Effects of Antenna Cross-Polarization Coupling on the Brightness Temperature Retrieval at L-Band

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011 1637

Effects of Antenna Cross-Polarization Coupling onthe Brightness Temperature Retrieval at L-Band

Seung-Bum Kim, Frank J. Wentz, and Gary S. E. Lagerloef, Member, IEEE

Abstract—Retrieval of the brightness temperature (TB) at theL-band is studied in the context of the remote sensing of oceansurface salinity. The measurement of antenna temperature andthe retrieval of TB are simulated with a radiative transfer modeland an observing system model of an orbiting spacecraft. Twosets of antenna gain patterns are used: 1) theoretical analysis and2) measurements of a 1/10th-size scale model. The latter set no-tably shows the large cross-polarization coupling from the firstStokes transmit into the third Stokes receive. The large cross-polarization coupling causes an error of up to 4◦ in the estimateof the Faraday rotation angle (the size of the angle itself is mostlyless than 15◦ in the severe ionospheric condition). By this amountof the error, an additional rotation is introduced to the retrieval ofthe second and third Stokes TBs in front of the feed horn beforethe Faraday rotation correction. The additional rotation also de-grades the performance of the antenna pattern correction (APC).However, when the Faraday rotation correction is performed bythe square sum of the two retrieved Stokes, the retrieved TB

below the ionosphere and at the top of the atmosphere after theFaraday correction becomes insensitive to the additional rotation(i.e., being insensitive to the error in the Faraday angle estimateand the rotational error in the APC). The formal proof of theinsensitivity is presented. The first and second Stokes TBs at thetop of the atmosphere observed at 5.6-s intervals from space maybe retrieved with an error smaller than 0.1-K rms without theaccurate ancillary information of the gain pattern and the Faradayrotation angle, assuming correct calibration, 0.08 K NEΔT for theradiometer noise, and accurate correction or flagging of the solarand galaxy radiation.

Index Terms—Antenna gain, brightness temperature, Faradayrotation, microwave radiometer.

I. INTRODUCTION

PASSIVE microwave radiation at the lower end of themicrowave spectrum (e.g., at 1.413 GHz in the L-band)

may be used to measure the sea surface salinity (SSS) of thetop few centimeters, exploiting the dependence of the dielectricconstant of sea water on salinity [1]. Surface salinity needs to bemeasured with an accuracy of 0.1–0.2 psu to monitor important

Manuscript received November 17, 2009; revised July 9, 2010; acceptedSeptember 19, 2010. Date of publication November 22, 2010; date of currentversion April 22, 2011. This work was supported in part by Remote SensingSystems and the Jet Propulsion Laboratory, California Institute of Technology,under a contract with the National Aeronautics and Space Administration.

S.-B. Kim is with the MS300-323 Jet Propulsion Laboratory, CaliforniaInstitute of Technology, Pasadena, CA 91109 USA (e-mail: [email protected]).

F. J. Wentz is with the Remote Sensing Systems, Santa Rosa, CA 95401USA.

G. S. E. Lagerloef is with the Earth and Space Research, Seattle, WA 98102USA.

Digital Object Identifier 10.1109/TGRS.2010.2087028

open ocean phenomena such as the North Atlantic thermohalinecirculation, ocean surface freshwater balance, surface oceanstability in the western tropical Pacific Ocean, and halostericeffect on sea level (Salinity and Sea Ice Working Group reports:http://www.esr.org/lagerloef/ssiwg). An analytical investigationand aircraft experiment demonstrated that such high-precisionmeasurements by remote sensing are feasible [2], [3]. A space-borne L-band radiometer for observing SSS was launchedin 2009 (Soil Moisture Ocean Salinity [4]–[7]), and anotherradiometer is due for launch in 2011 (Aquarius [8], [9]).

Critical to the salinity retrieval is the accurate retrieval ofbrightness temperature (TB). An experiment with an end-to-end simulator [10] demonstrated that TB at the top of theatmosphere may be retrieved with an accuracy better than0.1 K, which roughly corresponds to 0.2 psu in salinity. Thesimulation in [10] used the antenna gain pattern generated bya theoretical analysis. Recently, antenna patterns have beenmeasured at the Jet Propulsion Laboratory using a 1/10th-sizescale model of the spacecraft. The scale-model pattern exhibitslarge cross-polarization (cross-pol) coupling, which is differentfrom the theoretical analysis, as will later be described. Thispaper examines the effect of the large cross-pol coupling on TB

retrieval.The retrieval of TB from the radiometer recording of mi-

crowave radiation typically involves the calibration of antennatemperature (TA), correction for antenna pattern, and removalof environmental contamination. The calibration converts theradiometer recording to TA (see, e.g., [11] and [12] for a fullypolarimetric radiometer and [13] and [14] for calibration fun-damentals in general), which is beyond the scope of this paperand is assumed to correctly be performed. The antenna patterncorrection (APC) restores TB at the boresight by removing thecross-pol leakage and the spillover. Over the ocean surface, alinear combination of TA has successfully restored TB (e.g.,[15]), which is adopted in this paper, or the portion of TA asso-ciated with antenna side lobes may be modeled (e.g., [16]). Theenvironmental contamination includes celestial sky radiation,and emission and absorption by atmospheric molecules.

As a part of the environmental contamination for space-borne remote sensing at low frequencies such as the L-band,electromagnetic waves experience the rotation of polarizationvectors as they travel through plasma magnetic fields. Therotation, i.e., the Faraday rotation, affects the second Stokesparameter by up to ∼5 K. The Faraday effect may be alleviatedby retrieving TB with the first Stokes measurement only (e.g.,[17] and [18]), because the total power received is unaffectedby the rotation. Then, the polarization information becomes

0196-2892/$26.00 © 2010 IEEE

1638 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011

unavailable, resulting in the reduced capability to retrieve SSS,because the vertical polarization (V-pol) is more sensitive tothe SSS changes than the other channels [2] and also becausethe V-pol is less sensitive to wind roughening than the otherchannels [19], [20]. A ratio between the V-pol and the horizon-tal polarization (H-pol) may be utilized to remove the Faradayeffect, but this approach requires accurate knowledge of wind[17]. Instead, the Faraday angle itself may be estimated [21].This approach may incur errors in the presence of nonidealfeatures in the gain pattern, e.g., cross-pol coupling [22]. Suchan error was less than a degree for the rotation angle and afew tenths of kelvin for the first Stokes TA when the cross-pol coupling was small [22]. When the cross-pol coupling isnot small as is the case with the 1/10th-size scale model ofa spacecraft, the errors in the Faraday angle estimates havenot been understood. Furthermore, how these errors may affectthe APC and the retrieval of TB needs thorough investigation.This paper examines these issues by estimating the Faradayrotation angle with the approach in [21]. This paper finds that,although the cross-pol coupling leads to errors in the estimatedFaraday rotation angle and in the APC, the error in the APC is amere rotation of the APC obtained with no error in the Faradayrotation angle, and consequently, this error in the APC does notimpact the retrieval of TB from antenna temperatures.

This paper presents TB retrieval methods by focusing on thecorrection of the antenna pattern and the Faraday rotation effectin the presence of the large cross-pol coupling. The analysis em-ploys an end-to-end simulation of space-borne salinity remotesensing with the Aquarius radiometer [8], [9] as an example.The polarimetric radiometer has the three-beam pushbroomantenna pointing at the local incidence angles of 28.7◦ (innerbeam), 37.8◦ (middle), and 45.6◦ (outer), respectively, onboarda sun-synchronous spacecraft that orbits at a 657-km altitude.Other specifications of the space-borne radiometer will be des-cribed in the main text. The orbital simulation enables theglobal examination of the issues in TB retrieval (such asthe complicated geometry between the boresight vector and themagnetic field vector, which determines the Faraday rotation).Section II describes the forward simulation. Section III pre-sents the retrieval of TB . Section IV summarizes the findings.

II. FORWARD SIMULATION

The forward model simulates the measurements of antennatemperature vector. Complete details of the simulator and itsperformance with the theoretical antenna pattern are presentedin [10], and a summary is presented as follows. The forwardsimulation is performed in terms of the Stokes vector forantenna temperature (TA), i.e.,

TA ≡

⎡⎢⎣TA1

TA2

TA3

TA4

⎤⎥⎦ =

⎡⎢⎣

TAv + TAh

TAv − TAh

TA+45 − TA−45

TAL − TAR

⎤⎥⎦ (1)

where TAi is the ith Stokes parameter, and TAv , TAh, TA+45,TA−45, TAL, and TAR are the antenna temperatures forv−, h−, +45◦, −45◦, left-, and right-circular polarization chan-nels, respectively. TA3 is simulated, because it is sensitive to the

Fig. 1. Definitions of TA and TB used in this paper. TOA refers to “top of theatmosphere” (but below the ionosphere). The subscript R denotes the rotationof the polarization vector. est and fwd abbreviate “estimate” and “forward,”respectively.

Faraday rotation effect (e.g., [21]). The fourth Stokes vector isnot used during the simulation but is written for completeness.Likewise, brightness temperatures (TB) are defined as

TB ≡

⎡⎢⎣TB1

TB2

TB3

TB4

⎤⎥⎦ =

⎡⎢⎣

TBv + TBh

TBv − TBh

TB+45 − TB−45

TBL − TBR

⎤⎥⎦ . (2)

TA measurement (TA,mea) is contributed by the sum ofradiation from the earth (TA,earth) and space (TA,space) fieldof views as

TA,mea =TA,earth +TA,space

=1

4π

∫earth

G(b)Ψ(φ)TB,toa∂Ω

∂AdA

+1

4π

∫space

G(b)TB,spacedΩ. (3)

The first integral applies to the top-of-the-atmosphereTB (TB,toa) over the surface of the earth, where dA and dΩ arethe differential surface area and solid angle, respectively. Thetop of the atmosphere is defined as the base of the ionosphere(see Fig. 1). The second integral is over space. TB,space isthe sum of cosmic (2.7-K background radiation), galactic,and incident solar radiation. Each of the solar and galacticincidences consists of the following three components: 1) directincidence into the antenna side lobe; 2) specular reflection fromthe earth surface into the side lobe; and 3) bistatic reflectionfrom the rough ocean surface into the main lobe. Only the directincidence and specular reflection are modeled for the solarradiation. Both components enter the side lobe, because theboresight points to the sun shade by the design of the spacecraft.The effect of the neglected components, solar reflection and thegalaxy glint off the earth’s rough surface into the main beamwill be discussed in the Conclusion. The solar flux of the year2000 is used to represent the solar maximum. The matrix Gat view angle vector b is a 4 × 4 matrix of the high-densityantenna gain values (one million grid points). Ψ(φ) is a rotationmatrix, and the rotation angle φ is the sum of the Faradayrotation angle due to the ionosphere and the angle between theantenna polarization (according to the Ludwig-3 definition) andthe earth polarization vectors. The two vectors are aligned at the

KIM et al.: ANTENNA CROSS-POLARIZATION COUPLING ON BRIGHTNESS TEMPERATURE RETRIEVAL AT L-BAND 1639

boresight, but the misalignment further increases away from theboresight. Also added to TA is the instrument noise, defined bythe NEΔT of 0.08 K after integrating over 5.6 s.

The Faraday rotation effect is simulated using the totalelectron content from the International Reference Ionosphere(IRI) 2001 model and the earth’s magnetic field vector from theninth-generation International Geomagnetic Reference Field(IGRF). To simulate the worst case, an unusually active dayin the ionosphere is chosen to specify the electron content(303rd day in 2003). TB,space is unpolarized and does notexperience the Faraday rotation (except for the galactic andsolar backscatter, which are not modeled here).TB,toa is computed by a radiative transfer equation that

was developed for Advanced Microwave Scanning Radiometer-EOS (AMSR-E, [23]) and is adapted for the L-band. TB,toa isgiven, for a polarization P , as

TBP,toa =TBU + τ [EPTS + TBPΩ]

TBPΩ ≈ (TBD + τTspace)RP (4)

where TBU is the upwelling atmospheric radiation (unpolar-ized), τ is the atmospheric transmittance, EP and RP arethe surface emissivity and reflectivity, respectively, and TS isthe sea surface temperature (SST) from the Reynolds product.TBPΩ

is the integration over an upper hemisphere of down-welling radiation from the atmosphere (TBD, unpolarized) andthe space. TBPΩ

is approximated as the reflection at the bore-sight angle rather than the integration. TBU , TBD, and τ arecomputed by deriving absorption due to oxygen, water vapor,and cloud liquid water [23]. For the derivation, the products ofthe National Centers for Environmental Prediction (NCEP) at-mospheric model are used. RP (and, accordingly, EP ) over theocean surface is provided by the dielectric model [24] for thespecular component. RP is revised to accommodate the surfaceroughness effect using the WISE model [19] and NCEP winds.

In performing the earth integration, a very fine grid is usedover the antenna’s main lobe: dA corresponds to an earth pixelthat is 1/6× 1/27◦ wide in both latitude and longitude. Thisvery fine spacing for dA ensures the numerical accuracy of theintegration over the main lobe, i.e., 0.01% or better. Outside themain lobe, dA corresponds to an earth pixel that is 1/6◦ by 1/2◦

wide in latitude and longitude, respectively.The SSS input to the simulation and the forward TBv,toa

are shown in Fig. 2 for Nov. 18, 2004. Salinity estimates wereproduced by the Estimating the Circulation and Climate ofthe Ocean numerical simulation (ECCO, http://ecco.jpl.nasa.gov/external/). TBv shows an inverse relation to salinity. Thehigh SSS over the Arabian Sea and the Subtropical Atlantic(around 20◦ N and 20◦ S, respectively) corresponds to low TBv.The high TBv over the North Pacific and along the 50◦ S latitudeis due to high wind, whereas the low TBv over the westernequatorial Pacific is associated with low wind. The low TBv

near the Antarctica is due to low SST, even when SSS is lowthere.

III. SIMULATION OF RETRIEVAL

In this paper, the TB retrieval aims at estimating the first andsecond Stokes parameters. The third Stokes is used to correct

Fig. 2. (a) ECCO ocean numerical model’s surface salinity (in practicalsalinity units) for Nov. 18, 2004. Salinity is not available north of 80◦ N and isset to 30 psu. (b) Top-of-the-atmosphere V-pol TB (in kelvin) at 38◦ incidenceangle, simulated over one week around Nov. 18, 2004.

for the Faraday rotation effect. By deriving the V-pol TB usingthe two classical Stokes, SSS may be retrieved with the V-polTB , which is more sensitive to SSS [2] and is less affected bythe wind roughening [19], [20] than the H-pol TB , or SSS maybe derived with the dual polarization (dual-pol) TB to makeuse of the multiple polarization information. At the end of thissection, a preliminary assessment of the second approach ispresented to show how the TB retrieval error determines theSSS retrieval performance. The simulation of the TB retrievalconsists of the following sequential steps.

• Simulate the earth’s portion of the antenna temperaturemeasurements, TA,earth, by removing the contributionfrom the cosmic background.

• Compute TB in front of the feed horn using the forwardradiative transfer. This quantity is denoted as TBR,fwd,where the subscript R denotes that TB has been rotatedby the Faraday effect. During the forward calculation, theFaraday angle used is estimated with TA,earth in case thataccurate ancillary information of the angle is unavailable.

• Perform the APC using TA,earth and TBR,fwd as input.At this stage, the Faraday rotation correction is yet notapplied, and therefore, TB after the APC is still rotatedby the Faraday effect. The output is denoted as TBR,est.

• Remove the Faraday rotation effect from TBR,est andestimate the top-of-the-atmosphere TB , TB,toa,est.

Fig. 1 illustrates the definitions of various TA and TB vari-ables previously introduced. A space-view portion of 2.73-Kbackground radiation is removed from the antenna temper-ature, resulting in TA,earth. The solar direct incidence andbistatic specular reflection off the sea surface, which weresimulated during the forward process, are not removed fromTA. As a result, a positive bias would appear in the retrievedTB . However, these components are small (typically less than


TABLE IANTENNA PATTERN CORRECTION COEFFICIENTS OF (5). THE FARADAY ANGLES ARE EITHER THE ESTIMATE DURING THE RETRIEVAL WITH THE

SCALE-MODEL ANTENNA PATTERN [φf,est ; SEE (8)] OR THE REFERENCE USED FOR THE FORWARD SIMULATION (φf,ref , ALMOST THE SAME

AS AN ESTIMATE WITH THE THEORETICAL ANTENNA PATTERN). THE COEFFICIENT a23 SHOWS LARGE DIFFERENCES BETWEEN

TWO ESTIMATES FOR THE SCALE-MODEL PATTERN AND IS HIGHLIGHTED WITH AN UNDERLINE

0.04 K and rarely exceed 0.07 K with the solar maximum fluxfrom the year 2000 and with the configuration of the boresightpointing away from the Sun [25]). The effect of the neglectedcomponents, i.e., the solar reflection and galaxy glint off theearth’s rough surface into the main beam, will be discussed inthe Conclusion.

The APC converts TA,earth into TBR,est by correcting forthe antenna spillover and cross-pol leakage. The APC furtherremoves the effect of the 4π-integration over the antennapattern. The goal is to estimate TB,toa,est at the boresight,which, in turn, will be used to retrieve SSS at the boresight.Formally, the APC matrix (A) may be estimated by mini-mizing a cost function, defined by the magnitude of a vector,‖Fnonlinear(A TA,earth)−TB,toa‖. Fnonlinear is a nonlinearfunction that consists of the trigonometry functions that modelthe Faraday effect. The cost function may be linearized as‖A TA,earth −TBR,est‖, followed by a derotation of theFaraday effect. With this two-step approach, the inversion canbe simpler than the first approach, and we may obtain physicalunderstanding of each of the two inversion steps. The two-step approach is adopted in this paper. Because the spilloverand cross-pol leakage are properties of the antenna, the APCcoefficients would be static in space and time, as long as theproperties do not significantly change. Over the ocean surface,the APC has successfully been performed by multiplying TA

by a static set of APC coefficients (e.g., [15]). This heritage isadopted in this paper. A 3 × 3 matrix defines the APC in thispaper as⎡

⎣TBR1,est

TBR2,est

TBR3,est

⎤⎦ =

⎡⎣ a11 a12 a13a21 a22 a23a31 a32 a33

⎤⎦⎡⎣TA1,earth

TA2,earth

TA3,earth

⎤⎦ . (5)

The a-coefficients are assumed to be invariant in space andtime. The coefficients are derived by inverting (5) with TBR

of the forward radiative transfer, TBR,fwd, and TA,earth.TBR,fwd is obtained by

TBR,fwd = Ψ(φf,est)TB,toa (6)

where φf,est ≈ 0.5 atan(TA3,earth/TA2,earth)

Ψ(φf,est) =

⎡⎣ 1 0 00 cos 2φf,est − sin 2φf,est

0 sin 2φf,est cos 2φf,est

⎤⎦

and TB,toa = [TB1,toa TB2,toa 0 ]T.The Faraday angle (φf,est) is estimated as a function of

TAs, following [21], to avoid any errors in an ancillary datasource such as an ionosphere model. The rotation by Ψ isimplemented in the boresight target polarization basis ratherthan in the instrument basis. Strictly speaking, the formula forφf,est should apply to TAs measured by the pencil beam atthe boresight. Thus, the use of TA,earth in (6), which is theresult of the 4π-integration, implies the mixing of the Faradayangles across the antenna’s earth field of view. In practice,the mixing is not serious: it introduces less than 0.1◦ errorto the Faraday rotation angle in our scale-model simulation([22] reports a maximum of 0.5◦ error in the analysis with thetheoretical antenna pattern). TB,toa is computed by the forwardradiative transfer as described in Section II. TB3,toa is assumedto be zero. The assumption reflects that the natural third Stokesparameter from the ocean surface is about 0.1 K [21], muchsmaller than 3–15 K that may be generated by the Faradayrotation.

The Faraday rotation is corrected with an approach adaptedfrom [21] as

TB1,toa,est =TBR1,est

TB2,toa,est =√

T 2BR2,est + T 2

BR3,est. (7)

The APC coefficients estimated following the aforemen-tioned procedures are presented in Table I. The copolorizationdiagonal elements are several percentages larger than the unity,reflecting the correction of the spillover effect. The cross-pol off-diagonal elements may be associated with both thespillover and cross-pol leakage. Noticeable is the large off-diagonal element, a23, of the scale-model’s APC coefficients(0.17 for the inner and 0.12 for the middle horn, middle column


Fig. 3. Faraday angles along a satellite orbit. In thick gray is the referenceangle at the boresight (the same between the two patterns). It is computedusing the models of ionosphere and magnetic fields. In black is 0.5 atan(TA3,earth/TA2,earth), which is different between the two patterns.

in the table). In contrast, when the reference Faraday angle,φf,ref , is used during the derivation of the APC coefficients,the off-diagonal elements become small (Table I, right column).φf,ref is the angle at the boresight used during the forwardsimulation. φf,est is used during the retrieval to account forthe likely situation that accurate values of φf,ref may not beavailable. These experiments suggest that the excessive valuesof the off-diagonal APC coefficients are caused by the errorsin φf,est. The errors in φf,est deteriorates the APC, becausethe spacecraft flies within the ionosphere, and the antennatemperature is affected by the Faraday rotation. The causalitywill be investigated as follows.

The errors in φf,est are large for the inner and middle hornsof the scale-model pattern (see Fig. 3). The error in φf,est maybe understood by writing the expressions for φf,est, as definedin (6), in terms of TA2,earth and TA3,earth. Furthermore, letTA,earth [= GΨTB,toa; see (3)] be written using the defini-tion of the Mueller gain matrix in (11) and TB after the Faradayrotation. For simplicity, let the copolorization gain values foreach polarization be equal to G. In addition, let us consider onlythe dominant cross-pol coupling elements in the Muller matrix.The Muller matrix is evaluated for the two antenna patterns inTable II. As discussed in Appendix A-1, the comparison of thegain values in Table II shows that the dominant cross-couplingterm is between the first Stokes transmit and the third Stokesreceive, because the corresponding cross-pol gain and TB1,toa

are large. Then, it follows that φf,est of (6) may be written as in(8), shown at the bottom of the page. According to (8), φf,est

becomes φf,ref without the cross-coupling term; however, thelarge cross-coupling term results in the error in the Faradayangle estimate, φf,est − φf,ref . The error is presented in

TABLE IIMUELLER MATRIX OF THE THEORETICAL AND SCALE-MODEL ANTENNA

PATTERNS IN TERMS OF THE CLASSICAL STOKES AS DEFINED IN (11).THE GAIN VALUES ARE INTEGRATED OVER 4π-STERADIANS. SOME

CROSS-POL COUPLING TERMS EXHIBIT LARGE DIFFERENCES BETWEEN

THE TWO GAIN PATTERNS AND ARE HIGHLIGHTED WITH AN UNDERLINE

(WHEN THE RATIO OF THE GAIN BETWEEN THE SCALE MODEL AND THE

THEORETICAL PATTERN IS LARGER THAN ∼50, THE SCALE-MODEL

GAIN IS HIGHLIGHTED WITH A DOUBLE UNDERLINE)

TABLE IIIEFFECT OF THE CROSS-POL COUPLING ON THE FARADAY ANGLE

ESTIMATE, SHOWN BY THE DIFFERENCE (φf,est − φf,ref ). THE

DIFFERENCE IS COMPUTED FOR THE THREE BEAMS USING

TYPICAL VALUES OF TB AND THE ANTENNA GAIN

Table III. Nominal values are used to evaluate TB1,toa/TB2,toa,and they are 12, 7, and 4 for the inner, middle, and outer horns,respectively. The value of Re(gvvg

∗hv + gvhg

∗hh)/G

2 is takenfrom the Mueller matrix of the scale-model pattern in Table IIand is set to 0.015, 0.018, and 0.014 for the inner, middle, andouter horns, respectively. Table III shows that the outer horn hasthe smallest error in φf,est among the three horns, because itsTA2 is the largest. The size of the error in φf,est is consistentbetween the simulation on one orbit (Fig. 3) and the analysis(Table III). The error is 3.0◦, 3.7◦, and 0.4◦ for the inner, middle,and outer horns, respectively, when averaged over the globalocean. For the theoretical pattern where the cross-pol couplingis very small, the difference between φf,est and φf,ref is lessthan 0.6◦ (Fig. 3). The aforementioned analysis confirms thatthe errors in φf,est originate in the large cross-pol coupling.

φf,est ≈ 0.5atan

(Re(gvvg

∗hv + gvhg

∗hh)TB1,toa +G2 sin(2φf,ref )TB2,toa

G2 cos(2φf,ref )TB2,toa

)(8)


Fig. 4. Errors in the individual retrieval at 5.6-s intervals simulated using the theoretical antenna pattern. (a)–(d) Errors in the first and second Stokes, in kelvin,(ΔTB1,toa = TB1,toa,est − TB1,toa). (e)–(f) Errors in salinity (in practical salinity units). NEΔT of 0.08 K and the random error in SST and wind speed of0.3 ◦C and 0.5 m/s (1 sigma), respectively, are included in the simulation. Temporally static but spatially varying salinity and the worst case Faraday effect areused during the forward simulation.

The error in the Faraday angle estimate, however, does notaffect the second and third Stokes parameters of the retrievedTB as explained in the following discussion. As a result ofthe error in the estimated Faraday angle, the second and thirdStokes of the forward TB in front of the feed born (TBR,fwd)are rotated further [see (6)]. The additional rotation producesthe error in the APC coefficient estimates [see (16)] whencompared with the coefficients that we may derive using theaccurate Faraday angle (φf,ref ) and the consequently accurateTBR,fwd. In addition, because the APC intends to restoreTBR,fwd, the retrieved second and third Stokes TB in frontof the feed horn (TBR,est) would be subject to the sameadditional rotation that originates in the error in the Faradayrotation angle. However, the Faraday rotation correction isimplemented as the square-sum of the second and third Stokesparameters of TBR,est, and the square sum is invariant of anyrotation. As a result the estimate of TB2 at the top of theatmosphere after the Faraday correction, TB2,toa,est is the sameas the one derived using the accurate estimate of the Faradayangle and TA,earth measured by the antenna pattern with

very small cross-pol coupling. The formal proof is provided inAppendix A-2. With regard to the estimate of the first StokesTB at the top of the atmosphere, TB1,toa,est, the effect of thecross-pol coupling is small even with the scale-model antennapattern. For example, the largest cross-pol coupling occurs withthe third Stokes transmit to the first Stokes receive (e.g., −0.017for the middle horn in Table II), yet the third Stokes signalgenerated by the Faraday rotation is generally smaller than10 K. Then, the cross-pol contamination in the first Stokeswould be about −0.17 K, which is much smaller than the typicalfirst Stokes over the ocean of ∼200 K. To summarize, althoughthe cross-pol coupling generates the errors in the Faradayrotation angle and the small contamination of the first StokesTA, the retrieval of the first and second Stokes TB,toa remainsaccurate.

The retrieval performance of the first and second StokesTB,toa,est is shown in terms of ΔTBP,toa/2 = (TBP,toa,est −TBP,toa)/2, P = 1, 2 (Fig. 4 with the theoretical pattern andFig. 5 with the scale-model pattern). The TB errors are dividedby 2, because the salinity retrieval uses TBv and TBh. The


Fig. 5. Same as in Fig. 4, except that the simulation is made with the scale-model antenna pattern.

plotting range is 0.1 K for bias and, to represent the additionalrandom component, 0.2 K for rms. In addition, the statistics ofthe retrieval errors are tabulated in terms of mean and standarddeviation in Table IV(a) and (b). The mean errors over theopen ocean are very close to zero. The mean component ofΔTB2,toa/2 has the residual of about 0.05 K in the low-latitudePacific [Fig. 4(c)] and in the South Pacific [Fig. 5(c)]. Theresidual vanishes when the Faraday effect is not modeled duringthe forward simulation (not shown), suggesting that the residualoriginates in the incomplete Faraday correction. In contrast, TB

itself (shown in Fig. 1) does not have significant influence onthe spatial variation in ΔTB1 and ΔTB2. Closer to land, ΔTB1

rapidly increases because of the land emission [e.g., Fig. 4(a)].The speckle in ΔTB,toa results from the random noise in-troduced during the forward simulation, representing NEΔT.These results demonstrate that the retrieval of TB performs wellfor both antenna patterns in the severe ionospheric condition,with an error smaller than 0.1 K rms.

To estimate the salinity retrieval error associated with theTB,toa retrieval error, a simple model for retrieving salinityis applied to TB,toa,est. TB at the sea surface (TBP,sur, withP denoting polarization) is first estimated by removing theatmospheric emission terms TBU , TBD, and τ , which are com-puted with the NCEP atmospheric profiles. The ocean surface

emissivity E may be estimated by combining the two surfaceemission equations in (4), and in turn, TBP,sur is given as

TBP,sur =EPTS

=

[TBP,toa,est−TBU

τ − 〈TBD + τTB,space〉TS − 〈TBD + τTB,space〉

]TS . (9)

The model for SSS retrieval is based on dual-channel input.We have

SSSest = s0(θi, SST ) + s1(θi, SST )TBv,sur

+ s2(θi, SST )TBh,sur + s3(θi, SST )W (10)

where θi is the incidence angle, and W is the wind speed atthe sea surface. The s coefficients are trained to minimize thedifference from the reference salinity. Separate sets of s coef-ficients are found for incidence angles going from 25◦ to 50◦

and SST values going from −5 ◦C to 40 ◦C. To account for theerrors in ancillary data, the random noises of 0.03◦, 0.3 ◦C, and0.5 m/s (standard deviation) are introduced to the incidence an-gle, SST, and wind, respectively. Although Reynolds SST andNCEP wind fields are used in this paper, we refer to the errorsin the space-based observations, considering the after-launch


TABLE IVERRORS IN THE INDIVIDUAL RETRIEVAL OF TB AND SSS AT 5.6-sINTERVALS OF A SPACE-BORNE MEASUREMENT, SIMULATED WITH

NEΔT OF 0.08 K AND THE RANDOM ERROR IN SST AND WIND SPEED

OF 0.3 ◦C AND 0.5 m/s, RESPECTIVELY (1 SIGMA). THE MEAN AND

STANDARD DEVIATION OF THE INDIVIDUAL ERRORS ARE GLOBALLY

COMPUTED OVER SEVEN DAYS. TEMPORALLY STATIC BUT SPATIALLY

VARYING SALINITY AND THE WORST CASE FARADAY EFFECT ARE USED

DURING THE FORWARD SIMULATION. (a) ΔTB1,TOA/2 (K) [OCEANS OF

ALL SSTS AND LAND FRACTION < 0.001]. (b) ΔTB2,TOA/2 (K)[ALL SSTS, LAND FRACTION < 0.001]. (c) ΔSSS (psu)

[SST > 10 ◦C, LAND FRACTION < 0.001]

scenarios. Only random errors are simulated, assuming thatwe may remove the systematic errors that arise mostly fromcalibration and model functions. Achieving 0.3 ◦C accuracy forSST is challenging but is likely feasible. The absolute accuracyof the space-borne infrared approach is of similar magnitude[26]. A preliminary assessment of the wind-speed measurementby the L-band radar onboard the Aquarius instrument reports arandom error of less than 0.3 m/s. The use of 1-m/s randomerror in the wind speed increases the standard deviation ofthe SSS retrieval error by less than 0.04 psu. The impact ofthe greater wind uncertainty is small, because ΔTBv/Δwindranges from 0.1 K/(m/s) to zero K/(m/s) according to the WISEmodel within 29◦–46◦ incidence angles of interest in this paper[19] (the size of ΔTBv/Δwind needs further confirmation,because it was found larger according to another study [20]).

The errors in the retrieved SSS are shown in Fig. 4 withthe theoretical pattern and Fig. 5 with the scale-model pattern.Near islands and the coast, the retrieved SSS is lower thanthe reference by more than 1 psu. The land surface producesTB1 twice larger than the ocean’s TB1, resulting in the lowSSS. Over the cold ocean toward the Poles, the random errormay reach a few practical salinity units as a result of theweak sensitivity of TB to SSS over the cold seas (see [2]for example). The North Atlantic has higher SST than theNorth Pacific, resulting in slightly more northerly extent of theaccurate salinity retrieval. Noise in the retrieved SSS is largerthan that associated with TB,toa,est, reflecting the additionalerrors in the incidence angle, SST, and wind. The mean andstandard deviation of the errors of the individual 5.6-s retrievalare summarized in Table IV(c). With both patterns, the errorsare 0.04 psu (mean of the error) and less than 0.16 psu (standarddeviation of the error) over the warm ocean.

IV. CONCLUSION

To examine the effect of the antenna cross-pol couplingon the retrieval of brightness temperature (TB) for a space-borne L-band radiometer, the measurement and retrieval of TB

have been simulated using a radiative transfer model and amodel for an orbiting spacecraft. The simulation is globallyperformed so that the complete geometry between the antennaboresight vector and the earth’s environmental field vectors maybe accounted for. A forward simulation of the TB measurementis constructed as follows to satisfy the strict requirement onthe radiometric performance. A very fine grid is used whileintegrating the antenna pattern. The sun’s direct incidenceand specular reflection are modeled: their contributions toantenna temperature are small. The simulation also computesthe Faraday rotation effect, atmospheric emission, and surfaceroughness effect by wind. The worst case is projected for theionospheric effect and solar radiation. An instrument noiseNEΔT of 0.08 K is used.

Retrieval is simulated as follows. The APC is performedusing a set of static coefficients. To determine the coeffi-cients, the Faraday rotation angle is estimated as a ratio ofthe second and third Stokes antenna temperatures measuredby the radiometer. The large cross-pol coupling in the scale-model antenna pattern leads to the errors in the Faraday angleestimate. These results, in turn, introduce the errors in the APCcoefficients, because the spacecraft flies within the ionosphere,and the antenna temperature is affected by the Faraday rotation.The error in the estimated Faraday angle causes an additionalrotation of the retrieved second and third Stokes TB in front ofthe feed horn before the Faraday rotation correction. However,because the Faraday rotation correction is implemented as thesquare sum of these two Stokes, the retrieved TB at the topof the atmosphere and below the ionosphere after the Faradaycorrection (TB,toa,est) is insensitive to the error in the Faradayangle estimate and the rotational error in the APC coefficients.The retrieval result shows that the TB,toa,est error is below0.1 K in rms for the individual observation at 5.6-s intervalsover most of the world oceans. With the simple model for re-trieving salinity, the SSS error is smaller than 0.04 psu bias and0.16 psu standard deviation over the warm and open ocean forboth analytical and scale-model antenna patterns (Figs. 4 and 5and Table IV) when simulated with the random errors of 0.03◦,0.3 ◦C, and 0.5 m/s (1σ) for the incidence angle, SST, and wind,respectively.

Finally, we would like to discuss some sources of the errorsin TB retrieval, which have not been included in the simulation.Errors in the radiometer calibration (the conversion of radiome-ter counts into antenna temperature) are not considered, i.e., thecorrect calibration is assumed. The effects of rain, ice cover,and radio frequency interference are not considered, assumingthat their contaminations will be flagged. Forward scattering ofcelestial sky noise and backscattering of solar radiation into themain lobe are not included in the simulation. The effects ofthese neglected terms are discussed as follows in the contextof the APC and the TB retrieval. The solar reflection wassimulated [27] for the radiometer with the same specificationas studied in this paper. With a two-scale model for scattering


Fig. 6. V-pol antenna gain of the middle beam: total gain of the scale-model pattern (left), and the cut patterns of co-pol (middle) and cross-pol (right). Thecut patterns are for the scale model (solid) and for the theoretical pattern (dotted). The unit of the gain is given in decibels. The two axes of the 2-D pattern arepx = −θ cosφ and py = θ sinφ, where θ is the elevation angle from the boresight ranging from −180 to 180◦, and φ is the azimuth angle. px defines theabscissa of the two cut patterns. The 3-dB beamwidth is 6.3◦.

from the ocean surface, the solar contamination on TAv andTAh was up to 0.02 and 0.08 K, respectively, at 8-m/s wind.The APC proposed in this paper would work well, becauseTAv and TAh are considerably larger than the contamination.For the TB retrieval, however, the contamination of 0.08 K isnot small, but such a large reflection occurs at about 8% ofthe observation [27]. The galaxy glint into the antenna mainlobe exceeds 0.1 K for TB1/2 within 20◦ of the galactic plane,even over a specular surface [28]. Because the position of thegalaxy plane may accurately be predicted, the contaminatedareas may be flagged while training the APC coefficients. Forthe TB retrieval, the flagging of the contamination is againfeasible, but the correction is challenging, which is beyond thescope of this paper. Last, accurate knowledge of the relationshipbetween wind and TB (i.e., wind model function) is essential forboth the APC and the TB retrieval. The reason is that the APCproposed in this paper uses the forward simulation of TB,toa totrain the APC coefficients. From the perspective of TB retrieval,TB is sensitive to the wind speed: the sensitivity is up to0.3 K/(m s−1) [19], [20].

APPENDIX A

1) Antenna Pattern—Theoretical Versus Scale Model: Twosets of gain patterns of the Aquarius antenna are availablefrom the Jet Propulsion Laboratory. One theoretical model isgenerated by computer analysis, whereas the other pattern ismeasured using a 1/10th-size scale model of the spacecraft.The scale-model pattern is regarded more realistic than thetheoretical pattern, because the scale-model pattern includes

interference with surrounding structures. The cut patterns of thetwo antenna models are shown in Fig. 6. The scale-model mea-surements have phase imbalance between H- and V-pol mea-surements. The imbalance of 18◦, 180◦, and 22◦ is corrected forthe inner, middle, and outer horns, respectively. In terms of theclassical Stokes, the Muller matrix of antenna pattern is definedas in (11), shown at the bottom of the page. Here, g is the gain,with the first and second subscripts denoting the radiometeroutput and the input to the radiometer, respectively, and TBR

is the brightness temperature rotated by the Faraday effect (seeFig. 1 for illustration). The integration of the Mueller matrixover 4π-steradians produces the values shown in Table II. Thescale-model gain pattern has large cross-pol coupling betweenthe first and third Stokes parameters compared with the the-oretical pattern. Because the first Stokes is generally largerthan the third Stokes by two orders of magnitude, the couplingfrom TBR1 to TA3 differs most from the theoretical pattern.A smaller difference is found between the two patterns inthe coupling between the second and third Stokes. The largecross-pol coupling is attributed to the asymmetry in the cross-pol gain about the boresight in the scale-model pattern. Oneexample of the asymmetry is shown in Fig. 7, particularly in theimaginary part. The asymmetry in gain, in turn, may be causedby the unevenness in the reflector and the presence of otherspacecraft structures in the scale model. Furthermore, the threefeed horns share one parabolic reflector. The off-axis geometrywould also contribute to the large cross-pol coupling (personalcommunication, Joe Vacchione and Simon Yueh, 2008).

2) Errors in the Faraday Rotation Angle and TB Retrieval:The error in the estimated Faraday angle φest does not

⎡⎢⎣TA1

TA2

TA3

TA4

⎤⎥⎦=

⎡⎢⎢⎣

12

(|g2vv|+|g2vh|+|g2hv|+|g2hh|

)12

(|g2vv|−|g2vh|+|g2hv|−|g2hh|

)Re (gvvg

∗vh+ghhg

∗hv) −Im (gvvg

∗vh−ghhg

∗hv)

12

(|g2vv|+|g2vh|−|g2hv|−|g2hh|

)12

(|g2vv|−|g2vh|−|g2hv|+|g2hh|

)Re (gvvg

∗vh−ghhg

∗hv) −Im (gvvg

∗vh+ghhg

∗hv)

Re (gvvg∗hv+ghhg

∗vh) Re (gvvg

∗hv−ghhg

∗vh) Re (gvvg

∗hh+gvhg

∗hv) −Im (gvvg

∗hh−gvhg

∗hv)

Im (gvvg∗hv−ghhg

∗vh) Im (gvvg

∗hv+ghhg

∗vh) Im (gvvg

∗hh+gvhg

∗hv) Re (gvvg

∗hh−gvhg

∗hv)

⎤⎥⎥⎦

×

⎡⎢⎣TBR1

TBR2

TBR3

TBR4

⎤⎥⎦ (11)


Fig. 7. H-pol’s cross-pol antenna cut pattern (the source is the V-pol). Thescale model (black) and the theoretical pattern (thick gray). The ordinate is thenatural number. (a) Re(ghv). (b) Im(ghv).

deteriorate the retrieval of TB2,toa (Section III). The formalproof is presented here. Focusing on the second and third Stokesfor simplicity, the estimation of the APC coefficients (A′) maybe formulated as

A′T′A ≈ T′

BR,fwd = Ψ(φest)TB2,toa (12)

where A′ is a 2 × 2 output APC coefficient, and T′A is a 2 × 1

input of the second and third Stokes measurements. The symbol“≈” refers to the presence of an estimation error, because A′ isderived by the least square minimization. T′

BR,fwd is evaluatedby Ψ(φest) TB2,toa and is now a 2 × 1 input matrix thatconsists of the second and third Stokes. Ψ(φest) is a 2 × 2input, and TB2,toa is a 2 × 1 input that consists of the secondand third Stokes. As described in (6), φest is computed withthe ratio of the measured antenna temperatures, and TB2,toa

is derived using the forward radiative transfer. Subsequently,T′

BR,fwd is evaluated. The prime in T′BR,fwd denotes that the

brightness temperature vector has been rotated by the erroneousFaraday angle estimate (φest). The prime in A′ represents theerroneous APC matrix with very large off-diagonal elements(e.g., the APC coefficients for the scale model derived withφf,est in Table I). The prime in T′

A refers to the contaminationby the cross-pol coupling (TA,cross), i.e.,

T′A = TA +TA,cross. (13)

TA,cross may be approximated as [0 Re(gvvg∗hv +

gvhg∗hh)TB1,toa]

T in the example studied in the main text. T′A

and TA denote the antenna temperatures measured by the scalemodel and the theoretical model, respectively. Let φref and δrepresent the “truth” reference for the Faraday angle and theerror from the truth, respectively. We have

φest = φref + δ. (14)

When the antenna temperature is measured with the theoreticalpattern, the Faraday angle is accurately estimated to be φref .

Then

A TA ≈ TBR,fwd = Ψ(φref )TB2,toa (15)

where TBR,fwd is evaluated by Ψ(φref ) TB2,toa. In terms ofφref and δ in (14), (12) may be rewritten as

A′T′A ≈ T′

BR,fwd = RΨ(φref )TB2,toa (16)

where R is a 2 × 2 matrix and defines the rotation by 2δ.Equation (16) suggests that, as a result of the error in theFaraday angle estimate (δ), T′

BR,fwd, which we will use duringthe calculation of the APC coefficients, is further rotated by R.Comparing (15) and (16), we may deduce

A′T′A ≈ R A TA. (17)

Equation (17) defines the relationship between the two sets ofthe APC coefficients (A′ and A). A′ has very large off-diagonalelements compared with A. Again, “≈” refers to the presenceof an estimation error, because both A′ and A are estimated byminimization.

The relationship in (17) leads to the conclusion that theretrieval of TB2,toa is unaffected by the error in the Faradayrotation angle. In detail, the estimate of TB in front of the feedhorn before the Faraday rotation correction (T′

BR,est) may bewritten as

T′BR,est = A′T′

A (18)

where T′BR,est consists of the second and third Stokes parame-

ters. The prime again denotes an estimate due to the inaccurateAPC matrix. The Faraday correction of (7) gives an estimate ofT ′B2,toa (scalar) as

T ′B2,toa,est =

√([T′

BR,est

]TT′

BR,est

)=√(

[A′T′A]

TA′T′

A

)≈ √ (

[A TA]TRTR A TA

)≈ √ (

[A TA]TA TA

)(because RTR = I)

≈ TB2,toa,est. (19)

According to (19), T ′B2,toa,est is identical to TB2,toa,est, which

is the retrieval given by the accurate Faraday angle and theaccurate APC, when the minimization errors associated withthe APC derivation are ignored. The identity may also quali-tatively be understood as follows. As a result of the error inthe estimated Faraday angle, TB in front of the feed horn isfurther rotated by R, which provides T′

BR,fwd. The additionalrotation results in the error in the APC coefficients. However,because the Faraday rotation correction is the square sum of thesecond and third Stokes parameters, the retrieved second Stokesis not sensitive to such rotation. Therefore, the estimated TB,toa

is not affected by the error in the Faraday angle estimate or therotational error in the APC.

The APC coefficients represent the properties of the an-tenna. Therefore, they are often treated to be invariant in time


and space (in practice, the APC coefficients are derived byregressing a large set of TA,earth to TBR,fwd, typically col-lected over the near-global ocean and a long period). That is,both A and A′ are static. In contrast, T′

A and TA are variablein space and time in principle. Therefore, according to (17), theerror in φest may vary in space and time.

ACKNOWLEDGMENT

The authors would like to thank David Le Vine of theGoddard Space flight Center (GSFC) and Simon Yueh of theJet Propulsion Laboratory (JPL) for their valuable suggestionson numerous issues, Joe Vacchione of JPL for the provision anddiscussion of the theoretical and scale-model antenna patterns,Ichiro Fukumori and Ou Wang of JPL for providing the ECCOsalinity simulation, Thomas Meissner and Deborah Smith ofRemote Sensing Systems for providing the atmospheric emis-sion fields, and the anonymous reviewers for their thoroughsuggestions, which were very helpful in improving the qualityof this paper.

REFERENCES

[1] C. T. Swift and R. E. McIntosh, “Considerations for microwave remotesensing of ocean-surface salinity,” IEEE Trans. Geosci. Remote Sens.,vol. GRS-21, no. 4, pp. 480–491, Oct. 1983.

[2] S. H. Yueh, R. West, W. J. Wilson, E. G. Njoku, F. K. Li, andY. Rahmat-Samii, “Error sources and feasibility for microwave remotesensing of ocean surface salinity,” IEEE Trans. Geosci. Remote Sens.,vol. 39, no. 5, pp. 1049–1060, May 2001.

[3] W. J. Wilson, S. H. Yueh, S. J. Dinardo, and F. K. Li, “High-stabilityL-band radiometer measurements of saltwater,” IEEE Trans. Geosci.Remote Sens., vol. 42, no. 9, pp. 1829–1835, Sep. 2004.

[4] Y. H. Kerr, P. Waldteufel, J. P. Wigneron, S. Delwart, F. Cabot,J. Boutin, M. J. Escorihuela, J. Font, N. Ruel, C. Gruhier, S. E. Juglea,M. R. Drinkwater, A. Hahne, M. Martin-Neíra, and S. Mecklenburg, “TheSMOS mission: New tool for monitoring key elements of the global watercycle,” Proc. IEEE, vol. 98, no. 5, pp. 666–687, May 2010.

[5] J. Boutin, P. Waldteufel, N. Martin, G. Caudal, and E. P. Dinnat, “Surfacesalinity retrieved from SMOS measurements over global ocean: Impreci-sions due to surface roughness and temperature uncertainties,” J. Atmos.Ocean. Technol., vol. 21, no. 9, pp. 1432–1447, Sep. 2004.

[6] P. Waldteufel, J. Boutin, and Y. H. Kerr, “Selecting an optimal configura-tion for the soil moisture and ocean salinity mission,” Radio Sci., vol. 38,p. 8051, Mar. 2003. DOI:10.1029/2002RS002744.

[7] J. Font, G. S. E. Lagerloef, D. M. Le Vine, A. Camps, and O. Z. Zanifé,“The determination of surface salinity with the European SMOS spacemission,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 10, pp. 2196–2205, Oct. 2004.

[8] G. S. E. Lagerloef, F. R. Colomb, D. M. Le Vine, F. J. Wentz, S. H. Yueh,C. S. Ruf, J. Lilly, J. Gunn, Y. Chao, A. de Charon, G. Feldman, andC. T. Swift, “The Aquarius/SAC-D mission,” Oceanography, vol. 21,no. 1, pp. 68–81, 2008.

[9] D. M. Le Vine, G. S. E. Lagerloef, R. Colomb, S. Yueh, andF. Pellerano, “Aquarius: An instrument to monitor sea surface salinityfrom space,” IEEE Trans. Geosci. Remote Sens., vol. 45, no. 7, pp. 2040–2050, Jul. 2007.

[10] F. J. Wentz, “The estimation of TOA Tb from Aquarius observations,”Remote Sensing Systems Technical Report 013006, p. 21, Jan. 30, 2006.

[11] J. Z. Peng and C. S. Ruf, “Calibration method for fully polarimetricmicrowave radiometers using the correlated noise calibration standard,”IEEE Trans. Geosci. Remote Sens., vol. 46, no. 10, pp. 3087–3097,Oct. 2008.

[12] J. R. Piepmeier, “Calibration of passive microwave polarimeters that usehybrid coupler-based correlators,” IEEE Trans. Geosci. Remote Sens.,vol. 42, no. 2, pp. 391–400, Feb. 2004.

[13] F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing:Active and Passive, Volume I: Fundamentals and Radiometry. Norwood,MA: Artech House, 1981, 456 pp.

[14] N. Skou and D. M. Le Vine, Microwave Radiometer Systems: Design andAnalysis, 2nd ed. Norwood, MA: Artech House, 2006, 250 pp.

[15] F. J. Wentz, “A well-calibrated ocean algorithm for special sensormicrowave/imager,” J. Geophys. Res., vol. 102, no. C4, pp. 8703–8718,Apr. 1997.

[16] S. Brown, “Generation of Jason Microwave Radiometer TE Maps,” JetPropulsion Lab., Albuquerque, NM, Feb. 10, 2005, Jet Propulsion Lab.Jason Radiometer Memo, 8 pp.

[17] N. Skou, “Faraday rotation and L band oceanographic mea-surements,” Radio Sci., vol. 38, no. 4, p. 8059, May 2003,DOI:10.1029/2002RS002671.

[18] A. Camps, M. Vall-llossera, N. Duffo, F. Torres, and I. Corbella, “Aux-iliary datasets in 2-D L-band aperture synthesis interferometric radiome-ters,” IEEE Trans. Geosci. Remote Sens., vol. 43, no. 5, pp. 1189–1200,May 2005.

[19] C. Gabarro, M. Vall-llossera, J. Font, and A. Camps, “Determination ofsea surface salinity and wind speed by L-band microwave radiometryfrom a fixed platform,” Int. J. Remote Sens., vol. 25, no. 1, pp. 111–128,Jan. 2004.

[20] S. H. Yueh, S. Dinardo, A. Fore, and F. K. Li, “Passive and active L-bandmicrowave observations and modeling of ocean surface winds,” IEEETrans. Geosci. Remote Sens., vol. 48, no. 8, pp. 3087–3100, Aug. 2010.

[21] S. H. Yueh, “Estimates of Faraday rotation with passive microwave po-larimetry for microwave remote sensing of Earth surfaces,” IEEE Trans.Geosci. Remote Sens., vol. 38, no. 5, pp. 2434–2438, Sep. 2000.

[22] D. M. Le Vine, S. D. Jacob, E. P. Dinnat, P. de Matthaeis, and S. Abraham,“The influence of antenna pattern on Faraday rotation in remote sensingat L-band,” IEEE Trans. Geosci. Remote Sens., vol. 45, no. 9, pp. 2737–2746, Sep. 2007.

[23] F. J. Wentz and T. Meissner, “Algorithm Theoretical Basis Document(ATBD), AMSR Ocean Algorithm (Version 2),” Remote Sensing Syst.,Santa Rosa, CA, Tech. Rep. 121599A-1, Nov. 2, 2000, 66 pp.

[24] T. Meissner and F. J. Wentz, “The complex dielectric constant of pure andsea water from microwave satellite observations,” IEEE Trans. Geosci.Remote Sens., vol. 42, no. 9, pp. 1836–1849, Sep. 2003.

[25] F. J. Wentz, “Update to Simulation of Solar Contamination for Aquarius:Results From Scale-Model Antenna Patterns,” Remote Sensing Syst.,Santa Rosa, CA, Tech. Rep. 020907, Feb. 9, 2007, 12 pp.

[26] C. J. Donlon, I. Robinson, K. S. Casey, J. Vazquez-Cuervo, E. Armstrong,O. Arino, C. Gentemann, D. May, P. LeBorgne, J. Piollé, I. Barton,H. Beggs, D. J. S. Poulter, C. Merchant, J. Bingham, A. Heinz,S. Harris, A. Wick, G. Emery, B. Minnett, P. Evans, R. Llewellyn-Jones,D. Mutlow, C. Reynolds, R. W. Kawamura, and H. Rayner, “The globalocean data assimilation experiment high-resolution sea surface tempera-ture pilot project,” Bull. Amer. Meteorol. Soc., vol. 88, no. 8, pp. 1197–1213, 2007.

[27] E. P. Dinnat and D. M. Le Vine, “Impact of sun glint on salinity remotesensing: An example with the Aquarius radiometer,” IEEE Trans. Geosci.Remote Sens., vol. 46, no. 10, pp. 3137–3150, Oct. 2008.

[28] J. E. Tenerelli, N. Reul, A. A. Mouche, and B. Chapron, “Earth-viewing L-band radiometer sensing of sea surface scattered celestial skyradiation—Part I: General characteristics,” IEEE Trans. Geosci. RemoteSens., vol. 46, no. 3, pp. 659–674, Mar. 2008.

Seung-Bum Kim received the B.Sc. degree in elec-trical engineering from the Korea Advanced Insti-tute of Science and Technology (KAIST), Daejeon,Korea, in 1992 and the M.S. and Ph.D. degrees inremote sensing from the University College London,London, U.K., in 1993 and 1998, respectively.

He worked on space-borne photogrammetry togenerate land topography with the SPOT images andmicrowave radiometry with the AMSR-E data inKAIST until 2003 as a part of the national service.He conducted ocean science research of the mixed

layer dynamics with the Jet Propulsion Laboratory, California Institute of Tech-nology, Pasadena, until 2006. He was a scientist with Remote Sensing Systems,Santa Rosa, CA, studying the L-band radiometry for the Aquarius salinityobservations. Since 2009, he has been with the MS300-323 Jet PropulsionLaboratory. His current research interests include microwave modeling and soilmoisture retrieval with the radar data from the Soil Moisture Active Passive(SMAP) mission.

Dr. Kim received a graduate scholarship from KAIST and best paper awardsfrom the U.K. and Korean remote sensing societies.


Frank J. Wentz received the B.S. and M.S. degreesin physics from Massachusetts Institute of Technol-ogy, Cambridge, in 1969 and 1971, respectively.

In 1974, he established Remote Sensing Systems(RSS), a research company that specializes in satel-lite microwave remote sensing of the earth. Hisresearch focuses on radiative transfer models that re-late satellite observations to geophysical parameters,with the objective of providing reliable geophysi-cal data sets to the earth science community. As aMember of the SeaSat Experiment Team, National

Aeronautics and Space Administration (NASA) from 1978 to 1982, he pio-neered the development of physically based retrieval methods for microwavescatterometers and radiometers. Starting in 1987, he took the lead in providingthe worldwide research community with high-quality ocean products derivedfrom satellite microwave imagers (SSM/I). As the Director of RSS, he overseesthe production and validation of climate-quality satellite products, which aredispersed through the company’s web and FTP sites to a large community ofEarth Scientists. He is currently a Member of NASA Advanced MicrowaveScanning Radiometer (AMSR) Team, NASA Ocean Vector Wind Science(OVWST) Team, and NASA REASoN DISCOVER Project. He has servedon many NASA review panels, the National Research Council’s Earth StudiesBoard, the National Research Council’s Panel on Reconciling TemperatureObservations, and is a Lead Author for the CCSP Synthesis and AssessmentProduct on Temperature Trends in the Lower Atmosphere. He is currentlyworking on scatterometer/radiometer combinations, satellite-derived decadaltime series of atmospheric moisture and temperature, the measurement of seasurface temperature through clouds, and advanced microwave sensor designsfor climatological studies. He has a long list of publications on remote sensingand its application to oceanography, hydrology, and climate.

Gary S. E. Lagerloef (M’06) received the Ph.D.degree in physical oceanography from the Universityof Washington, Seattle, in 1984.

He currently serves as a Principal Investigatorof the NASA Aquarius Mission to study the in-teractions between the earth’s water cycle, oceancirculation, and climate. He has served on numer-ous science teams and working groups over the last20 years, including the Salinity Sea Ice WorkingGroup (Chair), Satellite Altimeter Requirements forClimate Research Working Group (Cochair), NRC

Committee on Earth Gravity Measurements from Space, the AMS Com-mittee on Sea Air Interaction and on NASA Science Working Teams forTopex/Poseidon/Jason missions, Ocean Vector Winds, and the Tropical RainfallMeasurement Mission. He has been a Guest Editor for the Journal of Geophys-ical Research—Oceans and is a Member of several professional associations,learned, and technical societies. He is currently with Earth and Space Research,Seattle, which he cofounded in 1995. He was with Science ApplicationsInternational Corporation and was the NASA Physical Oceanography ProgramManager from 1988 to 1990. He has served in the NOAA CommissionedOfficer Corps and in the U.S. Coast Guard. He is the author of more than60 publications and presentations. His research interests include ocean cir-culation and climate dynamics, with special emphasis in developing newapplications for satellite remote sensing.

Effects of Antenna Cross-Polarization Coupling on the Brightness Temperature Retrieval at L-Band

Documents

Transcript of Effects of Antenna Cross-Polarization Coupling on the Brightness Temperature Retrieval at L-Band