Compensation of elevation angle variations in polarimetric brightness temperature measurements from airborne microwave radiometers

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 39, NO. 1, JANUARY 2001 193 ACKNOWLEDGMENT The authors would like to thank their colleagues R. D. Kelly, D. Leon, J. French, and A. Pazmany for their participation in the data collection and processing. REFERENCES [1] A. L. Pazmany, R. E. McIntosh, R. D. Kelly, and G. Vali, “An airborne 95 GHz dual-polarized radar for cloud studies,” IEEE Trans. Geosci. Remote Sensing, vol. 32, pp. 731–739, July 1994. [2] G. Vali, R. D. Kelly, A. Pazmany, and R. E. McIntosh, “Airborne radar and in-situ observations of a shallow stratus with drizzle,” Atmos. Res., vol. 38, pp. 361–380, 1995. [3] G. Vali, R. D. Kelly, J. French, S. Haimov, D. Leon, R. D. McIntosh, and A. Pazmany, “Fine-scale structure and microphysics of coastal stratus,” J. Atmos. Sci., vol. 55, pp. 3540–3564, Dec. 1998. [4] E. E. Clothiaux, M. Miller, B. Albrecht, T. Ackerman, J. Verlinde, D. Babb, R. Peters, and W. Syrett, “An evaluation of a 94-GHz radar for remote sensing of cloud properties,” J. Atmos. Ocean. Technol., vol. 12, pp. 201–229, Apr. 1995. [5] R. Lhermitte, “Attenuation and scattering of millimeter wavelength radiation by clouds and precipitation,” J. Atmos. Ocean. Technol., vol. 7, pp. 464–479, June 1990. [6] H. J. Liebe, T. Manabe, and G. A. Hufford, “Millimeter-wave attenuation and delay rates due to fog/cloud conditions,” IEEE Trans. Antennas Propagat., vol. 37, pp. 1617–1623, Dec. 1989. [7] F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing. New York: Addison-Wesley, 1981, vol. 1, pp. 256–337. Compensation of Elevation Angle Variations in Polarimetric Brightness Temperature Measurements from Airborne Microwave Radiometers I. Corbella, A. J. Gasiewski, M. Klein, and J. R. Piepmeier Abstract—This paper presents a method for compensating the elevation anglefluctuationsoccurringinairborne radiometry due to aircraftrolland pitch. The correction is based on a radiative transfer model, and is demonstratedbyrealdatafromconicalscansovertheocean,showinggoodresults. Index Terms—Calibration, radiometry. I. INTRODUCTION Airborne microwave radiometry is very useful for retrieving important geophysical parameters such as surface wind speed and direction, with high spatial resolution and short revisit time. This requires brightness temperature T b to be measured at constant elevation angles, so a conically scanned system is highly useful. In practice, however, platform roll and pitch motion produces variations in the true incidence angle,thuscausing fluctuationsinthemeasuredbrightnesstemperature Manuscript received August 13, 1999; revised February 15, 2000. This work was supported by the Ministerio de Educacion y Cultura (Ref PR1997-0047 0046214076), Spain, Universitat Politècnica de Catalunya, Barcelona, Spain, and the NOAA/Environmental Technology Laboratory, Boulder, CO. I. Corbella and M. Klein are withUniversitatPolitècnica de Catalunya, 08034 Barcelona, Spain. A. J. Gasiewski is with the NOAA/Environmental Technology Laboratory, Boulder, CO 80303 USA. J. R. Piepmeier is with School of Electrical Engineering and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. Publisher Item Identifier S 0196-2892(01)00335-7. as well as rotation of the radiometer polarization basis. The problem is particularly acute for airborne platforms. Fora givenclass ofterrain, T b isafunction of the elevationangleand can be computed using models based on radiative transfer [1] and/or rough surface scattering theory. Whereas the absolute value of T b is difficult to predict due to its sensitivity to several often poorly known parameters, its slope with respect to the elevation angle at a given incidence angle, height, surface type, and atmospheric state, can be quite accuratelycomputed.Providedthattheplatformattitudeiswellknown, the theoretical slopes can be subsequently applied to the measured brightness temperatures to compensate to first order for variation in brightness as a function of the elevation angle. This attitude compensation has been successfully carried out on data gathered by the NOAA/ETL polarimetric scanning radiometer (PSR/A) [2] at frequencies of 10.7 GHz,18.7 GHz, 21.5 GHz, 37 GHz, and 89 GHz. The PSR was mounted onboard a NASA DC-8 aircraft during the third Convection and Moisture Experiment (CAMEX3, August–September 1998). Polarimetric brightness temperatures of the ocean surface were measured under a variety of meteorological conditions, particularly at high winds. Full (360  ) conical scans with 53.1  incidence (identical to the SSM/I) were used. At all the measurement frequencies and for both vertical and horizontal polarizations the compensation method shows a significant reduction of the correlation between the true brightness temperature and the true elevation angle as measured using aircraft inertial navigation system data, thus achieving an effective compensation. II. COMPENSATION TECHNIQUE The correction algorithm is based upon calculating the true elevation angle and polarization rotation given the PSR position encoder values and the aircraft pitch, roll, and heading data. First,the antenna pointing and horizontal polarization vectors are transformed into the world coordinate frame using five rotational transforms. Then the azimuth, elevation(fromnadir),and polarizationrotationanglesarecomputedfrom the output vectors. Once these angles are found, the corrections to the brightness temperatures can be made. The transformation of the antenna pointing and polarization vectors to the world coordinate frame is achieved using five rotational transform operations [3]. These rotations are performed about the scanhead elevation and azimuth axes, the aircraft roll andpitch axes, andfinally, the compass heading axis.Fig. 1 illustrates each of these coordinate frame rotations. In vector notation, the compound transformation is ^ X = R 0 1 z ( head ) 1 R 0 1 y ( pitch ) 1 R 0 1 x ( roll ) 1 R 0 1 z ( az ) 1 R 0 1 y ( el ) 1 ^ x (1) where ^ x is the pointing or polarization unit vector in the antenna coordinateframe,and ^ X istherespectiveunitvectorintheworldcoordinate frame. The antenna pointing unit vector is (0; 0; 1) T , and the horizontal polarization unit vector is (0; 1; 0) T . The rotation operators are given by the following: R 0 1 x (  )= 10 0 0cos  0 sin  0 sin  cos  ; R 0 1 y (  )= cos  0 sin  010 0 sin  0 cos  ; R 0 1 z (  )= cos  0 sin  0 sin  cos  0 001 (2) 0196–2892/01$10.00 © 2001 IEEE 194 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 39, NO. 1, JANUARY 2001 Fig. 1. The five rotational operations used to compute the PSR pointing and polarization vectors in the world coordinate frame. (a)–(c) describe the aircraft attitude, and (d) and (e) describe the instrument pointing with respect to the aircraft. X , Y , and Z denote world coordinates (North-East-Nadir), and x , y , z are airplane local coordinates (Front–Right–Bottom), and x , y , and z scanhead coordinates.  being a general symbol for the rotation angle which, while substituting the above in (1), will represent heading, pitch, roll, azimuth, or elevation angle. The true azimuth, elevation, and polarization angles can be found from the different vector components. The true elevation angle on ground (from zenith)  e is  e = tan 0 1 ^ k 2 x +^ k 2 y ^ k z (3) where ^ k x , ^ k y , and ^ k z are the x , y , and z components of the pointing vector in the world coordinate frame. The true azimuth angle  , in the compass rose orientation, is  = tan 0 1 ^ k y ^ k x : (4) The polarization rotation angle is found by first projecting the polarization vector in world coordinate frame ^ p =(^ p x ; ^ p y ; ^ p z ) T into the spherical polarization components using (1), and then taking an arctangent  = tan 0 1 ^ p x cos  cos  +^ p y cos  sin  0 ^ p z sin  0 ^ p x sin  +^ p y cos  (5) ThepolarizationrotationanglecanbeusedtocorrectthethirdStokes parameter with respect to the polarization basis rotation [4] T fU = T U cos 2  0 ( T v 0 T h )sin 2 : (6) Fig. 2. From top to bottom: Measured scanhead elevation angle referred to “downlooking” in local scanhead coordinates, measured pitch and roll angles of aircraft, and computed true ground elevation angle (from nadir). Foratypicalaircraftflight,thetrueelevationangleascomputedfrom the coordinate rotation is continuously changing during each scan, as illustrated in Fig. 2. In this particular example, the true elevation angle variedfromaminimumof 52.5  toa maximumof55.2  duringa single conical scan, whereas the nominal elevation angle was set to 53.1  .For meaningfulanalysesoftheradiometricdata,thiselevation angleshould be kept constant, particularly for comparison with satellite data. The compensation procedure is based upon a linear approximation of the brightness temperature with respect to the elevation angle for small increments T B (  e )  T B (  0 )+(  e 0  0 ) dT B d  (7) where T B represents vertical or horizontal brightness temperature, and  0 is the nominal elevation angle. Upon correction, the radiometer output is the first term of the above equation, and the compensated brightness temperature is its value at the nominal angle T B (  0 ) . The theoretical dependence of the brightness temperature with respect to the elevation angle can be computed using, e.g., the radiative transfer model (MRT) of [5]. Here, it is sufficient to use the statistical parameters of the atmosphere, the type of surface, and the altitude. To obtain the slope, a sixth degree polynomial approximation was fitted to data computed over the angular range of 0 to 89  (Fig. 3), and the derivative of the polynomial was used to estimate d T B =d . Table I shows the results of this computation for statistical fall, mid-latitudeatmosphere parameters at 10 km altitude and for wind-driven ocean with surface wind speed of 7 m/s. A cloud-free atmosphere was assumed. The surface model used is based on the Wilheit model [6] of a rough ocean surface and the sea water dielectric model of Klein and Swift [7]. III. RESULTS The results of the correction areshown in Fig. 4,in which the brightness temperatures measured at 10.7 GHz (vertical and horizontal) are plotted as a function of the true elevation angle. When no correction is performed, a high correlation (Table II) between T B and the true elevation angle 2 is clearly seen for both polarizations and for all frequencies. As predicted from the theory and shown in the curves of Fig. 3, at these elevation angles, for vertical polarization, the slope is positive, whereas the slope for horizontal polarization is negative. When corrected using the theoretical slope, the brightness temperatures are IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 39, NO. 1, JANUARY 2001 195 Fig. 3. Theoretical dependence of brightness temperature with incidence angle. The range of elevation angles during the experiment is shown. TABLE I COMPUTED SLOPE OF BRIGHTNESS TEMPERATURE WITH RESPECT TO THE ELEVATION ANGLE ( dT =d )AT  = 53.1 USING MICROWAVE RADIATIVE TRANSFER AND MODELS FOR THE OCEAN SURFACE AND THE ATMOSPHERE practically independent of the elevation angle, although some overcorrection is observed in the horizontal channel. Similar results are obtained for the remaining channels. IV. CONCLUSIONS A method for compensating the elevation angle variation in airborne microwave radiometry over the ocean has been presented. The method uses computed theoretical values of brightness temperature as a function of the elevation angle to determine the expected slope. By subFig. 4. Uncorrected and corrected brightness temperature as a function of elevation angle. TABLE II CORRELATION COEFFICIENT BETWEEN THE BRIGHTNESS TEMPERATURE AND THE ELEVATION ANGLE,BOTH BEFORE AND AFTER COMPENSATION.THEY HAVE BEEN COMPUTED FROM DATA COLLECTED ON SEPTEMBER 22, 1998 DURING THE CAMEX-3 CAMPAIGN tracting this theoretical slope, the brightness temperature at the nominal elevation angle is computed. Results are presented showing that this approach can effectively reduce the correlation between the true elevation angle and the brightness temperature. REFERENCES [1] F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing, Active and Passive. Reading, MA: Addison-Wesley, 1981, vol. 1. [2] J. R. Piepmeier and A. J. Gasiewski, “Polarimetric scanning radiometer for airborne microwave imaging studies,” in Proc. 1996 Int. Geoscience and Remote Sensing Symp. (IGARSS’96), Lincoln, NE, May 1996. [3] J. H. Ginsberg, Advanced Engineering Dynamics. New York: Harper and Row, 1988. [4] A. J. Gasiewski and D. B. Kunkee, “Calibration and applications of polarization-correlating radiometers,” IEEE Trans. Microwave Theory Tech., vol. 41, pp. 767–773, May 1993. [5] A. J. Gasiewski, “Atmospheric temperature sounding and precipitation cellparameterestimationusingpassive118-GHzO observations,”PhD dissertation, Mass. Inst. Technol., Cambridge, Dec. 1988. [6] T. T. Wilheit Jr., “A model for the microwave emissivity of the ocean’s surfaceas a function of wind speed,” IEEE Trans. Geosci. Electron.,vol. GE-17, pp. 244–249, Oct. 1979. [7] L. A. Klein and C. T. Swift, “An improved model for the dielectric constant of sea water at microwave frequencies,” IEEE Trans. Antennas Propagat., vol. AP-25, p. 104, 1977.