an RUC frecast having a 60-km hrizntal-reslutin grid and a 3-hr update rate. The RUC data are used t initialize an analysis with a 10-km hrizntal-reslutin grid and a 30-min update rate. The 10-km-reslutin wind field is used in turn t initialize an analysis with a -km hrizntal-reslutin grid and a 5-min update rate. Each analysis grid has a vertical reslutin f 50 millibars f atmspheric pressure; Table gives the nminal altitudes fr the analysis levels in bth millibars and feet. All f the data surces are used in the 10-km-reslutin analysis, but nly Dppler data and LLWAS data are used in the -km-reslutin analysis. The cascade-f-scales analysis matches the atmspheric dynamics and infrmatin cntent f the different data surces, and gives a unifrm rati f refinement as the analysis steps frm carser t finer reslutin. Stepping dwn this cascade f scales, the ratis fr tempral reslutin are bth 6:1, and the ratis fr hrizntal reslutin are 6:1 and 5:1, as shwn in Table 3. The nested cascade-f-scales analysis grids simplify the sftware implementatin. Ideally, the cascade-f-scales analysis wuld prvide a refinement f the vertical reslutin frm ne VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 481

8 Table. Pressure Levels in Millibars in the Cascade-f-Scales Analysis, and Crrespnding Altitudes in Feet (MSL) Altitude in millibars Altitude in feet , , , , , , , , , , , ,190 analysis scale t the next. A Dppler radar prvides high-hrizntal-reslutin wind measurements, but des nt prvide high vertical reslutin except near the radar. The current Terminal Winds system uses the same 50-mb vertical reslutin fr the 10-km analysis as fr the -km analysis. In the future we plan t examine the need fr a higher vertical reslutin ver the airprt, where the higher reslutin can be supprted by the data frm the TDWR. Figure 3 shws the data flw fr the Terminal Winds cascade-f-scales analysis. First, an analysis is perfrmed with a 10-km hrizntal reslutin, a 50- mb vertical reslutin, and a 30-min update rate utilizing all f the data surces. The 10-km-reslutin backgrund field is prduced by linear interplatin in space and time between the tw RUC frecasts that bracket the analysis time. All data used in the 10- km analysis must have cllectin times within ninety minutes f the analysis time. The current 10-km analysis is then used as the backgrund wind field fr an analysis with a -km hrizntal reslutin, a 50-mb vertical reslutin, and a 5-min update rate. Only Dppler radar data and LLWAS data are used in the -km analysis. The MDCRS aircraft reprts and ther surface data are nt used in the -km analysis because f data latency. On grid levels with n bservatins, the -km analysis is simply the 10-km analysis interplated t the -km-reslutin grid. Wind-Field Analysis frm Meterlgical Dppler Radar Data This subsectin prvides an verview f the basics f winds analysis using infrmatin frm meterlgical Dppler radars. We discuss three tpics: (1) data quality, () data resampling t prduce reginally representative wind estimates n a Cartesian grid frm pint measurements in spherical crdinates, and (3) estimating hrizntal winds frm infrmatin prvided by tw r mre Dppler radars. Dppler Radar Errrs Data-quality issues shuld be addressed befre an analysis f the wind field is perfrmed. There are three majr types f errr in meterlgical Dppler radar data: 1. Returns frm bjects that are nt mving with the wind, such as the grund and bjects n the grund (grund clutter), r flcks f birds and aircraft (pint targets).. Velcity values that are misrepresented by velcity flding. These errrs result frm the insufficient sampling rate in the Dppler velcity calculatin. Given a sampling rate, r the pulse repetitin frequency (PRF), the unambiguus velcity range is determined by c v =± PRF, 4 f where ƒ is the radar frequency and c is the speed f light. When velcity falls utside this range, it is flded back int the range f representable 48 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

9 Table 3. Scales f Analysis fr Rapid Update Cycle and Terminal Winds Update Rate Hrizntal Reslutin Dmain Size Rapid Update Cycle 180 min 60 km natinal Terminal Winds abve PBL 30 min 10 km 40 x 40 km Terminal Winds in PBL 5 min km 10 x 10 km velcities (velcity flding). Bth TDWR and NEXRAD have algrithms that attempt t crrect fr velcity flding. 3. Returns frm bjects beynd the unambiguus range f the radar. These errrs are the result f eches frm distant and bright reflectrs, such as large strms r tpgraphic features that are received after a subsequent pulse has been transmitted (multiple trip r range flding). Currently, the Terminal Winds system des nt try t classify radar errrs r crrect fr them. This errr detectin and crrectin is perfrmed by each radar system prir t prviding data t the ITWS. The Terminal Winds analysis system des attempt t identify incrrect r nnrepresentative wind estimates and remve them during the resampling prcess. Radar Data Resampling Resampling is the prcess by which radial velcity infrmatin is transfrmed frm radar crdinates t Rapid Update Cycle 60-km-reslutin grid 180-min update rate TDWR NEXRAD MDCRS LLWAS ASOS 10-km interplatin 40 x 40 km grid 10-km-reslutin grid 19 levels (100 mb, 53,000 ft) 30-min update rate 10-km-reslutin winds TDWR NEXRAD LLWAS -km interplatin 10 x 10 km grid -km-reslutin grid 11 levels (500 mb, 18,000 ft) 5-min update rate -km-reslutin winds FIGURE 3. Data flw fr the Terminal Winds cascade-f-scales analysis. The RUC data are used t initialize an analysis with a 10-km hrizntal-reslutin grid and a 30-min update rate. The 10-km hrizntal-reslutin wind field is used in turn t initialize an analysis with a -km hrizntal-reslutin grid and a 5-min update rate. All f the data surces are used in the 10-km analysis, but nly Dppler data and LLWAS data are used in the -km analysis. VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 483

10 the Cartesian crdinates used in the Terminal Winds analysis. Spatial averaging is used t prvide data values that represent a reginal average wind. Data-quality tests are used t remve questinable data. The radar reflectivity and radial velcity data are cllected in cntiguus, equally spaced gates alng each radar beam. Bth radars scan sectrs f the regin with a fixed elevatin angle during the scan. A tilt is a maximal cllectin f beams that are cntiguus in time and have the same elevatin angle. Gemetrically, a tilt is a sectin f a cne whse vertex is at the radar. All NEXRAD tilts are full cnes, cvering full 360 sectrs. NEXRAD has several different scan strategies, each with its wn set f tilt elevatin angles. TDWR can scan either with 360 sectrs (mnitr mde), r with tw 360 tilts near the surface and an intense pattern f apprximately 10 sectrs at varius elevatins ver the airprt (hazardus-weather mde). The TDWR tilt elevatin angles are preset fr each airprt installatin, s there are nly tw TDWR scan strategies fr each airprt. Each radar als interrupts its standard velcity scanning t make lng-range (lw-prf) scans that are used t detect the pssibility fr range flding. The lw-prf data are nt used in the winds analysis. They prvide an artificial tempral partitin f the tilts int vlume scans. The Terminal Winds analysis des nt make use f this vlume structure. Instead, at each analysis time, it cmpses a vlume scan ut f the mst recent tilts. This design als accmmdates the fact that the scan strategies f the radars can change during peratins. By cnstructing its wn vlume scan frm the mst recent tilts, the Terminal Winds analysis uses the mst current radar data and is able t cntinue prcessing during changes in the radar scan strategy. The resampling f the Dppler radar data is a twstep prcess tilt resampling and vlume resampling. Tilt Resampling. This prcess prduces a reginally representative estimate f the radial cmpnent f the hrizntal wind velcity at each tilt psitin (x,y,z*) n an (x,y) clumn f the analysis grid. The vertical height z* is the height at which the tilt intersects the (x,y) clumn f the analysis grid, and des nt necessarily crrespnd t an analysis height z. Each tilt is resampled immediately after its scan is cmpleted, an asynchrnus prcess cntrlled by the radar scan strategy. The resampled radial velcity fr (x,y,z*) is the median f all tilt data that lie within apprximately 0.5 km f (x,y,z*). A median filter is used instead f a linear filter, because f the pssibility f grss data errrs such as pint targets. Therefre, this step als has a data-quality editing benefit. The radial velcities are crrected t accunt fr elevatin angle by assuming that the vertical velcity is zer. The magnitude f the vertical velcity is usually very small except within strngly cnvective weather. This exceptin is accunted fr in the vlume resampling step. Vlume resampling. This prcess prduces a reginally representative estimate f the radial cmpnent f the hrizntal wind velcity at each analysis psitin (x,y,z) frm the resampled tilts by either linear interplatin r extraplatin in the vertical. This is a synchrnus prcess triggered by each winds-analysis cycle. Additinal data-quality editing is prvided by (1) a buddy check n each tilt f data t remve questinable data values r data that may nt be reginally representative, and () remval f data in regins f high reflectivity, since winds within highly cnvective strms may nt be reginally representative and the hrizntal wind estimates are likely t be cntaminated by a large vertical cmpnent. Multiple-Dppler Techniques Multiple-Dppler wind-field analysis prvides a valuable starting pint in the discussin and develpment f winds-analysis techniques when infrmatin frm tw r mre Dppler radars is available. The use f multiple-dppler radars is the nly practical methd available fr btaining clsely spaced measurements f wind fields in a three-dimensinal regin. Multiple Dppler analysis can be applied nly at pints with Dppler infrmatin fr tw independent cmpnents f the wind. When Dppler analysis can be applied, hwever, the resulting wind estimates are very accurate, as discussed belw. The hrizntal wind at a pint can be estimated frm tw r mre Dppler hrizntal wind-cmpnent estimates at that lcatin, if the difference in azimuth angles is sufficiently large. Least-squares estimatin is usually used fr this purpse. This prcess is numerically stable nly if the difference in azimuth 484 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

11 angles is sufficiently large s that the radars have at least tw independent estimates f the wind field. Even when the difference in azimuth angles is small, this wind-retrieval prcess returns ne high-quality wind cmpnent, the radial cmpnent measured by the radars; nly the azimuthal cmpnent is unstable. Techniques are being develped t estimate the azimuthal cmpnent frm the mtin f features in the reflectivity field. Wrk in this area is under way at the Cperative Institute fr Messcale Meterlgical Studies [15] and at the Natinal Center fr Atmspheric Research (NCAR) [16]. These azimuthalcmpnent analysis techniques are nt used in the current implementatin. When these techniques are develped t the pint that they can be used peratinally, they will be included in the Terminal Winds system as a new surce f infrmatin. Multiple-Dppler analysis is the prcess by which the best estimate f the hrizntal wind-velcity vectr is cmputed at an analysis psitin (x,y,z), n the basis f estimates f the radial velcity prduced by resampling the data frm tw r mre Dppler radars. We represent the hrizntal wind as a vectr (u,v), where u is the cmpnent in the east directin and v is the cmpnent in the nrth directin; hwever, any rthgnal crdinate system can be used. Fr an azimuth angle θ, with east at 0 and nrth at 90, the radar measures a radial velcity r given by Nrth v r Wind r 1 θ θ Radar 1 u East FIGURE 4. Simple gemetry fr tw Dppler radars. Each radar makes a measurement f the wind at the intersectin f the nrth and east axes. Fr small values f θ, the u cmpnent is nearly the radial cmpnent, and the radar measurement cntains little infrmatin abut v. θ Radar θ r = ucs θ + v sin θ. Given tw r mre Dppler wind cmpnent estimates, we can write a system f equatins with (u,v) as the wind vectr t be determined. The system f equatins fr tw Dppler measurements is given by cs θ cs θ sin θ u sin θ = r v r T illustrate the mathematical behavir f the slutin t the multiple-dppler system f equatins, we cnsider an example with tw Dppler estimates at a pint, and simple gemetry. Suppse we have tw radars, as shwn in Figure 4. The radars make measurements r 1 and r, respectively, f the radial cmpnent f the wind at the intersectin f the nrth and FIGURE 5. General gemetry fr tw Dppler radars. The measurement gemetry shwn in Figure 4 can always be created by perfrming a rtatin f crdinates int a suitable crdinate system. east axes. Fr small values f θ, the u cmpnent f the wind is nearly the radial cmpnent and the v cmpnent is nearly the azimuthal cmpnent. The radar measurement cntains little infrmatin abut v. Similar gemetry can always be arranged by using a rtatin f crdinates t chse a suitable crdinate system, as shwn in Figure 5. The dual-dppler equatins fr the simple gemetry f Figure 4 are VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 485

12 cs θ cs θ sin θ u sin θ = r v r The slutin t Equatin 1 is 1. u r r v = ( 1 + )/ cs θ ( r r )/ sin. 1 θ (1) Let u edd and v edd dente the errr in the u and v cmpnents f the dual-dppler slutin. Let σ R dente the average f the errr variances fr the tw radars. The dual-dppler errr variances, prvided that the radars have uncrrelated errrs, are and var( ) = u edd var( ) = v edd σr θ cs σr sin. θ TDWR Orland NEXRAD Distance frm Orland in km FIGURE 6. The shaded regin depicts the numerically stable TDWR/NEXRAD dual-dppler regin fr the Orland airprt verlaid n the -km-reslutin analysis dmain. 70 As θ appraches zer, the errr in the slutin fr v becmes numerically unstable. T cntrl this numerical instability, the angle between radar beams, θ, is generally cnstrained t be greater than 30. Figure 6 shws the regin where θ is greater than 30 fr a TDWR/NEXRAD dual-dppler analysis at the Lincln Labratry testbed in Orland. We nw cnsider the general case f multiple Dppler radars. Figure 7 shws an example f a situatin in which a given lcatin is cvered by three Dppler radars. In this case the Dppler equatins are cs θ1 sin θ1 r cs θ sin θ u cs θ3 sin = r v θ3 r 1 3 r 1 u,. = r A r v r3 The best-estimate slutin is prvided by least squares, given by r 1 u T T r v = ( A A) 1 A. r 3 Even thugh this system f equatins is verdetermined, it is nt numerically stable unless at least tw f the angles are significantly different. In this frmulatin f the least-squares prblem, each radar is treated as if it prduced radial measurements f equal quality. Hwever, many factrs can intrduce unequal errrs in the data, such as radar sensitivity r the distance frm the radar site t the analysis lcatin. In ur wind-field analysis, unequal errrs are accunted fr by means f the Gauss-Markv therem [17]. Terminal Winds Interplatin Technique: Optimal Estimatin The Lcal Analysis and Predictin System (LAPS), develped by NOAA/FSL, prvided the basis fr the initial Terminal Winds prttype. In 199, LAPS was the state-f-the-art peratinal 10-km-reslutin winds-analysis system fr fusing data frm Dppler radars as well as traditinal wind-data surces, numerical mdels, anemmeters, MDCRS, and ther meterlgical data surces. Hwever, while LAPS can utilize data frm mre than ne Dppler radar, it 486 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

13 Radar 3 NEXRAD Radar 1 NEXRAD Radar TDWR FIGURE 7. Radar gemetry fr the verdetermined case f three Dppler radars. was nt designed t take advantage f the large multiple-dppler data sets available in an ITWS. This initial Terminal Winds prttype was demnstrated in real time in the Lincln Labratry Orland testbed in the summers f 199 and The peratin f this prttype, as well as numerus discussins with FSL, prvided valuable insight int traditinal windsanalysis techniques. The initial prttype has been superseded by the Terminal Winds analysis described in this article. The Terminal Winds analysis is dminated by Dppler radar data. In regins with cverage by tw r mre radars, the Terminal Winds analysis system shuld prvide infrmatin abut winds with at least the quality f the infrmatin frm the multiple- Dppler analysis discussed earlier. The state-f-theart analysis technique fr nn-dppler meterlgical data analysis is ptimal interplatin [18, 19], which is a statistical interplatin technique that under certain hyptheses gives an unbiased minimumvariance estimate. In ther scientific fields, similar minimum-variance techniques have been used successfully. In gephysics a technique called Kriging, which is similar t ptimal interplatin, is used [0], and in ceangraphy ptimal interplatin is called the Gauss-Markv methd [1]. We wish t build n the fundatin laid dwn by the multiple-dppler analysis and by these ther statistical interplatin techniques. We have develped a minimum-variance technique that utilizes Dppler measurements directly. We call this technique ptimal estimatin t distinguish it frm ptimal interplatin. The initial fcus is n analyzing hrizntal wind data in a three-dimensinal grid; hwever, the methd als applies t ther weather variables such as temperature and humidity. The methd is based n the Gauss-Markv therem, and under suitable cnditins gives an unbiased minimum-variance estimate f the hrizntal winds. Optimal estimatin is an extensin f bth ptimal interplatin and multiple-dppler analysis. The develpment f ptimal estimatin is mtivated by the ease with which it incrprates Dppler radar data. Because ur sftware develpment lags behind ur theretical understanding f ptimal estimatin, we present nly that part f ptimal estimatin which has been tested, leaving a full treatment t a later time. Optimal estimatin has the fllwing prperties: (1) dual-dppler-quality winds are autmatically prvided in regins where dual Dppler is numerically stable, () small gaps in dual-dppler radar cverage are filled t prvide near dual-dppler-quality winds in these gaps, and (3) the analysis prduces wind vectrs that vary smthly between regins with data frm differing numbers f Dppler radars. Thrughut this sectin we use the fllwing ntatin cnventins: r dentes a radial wind cmpnent, u dentes an east wind cmpnent, v dentes a nrth wind cmpnent, superscript a dentes an analyzed quantity, superscript b dentes a backgrund quantity, superscript dentes an bserved quantity, and subscripts dente lcatin ( denting an analysis lcatin). We seek a linear minimum-variance unbiased estimate, and we emply the Gauss-Markv therem t generate this estimate. T apply the Gauss-Markv therem we need t pse the prblem in the frm where and the data vectr Ax a x = ( u0 v0) = d, () a T,, VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 487

14 d = ( u, v, u1, v1, K, u, v, r1, K, r ) b b m m n T cntains the backgrund estimate at the analysis lcatin and bservatins in a data windw centered n the analysis lcatin. The frm f the matrix A depends n the type f data, vectr, r radial t be analyzed. The Gauss-Markv therem states that the linear minimum-variance unbiased estimate f x is given by a a T 1 T T 1 = ( 0 0) = ( ) 1 x u, v A C A A C d, (3) if each element f d is unbiased, and C is the errr cvariance matrix fr the elements f d. The errr cvariance f the slutin is 1 T 1 ( A C A). (4) In the case f m vectr bservatins and n Dppler bservatins, Equatin has the frm M M cs M M cs θ sin θ a u um a v = v m θ1 sin θ1 r1 n n b u b v M M rn Unlike the multiple-dppler analysis, the ptimalestimatin slutin is always numerically stable because f the inclusin f the backgrund wind estimate. The inclusin f a ( u, v ) data pint prvides tw cmpnent estimates at right angles, giving a maximum spread f azimuth angles. Since the errr variances f the Dppler data are usually much smaller than the errr variances f the ther data, the ptimal-estimatin slutin clsely matches the multiple- Dppler slutin at lcatins where the multiple- Dppler prblem is well cnditined. Otherwise, the analysis gives a slutin that largely agrees with the b b radar bservatins in the radial cmpnent measured by the radars. The remaining cmpnent is derived frm the nn-dppler data surces. An example illustrating this feature is given in the next sectin. In practice, the errr cvariance matrix C is nt knwn and must be estimated. There are tw types f errrs t estimate. The first is the errr that arises frm imperfect sensrs. The secnd is the displacement errr due t taking the measurement at sme distance, in space and time, frm the analysis lcatin. Our initial errr mdels are based n the fllwing simplifying assumptins: (1) bservatins are unbiased; () sensr errrs frm different bservatins are uncrrelated; (3) errrs in u and v cmpnents, measured r backgrund, are uncrrelated; (4) displacement errrs and sensr errrs are uncrrelated; and (5) displacement errrs are independent f the cmpnent being measured. With these assumptins, the errr cvariance matrix C decmpses int the sum f a sensr-errr cvariance matrix and a displacement-errr cvariance matrix. The sensr-errr cvariance matrix is diagnal, and the sensr-errr variances are knwn. The remaining task is the estimatin f the displacement-errr cvariance matrix. The initial displacement-errr variance mdel is a linear functin f the displacement between the bservatin lcatin and the analysis lcatin. The initial displacement-errr crrelatin mdel fr tw like cmpnents is a decreasing expnential functin f the displacement between tw bservatin lcatins. The displacement-errr cvariance mdel fr tw nnrthgnal, nnparallel cmpnents must take int accunt the angle between the tw cmpnents. We dente the angle between the bserved cmpnent and the u axis by θ, with east at 0 and nrth at 90, and the displacement errr in bservatin i by δ i. Then the displacement-errr cvariance fr tw bservatins is given by the fllwing equatin: cv( δ, δ ) = cs( θ θ ) var( δ ) var( δ ) cr( δ, δ ), where cr( δ1, δ) is the displacement-errr crrelatin mdel. 488 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

15 Illustrative Examples We illustrate sme benefits f ptimal estimatin by applying it in tw examples fr which slutins are easily cmputed. The first example demnstrates sme advantages f the ptimal estimatin technique ver the standard dual-dppler technique. The secnd illustrates the benefit f accunting fr crrelated errrs that arise frm nnunifrm data distributins. The ability t accunt fr crrelated errrs is especially imprtant fr a system that utilizes Dppler infrmatin because the Dppler data are ften nt unifrmly distributed thrughut the analysis dmain. Fr ur first example, we cmpare ptimal-estimatin analysis t dual-dppler analysis at thse pints with cverage frm tw radars. We restrict ur discussin t the case in which we have nly a backgrund wind estimate and tw Dppler bservatins at a fixed analysis lcatin, as illustrated in Figure 4. We use the assumptins listed abve regarding the errr mdels. That is, we assume the errrs in the u and v cmpnents f the backgrund are nt crrelated with each ther r with the errr in the radar measurements, and we assume that the errrs in the radar measurements are nt crrelated. We als assume that the errr variance is the same fr each cmpnent f the backgrund wind, and that the errr variance is the same fr each radar. These are reasnable assumptins if the Dppler values are average (r median) values ver a fixed regin surrunding the analysis pint, and the backgrund is independent f the Dppler data. The backgrund is independent f the Dppler data, fr example, if the backgrund cmes frm a frecast mdel r is derived frm the radar reflectivity fields. Let σ B be the standard deviatin f the errr in the backgrund cmpnents, and let σ R be the standard deviatin f the errr in the radar measurements. This gives the errr crrelatin matrix C, where σ B C = 0 σb σ R σ R Let ρ = σ B / σ R dente the relative quality f the radar bservatins versus the backgrund bservatins. Typically, ρ is n the rder f 10. Then 1 C = 1 σb ρ ρ With these assumptins, the ptimal-estimatin slutin is cmputed frm Equatin 3, giving: and where and u v a a b r1 + r = αu + ( 1 α) cs θ r r = v b β + ( 1 1 β) sin, θ 1+ ρsin θ α = 1+ ρ + 4ρ cs θ sin θ 1+ ρcs θ β =. 1+ ρ + 4ρ cs θ sin θ The terms 1 α and 1 β represent the fractin f the ptimal-estimatin slutin that is given by the slutin t the dual-dppler equatins fr the u and v cmpnents. If α r β is zer, the crrespnding cmpnent f the ptimal-estimatin slutin is equal t the dual-dppler slutin, and if α r β is 1, the crrespnding cmpnent f the ptimal-estimatin slutin is equal t the backgrund estimate. We see that if ρ is large (i.e., the radar errr variance is small relative t the errr variance f the backgrund) and θ is nt near zer, then α and β are near zer, and the ptimal-estimatin slutin is nearly dual Dppler. If θ = 0, then β = 1, and ptimal estimatin returns a v cmpnent equal t the backgrund. In this last case, the u cmpnent is the stan- VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 489

16 1.0 and 0.8 ρ = 50 σb var( v eoe ) = 1 + ρsin, θ (6) β again demnstrating the numerical stability f the methd; the errr variance f the ptimal-estimatin slutin is bunded abve by the errr variance f the backgrund. Substitutin f ρ = σ B / σ R int Equatins 5 and 6 gives θ (deg) FIGURE 8. The fractinal cntributin f the dual-dppler term in the ptimal-estimatin slutin f the v cmpnent, as a functin f the angle between radar beams (θ) and the quantity ρ, which is a measure f the relative quality f the radar bservatins. If ρ is large and θ is nt near zer, the ptimal-estimatin slutin fr v is primarily the dual-dppler slutin. If θ is near zer, the dual- Dppler cntributin drps t zer. dard least-squares slutin; the backgrund and Dppler values are weighted inversely t their variances. Figure 8 shws hw 1 β varies with the angle between the tw radar beams (θ) fr different values f ρ. When the angle is greater than abut 30, ptimal estimatin returns a value fr v that is primarily the dual-dppler slutin. As the angle decreases belw 30, the weight given t the v cmpnent f the dual- Dppler slutin drps quickly t zer. In fact, as θ decreases t zer, the quantity r1 r ( 1 β) sinθ ges t zer, remving the dual-dppler instability fr small θ. The errr variances fr the ptimal-estimatin slutin, cmputed frm Equatin 4, are σb var( u eoe ) = + 1 ρcs θ (5) and σbσr var( u eoe ) = σr + σb cs θ σbσr σr = σb cs θ cs θ σbσr v eoe R B var( ) = σ + σ sin θ σbσr σr = σ sin θ sin B. θ (7) (8) These equatins shw that the errr variances f the ptimal-estimatin slutin are never greater than the errr variances f the dual-dppler slutin. Cmbining Equatins 5 thrugh 8, we cnclude that and var( u ) min var( u ), var( u ) { } eoe edd eb var( v ) min var( v ), var( v ). { } eoe edd eb In the secnd example we lk at an imprtant benefit f statistical methds such as ptimal interplatin and ptimal estimatin namely, their ability t handle crrectly situatins with a significant spatial variatin in the density f bservatins, resulting in bservatins with highly crrelated displacement errrs. Fr simplicity, we examine an example with a single variable, and we mit a backgrund estimate. Figure 9 shws an example with three bservatins. We assume that the sensr errrs are equal and uncrrelated. Observatin 1 is lcated far frm bserva- 490 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

17 Observatin T cmpute the ptimal-estimatin slutin, we invert C and apply Equatin 3, with A = (1 1 1) T. Examinatin f the weight f each bservatin gives Observatin 1 Observatin 3 w 1 = 1 + c 3 + c 3 3 1, w = w3 =. 3 + c 3 Analysis pint FIGURE 9. Nnunifrm data distributin gives rise t crrelatin errrs. Observatin 1 is lcated far frm bservatins and 3, s its displacement errr is nearly uncrrelated with the displacement errrs in the ther tw bservatins, which are clse tgether and are highly crrelated. The statistical analysis methds f ptimal interplatin and ptimal estimatin accunt fr the errr crrelatins caused by this distributin. tins and 3; therefre, its displacement errr is nearly uncrrelated with the displacement errrs in the ther tw bservatins. T simplify the example, we assume the displacement errr in bservatin 1 is uncrrelated with the displacement errrs in bservatins and 3. Observatins and 3, n the ther hand, are lcated clse tgether, s we assume that their displacement errrs are highly crrelated. Observatins and 3 are nearly repeat bservatins, and as such they shuld nt get twice the weight f a single independent bservatin, as is the case when errr crrelatins are nt accunted fr. Because the bservatins are equidistant frm the analysis pint, we assume that their displacement errr variances are equal, and withut lss f generality we assume that the sum f the sensr-errr variance and the displacement-errr variance is equal t ne fr each bservatin. Since we have assumed that the errrs in bservatin 1 are uncrrelated with the errrs in bservatins and 3, the errr cvariance matrix C has the fllwing frm: C = 0 1 c 3, 0 c 1 where 0 c 3 < 1. The entry c 3 cannt equal ne because the sensr errrs are uncrrelated. 3 We see that if the errrs are assumed t be uncrrelated (i.e., the errr crrelatins are nt accunted fr), the bservatins each get weight 1/3. As c 3 increases tward 1, the weight given t bservatin 1 increases tward 1/, and the weights given t bservatins and 3 decrease tward 1/4, r a cmbined weight f 1/. This is the desired weighting because if the errrs in bservatins and 3 are cmpletely crrelated, bservatins and 3 cntain the same infrmatin. Operatinal Experience and Evaluatin Starting in 199, Lincln Labratry has perated an ITWS testbed at Orland Internatinal Airprt. This testbed is a cntinuatin f the Lincln Labratry TDWR testbed that was initiated in In the summers f 199 and 1993 the initial Terminal Winds prttype perated in real time, and in the summer f 1993 the new ptimal-estimatin-based Terminal Winds prttype perated in real time. The evaluatin results presented here are frm data cllected in 199 and 1993 at the Orland testbed. The wind-data surces in the Orland testbed are the Messcale Analysis and Predictin System (MAPS), which is a prttype f the RUC system; the TDWR prttype Dppler radar at Kissimmee, Flrida, 10 km suth f Orland; the NEXRAD Dppler radar at Melburne, Flrida, 65 km sutheast f Orland; MDCRS-equipped aircraft bservatins; the LLWAS anemmeter netwrk; the ASOS autmatic bserving statins; and Surface Aviatin Observatins (SAO) hurly bservatins. The Dppler radars cmplete their vlume scans every five t six minutes. The ASOS statins prvide updates every twenty minutes, and the LLWAS anemmeters prvide updates every ten secnds. The LLWAS netwrk is lcated at the airprt and cntains furteen sensrs with a spacing f t 3 km. The SAOs are updated n the hur. The MDCRS reprts ccur with variable spacing, averaging abut ten per VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 491

18 10-km-reslutin grid -km-reslutin grid Surface statin Dppler radar MAPS grid FIGURE 10. Analysis dmains and sensr lcatins fr the 199 Orland Terminal Winds analysis. The 180 x 180- km analysis regin (10-km-reslutin grid) and the 10 x 10-km analysis regin (-km-reslutin grid) are shwn as squares centered n the airprt. hur during the hurs f peak aircraft peratin. Figure 10 shws the analysis dmains and sensr lcatins fr the 199 Orland Terminal Winds analysis. The 10-km and -km analysis regins are shwn as squares centered n the airprt. The dimensins are 180 km 180 km and 10 km 10 km, respectively. In 1993 the 10-km analysis regin was increased t 40 km 40 km. The backgrund field fr the 10-km analysis was derived frm the wind estimates n the 6 6 sub-dmain f the MAPS grid that cntains the 10-km-reslutin grid. The TDWR radar is lcated near the center f the -km dmain, and the NEXRAD radar is lcated near the sutheast crner f the -km dmain. Aircraft reprts were available primarily alng arrival and departure rutes, t the nrth and suth f the airprt. The basis f the evaluatin is the cmparisn f bservatins with analyzed and frecast winds at nearly cincident pints. This amunts t spt checks, since we cannt cntrl the availability f bservatins, except t select days n which they were plentiful. Each algrithm was evaluated n a twentyday subset f the 199 and 1993 Orland data ar- chive. These days were chsen t include a variety f weather, and gd cmparisn data. Statistics fr a number f perfrmance metrics have been cmpiled. We reprt statistics nly fr the nrm f the vectr difference between the analyses and frecasts and the cmparisn bservatins. Three cmparisn bservatin data sets were used MDCRS reprts, Crss-Lran Atmspheric Sunding System (CLASS) sundings, and TDWR and NEXRAD dual-dppler wind fields. These cmparisn data sets are discussed in detail belw. Results are presented fr tw analyses and ne frecast: Terminal Winds -km reslutin, Terminal Winds 10-km reslutin, and MAPS. Cmparisns between analyzed and frecast wind fields and bserved winds were cnstrained t the -km grid t ensure cnsistent evaluatin data sets and because prduct accuracy is paramunt in this regin. We used bilinear interplatin f the Terminal Winds 10- km analyses and MAPS frecasts t the -km grid. Fr each analysis, the bservatins were cmpared t the wind vectr frm the -km grid pint nearest the bservatin. Althugh each f the three cmparisn data sets is treated as a standard against which the analyzed wind fields are judged, it is imprtant t keep in mind that n bservatin is perfect. The perfrmance f each algrithm is referred t as relative t MDCRS, fr example, keeping explicit that any cnclusins we draw are subject t the errr characteristics f the cmparisn bservatins, as well as the errr characteristics f the analysis. We cannt expect the cmparisn with independent bservatins, n average, t be less than the average magnitude f the sensr errr. This limits the ability f the cmparisn t discern prduct accuracy t the accuracy f the cmparisn bservatins. The characterizatin f a perfect lcal winds analysis has nt been made. In particular, the desired degree f smthing f the wind field has nt been specified. At any given instant, a wind field is a superpsitin f wind structures with a wide spectrum f spatial and tempral scales. Fr a given applicatin, sme f these structures are at scales that are unimprtant, and ther structures are t small r shrt lived t be captured by the analysis. These subscale 49 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

19 features may influence an bservatin, hwever. When these bservatins are cmpared with the analysis, the differences reflect errrs in the analysis, errrs in the bservatin, and the structure f the subscale features captured in the bservatins. Given the limited set f bservatins used in the evaluatin, we have nt attempted t separate the effects f the different surces f errr. Cmparisn Observatin Data Sets There are three types f cmparisn bservatins used in the evaluatin. Tw f these MDCRS bservatins and CLASS sundings are independent f the assciated analysis fields. The independence f MDCRS is explained in the next paragraph. The third type f cmparisn bservatin dual-dppler winds based n TDWR and NEXRAD is nt independent f the analyzed wind fields because bth the Terminal Winds analysis and the dual-dppler analysis are derived frm the same Dppler radar data, including similar data-quality editing. Despite the fact that MDCRS bservatins are inputs t the analysis, they are independent f the analyzed wind fields t which they are cmpared. The MDCRS bservatins are used as inputs t the 10- km analysis, but are always at least fifteen minutes ld by the time they are assimilated. MDCRS-bserved winds are cmpared with the crrespnding analysis winds at the analysis update time clsest t the MDCRS measurement time, nt the MDCRS assimilatin time. This time delay results in cmparing the MDCRS bservatin t an analysis cmputed befre the MDCRS reprt was available t the Terminal Winds system. MDCRS bservatins are quite sparse in space and time (apprximately five per hur in the -km analysis dmain in which the evaluatin was perfrmed). They ffer the advantage that they are lcated where aircraft perate and thus are relevant t air traffic cncerns. Preliminary results frm a study cnducted by the NOAA FSL indicate that MDCRS bservatins have an rms vectr errr f apprximately 4 m/sec. Table 4. Height Distributin fr the Three Observatinal Data Sets Level Nminal Altitude MSL Observatinal Data Set (mb) (feet) MDCRS CLASS Dual Dppler , , k , k Sample , k Size k per k Level k k k k k Ttals k VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 493

20 The University f Massachusetts Lwell launched CLASS rawinsndes during August 199 frm the University f Nrth Dakta radar site lcated slightly east f the Orland airprt. Several sundings had t be mitted because f pr data quality r because f balln psitin alignment errrs. Fr the evaluatin, seven CLASS sundings were judged acceptable, representing seven vertical prfiles with a ttal effective sample size f rughly ne hundred data pints. The accuracy f rawinsnde wind-speed bservatins, measured by rms errr, is typically 3 m/sec. Fr wind directin, the accuracy is typically 14 when the true wind speed exceeds 5 m/sec []. When tw Dppler measurements exist at a given lcatin, a wind vectr can be reliably recvered frm the tw measured cmpnents, assuming certain gemetrical cnstraints are satisfied. The dual-dppler cmputatins were perfrmed nly in regins where the angle between the TDWR and NEXRAD radar beams is greater than 30 and less than 150 t avid numerical instability. Data frm high-reflectivity regins were additinally eliminated, since wind-velcity variatins in cnvective weather make it difficult t characterize a -km cell by a single representative value. Als, the interplatin and extraplatin limits in Percent MDCRS CLASS sundings Dual Dppler Wind speed (m/sec) FIGURE 11. Cumulative prbability distributin fr wind speeds in the MDCRS, CLASS sundings, and dual- Dppler analysis data sets. Percent Terminal Winds MAPS 10 km km Nrm f the vectr difference (m/sec) FIGURE 1. Cumulative prbability distributin fr the nrm f the vectr difference between the MDCRS reprts and each f the three sets f wind fields. the vlume resampler were reduced by a factr f tw t reduce errrs intrduced during the transfrmatin frm radar crdinates t Cartesian crdinates. Finally, n tilts with elevatin angle abve 0 were used in rder t limit the errr frm sampling the vertical cmpnent f the wind. We d nt have a sufficiently accurate set f wind measurements t establish the accuracy f ur dual-dppler winds empirically; hwever, theretical arguments shw that the rms vectr errr is apprximately.4 m/sec. Table 4 shws the height distributin fr the MDCRS, CLASS sundings, and dual-dppler analysis data sets. Bth MDCRS and CLASS are fairly unifrmly distributed in altitude. The dual-dppler wind vectrs are fairly unifrmly distributed in altitude abve 4000 feet, with a significant abundance clser t the grund. Only a few dual-dppler wind vectrs are at 1000 mb because f a very small regin f verlap in radar cverage at this altitude. Figure 11 gives the cumulative prbability distributin fr wind speeds f the bservatins in the three cmparisn data sets. Fr example, Figure 11 shws winds speeds f 5 m/sec r less fr apprximately 57% f the MDCRS data, 40% f the CLASS sundings data, and 45% f the dual-dppler wind vectrs. 494 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

21 Percent 40 Percent 40 0 Terminal Winds MAPS 10 km km 0 Terminal Winds MAPS 10 km km Nrm f the vectr difference (m/sec) Nrm f the vectr difference (m/sec) FIGURE 13. Cumulative prbability distributin fr the nrm f the vectr difference between the CLASS sundings and each f the three sets f wind fields. FIGURE 14. Cumulative prbability distributin fr the nrm f the vectr difference between the dual-dppler analysis and each f the three sets f wind fields. Evaluatin Results The statistical evaluatin indicates hw well the Terminal Winds algrithm matches the cmparisn bservatins ver a large perid f time. Statistics cllected ver a large perid f time d nt allw perfrmance quantificatin fr different weather situatins. Fr example, when the winds are relatively unifrm, a -km analysis is nt expected t perfrm better than a 10-km analysis, since the wind field des nt cntain structures smaller than tens f kilmeters. When the wind fields are mre cmplex, we expect t see a variatin in perfrmance. The cmparisn with dual-dppler bservatins did nt target specific weather situatins; hwever, the majrity f the dual-dppler bservatins are in the PBL, and they are mre numerus in regins f mderate reflectivity. Cmplex wind fields are expected in the PBL and during cnvectin, s the results f the cmparisn with dual Dppler are indicative f algrithm perfrmance when small-scale wind features are present in the atmsphere. In additin, we discuss an example in the next sectin that qualitatively indicates the differences in the tw scales f analysis during cnvectin. Unlike dual Dppler, the presence f MDCRS and CLASS bservatins is nt crrelated with the type f weather. These data sets are t small t be partitined by weather type, s the results f the cmparisn with MDCRS and CLASS represent an average ver all the weather situatins ccurring during MDCRS and CLASS data cllectin. Figures 1, 13, and 14 are plts f cumulative prbability distributins fr the nrm f the vectr difference between each analysis and frecast, and each f the three sets f cmparisn bservatin data sets. Fr example, Figure 1 shws that the vectr difference between MAPS frecasts and MDCRS is 5 m/sec r less abut 70% f the time. Table 5 gives the RMS and median values fr the nrm f the vectr differences between the analyses and frecasts, and the cmparisn bservatins. Figures 1 and 13 prvide the cmparisns f the Terminal Winds analyses and the MAPS frecasts t MDCRS and CLASS bservatins, respectively. These cmparisns (summarized in Table 5) indicate that bth the -km and 10-km analyses cnsistently have better agreement with the bservatins than d the MAPS frecasts. These cmparisns d nt indicate that the -km analysis prvides an imprvement VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 495

22 Table 5. Rt Mean Square and Median (in Parentheses) Values fr the Nrm f the Vectr Difference between the Terminal Winds Analyses and MAPS Frecasts, and the Three Cmparisn Observatins (m/sec) km 10 km MAPS MDCRS 4.1 (3.1) 3.8 (.8) 4.6 (3.6) CLASS.9 (.).7 (.) 3.7 (3.0) Dual Dppler.0 (1.0) 3.8 (.6) 5.4 (4.1) ver the 10-km analysis. This result is nt t surprising, since these cmparisns are ver all weather situatins. The similarity in perfrmance f the tw scales f analysis may als reflect that we have reached the limit f these data sets t discern algrithm perfrmance. Against MDCRS, the tw analyses have apprximately a 4 m/sec rms errr, and against CLASS they have apprximately a 3 m/sec rms errr, which are the reprted RMS accuracies f the MDCRS and CLASS bservatins. The wind fields, including MAPS frecasts, agree mre clsely with the CLASS sundings than with the MDCRS reprts. This clser agreement may be due t superir accuracy f the CLASS sunding measurements, r it may be due t the expected variatin in the statistics when small data sets are used. The cmparisn with the dual-dppler winds analysis prvides greater distinctin between the varius analyses; the -km analysis matches the dual- Dppler winds mre clsely than the 10-km analysis. The rms vectr difference between the -km analysis and the dual-dppler wind vectrs (as shwn in Table 5) is less than the theretical rms vectr errr f the dual-dppler winds (.4 m/sec), reflecting the statistical dependence between the tw estimates f the wind field. Bth the -km and 10-km Terminal Winds analyses shw a greater imprvement ver MAPS frecasts than they shw in the cmparisns t MDCRS. This imprvement is expected. The dual- Dppler data set cntains bservatins frm mre cmplex wind fields than the ther tw cmparisn data sets, since the Dppler data are dminated by bservatins in the PBL, and relatively mre Dppler returns are available during and near cnvective weather than in weather with mre clear air. Thus the dual-dppler data set cntains bservatins in regins where MAPS is nt expected t perfrm well. The relatinship between the ptimal-estimatin algrithm and the dual-dppler algrithm is als in evidence. Because care was taken t ensure that dual- Dppler winds were prduced nly when gd Dppler data were available, and nly in regins where the dual-dppler prcess is numerically stable, the ability t match the dual-dppler winds is imprtant. An Example The bulk statistics reprted abve address the questin f hw the different analyses perfrm n average. Hwever, there are differences in the analyses that are nt explred by this type f evaluatin. In this sectin we give an example that shws the ability f the different winds analyses t capture imprtant small-scale wind-field structures. We discuss the -km-reslutin and 10-km-reslutin Terminal Winds analyses and MAPS frecast fields fr tw time perids n the afternn f 0 August 199. The behavir discussed is typical fr cnvective weather situatins. Each figure discussed in this example shws an analyzed wind field at apprximately 1800 feet MSL in the regin cvered by the -km analysis. Each wind field is displayed n a 4-km-reslutin grid t aid the cmparisn. The 4-km grid was chsen t avid visual clutter. The wind vectrs are scaled t wind speed, with a 5-m/sec reference vectr shwn in the upper right crner. The Orland airprt is at the center f the wind field, the cast f Flrida is shwn alng the right, and the utlines f fur lakes are shwn. The clred backgrund indicates the radar reflectivity. Figure 15 shws three wind fields fr :10 Greenwich mean time (GMT). A gust frnt and its assciated reflectivity thin line can be seen t the east f the airprt. This gust frnt was generated frm a strm east f the cast. A cnvergence pcket in the wind field exists suthwest f the airprt. Just after this cnvergence pcket develped, a strm began t frm at this lcatin. The cnvergence strengthened alng with the reflectivity assciated with the grwing strm. This cupling f cnvergence and strm 496 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

23 (a) (b) (c) FIGURE 15. Wind-field analyses arund Orland n 0 August 199 at :10 Greenwich mean time (GMT). (a) The -km-reslutin ptimalestimatin wind field, (b) the 10-km-reslutin ptimal-estimatin wind field, and (c) the MAPS wind field. Each f these wind fields is displayed n the same 4-km-reslutin grid fr cmparisn. Orland Internatinal Airprt is at the center f each grid, and the east cast f Flrida is shwn at the right. The wind vectrs are scaled t wind speed, with a 5-m/sec reference vectr shwn in the upper right crner f part c. VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 497

24 (a) (b) (c) FIGURE 16. Wind-field analyses arund Orland n 0 August 199 at 3:10 GMT, ne hur after the wind fields shwn in Figure 15. (a) The -km-reslutin ptimal-estimatin wind field, (b) the 10-km-reslutin ptimal-estimatin wind field, and (c) the MAPS wind field. Each f these wind fields is displayed n the same 4-km-reslutin grid fr cmparisn. Orland Internatinal Airprt is at the center f each grid, and the east cast f Flrida is shwn at the right. The wind vectrs are scaled t wind speed, with a 5-m/sec reference vectr shwn in the upper right crner f part c. 498 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

25 grwth cntinued at varius lcatins fr the remainder f the afternn. The lifting f water vapr in the atmsphere, and the resulting release f heat as the water vapr cls, is the driving frce behind the frmatin f thunderstrms. Frecasting the frmatin f these strms requires that the wind-field cnvergence, and hence the vertical mtin f the air, be crrectly analyzed. The -km-reslutin Terminal Winds analysis shwn in Figure 15(a) prvides an excellent reslutin f bth the wind-field cnvergence assciated with the gust frnt, and the cnvergence pcket suthwest f the airprt. The 10-km-reslutin Terminal Winds analysis shwn in Figure 15(b) captures these features, but underestimates the magnitude f the cnvergence and is missing the detail cntained in the finer-reslutin analysis. The MAPS frecast field shwn in Figure 15(c) is nt well crrelated with the Terminal Winds analyses. Figure 16 shws wind fields fr 3:10 GMT, an hur later than the wind fields shwn in Figure 15. The strm system generated by the cnvergence pcket seen at :10 GMT has grwn int a large, strng cnvective strm that has evlved t the nrtheast f its riginal psitin. The -km-reslutin Terminal Winds analysis shwn in Figure 16(a) shws tw regins f strng winds, nrthwest and sutheast f the airprt. The winds sutheast f the airprt began with the cnvergence pcket that existed at :10 GMT, and they started t die ff after this time. The winds began t pick up in the regin nrthwest f the airprt at :40 GMT. These winds strengthened as the regin f surface-wind cnvergence mved nrth alng with the strm, and cntinued beynd the end f the day (4:00 GMT). The winds behind the gust frnt remained, althugh the gust-frnt thin line disappeared when the gust frnt cllided with the strm system. The cnvectin cntinued t build in the regin f cnvergence that extends tward the nrthern bundary f the analysis. The 10-km-reslutin Terminal Winds analysis shwn in Figure 16(b) captures the general tendency f this cnvergence, but underestimates the strength f the strnger winds and the strength f the cnvergence. Again the MAPS frecast field shwn in Figure 16(c) is nt well crrelated with the Terminal Winds analyzed wind field. Future Wrk Tw types f future wrk are discussed belw. The first is analysis enhancements, including imprvements t Terminal Winds and the develpment f a gridded temperature analysis. The secnd is real-time demnstratins at selected airprts. Analysis Enhancements The ITWS gridded analysis system will underg cntinued refinement and testing. A number f analysis upgrades are planned, including the use f the last analysis t refine the backgrund wind field, the estimatin and remval f errrs arising frm using an bservatin at lcatins away frm the bservatin lcatin, and the use f ITWS gust-frnt detectins t increase the wind-field accuracy by suppressing averaging acrss the gust-frnt bundaries. A majr effrt will be undertaken t add surface frcing t refine the winds in the PBL, which is imprtant fr regins with cverage frm nly a single Dppler radar r with significant tpgraphical variatin. We are als assessing the ability f develping technlgies t derive wind infrmatin frm time variatins in the radar reflectivity fields [15, 16]. When sufficiently develped, these technlgies will be an imprtant new surce f wind infrmatin. Accurate errr mdels are required t ensure the success f any statistical technique. The vlume f data at an ITWS site is nt sufficient t estimate errr mdels in real time; instead, we utilize a priri errr mdels. Our current errr mdels are qualitatively crrect but can be refined n the basis f extensive examinatin f bserved winds. A survey f the literature shws that past studies were cnducted t cnstruct errr mdels fr analyses with natinal r glbal dmains in which bservatin separatins are n the rder f hundreds t thusands f kilmeters. The results f these studies are nt apprpriate t errr mdels fr the Terminal Winds scale f analysis. We nw have an archive f data including data frm tw summers and ne winter in Orland, and ne summer in Memphis. We will use these data t cnstruct quantitatively crrect errr mdels. Starting in the summer f 1995, we will begin t develp a gridded temperature analysis. This analysis VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 499

26 will use a scalar versin f the ptimal-estimatin winds analysis. The initial temperature-analysis system will use infrmatin frm the RUC, MDCRS, and surface reprts. The infrmatin frm these surces will supprt a temperature analysis n the Terminal Winds 10-km-reslutin grid. The temperature field and wind field are linked thrugh physical prcesses. In an ITWS the wind field is knwn mre precisely than the temperature field, s the knwledge f the wind field can be explited t refine the temperature field. Current research at the University f Oklahma and at NCAR prvides techniques t retrieve temperature fields frm wind fields. After develpment f the initial temperature analysis, we will assess the ability f the temperature retrieval t refine the temperature field. Real-Time Demnstratins A number f real-time demnstratins are planned. The ITWS had an FAA Demnstratin and Evaluatin at Memphis during the spring and summer f 1994, and at Orland during the winter f The Demnstratin and Evaluatin cntinues at Dallas Frt Wrth in the summer f 1995 in cnjunctin with the Terminal Air Traffic Cntrl Autmatin Center TRACON Advisry System, which is the primary initial custmer f the Terminal Winds infrmatin, and at Memphis. These Demnstratin and Evaluatin exercises will prvide valuable testing in a variety f meterlgical envirnments. Summary The Terminal Winds analysis is an imprtant cmpnent f the ITWS. The Terminal Winds prvides an accurate, high-reslutin analysis f the hrizntal winds in a three-dimensinal grid in the terminal area. The wind infrmatin frm this system is prvided t a number f users, including air traffic autmatin systems and ther ITWS algrithms. Terminal Winds cmbines wind infrmatin frm a natinal-scale numerical-frecast mdel, meterlgical Dppler radars, cmmercial aircraft, and anemmeter netwrks. It is flexible enugh t run reliably with any available subset f these data, adding value t the natinal winds frecast in the terminal area as lcal sensrs prvide infrmatin. The Terminal Winds system perated in the summers f 199 and 1993 and the winter f 1995 in the Lincln Labratry ITWS testbed at Orland, Flrida, and in the spring and summer f 1994 at Memphis. The Terminal Winds system has demnstrated that it is a reliable peratinal system incrprating data frm multiple surces, including peratinal TDWR and NEXRAD Dppler radars. The terminal airspace extends frm the surface t 18,000 feet abve grund level, and is divided int tw regimes. The planetary bundary layer (PBL) cntains the atmsphere near the Earth s surface, and ften cntains wind structures with spatial scales n the rder f kilmeters and tempral scales n the rder f minutes. Abve the PBL, wind structures typically have spatial scales f at least tens f kilmeters and tempral changes ccur ver at least tens f minutes. Dppler radars prvide high-reslutin infrmatin in the PBL, where small-scale wind structures are expected. Abve the PBL, Dppler infrmatin becmes mre sparse and the RUC and MDCRS are imprtant surces f additinal infrmatin. A cascade-f-scales analysis is used t capture these different scales f atmspheric activity. A new winds-analysis technique, ptimal estimatin, was develped fr the Terminal Winds prduct. This technique is an extensin f bth ptimal interplatin and multiple-dppler analysis. Under certain restrictive hyptheses, high-quality estimates f the hrizntal winds can be derived frm multiple- Dppler data sets. The ITWS will usually have data frm at least tw Dppler radars. Optimal interplatin, a statistical interplatin technique, is used in the current state-f-the-art peratinal nn-dppler winds analysis. Optimal estimatin prvides wind estimates that are f higher quality than multiple-dppler analysis and des nt suffer frm the numerical instabilities that arise in multiple-dppler analysis. The ptimal-estimatin analysis als prduces wind vectrs that vary smthly between regins with cverage frm differing numbers f Dppler radars. The ITWS gridded analysis system will underg cntinued refinement and testing. A number f analysis upgrades are planned, including the use f the last analysis t refine the backgrund wind field, the estimatin and remval f errrs arising frm estimat- 500 THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994

27 ing winds at lcatins remved frm the bservatin lcatin, and the use f ITWS gust-frnt detectins t increase the wind-field accuracy. A majr effrt will be undertaken t add surface frcing t refine the winds in the PBL. We are als assessing the ability f develping technlgies t derive wind infrmatin frm radar reflectivity fields. When sufficiently develped, these technlgies will be an imprtant new surce f wind infrmatin. Acknwledgments A number f peple at NOAA/FSL prvided imprtant cntributins t the Terminal Winds effrt. In particular, we thank Jhn McGinley and Steve Albers fr the generus use f their Lcal Analysis and Predictin System cde t build ur initial prttype, and their many cmments and general supprt. We als thank Thmas Schlatter and Stan Benjamin fr prviding wind frecasts frm the Messcale Analysis and Predictin System. We thank the Melburne Natinal Weather Service Office fr access t the NEXRAD base data. Prviding this access was n mean feat. We als thank Russ Bltn and Jerry Starr at Cmputer Science Raythen fr mdifying their database t prvide the ff-airprt grund-statin data in ur analysis regin. Finally, we thank the LLWAS prgram ffice fr expediting the installatin f the LLWAS-3 anemmeter netwrk at the Orland Internatinal Airprt. The develpment f the Terminal Winds system represents the cmbined effrts f a number f Lincln Labratry emplyees. Significant cntributins were made by Steve Olsn, Sue Ya, Cindy McLain, Russell Tdd, Steve Kim, William Cmery, Jim Cappucci, Gary Rasmussen, and Steve Finch. REFERENCES 1. Seagull Technlgy, Inc., Center-TRACON Autmatin System Descriptin t Supprt an Operatinal Cncept Dcument, (1990).. F.W. Wilsn, J. Keller, R.G. Rasmussen, and P. Zwack, ITWS Ceiling and Visibility Prducts, Fifth Int. Cnf. n Aviatin Weather Syst., Vienna, VA, 6 Aug. 1993, p J.E. Evans and E.R. Duct, The Integrated Terminal Weather System (ITWS), Linc. Lab. J., in this issue. 4. R. Cle, F.W. Wilsn, J.A. McGinley and S.C. Albers, ITWS Gridded Analysis, Fifth Internatinal Cnference n Aviatin Weather Syst., Vienna, VA, 6 Aug. 1993, p. 56 (1993). 5. S.R. Finch, R.E. Cle, R.G. Rasmussen, F.W. Wilsn, and S. Kim, Summer 199 Terminal Area Lcal Analysis and Predictin System (T-LAPS) Evaluatin, ATC-18, MIT Lincln Labratry (7 Oct. 1994), DOT/FAA/RD-94/ S.C. Albers, The LAPS Wind Analysis, Furth Wrkshp n Operatinal Meterlgy, Whistler, BC, Canada (199). 7. J. McGinley, S. Albers, and P. Stamus, Validatin f a Cmpsite Cnvective Index as Defined by a Real-Time Lcal Analysis System, Weather Frecast 6, 337 (1991). 8. M.W. Merritt, D. Klingle-Wilsn, and S.D. Campbell, Wind Shear Detectin with Pencil-Beam Radars, Linc. Lab. J., 483 (1989). 9. T.D. Crum, R.L. Alberty, and D.W. Burgess, Recrding, Archiving, and Using WSR-88D Data, Bull. Amer. Meter. Sc.. 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 Isentrpic Three- Hurly Data Assimilatin System Using ACARS Aircraft Observatins, Mn. Weather Rev. 119, 888 (1991). 11. F.W. Wilsn and R.H. Gramzw, The Redesigned Lw Level Wind Shear Alert System, Furth Int. Cnf. n Aviatin Weather Syst., Paris, 4 8 June 1991, p ASOS Prgram Office Staff, Autmated Surface Observing System Users Guide Preliminary, Natinal Weather Service ASOS Prgram Office, 84 pp. (1991). [Available frm NWS ASOS Prgram Office, Silver Spring, MD 0910.] 13. K.A. Brewster, S.G. Benjamin, and R. Crawfrd, Quality Cntrl f ACARS Meterlgical Observatins A Preliminary Data Survey, Preprints, Third Int. Cnf. n Aviatin Weather Syst., Anaheim, CA, 30 Jan. 3 Feb. 1989, p L. Armij, A Thery fr the Determinatin f Wind and Precipitatin Velcities with Dppler Radars, J. Atmspheric Sciences 6, 570 (1969) 15. C.-J. Qui and Q. Xu, A Simple Adjint Methd f Wind Analysis fr Single-Dppler Data, J. Atms. Oceanic Technl. 9, 588 (199). 16. J.D. Tuttle and G.B. Fte, Determinatin f the Bundary Layer Airflw frm a Single Dppler Radar, J. Atms. Oceanic Technl. 7, 18 (1990). 17. D.G. Luenberger, Optimizatin by Vectr Space Methds (Wiley, New Yrk, 1969). 18. L.S. Gandin, Objective Analysis f Meterlgical Fields, Leningrad, translated by Israel Prgram fr Scientific Translatins, Jerusalem, 1965 (1963). 19. R. Daley, Atmspheric Data Analysis (Cambridge University Press, Cambridge, UK, 1991). 0. F.P. Brethertn and J.C. McWilliams, Estimatins frm Irregular Grids, Reviews f Gephysics and Space Physics 18, 789 (1980). 1. A.F. Bennett, Inverse Methds in Physical Oceangraphy (Cambridge University Press, Cambridge, UK, 199).. M. Cairns et al., A Preliminary Evaluatin f Aviatin-Impact Variables Derived Frm Numerical Mdels, NOAA Tech. Mem. ERL FSL-5 (1993). VOLUME 7, NUMBER, 1994 THE LINCOLN LABORATORY JOURNAL 501

28 RODNEY E. COLE is a staff member in the Weather Sensing grup. His research interests are in autmated weather analysis and frecast algrithms, and linear and nnlinear ptimizatin. He received a B.S. degree with a duble majr in mathematics and physics frm the Virginia Plytechnic Institute and State University (VPI), an M.S. degree in mathematics frm VPI, and a Ph.D. degree in mathematics frm the University f Clrad at Bulder. Befre jining Lincln Labratry in 1990, he wrked at the Natinal Center fr Atmspheric Research. His first prject as a staff member at Lincln Labratry was t lead the integratin f the Terminal Dppler Weather Radar (TDWR) system and the Lw Level Wind Shear Alert System (LLWAS) III, which is currently being installed in the field. WESLEY F. WILSON is a staff member in the Weather Sensing grup. His primary fcus f research is in the develpment f weather nwcast algrithms. He received B.S. and Ph.D. degrees in mathematics frm the University f Maryland. He was an assistant prfessr f mathematics at Brwn University in 1965 and the University f Michigan in 1966, and a prfessr f mathematics at the University f Clrad at Bulder frm 1967 t Befre jining Lincln Labratry in 1990 he wrked at the Natinal Center fr Atmspheric Research. In 199 Wes received the Aviatin Week Lauriat Award fr his inventin f the Lw Level Wind Shear Alert System (LLWAS) III, which was credited with saving a cmmercial aircraft frm a wind-shear crash in Denver n 8 July THE LINCOLN LABORATORY JOURNAL VOLUME 7, NUMBER, 1994