LLA DOBSON, FRANK MONALDO, JULIUS GOLDHIRSH, and JOHN WILKRSON VALIDATION OF GOSAT ALTIMTRDRIVD WIND SPDS AND SIGNIFICANT WAV HIGHTS USING BUOY DATA GOSA T radar altimeterderived wind speeds and signifiant wave heights are ompared with those measured by buoys in the National Data Buoy Center network. Measurements from a subset of 43 buoys moored in oastal regions and deep within the North Paifi, North Atlanti, and Gulf of Mexio were examined. Altimeter omparisons were obtained during the GOSA T geodeti mission from May through August and Otober through Deember 1985. Only GOSAT data within kilometers of buoy loations were aessed, resulting in 1166 windspeed and signifiantwaveheight pairs. An error analysis was performed to better understand the differenes between altimeter and buoyderived results and to establish onsisteny between the two data sets. Four algorithms relating altimeter radar ross setion to oeansurfae wind speed were investigated. Measurement goals for GOSA T were 1.8 meters per seond rms for wind speeds of 1 to 18 meters per seond and meter rms for signifiant wave height, or 1 perent, whihever was greater. These goals were met. INTRODUCTION Wind speed and diretion over the world's oeans are required as inputs to meteorologial and waveforeasting models and are desirable inputs to oeanirulation models. While winds are measured regularly and aurately over land areas, winds over the oean are muh more diffiult to measure. The National Oeani and Atmospheri Administration uses 2 to 4 reports per day from buoys and widely sattered ship reports. GOSA T data in the reporting system add over 5, global values per day to that total, with the following potential benefits: 1. Improved tropial and extratropial storm analyses result in inreased warning time for hurrianes and winter storms; 2. Improved initial onditions for regional, hemispheri, and global numerial models result in improved foreast auraies; 3. A homogeneous, global set of wind and wave data that improves estimates of seasonal and annual variations for limate researh; 4. Wind data for deriving winddriven urrents within the right time frames to produe yield preditions for improving fisheries management and inreasing fish athes. Radar remote sensing requires an understanding of the relationships between the signal the instrument is measuring and the physial harateristis of the medium J. Wilkerson is with the ational Oeani and Atmospheri Admini tration, Rokville, MD 2852. The other authors are members of the Spae Department, The Johns Hopkins University Applied Phys is Laboratory, Laurel, ;VID 277. 222 from whih the signal baksatter. In many ases, these relationshjps an be established by quasiempirial means with the aid of insitu measurements. The determination of oean wind speed and signifiant wave heights from GOSA T radar altimeter measurements represents suh a ase. Two parameter that an be derived from the altimeter measurements are oeansurfae wind speed and signifiant wave height. Wind speed is related to baksattered power, and signifiant wave height is determined from the slope of the leading edge of the returned pulse. Algorithms used to extrat these parameters and the assoiated auraies of these algorithms are addressed here. We fir t desribe results of a simulation onduted before the GOSAT launh. We next show omparisons of wind and wave measurements with buoys, and then desribe the errors inherent in any omparison of the two instruments. VALIDATION APPROACH Before the GOSAT launh, omputer simulations were performed to predit the number of expeted omparisons and the time periods required to obtain enough samples for statistial onfidene levels. I The simulations involved "flying" the altimeter over the buoy network and determining the number of times the altimeter ground traks were within kilometers of buoy loations and within 3 minutes of measurement. Sine the overflight of GOSA T rarely oinides with either buoy measurement times or loations, there almost always exist temporal and spatial separations between paired GOSAT and buoy observations. Beause the buoys used in this study report every hour, time separations are never greater than 3 minutes. The validation John H opkills APL Tehnial Dige, Volume 8, Number 2 (1987)
strategy limits spatial separations to a maximum of kilometers. Typial histograms of the number of potential omparison pairs as a funtion of these simulated time and spae separations for a given buoy during April to June are shown in Figs. I and 2. Figure 3 shows the typial pattern of ground traks laid down by GOSA T within a ISOkilometer radius of a buoy over the same time period. The ordinates of Figs. I and 2 represent the number of altimeter/ buoy omparisons within the indiated absissa range and time separations, respetively. In Fig. 1, a "hit" represents the losest approah distane between the satellite subtrak and the buoy loation. In Fig. 2, a hit represents any ase for whih the losest approah distane is within kilometers. We note from Fig. 1 that for any given buoy, a relatively small perentage of the total number of hits ours within 5 kilometers. We also note from Fig. 2 that the distribution of time separations is for the most part uniformly spread over the 3minute period. The histograms of Figs. 1 and 2 further show relatively few satellite and buoy observations that oinide either in time or spae over a 9day period. Ideally, omparisons should be made using only those data sets that are oinident in time and spae. The total number of hits orresponding to maximum separation distanes of 5 and kilometers is given in Table 1 for 43 buoy platforms loated in different regions of the world. These were obtained for the period April through June. Table 2 gives similar information for those buoys that also measure wave height. Buoys loated at higher latitudes in the Paifi have slightly larger numbers of hits, and buoys in the Gulf of Mexio have somewhat fewer hits. If only buoy data taken within 5 kilometers of the GOSA T ground trak are used, the total number of observation pairs available for performane evaluation is about per year. If all GOSAT observations within kilometers of a buoy are used, the total inreases to about 4 per year. xperiene with atual data sets has indiated that this total is signifiantly redued, the dominant reason being the elimination of measurements made by buoys that are very lose to land. 1.I,_I..I,IrI,. Range separations for wind and waves (one bin == 5 kilometers) g. 8 en (]) 6 5. 4 :. ' J 2 rtf o 25 5 75 1 125 Range separation (kilometers) Figure 1A histogram of hits for range separations between altimeter ground trak positions and buoy 445 over a three month period. A hit is defined as a groundtrak buoy separation distane less than kilometers. 46 44 (]) ::!:: (]) 3. 42 5 4 z 38 73 71 69 67 65 West longitude (degrees) Figure 3A map showing predited ground traks of the GO SAT altimeter within a kilometer distane from buoy 445 over a threemonth period.. o ro Q. (]) en (]). 5. :. ' Cii.. :::J Z 14 12 r 1 r 8 f 6 f 4 2 I n I Time separations for wind (one bin == 6 seonds) r r r r r r 1 rt lfn 1 2 Time separation (minutes) Figure 2A histogram of time separations orresponding to altimeter hits over a threemonth period for buoy 445. Johns H opkins APL Tehnia l Digesl. Vo lume 8, N umber 2 (/987) I l 3 Table 1Number of GOSAT/buoy data pairs for various buoy loations during the period April through June for measuring wind speed. Points of Points of Number of Closest Closest Buoys/ Approah Approah Region Platforms < km <5 km North Paifi 19 515 178 North Atlanti 1 25 86 Great Lakes 7 192 72 Gulf of Mexio 6 139 48 Hawaii 53 17 Totals 43 1149 41 223
Dobson et al. Va lidation of GOSA T A ltimeterderived Wind Speeds and SWH Using Buoy Data Table 2Number of GOSAT/buoy data pairs for various buoy loations during the period April through June for measuring signifiant wave height, Points oj Number of Closest Buoys/ Approah Region Platforms < km North Paifi 19 515 North Atlanti 8 142 Great Lakes 7 192 Gulf of Mexio 5 139 Totals 39 988 TH BUOY NTWORK OF TH NATIONAL DATA BUOY CNTR Points oj Closest Approah <5 km 178 69 72 48 367 Figure 4 shows the loations of the 66 reporting stations in the National Data Buoy Center network of buoys overing the North Paifi, North Atlanti, Great Lakes, Gulf of Mexio, and Hawaii. Most are in oastal regions but 16 are loated in the open oean. Beause of land effets on oastal waters and the nature of the wind fields there, stations lose to land have not been used in the effort. All buoys in the network measure wind speed and diretion, atmospheri pressure, air temperature, and seasurfae temperature eah hour. A subset of the buoys also makes hourly measurements of signifiant wave height, signifiant wave period, and, in some ases, wave spetra. However, within the hour, the times of measurement and the periods of integration differ for these measurements. Wave data that are averaged for 2 minutes are reported at 29 minutes after the hour. Winds are averaged for 8.5 minutes starting at 4 minutes after the hour. On most buoys, anemometers are loated 1 meters above mean sea level. For those buoys in whih windspeed measurements were made at other elevations, a boundary layer model was used to adjust the values to 1 meters before omparison. WINDSPD VALIDATION Wind speed at the oean surfae is dedued from the altimeterbaksattered radar ross setion. At nadir inidene angle, the energy bak sattered from the oean is diretly proportional to the normal inidene Fresnel powerrefletion oeffiient and inversely proportional to the mean square slope of the lowpassfiltered version of the oean surfae. 2 The onstant of proportionality in this relationship depends on the probability density of surfae slopes. Cox and Munk 3 measured this probability density and determined that there was a logarithmi relationship between density funtion and wind speed. As the winds inrease, the surfae slopes inrease and the bak sattered ross setion dereases. This relationship between wind and a D is based on an empirial probability density, although it does not neessarily hold at all wind speeds. The relationship is known to break down at Jow wind speeds when the slopes on the surfae are low and the wave heights are equal to or shorter than the wavelength of the eletromagneti energy. 4 Four algorithms that are used to infer surfae wind speed from radar rosssetion measurements are desribed below. Brown's Algorithm Brown et al..5 ompared the normalized baksatter oean ross setion derived from the altimeter power measured on board the GOS3 satellite with wind 7...= 6 Figure 4National Buoy Data Center buoy loations (shown as dots), Ul (!) (!) (!) 5.3 '';:::; 5 4 (; z 3 2 1LLL 18 16 14 12 1 8 6 West longitude (degrees) 224 Johns Hopkins APL Tehnial Digest, Volume 8, Number 2 (1987)
Dobson et al. Va/idarion of GOSA T A/fill1eferDerived Wind Speeds and SWH Using Buoy Dafa speeds derived from buoy measurements. In partiular, 184 measurements of baksatter power were ulled over an approximate threeyear period; they orrespond to measurements made during the "near" overflights of National Oeani and Atmospheri Administration data buoys from whih surfaewind speeds were obtained. Brown used buoy data from the North Atlanti and North Paifi taken within 1.5 hours and kilometers of a GOS3 overpass. The resultant algorithm relating predited wind speed to altimeter ros etion is given in two stages. The first stage is given by W I = exp [ D 1O (2I XOI IO) B] A.874 B.124651 fora < 1.12, A.39893 B.31996 for 1.12 :s a :s 1.9 deibels, A.1595 B.172 15 for a 1.9 deibels. (2) In q. 1, ao is the altimetermeasured normalized baksatter ross setion expressed in deibels relative to 1 square meter, and A and B assume the defined values. Here, W I represents the first e timate of the predited wind speed. In omparing predited and buoymeasured wind speed, Brown et ai. found the distribution of the differene values between buoy and altimetermeasured wind speed to be skewed. To mitigate the skewness, a seondstage estimate of the predited \\'ind speed, vv 2, was gi ven by where (I I (I, WI A :s 16 meter per seond, (1) (3) W I > 16 meters per seond, (4) 87799,.3649928,.462421,.194952, and.3288189. qs. 1 and 3 together represent the resultant Brown et ai. algorithm that orresponds to a windspeed measurement at a height of 1 meters above the oean surfae (Fig. 5). The Chelton and MCabe Algorithm In applying the Brown algorithm to the Seas at database, Chelton and MCabe li demonstrated that the algorithm produed a multimodal windspeed distribution. They attributed it s form to disontinuities in the slope of the windspeed algorithm at 1.12 and 1.9 deibels. Johns H opkin.,.4 PL Tehnial Dig esl. \ 'oluille 8. N um ber :1 (J 98 7) (5) 12 (/).D 'u (J) " o b 1 14r CheltonMCabe CheltonWentz Brown Smoothed Brown 8 o 4 8 12 16 2 Wind speed (meters per seond) Figure 5A omparison of algorithms relating altimeterderived radar ross setion with surfae wind speeds. Beause there are no physial reasons for a multimodal distribution, they developed another algorithm given by where W = 1 [C C)!H], (6) G = 1.52 and H =.468, (7) and where a D (the radar ross setion) and Ware expressed in deibels and meters per seond, respetively. The values of G and H in q. 6 were estimated by using a regression analysis orresponding to 96 days of Seasat measurements. The values of a D were derived from the Seas at altimeter, and wind speeds were estimated from offnadir vertially polarized satterometer returns. Both time and spatial averaging were performed within gridded regions defined by 2degree latitude by 6degree longitude intervals. Only data between the latitudes of 65 Nand 55 os were inluded and only data for distanes greater than 2 kilometers from land were used. Within eah grid, ross setions and wind speeds were averaged in both time and spae over the 96day period; hene, eah of the 1947 grids within whih data existed provided a single averaged data point of satterometerestimated wind speed and altimeterderived radar ross etion (Fig. 5). The Goldhirsh and Dobson Algorithm In an attempt to eliminate the effets of disontinuities in windspeed slope (with ross setion) intrinsi to the Brown algorithm, Goldhirsh and Dobson 7 fitted a fifthdegree polynomial to the original Brown data (184 points). The fit produed a smooth funtion that was nearly idential to the original algorithm but it produed no multimodal distribution. The derivation, the smoothed Brown algorithm, was onsidered to be a temporary solution to the problems assoiated with the Brown algorithm. When a larger GOSAT / buoy database beomes available, at 225
.Dobson et al. Vatidar ion of GOSA T A/rilllererDerived Wind Speeds and SWH Using Buoy Dara tempts to improve the algorithm will be made. The smoothed Brown algorithm is given by (Fig. 5) w all ao a ll, < 15 deibels, (8) 11= where 15.383, 16.77, 2.35,.9896,.18,.6414. (9) The ondition a O < 15 deibels implies that the algorithm is restrited to windspeed values greater than 2 meters per seond. The Chelton and Wentz Algorithm Chelton and Wentz 8 noted several weaknesses in the windspeed model funtion derived from Seasat data as proposed by Chelton and MCabe. 6 A fundamental problem was that the satterometer windspeed algorithm was flawed. In addition, temporal and spatial averaging over a 2 by 6degree grid resulted in satterometer wind speeds limited to the 4 to 14meterperseond range. Furthermore, sine the spatial (2 by 6degree) and temporal (threemonthperiod) averages were rather large, performane of the algorithm for individual measurements was unertain. Hene, Chelton and Wentz developed a new algorithm based on measurements of the Seasat altimeter radar ross setion averaged in 5kilometer bins in the alongtrak diretion. These averaged values were then ompared with wind speeds estimated from the nearest lkilometerbinned satterometerdetermined wind speeds ( to 25 kilometers from nadir). In that way, 241, omparisons of radar ross setions at nadir versus satterometer wind speeds ranging from to 25 kilometers off nadir were obtained. The resultant algorithm is in the form of a tabulation over the range of radar ross setions from 8 to 19.6 deibels and wind speeds from 21 to.1 meters per seond. The tabulation is given in Ref. 9 and is plotted in Fig. 5. WINDSPD VALIDATION The windspeed measurement goal of th.e GOSA T altimeter was speified as 1.8 meters per seond rms for wind speeds over the range of 1 to 18 meters per seond. 9 One of the objetives of the validation effort was to assess whether the GOSAT altimeterderived wind speeds met that goal. The GOSAT Database The raw GOSA T database is reeived in the form of a Sensor Data Reord and is ombined with an ephemeris to reate a Geophysial Data Reord in whih all instrument orretions are inorporated. Oneseond 226 averages of radar ross setion and signifiant wave height were extrated from the Geophysial Data Reord orresponding to ground traks within kilometers of 43 buoys. In that effort, data were ompiled over two periods totaling seven monthsmay through August and Otober through Deember 1985. The overall derived database was ulled, and hits were removed on the basis of the following riteria: (a) the lose proximity of buoy stations to land, (b) flagged signifiantwaveheight data errors on the Sensor Data Reord, () obvious buoy data errors, (d) altimeterheight dataerror flags, and (e) errati hanges of radar ross setion. The resulting database after ulling onsisted of 1166 satellite/ buoy data pairs. A subset of these measurements onsisted of 698 hits orresponding to 13 openoean buoys, i.e., buoys loated at least 4 kilometers from the nearest shoreline. These data were also stratified aording to region, altimeter pointing angle, altimeter trak / buoy separation distane, number of ross setions averaged, and the variability of measured ross setions in the averaging interval. Stratifiation by region should establish whether some areas are more suitable for omparison than others. Pointingangle hanges ould playa signifiant role in the determination of radar ross setions, espeially for alm sea onditions when the speular omponent is diminished in the baksatter diretion as the pointing angle moves off nadir. The separation distane and averaging interval determine the spatial sales over whih omparisons are valid. Radar rosssetion variability is important beause it indiates the homogeneity of the wind field and helps to identify those times when rain is present in the measuring area. Table 3 presents the stratifiation parameters used to ompare altimeter and buoy data. Item 4 of the table orresponds to either a 5 or 1point average in the ross setion around the minimum range, where eah "point" represents a Iseo nd time interval onstituting a 7kilometer groundtrak distane interval. Item 5 orresponds to two levels of rms flutuations over the averaging interval. In the ulling proess, a detailed haraterization of eah hit was obtained through a series of plots as shown in Fig. 6. Figure 6(a) shows a plot of the buoy position (.) and the GOSA T ground trak. When land is in the area displayed, its boundaries are also indiated. Shown in Fig. 6(b) is signifiant wave height as measured over a 24hour period for the day of the omparison. The olored irles in this figure indiate the airsea temperature differene (in degrees entigrade) at the oean surfae as measured by the buoys (righthand sale). The wind speed (olored sq uares) and wind gust (.. ) over a 24hour period are given in Fig. 6(). Figure 6(d) and 6(e) give the altimetermeasured signifiant wave height and radar ross setion as a funtion of range between the buoy and ground trak. In the desendingpass example shown, the range starts at near kilometers, reahes a minimum of 37 kilometers, and then inreases again. Parameters listed in Fig. 6 orrespond to the time of minimum range and represent the following: radar ross setion (5point average); wind speed from the Johns Hopkin s APL Tehnial Digest, Volume 8, N umber 2 (/98 7)
Dobson et al. Validation of GOSA T AltimeterDerived Wind Speeds and SWH Using Buoy Data Table 3Stratifiation parameters for omparing altimeter and buoy data. I. Regions Open Pai fi Coastal Paifi Open Atlanti Coastal Atlanti Gulf of Mexio quatorial Paifi All regions Open oean Parameters: ao (db) Poly wind (m/se) Chelton (m/se) Buoy wind (m/se) GOSAT SWH (m) Buoy SWH (m) Buoy (number) Day (Julian) Airsea temp diff. (OC) Time (GMT), min Min. range (km) Altim. attitude (deg) 12.3 3.18 3.27 2.32 1.41 1.6 463 189.29 11 67.86.95.19 22 2. Antenna angle off vertial (degrees).75 1. 3. Range between buoy and altimeter subtrak (kilometers) 5 1 4. Number of radar ross setion measurements averaged * Five Iseond measurements Ten Iseond measurements 5. Standard deviation of radar ross setion over averaging area for ases listed under item 4 (deibels) 1. *The spatial equivalent of Iseond measurements of radar ross setion is 7 kilometers along trak. smoothed Brown algorithm; wind speed from the CheltonWentz algorithm; buoy wind speed; GOSA T signifiant wave height; buoy signifiant wave height; buoy number; Julian day; airsea temperature differene; hour of altimeter pass; minimum range between buoy and altimeter subtrak; and altimeter attitude angle. Numbers to the right of these parameters represent the differene between buoy and altimeter measurements; e.g., "hour (GMT, min)" indiates that the altimeter passed at 11 hour and that there was a 22minute differene in time between the two measurements. Composite figures of this type were prepared for the 1166 data pairs to aid in the assessment of the temporal and spatial behavior of the wind and wave fields. Radar CrossSetion Statistis The global distribution of radar ross setions was obtained for two threemonth periods to determine its onsisteny and to ompare it with Seasat altimeter distributions. The distribution for Otober through Deember 1985 is shown in Fig. 7. With a bin size of.2 deibel, Johns H opkins A PL Tehnia l Digesl. Volume 8. N umber 2 (/987) i> :3 " ''::; Z 55 (a) 53 51 49 47 2 22 24 26 W. longitude (deg.) 28 24r... 15 (b) 1 2 5 1 16 o ::::: I 12 8 4 u 24 2 16 " 12 a. I/) 8 " : 4 (e) & 4 8 12 16 2 24 Period (hours) 6 8 1 12 14 16 Range (kilometers) 5 : 1 i. 15 2 I Figure 6A series of plots desribing the temporal and spatial behavior of buoy and altimeter data. A summary of pertinent data at the top of the figure inludes a seond olumn denoting the differene between buoy and altimeterderived measurements. (SWH is signifiant wave height.) the distribution peaks at 1.9 deibels with a mean of 1.9 deibels and a standard deviation of.9 deibel. The global distribution from the Seasat mission had a mean of 1.8 deibels. 227
Dobson et al. Validation of GOSA T A ltimeterderived Wind Speeds and SWH Using Buo)' Data 1r,. 6 o C Q.) u CD CL 4 2 1 12 14 16 18 Radar ross setion (deibels) Figure 7The distribution of GOSAT altimeterderived radar ross setion for Otober through Deember 1985. The distribution peaks at 1.9 deibels, has a mean of 1.9 deibels, and has a standard deviation of.9 deibel. Seasat had a mean of 1.8 deibels. Altimeter and Buoy WindSpeed Comparisons Figure 8 presents omparisons between GOSA T al: timeterderived wind speeds and buoy wind speeds for the Brown, smoothed Brown, CheltonMCabe, and CheltonWentz algorithms using all buoys (121 omparisons). The solid lines represent the perfetagreement ase and the ±2meterperseond ases. The data shown here are for a maximum range separation of 5 kilometers with 5point averaging and an attitude restrited to less than.75 degree. The Brown and smoothed Brown algorithms (Fig. 8a and 8b) gave the smallest rms differene of 1.7 meters per seond between buoy and altimeter measurements. These ompare with 3.1 and 2.3 meters per seond for the CheltonMCabe (Fig. 8) and CheltonWentz (Fig. 8d) algorithms, respetively. There appears to be an overestimation of wind speeds by both Chelton algorithms as evidened by the means of 1.8 and 1.3 meters per seond, ompared to means of.3 and meter per seond for the other two algorithms. Very few high wind speeds were measured from buoys; they are required to truly establish the best algorithm. Several data points in Figs. 8 and 8d are not shown beause they orrespond to predited wind speeds larger than the sale maximum of 2 meters per seond. Algorithm omparison results for range and attitude stratifiations for both the "all buoys" and "openoean" oean buoy ases (43 and 13, respetively) are summarized in Table 4. Comparisons of the mean differene wind speed and the rms differene (GOSAT versus buoyderived) are listed for the four algorithms mentioned above. The smallest rms differenes (*) for eah of the algorithms our for range intervals of 5 kilometers or smaller. When all buoys are onsidered, the best auray ours when the altimeter pointing has an attitude within.75 degree. The openoean buoys do not show a strong dependene with attitude within 1 degree. In every stratifiation indiated, the Brown and smoothed Brown algorithms do better than the others. While ranges of kilometers may be too large to assure homogeneity over an area, reduing the range to 5 kilometers severely limits the number of data points and hene introdues smaller onfidene levels pertaining to the results. VALIDATION OF SIGNIFICANT WAV HIGHT The GOSAT signifiantwaveheight measurement goal was set at ± meter or 1 perent. 9 Based on omparisons of GOSATderived radar altimeter and buoy data, that goal has been met. Figure 9 shows GO SAT / buoy signifiant wave heights for a shorter distane than 5 kilometers. These data are for the 43 openoean buoys and onstitute 116 omparisons. The rms differene is.49 meter with a mean deviation of.36 meter. The rms waveheight deviations were between.4 and.8 meter for the range of offnadir angles and range separations shown in Table 4. Mean differenes are generally around +.4 meter, indiating that the GOSA T signifiant wave height is lower than the buoy level by that amount. The global distribution of signifiant wave heights for May is shown in Fig. 1. The mean and standard deviation of the distribution are 2.4 meters and.6 meter, respetively. XPCTD DIFFRNCS IN ALTIMTRBUOY COMPARISONS In omparing altimeterderived wind speed and signifiant wave height with buoy e timates, it is important to establish selfonsisteny between the omparisons and the expeted unertainty. The following disussion fouses on five distint error oures that will ause altimeter and buoy estimates of wind speed and signifiant wave height to differ: (a) buoy instrument inauraies, (b) temporal separation, () spatial separation, (d) time and area averaging, and (e) altimeterrelated errors. Referene will be made to Fig. 11 desribing individual soures of differenes a a funtion of wind speed. 1, 11 Buoy Instrumentation The instrument error a soiated with buoy estimates of wind speed or signifiant wave height will ontribute to the observed differenes with altimeter estimates. Anemometers mounted on board the National Data Buoy Center network of operational buoys are speified to an rms auray of meter per seond or 1 perent of wind speed, whihever is greater. 12 Interomparisons of windspeed measurements from twin anemometers loated on single buoys are onsistent with these speifiations. In an effort by Monaldo, lo wind speeds measured by dual anemometer systems on four buoys were examined over a onemonth period, and rms differenes between the pairs of anemometers on eah buoy were 228 Johns Hopkins APL Tehnia l Digest, Volume 8, Number 2 (1987)
Dobson et al. Validarion of GOSA T A /rimererderived Wind Speeds and SWH Using Buoy Dara 2 2 = (a) u CIl 16 CIl ')12 = (b) u CIl 16 ') 12 CIl 8 CIl 8 C C. l I «4 «4 (j) (j) UJ UJ t.9 t.9 3 6 9 12 15 18 3 6 9 12 15 18 Buoy wind speed (meters per seond) 2 2 = () = (d) u u CIl 16 CIl 16 CIl CIl ')12 ') 12 CIl 8 CIl 8 C. l I «4 «(j) (j) 4 UJ UJ t.9 Buoy wind speed (meters per seond) 3 6 9 12 15 18 3 6 9 12 15 18 Buoy wind speed (meters per seond) Buoy wind speed (meters per seond) Figure awind speeds derived using GOSAT altimeter data and (a) the Brown et al. algorithm 5 (rms deviation 1.7 meters per seond), (b) the smoothed Brown algorithm 7 (rms deviation 1.7 meters per seond), () the CheltonMCabe algorithm 6 (rms deviation 3.1 meters per seond), and (d) the CheltonWentz algorithm 8 (rm s deviation 2.3 meters per seond). In eah ase, the separation distane is within 5 kilometers, the altitude is within.75 degree, and the number of GOSAT/buoy omparisons is 121 using 43 buoys. found to be.48,.72,.49, and.6 meter per seond. These omparisons are important in that altimeters annot be expeted to agree with buoy measurements any better than anemometers on the same buoy an be expeted to agree with eah other. Using the National Data Buoy Center buoy auray speifiations and a global average oean wind speed of 8. meters per seond, altimeter and buoy estimates of wind speed an be expeted to differ by.8 meter per seond (Fig. 11) beause of auray limitations on the buoy estimate of wind speed. The auray of buoy estimates of signifiant wave heights is somewhat more diffiult to speify. A dediated experiment omparing wave heights measured by an operational National Data Buoy Center buoy with those Johns H opkins APL Tehnial D igesl. Volume 8. N umber 2 (/987) measured by a Waverider Analyzer Satellite Communiator buoy, whih is onsidered a measurement standard, indiates rms differenes in the estimation of wave heights of about 7 perent. 13 This differene is shown below to be onsistent with sampling variability errors. The instrument error assoiated with buoy measurement of signifiant wave heights may therefore be onsidered negligible. Temporal Separation In order to obtain a reasonably large number of altimeter buoy omparisons, a temporal window of aeptability is established, for example, a window wherein altimeterbuoy omparisons made within one hour of eah oth 229
Dobson et al. Validation oj GOSA T A ltimeterderived Wind Speeds and SWH Using Buoy Dala Table 4Summary of mean and rms windspeed errors stratified as a funtion of antenna pointing and losest approah range. Four algorithms are onsidered. Off Vertial (deg) Range (km) Points (no. ) Smoothed Brown Mean rms (m/se) Brown Mean rms (m/se) Chelton Wentz Mean rms (m/se) Chelton MCabe Mean rms (m/se) All buoys (43) 1..75 5 1 5 1 5 1 192 428 682 121 269 443 61 248.1.2.4.3.3.4.4.6 1.9 2.3 1.7* 1.7*.7.8 1..8.9 1..9 2.4* 3. 2.7 2.9 * 2.7 2.9.3.4.6.6.7.6.7.8 2.3 1.7* 1.7* 1.4 1.4 1.4 1.4 3.1 3.3 3. 3.2 2.3 2.9 2.9 Openoean buoys (13) 1..75 5 1 5 1 5 1 98 29 32 61 135 27 31 8 125.3.3.4.7.3.6 1.7 1.5 * 1.9 1.6 1..9.9 1.3 2.6 2.7 1.9* 2.5 2.6 2.9.7.6.7.9.8.7.8 1.7 1.5* 1.9 1.7 2.3 1.4 1.3 1.5 1.3 1.5 2.6 1.9 2.5 2.9 *Minimum rms for the indiated ategory. 14rrr_r_ 12 1 +' C o u 2 ;;:: ' 'en f <! (f) o w <.9 2 4 6 8 Buoy signifiant wave height (meters) Figure 9GOSAT altmeterderived signifiant wave heights ompared with buoy measurements for a distane separation within 5 kilometers. Comparisons were made using 43 openoean buoys (116 data points). The rms deviation is.49 meter with a mean deviation of.36 meter. 8 6 CL 4 2 2 4 6 8 1 Signifiant wave height (meters) Figure 1Global distribution of signifiant wave heights for May 1985. Bin size is.25 meters. The mean sign ifiant wave height is 2.4 meters and the standard deviation is.6 meter. er are aeptable in the omparison data set. The farther apart in time two measurements are made, the larger the 23 differene that an be expeted between the two measurements. stablishing smaller windows of aeptability re Johns Hopkins A PL Tehnial Digest, Volume 8, Num ber 2 (1987)
Dobson et al. reords of 35 kilometers in length. Using the logi that we annot expet the altimeter and buoy to agree when their measurements are separated by a ertain distane any more than we an expet the altimeter estimates to agree with eah other when separated by the same distane, we estimated the expeted differenes due to spatial separation. A 2kilometer window of aeptability with an average separation of 14 kilometers resulted in expeted differenes of meter per seond in wind speed and.2 meter in signifiant wave height. Using a 5kilometer window and an average separation of 35 kilometers resulted in expeted differenes of 1. meter per seond in wind speed and.3 meter in signifiant wave height. 1 Total Radar ross setion impreision 5 (l) Time /area averaging u Total non altimeter 4 COu (f) Validarion of GOSA T A/rimererDerived Wind Speeds and SWH Using Buoy Dara (l) 3 ' " 2u 2 (l) Q. X L.U o o 2 6 8 1 12 14 Wind speed (meters per seond) 4 16 18 Figure 11Plots of rms deviations versus wind speed for indiated error soures. dues this error, but at the ost of having fewer omparisons available. To estimate the magnitude of the expeted differene between two measurements separated in time, several temporal buoy reords from openoean buoys were examined that provided hourly windspeed and signifiant wind height estimates for monthly periods. Sine buoy measurements of wind speed and signifiant wave height are made hourly, the maximum temporal separation between a buoy and an altimeter estimate of wind speed and signifiant wave height is 3 minutes, with an average separation of 15 minutes. The examination of tem poral buoy reords indiated that the average separation of 15 minutes in buoy and altimeter estimates would ause a.3meterperseond rms differene in wind speed and a O.I meter rms differene in signifiant wave height. 1 Spatial Separation The effets of spatial separations are similar to those of temporal separations. In order to inrease the number of available altimeterbuoy omparisons, altimeter and buoy measurements of wind speed and signifiant wave height separated by less than the spatial window of aeptability are inluded in the omparison data set. For example, a window of 5 kilometers would mean that every altimeter and buoy measurement omparison having a spatial separation of less than 5 kilometers that additionally falls within the temporal aeptability window is inluded in the omparison data set. The larger the spatial window of aeptability, the larger the number of omparisons available. Unfortunately, the larger that window, the greater the differenes in buoy and altimeter measurements assoiated purely with the fat that the measurements are not oinident. To estimate the effet of the spatial variability of wind and wave fields, we examined a global representation of approximately 5 Seas at and 5 GOSATaltimeterderived windspeed and signifiantwaveheight data.jo hn s H opkins APL Tehnial Diges r. \ 'o lum 8. N um ber :2 ( /98 7) Time and Area Averaging The altimeter estimates of wind speed and signifiant wave height (SWH in the examples below) are the result of spatial averaging; at a given instant of time, the altimeter estimate of radar ross setion is an average over a footprint diameter given by 14, 15 (1) where H is the height of the satellite (e.g., 8 kilometers) and is the veloity of light. The parameter Te is the effetive pulse width given by where To is the effetive hirped pulse width (e.g., 3.125 nanoseonds) and N is \12 the number of sampled gates in the averaging interval (e.g., 24), and (12) The estimate TswH is the additional ontribution of the pulse width aused by oean waves having a given signifiant wave height. Assuming a nominal signifiant wave height of 2.5 meters and the indiated GOSAT values (given within parentheses speified above), we arrive at an effetive footprint diameter of 8.5 kilometers assoi at ed with the instantaneous radar rosssetion measurement. Averaging 5 and 1 seonds of altimeter data (as was done here) produes a resolution swath 35 and 7 kilometers long, respetively. Pierson II and Donelan and Pierson 16 have investigated the relationship between spatial and temporal averaging of wind speed and signifiant wave height, respetively. Their results suggest that the sampling variability assoiated with an area average is very small. Most of the differenes between altimeter and buoy estimates of wind speed and signifiant wave height assoiated with sampling variability are the result of limited time averages. The 8.5minute average of buoy wind speed is expeted to result in sampling variability of roughly.3 meter per seond in rms differene when ompared with the altimeter spatial average. II 231
Dobson et al. Validalion of GOSA T Altil71elerDerived Wind Speeds and SWH Using Buoy DOlO Donelan and Pierson 16 estimate that a 2minute average of signifiant wave height would result in an 8 perent sampling variability. For a typial oean signifiant wave height of 3 meters, this would imply an rms differene of.24 meter of sampling variability. We mentioned above that omparisons of signifiant wave heights estimated by buoys 1 meters apart exhibit roughly a 7 perent differene. This is onsistent with the Pierson and Donelan predition. In Table 5, we summarize the above error soures and the orresponding rms values for both wind speed and signifiant wave heights. The bottom row gives the ombined rms levels (the square root of the sum of the squares). We note overall unertainties of 1 to 1.3 meters per seond for wind speeds and.4 to meter for signifiant wave heights. One should not expet to obtain rms differenes smaller than these levels in omparing altimeterderived and buoy measurements. It should, however, be stressed that these error soures do not inlude altimeter performane unertainties as desribed below. Altimeter InstrumentRelated rrors Fundamental error soures are also related to the auray with whih the desired radarsignal harateristis an be measured. These harateristis are radar ross setion for determining wind speed, and signature slope for determining signifiant wave height; given an unertainty in the radar ross setion and an algorithm that is assumed to be "true," orresponding error values in the wind speed may be derived. A family of urves for various unertainties in the measurements of altimeter ross setions is plotted in Fig. 12. The vertial sale represents windspeed error and the absissa represents true wind speed. The smoothed Brown algorithm was used in determining urves. The nominal unertainty in measuring radar ross setion is estimated to be deibel. 11 Assuming this figure and the global average oean wind speed of 8 meters per seond, the expeted error in wind speed aused by inauray in the radar ross setion is observed to be meters per seond. The altimeter estimate of signifiant wave height is derived from the return pulse shape. Limitations on the ability of the altimeter to reonstrut the return pulse shape will ause errors in the signifiant wave height estimate. The return waveform is sampled disretely in "range bins." Calibration errors for the range bins will ause errors in pulse reonstrution. In addition, Rayleigh fading noise orrupts the return pulse shape. That noise is unrelated to instrument problems but is aused by the random onstrutive and destrutive interferene of oherent radar signals refleting off a rough surfae. Generally, many waveforms have to be averaged to make good estimates of the return pulse shape. Nonetheless, errors in signifiant wave height assoiated with the inability to reonstrut exatly the return pulse shape are small. The noise levels of altimeter signifiant wave height masurement have been estimated at.3 meter. 1 An additional, but oupled, error soure also pertains to the unertainty in the algorithm itself. It is apparent from Fig. 5 that the seletion of the CheltonWentz algorithm in the determination of windspeed errors of the type plotted in Fig. 11 leads to larger errors at higher wind speeds. CONCLUSIONS Seven months of altimeterderived radar ross setions and signifiant wave heights obtained from the GOSAT geodeti mission have been ompared to measurements from buoys operated by the National Data Buoy Center. The omparisons demonstrate that for offnadir angles of up to I degree, over the measured windspeed range, the Brown and smoothed Brown algorithms give the lowest rms and mean differenes between the two sets of measurements for all ranges. The other algorithms onsidered were those of Chelton and Wentz and Chelton and MCabe. Questions remain onerning the perfor Table 5 Su mmary of rms error differenes between altimeterderived and buoymeasured wind speeds and signifiant wave heights. Soure oj rror Buoy instrument Temporal separation Spatial separation Sampling variability (time vs. area averaging) Overall rms *2kilometer spae window t 5kilometer spae window 232 Wind Speed (m/se).8.3 *1.t.3.11.3 SWH (m).1.2*.3t.24.4 U en g 1.5 1.. en.5 S db 5 1 15 Wind speed (meters per seond) Figure 12 A family of urves showing windspeed errors resulting from various levels of radar rosssetion unertainties assuming the smoothed Brown algorithm. 1o Johns Hopkins APL Tehnial Digesl, Volume 8, Number 2 (1987)
Dobson et al. manes of the algorithms at wind speeds greater than 14 meters per seond beause of insuffiient high windspeed values in the sevenmonth data set. The above disussion of error budget analysis demonstrated that within a 5kilometer range spaing between the buoy and altimeter subtrak, an expeted windspeed differene of 1.3 meters per seond between the altimeter and the insitu measurement may be expeted. This differene is exlusive of any altimeter instrument or algorithm errors. A nominal I.2meterperseond error may, in addition, be expeted due to a deibel unertainty in the radar ross setion. Combining these two errors results in an overall I.8meterperseond error exlusive of any algorithm unertainty (Table 5; Fig. 11). When omparing the altimeterderived wind speed with buoy values for ranges within 5 kilometers (attitude of less than.75 degree) using the Brown or smoothed Brown algorithms, a I.7meterperseond rms unertainty was obtained. The error analysis is thus observed to be onsistent with measurements, and the altimeter is therefore performing within measurement goals with regard to the measurement of wind speed (i.e., I.8meterperseond rms). ' The error analysis also suggested a meter unertainty in the measurement of signifiant wave height that is onsistent with the altimeter versus buoyderived signifiantwaveheight unertainty that was shown to be.49 meter (Fig. 9). Hene, the altimeterderived measurement of signi fiant wave height has also been demonstrated to be perfo rming within its meas urement goal (meter rms or 1 perent of signi fiant wave height). Validation oj GOSA T A ltimeterderived Wind Speeds and S WH Using Buoy Data 2 G. S. Brown, " Baksan ering from a Gaussian Distributed Perfetl y Conduting, Rough Surfae," I Trans. A ntennas Propagat. 26,472482 (1978). 3. Cox and \V. Munk, " Sta ristis of rhe Sea Surfae Derived from Sun Glirler, " 1. Mar. Res. 13, 198227 (1 954). I G. S. Brown, "srimarion o f Surfae Winds Using SarellireBorne Radar Measurement s ar Normal Inidene," 1. Geophys. Res. 84, 39743978 (1979). 5 G. S. Brown, H. R. Sranley, and. A. Roy, " T he Wind Speed Measurement Capabiliry of Spaeborne Radar Altimerers, " I J. Oeani ng. 6 (198 1). 6 D. B. Chelt on and P. J. MCabe, "A Review of Satellite Altimerer Measurement of Sea Surfae Wind Speed : With a Proposed New Aigorirhm," 1. Geophys. Res. 9, 477472 (1 985). 7 J. Goldhirsh and. B. Dobson, A Reommended Algorithm for the DeterlIIination of Oean Surf ae Wind Speed Using a SatellileBome Radar A I tillleter, JHU/ APL S IR85U5 (Mar 1985). H D. B. Chelron and F. J. Wentz, "Further Development o f an Im proved AIlimeter Wind Speed Algorithm," 1. Geophys. Res. 91 (1986). 9 W.. Frai n, S. C. Jones, C. C. Ki lgus, and J. L. MaArthur, "Navy GO SA T Mission Radar Aitimerer Satellite Program," Monitoring arth 's Oean, Land, and A tmosphere from SpaeSensors, Systems and Appliations, Vol. 97, in Progress in Astronautis and Aeronautis Series, A. Shnapf, ed., A IAA, pp. 44 463 (1 985). 1 F. M. Monaldo, xpeted Differenes in the Comparison of Wind Speed and Signifiant Wa ve Height by Spaebom e Radar A /timeters, JHUI A PL S I R86U17 (1986). II \1.,1. J. Pierson, J r., " T he Measurement of Synopti Sale Wind Over the Oean," 1. Geophys. Res. 88, 1683 178 ( 1983). 12 D. B. G ilho usen, "An Auray Srarement for Meteorologial Measurement s Oblai ned from NDBC Moored Buoys," in Pro. MDS '86 Marine Data Systellls Int. Symp., pp. 198 24 (Apr 1986). 13 K.. Steele and M. D. arle, "The Starus of Dara Produed by DBC Wave Dara Ana lyzer Systems," in Pro. OCA NS '79, I (1979). 11 J. L. MaArrhur, SeasatA Radar A ltimeter Design Desription, J H UI APL SDO5232 (1 978). 15. J. Walsh,. A. Uliana, and B. S. Yaplee, " Oean Wave Heights Measured by a High Resolurion PulseLimired Radar A lr imerer," Bound.Lay. Meteoro/. 13, 263 276 (1978). 16 M. Donelan and W. J. Pierson, J r., " The Sampling Variability of Sperra o f Wi nd Generated Waves," 1. Geophys. Res. 88, 43814392 (1983). RFRNCS I _ B. Dobson and J. Goldhirsh, Deterlllillatioll of Closest Approah Statistis Assoiated with the GOSA T A ltillleter Grolilld Trak and the NDBC Bllo.l' Network, Vols. I a nd 2, J H I A P L S IR85 U4 (1985). ACKNOWLDGM T This efforr was in large pan supporred by the Nalio na l mironmenra l Satellir e, Dara, and 1nformarion Servie of rhe Narional Oani and Atmospheri Adminisrralion. We are grarefullo B. Do uglas of rhe Geoderi Researh and Development LaboralOry at OAA for his guidane, and.\rend many rhanks ro J. MaArrhur and C. Kilgu of APL for rheir ontribul ions. Johns Hopkins A PL Tehnia l Digest. Vo lume 8. Number 2 (1987) 233