C55,/3:/ve: NOAATR NESS 68 A UNITED STATES DEPARTMENT OF COMMERCE PUBLICATION NOAA Technical Report NESS 68 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Environmental Satellite Service Dependence of Antenna Temperature on the Polarization of Emitted Radiation for a Scanning Microwave Radiometer NORMAN C. GRODY WASHINGTON, D.C. January 1974 . NOAA TECHNICAL REPORTS National Environmental Satellite Service Series tional Environmental Satellite Service (NESS) is responsible for the establishment and operation Operational Meteorological Satellite System and of the environmental satellite systems The three principal offices of NESS are Operations, Systems Engineering, and Research. 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Beginning with 51, printed copies of the reports are available through the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. Price as indicated. Microfiche available from NTIS (use accession number when available). Price $1.45. ESSA Technical Reports NESC 38 Angular Distribution of Solar Radiation Reflected From Clouds as Determined From TIROS IV Radi- ometer Measurements. I. Ruff, R. Koffler, S. Fritz, J. S. Winston, and P. K. Rao, March 1967. (PB-174-729) NESC 39 Motions in the Upper Troposphere as Revealed by Satellite Observed Cirrus Formations. H. McClure Johnson, October 1966. (PB-173-996) 40 Cloud Measurements Using Aircraft Time-Lapse Photography. Linwood F. Whitney, Jr., and E. Paul McClain, April 1967. (PB-174-728) NESC 41 The SINAP Problem: Present Status and Future Prospects; Proceedings of a Conference Held at the National Environmental Satellite Center, Suitland, Maryland, January 18-20, 1967. E. Paul McClain, October 1967. (PB-176-570) NESC 42 Operational Processing of Low Resolution Infrared (LRIR) Data From ESSA Satellites. Louis Rubin, February 1968. (PB-178-123) NESC 43 Atlas of World Maps of Long-Wave Radiation and Albedo--for Seasons and Months Based on Measure- ments From TIROS IV and TIROS VII. J. S. Winston and V. Ray Taylor, September 1967. (PB-176- 569) ] 44 Processing and Display Experiments Using Digitized ATS-1 Spin Scan Camera Data. M. B. Whitney, R. C. Doolittle, and B. Goddard, April 1968. (PB-178-424) NESC 45 The Nature of Intermediate-Scale Cloud Spirals. Linwood F. Whitney, Jr., and Leroy D. Herman, May 1968. (AD-673-681) 46 Monthly and Seasonal Mean Global Charts of Brightness From ESSA 3 and ESSA 5 Digitized Pic- tures, February 1967-February 1968. V. Ray Taylor and Jay S. Winston, November 1968. (PB-180- 717) : 47 A Polynomial Representation of Carbon Dioxide and Water Vapor Transmission. William L. Smith, February 1969. (PB-183-296) NESC 48 Statistical Estimation of the Atmosphere's Geopotential Height Distribution From Satellite Radiation Measurements. William L. Smith, February 1969. (PB-183-297) : 49 Synoptic/Dynamic Diagnosis of a Developing Low-Level Cyclone and Its Satellite-Viewed Cloud Patterns. Harold J. Brodrick and E. Paul McClain, May 1969. (PB-184-612) : 50 Estimating Maximum Wind Speed of Tropical Storms From High Resolution Infrared Data. L. F. Hubert, A. Timchalk, and S. Fritz, May 1969. (PB-184-611) (Continued on inside back cover) .„Q ATMQSp^ ~^wr^ U.S. DEPARTMENT OF COMMERCE Frederick B. Dent, Secretary NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION Robert M. White, Administrator NATIONAL ENVIRONMENTAL SATELLITE SERVICE David S. Johnson, Director NOAA Technical Report NESS 68 Dependence of Antenna Temperature on the Polarization of Emitted Radiation for a Scanning Microwave Radiometer Norman C. Grody a u WASHINGTON, DC. January 1974 o a © a c/5 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. Price $0.50 CONTENTS Abstract 1 Introduction 1 Theory 2 Linear polarization results 6 Cross -polarization effects 8 Conclusions 9 Acknowledgments 10 References 10 Appendix: Derivation of the geometric matrix elements.. 10 ii DEPENDENCE OF ANTENNA TEMPERATURE ON THE POLARIZATION OF EMITTED RADIATION FOR A SCANNING MICROWAVE RADIOMETER Norman C. Grody National Environmental Satellite Service, NOAA, Washington, D.C ABSTRACT. The antenna temperature is deter- mined for a scanning Earth-viewing satellite- borne microwave radiometer. The result is in the form of an integral that includes the an- tenna gain function and brightness tempera- ture. A composite emissivity term appears in the brightness temperature equation that con- tains the horizontal and vertical components of surface emissivity weighted by their re- spective antenna gains. Analysis is performed to obtain the antenna temperature components corresponding to the emission of horizontally and vertically polarized radiation. Calcula- tions are performed showing the effects of beam width and scan angle on the two compon- ents of antenna temperature for a linearly polarized antenna scanned about its polariza- tion axes. Effects resulting from antenna cross -polarization are also analyzed. INTRODUCTION Interpretation of radiometric data generally requires the de- termination of brightness temperatures from antenna temperature measurements as the first step in the complete analysis of the data. A review of some of the recent inversion techniques for estimating brightness temperatures is contained in the report by Claassen and Fung (1973). The purpose of our report, however, is to illustrate the influence of antenna characteristics, as defined by their beam width and cross polarization, on the in- terpretation of antenna temperature measurements for a scanning microwave radiometer. By considering simple antenna models, a number of general results are obtained that are of importance in antenna design considerations for radiometric applications. THEORY Figure 1 shows the antenna coordinate system (x\y\z') that is rotated by the scan angle S with respect to the Earth(2,^',2). Also shown is an arbitrary an- tenna propagation direction, as defined by the unit vector k' , that intersects the Earth's sur- face where the unit normal vec- tor is designated by n. In the antenna far field, the electric field received can be decom- posed into the spherical corn- pone nts E*' and E. as indicated Figure 1. --Antenna and Earth co- ordinate systems in figure 1. However, with respect to the Earth coordinates, the electric field is designated by its horizontal and vertical polar ization components ^ and E vi respectively. The total electric field Fcan be written as E ^jil + aj^a^+i^i/ 6 ^6 CD where the terms a. h , a. v , 8. 3 - , and a./ are unit vectors that define the polarization directions of the field components. Solving eq (1) for the antenna fields in terms of the horizon- tal and vertical polarization components, we find M W21 9izJ\E vt (2) where $\v 9* fci-V 4 *. and i 7 22 The geometric matrix elements g are computed using the horiz ontal and vertical polarization vectors \n xAT'l and |(n*£W| (3) and the orthogonality relationships a ,.x *'=a^' and a^x^'=-a^- After some algebraic manipulations (see appendix) , we find that eq (2) becomes ^ /v., /i^U \-t-a'. '\-9l -fn )\K (4a) where ff\x (4b) The geometric factor ^ u is evaluated for a flat surface with its normal in the x direct ion (fig. 1) so that n^a^^a^, cos 9 s -a. y sin 2L*' = -a x . sin^' + a.,, cos 0', and £'=3. x . sin <5' cos /#'+ a> y - sin (9' sin ^' + a. z . cosd' . Substituting eq (5) into eq (4b), we find 9v. -si n 10 +i (5a) (5b) (5c) 'l-s'm 2 0'cos 2 {.<£ + 0j where ^ u is a function of the scan angle s and the angular coor dinates 0' and 0' within the antenna beam. (6) The power received by an antenna P (flj can be expressed in terms of the antenna gain function and far fields, namely: P "^ //[£,.+ £,] sin aV and 6r, ■&&*'+$- 9$ &&' • (8a) (8b) (8c) Here, use was made of the fact that the fields E h and E v are uncor- rected random variables with zero mean so that terms involving \E h E v \ have zero average value [eq (19), Stogryn 1970J. Equation (8a) can also be written in terms of equivalent noise temperatures, namely: 71 1 SJ& r h + Gr^mQ' ti\6 h + QfwO'dO'd-izr a /?. K (9b) (9c) (9d) The temperatures T k and T^ are the horizontal and vertical bright- ness temperatures; and T a is the antenna temperature , K is Boltzman's constant , fj is the equivalent noise bandwidth, and A is the radia- tion wavelength. 4 For a nonscattering atmosphere in local thermodynamic equilib- rium, the brightness temperatures are given by and T^Tu +r\e l T,+(l-cJT d tt+r ^£ + (1-0 £ (10a) (10b) where C h and £ v are the horizontal and vertical polarization sur- face emissivities and 7^ is the surface temperature. The tempera- tures T u and Tj are the brightness temperature components correspond ing to upward atmospheric emission from the surface to the anten- na position T u and downward atmospheric radiation to the surface Tj . The term r is the total atmospheric transmittance from the surface to the antenna level. Substituting eq (10) into eq (9a) , we obtain ffGT £ sin dd I t r\> 1 i I where ffGw&dOdp U \ S iS and £. G,+G„ (11a) (lib) (lie) (lid) Hence, the antenna temperature is given by an integral contain ing the antenna gain function G and a brightness temperature T$. The brightness temperature equation contains a composite surface emissivity € s that depends on the horizontal and vertical emis- sivity components weighted by their respective antenna gains. LINEAR POLARIZATION RESULTS For a linearly ' polarized an- tenna lying in the;'- z' plane (fig. 1) with current excita- tion along z' , the far field is in the <3^' direction so that 6 = (rd' • The composite emissiv- ity then becomes 1.0 0.8 0.6 0.4 ^.^ s* + (i-^K (12) 0.0 where the y u dependence of an- gles , / , and :p £ is given by eq (6) for a flat surface. III!" * s + *'=90° _ - X^ * s ++' =45°_ - \ >s>,+ t>'= 30° - 1 \ ^v4> s + <>> = ] 5 \ ^\^^ - \. <» s + 0" = 1° - 1 1 1 1 1 1 1 1 1 0° 10" 20" 30" («'— 90°) 40" 50° Figure 2 .- -Normalized horizontal emissivity component (yfjas a function of antenna angles Figure 2 shows a plot of g\^ \& , P > r* ) as a function of zenith angle for a different azimuthal and scan angle. At nadir (here, 0' + s = O° and &'=90°) ^ 2 = 1 so that /> 30°-^ and £,' (0 for all anqles (15a) (15b) Equation (15) defines the gain functions for a linearly polar- ized antenna with its polarization direction along a. 0f . Effects due to cross polarization [tip* £ 0) will be discussed later. Substituting eq (6) , (8b) , and (15) into eq (14b) , we find that //-- fM^'S\nOdo r -I ^' -t / ' ff£ys\r\ d'dO > ^ &' ^ j f 2 f s >' tan -1 sin — • cot^+^J 3 J 5 i H f -cot^VJ (16) where the angleB is the antenna beam width 7 Equation (16) is plotted in figure 3 as a function of scan angle #, for different beam widths J? . Note that, for zero beam width h=l , V=0 so that all energy received is in horizon- tal polarization independent of scan angle. However, for increasing beam width, there are larger vertical pol- arization contributions for scan angles near nadir. This result indicates that a linearly polarized antenna scanned about its polarization axes receives predominantly horizontally polarized radia- 20 30 # s in Degrees 40 50 Figure 3 .- -Normalized power re- ceived in horizontal polariz- ation iff) as a function of scan angle (^ ) for different beam widths (B) tion; the influence of the vertically polarized radiation is sig- nificant only near nadir. At near-nadir directions, however, the horizontal and vertical emissivities are almost identical (see Stogryn 1972) so that the antenna temperature is essentially des- cribed by the horizontal component of emissivity for all scan angles . CROSS-POLARIZATION EFFECTS The effects due to antenna cross -polarization are obtained us- ing eq (14) and considering the primary polarization along a g > with gain 6- d > and cross polarization along a./ with gain Q /7>0 (17) where /0=Q corresponds to a linearly polarized antenna with polar ization a. d - and /3=1 refers to a linearly polarized antenna with orthogonal polarization sup' (considered cross -polarized direc- tion) . 8 Substituting eq (17) into eq (14) , we obtain H=p+{\-2p)H (18a) and _ ff?&e'Wd<30 . After we use the gain func- tion Ctq' of eq (15a), // is given by eq (16). From figure 3, ob- serve that v^o is approximately unity for scan angles larger than the beam width. It then follows from eq (18a) that, for such scan angles, ff~\-p and V=p, or the power received in ver- tical polarization is linearly related to the percent of cross polarization as given by the parameter/?. Equation (18a) has the form shown in figure 4 for an antenna beam width of 10°. The effects due to cross polarization are to increase the level of power received in vertical polarization and alter the scan angle dependence of received radiation. It also appears that a min- imization of the scan angle dependence can be achieved by re- ceiving equal polarization in 3i d > and a^ (i.e., p=l/2 ). n Degrees Figure 4 .- -Normalized power re ceived in horizontal polar- ization {//) as a function of scan angle {0 S ) for dif- ferent amounts of cross polarization (/?) ; antenna beam width (2? = 10° ) CONCLUSIONS Analysis of a linearly polarized antenna scanned about its polarization axes leads to the interesting result that the power received is predominantly of horizontal polarization, except for near-nadir scan angles. Hence, the horizontal emissivity is to be used in such antenna temperature calculations. We found that cross-polarization effects increase the level of vertical polar- ization received and so increase the contribution attributable to vertical emissivity in antenna temperature calculations. The influence of Earth's curvature has not been analyzed; however, one can argue that its effect is to give the appearance of a larger scan angle with respect to that employed in the flat sur- face analysis. Its effect is generally small for scan angles not approaching Earth's horizon. ACKNOWLEDGMENTS Grateful acknowledgments are made to A. Stogryn of the Aero- jet Electro-System Corporation and to J. Shue of Goddard Space Flight Center, National Aeronautics and Space Administration, for their suggestions and discussions during the preparation of this report. REFERENCES Claassen, J. P., and Fung, A.R., "An Efficient Technique for De- termining Apparent Temperature Distributions From Antenna Temp erature Measurements," Technical Report 186-8, University of Kansas Center for Research, Lawrence, Kans . , Sept. 1973, 33 pp Stogryn, A., "The Brightness Temperature of a Vertically Struc- tured Medium," Radio Science , Vol. 5, No. 12, Dec. 1970, p. 1400. Stogryn, A., "A Study of Radiometric Emission From a Rough Sea Surface," Technical Report 300R-1, Aerojet Electro-System Corporation, Azusa, Calif., July 1972, pp. 40-42. APPENDIX: DERIVATION OF THE GEOMETRIC MATRIX ELEMENTS nxr _ fafXK'yn rig) f') x^'- (nx at') x#' = /[/r'-n(/r'«n)]»|V-n(Af'»ii)] = /f>if.r>) z +l-2 0r-n) 2 = yi-(^'-n) 2 . (24) Using the relationships, s rxx / --i^ and £?'* K' = a.