The Level 3 SM (L3SM) processor consists of a set of several algorithms. The forward model in L3SM uses the same physically based forward models as the ESA SMOS Level 2 SM processor, but in a MO retrieval context. A short summary of the main features of this processor is provided here and a detailed description can be found in Kerr et al. (2012). The SMOS L2 retrieval can be divided into two main components:

The first component is a physical model that computes TB at the antenna reference frame forced by ancillary data (land classification and soil properties) and physical parameters (skin or near-surface temperature and soil temperature). The selected physical model for the SMOS mission is L-MEB from Wigneron et al. (2007). The main features of the L-MEB physical model implementation in the SMOS operational processor are as follows:

Effective scattering albedo is considered.

2.

The second component of the retrieval algorithm is an iterative optimisation scheme that minimises a Bayesian cost function constructed from the observed and the modelled TBs in order to retrieve the physical parameter values. Preprocessing and post-processing steps are implemented to filter the input and output data for undesired effects like the decrease in quality due to spatial sampling or radio frequency interferences (RFIs) (Oliva et al., 2012; Richaume et al., 2014).

The physical approach at Level 3 MO is the same as that of Level 2 SO. In fact the core processing uses the same implementation of the L-MEB radiative transfer model. The main difference in Level 3 is the use of several orbits, rather than one, to retrieve SM and VOD. This has an impact first on the post-processing steps for selecting the orbits and second on the optimisation scheme to retrieve the parameters. Since the Level 2 retrieval is a multi-parameter retrieval, the Level 3 is thus a multi-orbit multi-parameter retrieval. The reasons that motivated the use of the MO approach are the following:

The angular sampling and radiometric accuracy at the border of the swath are reduced. Figure 1 shows the cumulative number of records for several descending orbits. The asterisk in each panel represents the same location in the La Plata region in South America. The orange regions inside the orbits observed on 18, 20 and 23 May 2010 depict the mild decrease in the number of TB measurements (15–35) during the instrument calibration phases. However, most important is the low number of TB measurements (35) observed on 21 May when the point of interest is at the border of the swath. A low number of TB measurements spanning a narrow range of incidence angles generates failures in the iterative retrieval of SM and VOD. The use of MO can help improve the number of successful retrievals at the border of the swath.

Other general motivations for Level 3 products are to provide a global gridded product, in contrast to swath-based products and to provide fixed-angle-binned TB products. The 25 km Equal-Area Scalable Earth Grid version 2.0 (EASE-Grid 2.0) (Brodzik and Knowles, 2002), which was selected for the Level 3 MO product also has a spatial sampling closer to the sensor's nominal resolution. The main input TB for the processing is generated from the snapshot-based L1B products, which are TBs in the Fourier domain. This consists of an inverse fast Fourier transform (IFFT) to make the transition from the Fourier domain to the spatial domain using the L3 EASE-Grid 2.0. In a subsequent step, TB measurements corresponding to the same grid point are selected from the different snapshots (for a given grid point, the incidence angle of the observation is different for each snapshot) to construct a grid-point-based product similar to the ESA L1C TB product but in EASE-Grid 2.0. The alternative is to interpolate the ESA L1C TB dataset from the 15 km Icosahedral Snyder Equal Area (ISEA) grid to the 25 km EASE-Grid 2.0 grid. This option was excluded because it could have generated interpolation artefacts on the TB products that would have propagated through the processing chain.

The selection of orbits is needed to select TBs at high latitudes where a sub-daily revisit is available and to generate the time series dataset on the EASE-Grid 2.0 as input to the MO retrieval. The following criteria are applied for the selection of revisits:

Ascending and descending orbits are processed separately since the impact of RFI (Oliva et al., 2012) and sun corrections (Khazâal et al., 2016) between ascending and descending orbits are very different.

At this level the acquisitions for a given day for ascending and descending orbits are separately stored in a three-dimensional matrix accounting for snapshots, longitude and latitude. A snapshot is an image associated to the acquisition of SMOS during a given integration time (epoch). Snapshots have different epochs and polarisation following a preprogrammed acquisition sequence. From this product a fixed-angle-binned TB product is generated as presented in Sect. 3. The product is also used in the next processing steps of L3SM MO.

For each retrieval and over each node a 7-day period is considered in which three revisits are selected from the complete list of revisits (Fig. 2). The first coincides with the central date (date of main product). The two others correspond to selected dates either before (previous 3.5 days) or after (3.5 days posterior) the considered date. Like in the previous processing step, the selection is done based on minimum distance from the swath centre for each node.

Observed TBs at the antenna reference frame from the precedent, actual and succeeding dates are assembled for each node. The forward algorithm is run to generate the modelled TB for each of the TB dataset records. The ancillary data and parameters are independently considered for each record. A Bayesian cost function that includes the aforementioned MO observed TB and modelled TB is then constructed. This is achieved by incorporating in the retrieval approach a temporal autocorrelation function for the VOD. The cost function is as follows: Cost=TBM-TBFt⋅COVTB-1⋅TBM-TBF+∑pP-P0t⋅COVp-1⋅P-P0, where COVTB=σTB2 is the error covariance matrix of TB data when assuming no auto-temporal correlation, TBM is the measured TB from SMOS, TBF is the forward modelled TB using L-MEB, P is the vector of retrieved parameters (SM and VOD) at the three times of acquisition, COVP is the error covariance matrix for parameter P and P0 is the a priori value of parameter P.

It is important to note that three SM values are retrieved simultaneously at each node: SMP for the preceding date, SMA for the actual date and SMF for the succeeding date. The same applies to VOD. In the case of SM, the a priori values are retrieved from ECMWF reanalysis data.

Where P=[SMP,SMA,SMF], the error covariance matrix considering no cross- or autocorrelation is given by COVSM=σSM02⋅I, where σSM02 is the standard-deviation error associated with SM. It is set to a high value: 0.7 m3m-3. I is the (3×3) identity matrix.

When P is equal to VOD, the error covariance matrix, considering temporal autocorrelation and no cross correlation between the different parameters, is given by COVVOD=σVOD021……ρtP,tA1…ρtP,tFρtA,tF1, where σVOD02 is the standard-deviation error associated with VOD, and ρ is the correlation function modelled assuming a Gaussian autocorrelation distribution: ρVODt1,t2=ρmaxt1,t2⋅exp⁡-t1-t22Tc2, where t1 and t2 are the times (expressed in days) corresponding to the VOD retrieval dates (P, A or F), ρmax⁡(t1,t2) is the maximum amplitude of the correlation function between t1 and t2 and Tc is the characteristic correlation time for VOD (Tc=30 days for forests and Tc= 10 days for low vegetation).

Figure 3 shows the shape of the correlation function for the two correlation lengths used in the processing. The green curve corresponds to the forested surfaces and the blue one to the nominal surfaces (bare soil and low vegetation).

The parameter values namely (SMP, SMA, SMF, VODP, VODA and VODF) are retrieved by minimising the cost function in an iterative procedure using the Levenberg–Marquardt optimisation algorithm. Thus, at the end of each daily retrieval, three SM values are available. The retrieval associated with the best goodness of fit (X2) value is then selected and delivered in the 1-day product. This product is only available when the filtering is finished, and thus with 7 days of lag time. Using the daily maps, time synthesis products (3 days, 10 days and monthly) are then provided. A detailed description of the algorithm is presented in the CATDS L3 Algorithm Theoretical Basis Document (Kerr et al., 2013).

The filtering eliminates brightness temperatures that are impacted by anthropogenic effects (such as RFIs), or spurious effects (such as sun impact). The filtering criteria, shown in Table 1, are similar to those for L3 MO SM and L2 SO retrievals. A detailed description of the filtering criterion is provided in the SMOS L2 ATBD (Algorithm Theoretical Basis Document). The reader can refer to Khazaal et al. (2016) for a more detailed evaluation of the impact of sun corrections and Richaume et al., 2014 and Soldo et al., 2014 for the impact of RFIs. All filtering criteria should be met, otherwise the acquisition is discarded. In case a cross polarisation is discarded, the associated X and Y acquisitions are also removed.

The acquisition sequence of SMOS is shown in Table 2. At each epoch an acquisition can be co-polarised (X, Y) or combined cross (XY, YX) and co-polarised. The table shows that there is no complete dataset for any epoch. A weighted linear interpolation is used to compute the missing acquisitions based on adjacent ones.

The weighting function accounts for the two following elements:

The TB acquisitions have different accuracy levels since the integration time is longer when only co-polarisation is acquired (pure acquisition) when compared to the case where combined cross and co-polarisation are acquired.

The time interpolation function of TB at time i (TBi) is as follows: TBi=Wi-1⋅TBi-1+Wi+1⋅TBi+1Wi-1+Wi+1Wi-1=1σi-1⋅nb_epoi-1Wi+1=1σi+1⋅nb_epi+1, where nb_epoi is the number of epochs between acquisitions at time i, σ is the corresponding radiometric accuracy and Wi is the weighting coefficient at time i. The standard deviation of the interpolated field is computed based on the square root of the weighted variances of the adjacent acquisition. We assume that the acquisitions are not correlated; therefore, no cross correlation term is considered in the equation. The following formulation is used: σi=Qi-1⋅σi-12+Qi+1⋅σi+12Qi-12+Qi+12Qi=1nb_epoi. The same approach as Eq. (5), while applying a constant weight, is used to compute the interpolated values of auxiliary information such as major and minor semi-axis length, incidence angle, Faraday angle and geometric angle.

In this step, the TBs are transformed from the antenna reference frame (X, Y) to the ground reference frame (H, V). This is done without accounting for atmospheric and galactic contributions. They are considered as TOA TBs. The TB components at antenna reference frame exhibit polarisation mixing due to the geometry of the acquisition (Fig. 4). Faraday rotation will also slightly alter the polarisations.

The inverse of the rotation matrix is used to transform the TB data from antenna to ground reference frame: TBHTBVTB3TB4=IRMTBXTBY2⋅realTBXY-2⋅imagTBXY. TB3 and TB4 are the Stokes 3 and Stokes 4 components. The inverse of rotation matrix (IRM) is given by IRM=cos⁡2asin⁡2acos⁡a⋅sin⁡a0sin⁡2acos⁡2a-cos⁡a⋅sin⁡a0-sin⁡2asin⁡2acos⁡2a00001, where a=Θg+ωf, with Θg being the geometric angle and ωf being the Faraday rotation angle as shown in Fig. 4.

The accuracies of the TB data are then computed by propagating the accuracies using the matrix below: σTBH=IRM1,12⋅σTBX2+IRM1,22⋅σdTBY2+4⋅IRM1,32+IRM1,42⋅σTBXY20.5σTBV=IRM2,12⋅σTBX2+IRM2,22⋅σdTBY2+4⋅IRM2,32+IRM2,42⋅σTBXY20.5σTB3=IRM3,12⋅σTBX2+IRM3,22⋅σdTBY2+4⋅IRM3,32+IRM3,42⋅σTBXY20.5σTB4=IRM4,12⋅σTBX2+IRM4,22⋅σdTBY2+4⋅IRM4,32+IRM4,42⋅σTBXY20.5, where IRMi,j are the ith column and jth row components of the IRM matrix.

This step consists in averaging the TOA TBs at fixed-angle intervals using an arithmetic mean. The selected incidence angle bins, shown in Table 3, are designed to also cover the SMAP acquisition angle (40∘).

All TB values outside the interval defined by mean (TB) ± 2 SD (TB) are considered as outliers and removed from the binning. The SD (TB) corresponds to the standard deviation of TB values inside each angle bin, not to be confused with the radiometric accuracy. The filtered outlier values are mainly associated with low RFI effects. If one component of TB (TBH, TBV and TBHV) is filtered out, all the other components are disregarded.

In this study, the SMOS SM products are evaluated against in situ SM from two networks with spatially distributed SM data at the footprint scale (USDA Watershed and AMMA-CATCH).The in situ soil moisture data from probes installed near the surface are used. These sites provide a soil moisture reading, representative of the first 5 cm of the top soil layer, as they are vertically installed. This may lead to a mismatch between the sensor sampling depth and the expected representative depth 0–2 or 0–3 cm of the L-band microwave radiometers (Escorihuela et al., 2010). This mismatch induces errors that are to be considered in conjunction with the sampling errors due to the spatial heterogeneity. The choice of the sites is made to cover contrasting environments over two different continents to provide an overview of the SM MO processor performances. The statistics over the sites are computed for data available within 1 h of space-borne acquisitions (SMOS and SMAP).

In order to compare the SMOS TB product to SMAP TB, the SMOS daily product was averaged following the same interpolation procedure as the one suggested in the SMAP mission. The method consists of using an inverse distance weighting for all the SMOS EASE 2.0 25 km grid points at the limits of the EASE 2.0 36 km grid of the SMAP product. The TBH and TBV from SMAP products are extracted and used without modification. The comparison is done over the pixels with a water fraction of less than 0.01 (i.e. 1 %) since the SMAP TBs are provided with subtracted open surface water. The contribution of the water surface is computed considering surface fraction from MODIS MOD44W and the emission of water using the Klein–Swift (1977) dielectric constant model forced by the surface soil layer temperature from GSFC (Goddard Space Flight Center) (O'Neil et al., 2015).

Global comparison is done over the EASE-Grid 2.0 25 km used for the L3 MO SM product. The L3 MO SM field is extracted directly from the product. The L2 SO SM product is interpolated to the EASE-Grid 2.0 25 km using a three-stage interpolation strategy where the availability of the products inside the limits of the grid node is considered

bilinear, if more than two soil moisture retrievals are available;

No interpolation is used after the extraction of the SM time series. The comparison is based on the following statistical indicators:

mean bias: (in situ – retrieved soil moisture) (m3m-3)

Figures 5a, b and 6a, b show the comparison between the SMOS L3 TB and SMAP L3 TB at a 40∘ incidence angle. Figure 5a shows the average of SMOS and SMAP TBH and TBV for the winter (January, February and March) and summer (July, August and September) seasons for 2016. The gaps (in dark blue) in the SMOS images are due to RFI with a differentiated impact for ascending and descending orbits. The difference in TBs between H/V acquisitions is smaller than between ascending and descending configurations. The main explanations for these differences are that, first, the L1 algorithm in SMOS and SMAP does not use the same configuration for the computation of the Faraday rotation. The Faraday rotation is impacted by the TEC (total electronic content) in the ionosphere. The SMAP algorithm uses the STOKES 3 parameters to account for the Faraday rotation. The SMOS algorithm uses auxiliary TEC files to compute the Faraday rotation. The ionosphere TEC is very different between ascending and descending orbits as the heating during the day increases the TEC. The second explanation is that the RFI probabilities are very different between ascending and descending orbits due to directional aspects and they are closer between H/V polarisations. The SMAP products show a higher coverage because SMAP has on-board RFI filtering and mitigation, which enables a better coverage but at the cost of a lower radiometric accuracy. The spatial patterns of TB are highly consistent for the two missions. Figure 6a and b show the distribution of difference of TBH and TBV from SMOS and SMAP for the winter (January, February and March) and summer (July, August and September) seasons during 2016. As described in Sect. 5.1, only nodes with a water fraction of less than 0.01 (i.e. 1 %) are considered. The mean difference is about -3.67 to -4.16 K, with SMAP being colder independent of polarisation or season. The standard deviation of all comparisons is about 3.65 K. This value is due to differences in calibration of the sensors and to the impact of differences in the acquisition time.

Based on the aforementioned evaluation methodology, the L3SM MO retrievals are compared to those of L2SM SO on the global scale over the 2010–2015 period. The auxiliary maps of mean forest cover percentage (Fig. 7a) and average RFI probabilities (Fig. 7b) for 2011 are provided as complementary information. These maps are obtained from the L3SM product.

Figure 8a and b show the mean number of successful retrievals per year (2010–2015) obtained from L3SM and L2SM, respectively. White (blank) pixels in panel (a) show the areas where no successful soil moisture retrieval is available. These pixels are mostly located in areas of dense vegetation (Congo), areas that are seasonally inundated (Amazon Basin) and/or areas with high RFI (South-East Asia and the Middle East). From Fig. 10a it is clear that the coverage area of the L3SM product is higher in these areas.

Figure 9a and b show the difference (MO–SO) in the number of successful soil moisture retrievals between the L3SM and L2SM products. The general behaviour shows a systematic increase in the number of retrievals of the MO with respect to the SO retrievals. The number of retrievals moderately increases in desert and plain areas (10–20 retrievals per year per orbit). The increase is much higher for forested areas. The L2SM showed a higher number of successful retrievals in the area between 62–70∘ longitude and 35–55∘ latitude. This is due to an anomaly in the processing of TB products. The ancillary data containing the TEC are not properly used over this region. This has been corrected and all operational products are now properly processed. The archive products will be corrected for this error in the next processing campaign. Also, from Figs. 7 and 8 it is clear that no enhancement in number of retrievals has been observed in areas with very high RFI probabilities in descending orbits (not shown here) like the north Asian region.

The mean soil moisture from L3SM and L2SM for ascending orbits is provided in Fig. 10a and b. These figures show that the soil moisture spatial patterns are very similar between the SO and MO SM retrievals. The coverage of the multi-orbit product is higher, as already shown in the previous figures. Nevertheless, some discrepancies can be observed from the difference map (Fig. 10c). The L3SM MO soil moisture values are generally higher than those of L2SM SO. This is most visible in forested areas (Fig. 7a), and this is consistent with climatic conditions over these areas. They are also higher in areas with high RFI pollution (Fig. 7b). This generally leads to a decrease in the value of the retrieved soil moisture values. Thus, the higher L3SM can be due to the positive impact of using multiple dates during RFI prone periods.

The statistics for the comparison of L2SM SO and L3SM MO with in situ networks is shown in Tables 3 and 4 for ascending and descending orbits, respectively. The number of retrievals is systematically higher for the L3SM than the L2SM as expected from the global analysis. Note that, contrary to the global analysis, the in situ analysis is done without any grid interpolation by considering the closest node. Tables 6 and 7 show the statistics for the on-site comparison for ascending and descending orbits, respectively. The skills are of similar magnitudes for the LW and Niger sites and the lowest skill is obtained for the Benin site in descending overpasses. No site showed a lower number of successful retrievals for L3SM. The bias values are not much improved by the L3SM. They seem to increase at the majority of the sites. The comparison shows a slight negative bias for the two datasets. The absolute value of bias is less than 0.04 m3m-3, except for the L3 retrieval over the Benin site, which is 0.058 m3m-3. Thus, in general the bias is within the uncertainty of the in situ data if we consider the combined errors from sensor errors, spatial heterogeneity and sensing depth mismatch. The correlation values range from 0.65 to 0.88 for the different sites. Increased correlation was found for the L3SM products over the Niger site and slightly over WG in descending overpasses. The majority of the correlation values remain high with L3SM retrieval with no significant difference between L2SM and L3SM.

More in-depth analysis can be obtained by inspecting the time series of soil moisture. Figures 11 and 12 show the time series for the selected sites for the period 2010–2016 and for ascending and descending overpasses. The Niger and Benin sites present a very pronounced seasonal signal typical of the Sahelian sites. Over these sites the L3SM shows consistently lower soil moisture than L2SM for high soil moisture values. The L3SM is closer in this case to the site data. The time series for LW show that the SMOS data closely follow the behaviour of the soil moisture dynamics over this site. One of the reasons for this is that the rainfall events are well separated, enabling the remote sensing data to capture the dynamics of physical processes (e.g. infiltration and evaporation) on a coarse scale. Thus, the exponential behaviour typical of a drying soil is well depicted.

Figures 13 and 14 show the CDF of the in situ, L2SM and L3SM data for ascending and descending orbits. From these figures it can be concluded that the SMOS soil moisture is drier than the 5 cm in situ data across the different values of soil moisture. This can be explained by the SMOS penetration depth with respect to the depth of the installation of the in situ sensors. Nevertheless, the shape of the distribution function, describing the extreme and seasonal cycles, is well captured in most cases. The Niger site's Sahelian climate is well captured, with a high probability of low soil moisture values and a small number of extreme values. The differences between the L2SM and L3SM data are mainly observed for the Benin and LW sites. When comparing Figs. 13 and 14, small differences can be noted between ascending and descending orbits.