under high-wind conditions

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. C, PAGES 11,48-11,497, MAY 1, 1999 Revised ocean backscatter models at C and Ku band under high-wind conditions William J. Donnelly, James R. Carswell, and Robert E. Mcintosh Microwave Remote Sensing Laboratory, University of Massachusetts, Amherst Paul S. Chang and John Wilkerson Office of Research and Applications, National Oceanic and Atmospheric Administration, National Environmental Satellite Data and Information Service, Camp Springs, Maryland Frank Marks and Peter G. Black Hurricane Research Division, National Oceanic and Atmospheric Administration, Miami, Florida Abstract. A series of airborne scatterometer experiments designed to collect C and Ku band ocean backscatter data in regions of high ocean surface winds has recently been completed. More than 100 hours of data were collected using the University of Massachusetts C and Ku band scatterometers, and KUSCAT. These instruments measure the full azimuthal normalized radar cross section (NRCS) of a common surface area of the ocean simultaneously at four incidence angles. Our results demonstrate limitations of the current empirical models, C band geophysical model function 4 (), SeaSat scatterometer 2 (SASS 2), and NASA scatterometer 1 (NSCAT) 1, that relate ocean backscatter to the near-surface wind at high wind speeds. The discussion focuses on winds in excess of 1 m s - in clear atmospheric conditions. The scatterometer data are collocated with measurements from ocean data buoys and Global Positioning System dropsondes, and a Fourier analysis is performed as a function of wind regime. A three-term Fourier series is fit to the backscatter data, and a revised set of coefficients is tabulated. These revised models, HW and KUSCAT 1, are the basis for a discussion of the NRCS at high wind speeds. Our scatterometer data show a clear overprediction of the derived NRCS response to high winds based on the, SASS 2, and NSCAT 1 models. Furthermore, saturation of the NRCS response begins to occur above 1 rn s -. Sensitivity of the upwind and crosswind response is discussed with implications toward high wind speed retrieval. 1. Introduction and aircraft scatterometer measurementstill relies on empirical models rather than physically based theoretical models Motivation The current operational C band wind retrieval algorithm is A key parameter required to improve track and intensity based on the C band geophysical model function 4 () forecasts, as well as our understanding of severe storm strucmodel [Stoffelen and Anderson, 1997] that was developed to invert the backscatter measurements collected with the active ture, is the ocean surface wind field. Airborne and spaceborne scatterometers can help provide this information. Microwave microwave instrument (AMI) aboard the European Remote scatterometers measure the normalized radar cross section Sensing Satellites (ERS i and ERS 2) [Lecomte, 1993; Of-filer, (NRCS), rr ø, of the ocean surface from which one can then 1994]. This empirical model, derived from collocated AMI infer the ocean surface wind speed and direction. The NRCS at backscatter and buoy-based wind measurements, has been intermediate incidence angles (20 ø to 0 ø ) and microwave fre- shown to be accurate to approximately 2 m s - for winds quencies is a function of the spectral density of capillary and from to 1 m s -. The characterization of an empirically short gravity waves, which in turn is strongly correlated to the derived relationship strongly depends on the data set from local surface winds [Moore, 1979]. A historical summary of which it is derived. Given the low probability of having a scatterometry is given by Carswell et al. [1994]. satellite pass over a moored buoy during a high-wind event, it is understandable that the model is not well defined 1.2. Current Models for high winds. Furthermore, the relatively coarse spatial resolution of AMI cells (0 km x 0 km) results in the averaging Numerous investigators have attempted to describe the theof high and moderate surface winds within the cell. Conseoretical relationship between the surface wind and ocean backquently, winds derived from AMI have been shown to underscatter with some success over limited conditions [Donelan and estimate high winds, resulting in the incorporation of a wind Pierson, 1987; Plant, 1986]. However, inversion of spaceborne speed dependent correction term to the European Centre for Copyright 1999 by the American Geophysical Union. Paper number 1998JC /99/1998JC Medium-Range Weather Forecasts (ECMWF) operational form of [Gaffard, 199]. Recent work by Quilfen et al. [1998] shows the potential of C 11,48

2 11,486 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS Incidence Angie Switching at KHz Azimuthal Scanning at 80 RPM Figure 1. Conical scanning measurement technique used by the C band scatterometer () and the Ku band scatterometer (KUSCAT). The pointing angle is frequency steered off nadir as the antenna rotates at 80 rpm. band scatterometers to aid in monitoring and forecasting tropical cyclones. However, the authors show that the coarse resolution and the current operational retrieval algorithms limit the usefulness of the AMI data with regard to estimating tropical cyclone winds. They show the NRCS sensitivity for winds temporally filtered to within 2 hours of the NSCAT observations. For winds above 1 m s-, ECMWF model winds interpolated in time and space were used. ECMWF model wind fields have a spatial resolution of 1 ø in latitude and 1 ø in longitude and a temporal resolution of 6 hours. A combination greater than 1 m s - is less than that predicted by the of SSM/I and ECMWF surface wind estimates were used for model and other models, and they conclude that an improved high wind speed branch of the model is needed. The SASS 2 model was developed using 3 months of SeaSat scatterometer (SASS) measurements, and maps assumed wind winds between and 1 m s -. The modeled NRCS response was adjusted to normalize the probability density functions for wind speed retrievals at each incidence angle in the instrument swath. The mean NRCS response is based on work conducted vector statistics into the observed SASS NRCS statistics. No in by F. J. Wentz, and the azimuthal modulation characterization situ observations were included. The distribution of global was done by M. Freilich (as discussed by Wentz and Smith, this winds observed from satellite instruments was assumed to be a issue). bivariate normal probability function with a mean of approximately 7. m s - [Wentz et al., 1984]. As a result, winds greater 1.3. Study Summary than 1 m s - were not heavily weighted in the model development. The SASS data were collected at 0-km resolution cells, which also limited the ability to sample high-wind regions without incorporating regions of moderate winds. As with the model, the SASS 2 model has been proven to be accurate at moderate winds, but it tends to overestimate the NRCS at higher winds. In April 1997 the NASA scatterometer 1 (NSCAT 1) model was completed. It is based on 3 months of the National Aero- This paper presents measurements obtained with the University of Massachusetts C and Ku band airborne scatterometers in clear-sky conditions. and KUSCAT simultaneously measure the full azimuthal NRCS of the same surface area of the ocean at four incidence angles. Over the past 18 months a series of experiments were conducted with an emphasis on collecting collocated C and Ku band NRCS measurements during high-wind events. Our data show how (1) the operational models (, SASS 2, and NSCAT 1) overnautics and Space Agency (NASA) scatterometer observations predicthe backscatter values for winds above 1 m s- and (2) from September to December This empirical model was the NRCS starts saturating for wind speeds above 20 m s -. derived from collocated NSCAT backscatter measurements Ocean backscatter saturation has been suggested previously in and a combination of special sensor microwave/imager (SSM/I) surface wind estimates and model winds from the ECMWF model. The NSCAT level 1.7 data product, which provides NRCS estimates binned to 0-km resolution cells, was used for the derivation. For low-wind speeds (< m s- ), SSM/I wind estimates were collocated with NSCAT cells and the literature [Donelan and Pierson, 1987]. New empirical models, developed from our C and Ku band data, serve as a basis for our discussion of the NRCS in the high wind speed regime. Section 2 describes the recent experiments and provides an overview of the data obtained. The processing methods are outlined, and the Fourier analysis of the data is discussed.

3 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS 11,487 Table 1. Experiment Matrix Station Surface Time, Winds, GPS NOAA Experiment Date hours m s- Sondes Buoys Location Instruments Hurricane Fran Sept., NA NA CAL/VAL I Dec. 16, NA 7 CAL/VAL I Dec. 9, NA OWI March 1, OWI March 3, NA OWI March 4, NA OWI March 7, NA OWI March 9, NA OWI March 10, NA 2 CAL/VAL II April 1, CAL/VAL II April 2, CAL/VAL II April 3, CAL/VAL II April 7, CAL/VAL II April 8, CAL/VAL II April 11, RADARSAT Aug. 21, NA 3 RADARSAT Aug. 24, NA 1 HOWE Aug. 1, NA 4 HOWE Sept. 10, NA HOWE Sept. 11, NA WINDEX Nov. 12, WINDEX Nov. 13, WINDEX Nov. 18, WINDEX Nov. 19, NA 4 Labrador Sea Labrador Sea Labrador Sea Labrador Sea Gulf of Mexico SE Atlantic Atlantic Atlantic NW Pacific NW Pacific NW Pacific NW Pacific Total NA NA NA GPS is Global Positioning System; NOAA is National Oceanic and Atmospheric Administration. Experiment abbreviations are CAL/VAL, NOAA/NASA NSCAT Calibration/Validation Experiment; OWl, Ocean Winds Imaging Experiment; RADARSAT, Canadian Radar Satellite; HOWE, Hurricane Ocean Winds Experiment; and WINDEX, NOAA WINDS EXPERIMENT. Instruments included the C band scatterometer () and Ku band scatterometer (KUSCAT). NA is not available. Section 3 presents the backscatter measurements and details the high-wind model development. A discussion of the resulting models is included, focusing on NRCS sensitivity and sat- uration. Section 4 summarizes our results. 2. Experiments and Measurements 2.1. Instrument Descriptions The Microwave Remote Sensing Laboratory (MIRSL) at the University of Massachusetts has developed a number of scatterometers. The C band scatterometer () was first designed in the late 1980s but has since undergone several modifications for improved performance. A Ku band scatterometer (KUSCAT) was built in 1992, as a frequency scaled version of. Both share a central data acquisition and control system to allow simultaneous NRCS measurements at C and Ku band from the same aircraft platform, which typically travels at an airspeed of 12 m s -. Both instruments also use Table 2. Instrument Kp and Collocation Distances Radial K v Distance, Instrument km Single Bin Entire Scan KUSCAT SASS, 0-km pixel AMI, 0-km pixel NSCAT, 0-km pixel Abbreviations are SASS, SeaSat scatterometer; and AMI, microwave instrument. active frequency scanning to electronically vary the incidence angle of the radar beams. The antennas are rotated in azimuth at 80 rpm, as shown in Figure 1. Operation of these radars provides full azimuthal NRCS measurements at four incidence angles for a common footprint area of ocean surface. For additional information, see Carswell et al. [!994] Experiment Summaries Backscatter measurements were collected over a 2-year period during five separate field experiments: (1) the National Oceanic and Atmospheric Administration (NOAA) 1996 Hurricane Field Program, (2) the NOAA/NASA NSCAT Calibration/Validation Experiment (CAL/VAL), (3) the Ocean Winds Imaging (OWI) Experiment, (4) the Hurricane Ocean Winds Experiment (HOWE), and () the NOAA Winds Experiment (WINDEX). In conjunction with the HOWE experiment, two underflights of the Canadian Radar Satellite (RADARSAT) were made. NOAA ocean data buoys and Global Positioning System (GPS) dropsondes provided the required in situ measurements. A summary of the analyzed data presented in this paper can be found in Table 1. As part of the 1996 Hurricane Field Program, was installed on the NOAA WP-3D N42RF aircraft at the NOAA Aircraft Operations Center (AOC), McDill Air Force Base, Tampa, Florida. A research mission was flown through Hurricane Fran on September -6, Winds exceeding 4 m s - were encountered over the ocean. Flight level data and coincident radar reflectivity measurements from the aircraft's tail Doppler radar (TDR) were recorded. As part of the NSCAT CAL/VAL experiment, the National Environmental Satellite, Data and Information Service (NES-

4 ß ß ß 11,488 DONNELLY ET AL.' HIGH WIND OCEAN BACKSCATTER MODELS Degrees I I I I I I I ør.i', '... ::4:.., :., '.., Degrees I I I I I ""...,i. o I CSC AT-.1 De rees I I I. ' / ' "'["l',,.'-.';'.._>.'.'.,::,,<,, :..".".: ',:.' '... ' ' :',.':,,!",,'i:!" "'""' ! I t t t t t -23 ' t: I I I I I I Figure 2. Mean C band normalized radar crossection (NRCS) measurements gathered (a) 22.0 ø, (b) 32.3 ø, (c) 43. ø, and (d) 4.1 ø incidence plotted versus collocated U o2v estimates. The dashed line is the mean NRCS response to the 10-m neutral stability wind speed U o2v as predicted by the model function. DIS) division of NOAA in conjunction with MIRSL conducted unique complement of active and passive microwave instruseveral flight experiments off the east coast of the United mentation. The experiment was designed to collect collocated States. and KUSCAT were installed on the NOAA scatterometer and passive polarimetric measurements of the WP-3D N42RF aircraft, and two sets of flights were com- ocean surface during high-wind events. The aircraft deployed pleted. The first set focused on outbreaks of polar air over the to Goose Bay, Labrador, where five data missions were flown. eastern Atlantic in early December Data missions were Surface winds up to 20 m s - were recorded. conducted in the vicinity of moored NOAA buoys, and flight In conjunction with the Naval Research Laboratory (NRL) planning ensured the aircraft would be on station at the time of and the Jet Propulsion Laboratory (JPL), an experiment was a NSCAT overpass. GPS dropsondes were also used for in situ designed to collect collocated scatterometer and passive poladata. In April 1997 the second set of flights was completed rimetric measurements in the vicinity of tropical cyclones. In based out of the Patuxent River Naval Air Station, Lexington September 1997, and KUSCAT were installed on the Park, Maryland. As before, flight planning targeted high-wind NASA WP-3B N426NA aircraft. Two data flights were flown in events and ensured the aircraft would be on station during a the vicinity of Hurricane Erika as it approached Bermuda NSCAT overpass. Surface winds up to 2 rn s - were sampled. Island. Surface winds in excess of 30 m s - were encountered. During March 1997, was installed on the NASA WP-3B N426NA aircraft for the OWI Experiment. The aircraft, based at Wallops Island, Virginia, was equipped with a Concurrent with the HOWE experiment, two RADARSAT underflights were conducted in the vicinity of Wallops Island, Virginia, in low to moderate (-10 m s - ) wind conditions.

5 ß DONNELLY ET AL.' HIGH WIND OCEAN BACKSCATTER MODELS 11, NSCAT1 KUSCAT Degrees... NSCAT1 KUSCAT- 30. Degrees... ';?'>.:...:...:.- -'..'..:..'...'.-.'- -18 [ i KUS CAT-410'9 De grees i,... NSCAT1 KUS icat- 1 Delgrees I I I I... NSCAT1-8 -1o < -1..!i': ' ß I I ß i1' '.1oo 0. 1o /[ " 11 i I øø I I -20 ] -13 < I,, Iill I I I I i I ] Figure 3. Mean Ku band NRCS measurements gathered at (a) 20.0 ø, (b) 30. ø, (c) 4 ø, and (d) ø incidence plotted versus collocated UsoN estimates. The mean NRCS response to UsoN as predicted by the SeaSat scatterometer 2 (SASS 2) model function (dashed line) and the NASA scatterometer 1 (NSCAT 1) model function (dotted line) are also plotted. As a follow-on to the NSCAT CAL/VAL flights in December 1996 and April 1997, the WINDEX experiment targeted high-wind (>20 m s -s) events. and KUSCAT were reinstailed on the NOAA WP-3D N42RF aircraft and de- ployed to Seattle, Washington. Five data flights were conducted in the northwestern Pacific during two rapidly intensifying low-pressure systems. Surface winds in excess of 30 m s-s were encountered Processing Techniques Normalized radar cross section. and KUSCAT measure the backscattered power from a common ocean surface area at four incidence angles as they conically scan at 80 rpm. The incidence angles, 22.0 ø, 32.3 ø, 43. ø, and 4.1 ø for and 20.0 ø, 30. ø, 4 ø, and ø for KUS- CAT, are switched sequentially at khz using a high-speed microwave switch and four separate local oscillators for each system. The backscatter measurements from a single conical scan are subdivided into seventy-two ø azimuth bins, with each bin being the average of approximately 13 samples. The averaged measurements are then corrected for gain drifts, and the receiver noise power is subtracted. The aircraft platform data are used to reference each azimuthal bin to true north and to calculate the instantaneous incidence angle for computation of the NRCS. The pitch and roll motions of the aircraft cause the instantaneous incidence angle to vary about the nominal pointing angles. Using the or SASS 2 models, corrections are applied to the NRCS measurements to normalize them to the nominal pointing angles of each system. These corrections are small, and they are only applied to those data where the

6 . 11,490 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS Degrees Degrees I 1.2 I I ß,...,.., 1: [ ' '!h i. t _[,,..., -, [::':." '. ':". t f :"" I{" "t, 7:'" ':::.... '--'-'--. '.aa.,.!,l..r. l: l.. :,,.,. :.,... -, :. :...:. :.,. h '.. -.., Ii :- _ ' '[ ri!]i l: 17:.[......!'..;?.,......,,..... '. ".',?",. :': 0.0 r: 0.0 ' 10-m Neutral Stability Winds ( s, 10 minute average) 10-m Neutr Stability Winds ( s, 10 minute average) 1.2, CSC AT De rees I I I 1.2,, CSC AT- 4.1De rees,, :'.'.!".r, I : ' j ' ': ß.;'...":'. _..'.t:-';j.',;,.: : ' "'"':"';'?:...',c.:.: '... ß,,,,,, ß I I I I i I I ø'6t"l! ',l.']:l'- jill!, ii =,. ' ' ' i. '., '...c.::.., ':j.:.. ß.,,. D.0 I I I ß '1" I 40 4 Figure 4. C band NRCS normalized second-harmonic measurements gathered at (a) 22.0 ø, (b) 32.3 ø, (c) 43. ø, and (d) 4.1 ø incidence plotted versus collocated U1ON estimates. The dashed line is the NRCS normalized second-harmonic response to U1ON as predicted by the model function. instantaneous incidence angle is within 2 ø of the nominal pointing angle. Two averaging schemes were employed. For the flights where the encountered wind gradients were relatively weak (all center calculations were provided by the Hurricane Research Division (HRD) of NOAA. The NRCS data were binned within concentric 1-km-wide rings, relative to the storm center. Data at each azimuth bin were averaged along track as the flights except Hurricane Fran), the NRCS data from consecu- aircraft traversed across the ring, and from these averaged tive conical scans were averaged to form averaged NRCS scans consisting of at least 0 samples in each of the 72 azimuth bins. NRCS azimuth bins, complete azimuthal scans were reconstructed. This averaging technique minimizes wind gradient The normalized standardeviation Kp in each bin is a function smoothing since tropical storm radial wind gradients are alof the number of independent samples averaged and the sig- ways greater than azimuthal gradients. One-kilometer radial nal-to-noise ratio (SNR) in each bin. The average resolution was chosen since the normalized standard deviation (KUSCAT) Kp values for each incidence angle in increasing Kp of the NRCS measurements at this resolution was approxorder are 0.23 (0.34), 0.36 (0.42), 0.44 (0.48), and 0.3 (0.7). Note the KUSCAT values are slightly higher than the values because the SNR is higher at C band than at Ku band, with the SNR decreasing with increasing incidence angle. imately unity (indicating that the variance in the measurements is due only to fading and not to variations in the sampled wind field) Fourier analysis. Fourier analysis of the averaged For the Hurricane Fran NRCS data the radial distance from NRCS scans was performed to estimate the first three Fourier the storm center to each azimuth bin was calculated. Storm coefficients. A three-term Fourier cosine series of the form,

7 ß ß DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS 11, NSCAT1 KUSCAT Degrees KUSCAT- 30. Degrees i i i i i 1.2 i... NSCAT1.' < i "i,,,:,, ß _... "'"'i: 0.3!, i : 0'0 1.2,, KUS CAT-4 De grees,... NSCAT1 1.2,, KUS CAT- De rees,... NSCAT < 0.3.:,', ;I 0.3 Figure. Ku band NRCS normalized second-harmonic measurements gathered at (a) 20.0 ø, (b) 30. ø, (c) 4 ø, and (d) ø incidence plotted versus collocated U1o2v estimates. The NRCS normalized secondharmonic response to Ulo2v as predicted by the SASS 2 model function (dashed line) and the NSCAT 1 model function (dotted line) are also plotted. rr ø = A0 + A1 cos (X) + A2 cos (2X) (1) overpasses are contained in this data set. Scatterometer data are filtered spatially to a 20-km maximum radial distance from was fit to each averaged NRCS scan, where X is the azimuth buoy position to the conical scan center and temporally to pointing angle relative to the wind direction, A o equals the within 10 min. Given the high system data rate, many NRCS mean NRCS, and A 1 and A 2 are the magnitude of the first and second harmonics, respectively. These harmonics describe the points are collocated for each buoy overpass. This data set contains 108 collocated NRCS scans, which were taken an NRCS dependence on wind direction. In general, the A 1 term does not exhibit a strong wind speed dependence, so we will average radial distance of 13.2 km from the location of a buoy. focus our discussion on the A o and A 2 terms. The Atmospheric Technology Division (ATD) at the Na Collocation with in situ measurements. The Na- tional Center for Atmospheric Research (NCAR) developed tional Data Buoy Center (NDBC) at NOAA operates and maintains a moored buoy network of 60 stations. All stations measure numerous environmental parameters on an hourly basis including wind speed, wind direction, peak wind gust, barometric pressure, air temperature, and sea temperature. Many of the buoys also report wind vector measurements every 10 min. Collocated measurements from a total of 308 buoy the first Omega-based dropwindsonde system in the early 1970s. The Omega and Loran navigation systems are being replaced by the more accurate and universally available GPS navigation system. As a result of mutual requirements for a GPS dropsonde system, NCAR and NOAA agreed to jointly develop the new aircraft GPS dropsonde systems. These systems were delivered to NOAA for testing in tropical cyclones

8 11,492 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS Table 3. C Band Power Law Fit Parameters as a Function of Incidence Angle Angle, deg Incidence Scaling Parameter/ x X x X 10-3 Table 4. Ku Band Power Law Fit Parameters as a Function of Incidence Angle Wind Speed Angle, Exponent T deg / x x x x X x X x X in August The GPS dropsonde system was subsequently pixels at the four lowest altitudes directly above the surface used in the international Fronts and Atlantic Storm Tracks sampled by. Reflectivity values greater than 10.0 dbz Experiment (FASTEX) that took place during January and February The GPS dropsonde system has proven to be a reliable source of surface wind vector data. A total of 11 GPS were flagged as rain, and the NRCS values in these regions were not used. The entire collocated data sets for and KUSCAT dropsondes were deployed during the course of our flights. were filtered to remove data collected in the presence of pre- Scatterometer data were collocated to within a 20-km maxicipitation. A combination of the TDR, flight notes, dropsonde mum radial distance and filtered to within 10 min of the surface wind vector measurement. This data set contains 146 NRCS scans, which were taken at an average radial distance of 10. km from a GPS dropsonde. humidity data, and radiometric brightness temperatures was used to remove data collected in the presence of rain. The presented results are therefore limited to ocean backscatter measurements in nonprecipitating conditions. For the Hurricane Fran data set, surface wind analysis was provided by HRD, based on a hurricane planetary boundary layer (PBL) model for surface wind estimation [Powell and 3. Analysis Black, 1990]. The hurricane PBL model estimates 10-m neutral stability wind speed U ON based on 1-min flight level wind 3.1. NRCS Response Figures 2a-2d plot A o for C band, measured at 22.0 ø, 32.3 ø, measurements and estimates of PBL stability. Wind estimates 43. ø, and 4.1 ø incidence, versus collocated U o v estimates. are 1-min averages along the flight track, which correspond to The model predicted response is overlaid in each stationary 10-min wind speed averages. NRCS esti- plot. For all incidence angles the model significantly mates are collocated in time and space to be coincident with overpredicts the mean NRCS for winds exceeding 20 m s -. the HRD surface wind estimates. Furthermore, the measurements show a substantial reduction A comparison of our aircraft-based measurements and sat- in the sensitivity to wind speed for winds exceeding 20 m s-. ellite-based measurements is presented in Table 2. For each In a similar manner, Figures 3a-3d plot A o for Ku band, instrumenthe table lists the average radial distance between a gathered at 20.0 ø, 30. ø, 4 ø, and ø incidence, versus colscatterometer NRCS measurement and an in situ wind vector located U o v estimates. The SASS 2 model and NSCAT 1 estimate. For and KUSCAT the average radial dis- model predicted responses are overlaid in each plot. For all tance is computed from the center of the collocated NRCS incidence angles both models overpredict the mean NRCS for scans. For the satellite measurements a uniform distribution of winds exceeding 1 m s -. As with the C band data, these collocated points within a satellite pixel was assumed and the measurements also show a reduction in the sensitivity to wind average radial distance computed. A Kp value of 0.2 is assumed speed for winds exceeding 20 m s-. for the satellite systems. For and KUSCAT the Kp Figures 4a-4d and a-d plot the measured A 2 values, norvalues for a single azimuth bin are given, along with the Kp malized to the mean NRCS (a2 = A2/Ao), versus collocated values for an entire averaged NRCS scan. The precision of our U o v estimates for C and Ku bands, respectively. A2 is also measurements is better owing to the large number of NRCS overestimated by the and SASS 2 models for high samples in the vicinity of a single in situ wind vector estimate. wind speeds. Note that the NSCAT 1 model accurately predicts Precipitation filtering. During Hurricane Fran, the second-harmonic response. Also note that the magnitude of volume reflectivity measurements of precipitation were ac- a2 starts decreasing with wind speed for winds exceeding 1 m s- quired with the NOAA TDR and mapped into a storm relative and appears to begin saturating for winds exceeding 3 m s -. rectangular coordinate system. The along-track, cross-track, and vertical resolutions of each pixel are 1.0, 0., and 0.1 km, respectively. Volume reflectivity estimates were collocated with backscatter measurements by averaging the TDR 3.2. Radar Cross-Section Model at High Winds To quantify the change in NRCS sensitivity to wind speed at high winds, a power law model of the form Table. C Band Fourier Expansion Coefficients as a Function of Incidence Angle Angle, deg c o c d o d d 2 d x X x X X X X x x x x X x x x x X x x x

9 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATI'ER MODELS 11,493 Table 6. Ku Band Fourier Expansion Coefficients as a Function of Incidence Angle Angle, deg Co c do d d 2 d x x x x x x x x x x x X x x x x x x x x SION) - A0 (sion)' [U10N]'v (2) The mean NRCS measurements were placed into 2 m s- bins, averaged and converted to decibels. Equation (2) was then fit in log space to the averaged A o values using an orthogonal was derived from the collocated mean NRCS measurements and U o v estimates for points where U o v is greater than 19 m linear regression procedure to determine/ and % The results s - for C band and 12 m s- for Ku band. These cutoff points are given in Tables 3 and 4 for the C and Ku band data, were chosen as the wind speed where the NRCS measurements respectively. Note that /is the wind speed exponent. began to visibly diverge from the model-predicted response. The azimuthal modulation of the backscatter for both C and - HW ' Degrees _ Degrees 0 f I I I I I I HW..--".. i" Degrees I I I I / I I - HW,,""' I - ' '.. -3,, CSC, AT-?.I De rees, HW u 10-m Neutr Stability Winds ( s, 10 minute average) Figure 6. Mean C band NRCS measurements gathered (a) 22.0 ø, (b) 32.3 ø, (c) 43. ø, and (d) 4.1 ø incidence and averaged into 2 m s - wind speed bins, plotted versus collocated U o v estimates. The solid and dashed lines are the mean NRCS response to U o v as predicted by the high-wind model and the model function, respectively.

10 . - 11,494 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS KUSCAT Degrees 10 i KUSCAT1... NSCAT1 KUSCAT- 30. Degrees I I I I I I I.... ;..... NSCAT '... ß ' 0 <...::.::.::...: ' ', KUS,CAT- 4, Degrees,, -3[,, KUS?AT-, De rees - KUSCAT1 [ ' KUSCAT1 ' - t... NSCAT1 NSCAT1...:...:..:. f...'...' :.:.; " '?' 'Iv] ]' ' ' ' ' ' ' Figure 7. Mean Ku band NRCS measurements gathered at (a) 20.0 ø, (b) 30. ø, (c) 4 ø, and (d) ø incidence and averaged into 2 m s - wind speed bins, plotted versus collocated U ON estimates. The mean NRCS response to U ON as predicted by the SASS 2 model function (dashed line) and the NSCAT 1 model function (dotted line) are also plotted. Ku band was modeled using a form similar to the model and is shown below tr ø= A0[1 + al cos (X) + a2 cos (2X)] (3) a = Co + c U on (4) a2 = do + d + d2 tanh d3 J U ON () Attempts were made to use the SASS 2 azimuthal functional for the Ku band data: a 2 response at moderate winds. The NSCAT 1 azimuthal modulation model form was not available for comparison. Using orthogonalinear regressions, the coefficients Co, c, do, d, and d 2 were determined. The d 2 and d 3 terms determine the wind speed at which the a 2 term peaks. Several d 3 terms where evaluated, and the value that resulted in the best fit in a least mean square error sense was used. Table presents the C band fit coefficients for each incidence angle. Likewise, Table 6 presents the Ku band fit coefficients for each incidence angle. a = Co + c log (UloN) (6) a2 = do + d log (U10N) (7) but the resulting fits did not accurately model the peak in the 3.3. Model Performance Figures 6a-6d and 7a-7d plot the mean NRCS as a function of U ON for C and Ku band, respectively. The averaged values are plotted as solid circles, with vertical lines displaying the

11 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS 11, Degrees Degrees 1.2 HW HW , CSC AT De rees HW I i i.2 -,4.1 De rees. I I I I I HW Figure 8. C band NRCS normalized second-harmonic measurements gathered at (a) 22.0 ø, (b) 32.3 ø, (c) 43. ø, and (d) 4.1 ø incidence and averaged into 2 m s - wind speed bins, plotted versus collocated U o v estimates. The solid and dashed lines are the NRCS normalized second-harmonic response to U o v as predicted by the high-wind model and the model function, respectively. standard deviation of the measurements within each bin. The new high-wind models, HW and KUSCAT 1, and the existing operational models are plotted for each frequency band. Note that the HW represents a composite of the model and the high wind speed power law derived from the data. The mean NRCS for wind speeds less than 1 m s - are derived from, and the mean NRCS for wind speeds greater than 19 m s - are derived from the high wind speed power law. A moving average is used to smooth the transition from the model to the high wind power law. As a result, the and HW models agree well for wind speeds less than 1 m s -, but they diverge at the higher wind speeds, with overpredicting the mean NRCS. The overprediction increases with incidence angle, and it ranges from a few decibels at 22 ø incidence to over 6 db at 4.1 ø for winds at 3 m s -. Likewise, both the SASS 2 and NSCAT 1 models overpredict the mean NRCS for the higher winds, although to a lesser extent than the model. Note that the NSCAT 1 and KUSCAT 1 models are similar in shape, although a bias of 1., 1.6, 2., and 1.6 db at 20.0 ø, 30. ø, 4 ø, and ø incidence, respectively, appears to exist between the two. This bias is calculated by comparing the models over the wind speed range of 7 to 10 m s -. This NSCAT 1 bias has been seen in other comparisons [Jones et al., 1998]. The NRCS sensitivity to U o v at high winds is given by the derived wind speed exponent 3/. If the wind speed doubles from 20 to 40 m s -, the mean NRCS increases by 33/ db. The HW model predicts increases of 1.8, 2.0, 3.2, and 3.0 db at 22.0 ø, 32.3 ø, 43. ø, and 4.1 ø incidence, respectively. Note that sensitivity improves with increasing incidence angle. In comparison, the model predicts increases of 3.8, 6.2,

12 11,496 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS < KUSCAT Degrees I I I I KUSCAT1... NSCAT! KUSCAT- 30. Del rees 1.2 / KUSCAT1 ' I'... - [... NSCAT1 - ø 0' = < ß J' ' - 0.% I I I I I I I 0 1.2,, KUS?AT-4, De/grees, i - KUSCAT1 NSCAT1,, KUS,CAT-, Delgrees, KUSCAT1... NSCAT1 <.6 0.3,3 0.0 I I t,0 Figure 9. Ku band NRCS normalized second-harmonic measurements gathered (a) 20.0 ø, (b) 30. ø, (c) 4 ø, and (d) ø incidence and averaged into 2 m s - wind speed bins, plotted versus collocated U o v estimates. The NRCS normalized second-harmonic response to U o v as predicted by the SASS 2 model function (dashed line) and the NSCAT 1 model function (dotted line) are also plotted. 8.0, and 8.7 db for the same change in surface wind. Clearly, NSCAT 1 and KUSCAT 1 models predict a similaresponse. the model increasingly overpredicts the NRCS sen- Although the sensitivity at Ku band is greater than at C band, sitivity to U o v at wind speeds greater than 1 m s -. Further- these measurements demonstrate that the Ku band NRCS also more, the smaller increase in the measured backscatter as the starts to saturate. wind speeds increase is indicative of the NRCS approaching a Figures 8a-8d and 9a-9d plot the normalized secondmaximum value or saturation level with respect to U o v. harmonicoefficient a2 as a function of U o v for C and Ku The KUSCAT 1 model exhibits greater sensitivity to U o v band, respectively. The averaged normalized measurements than the HW model at higher wind speeds, yet the are plotted as solid circles, with vertical lines indicating the sensitivity is still less than that predicted by either SASS 2 or standar deviation. As expected for low to moderate winds NSCAT 1 models. For a change in surface winds from 20 to (-1 m s- ), the models agree reasonably well, but the 40 m s -, the KUSCAT 1 model predicts increases of 1.6, 2.9, and SASS 2 models begin to diverge from the 4., and 3.3 db at 20.0 ø, 30. ø, 4 ø, and ø incidence, HW and KUSCAT 1 models as wind speeds become respectively. In contrast, the SASS 2 model predicts an in- greater than 1 m s -. Both and SASS 2 models crease of 2., 4.8,., and.2 db. Likewise, the NSCAT 1 overpredict the a 2 response by as much as twice the measured model predicts an increase of 1.9, 3.4, 3.7, and 3.6 db. Note value. The NSCAT 1 and KUSCAT 1 models predict a2 rethat the SASS 2 model overpredicts the sensitivity, while the sponses that agree with one another within the measurement

13 DONNELLY ET AL.: HIGH WIND OCEAN BACKSCATTER MODELS 11,497 precision. The position of the a 2 term peak appears to be a function of a frequency. In general, the peak is at lower wind speeds for Ku band than at C band and is at decreasing wind speeds with increasing incidence for both frequencies. The Bragg wavelength is greater at C band than at Ku band, and for each band it increases with increasing incidence angle. This suggests a correlation between the peak of the a 2 response and Bragg wavelength. From this peak at moderate winds both the C and Ku band a 2 responses decrease rapidly to saturation levels of approximately 0.1 and 0.24, respectively. The measurement variance is noticeably smaller at higher wind speeds than at lower wind speeds. This phenomenon is partially due to the decreased NRCS sensitivity to Ulo N at higher wind speeds. Variations of the surface winds at high wind speeds will cause small variations in the measured NRCS. Therefore the measurement variance is primarily caused by target fading effects, which are small due to the high number of independent samples averaged. Analyses of the upwind (X = 0ø), downwind (X = 180ø), and crosswind (X = -+90ø) NRCS of the high-wind model for both frequency bands reveal that the crosswind NRCS starts saturating at higher wind speeds than does the upwind or downwind NRCS. The greater crosswind NRCS sensitivity for wind speeds higher than 20 m s- suggests that the crosswind NRCS could be useful for high wind speed retrievals. The upwind to crosswind ratio decreases from a peak of a few decibels at low to moderate winds to near unity at 4 m s Conclusion The operational models, SASS 2, and NSCAT 1 were found to overpredict the NRCS at high wind speeds. New high wind speed models, HW and KUSCAT 1, were developed to better characterize the ocean backscatter at these higher winds. The NRCS sensitivity to wind speed was determined to be significantly less than that predicted by the and SASS 2 models for wind speeds greater than 20 m s -. The NSCAT I model performed better than the SASS 2 model at predicting the Ku band NRCS at high wind speeds; although, it appears to have a bias. Our data set indicates that the mean NRCS starts to saturate at wind speeds greater than 20 m s -. This saturation suggests an upper limit on wind retrieval at C and Ku band, which will be dependent on incidence angle. The NRCS sensitivity change was most pronounced at C band. NRCS values were simulated based on HW and KUSCAT I models, and analyses were performed to estimate the standard deviation of wind speed estimates based on mean NRCS measurements in high-wind regions predicted by these new high-wind models. This standard deviation is a function of the NRCS variance and is related to the number of independent samples averaged. For C band NRCS estimates based on 0 independent samples (Kp = 0.14), the wind speed standard deviation is approximately 3 m s- for 20 m s- winds and 7 m s - for 40 m s - winds. For Ku band, using the same number of independent samples, the wind speed standard deviation is 2 m s - for 20 m s - winds and m s - for 40 m s - winds. To decrease this standard deviation, it is necessary to use a large number of independent NRCS samples, particularly at high wind speeds because of the lower backscatter sensitivity. With conically scanning systems, such as and KUSCAT, use of the full azimuthal scan greatly increases the mean NRCS precision without reducing spatial resolution. For a factor of 10 increase independent averages (Kp ), the standard deviation of the C band wind speed estimates decreases to 1 m s- ' for 20 m s - winds and 2 m s - for 40 m s- winds. Similarly, the standar deviation of the Ku band wind speed estimates decreases to 1 m s - for 20 m s- winds and 1. m s - for 40 m s - winds. Acknowledgments. The authors wish to thank J. McFadden, J. Roles, and S. Czyczk, along with the pilots and crew of NOAA N42RF for their countless hours of support. In addition, the authors wish to thank P. Bradfield and D. Young, along with the pilots and crew of NASA N246NA. Above all, the authors would like to thank Robert E. Mcintosh. His lifetime achievements in remote sensing and dedication toward education made this work possible. This investigation was funded by NOAA/NESDIS grants 43AANE70324 and 43AANE70117, NOAA/IP0 grant 0-SPNA-00022, NASA/JPL grant , NRL grant N G016, NASA grants NAG-11 and NAG8-1490, and ONR grant N References Carswell, J. R., R. E. Mcintosh, S.C. Carson, F. K. Li, G. Neumann, D. J. McLaughlin, J. C. Wilkcrson, and P. G. 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Mcintosh, Microwave Remote Sensing Laboratory, University of Massachusetts, Amherst, MA (donnelly@mirsl.ecs.umass.edu; carswell@mirsl.ecs.umass.edu) P. Chang and J. Wilkerson, Office of Research and Applications, National Oceanic and Atmospheric Administration, National Environmental Satellite Data and Information Service, World Weather Building, 200 Auth Road, Camp Springs, MD (pchang@nesdis.noaa.gov; jwilkerson@nesdis.noaa.gov) F. Marks and P. Black, Hurricane Research Division, National Oce- anic and Atmospheric Administration, 4301 Rickenbacker Causeway, Miami, FL (black@aoml.noaa.gov; marks@aoml.noaa.gov) (Received February 12, 1998; revised September 8, 1998; accepted September 23, 1998.)