Abstract—The celestial sky brightness temperature reflected

by the ocean surface toward an L-band radiometer induces a signal that needs to be known in order to retrieve sea surface salinity. To provide an accurate correction, the effects of the surface roughness and the antenna gain pattern need to be included. We assess the impact of these effects on the reflected sky signal using the Aquarius radiometer as an example.

Index Terms—Sea surface salinity, L-band, radiometry, galaxy

I. INTRODUCTION EMOTE sensing of sea surface salinity (SSS) using L-band radiometry requires estimation of the brightness

temperature (Tb) of the surface with a challenging accuracy of the order of 0.1 K. Achieving such accuracy imposes requirements on the radiometric accuracy, but also on the correction for the signal induced by geophysical sources other than SSS. Among the potentially important sources at L-band is radiation from the celestial sky that is reflected at the Earth surface toward the instrument. The celestial sky Tb is mostly between 3 K and 10 K. If one assumes a reflectivity for the ocean surface of the order of 0.7 (perfectly smooth surface, nadir direction), it is clear that the reflected radiation can have a relatively large impact on the signal, and that the variation is larger than the required accuracy of 0.1 K. However, it should be noted that 1) the ocean surface is not smooth and 2) the measured signal is the result of integration over the scene weighted by the antenna gain pattern. The first point will impact the reflectivity and, hence, the scene observed by an antenna. The second point will impact how variation of Tb over the scene is manifested in the final signal. We address these two points here using the Aquarius radiometers [1] as an example.

Aquarius has three L-band radiometers pointing at 25.8º, 33.8º and 40.3º with respect to nadir. The antenna HPBW is of the order of 6º. The platform is in sun-synchronous orbit with

Manuscript received April 18, 2008. E. P. Dinnat is with the Goddard Earth Sciences and Technology Center,

University of Maryland Baltimore County, Baltimore, Maryland, USA (phone: 301-614-6871; fax: 301-614-5558; e-mail: emmanuel.dinnat@nasa.gov).

D. M. Le Vine, is with the Instrumentation Sciences Branch NASA Goddard Space Flight Center Greenbelt, MD 20771, USA (e-mail: david.m.levine@nasa.gov).

S. Abraham is with the Wyle Information Systems, Inc., Goddard Space Flight Center, Greenbelt, MD 20771, USA. (e-mail: saji.abraham@gsfc.nasa.gov).

a 6am/6pm equatorial crossing (descending and ascending, respectively) with the antennas pointing roughly perpendicular to the satellite ground track away from the sun toward the night-time side. The mission is scheduled for launch in May 2010.

In Section II we describe the model used to quantify the impact of roughness and the gain patterns on the reflected radiation. In Section III examples are presented showing the impact of the reflected sky radiation using the Aquarius antennas. The last section reports a simple uncertainty analysis of our results and our conclusions.

II. DESCRIPTION OF THE MODEL

A. Increase in antenna temperature We compute the increase in antenna temperature induced by

the reflected sky (hereafter referred as sky Ta) as

, ,

, ,

,3 ,3

,4 ,4

14

a v b v

a h b hap a b ap

a b

a b

T TT T

M M dT TT T

π⊕

∗

∗→ ∗→

∗Ω

∗

= Ω

∫ (1)

where ap aM → and b apM ∗→ are 4x4 matrices accounting for antenna gains and misalignment of the surface polarization relative to the antenna polarizations, respectively [2]. The complex co-pol and cross-pol gain patterns are sampled in the directions around the antenna at a resolution of 0.5º in polar and azimuth angles. The integral is performed over the solid angle subtended by the Earth surface. bT ∗ is the Stokes vector of the sky Tb at the ocean surface after reflection. Rigorously,

bT ∗ should be modified to account for atmospheric effects. As our purpose here is to focus on the impact of the reflected sky, we have not included these effects in the present analysis. Two different approaches (smooth and rough surface) for modeling

bT ∗ are discussed in the next section.

B. Reflected brightness temperature 1) Ocean surface assumed a perfectly smooth surface

A first simple approach is to consider that the ocean surface is perfectly smooth and induces specular reflection only. Each ray from the galaxy to the surface is specularly reflected. Therefore the surface Tb in a given direction is

L-band radiometry and reflection of the Galaxy by a rough ocean surface

Emmanuel P. Dinnat, David M. Le Vine, Fellow, IEEE, and Saji Abraham, Senior Member, IEEE

R

978-1-4244-1987-6/08/$25.00 ©2008 IEEE

( )( ) ( )

,

,

,3

,4

', '00

b v v t

b h h tSky

b

b

T RT R

TTT

θθ θ φ

∗

∗

∗

∗

=

(2)

where vR and hR are the reflectivity in vertical and horizontal polarization, respectively, derived from the Fresnel coefficient. Reflectivities are computed at the polar angle ( tθ ) of the ray in the plane tangent locally to the Earth surface. SkyT is the sky Tb (see Section II.C) in the direction of the specularly reflected ray defined by the angles ( )', 'θ φ .

2) Ocean surface as a rough surface In the examples presented here, we use a geometric optics

(GO) model. This was done to limit an already complex and computationally intensive problem. The surface Tb results from the weighted integral of the contribution of ocean waves with various slopes uS and cS in the upwind and crosswind directions:

( ) ( ), , .b Sky l u c u cT T P S S dS dSθ α ∗

∗ = Γ∫∫ (3)

Each wave is treated as a flat tilted facet that reflects

radiation specularly. Therefore the individual contribution of a facet is as given in (2) except that both the local polar angle ( lθ ) of the ray that is used to derive the reflectivity Γ and the specular direction along which SkyT is computed account for the tilt of the facet. The reflectivity is still derived from the Fresnel coefficients, but accounts for the rotation of surface polarization by an angle α due to the tilting. Individual contributions are weighted by the probability of occurrence of the slopes, hence the integral is over the uS / cS domain (excluding slopes for which the facet is not visible by the radiometer) with ( , )u cP S S∗ the probability density function of the slopes. P∗ is assumed Gaussian (including a factor for the facets solid angle), and its width is determined by the RMS of the slopes for the long ocean waves only.

We derive the long waves slope RMS from the second moment of the sea surface power spectrum after filtering out wavelengths shorter than 0.84 m (i.e. 4 times the radiometer’s wavelength). We use the Durden and Vesecky spectrum model [3]. The impact of this choice is discussed in Section IV. An example of a scene in the antenna field of view for the smooth surface and rough surface models is shown in Fig. 1.

3) Model Simplifications Due to numerical efficiency constraints, we have adopted a

few simplifications for our simulations. First, the integration over the gain pattern was limited to the full-beam defined here by a total aperture angle of 23º, accounting for most (95%) of the integrated gain. Second, we ignored the potential impact of ocean scales smaller than 0.84 m by using the GO model. This could result in overestimating the scattering around the

specular direction, and underestimating it further from that direction. Tilt angles (for slopes in (3)) are limited to +/- 21º (sampled at 0.29º resolution). Computations for wind speeds larger than 8m/s (at 10 m height) would require increasing the angle limits. Two additional simplifications were adopted for the results including roughness: the antenna pattern resolution was decreased to 5º in azimuth, and temporal sampling of the orbit was limited to 48 seconds. As illustrated in Fig. 1, the scene is significantly smoothed out by the roughness so that the decrease of the pattern resolution has little impact on the results. The limitation on the orbit sampling is discussed in Section III.

Fig. 1. Reflected sky Tb at vertical polarization for (top) a smooth surface and (bottom) a rough surface (wind speed of 8 m/s at 10 m height). The color scale is between 0 K (dark blue) and 5 K (red). Note that the scale is saturated for the top figure (maximum Tb is ~35 K). The red line is the subsatellite track, the green circle is the 3dB antenna footprint.

C. The Sky brightness temperature map The brightness temperature map for the sky is the sum of

four components: the Galactic radio continuum, the cosmic microwave background (CMB), the neutral hydrogen line (HI) and Cassiopeia A. The combined contributions of the continuum and CMB was measured between the frequencies 1410-1430 MHz and mapped at 0.25ºx0.25º resolution for the whole sky [4,5,6,7]. The band 1419-1421 MHz was filtered out in order to exclude the HI contribution. The HI contribution is included here using the spectral map by Kalberla et al [8]. The actual HI Tb varies considerably over the 2 MHz bandwidth. We derive an effective HI Tb by normalizing the integral of the actual Tb over the 2 MHz bandwidth by the 26 MHz bandwidth of the Aquarius window. As the frequency changes little over this frequency band, the power actually emitted over the 2 MHz band and the power derived from the effective Tb are very close. The last component accounts for the fact that Cassiopeia A Tb was too large to be measured by the continuum sky surveys and needs

to be added to the map. A small polarized component in the sky emission has been

observed [9]. Measured third Stokes parameter for the northern sky is mostly between +/- 0.5 K and at most of 2 K at rare locations. Due to the lack of availability of a whole sky map and the relative small intensity of the polarized signal for most of the sky, we have assumed the sky unpolarized in this paper.

III. RESULTS: REFLECTED CELESTIAL SKY AND IMPACT OF ROUGHNESS AND GAIN PATTERNS

Fig. 2. Map of the sky Tb, and track of the three reflected antenna boresight of Aquarius for the first orbit of 2011 (ellipsoids on the left). The red square shows the focus area for the results presented in the paper.

The boresight of the three beams have been projected and specularly reflected at the Earth surface to identify where in the galaxy the beams were pointing during the first orbit of year 2011 (see Fig. 2). As time passes, the ellipsoids reported in the figure shift to the right of the figure. This illustrates that even when only accounting for the boresight, most areas of the galaxy will influence the signal at some time. Once the tilting by the waves and the field of view of the antenna are taken into account, one finds that broad areas of the sky contribute to the signal at any given time.

Fig. 3. Sky Tb specularly reflected at vertical polarization along the three boresights for the orbit excerpts shown in the red square of Fig. 2.

For reporting the sky Ta results, we have focused on a region of interest in the sky where the three reflected boresights cross the galactic plane (Fig. 2, red square). The sky Tb specularly reflected along the boresight of the three beams is reported in Fig. 3 for the vertical polarization. This is the sky Ta that would be measured by a perfect antenna with narrow beam and for a perfectly smooth surface. The signal exhibit large variability, going from ~2.5 K to ~ 19 K, with a sharp peak when the beams cross the galactic plane. It also exhibits high frequency variations that are relatively small compared to the dynamic range reported in the figure, but are nonetheless of the order of 0.2 K, which is the order of magnitude of the accuracy requirement. The results for the horizontal polarization are similar.

Fig. 4. Reflected sky Ta in vertical polarization for three different models (see text).

Fig. 4 reports the results for the inner beam, for three different models: (S+N) assuming a smooth surface (S) and a narrow beam (N) as in Fig. 3; (S+P) assuming a smooth surface (S) and accounting for the gain pattern (P); and finally (G+P) accounting for the glint (G) induced by the roughness (8 m/s wind speed) and the pattern (P). Introduction of the gain pattern results in smoothing the signal variation (S+P compared to S+N). The peak around the galactic plane is broadened and its amplitude decreased. Also, the high frequency variation is smoothed. This smoothing makes the temporal resolution of 48 seconds (Section II.B.3)) acceptable. Introduction of roughness into the model results in an additional smoothing of the signal (G+P compared to S+P). The peak is additionally broadened and its amplitude decreased. Results for the horizontal polarization are similar.

Fig. 5 reports the differences between the models (S+N – S+P and S+P – G+P). In the case of a smooth surface (solid line), ignoring the effect of the antenna pattern would lead to overestimate the signal by about 12 K near to the galactic plane and underestimate the signal by a few tenths of a Kelvin up to 1000 km away from the galactic plane with an error of the order of +/- 0.2 K further away. Accounting for the antenna pattern but ignoring the roughness results in an overestimation of the order of 2 K at the galactic plane and an underestimation of a fraction of a Kelvin further away (dashed

line in Fig. 5). It is not clear what would be the error when accounting for the roughness but ignoring the pattern effect. It is out of the scope of this paper but this should be investigated as ignoring the effect of the pattern would greatly increase the numerical efficiency. Results for horizontal polarization are similar.

Fig. 5. Differences between the models in Fig. 4 (see text).

An important potential impact of the gain pattern and

roughness is to modify the third Stokes parameter. The third Stokes parameter from the ocean surface is small at L-band. Therefore, it has been suggested by Yueh [10] to use the measured third Stokes for estimating the Faraday rotation. The third Stokes parameter associated with radiation from the sky is relatively small (not shown), being always less than 0.05 K for the orbit excerpt considered here when both the gain pattern and roughness effects are included. Considering the demanding accuracy required for SSS retrieval, it is not clear if this effect is negligible or should be taken into account.

IV. ERROR ANALYSIS AND CONCLUSION There are several sources of uncertainty in our model. One

of the largest is probably the sea spectrum model. Large differences in ocean Tb occur with use of various spectrum models [11] and it is not clear which model is accurate enough if any [12]. Fig. 6 shows the results obtained with two different models for the case (G+P), the one in Section II.B.2) (plain line) and the same model multiplied by two (dashed line) as suggested in [11,12]. The Elfouhaily et al model, frequently used in remote sensing, would lead to results intermediate to those shown in Fig. 6. The results for the two models exhibit similar order of magnitude and trends, and conclusions are conserved qualitatively. Namely, the roughness induces a significant smoothing of the signal in general and a broadening and decrease of several Kelvin of the peak in particular. However, the difference between the two models is up to 0.4 K (at the peak), which is a too large uncertainty for a theoretical correction to be relied on.

We have showed that the impacts of the roughness and the gain pattern on the signal induced by reflected radiation from the celestial sky is large, up to several Kelvin for both vertical

and horizontal polarization, near the galactic plane. They are still noticeable elsewhere. Therefore the reflected radiation will have to be taken into account. The impact on the third Stokes parameter is more moderate, of the order of 0.05 K. Further investigation will be required to assess the impact of the small scale roughness, the importance of polarization of sky Tb, and finally the use of Aquarius scatterometer to help achieve an accurate correction.

Fig. 6. Results for the G+P model for two different sea spectrum models (see text).

REFERENCES [1] D. M. Le Vine et al., “Aquarius mission technical overview,” in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, 2006, pp. 1678−1680. [2] E. P. Dinnat and D. M. Le Vine, “Effects of the antenna aperture on remote sensing of sea surface salinity at L-band,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no.7, pp. 2051−2060, Jul. 2007. [3] S. L. Durden and J. F. Vesecky, “A physical radar cross-section model for a wind-driven sea with swell,” IEEE Journal of Oceanic Engineering, vol. OE-10, no. 4, p. 445−451, Oct. 1985. [4] W. Reich, “A radio continuum survey of the northern sky at 1420 MHz. Part I,” Astronomy and Astrophysics Supplement Series, vol. 48, pp. 219−297, May 1982. [5] P. Reich and W. Reich, “A radio continuum survey of the northern sky at 1420 MHz. Part II,” Astron. Astroph. Suppl. Ser., vol. 63, p. 205−292, 1986. [6] J. C. Testori et al., “A radio continuum survey of the southern sky at 1420 MHz Observations and data reduction,” Astronomy & Astrophysics, vol. 368, pp. 1123−1132, 2001. [7] P. Reich, J. C. Testori, and W. Reich, “A radio continuum survey of the southern sky at 1420 MHz The atlas of contour maps,” Astronomy & Astrophysics, vol. 376, pp. 861−877, 2001. [8] P. M. W. Kalberla et al., “The Leiden/Argentine/Bonn (LAB) survey of Galactic HI. Final data release of the combined LDS and IAR surveys with improved stray-radiation corrections,” Astronomy and Astrophysics, vol. 440, no. 2, pp. 775−782, Sep. 2005. [9] M. Wolleben et al., “An absolutely calibrated survey of polarized emission from the northern sky at 1.4 GHz Observations and data reduction,” Astronomy & Astrophysics, vol. 448, pp. 411−424, 2006. [10] S. H. Yueh, “Estimates of Faraday rotation with passive microwave polarimetry for microwave sensing of Earth surfaces,” IEEE Transactions on Geoscience and Remote Sensing, vol. 38, no. 5, p. 2434−2438, Sep. 2000. [11] E. P. Dinnat et al., “Issues concerning the sea emissivity modeling at L-band for retrieving surface salinity,” Radio Science, vol. 38, no. 4, pp. 25−1−25−11, May 2003. [12] J. Etcheto et al., “Wind speed effect on L-band brightness temperature inferred from EuroSTARRS and WISE 2001 field experiments,” IEEE Transactions on Geoscience and Remote Sensing, vol. 42, no. 10, p. 2206−2213, Oct. 2004.