SMOS Semi-Empirical Ocean Forward Model Adjustment

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SMOS Semi-Empirical Ocean Forward Model Adjustment Sébastien Guimbard, Jérôme Gourrion, Marcos Portabella, Antonio Turiel, Member, IEEE, Carolina Gabarró, and Jordi Font

Abstract—A prerequisite for the successful retrieval of geophysical parameters from remote sensing measurements is the development of an accurate forward model. The European Space Agency Soil Moisture and Ocean Salinity (SMOS), carrying onboard an L-band interferometric radiometer (Microwave Interferometric Radiometer using Aperture Synthesis), was launched on November 2009. Due to the lack of L-band passive ocean measurements from space, several prelaunch forward models were developed and initially used in the SMOS ocean salinity operational processor. In this paper, an update of the prelaunch semi-empirical forward model is presented, using for the first time, real SMOS data. In particular, the ocean surface emissivity modulation at L-band due to rough sea surface is reviewed and reanalyzed. A new model definition is provided with the help of a simple neural network. The improvement is quantified in terms of retrieved salinity accuracy compared with the climatology and concerns essentially the range of wind speeds higher than 12 m · s−1 . Index Terms—Microwave, radiometer, roughness, salinity, sea surface, Soil Moisture and Ocean Salinity (SMOS).

I. I NTRODUCTION

T

HE SOIL Moisture and Ocean Salinity (SMOS) mission from the European Space Agency, launched in November 2009, has initiated the era of satellite-based salinity observations. The Microwave Interferometric Radiometer using Aperture Synthesis (MIRAS) instrument provides information on the correlation between the measurements done by its set of 69 antennas. However, because of the instrument complexity and its inherent high radiometric noise, the numerous geophysical contamination sources, and the retrieval complexity, salinity products have a low signal-to-noise ratio at Level 2 (L2). Today, averaging data in space and time allows reduction of the observational error at Level 3 (global maps with regular distribution) but still far from mission requirement accuracy (0.1–0.4 over 100–300 km in 10–30 days [1], [2]). To meet

Manuscript received May 16, 2011; revised October 20, 2011 and February 3, 2012; accepted February 10, 2012. Date of publication April 3, 2012; date of current version April 18, 2012. This work was supported by the Spanish National R+D Plan for the SMOS Barcelona Expert Center on Radiometric Calibration and Ocean Salinity activities, through project MIDAS-6 AYA2010-22062-C05 and previous grants. S. Guimbard, J. Gourrion, A. Turiel, C. Gabarró and J. Font are with the Physical Oceanography Department and SMOS-BEC, Institut de Ciencies del Mar (ICM/CSIC), 08003 Barcelona, Spain (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; jfont@ icm.csic.es). M. Portabella is with the Unitat de Tecnologia Marina (UTM/CSIC) and SMOS-BEC, 08003 Barcelona, Spain (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2012.2188410

such requirement, it is crucial to improve the overall quality of reconstructed and modeled brightness temperatures. The present study takes place in this context and focuses on the improvement of the sea surface roughness modeling. For SMOS ocean measurements, the geophysical model function (GMF) relates the L-band brightness temperature (TB ) to several ocean surface related geophysical parameters, i.e., mainly sea surface salinity (SSS), sea surface temperature (SST), and sea surface roughness related parameters. Owing to the lack of sufficient satellite-based L-band brightness temperatures and the existence of a number of conflicting empirical [3]–[5] and theoretical models of roughness emission at L-band, a unique and validated GMF was not available at the time of the definition of the SMOS SSS L2 Operational Salinity (L2OS) processor, i.e., prior to SMOS launch. As such, the L2OS Processor is designed to run in parallel three different GMFs: the first two are theoretical, while the third one is semiempirical. Although with different slopes, these three models roughly agree on a linear increase of emissivity with wind speed (WS) for low and medium wind conditions. However, they well differ in describing the emissivity modification under intense wind conditions. In this paper, SMOS brightness temperatures are analyzed to revisit the modification of L-band emissivity by sea surface roughness, with a particular focus on the TB modulation at high winds. In Section II, the theoretical basis of the forward model is briefly discussed, and a review of previous experimental works is proposed. Section III describes the data used in the analysis as well as the strategy used to correct for biases in the SMOS brightness temperatures. The neural network (NN) approach used to revisit the empirical roughness model is explained in Section IV. The new formulation is analyzed and validated in Section V. Section VI summarizes the results and provides some concluding remarks. II. T HEORETICAL AND E MPIRICAL BASIS A. Theoretical Basis The brightness temperature T observed looking down through the Earth’s atmosphere is approximated by the radiative transfer equation. In the context of SMOS, this equation (also referred to as the forward model) can be defined in the sea surface polarization basis at the top of the atmosphere, as a sum of different contributors   H,V H,V −τ e−τ + Tu . (1) Td + TH,V TH,V f wm = Tsurf + R sky e

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GUIMBARD et al.: SMOS SEMI-EMPIRICAL OCEAN FORWARD MODEL ADJUSTMENT

H and V denote, respectively, horizontal and vertical linear polarization states, Tu is the upwelling brightness of the atmosphere, R is the reflectivity of the rough sea surface, Td is the downwelling atmospheric brightness temperature, Tsky is the scattered celestial sky noise, and τ is the opacity of the atmosphere. As written in (1), it is assumed that the atmospheric attenuation of the celestial radiation during the downward path toward the surface is uniform within the upper hemisphere and equal to its value at the specular direction. Although this approximation is not optimal, the error is quite small (∼10−2 K) and should not significantly impact our results. The sea surface brightness temperature TH,V surf is defined, for microwave frequency and using the Rayleigh-Jeans approximation, as the product of the linearly polarized sea surface emissivity (eH,V ) and the SST H,V TH,V . surf = SST × e

(2)

Based on Kirchhoff’s law of thermal radiation, one can write the emissivity as eH,V = 1 − RH,V

(3)

where R is the reflectivity of the sea surface. To model the reflectivity of the sea surface, it is usually assumed that the surface can be divided into foam-free and foam-covered areas within the radiometer foot print. Then, a foam model (TH,V f oam ) and a foam coverage parameter (F ) have to be included in the forward model. The sea surface brightness temperature for this type of composite surface is given by H,V H,V TH,V surf = (1 − F )Tf oam,f ree + F Tf oam .

(4)

The reflectivity of foam-free areas can be divided into two additive terms: an ideal flat sea surface term Tf described by the Fresnel reflection coefficient and a correction term accounting for roughness characteristics of the sea surface Tr H,V TH,V + TH,V . r f oam,f ree = Tf

(5)

Tf is a function of polarization, incidence angle, and dielectric constant. The dielectric constant is a function of the radiation frequency, SST, and SSS. In the context of SMOS, the expressions of the dielectric constant given by [6] is used. In other words, Tf is the specular contribution of a perfectly flat sea surface which explain approximately 96% and 99% of the sea surface emissivity in H and V polarization, respectively. Tr can be viewed as a correction term taking into account sea surface roughness impact and potentially, ad-hoc foam contribution if the formulation given in (4) is not adopted (i.e., F = 0). In the ideal case of well-calibrated measurements, it has been shown that the major source of model errors comes from the roughness-induced brightness temperature [4], [7]–[10]. As mentioned in the introductory section, in the SMOS L2OS, three different roughness models based on three different approaches have been implemented to anticipate the problem of bad prediction of this contribution. Two are based upon a

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similar theoretical electromagnetic scattering approach [11], [12]. The first one is referred as the two-scale model [13] and the second one as the small slope approximation/small perturbation method (SSA/SPM) model [14], [15]. The latter has been defined in the L2OS as the weighted sum by foam fraction of the SSA/SPM emission and foam emission [(4)]. The foam model is based on [16], and full description of its implementation can be found in [17]. The L2OS processor has been developed in a way that the use of the two-scale can follow the same formulation [i.e., (4)] but it has not been the case until now. The differences in prediction between the two are mostly dominated by the use of two different sea wave spectra, [18] with an amplitude multiplied by 2 for the two-scale model, [19] for SSA/SPM model. If the same sea surface description were used for these two electromagnetic approaches, differences in prediction would appear essentially in V-pol at high incidence angles (> 50◦ ) where the tilt effect of the local incidence angle by the larger scales of the sea surface has a non-negligible impact due to the behavior of the Fresnel coefficient in V-pol. Nevertheless, the use of the foam model in conjunction with the SSA/SPM model reduces this difference. The third model developed at the SMOS Barcelona Expert Center (SMOSBEC) has been empirically derived using WISE oil-platform campaign measurements [4], [9]. In the development of our empirical model, the distinction between foam and roughness impact on emission will not be considered. Additional factors that affect wave characteristics such as fetch, wave age, and duration of the wind effect on the sea surface will not be taken into account in our analysis. To avoid atmosphere stratification effects, neutral wind information is considered. In particular, the 10-m height equivalent neutral WS (U10 ) is used as a parameter for describing sea surface roughness.

B. Empirical Basis During the last 40 years, the roughness sensitivity of sea surface emissivity has been characterized by authors through WS sensitivities [20]. Although the WS only cannot give a full description of the sea surface roughness, the wind vector is easier to measure, and for this reason, WS is used to characterize the sea surface roughness at first order. Furthermore, most of the other roughness-related parameters like the significant wave height (SWH), the mean square slope (MSS), or the whitecaps production intensity are at first-order WS dependent. The WS sensitivity has been specified in term of slope estimations assuming linear dependence with WS for a given in(θ, W S) = AH,V (θ) × W S and A is cidence angle, i.e., TH,V r the incidence angle and polarization-dependent slope. Following the same approach as already proposed in [21] (WS → U10 and TB → e), the WS sensitivities estimated from all available L-band data sets are reported in Tables I and II, respectively, for the horizontal and vertical polarization. We can state from these tables that the WS sensitivity of the sea surface emissivity at L-band is known empirically with an accuracy of the order of ±3 · 10−4 , in both vertical and horizontal polarizations.

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TABLE I deH (10−4 (m/s)−1 )F ROM A LL L-BAND DATA C OMPARISON OF dU 10 S OURCES. (∗ : θi = [23.3, 29.2, 33.3, 41.2, 47.5, 53, 59.2, 65.2, 71.1])

Fig. 1. Sensitivity of the sea surface emissivity at L-band to wind speed at 10-m height as function of incidence angle for horizontal and vertical polarization. The square and circle correspond to the mean of all slope estimations at each incidence in H and V polarizations, respectively, associated with one standard deviation error bar. The solid and dashed lines correspond, respectively, to the cubic polynomial fit given in 6 and 7.

TABLE II deV C OMPARISON OF dU (10−4 (m/s)−1 ) F ROM A LL 10 L-BAND DATA S OURCES. (∗ : θi = [21.5, 38.4])

A cubic polynomial fit on all slope estimations for vertical and horizontal gives deV = 6.865 × 10−4 − 3.189 × 10−6 θ + 2.147 × 10−7 θ2 dU10 − 5.961 × 10−9 θ3

(6)

H

de = 6.465 × 10−4 − 3.370 × 10−6 θ + 3.589 × 10−7 θ2 dU10 − 1.260 × 10−9 θ3 .

(7)

Although H and V pol sensitivites are not equal at nadir, they are not significantly different relatively to the uncertainty in the estimates. As we can see in Table II, differences in the slope estimations in terms of emissivity can reach a maximum of ∼10−3 (m/s)−1 between [4] and [5] at 40◦ in V-pol. This translates into an uncertainty in brightness temperature contrast due to roughness impact of about ±2 K at SST = 17 ◦ C and U10 = 7 m · s−1 , which is equivalent to an uncertainty on the retrieved salinity of about ΔSSS = ±4. The differences observed in the reported values for a given incidence angle can be explained by many factors such as errors in the height reduction for measured WS values (effects of air-sea temperature differences were not taken into account except for WISE2001 campaign [4]), differences in signal processing, number of data points used to derive

statistics, instrumental errors and noises, varying geophysical conditions, or uncertainties in the sun and galactic radiations impact. In spite of all these possible error sources, it seems that part of the slope estimation differences come from the linear assumption used to characterize the WS sensitivity over all the range of WS values, when in fact, the different experimental data sets correspond to different ranges of WSs. This statement has been anticipated in [21] as a possible explanation without being able to prove it due to the lack of a L-band satellite data set. As shown later (Section V), the L-band sea surface emissivity as derived from SMOS data exhibit a clear nonlinear dependence with WS, particularly at low incidence angles and when considering WS values between 2 m · s−1 and 22 m · s−1 . By considering two different ranges of WS, for example [2–16] m · s−1 and [5–22] m · s−1 at a 40◦ incidence angle to derive the slope in SMOS data, we obtained a 20% difference between the two estimates. This result can explain, for example, part of the differences observed between slope estimations reported in [3] (2 < U10 < 16 m · s−1 ) and [5] (5 < U10 < 25 m · s−1 ) for angles greater than 40◦ . The overall mean WS sensitivity from all existent slope estimations at L-band is plotted in Fig. 1. Two main characteristics are clearly seen: • horizontally polarized signals are more sensitive to WS than the vertically polarized ones, particularly at incidences larger than 20◦ . • The WS sensitivity increases in H-pol and decreases in V-pol with increasing incidence angle. This last point is in contradiction with the fit proposed in [5] which predicts a decrease of sensitivity for incidence angles greater than 45◦ for H-pol. In summary, the linear wind-speed dependence of the historical sea surface roughness models is questioned due to their associated uncertainties and the discrepancies between them. We therefore revisit this assumption with SMOS data in Section V.

GUIMBARD et al.: SMOS SEMI-EMPIRICAL OCEAN FORWARD MODEL ADJUSTMENT

III. DATA S ET F ILTERING AND S YSTEMATIC E RROR C ORRECTION In this section, the SMOS data set is presented together with the filtering criteria and ad-hoc bias correction method, i.e., the so-called ocean target transformation (OTT), used to correct for systematic errors in the image reconstruction process. A. Data set and Filtering Criteria The data used in this study correspond to Level 1B (L1B) products from the SMOS Data Processing Ground Segment processed by L1OP (v3.4) covering the period from 03/08/2010 to 31/08/2010. These products contain brightness temperature images (or snapshots) in the Fourier domain for each 1.2 s acquisition interval (or epoch). Odd epochs contain single XX or YY polarization images where XX and YY are the linear polarized brightness temperatures in the instrument polarization basis. Even epochs contain noisier XX or YY-pol images but also XY information. In this paper, we only consider data from odd epochs. A Blackman window is used to filter the TB Fourier components, and an inverse fast Fourier transform is applied to obtain TB images in the physical space which are referenced to the cosdir antenna frame. To get the TB in the surface frame, we apply the following basis rotation:  V   X   1 T T cos2 (α+Ω) − sin2 (α+Ω) = (8) TH TY M − sin2 (α+Ω) cos2 (α+Ω) where M = cos(2(α + Ω)). α is the geometrical rotation angle, and Ω is the faraday rotation angle. When α + Ω  45◦ , M → 0, and this leads to singularities (45◦ ambiguity lines). In order to remove them, a constraint based upon the noise amplification is used. Only points in the antenna frame which respect the condition |M | > 1/5 are kept. Only ascending passes have been considered since the solar activity has a weaker impact on the ionosphere in the morning and, as a consequence, total electron content (TEC) values are very low (between 0 and 7 TECU). Furthermore, the module of the Earth magnetic field is around 35 μT, resulting in very small faraday rotation angles between −1.5◦ and 0◦ . An error of 100% on the estimated TEC values can lead to a maximum error of 0.05 K on TH or TV . Land presence in snapshots is detected at L1B in order to keep only pure ocean scenes. A systematic outlier detection procedure to discard snapshots contaminated by sea-ice or radio frequency interference presence is applied. This is achieved by filtering all departures of the measurement greater than 20 K from the forward model. To minimize the impact of the scattered celestial sky noise (Tsky ), snapshots contaminated by reflected galactic plane are detected and filtered (threshold on incidence galactic map < 5.5 K, tradeoff between filter quality and number of remaining snapshots). First analysis during commissioning phase has shown that there is still some issues regarding the modeling of Tsky and its dependence on WS. This model makes use of the Kirchhoff approximation to calculate the scattering coefficients [26]. First results (personal communication with Joe Tenerelli) seem to show that the model predicts too much scattering. This leads to under (over) predictions of the scattered celestial sky noise in the vicinity of

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(away from) the galactic equator by several Kelvin. This rough surface scattered celestial sky noise is then modeled for a fixed WS of 3 m/s in order to reduce over scattering. This solution provides a good match to the data at around 7 m/s surface WS. Because of limitations in the instrument design, full MIRAS images are subject to aliasing. Image areas with land aliases are systematically discarded. In order to reduce errors due to sky aliases (even if corrected during the reconstruction process), we only consider the alias-free field of view (FOV), reducing the range of incidence angles to values larger than 15◦ . Brightness temperatures for incidence angles below 15◦ are obtained by considering all points in the extended alias-free FOV for which the transformation to the surface polarization basis may be performed. The selected reconstructed brightness temperatures are expressed in the surface polarization frame accounting for geometrical and Faraday rotation effects. We then subtract from TB measurements TH,V smos the best estimate of all contributions except for the sea surface roughness contribution (Tr )  ˆ H,V = TH,V −Tu eτ −TH,V −RH,V Td −TH,V e−τ . (9) T r smos f sky ˆ r for the The top panels of Fig. 2 show histograms of T horizontal (left) and the vertical (right) polarizations. The data set has more than 10 million measurements, the mean ˆ r is 2.66 K (1.55 K), horizontally (vertically) polarized T and its standard deviation (std) is 3.14 K (3.07 K). Both polarizations have similar variance, but the roughness impact is in average more than twice higher in H than in V-pol. The departure from normality in both roughness residuals is characterized mainly by a high excess kurtosis, 2.05 in H-pol and 2.20

in V-pol. In fact, when considering only the circle such as ξ 2 + η 2 < 0.3 to avoid major contaminations by aliasing effect, the number of measurements is divided by 1.6, with almost the same mean, 2.77 K for H-pol and 1.53 K for V-pol, but the std is significantly reduced to 2.49 K and 2.43 K, and the excess kurtosis to 0.49 and 0.36, respectively, for H and V-pol. The bottom panels of Fig. 2 show the WS and incidence angle distribution. After the filtering process, the mean WS of the data set is 10 m · s−1 , which is about 2.2 m · s−1 higher than the global mean WS. During the period used in this study, all the northern hemisphere is contaminated by a large celestial signal coming from the galactic equator. Table III gives the basic statistical parameters (minimum, maximum, mean, and standard deviation) for the upwelling atmospheric contribution, SST, SSS, sea–air temperature difference (ΔTs,a ) and atmospheric attenuation (e−τ ) of the global data set for three ranges of incidence angles: 10◦ ± 2.5, 32.5◦ ± 2.5 and 55◦ ± 2.5◦ . B. Systematic Error Correction Owing to imperfections in the calibration and residual errors in the image reconstruction process, systematic errors are present in the SMOS FOV and have to be quantified. Although the MIRAS 69 antennas have been manufactured to be as much identical as possible, the residual differences between their respective antenna patterns induce biases in the reconstructed images, as shown by [27]. Additionally, the imperfect knowledge of such antenna patterns, and more generally

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Fig. 2. Normalized distribution of the roughness contribution estimates from SMOS data for horizontal and vertical polarization (top plots). Wind speed and incidence angle distributions (bottom plots). TABLE III R ANGE VALUES OF Tu (K), SST (◦ C), SSS (PSU), ΔTs,a (K) AND e−τ OF THE DATA S ET

of the instrument characteristics, increase the errors in the FOV, even in the alias-free domain, see [28] (it shall be noted that, as the relative differences and errors in the antenna patterns increase with decreasing antenna gain, the reconstructed biases are expected to increase with distance from boresight). Further, residual visibility calibration errors are expected to be an extra source of error patterns in the SMOS brightness temperature images. If the former error sources are of the order of a few kelvins and stable in time, the latter is certainly more transient but with lower magnitude. Corrections to minimize such errors are implemented as a preprocessing step in the L2 salinity processing chain [29]. The methodology to estimate such corrections has been assessed in [30] and [31]. Characterizing systematic errors requires statistical analysis of a large data set. During SMOS commissioning, it has been proposed to derive the corrections from the mean deviation, over one half-orbit, between reconstructed and modeled TB . Such an approach assumes perfect forward model without specific strategy to minimize the impact of model errors, while both model and auxiliary information errors are known to be inhomogeneous

and non-negligible. Even more, several factors may control the quality of the final error estimate. For example, the data should not be contaminated by surface-reflected foreign source signals, e.g., galaxy, sun, moon. The accuracy of the estimate depends also on the noise reduction related to the number of independent images used in the computation, while a large duration of the time period may degrade the estimate since residual instrument calibration errors induce apparent measurement drift. Since different methodologies to correct for systematic errors are currently under investigation (preliminary results are found in [32] and [33]), we assume here that the systematic error correction is the mean difference between SMOS brightness temperature measured and modeled at the antenna frame over the period of the data set (1 month) and after the data filtering described in Section III-A. This type of correction is often referred as an OTT  X,Y (ξ, η, t) − T (ξ, η, t) (10) OTTX,Y (ξ, η) = TX,Y smos f wm where X and Y refer to the two linear polarizations in the instrument basis. As defined, the OTT depends on the forward model which contains the modeled roughness contribution. The top panels of Fig. 3 show the computed OTTs for this study. It is understood that the estimation of roughness contributions ˆ r from the data will depend on the roughness model used in T the OTT estimation since the corrected SMOS measurements is given by ˇ X,Y = TX,Y − OTTX,Y . T smos smos

(11)

To derive the new model, we use the SSA/SPM roughness model in the estimation of the OTT. To illustrate an issue regarding the incidence angle dependence, the bottom panels

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Fig. 3. Ocean target transformation or mean biases between SMOS TB measurements and forward model at the antenna frame for XX (left column) and YY (right column). The different panels show: OTT used to correct the data for this study (top) and difference between the OTT calculated with model 2 and model 1 (bottom). In the top panel, the circle with radius r = 0.3 is also shown.

of Fig. 3 show the difference between two OTTs calculated with two different prelaunch roughness models, i.e., the twoscale (model 1) and the SSA/SPM+foam (model 2). Differences of the order of 0.5 K are observed at low incidence angles for both polarizations. This is mainly due to the amplitude difference of the two sea wave spectra used for each model. The behavior with the incidence angle is the same for the horizontal polarization, but differences up to 1.5 K are observed at high incidence angles for the vertical polarization. It is clear that the incidence angle mean variation of the adjust TB images may be biased in incidence angle and controlled by the shape of the model used to compute the correction. A strategy to reduce such uncertainty is proposed in the next section. IV. ROUGHNESS M ODEL A DJUSTMENT: N EURAL N ETWORK A PPROACH Since numerous parameters are involved in the physical process of sea surface emission, a multilayer perceptrons is considered in order to be able to vary the complexity of the model from a simple parametric model to a highly flexible nonparametric model [34]. This kind of NN is an effective tool to make nonlinear regression of the complex SMOS noisy data for an arbitrary number of parameters. A number of tests are carried out to check all possible ˆ H,V . It is found that the incidence angle dependencies of T r (θ) and the 10-m equivalent neutral WS (U10 ) explain most of ˆ H,V variances. For example, the dependence on SWH is the T r tested and found to be very correlated with the WS in general. Nevertheless, it seems that at high incidence angles, SWH can

ˆ H,V (see Fig. 6 and potentially have a significant impact on T r related discussion in the concluding section). In order to have a simple analytical expression of our model with a limited number of coefficients, a two-layer feedforward network is found to suit our purposes. The network consists of a single hidden layer and an output layer. The hidden layer ˆ r . This kind has four neurons and the output layer has one, T of network is usually used as a general function approximator. It can approximate any function with a finite number of discontinuities arbitrarily well, given enough neurons in the hidden layer [35]. A tan-sigmoid transfer function is used for the hidden layer and a linear one for the output. The final NN takes the following form:   m n

net ˜ (12) = Wj tanh bj + wij xi + B T r

j=1

i=1

˜U ˜10 ], where x is the normalized input two-row vector [θ, (w1j , bj ) are, respectively, the weights and biases of the hidden layer, (Wj , B) of the output, j the number of neurons, and i the number of input variables. Each layer’s weights and biases have been initialized with a Nguyen–Widrow layer initialization algorithm. This algorithm chooses values in order to distribute the active region of each neuron in the layer. The two NN (H and V-pol) have been trained in the same way as proposed in [36]. Due to the sparse distribution of WS at the extremes, we equalize the distribution of points placed into any given training set, effectively compressing the training set size at the same time. The size reduction enables a large portion of data to be held aside for validation. Training set equalization

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TABLE IV C OEFFICIENTS FOR THE N EURAL N ETWORK M ODEL IN V-P OL AND I NPUT /O UTPUT DATA S CALING C OEFFICIENTS

TABLE V C OEFFICIENTS FOR THE N EURAL N ETWORK M ODEL IN H-P OL AND I NPUT /O UTPUT DATA S CALING C OEFFICIENTS

it is possible that the reconstructed images have themselves some systematic incidence angle-dependent biases. Such error may propagate into the roughness-related residuals. In order to reduce such contamination, it is assumed that such systematic biases are WS independent. As such, previous to NN regression, the roughness residuals are corrected from an incidence angledependent offset. These offsets are computed for each incidence angle so that the adjusted residuals vanish when extrapolated linearly down to zero wind conditions. The extrapolation is conducted using only WS conditions corresponding to U10 < 10 m · s−1 . As a result, the proposed updated model will characterize the increase of emissivity with WS rather than the absolute emissivity increment relative to the predicted emissivity of a flat sea surface. Finally, as an additional guarantee of independence from the initial model, an iterative procedure is also applied: the model obtained using the initial OTT is used to update the OTT and, further, the model itself through a second NN regression. It has been checked that, after the second iteration, the results are already stable within the method accuracy. In other words, no matter what initial model is used, the resulting new model is the same. V. R ESULTS AND D ISCUSSION A. Incidence Angle and Wind Speed Dependence

involves partitioning the data into 22 equally spaced WS bins spanning from 1 to 22 m/s. Only 100 000 randomly selected sample data pairs from each bin are allowed into any given training vector set. Note that this training method provides a solution that is ultimately derived from a subset of the total data; that is, a given model solution is only derived from one equalized training subset containing more than 2 million data points. An enhanced error backpropagation technique, called the Levenberg–Marquardt algorithm, is used to increase training speed. This Levenberg–Marquardt algorithm minimize the mean sum squared error (msse) and is run toward a convergence limit easily obtained after 10 iterations. A “goodness-of-fit” test is computed using a χ2 test statistic between the known and neural-calculated distributions and serves as an additional optimization criterion to the Levenberg–Marquardt training. The combined χ2 goodness-of-fit and msse optimizations lead to computed and known data distributions that are equalized and a solution where bias and variance variation are minimized. The scaling coefficients and the ones appearing in (12) are, respectively, given for V and H-pol in Tables IV and V and a rescaling ˜ net T r ) = (Tr aT−b . process of the NN output is necessary as Tnet r r As commented in Section III-B, it is clear that the corrected brightness temperatures follow a distribution along incidence angle that is dependent on the choice of the roughness model used to compute the OTT correction. In addition, other components of the forward model such as atmospheric emission/attenuation, and Faraday rotation are strongly incidence angle dependent; errors in the auxiliary parameters used to estimate such contribution combined with oversimplification of their modeling may also induce systematic errors that are likely correlated with the observation incidence angle. Further,

Fig. 4 shows the mean residual brightness temperatures as a function of ECMWF U10 for different incidence angles adjusted from the offset described in the previous section. The three prelaunch roughness models and the new derived empirical ˆ r and all models shown model are shown for comparison. T are bin averaged with 5◦ and 1 m/s bin sizes. It should be noted that, to be consistent with the offset removed from the data roughness residuals, the models are also displayed as increments relative to zero wind conditions. We can see in these figures that for all incidence angles and both polarizations, the mean behavior of Tr given by all prelaunch roughness models as a function of WS is in poor agreement with the data. In particular, the two-scale model predictions for low (high) WS are always higher (lower) than shown by the SMOS measurements. This behavior is certainly due to the use of an overtuned sea wave spectrum [18] for WS lower than 16 m/s. Indeed, the spectral amplitude has been multiplied by a factor two in order to fit the data [10], [25], [37]. The too low predictions at higher WS are due to the lack of a foam term in this model. It is the opposite for the SSA/SPM+foam model. The predicted values are too low (high) when the WS is low (high). At low WS, this may be due to the behavior of the sea wave spectrum [19] around the electromagnetic wavenumber value (k0 = 29.53 rd/m). For WS greater than 16 m/s, the foam contribution is clearly overestimated by the model. The discrepancies between the old model 3 and the SMOS measurements are large for all incidence angles. It may be due to the particular local geophysical conditions for which the old model was developed [4], in addition to the fact that linear regressions with WS and SWH have been used. As mentioned in Section II-B, this kind of assumption can lead to non-negligible differences. The new model 3 is generally in good agreement with the bin averaged SMOS data (see Fig. 4).

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Fig. 4. SMOS TB roughness residual for three different incidence angles: 10◦ (top panel), 32.5◦ (middle panel), and 55◦ (bottom panel). Horizontal and vertical polarization are respectively in the right and left column. Prelaunched two-scale (dashed-dotted line), SSA/SPM+foam (dashed line), old model 3 (solid line with triangles), and the new empirical model 3 (solid line) are compared to bin averaged SMOS data (circles). We used bin sizes of 5◦ for incidence angles and 1 m/s for wind speed.

If we make the usual assumption that the microwave emissivity of typical sea-foam layers is WS independent, and only a function of frequency, incidence angle, and polarization [38], [39], the dependence with WS comes only from the foam fraction F. In order to give an estimation of the foam impact at Lband, Table VI gives the slopes of linear least-squares solutions fitted to the vertical and horizontal components of the brightness temperatures for four incidence angles and two ranges of WS. The first range, 4  U10  12 m/s, should provide information on the behavior of the sea surface emissivity assuming that the foam has a negligible impact on the measurements. The

TABLE VI L EAST-S QUARE S LOPE S OLUTIONS

slope estimates of the second range, 14  U10  22 m/s, when compared to the first one should give an idea of the foam impact on SMOS measurements. An increase of the slopes of about

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TABLE VII SSS A NOMALY FOR 150 A SCENDING PASSES, 170◦ W − 110◦ W, 40◦ S-E QUATOR , AUGUST 13 TH –22 ND

Fig. 5. Top panels correspond to bin averaged lat/lon (0.5◦ × 0.5◦ ) ECMWF wind speed (left) and WAM significant wave height (right) for one orbit (20100816T131313/20100816T140713). The middle and bottom panels show the anomaly between SMOS retrieved and World Ocean Atlas 2009 SSS. The SMOS retrieved SSS are derived using H-pol (left) and V-pol (right) TB measurements, and prelaunch SSA/SPM+foam model 2 (middle) and new model 3 (bottom).

50% is observed for a given incidence angle and a polarization state (48% ± 4% in V-pol and 53% ± 10% in H-pol). ˆ r increase (decrease) in H-pol (V-pol) For a given WS, the T with incidence angle is in qualitative and quantitative agreement with the historical data set of Section II-B. Table VI shows the order of magnitude of these variations. For example, a 40% increase of the slope in H-pol is observed between 20◦ and 50◦

for the first range of WS, when a 15% decrease is observed in V-pol. For the second range of WS, the slope increase in H-pol is of the same order to the slope decrease in V-pol (22% increase in H-pol and 17% decrease in V-Pol). At nadir, no polarization effect is expected. Indeed, the SMOS data show very small differences between the two linear polarizations at 10◦ for WS lower than 16 m/s (Fig. 4, top panel). From a theoretical point of view, the geometrical optics (GO) model [40] disagree with brightness temperature measurements that exclude foam [3], [41], [42]. The GO model assumes that the large-scale roughness can be approximated by an ensemble of reflecting plane facets, whose lengths are much larger than the electromagnetic wavelength (∼21 cm). Diffraction is thereby ignored, and the resultant averaged scattering coefficient depends on the slope distribution of the ocean surface. As shown by [43], the slope distribution is nearly Gaussian, so it is possible to express the brightness temperature increments due to all surface waves with wavelengths longer than the wavelength of the microwave radiation as a power series of the MSS (i.e., ΔTB = a0 + a1 M SS + a2 M SS 2 + . . .). Due to the very low incidence angle dependence of the Fresnel reflection coefficient near nadir and as shown analyticaly by [44], the roughness-induced brightness temperature predicted by a GO model is proportional to the square of the MSS (a1 = 0) at nadir. The predictions compared to data are two orders of magnitude lower. The roughness-induced emissivity at low incidence angles is then mainly controlled by the small scales of the sea surface and the foam. As the incidence angle increase, the longer scales of the surface contribute more and more to the sea surface emissivity by increasing (decreasing) the H-pol (V-pol) brightness temperature roughness sensitivity. In other words, all the surface scales act in the same way in H-pol, i.e., increasing the roughness contribution as the WS increases. In V-pol though, the larger and the smaller scales act in opposite ways, which is why the observed emission of the sea surface appeared less WS dependent in the range 50◦  θ  60◦ [45]. Nevertheless, Fig. 4 (right, bottom panel) shows relatively high ˆ r at θ = 55◦ in V-pol which may be due to foam sensitivity of T and/or to the very low impact of the longer scales on the sea surface emissivity at L-band. B. SSS Retrieval Validation To intercompare the performance of the different roughness models, including the new model 3, in terms of SSS accuracy, a simplified SSS retrieval algorithm is developed. The retrieval scheme, although less rigorous than the L2OS one, is suitable for intercomparison purposes and much less computationally

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Fig. 6.

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Significant wave height impact at 55◦ .

expensive. For each individual (vertically or horizontally polarized) brightness temperature, a SSS inversion scheme is    ∂TH,V −1  f wm H,V H,V H,V ˇ SSSr = SSSclim + T . (13) smos −Tf wm ∂SSS

Faraday rotation, atmospheric emission). A more robust validation of the different roughness model formulations will be possible after the first general SMOS data reprocessing, early 2012.

The ECMWF auxiliary WS and SST data are assumed to be ground truth. The SSS climatology (SSSclim ) obtained from the World Ocean Atlas [46] is used to derive both the first guess of TB and its gradient with respect to SSS. The retrieved SSS (SSSr ) is a linear correction to climatology and is proportional to the difference between the measured and the modeled TB weighted by the modeled TB gradient as a function of SSS evaluated at the constant value SSSclim . To reduce the SSS uncertainty in the retrievals inherent to the high radiometric noise of the SMOS brightness temperatures, the retrieved salinity departures from the climatology are averaged over 0.5◦ × 0.5◦ geographical boxes for H and V polarization. Fig. 5 shows the geographical distribution of SSS anomaly from an ascending pass on August 16, 2010. The strong SSS biases at high WS observed in the middle panel when using the SSA/SPM+foam model (saturated red patch) are strongly reduced when using the new roughness model (bottom panel). However, there are still some issues as illustrated by the pseudocircular negative bias around 50◦ S. This may be due to an error in the ECMWF WS or a particular characteristic of the sea surface roughness that is not well parameterized by the sole WS information. To provide a statistical assessment of the new model improvement, linear salinity anomalies are computed for about 150 ascending passes in the Pacific over the period August 13th to 22nd. Inside each pass, salinity anomalies are first averaged over 1/2◦ geographical boxes and both polarizations in order to mimic the usual SMOS Level 2 salinities obtained from the whole dwell-line information. Statistics of the residual salinity anomalies are computed for two separate regimes of WS conditions in two regimes, i.e., lower and higher than 12 m · s−1 . Results are summarized in Table VII. The table clearly shows that the SSS bias and standard deviation (std) are much lower for the new model as compared with model 2 for winds higher than 12 m/s. As expected, the validation scores are very similar for both models at WSs below 12 m/s. The residual 0.2 psu bias obtained for both models is likely due to errors in roughnessindependent forward model components (e.g., sky reflections,

The present study revisits the roughness-induced sea surface emissivity at L-band using the unprecedented data set provided by the recently launched SMOS satellite. Using selected and corrected (for systematic error patterns) residual (roughness-induced) brightness temperatures and required auxiliary (ECMWF) information together with a NN technique, an improved empirical roughness model is derived. The model well fits the incidence angle and U10 dependence of the roughness impact on emissivity. It has been shown that the use of this empirical model results in a significant reduction of the salinity biases at high WSs. However, other important error sources are still present. Indeed, substantial calibration and reconstruction errors have been recently identified [33] which may induce latitudinal and temporal errors of the order of 1 K. Such errors prevent from gathering a consistent multimonth data set that would allow to: 1) filter for poorly modeled conditions (e.g., galactic reflections) while keeping a good sampling of global geophysical conditions, 2) detect external sources contaminations over a range of conditions adequate to properly characterize them. The quality of the current roughness model is also limited by the quality of the other components of the forward model (galactic reflections, Faraday rotation effects) and the auxiliary parameters used to quantify them (e.g., SSS for the dielectric contribution, ECMWF WS, TEC, etc.). Near-future work will focus on reducing such errors. Furthermore, the use of U10 as a surrogate for the surface roughness is a well-known limiting assumption. Fig. 6 shows some preliminary results on identified sea state signature in the SMOS reconstructed brightness temperatures. To obtain this figure, we trained the NN with SWH as an additional input. The signature of SWH is very clear in Hˆ r tend to increase as SWH pol at high incidence angles where T increase for a given WS. The fact that no impact is observed in V-pol at low WS limits the possible statistical artefact due to some misplacement of midlatitude cyclones. The observed Lband brightness temperature sensitivity to SWH seems to exist only at high latitudes (higher than 35 ◦ S). The frequency of high winds in this region induces young sea states, and as such, the

VI. C ONCLUSION

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longer waves at the sea surface are statiscally more curved than anywhere else. It has a direct impact on the slope distribution of the ocean surface and at first order on its variance. Using a GO approach, it becomes obvious that when the SWH increases, the MSS take higher values and tend to increase the roughnessinduced emissivity in H-pol and should decrease it in V-Pol. Nevertheless, the inclusion of SWH in the roughness model may not add additional information in other regions, and worst, it may degrade its predictions resulting in biased retrieved SSS. As such, we plan to investigate the inclusion of other sea state-related parameters in the empirical roughness model. We will also attempt to further constrain the polarimetric sensitivity by jointly deriving the H-pol and V-pol models. Improvement in the other components of the forward model (e.g., Faraday rotation, celestial contamination) and the use of more accurate input parameters (WS, TEC, etc.) as well as undergoing work on improved characterization of the systematic errors of the TB images will certainly contribute to the subsequent improvements of the roughness model and, in turn, the retrieved salinity quality.

ACKNOWLEDGMENT The authors are indebted to the anonymous reviewers for their helpful hints and advice which contributed to improve and clarify several aspects of the paper. R EFERENCES [1] C. J. Koblinsky, P. Hildebrand, D. Le Vine, F. Pellerano, Y. Chao, W. Wilson, S. Yueh, and G. Lagerloef, “Sea surface salinity from space: Science goals and measurement approach,” Radio Sci., vol. 38, no. 4, p. 8064, Jun. 2003. [2] J. Font, A. Camps, A. Borges, M. Martín-Neira, J. Boutin, N. Reul, Y. Kerr, A. Hahne, and S. Mecklenburg, “SMOS: The challenging sea surface salinity measurement from space,” Proc. IEEE, vol. 98, no. 5, pp. 649–665, May 2010. [3] J. P. Hollinger, “Passive microwave measurements of sea surface roughness,” IEEE Trans. Geosci. Electron., vol. GE-9, no. 3, pp. 165–169, Jul. 1971. [4] A. Camps, J. Font, M. Vall-llossera, C. Gabarró, I. Corbella, N. Duffo, F. Torres, S. Blanch, A. Aguasca, R. Villarino, L. Enrique, J. J. Miranda, J. J. Arenas, A. Julià, J. Etcheto, V. Caselles, A. Weill, J. Boutin, S. Contardo, R. Niclós, R. Rivas, S. C. Reising, P. Wursteisen, M. Berger, and M. Martín-Neira, “The WISE 2000 and 2001 field experiments in support of the SMOS mission: Sea surface L-band brightness temperature observations and their application to multi-angular salinity retrieval,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 4, pp. 804–823, Apr. 2004. [5] S. Yueh, S. Dinardo, A. Fore, and F. Li, “Passive and active L-band microwave observations and modeling of ocean surface winds,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 8, pp. 3087–3100, Aug. 2010. [6] L. A. Klein and C. T. Swift, “An improved model for the dielectric constant of sea water at microwave frequencies,” IEEE Trans. Antennas Propag., vol. 25, no. 1, pp. 104–111, Jan. 1977. [7] G. S. E. Lagerloef, C. Swift, and D. Le Vine, “Sea surface salinity: The next remote sensing challenge,” Oceanography, vol. 8, no. 2, pp. 44–50, 1995. [8] S. H. Yueh, R. West, W. J. Wilson, K. K. Li, E. G. Njoku, and Y. Rahmat-Samii, “Error sources and feasibility for microwave remote sensing of ocean surface salinity,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 5, pp. 1049–1060, May 2001. [9] C. Gabarró, J. Font, A. Camps, M. Vall-llossera, and A. Julià, “A new empirical model of sea surface microwave emissivity for salinity remote sensing,” Geophys. Res. Lett., vol. 31, p. L01 309, Jan. 2004. [10] E. P. Dinnat, J. Boutin, G. Caudal, and J. Etcheto, “Issues concerning the sea emissivity modeling at L-band for retrieving surface salinity,” Radio Sci., vol. 38, no. 4, p. 8060, May 2003.

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Sébastien Guimbard was born in Paris, France, in 1983. He received the B.S. degree in environmental sciences in 2006 and the Ph.D. degree in metrology, oceanography, environment, and physical methods in remote sensing from the University of Versailles, Versailles, France, in 2010. He is currently working at the Physical Oceanography Department of the Institut de Ciències del Mar (ICM-CSIC), Barcelona, Spain, where he is involved in L2 SMOS products improvement. His research interests span the areas of signal processing, electromagnetic wave theory, and its application to ocean active and passive remote sensing.

Jérôme Gourrion was born in Toulon, France, in 1972. He received the B.Eng. degree in marine technologies from Université de Toulon, Toulon, France, in 1994, the M.Sc. degree in physical oceanography from Université de Bretagne Occidentale, Brest, France, in 1995, and the Ph.D. degree in physical oceanography from Université de Bretagne Occidentale, Brest, in 2003. His main research experience concerns the analysis of in situ and remote sensing data over the ocean to improve the description of air–sea fluxes. He is currently with the Physical Oceanography Department of the Institut de Ciencies del Mar, CSIC, Barcelona, Spain, where, in the context of the Soil Moisture and Ocean Salinity mission, he contributes to the validation of brightness temperature images and the improvement of sea surface salinity retrieval.

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Marcos Portabella was born in Spain, on October 14, 1970. He received the B.Sc. degree in physics from the University of Barcelona, Barcelona, Spain, in 1994, the M.Sc. degree in remote sensing from the Institute of Space Studies of Catalonia, Barcelona, Spain, in 1995, and the Ph.D. degree in physics from the University of Barcelona, in 2002. He is currently with the Unidad de Tecnología Marina (UTM-CSIC), Barcelona, working on satellite remote sensing. In particular, he is involved in scatterometry and L-band radiometry.

Antonio Turiel (M’11) was born on May 1, 1970 in Spain. He received the B.Sc. degree in physics, the B.Sc. degree in mathematics, and the Ph.D. degree in theoretical physics from the Autonomous University of Madrid, Madrid, Spain, in 1993, 1994, and 1998, respectively. He is currently working in the Department of Physical Oceanography at the Institute of Marine Sciences of CSIC, Barcelona, Spain. His research topics include signal and image processing applied to remote sensing of the oceans, marine turbulence at mesoscale, and ocean circulation at different scales.

Carolina Gabarró was born in Barcelona, Spain, in 1974. She received the B.Eng. degree in telecommunications engineering and the Ph.D. degree in ocean science from the Universitat Politècnica de Catalunya, Barcelona, in 1998 and 2004, respectively. From 1997 to 1999, she was with the European Space Research and Technology Centre, European Space Agency, Noordwijk, The Netherlands, where she worked on ocean-color remote sensing (for the ENVISAT mission). Since 2000, she has been with the Physical Oceanography Department, Institut de Ciencies del Mar, Consejo Superior de Investigaciones Cientificas, Barcelona, where she has been working on the Soil Moisture and Ocean Salinity (SMOS) mission. She is currently also a member of the SMOS Barcelona Expert Centre, Barcelona. Her work is focused on the retrieval of salinity from SMOS images. Her research interest includes microwave remote sensing.

Jordi Font received the B.Sc. degree and the Ph.D. degree in physics from the University of Barcelona, Barcelona, Spain, in 1973 and 1986, respectively. He is a Research Professor at the Physical Oceanography Department of the Institut de Ciències del Mar (Spanish Research Council, CSIC), Barcelona. He is a member of several international societies and committees and a participant in 42 oceanographic campaigns. He is author or coauthor of 300 communications to scientific symposia and 260 published papers (75 in SCI journals), an adviser of nine Ph.D. theses, and a Principal Investigator in several Spanish and European research contracts. His main research interests are ocean remote sensing (determination of sea surface salinity by microwave radiometry); physical oceanography of the Mediterranean Sea (water masses, circulation, and climate change); ocean circulation (operational measurements of ocean currents, technological improvements); and mesoscale dynamics (fronts, eddies, topographic interactions, physical-biological processes coupling). He is currently Co-Lead Investigator for ocean salinity in the European Space Agency Soil Moisture and Ocean Salinity mission. Until May 2010, he was Chairman of the Ocean Physics and Climate Committee of the International Commission for the Scientific Exploration of the Mediterranean Sea CIESM. Dr. Font received the National Arts Award 2011 of the Catalan Government in the category of Thought and Scientific Culture.