Soil Moisture and Ocean Salinity (SMOS) was chosen as the European Space Agency’s second Earth Explorer Opportunity mission. One of the objectives is to retrieve sea surface salinity (SSS) from measured brightness temperatures (TBs) at L band with a precision of 0.2 practical salinity units (psu) with averages taken over 200 km by 200 km areas and 10 days [as suggested in the requirements of the Global Ocean Data Assimilation Experiment (GODAE)]. The retrieval is performed here by an inverse model and additional information of auxiliary SSS, sea surface temperature (SST), and wind speed (W). A sensitivity study is done to observe the influence of the TBs and auxiliary data on the SSS retrieval. The key role of TB and W accuracy on SSS retrieval is verified. Retrieval is then done over the Atlantic for two cases. In case A, auxiliary data are simulated from two model outputs by adding white noise. The more realistic case B uses independent databases for reference and auxiliary ocean parameters. For these cases, the RMS error of retrieved SSS on pixel scale is around 1 psu (1.2 for case B). Averaging over GODAE scales reduces the SSS error by a factor of 12 (4 for case B). The weaker error reduction in case B is most likely due to the correlation of errors in auxiliary data. This study shows that SSS retrieval will be very sensitive to errors on auxiliary data. Specific efforts should be devoted to improving the quality of auxiliary data.
Salinity is an important parameter for describing ocean processes. Together with temperature and pressure, salinity determines the density of seawater. So changes in salinity and temperature modify the seawater density. Antonov et al. (2002) found that 10% of the observed sea level rise in the 0–3000-m layer during 1957–94 was due to a decrease of the ocean mean salinity. Water masses are also identified by their temperature and salinity, which, except for mixing of two different water masses, remain almost constant. In the western equatorial Pacific region of the ENSO phenomenon, salinity can create barrier layers that limit the mixed layer depth and modify the ocean–atmosphere interactions (Lukas and Lindstrom 1991).
Sea surface salinity (SSS) is also important. Within the mixed layer, salinity is almost constant and equal to SSS, except for freshwater lenses. Furthermore, it is possible to estimate salinity profiles from SSS and temperature–salinity relations (Hansen and Thacker 1999). SSS also plays a key role in the North Atlantic Deep Water formation, which is involved in the global thermohaline circulation. SSS is moreover correlated to the evaporation and precipitation budget, and therefore could give access to knowledge about the global water cycle (Delcroix et al. 1996).
In spite of considerable efforts to increase the spatial and temporal resolution of salinity measurements (principally the Argo program, voluntary ships, scientific campaigns, and moorings), large regions with only a few measurements persist, in particular in the Southern Hemisphere. Bingham et al. (2002) point out that 27% of the oceans 1° squares have never been sampled for SSS. A satellite mission is therefore essential to get global SSS coverage with high temporal resolution.
Soil Moisture and Ocean Salinity (SMOS) was chosen by the European Space Agency (ESA) as the second Earth Explorer Opportunity mission with an expected launch in 2007. The satellite will be equipped with the Microwave Imaging Radiometer Using Aperture Synthesis (MIRAS) instrument, an innovative 2D synthetic aperture interferometer in L band (Kerr 1998; Silvestrin et al. 2001). The acquired brightness temperatures (TBs) will give access to soil moisture over land and sea surface salinity over the ocean in a somewhat hexagonal field of view (FOV) of about 900 km along track and 1200 km across track (Fig. 1).
Due to errors on the measured TBs (around 1 K, depending on the location within the FOV) and a relatively low sensitivity of TBs to SSS (0.5 K psu−1 at 20°C and only 0.3 K psu−1 at 5°C), the mean RMS error on a single SSS measurement is expected to be large (∼1 psu). In contrast, temporal and spatial resolution will be quite high with a pixel size of about 40 km and a 3-day revisit time. Taking averages over 200 km × 200 km and 10 days should thus lead to smaller errors since far more than 100 singular measurements, depending on the latitude, can contribute to this average. Assuming independence between the measurements, the RMS error on the retrieved SSS could be lowered to less than 0.1 psu. This would fulfill the Global Ocean Data Assimilation Experiment (GODAE) requirements (Global Ocean Data Assimilation Experiment 2001).
At L band, TB not only depends on SSS, but also on SST and sea roughness. Sea roughness is described by instantaneous 10-m wind speed in a first approximation. During the inversion from TBs to SSS, collocated sea surface temperature (SST), wind speed (W), and SSS (hereafter auxiliary data) with the measurements are needed in the method used herein. Since SMOS is not equipped with instruments to estimate SST and W, it will thus be necessary to obtain them from other sources, for example, Advanced Very High Resolution Radiometer (AVHRR), Quick Scatterometer (QuikSCAT) measurements, model outputs, etc. Differences between these auxiliary values and real SST or W values occur and are likely correlated. As a consequence, an average over the GODAE scale (200 km × 200 km and 10 days) will not lead to as large an error reduction as theoretically possible.
Several studies have already been performed on the SSS retrieval of SMOS, such as that by Gabarró et al. (2004), who worked with the Wind and Salinity Experiment (WISE) campaigns measurements (Camps et al. 2004) or Boutin et al. (2004) who did a theoretical study on the error of the individual retrieved SSS at pixel scale and the error on the retrieved SSS after averaging over the GODAE scale.
In this paper, we study the impact of the auxiliary data errors on SSS retrieval at the pixel and GODAE scales, and more specifically the impact of the correlated errors of auxiliary data at the GODAE scale.
Section 2 presents the SMOS simulator including the emissivity model at L band and the inversion method to retrieve the SSS. The different datasets used to simulate the SMOS brightness temperatures and to perform the retrieval (auxiliary dataset) are presented in section 3. Section 4 describes the pixel selection and GODAE averaging processing. The results of this study are gathered in section 5 (sensitivity of the retrieval to errors on auxiliary data and brightness temperatures and error budgets at pixel and GODAE scales). Finally, conclusions are given in section 6.
a. SMOS simulator
The simulator we used is designed for soil moisture retrieval over land and SSS retrieval over oceans. Only the SSS retrieval part is discussed here.
This simulator takes into account SMOS specificities (see Waldteufel et al. 2003). We added a SMOS theoretical orbit. It is sun-synchronous with a local solar time of 0600 and circular with a repetition of about 3 days. The average SMOS pixel size is about 40 km. For a swath width of about 1040 km, this results in 27 pixels perpendicular to the direction of the satellite’s motion. Satellite speed is 6.67 km s−1. Measurements of TBs in horizontal and vertical polarization take about 1.2 s. These values are consistent with parameters given by ESA at the time of this work. The incidence angles in the alias-free FOV are shown in Fig. 1. The arrow indicates the direction of the satellite motion. The across-track distance from nadir is in abscissa, and the ordinate shows along-track distance from nadir. An illustration of the simplified functionality of the simulator is displayed in Fig. 2: TBs (3) are simulated with a direct model (2) from a set of reference geophysical parameters (1) and noise is added to the TBs (4). These noisy TBs represent the SMOS measurements and are used to retrieve SSS (7) with an inverse algorithm (6) and a set of auxiliary parameters (5).
It is necessary to provide the simulator with SSS, SST, and W (1 in Fig. 2) to simulate TBs as would be measured by SMOS. We assume that the ocean state at a given surface location remains constant during the few minutes necessary for its sampling. The ocean is therefore assumed to be homogenous within the FOV. Brightness temperatures are computed within the scene of Fig. 1 depending upon the incidence angle under which the pixels are seen. Along a dwell line, for an across-track distance of 200 km, for example, the emerging TBs of the pixels are measured from the lowest point of the FOV to the highest point in the FOV at a given time. It is also possible to interpret this as the TBs of one pixel seen under different incidence angles as the satellite passes over it. We therefore consider that the about 2 min necessary for the satellite to overflow a constant location (thus seeing a fixed point at all angles) is almost instantaneous considering SST, SSS, and W time scales. So a pixel on the subsatellite track is first seen at the highest incidence angle (θ) of about 47°, then as the satellite moves on, θ decreases to reach subsatellite point, and last the pixel is seen for θ about 8° in the backlooking direction of the satellite motion. As a consequence, there are many TBs available to retrieve the SSS (40 incidence angles ranging from −8.4° to 47.7° at the subsatellite track) in the inversion step. Note that as the across-track distance increases, the range of θ decreases, which degrades the quality of the retrieved SSS.
b. Emissivity model
Brightness temperature measurements at L band covering a large spatial and temporal area are not available; thus we use an ocean emissivity model (2 in Fig. 2) composed of a set of submodels to simulate TBs. The dielectric constant model (only function of SSS and SST) used in this study is from Klein and Swift (1977). It is used to compute the emissivities at 1.4 GHz for a flat sea. To compute the contribution of the sea roughness to the emissivities, another model is added. In our case, to reduce calculation time, we use a tabulation in wind speed and incidence angle provided by Dinnat et al. (2002) based on Yueh’s (1997) 2-scale model. This model approximates the sea surface as large-scale surfaces topped by small-scale surfaces or capillary waves. The Durden and Vesecky (1985) sea surface spectrum multiplied by 2 (Yueh 1997) has been chosen, because it predicts at 1.4 GHz a TB sensitivity to the wind speed in quite good agreement with WISE 2000 measurements (Camps et al. 2002). Other models and spectra exist but are not used for this study.
The surface emissivities are then used in the radiative transfer equations to compute the horizontally and vertically polarized emerging TBs at the surface. A correction for wind ripples is applied, but there is no correction for atmospheric and Faraday effects. Foam effect is not taken into account here since it is expected to be lower at L band than at higher frequency (Reul and Chapron 2002). Furthermore, recent foam effect models derived from campaigns (Camps et al. 2005) have shown a negligible foam coverage for wind speed lower than 10 m s−1, and a complex and unknown dependence on other parameters (fetch, salinity, atmospheric stability) for higher wind speed.
The resulting TBs (3 in Fig. 2) are simulated for the surface level in the dual-polarization mode. SSS retrieval is done in the antenna reference frame to avoid the problem of singularities during the geometrical transformation of TBs into the surface reference frame (Waldteufel and Caudal 2002) when the dual-polarization mode is chosen for the SMOS measurement. At this point a realistic random noise depending on the pixel position within the FOV is applied to take into account imperfections in TB measurements.
c. Method of inversion
Once the measured TBs (TBmeasi) (4 in Fig. 2) are simulated (which corresponds to the SMOS measurements), an iterative method, based on the Levenberg–Marquardt algorithm, retrieves the SSS. During the inversion, auxiliary data (5 in Fig. 2) are used as a first-guess solution to compute the TBs, which are then compared to the “measured” ones. The auxiliary data (SSS0, SST0, W0, where the subscript represents the iteration number) are used as the first guess of the iteration and are adjusted to minimize the cost function χ2 below [Eq. (1)]. For a given iteration j, χj2 is chosen as the sum of the squared difference between “measured” (TBmeasi) and simulated TBs (TBsimij) from SSSj, SSTj, and Wj [horizontal and vertical polarization for all incidence angles (i) for a given across-track distance] plus the squared difference between the SSTj (Wj) and the auxiliary SST0 (W0). All differences are weighted with their respective uncertainties (σi, σSST, and σW). When the minimum is reached, the modified auxiliary data become the retrieved data. With this method we not only retrieve SSS but also SST and W, because all three values are modified in order to minimize the cost function. The uncertainties on SST and W, namely, σSST and σW, keep the retrieved SST and W values within a certain range from their a priori value, also preventing unrealistic solutions since SSS is not constrained to allow free adjustment as shown in Eq. (1).
The cost function is written (see Waldteufel et al. 2003) as
where j is the iteration step, N is the number of SMOS measurements along a dwell line (twice the number of incidence angles within a dwell line due to horizontal and vertical polarization of TBs), (SST, SSS, W) is the vector of the parameters to be found, SST0 and W0 are the auxiliary values for SST and W, TBmeasi is the ith TB measured by SMOS, TBsimij is the ith TB simulated for the (SSTj, SSSj, Wj) set of parameters at step j, σi is the assumed uncertainty of TBmeasi (realistic noise on TBs that mainly depends on the incidence angle; see Fig. 3), σSST is the assumed uncertainty of the initial SST value (error on auxiliary SST0), and σW is the assumed uncertainty of the initial W value (error on auxiliary W0).
The uncertainties in TBs (Fig. 3) depend on the location of the pixel in FOV, the incidence angle of the measurement, the radiometric sensitivity, and the TB values of the whole scene.
Two distinct datasets of SSS, SST, and W are used for our simulation: one representing the ocean (reference dataset), and the other representing our a priori knowledge of the ocean (auxiliary dataset).
a. Reference ocean dataset (D1)
The ocean state used to simulate the TB as seen by SMOS is given by numerical oceanic and atmospheric model outputs, and will thereafter be referenced as D1. SST and SSS are provided by the Mercator data assimilation system PSY1-V1 (Greiner 2001). European Centre for Medium-Range Weather Forecasts (ECMWF)-analyzed wind stress values are converted to 10-m wind speed (W) on the same grid (temporal and spatial resolution) as the Mercator fields. These fields have ⅓° spatial resolution and a 1-day temporal resolution.
The 10-day averages of these fields, from 15 to 24 January 2001, are displayed in Figs. 4 –6. High SSS values of about 37 psu are found in subtropical gyres, where evaporation is larger than precipitation; relatively low SSS of about 35 psu are found in the Tropics and high latitudes. Very low SSS, less than 30 psu, are found near river mouths due to the freshwater contribution. SST shows the evident latitude-dependent distribution with values ranging from −2°C in high latitudes to 28°C toward low latitudes. Wind speed distribution is rather the inverse of SST distribution, showing generally low wind speed in low latitudes and high wind speed at high latitudes (for winter 2001 of our dataset).
b. Auxiliary ocean datasets (D2 and D3)
To assess the high dependence of the SSS retrieval on the auxiliary data, we will check the impact of two different sets of auxiliary data.
The first one, D2 is derived from D1, onto which a white noise is applied. The noise characteristics are derived from the statistics between Mercator and Levitus monthly climatology for SSS, Mercator and Reynolds weekly optimally interpolated for SST. It leads to a standard deviation (σ) of 0.5 psu for SSS and 1°C for SST. The wind speed σ is modeled dependent on wind intensity as follow: if W is less than 3 m s−1, σ is chosen equal to 2 m s−1, for W between 3 and 15 m s−1, σ is 1 m s−1, and for W higher than 15 m s−1, σ is 10% of W. These fields (especially monthly climatological SSS) have large-scale resolution and are smooth in comparison to the pixel resolution. It is therefore possible, that for SMOS, the standard deviation between real and auxiliary SSS will be higher than 0.5 psu. Note that these values are similar to the ones used by Boutin et al. (2004), thus allowing comparisons between their study and ours.
The auxiliary dataset D3 is composed of the weekly optimally interpolated Reynolds SST, the monthly Levitus climatology of SSS, and the daily QuikSCAT wind speeds. Note that QuikSCAT wind speeds are not assimilated for that year in the ECMWF model, thus ensuring independence between the scatterometer measurements and numerical model. The fields of SSS and SST both have a spatial resolution of 1°, whereas QuikSCAT W has a spatial resolution of ½°. These datasets were spatially and temporally interpolated at the same resolution as the reference datasets (1/3°) for easier comparison (section 3c).
c. Comparison between reference and auxiliary dataset
The influence of the auxiliary data from the two analyses on the retrieved SSS can already be partly inferred from the comparison between the reference dataset (D1) used for the TB simulation and the two chosen auxiliary datasets (D2 and D3). The data differ only by a white noise between D1 and D2, which means that their difference is zero on average and the standard deviations correspond to the chosen values (1°C for SST, 0.5 psu for SSS, and wind speed dependent for W; see section 3b).
The SSS retrieval is performed for two cases: case A uses a combination of D1 and D2 and allows the interpretation of SSS results without interference from local bias, while case B uses the independent sets D1 and D3. Case B is thus more realistic since it better mimics the real in-flight SMOS conditions. In this section, we are therefore going to primarily talk about case B.
The satellite will measure TBs, which depend on the real ocean state, which is represented here by the reference dataset (D1). Our a priori knowledge of these parameters will come from different sources such as other satellite observations and models. The SST and W will thus not be measured at the exact spatiotemporal location as the TBs, leading to some approximation errors.
The average difference (over the whole year 2001) between reference (PSY1_V1) and auxiliary (Reynolds) SST is illustrated in Fig. 7 and shows by example that regional biases do exist. Several zones of SST differences can be distinguished: the Gulf Stream, the Labrador Sea, the large region of West Africa, and the southern region of the model zone (10°–20°S). The difference in the Gulf Stream comes from the model that is too close to the coast. In the Labrador Sea, the bias may result from difficulties with convection and forcing. Problems near the southern edge of the Mercator zone may be related to the buffer zone. See Greiner (2001) for a more extensive discussion. Over the time period from 15 to 24 January 2001, the SST data (Fig. 8, left) show a mean difference of 0.4°C between Reynolds and Mercator SST and a standard deviation of 1.3°C.
The wind speed differences are shown in Fig. 9 (average of the difference between daily ECMWF wind speed and QuikSCAT wind speed for the whole year of 2001). QuikSCAT wind speed is on average higher than ECMWF wind speed. This is in agreement with a study related in the user manual of QuikSCAT mean wind fields (CERSAT-Ifremer 2002). It was found that QuikSCAT wind speeds are almost everywhere higher than ECMWF wind speed, with especially high differences (2 m s−1) at the equator. Overall, wind speeds during our study period (Fig. 8, right) show on average a bias of 1.3 m s−1 and a standard deviation of 1.8 m s−1. In summary, it appears that for auxiliary SST as well as W, the differences to the reference fields will be very different from white noise, thus the importance of studying case B.
4. Data processing
This chapter describes the data treatment to simulate SMOS measurements at pixel scale and the averaging over GODAE scales.
a. Pixel selection
The theoretical SMOS orbit is interpolated every 3 s to calculate the FOVs. GODAE box averages of 200 km × 200 km × 10 days are selected every 2° in the tropical and North Atlantic to retain a broad ocean coverage while reducing computer time.
All pixel positions of the interpolated orbit that are located within a GODAE box are selected and attributed to this specific GODAE box. Reference and auxiliary SSS, SST, and W are spatially and temporally interpolated to the pixel positions.
The results from the statistical comparisons between reference and auxiliary data over year 2001 (see section 3c) are used to minimize the impact of the differences between reference and auxiliary data, and to estimate the uncertainties of auxiliary SST and W in B. The annual means of the differences (Figs. 7 and 9) are thus removed from the auxiliary data after spatial interpolation of these annual means on the SMOS pixel location. The standard deviation of the difference between the reference and auxiliary data is an indicator of the error in the auxiliary data, leading to the estimated values of σSST and σW in Eq. (1).
For each pixel, SSS is retrieved with the simulator. To consider the Faraday effect, a distinction is made between pixels belonging to a morning or to an evening orbit. The Faraday effect is less important during the morning orbits and can therefore be corrected (Skou 2003), so inversion is done with both horizontally and vertically polarized TBs. During evening orbits, the inversion is done from the first Stokes parameter (sum of horizontally and vertically polarized TBs) to avoid the Faraday contamination.
b. Averaging over GODAE scales
The error in retrieved SSS is quite high at pixel scale (∼1 psu). A weighted average of the SSS should decrease the error at the expense of the resolution. For an average cell size of 200 km × 200 km and 10 days of sampling, the expected SSS accuracy should be around 0.1 psu to meet the GODAE requirement. The averaging is thus performed here with the outputs from cases A and B. The SSS pixels are weighted with the theoretical uncertainty in the SSS retrieval (σth_SSS) in the averaging [Eq. (2)]; σth_SSS, σth_SST, and σth_W are the theoretical estimators of the standard deviations of the retrieved SSS, SST, and W. They are outputs of the inversion (section 2c).
These theoretical estimators are given by [σ2th] = [𝗤T𝗦−1𝗤]−1, where 𝗦 is the covariance matrix for data and auxiliary parameters, and 𝗤 is the derivative matrix of the cost function χ2 (Waldteufel et al. 2003):
where SSSretr is the retrieved SSS (at pixel resolution), σth_SSS is the theoretical estimator of the retrieved SSS error, and Nb_Pixel is the number of pixels within a GODAE box. The number of pixels within a GODAE space–time box is latitude dependent, varying between 300 to about 850 pixels (mostly due to many orbit passes over locations at high latitudes). Even with a large number of pixels in GODAE boxes at high latitudes, the weighted average of retrieved SSS will not decrease the error considerably since pixels are correlated. The lower SST at high latitudes also compensates the benefit from a high pixel number.
In this section, we first look at the dependence of the retrieved SSS on auxiliary data and noisy TBs for test cases. We then present the results of retrieved SSS for 10 days (15–24 January 2001) over the tropical and North Atlantic at pixel scale in the two cases, A and B, mentioned earlier. To conclude, we present the resulting retrieved SSS at GODAE scales in these two cases.
a. Study cases at pixel resolution
Several tests are conducted to check the consistency with previous studies (Waldteufel et al. 2003; Boutin et al. 2004) and to investigate the influence of the precision of the auxiliary data and of the TBs on the retrieved SSS. First, the influence of the precision of the TBs is studied. Second, we test the importance of the precision and the influence of the auxiliary data on the retrieval. Standard values of W = 10 m s−1 and SSS = 36 psu are used. When not mentioned, the values for σtb are the one used to generate Fig. 3, σSST = 1°C, and σW = 2 m s−1. The TBs’ sensitivity to SSS is highly dependent on SST; thus calculations are made for SST varying between 0° and 30°C. For statistical purposes the calculations are repeated 50 times.
1) Influence of imperfectly measured brightness temperatures
To study the influence of instrumental noise leading to uncertainties in the TBs, the auxiliary data are chosen to be identical to the reference data. So, the only source of error is the uncertainty in the TBs. This uncertainty is simulated by a white noise, which is dependent on the location of the pixel within the FOV (Fig. 3). Each time a different noise is added to the TBs in the statistics. The SSS retrieval is oversampled with a resolution of 10 km in the across-track direction. The error in the retrieved SSS is given by the RMS of the reference and retrieved SSS differences. This RMS is calculated over the 50 runs and then averaged to obtain a spatial resolution of 40 km (corresponding to the average pixel size). The curves in Fig. 10 are the equi-RMS SSS error, the across-track distance is in abscissa, and SST in ordinate. This plot shows that even with perfect knowledge of auxiliary data, noisy TBs lead to an error of at least 0.4 psu at an SST of 30°C within ±200 km of the subsatellite track. The structure of the RMS error of the retrieved SSS clearly shows a dependency on the SST value and on the distance to the subsatellite track: the lower the SST, the higher the error, since TBs show little sensitivity toward SSS at low SST. The error also increases with the distance to the subsatellite track, as noise on TBs increases and number of incidence angles decreases. At an SST value of 15°C the SSS error increases in the vicinity of the subsatellite track to about 0.6 psu. The error increases rapidly toward the edges of the FOV: 0.8 psu at ±400 km, 1.25 psu at ±500 km, and 1.8 psu at ±600 km.
So, imperfectly measured TBs alone make a contribution to the error in retrieved SSS on the pixel scale of the order of 0.4 to 3.9 psu.
2) Influence of the uncertainties of the different auxiliary data
During these tests, we now assume a perfect instrument; thus no noise is put on the TBs, but the auxiliary data are assumed to have errors.
(i) Impact of imperfect auxiliary SSS
A random noise of about 0.5 psu is used on the auxiliary SSS. The inversion algorithm performs very well (see Fig. 11) to retrieve a correct SSS, with largest errors around 0.002 psu, at low SST. This test shows that the uncertainty in the auxiliary SSS has little influence on the quality of the SSS retrieval, when the cost function is expressed as in Eq. (1). Since there is no constraint on SSS, and all other values (TBs, SST, and W) are perfect, the inversion algorithm is able to retrieve an almost perfect SSS.
If we include a term in SSS in the cost function [Eq. (3)], the noisy auxiliary SSS considerably degrades SSS retrieval since the retrieved SSS stays close to the auxiliary SSS. The RMS error of retrieved SSS, ranging from 0.3 to 0.45 psu, will therefore be close to the standard deviation of the noise on the auxiliary SSS (0.5 psu):
(ii) Impact of imperfect auxiliary SST
A random noise of 1°C is applied to simulate imperfect auxiliary SST (Fig. 12). The SSS is retrieved with an error varying between about 0.02 and 0.5 psu. During inversion the auxiliary data are modified, as well as the TBs. As SST is constrained within 1°C, the inversion stops after only a few iterations, since retrieved SST already fulfills the 1°C constraint. In the meantime the former perfect auxiliary SSS has also been modified to minimize χ2. Between 0° and 16°C, the retrieved SSS error decreases with increasing SST. Above 16°C, however, the error increases with increasing SST, up to 0.2 psu at 30°C. Two regimes need to be considered here. On the one hand, the TBs are not very sensitive to SSS at low SST (dielectric constant variations), so the small deviations from the correct TBs can lead to large errors in retrieved SSS. On the other hand, a slight modification of the SST at higher temperatures during the inversion process leads to a larger modification of TBs, changing the SSS, departing it from the initial value which was, in this case, the solution. Nevertheless, this high sensitivity of TBs for SST is less important for SSS retrieval than the low sensitivity of TBs for SSS at low SST.
Imperfect auxiliary SST degrades the SSS retrieval (0.02–0.5 psu), but compared to the impact of imperfectly measured TBs [0.4–3.9 psu; see section 5a(1)], this effect is minor.
(iii) Impact of imperfect auxiliary W
A random noise of 2 m s−1 on the wind (Fig. 13) leads to a retrieved SSS with an error of about 0.5 to 2 psu depending on the SST value and the azimuthal position of the pixel. As expected, the error is lower at high SST and near the subsatellite track (between ±300 km).
At 15°C, the retrieved SSS error is about 0.8 psu under the subsatellite track and increases continuously to 1.2 psu 400 km away from the subsatellite track.
One can hope that the future auxiliary W will hopefully be known with a higher precision of about 1 m s−1. In that case (Fig. 14) the RMS error of retrieved SSS is considerably lowered, with values varying between 0.3 and about 1 psu. At 15°C, the error is about 0.5 psu at the subsatellite track and rises to 0.6 psu at an across-track distance of 500 km. The reduced uncertainty in auxiliary W not only decreases the error in retrieved SSS in general but also lessens the gap between error at subsatellite track and at the edges of the FOV since the wind brings information where the noise in TBs is the highest.
These preliminary tests show that the main error contributors are uncertainty in auxiliary W and instrumental noise. By reducing uncertainty in auxiliary W by a factor of 2, the RMS error of retrieved SSS will be reduced by a factor of 1.5 to 1.95. Most of the error reduction can be found at the edges of the FOV, between 400- and 600-km distance from the subsatellite track.
3) Influence of imperfectly measured tbs and auxiliary data
Here we test a more realistic case, where all auxiliary data (SSS, SST, and W) and the TBs are imperfectly known with an error of 0.5 psu in SSS, 1°C in SST, and 2 m s−1 in W. The RMS error of retrieved SSS (Fig. 15) varies between 0.7 and 4.5 psu. The lowest errors are obtained for near subsatellite tracks and high SST, whereas the highest errors are found for low SST at large across-track distances. The high errors at low SST are caused by the low sensitivity of TB to SSS at low SST. The dependency on across-track distance of the quality of retrieved SSS is due to the decreasing number of incidence angles, as well as the increasing noise on the TBs. The error of retrieved SSS for this case is mostly due to the influence of imperfect TBs and imperfectly known auxiliary W. These results are similar to the test done with SSS = 35 psu and W = 7 m s−1 by Boutin et al. (2004).
4) Benefits of tbs in the cost function
In the following we look at the benefit of including TBs in the cost function. We therefore compare the case from section 5a(3) to a case where the contribution of the TBs is negligible in the cost function in comparison to the terms in SST and W. The TB influence becomes negligible through a very high uncertainty of the σi value in χ2. The inversion algorithm is not able to retrieve a realistic SSS when all auxiliary data and TBs are imperfect, yet it was possible in section 5a(3). It is therefore indispensable to have TBs with sufficient precision in the cost function to be able to retrieve realistic SSS. Could we now ameliorate the SSS retrieval if an SSS term is added to the cost function [Eq. (3)]? As before, auxiliary data and TBs are imperfect. Uncertainties on SSS, SST, and W are chosen to be σSSS = 0.5 psu, σSST = 1°C, σW = 2 m s−1. With negligible contribution of TBs in the cost function, SSS can be retrieved and has an RMS error of about 0.46 psu, which is independent of the SST and the across-track distance. Since the TBs have no longer an influence in the cost function, the spatial pattern of their error does not follow the one resulting from the estimates in section 5a(3) (Fig. 15). The RMS error of retrieved SSS stays beneath the allowed standard deviation of 0.5 psu (the constraining value of SSS in the cost function).
If we restore the influence of the TBs in the cost function [Eq. (3)], using the realistic uncertainties from (Fig. 3) the solution in terms of SSS is the best at high SST and near the subsatellite track with a benefit with respect to the case without TB in χ2 of about 7.5%. For low SST there is no benefit from using TBs in the cost function. It has to be considered, however, that with a noise of only 0.5 psu on auxiliary SSS, the SSS is still quite close to the reference SSS value. This value is consistent with the mesoscale and fairly smooth fields used in sections 5b and 5c. But locally, at pixel scale, difference between reference and auxiliary SSS may be greater. Figure 16 shows the percentage of benefit having TBs in the cost function compared to the case without them, using a 1-psu noise on auxiliary SSS; that is, SSS is constrained in the cost function with σSSS = 1 psu. In this case the benefit reaches 30% at high SST. If auxiliary and reference SSS are even further apart, the benefit of TBs in the cost function will be also greater (20%–60% in the subsatellite track for σSSS = 2 psu).
The retrieval of SSS is better when SSS is strongly constrained in the cost function, which implies that the SSS accuracy is good and already well known. An ESA study (Barnier et al. 2002) shows that we can expect differences between models and in situ SSS with values that may exceed 1 psu. We therefore choose for further calculation to use the cost function without the SSS term to allow free adjustment of SSS.
b. Retrieval at pixel scale in the Atlantic
The results from the case study are confirmed with realistic tests in the tropical and North Atlantic for the time period of 15–24 January 2001. The datasets used are described in sections 3a and 3b. Results from reference versus retrieved SSS in both cases A and B are shown in Fig. 17. We discarded all pixels with reference SST less than 3°C, since SSS retrieval is very difficult at these low temperatures and they only represent 1.8% of our studied region. In this case, the overall RMS error of retrieved SSS is about 0.99 psu in A (Fig. 17, left) and 1.24 psu in B (Fig. 17, right).
c. Results after averaging over GODAE boxes
The errors at the pixel scales are too high in most cases to be useful in oceanography. Thus averages over the GODAE boxes are performed, reducing the error but increasing the spatiotemporal SSS scales. These fields would thus provide important information on the seasonal and interannual SSS variability for example.
The averaging, using Eq. (2), leads to a statistical retrieved SSS error of 0.08 psu in case A over the whole region of tropical and North Atlantic (Fig. 18, left), which meets the GODAE requirement, but an error of 0.31 psu in case B (Fig. 18, right). In fact, the reason for this result is that the SSS retrieval is difficult and inaccurate in cold water, especially since we chose a winter period, which is the most unfavorable one. Nevertheless, the results of retrieved SSS in case B are statistically 22% better than the a priori error on SSS, which is 0.40 psu (Fig. 19). Thus while SMOS/GODAE measurements might not be of great benefit for climatologies of the subpolar regions so far, it will still improve the knowledge of midlatitude and tropical regions’ SSS. For example, when averaging is done with pixels with SST greater than 10°C, an RMS error of retrieved SSS is 0.24 psu. This value is 42% better than the RMS error for auxiliary SSS (which is 0.41 psu for pixels with SST ≥ 10°C). This is coming close to what Durand et al. (2002) found in a theoretical study, where even an SSS error of 0.2 psu in a GODAE box is useful for assimilation in a tropical ocean general circulation model. In the ESA report of Barnier et al. (2002) it is also found that 40% of the Atlantic Ocean has an SSS variability larger than 0.2 psu.
To come back with more detail to the geographical distribution of the SSS retrieval errors depending on the case used, we find in A (Fig. 20) that the difference between averaged reference SSS and weighted average of retrieved SSS is for most regions less than 0.1 psu. This is similar to the results found by Boutin et al. (2004). Nevertheless, in our study error reduction is not everywhere as high as theoretical possible, considering the quantity of pixels in GODAE boxes (300 to more than 850 pixels per box, depending on latitude). In the Guinea basin, for example, the RMS error of averaged retrieved SSS is about 0.2 psu or higher. The wind speed is generally very low in this region, and when a white noise is applied to the wind to simulate the auxiliary W, nonphysical negative wind can be generated. These values are thus removed from the study when they occur, but in doing so we change the number of pixels in a GODAE box, and skew the distribution toward a higher mean wind speed. For the statistics over the whole tropical and North Atlantic, this removal does not have an impact with a mean of the difference between reference and auxiliary W of 0.01 m s−1 and an RMS of 1.12 m s−1. But for statistics in GODAE boxes, this removal is visible especially in the Guinea basin, where the mean between reference and auxiliary W is not zero, but negative (about −0.4 m s−1).
For case B (Fig. 21), the error is only in some regions such as the Angola basin or the Canary basin less than 0.1 psu. Errors higher than 0.5 psu are especially present in regions of cold SST (Labrador Sea, Greenland Sea).
One can conclude that, on the one hand, results from case A are too optimistic, as real and auxiliary data will probably not differ by only a white noise. On the other hand, case B is probably quite pessimistic. First, the quality of available auxiliary databases will certainly improve by the time SMOS is launched. Second, our study time period is in January, when SSS retrieval is especially difficult due to very low SST in the North Atlantic. SMOS with its lifetime of 3 yr will also do measurements during seasons and in regions where SST is higher. As a consequence, the quality of SMOS retrieved SSS is bound to be better than the results from case B.
One can notice in Fig. 22 that the distribution of the error of averaged retrieved SSS is quite similar to the distribution of the error of auxiliary W (absolute value of differences between averaged reference and auxiliary W). This shows that since W errors are correlated, the averaging of retrieved SSS over a GODAE box does not reduce the error as much as theoretically possible with uncorrelated data. The retrieved SSS values perform especially well (in comparison to auxiliary SSS) in regions of river mouths, whereas they perform worse in the North Atlantic.
The objective of this paper was to study the impact of the auxiliary data on SSS retrieval at the pixel scale and at the GODAE averaging scale.
First of all, we did a sensitivity test to look at the influence of the different parameters (TBs, SSS, SST, and W) on the quality of SSS retrieval. This confirms that imperfectly measured TBs and imperfectly known auxiliary W, as well as low SSTs, are the main contributors to the error of the retrieved SSS on the pixel level. When all parameters are imperfectly known, this individual error has RMS values from 0.7 to about 4.5 psu, depending on the across-track distance of the pixel and the value of the SST.
To enlarge our study, we simulated the SSS retrieval in the tropical and North Atlantic for a 10-day period with two auxiliary datasets. The first one (D2) is built using a procedure commonly found in the literature where the auxiliary dataset is built from the reference (D1) (Mercator SSS, SST, and ECMWF winds) and an added random noise. It has the benefit of being simple to simulate and giving good insight into the processing, but it does not represent well the real in-flight SMOS situation. Therefore, we also tested a second case (B) where the reference and auxiliary fields come from independent sources, thus allowing, for example, error correlation in the auxiliary data arising from local features that can be displaced or under- or overestimated. In the B case, the auxiliary set chosen is composed of the Levitus SSS, the Reynolds SST, and the QuikSCAT winds (D3).
The results are presented on pixel scale and after the GODAE averaging (200 km × 200 km × 10 days). The RMS of the error of retrieved SSS for a pixel is 1 psu for A and 1.2 psu for B. The individual measurements might be useful for detecting strong salinity variations in the warmer tropical oceans where significant upper-layer salinity variations in excess of 1 psu occurred during the 1997/98 El Niño–La Niña cycle in the Pacific (Johnson et al. 2000).
The SSS results are averaged, to lower the SSS error, over a GODAE box such that large and mesoscale phenomena can be observed and monitored. Indeed, the results are better in A, where the SSS RMS error is 0.08 psu (meeting the 0.1-psu GODAE requirement in 92% of the studied surface), and the SSS RMS error is 0.31 psu for B, meeting the 0.1 psu GODAE requirement in 37% of the studied surface. When considering the less demanding error limit of 0.2 psu in a GODAE box, 97% of the studied surface fulfils this criterion for A and 65% for B.
In conclusion, results from case A are too optimistic for SMOS, since difference between reference and auxiliary data will not be a white noise. Case B, in contrast, is probably quite pessimistic: the auxiliary dataset chosen is not optimal, by far, in quality, but they ensured the independence between the dataset used to simulate the TBs and the one used for the retrieval initialization. These studies were furthermore carried out for a period in January, the coldest period in the North Atlantic. By the time SMOS is launched, the intrinsic measurement quality (higher radiometric signature at high temperature than at low temperature) will still produce regional disparity in SSS accuracy, yet the quality of the auxiliary data will be improved, leading to a better retrieved SSS salinity. It is important to note that, in both A and B cases, we have neglected the correlation between salinity retrieved in adjacent pixels due to correlated brightness temperatures (for some incidence angles, the spatial resolution may reach 100 km). This effect should increase the error budget at GODAE scale.
As shown in this paper, the SMOS SSS retrieval errors are reduced with a better auxiliary dataset. The iterative restitution method seeks the solution from a set of auxiliary data (SST, W, and SSS); thus the retrieved SSS error depends directly on the quality and knowledge of these auxiliary data at the pixel scale. Furthermore, the possible correlation errors in these data degrade the benefit of the space–time averaging at GODAE scales. For these two reasons, quality of the auxiliary data will be crucial for the SSS part of the SMOS mission.
We are grateful to P. Waldteufel for providing us his simulation tool. We also thank Y. Kerr for the theoretical SMOS orbit. This study was done as part of a Ph.D. thesis funded by CNES.
Corresponding author address: Sabine Philipps, CLS Space Oceanography Division, 8-10 rue Hermes, 31520 Ramonville St Agne, France. Email: firstname.lastname@example.org