# A new calibration of the effective scattering albedo and soil roughness parameters in the SMOS SM retrieval algorithm

Roberto Fernandez Moran, Jean-Pierre Wigneron, G. de Lannoy, E.

Lopez-Baeza, Marie Parrens, Arnaud Mialon, Ali Mahmoodi, Amen Al Yaari, Simone Bircher, Al Bitar Ahmad, et al.

► To cite this version:

Roberto Fernandez Moran, Jean-Pierre Wigneron, G. de Lannoy, E. Lopez-Baeza, Marie Parrens, et al.. A new calibration of the effective scattering albedo and soil roughness parameters in the SMOS SM retrieval algorithm. International Journal of Applied Earth Observation and Geoinformation, 2017, 62, pp.27-38. 10.1016/j.jag.2017.05.013. hal-01604901

HAL Id: hal-01604901

https://hal.science/hal-01604901v1

Submitted on 15 Jul 2025

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<figure><img src="image_1.png" /></figure>
1 A new calibration of the effective scattering albedo and soil roughness parameters in the SMOS

2 SM retrieval algorithm

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4 Fernandez-Moran, R. (1, 2), Wigneron, J.-P. (1), De Lannoy, G. (3, 4), Lopez-Baeza, E. (2), Parrens,

5 M. (5), Mialon, A. (5), Mahmoodi, A (5), Al-Yaari, A. (1), Bircher, S. (5), Al Bitar, A. (5), Richaume, P (5), Kerr,

6 Y. (5)

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8 (1) INRA, UMR1391 ISPA, 33140 Villenave d'Ornon, Centre INRA Bordeaux Aquitaine, France

9 (2) University of Valencia. Faculty of Physics. Dept. of Earth Physics & Thermodynamics.

10 Climatology from Satellites Group. 46100 Valencia

11 (3) NASA Goddard Space Flight Center, Code 610.1, Greenbelt, MD 20771, USA

12 (4) KU Leuven, Department of Earth and Environmental Sciences, Heverlee, B-3001, Belgium

13 (5) CESBIO, CNES/CNRS/IRD/UPS, UMR 5126, 18 Avenue Edouard Belin, Toulouse,
14 France

15 * Correspondence: roberto.fernandez-moran@inra.fr; tel.: +33 7 52 04 30 85

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This study focuses on the calibration of the effective vegetation scattering albedo (ω) and surface
soil roughness parameters (H<sub>R</sub>, and N<sub>Rp</sub>, p = H, V) in the Soil Moisture (SM) retrieval from L-band passive
microwave observations using the L-band Microwave Emission of the Biosphere (L-MEB) model. In the
current Soil Moisture and Ocean Salinity (SMOS) Level 2 (L2), v620, and Level 3 (L3), v300, SM retrieval
algorithms, low vegetated areas are parameterized by ω = 0 and H<sub>R</sub> = 0.1, whereas values of ω = 0.06 - 0.08
and H<sub>R</sub> = 0.3 are used for forests. Several parameterizations of the vegetation and soil roughness parameters
(ω, H<sub>R</sub> and N<sub>Rp</sub>, p = H, V) were tested in this study, treating SMOS SM retrievals as homogeneous over
each pixel instead of retrieving SM over a representative fraction of the pixel, as implemented in the
operational SMOS L2 and L3 algorithms. Globally-constant values of ω = 0.10, H<sub>R</sub> = 0.4 and N<sub>Rp</sub> = -1 (p
= H, V) were found to yield SM retrievals that compared best with *in situ* SM data measured at many sites
worldwide from the International Soil Moisture Network (ISMN). The calibration was repeated for
collections of *in situ* sites classified in different land cover categories based on the International Geosphere-
Biosphere Programme (IGBP) scheme. Depending on the IGBP land cover class, values of ω and H<sub>R</sub> varied,
respectively, in the range 0.08 - 0.12 and 0.1 - 0.5. A validation exercise based on in situ measurements
confirmed that using either a global or an IGBP-based calibration, there was an improvement in the
accuracy of the SM retrievals compared to the SMOS L3 SM product considering all statistical metrics (R
= 0.61, bias = -0.019 m<sup>3</sup>·m<sup>-3</sup>, ubRMSE = 0.062 m<sup>3</sup>·m<sup>-3</sup> for the IGBP-based calibration; against R = 0.54,
bias = -0.034 m<sup>3</sup>·m<sup>-3</sup> and ubRMSE = 0.070 m<sup>3</sup>·m<sup>-3</sup> for the SMOS L3 SM product). This result is a key step
in the calibration of the roughness and vegetation parameters in the operational SMOS retrieval algorithm.
The approach presented here is the core of a new forthcoming SMOS optimized SM product.

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**Keywords:** L-band, effective scattering albedo, soil moisture, soil roughness, SMOS
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# 1. Introduction

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L-band (1.1–2 GHz) microwave radiometry is one of the main remote sensing techniques to monitor Soil Moisture (SM) worldwide, a key element of the global water cycle. SM is a physical parameter of interest for many hydrological applications (Brocca et al., 2010), weather and climate predictions (de Rosnay et al., 2013), agricultural applications (Guerif & Duke, 2000) and early warning of natural hazards.

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SM in the first centimeters of the soil surface (~ 0 - 3 cm) is strongly related to the measurements of the emitted Brightness Temperature (TB) at L-band (Escorihuela et al., 2010; Njoku and Kong et al., 1977). However, other parameters must be accounted for in order to produce accurate estimates of SM, such as soil and canopy temperatures, soil roughness, texture and the vegetation optical depth and effective scattering albedo (Wigneron et al., 2017). Currently, the SMOS Soil Moisture and Ocean Salinity (SMOS) mission from European Space Agency (ESA), launched in November 2009 (Kerr et al., 2012), and the Soil Moisture Active Passive (SMAP) mission from National Aeronautics and Space Administration (NASA), launched in January 2015 (Entekhabi et al., 2010a), provide global maps of soil moisture and vegetation optical depth $\tau_{NAD}$ (only operational in the case of SMOS for this latter). The vegetation optical depth is related to vegetation features such as water content and vegetation structure (Grant et al., 2016).

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SMOS uses an interferometric L-band radiometer which measures brightness temperature at different angles whereas SMAP was originally conceived to combine the radiometer (passive) information at a constant incidence angle with radar (active) information to improve spatial resolution (the radar stopped working on July 7, 2016). These continuous measurements improve our knowledge of the soil-water processes which link water, energy and carbon cycles over land in order to advance in the prediction of droughts, flooding and climate forecasts (Entekhabi et al., 2014).

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The L-band Microwave Emission of the Biosphere (L-MEB) model is the core of the SMOS level 2 retrieval algorithm (Kerr et al., 2012). In this algorithm, the radiative transfer model (Mo et al., 1982)
parameters related to soil roughness and some vegetation parameters (Wigneron et al., 2007, 2008, 2011, Grant et al., 2007) are considered to be time independent and their values are computed based on a land cover map (ECOCLIMAP, Masson et al., 2003). Likewise, the SMAP algorithm is based on the land use classification scheme of the International Geosphere-Biosphere Programme (IGBP), which is composed of 17 classes. In this algorithm, the vegetation optical depth is estimated through the vegetation water content (VWC, kg/m²), calculated using both the Normalized Vegetation Difference Index (NDVI) and values from a look-up table based on the IGBP classification (O'Neill et al., 2012).

The first objective of this study was to investigate the impact of the effective scattering albedo, $\omega$, on the soil moisture retrieval accuracy. The effective scattering albedo $\omega$ accounts for absorption and scattering effects within the vegetation canopy (Kurum et al., 2013). The value of $\omega$ is currently assumed to be zero over low vegetation canopies (non-forested biomes) in the SMOS level 2 (L2) and level 3 (L3) algorithms and 0.06 – 0.08 over forests (Kerr et al., 2012). However, the value of $\omega$ assigned to low vegetation was based on the analysis of tower-based L-band radiometric measurements (Wigneron et al., 2007) limited to a few specific agricultural sites and it may not be accurate for all canopy types and for measurements made by space-borne sensors such as SMOS and SMAP (Kurum et al., 2013, Konings et al., 2016; Wigneron et al., 2004). Few studies can be found in the literature investigating $\omega$ at a global scale. The study of Konings et al. (2016) provides values of $\omega$ = 0.02 – 0.04 over low vegetation and 0.03 – 0.06 over forested areas. On the other hand, Van der Schalie et. al (2016) applied the Land Parameter Retrieval Model (LPRM) on SMOS observations against modelled SM from MERRA-Land (MERRA) and ERA-Interim/Land (ERA) and found a value of $\omega$ = 0.12 globally. In the SMAP L2 algorithm, the values of $\omega$ are based on the vegetation type (O'Neill et al., 2012). Additionally, the SMAP level 4 product provides globally variable estimates of the effective scattering albedo (and all other parameters) (Reichle et al., 2016; de Lannoy et al., 2013).

The second objective of this study was to investigate the effects of the soil roughness parameters on SM retrievals. Presently, the modelling of the roughness effects in the level 2 SMOS retrieval algorithm
is based on four parameters ($H_R$, $Q_R$, $N_{RH}$ and $N_{RV}$) (Wigneron et al., 2007). The parameter $H_R$ accounts for the decrease in the soil reflectivity due to soil roughness effects, $Q_R$ accounts for polarization mixing effects, and $N_{Rp}$ ($p = H, V$) accounts for the angular dependence of reflectivity. Some studies have been done over specific vegetation types. For instance, Wigneron et al. (2007) found values of $H_R$ ~ 0.1 - 0.2 for soybean and wheat crops and ~ 0.7 for corn fields. Over Spain, Cano et al. (2010) estimated that $H_R$ ~ 0.35 over Mediterranean vegetation. Regarding the $Q_R$ parameter, Lawrence et al. (2013) found that $Q_R$ = 0 is a reasonable value for cases where roughness conditions are not extreme. As for the parameters $N_{RH}$ and $N_{RV}$, Escorihuela et al. (2007) and Lawrence et al. (2013) proposed a difference of $N_{RH} - N_{RV}$ ~ 2 for smooth surfaces and (~ 1 - 1.5) for rough soils. In the SMOS L2 and L3 SM retrieval algorithm, $Q_R$ is fixed globally to 0, while $N_{RH}$ and $N_{RV}$ are set to 2 and 0 respectively. The value of $H_R$ is defined based on the ECOCLIMAP classification schema, with $H_R$ = 0.3 for forests and $H_R$ = 0.1 for the rest of the cover types (Kerr et al., 2012). In the SMAP L2 SM algorithm, $N_{Rp}$ ($p = H, V$) is considered to be equal to 2 and the value of $H_R$ is provided based on the IGBP classes (Entekhabi et al., 2014). Some studies have suggested the possibility of combining soil roughness and vegetation contributions as a single parameter in the retrieval algorithm (Fernandez-Moran et al., 2015; Parrens et al., 2016; Parrens et al., 2017), due to the existing relationship between the two contributions (Patton et al., 2013). This is done by setting the value of the $N_{Rp}$ ($p = H, V$) parameter equal to -1 at both polarizations and by considering that the effective scattering albedo $\omega$ is equal to 0.

To achieve the above-mentioned objectives, we investigated the calibration of the vegetation and soil roughness parameters ($\omega, H_R, N_{RH}$ and $N_{RV}$) based on SMOS SM retrievals. To simplify the retrieval process, the SMOS pixels were assumed to correspond to homogeneous surfaces over land as suggested by Wigneron et al. (2012), contrary to the currently operational SMOS L2 and L3 SM retrieval algorithms which use auxiliary data sets to characterize the pixel heterogeneity. The simplicity of the assumption of "homogeneous surface" allows to produce fast retrievals in order to perform very intensive and time consuming calibration processes as the one presented here.
In this study, retrieved values of SMOS SM were compared with *in situ* SM data measured at several sites worldwide available from the International Soil Moisture Network (ISMN) representing various land cover and soil types. The calibration was done by finding the values of the vegetation and soil roughness parameters which minimize the difference between the retrieved SM values and the *in situ* ISMN data, considering the following metrics: correlation (R), bias, root mean square error (RMSE) and unbiased RMSE (ubRMSE). We evaluated if the parameter calibration we computed changed depending on the degree of heterogeneity of the pixel.

In Section 2, the *in situ* data used in the study is presented along with the method which was followed for the calibration and the validation process. The Section 2.1 includes a description of the SMOS TB, soil temperature and soil texture data, as inputs required to run the L-MEB model. A description of the level 3 SMOS SM product, the IGBP classification and the *in situ* sites used for calibration is also covered in this section. The Section 2.2 describes the L-MEB model, SM retrievals and addresses the calibration and performance analysis steps. The results presented in Section 3 are divided in three subsections: calibration step of $N_{RH}$ and $N_{RV}$ (3.1), calibration step of $\omega$ and $H_R$ (3.2) and analysis (3.3). Discussion and conclusions are given in Section 4.

## 2. Available Data and Applied Methodology

In order to synthesize the content of this section, Figure 1 shows a flow chart that helps the reader to follow the use of the data described in Sections 2.1.1 to 2.1.4 and the methodology, as explained in Sections 2.2.1 to 2.2.4.
<figure><img src="image_2.png" /><figcaption>Figure 1: Methodology flow chart</figcaption></figure>

## 2.1. Data

### 2.1.1. SMOS data

The main inputs of the L-MEB model inversion are the multi-angular dual-polarization SMOS TB observations. The SMOS L3 TB (Version 310) product which is produced by the Centre Aval de Traitement des Données (CATDS) was chosen in this study. The resolution of this product is 25 km and uses the Equal-Area Scalable Earth (EASE) grid 2.0 (Amstrong, Brodzik & Varani et. al, 1997) whereas the resolution of the SMOS radiometer corresponds to a 43-km footprint on average (Kerr et al., 2012). TB is expressed at
the top of the atmosphere (at H and V polarizations) and at predefined incidence angles, θ, from 2.5 to 62.5° (in 5° steps). Each TB at an incidence angle, θ, is estimated from a bin of SMOS TB observations at θ ± 2.5°; the standard deviation of those TB observations is given in the SMOS L3 TB product. The availability of the TB data at different angles depends on the day and the location, taking into account the globe is fully imaged twice every three days. SMOS has a sun-synchronous orbit with a 06:00 LST ascending equator crossing time and 18:00 LST descending equator crossing time.

In this study, for each location and time (only ascending overpasses were used), the retrievals were performed only if the range of available incidence angles was larger than 10° (the retrieval error in SM decreases as the incidence angle range broadens: Wigneron et al., 2000), i.e. at least there was a difference of 10° between the largest and the smallest angle for each angle bin. Also, observations at incidence angles lower than 20° and larger than 55° were discarded as the former correspond to TB measurements of less quality outside of the optimal SMOS alias free field of view (Waldteufel et al., 2011) and the latter correspond to very large Earth antenna footprint (larger than 90 km x 50 km -3dB ellipses) (Kerr et al., 2016). Although SMOS operates in a protected band, some regions around the world are strongly affected by Radio Frequency Interferences (RFI). This contamination could be due to several sources such as radars, radio transmitters, TV communications, wireless cameras or even other satellites (Oliva et al., 2012). In order to limit the impact of RFI effects and to improve the quality of the TB data which were selected for the SM retrievals, TBp(θ) was filtered out when its standard deviation (given in the L3 TB SMOS product) exceeded radiometric accuracy by 5 K.

In this study, we also used the level 3 SMOS SM daily product (reprocessed R04, v300) for the performance analysis (Section 2.2.4). This product is processed by the CATDS and uses the EASE grid 2.0 with a spatial resolution of 25 km. The data quality index (DQX) present in this product estimates the retrieval quality; a maximum value of 0.06 m³·m⁻³ was established as an upper threshold (Al-Yaari et al., 2014a, 2014b). In parallel, the RFI probability flag was used to filter out SM data contaminated by RFI.
166 SM retrievals with an associated RFI probability higher than 10% were removed. Additionally, SM values
167 below 0 and over 0.6 m³ m⁻³ (Dorigo et al., 2013) were filtered out.

168 In the operational SMOS L3 SM retrieval algorithm (similar to SMOS L2) (see Section 2.2.2), the
169 total TB (TB<sub>TOTAL</sub>) is simulated as the sum of several fractions contribution (F<sub>NO</sub>: nominal, F<sub>FO</sub>: forest, and
170 others as urban, water, etc.), i.e. TB<sub>TOTAL</sub> = TB<sub>FNO</sub> + TB<sub>FFO</sub> + TB<sub>OTHERS</sub>. The FNO is a non-forest fraction
171 where the retrieval can be done (bare soil, low vegetation, ...). With the exception of some specific cases
172 in which the SM retrieval is attempted over F<sub>FFO</sub>, TB<sub>FFO</sub> is computed from the SM value over the 0 – 7 cm
173 layer coming from the ECMWF model to serve as auxiliary input to the retrieval over the nominal fraction
174 FNO.

175 **2.1.2. ECMWF soil temperature and soil texture**

176 Soil temperatures were provided by the European Centre for Medium-range Weather Forecasting
177 (ECMWF) for levels 1 (0-7 cm depth) and 3 (28-100 cm). It is based on the ERA-Interim dataset, which
178 uses a numerical weather prediction (NWP) system (IFS - Cy31r2) to produce reanalyzed data (Berrisford
179 et al., 2011). These data were reprocessed afterwards by the SMOS L3 preprocessor and provided on the
180 EASE grid 2.0. Data from frozen soils were discarded, using the ECMWF level 1 surface temperatures as
181 a threshold (T < 275.3 K). The effective soil temperature was computed from the surface (level 1) and deep
182 temperature (level 3) following the parameterization of Wigneron et al. (2001).

183 In the L-MEB model, the soil permittivity (ε) computation using the model by Mironov et al. (2013)
184 requires the soil clay content at global scale; the latter information was obtained from a map provided on
185 the EASE 2.0 grid computed from the Food and Agriculture Organization map (FAO, 1988), the same as
186 the one used in the SMOS L3 algorithm (Al Bitar et al., 2017).

187 **2.1.3. In situ data**
In order to calibrate the effective scattering albedo and the soil roughness parameters over different cover types, the maximum number of *in situ* sites with a sufficiently long time series of soil moisture data was selected. Following this criteria, different sites were selected from the International Soil Moisture Network (ISMN) (Dorigo et al., 2011): Soil Climate Analysis Network (SCAN) in North America (Schaefer et al., 2007), Soil Moisture Observing System - Meteorological Automatic Network Integrated Application (SMOSMANIA) in the South of France (Calvet et al., 2007), African Monsoon Multidisciplinary Analysis (AMMA) in West Africa (Lebel et al., 2009), Valencia Anchor Station (VAS) in Spain (Wigneron et al., 2012), Red de Estaciones de Medición de la Humedad del Suelo (REMEDHUS) in Spain, (Leng et al., 2016), DAHRA in Senegal (Olsen et al., 2013), Atmospheric Radiation Measurement (ARM) in Central USA (Jin et al., 2014), Plate Boundary Observatory (PBO_H2O) in North and Central America (Larson et al., 2008), SNOpack TELemetry (SNOTEL) in West USA, including Alaska (Serreze et al., 2001), The U.S. Climate Reference Network (USCRN) in the USA (Coopersmith et al., 2015), OzNet in Australia (Rüdiguer et al., 2010) and four watersheds in the USA (Little Washita in Oklahoma, Little River in Georgia, Walnut Gulch in Arizona and Reynolds Creek in Idaho) (Jackson et al., 2012).

A total of 1001 *in situ* stations providing the volumetric soil moisture (m³·m⁻³) of the top 0-5 cm soil layer were considered. The period of analysis was three years (2011-2013). For the global analysis of the statistical records, *in situ* stations with low quality data were discarded. For this purpose, we computed the p-value associated with the comparison of the SM retrievals and the *in situ* measurements. We accounted only for the stations fulfilling the condition p-value < 0.05 and R > 0.3 (for at least one of the cases of analysis) and for which the number of data available N > 50 (Al-Yaari et al., 2016). To ensure a proper inter-comparison, we used strictly the same number of data (namely the same dates) for all the retrieval configurations which were evaluated in terms of input values of effective scattering albedo and roughness parameters. Figure 2 shows the locations of all stations: the *in situ* stations used for the calibration and performance analysis steps, and those discarded (as described in the following sections).
<figure><img src="image_3.png" /><figcaption>Figure 2: In situ sites used for calibration (391), performance analysis (279, excluding the calibration sites) and filtered out (331)</figcaption></figure>

### 2.1.4. IGBP

The IGBP land cover classification scheme was developed during a series of meetings of the IGBP Land Cover Working Group in 1995 (Belward, 1996). The IGBP schema considers 17 different cover types. In this study, we used the 0.5 km Moderate-Resolution Imaging Spectroradiometer (MODIS)-based Global Land Cover Climatology map. It is based on 10 years (2001-2010) of the MODIS MCD12Q1 product, which contains land cover information. The map is generated by choosing, for each pixel, the land cover classification with the highest overall confidence from 2001-2010, as described in Broxton et al., 2014. This data has been re-gridded from the MODIS sinusoidal 0.5 km grid to a regular latitude-longitude grid (corresponding to a spatial resolution of 15 arc seconds. All IGBP pixels (0.5 km grid) contained in each SMOS L3 pixel (EASE 2.0 grid) were accounted for in order to calculate its composition, i.e. the percentage of each IGBP class within the SMOS L3 pixels.

## 2.2. Methodology

### 2.2.1. L-MEB model
Retrievals of SM from SMOS L-band measurements are based on the inversion of the L-MEB model. This model has been progressively refined and improved (Wigneron et al., 2017) and it is based on the zero-order $\tau-\omega$ radiative transfer model (Mo et al., 1982). The latter simulates the thermal emission of a vegetated soil. The soil microwave emission expressed in terms of brightness temperature ($TB_{Gp}$, p = V, H) can be written as a function of the ground emissivity ($e_{Gp}$, p = H, V) and the effective soil temperature ($T_G$) as (Ulaby et al., 1981 & 1986):

$$TB_{Gp}(\theta) = e_{Gp}(\theta) \cdot T_G \qquad (1)$$

The soil emissivity ($e_{Gp}$) at the observation angle $\theta$ can be computed from the corresponding soil reflectivity ($r_{Gp}$):

$$e_{Gp}(\theta) = 1 - r_{Gp}(\theta) \qquad (2)$$

To model soil roughness effects, a semi-empirical approach was developed originally by Wang and Choudhury (1981) and modified to include the $N_{RH}$ and $N_{RV}$ parameters (Escorihuela et al., 2007; Wigneron et al., 2007). The p-polarized soil reflectivity, $r_{Gp}$ is given by:

$$r_{Gp}(\theta) = r'_{Gp}(\theta)\exp[-H_R\cos^{N_{RP}}(\theta)] \qquad (3)$$

where

$$r'_{GH}(\theta) = [1 - Q_R(\theta)]r_{GH}^*(\theta) + Q_R(\theta)r_{GV}^*(\theta) \qquad (4)$$

$$r'_{GV}(\theta) = [1 - Q_R(\theta)]r_{GV}^*(\theta) + Q_R(\theta)r_{GH}^*(\theta) \qquad (5)$$

where $r'_{Gp}$ depends on the smooth surface reflectivity $r_{Gp}^*$ (p = H, V), i.e. the reflectivity of a plane (specular) surface (equation 4 and 5). The latter can be computed from the Fresnel equations as a function of $\theta$ and soil permittivity ($\epsilon$). The latter was computed as a function of SM, soil effective temperature ($T_G$), and soil texture in terms of clay fraction from the dielectric model of Mironov et al. (2013). This model is
based on the Generalized Refractive Mixing Dielectric Model (GRMDM) and accounts for the measured dielectric spectra of moist soil samples for a given texture and temperature (Wigneron et al., 2017).

The semi-empirical roughness model includes four roughness parameters $Q_R$, $H_R$ and $N_{Rp}$ ($p = H$, V) (Wigneron et al., 2007). The parameter $H_R$ accounts for the decrease of the specular reflectivity $r_{Gp}^*$ ($p = H$, V) due to soil roughness effects, $Q_R$ accounts for polarization mixing effects, and $N_{Rp}$ ($p = H$, V) accounts for the change in the angular dependence of reflectivity caused by a rough surface.

From a large data set based on both experimental measurements and simulations, Lawrence et al. (2013) found that setting $Q_R = 0$ led to a simplified model with good performance in terms of both TB modelling and SM retrievals. The assumption of $Q_R=0$ was made here, in line with SMOS L2 and L3 (Kerr et al., 2012; Al Bitar et al., 2017), SMAP (O'Neill et al., 2012) and LPRM (Van der Schalie et al., 2015) SM retrieval algorithms.

Using the $\tau-\omega$ model, the emission of a soil covered with vegetation can be calculated for each polarization as a sum of: (i) the direct upwelling vegetation emission; (ii) the upwelling soil emission attenuated by canopy; (iii) the downwelling vegetation emission reflected by soil and attenuated again by the canopy layer:

$$TB_p(\theta) = (1 - \omega_p)[1 - \gamma_p(\theta)][1 + \gamma_p(\theta)r_{Gp}(\theta)]T_C + [1 - r_{Gp}(\theta)]\gamma_p(\theta)T_G \quad (6)$$

where $T_G$ and $T_C$ are the soil and vegetation effective temperatures, $\gamma_p$ is the vegetation attenuation factor (also referred as vegetation transmissivity) and $\omega_p$ ($p = H$, V) is the effective scattering albedo (Kurum et al., 2013). The latter is generally considered to be close to zero over low vegetation covers (Wigneron et al., 2007; Kurum et al., 2013), while it is considered to be 0.08 for boreal forests and slightly lower for tropical forests (Rahmoune et al., 2013). In the following, $\omega_p$ is referred to as $\omega$ since we did not consider the dependence of the effective scattering albedo on polarization, as done in the SMOS L2 and L3, SMAP and LPRM algorithms.
According to Beer's law, the vegetation attenuation factor $γ_p$ is related to $τ_p$ as:

$$γ_p = \exp [-τ_p/\cos (θ)] \qquad (7)$$

where the vegetation optical depth ($τ_p$) at observation angles $θ > 0$ and polarization p = H, V is expressed as a function of the vegetation optical depth at nadir $τ_{NAD}$ ($θ = 0$):

$$τ_p(θ) = τ_{NAD}[\sin^2(θ)tt_p + \cos^2(θ)] \qquad (8)$$

where $tt_V$ and $tt_H$ quantify the dependence of $τ_p$ on the incidence angle $θ$. The value $tt_H = tt_V = 1$ corresponds to the isotropic case for Vertical and Horizontal polarizations, where $τ_H(θ) = τ_V(θ) = τ_{NAD}$. This assumption was made in this study, according to the SMOS L2 and L3 SM retrieval algorithm (Kerr et al., 2006).

### 2.2.2. SM retrieval

The retrieval of soil moisture relies on the inversion of the L-MEB model. The process involves the minimization of the following cost function (9), which accounts for all incidence angles between 20 and 55° and both polarizations (H and V):

$$x = \frac{\sum_{i=1}^{N}(TB_p(\theta)_{mes} - TB_p(\theta))^2}{\sigma(TB_p(\theta))^2} + \sum_{i=1}^{2} \frac{(P_i^{ini} - P_i)^2}{\sigma(P_i)^2} \qquad (9)$$

where N is the number of observations for different viewing angles ($θ$), $TB_p(θ)_{mes}$ is the measured value over the *in situ* sites (SMOS L3 pixels), $σ(TB_p(θ))$ is the standard deviation associated with the brightness temperature measurements (taken from the SMOS L3 SM product), $TB_p(θ)$ is the brightness temperature calculated using equation (6), $P_i$ ($i = 1, 2$) is the value of the retrieved parameter (2-P parameter retrieval in this study, SM, $τ_{NAD}$); $P_i^{ini}$ ($i = 1, 2$) is the initial value of each parameter in the retrieval process and corresponds to an a priori estimate of the parameter $P_i$; and $σ(P_i)$ is the standard deviation associated
with this estimate. An initial value of 0.2 m³·m⁻³ was selected for SM and σ(SM), while it was equal to 0.5 for τ<sub>NAD</sub> and 1 for σ(τ<sub>NAD</sub>).

Taking into account that retrievals were only considered at SMOS ascending orbit (around 6 am LST), a thermal equilibrium for the soil-vegetation layers can be assumed (Jackson et al., 1980; Wigneron et al., 2007). The atmospheric contribution was neglected in this study.

### 2.2.3. Calibration

The calibration process consists of two main steps and was carried out over three years of SMOS data (2011-2013). In the first step, our focus was on the calibration of the N<sub>Rp</sub> (p = H, V) parameter. In the second one, it was on the calibration of the effective scattering albedo (ω) and the soil roughness parameter (H<sub>R</sub>), using the value of N<sub>Rp</sub> (p = H, V) which was previously calibrated.

In the first step, the SM retrievals were carried out over the calibration sites using a range of values of ω, H<sub>R</sub> and N<sub>Rp</sub> (p = H, V) as follows:

* ω = {0, 0.05, 0.08, 0.12}

* H<sub>R</sub> = {0, 0.2, 0.5}

* N<sub>RV</sub>, N<sub>RH</sub> = {(-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (2, 2)}

The range of values selected here correspond to common values of the model parameters used at L-band in the literature (Fernandez-Moran et al., 2015; Miernecki et al., 2014; Rahmoune et al., 2013; Wigneron et al., 2007; Escorihuela et al., 2007). The combination of inputs led to 120 (= 4 x 3 x 10) cases of analysis. Different statistical performance criteria were then computed: correlation coefficient (R), root mean square error (RMSE), bias and the unbiased root mean square error (ubRMSE), derived from the comparison between the retrieved soil moisture and the *in situ* SM measurements. As the focus in the first step was on the N<sub>Rp</sub> (p = H, V) parameter, only a few values of ω and H<sub>R</sub> were considered. Taking into account that the sampling depth of the *in situ* measurements (5 cm) does not correspond well to the
estimated sampling depth of SM at L-band (~3 cm) (Escorihuela et al., 2010; Njoku and Kong et al., 1977),

bias was considered as the less important metric in the calibration process (and RMSE by extension, due to

its bias inclusion).

In the second step, the best N<sub>Rp</sub> (p = H, V) estimate obtained from the first step was withheld and
a new analysis was done considering the following values of ω and H<sub>R</sub> (72 cases in total):

• ω = {0, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16}

• H<sub>R</sub> = {0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7}

Each *in situ* site was classified according to the IGBP schema (see number of *in situ* stations for
each class in Table 1). Only "representative" *in situ* stations of the SMOS L3 pixels to which they belong
were selected. For that purpose, a filtering was applied according to the following criteria:

• The IGBP class of the in situ station was the same as the predominant class of the L3 pixel
(EASE 2.0 grid, 25 km to which it belongs).

• The predominant class covered at least 50% of the L3 pixel.

• The sum of the surface fraction of water, permanent wetland, urban and snow/ice classes represented less than 10% of the L3 pixel.

Table 1 shows the number of calibration candidate sites after applying the selection of
"representative" stations.

<table><caption>Table 1: Total and filtered number of *in situ* stations used for calibration according to IGBP classes</caption><thead><tr><td>Class</td><td>Number of in situ stations</td><td>Number of "representative" stations for calibration</td></tr></thead><tbody><tr><td>0 – Water</td><td>4</td><td>0</td></tr><tr><td>1 – Evergreen needle leaf forest</td><td>122</td><td>41</td></tr><tr><td>2 – Evergreen broadleaf forest</td><td>9</td><td>0</td></tr><tr><td>3 – Deciduous needle leaf forest</td><td>0</td><td>0</td></tr><tr><td>4 – Deciduous broadleaf forest</td><td>12</td><td>4</td></tr><tr><td>5 – Mixed forests</td><td>27</td><td>1</td></tr></tbody></table>
<table><tr><td>6 – Closed shrublands</td><td>2</td><td>0</td></tr><tr><td>7 – Open shrublands</td><td>100</td><td>25</td></tr><tr><td>8 – Woody savannas</td><td>59</td><td>16</td></tr><tr><td>9 – Savannas</td><td>4</td><td>1</td></tr><tr><td>10 – Grasslands</td><td>419</td><td>214</td></tr><tr><td>11 – Permanent wetland</td><td>7</td><td>0</td></tr><tr><td>12 – Croplands</td><td>119</td><td>63</td></tr><tr><td>13 – Urban and built-up</td><td>16</td><td>0</td></tr><tr><td>14 – Cropland/Natural Vegetation Mosaic</td><td>91</td><td>23</td></tr><tr><td>15 – Snow and ice</td><td>0</td><td>0</td></tr><tr><td>16 – Barren and sparsely vegetated</td><td>10</td><td>3</td></tr><tr><td><strong>TOTAL</strong></td><td><strong>1001</strong></td><td><strong>391</strong></td></tr></table>

334

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Once the selection of “representative” stations was made, two calibrations were proposed: (1) globally-constant values of $H_R$, $\omega$ and $N_{Rp}$ ($p = H, V$) across all *in situ* stations (2) specific values of $H_R$, $\omega$ and $N_{Rp}$ ($p = H, V$) for each IGBP class (hereinafter “IGBP-based” calibration). Due to the lack of “representative” stations for some IGBP classes, the estimated parameters in those underrepresented classes were assigned the globally-constant values. Conversely, specific values were found for the following classes: evergreen needle leaf forest, open shrublands, woody savannas, grasslands, croplands, cropland/natural vegetation mosaic, and barren or sparsely vegetated.

342

### 2.2.4. Performance analysis

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347

348

349

350

In the validation process, the SM retrievals obtained from the following four different approaches were compared to the *in situ* SM data: (1) a homogeneous retrieval using the globally-constant inputs ($H_R$, $\omega$, $N_{RH}$ and $N_{RV}$) obtained in the calibration phase, (2) the same as (1) where the values of the soil and vegetation parameters ($H_R$, $\omega$, $N_{RH}$ and $N_{RV}$) were estimated as a function of the IGBP land use class, (3) the SMOS L3 SM daily product (namely the official SMOS SM product available from the CATDS center) and (4) a homogeneous retrieval using the model parameter ($H_R$, $\omega$, $N_{RH}$ and $N_{RV}$) used in the SMOS L3 algorithm. For Cases (2) and (4), over a single pixel, each parameter $P$ ($H_R$, $\omega$, $N_{RH}$ and $N_{RV}$) was weighted according to the percentage of each IGBP class as:
$$P = \sum P_i \cdot \frac{\%i}{100} \qquad (10)$$

where $P_i$ is the calibrated value of the parameter P for the class i and $\%i$ is the percentage of the class i present within the SMOS L3 pixel.

After the filtering of *in situ* sites presented in Section 3, the analysis process was firstly performed over all the stations (670) and secondly over all sites excluding those employed in the calibration steps (279). Concerning data filtering, the same procedure as that described in the calibration Section 2.7 was applied. Additionally, the post filtering consisted of: (1) removing SM values out of the 0 - 0.6 m³·m⁻³ range and (2) a quality control based on the RMSE value between the L3 TB SMOS and the L-MEB modelled TB (retrievals where RMSE was above 12 K were discarded as proposed in Wigneron et al. (2012).

# 3. Results and discussion

## 3.1. Calibration of N<sub>Rp</sub>

This section presents the results from the first step of the calibration process which focused on the calibration of the N<sub>Rp</sub> (p = H, V) parameter globally, as the behavior of this parameter was found to be rather similar across all IGBP classes. All results were obtained through a direct comparison between retrievals over rather homogeneous pixels and *in situ* measurements. Figure 3 shows the median correlation values (R) for each retrieval case (considering 120 combinations of $\omega$, H<sub>R</sub>, N<sub>RH</sub> and N<sub>RV</sub> parameters). Values range from R = 0.28 (for the case $\omega$ = 0) to R = 0.53 (for the case $\omega$ = 0.12), highlighting the strong influence of effective scattering albedo on this metric. Conversely, for a given value of $\omega$, changes in the values of H<sub>R</sub> and N<sub>Rp</sub> (p = H, V) do not lead to significant changes in the median value of R. Note that for H<sub>R</sub> = 0, N<sub>Rp</sub> has no influence on the retrievals, so all R values are the same.
<figure><img src="image_4.png" /><figcaption>Figure 3: Median correlation (all calibration sites: 391 stations) between *in situ* and retrieved SM for each H<sub>R</sub>, ω and N<sub>Rp</sub> (p = H, V) case</figcaption></figure>

In parallel to the correlation analysis, the absolute value of bias (|bias|) is shown in Figure 4. The worst case (|bias| = 0.20) was found for ω = 0, H<sub>R</sub> = 0.5, N<sub>RV</sub> = -1 and N<sub>RH</sub> = 2. The soil roughness parameter's impact on the absolute values of bias can be clearly noted, especially for the lowest albedo value (ω = 0). An increase in ω leads to higher |bias| values when H<sub>R</sub> is set equal to zero. The best case (|bias| = 0.06) was found for several H<sub>R</sub> and ω scenarios, namely: H<sub>R</sub> = 0, ω = 0; H<sub>R</sub> = 0, ω = 0.05; H<sub>R</sub> = 0.5, N<sub>Rp</sub> = -1 (p = H, V) and other cases in which there is a dependency of ω on the three parameters (ω, H<sub>R</sub> and N<sub>Rp</sub>, p = H, V). Furthermore, we can note the low impact of N<sub>Rp</sub> (p = H, V) on |bias| when ω = 0.08 – 0.12. In any case, N<sub>Rp</sub> = -1 (p = H, V) was the best choice to obtain the lowest |bias| values.
<figure><img src="image_5.png" /><figcaption>Figure 4: Median absolute bias (all calibration sites: 391 stations) between *in situ* and retrieved SM for each H<sub>R</sub>, ω and N<sub>Rp</sub> (p = H, V) case</figcaption></figure>

Figure 5 shows, similarly to Figures 3 and 4, the SM retrievals analysis in terms of unbiased root mean square error (ubRMSE). The ubRMSE and the bias together cover the information in the root mean square error (RMSE, Entekhabi et al., 2010b). Increasing values of ω yields lower ubRMSE values (from 0.11 - 0.18 for ω = 0 to 0.07 - 0.11 for ω = 0.12). Conversely, larger H<sub>R</sub> tend to increase ubRMSE values and lead to larger differences between the different N<sub>Rp</sub> (p = H, V) parameterizations. This effect becomes less remarkable as ω increases. As it was found for |bias|, N<sub>Rp</sub> = -1 (p = H, V) generally leads to the lowest ubRMSE values for any given values of ω and H<sub>R</sub>.
<figure><img src="image_6.png" /></figure>

Figure 5: Median ubRMSE (all calibration sites: 391 stations) between *in situ* and retrieved SM for each H<sub>R</sub>, ω and N<sub>Rp</sub> (p = H, V) case

**3.2. Calibration of ω and H<sub>R</sub>**

This section presents the second part of the calibration process. In the previous step it was shown that there was a low impact of N<sub>Rp</sub> (p = H, V) on the correlation values between the retrieved and measured SM values for high values of ω.

Furthermore, it was found that the values of |bias| and ubRMSE between the retrieved and measured SM values were generally lower when N<sub>Rp</sub> = -1 (p = H, V). Considering this result, hereinafter, N<sub>Rp</sub> = -1 (p = H, V) was selected to be used in the second step of the calibration process, which consists in the calibration of the H<sub>R</sub> and ω parameters (the subscript "p" for the N<sub>Rp</sub> parameter will be dropped in the following). Two calibration approaches were evaluated in this study for the SM retrieval process: (i) a so-called "globally-constant" calibration, in which case globally-constant values of H<sub>R</sub>, ω and N<sub>R</sub> were estimated, and (ii) a so-
called "IGBP-based" calibration, in which case values of $H_R$, $\omega$ and $N_R$ were estimated for different land cover classes, tabulated by the IGBP classification scheme.

### 3.2.1. Globally-constant calibration

Figure 6 shows the median metrics based on four criteria (R, bias, RMSE and ubRMSE) obtained through a direct comparison between the *in situ* SM measurements and SM retrievals over the calibration sites contained in rather homogeneous pixels. According to correlation results, the increase in $\omega$ leads to an increase in the values of R, whereas the effect of $H_R$ on results is rather low. On the other hand, the bias values are clearly influenced by the values of both $H_R$ and $\omega$. For the case $H_R = 0$, increasing $\omega$ values from 0 to 0.16 leads to a significant decrease in bias values, from ~0 to -0.11 m³·m⁻³. A negative value of bias leads to an underestimation in the retrieved soil moisture as compared to the *in situ* measurements. Increasing the value of $\omega$ or decreasing the value of $H_R$ leads to "dry" SM retrievals. To make an optimal choice in terms of bias reduction, a compromise has to be found between both values of $H_R$ and $\omega$. Regarding RMSE, an increase in both $\omega$ and $H_R$ leads to decreasing errors. Regarding ubRMSE, it was observed that increasing $\omega$ and decreasing $H_R$ tends to minimize this error. The largest impact of $H_R$ on bias, RMSE and ubRMSE was found for high $\omega$ values (0.10 - 0.16).

In order to find a global calibration of the $H_R$ and $\omega$ parameters, a best compromise among all statistical metrics was attempted by visual assessment of Figure 6. Considering mainly two criteria (R and ubRMSE) a value of $\omega = 0.10$ and $H_R = 0.4$ was estimated. Note that this $H_R$ value might cause a slight drying effect (negative SM bias), which could be explained over many sites by the different sampling depth between the L-band space-borne observations and the *in situ* measurements.
<figure><img src="image_7.png" /><figcaption>Figure 6: Median R, bias, RMSE and ubRMSE (all calibration sites: 391 stations) between *in situ* and retrieved SM for each H<sub>R</sub> and ω case (N<sub>R</sub> = -1)</figcaption></figure>

**3.2.2. IGBP-based calibration**

In this section, instead of calibrating a single and global value of the soil and vegetation parameters ω and H<sub>R</sub>, we estimated those parameters for different land cover classes, tabulated by the IGBP classification schema. Metrics were calculated following the same methodology as presented in Section 3.2.1 but now for subsets of *in situ* sites corresponding to each land cover class. Only classes including a representative number of calibration sites were considered, namely: evergreen needle leaf forest, open shrublands, woody savannas, grasslands, croplands, cropland/natural vegetation mosaic and barren or sparsely vegetated. Figures 1S to 7S present the statistic records in terms of R, RMSE, bias, ubRMSE for each class.

The optimal values of ω (ranging from 0.08 to 0.12) were found to be relatively stable for the different IGBP vegetation classes and for the different statistical criteria and they are summarized in Table
2. These values are consistent with the ones computed by Van der Schalie et al. (2016), who found ω = 0.12 using the LPRM algorithm globally. The latter study showed that increasing ω produces increasing R and decreasing ubRMSE values, and a dry bias effect, exactly as we did in this study (see Figures 1S to 7S). A saturation effect was also found for values of ω > 0.12. Moreover, our findings are consistent with the SMAP L4 ω product as well. This product was obtained through calibration with SMOS TB data (De Lannoy et al., 2013, 2014) and shows an average value of ω = 0.09 ± 0.07 depending on the IGBP class, as shown in Table 2. The values of SMAP L4 ω are slightly higher than the ones found in this study, with the exception of the grasslands class, for which SMAP L4 ω = 0.07 against 0.10 in the present study.

In terms of H<sub>R</sub>, all classes presented similar and clear patterns, with exception of open shrublands.
For that latter class, the only clear pattern was found for bias. The best compromise for all metrics was
generally found when H<sub>R</sub> = 0.4 - 0.5 with the exception of some low vegetation classes (open shrublands
and barren or sparsely vegetated). For these latter, the best compromise was obtained with a rather low H<sub>R</sub>
value (~ 0.1) in order to avoid SM overestimation. The best R performances were obtained for croplands
and cropland/natural vegetation; with a median R varying, respectively, from 0.58 to 0.72 and from 0.35 to
0.70. On the other hand, the poorest R value was obtained for the evergreen needle leaf forest and barren
or sparsely vegetation classes (R varying respectively, from 0.2 to 0.4 and from 0.32 to 0.42 respectively).

Based on the analysis made above, the selected values of H<sub>R</sub> for each vegetation class are summarized in Table 2. These values will be referred to as "IGBP-based" values, in contrast to the "globally-constant" values estimated in the previous section. This table also shows the H<sub>R</sub> values which were found by Parrens et al. (2017), based on SMOS TB and Leaf Area Index (LAI) data from MODIS.

There is a good general agreement between the values computed by Parrens et al. (2017) and the
ones found in the present study. As an exception, in the grasslands and cropland/natural vegetation mosaic
classes, Parrens et al. (2017) found lower H<sub>R</sub> values (0.13 and 0.22 respectively, instead of 0.5 for both
vegetation cover types in this study).
<table><caption>Table 2: Calibration of $H_R$ and $\omega$ as a function of the vegetation IGBP classes ("IGBP-based" values)</caption><thead><tr><th>IGBP Class</th><th>Number of filtered stations</th><th>ω</th><th>ω (SMAP L4)</th><th>H<sub>R</sub></th><th>H<sub>R</sub> (Parrens et al., 2017)</th></tr></thead><tbody><tr><td>Evergreen needle leaf forest</td><td>41</td><td>0.10</td><td>0.12</td><td>0.4</td><td>0.35</td></tr><tr><td>Open shrublands</td><td>25</td><td>0.08</td><td>0.11</td><td>0.1</td><td>0.17</td></tr><tr><td>Woody savannas</td><td>16</td><td>0.12</td><td>0.13</td><td>0.4</td><td>0.35</td></tr><tr><td>Grasslands</td><td>214</td><td>0.10</td><td>0.07</td><td>0.5</td><td>0.13</td></tr><tr><td>Croplands</td><td>63</td><td>0.12</td><td>0.12</td><td>0.4</td><td>0.17</td></tr><tr><td>Cropland/Natural vegetation mosaic</td><td>23</td><td>0.12</td><td>0.15</td><td>0.5</td><td>0.22</td></tr><tr><td>Barren or sparsely vegetated</td><td>3</td><td>0.12</td><td>-</td><td>0.1</td><td>0.02</td></tr></tbody></table>

### 3.3. Performance analysis

The calibration process, presented in the above section, was performed over a selection of *in situ* stations which were filtered based on criteria defined in Section 2.7 (only 391 stations out of a total of 1001 were selected). The selected stations correspond to SMOS pixels which are rather homogeneous and, as among others selection criteria, where the predominant class covers at least 50% of the L3 pixel.

In the present section, the calibrated values of the soil and vegetation parameters ($\omega$, $H_R$ and $N_R$) are tested. Two datasets were used in the computation of the statistics of this analysis:

(a) the whole collection of *in situ* sites, namely, all the selected *in situ* stations (391, corresponding to rather homogeneous SMOS L3 pixels) used for the calibration process plus all other *in situ* stations (670, corresponding to both rather homogeneous and heterogeneous SMOS L3 pixels), and

(b) exclusively *in situ* sites (279 stations) which were not previously accounted for in the calibration step (these *in situ* sites correspond to rather "heterogeneous" SMOS L3 pixels).
In the performance analysis process, three cases were taken into account (Case (1) and (2))
corresponds to the two "optimized" approaches which have been developed in this study):

• Case (1): SM retrievals using globally-constant calibrated values, namely $\omega = 0.10$, $H_R = 0.4$ and $N_R = -1$.

• Case (2): SM retrievals using IGBP-based calibrated values, namely the calibrated values of soil roughness and $\omega$ which are dependent of the IGBP classes, as given in Table 2 and computed following equation 12.

• Case (3): the original SMOS L3 SM product.

• Case (4): SM retrievals over homogeneous pixels, as done in Case (1) and (2), but using the model parameters of the SMOS L3 algorithm, namely:

o Forest class: $\omega = 0.06$ and $H_R = 0.3$

o Other classes: $\omega = 0$ and $H_R = 0.1$

Cases (1) (2) and (4) are thus based on SM retrievals under the consideration of homogeneous pixels. In those cases, SM and $\tau_{NAD}$ retrievals were performed over the whole pixel rather than over the fraction designated as either low vegetation or forest. Note that this approach is similar to the one considered in the AMSR-E (Owe et al., 2008), LPRM and SMAP level 2 SM algorithms.

The results are reported in Table 3 in terms of statistical criteria. It can be seen that the obtained results for configurations (a) and (b) are rather similar. This shows that our results are relatively independent on the selection of the *in situ* sites used in the calibration steps. Taking into account the configuration (a), slight differences between Case (1) and Case (2) were found, mainly in terms of R and bias values ($R = 0.60$, $bias = -0.023 \text{ m}^3\cdot\text{m}^{-3}$ and $R = 0.61$, $bias = -0.019 \text{ m}^3\cdot\text{m}^{-3}$ respectively). This result shows that the use of constant values of the soil and vegetation parameters $\omega$, $H_R$ and $N_R$ is an interesting and simple alternative, as considering the dependence of these parameters on the IGBP classification do not lead to significant improvement in the results.
Compared to the SMOS L3 SM product, results for both approaches (1) and (2) show an improvement in all metrics. In particular, considering case (2) R improves by 0.07, and |bias| and ubRMSE errors decrease by 0.015 and 0.008 m³·m⁻³ respectively. However, this improvement cannot be explained by the use of homogeneous pixels, as Case (4) leads to poorer R (0.44) and ubRMSE (0.086 m³·m⁻³) than SMOS L3. The obtained statistical results highlight the impact of using the calibrated values obtained in Cases (1) and (2), as all metrics are poorer for Case (4). The inter-comparison of bias for Cases (3) and (4) is particularly interesting. The difference between these approaches lies fundamentally in the consideration of pixel heterogeneity. The median bias given by (3) is -0.034 m³·m⁻³, meaning the SMOS L3 SM product underestimates SM. Nonetheless, the same approach under the assumption of "homogeneity" (4) leads to a wet bias equal to 0.028 m³·m⁻³.

Contrary to Case (4), the SMOS L3 SM retrieval algorithm does not consider the total TB contribution in the SM retrieval. As it was noted in Section 2.1.1, in both the SMOS L2 and L3 algorithms, TB is modelled over the forest fraction ($TB_{FFO}$) as a function of ECMWF SM as auxiliary information, when the retrieval is performed over the nominal fraction ($TB_{FNO}$). The well-known ECMWF SM overestimation compared to *in situ* SM values (Albergel et al., 2012) is causing a $TB_{FFO}$ underestimation (Ulaby et al., 1981-1986). This underestimation may lead, by compensation, to an increase in the simulated value of $TB_{FNO}$ during the inversion process. Considering that the SMOS L3 SM retrieval is performed mainly over the FNO, the resulting SM tends to decrease. Such an issue has been revealed over the Valencia Anchor Station site by Wigneron et al., (2012). This could partly explain the dry bias obtained by the SMOS L3 SM product (Case (3)) over some pixels including forested areas, despite the fact that assuming $\omega = 0$ (FNO) or $\omega = 0.06$ (FFO) instead of higher $\omega$ values (as the ones found in this study) leads to wetter SM retrievals.

Table 3: Median statistical metrics for each case (considering all stations (a) and all stations except the ones used in calibration (b))

| a | b |
<table><thead><tr><th>CASE</th><th>R</th><th>bias (m<sup>3</sup>·m<sup>-3</sup>)</th><th>ubRMSE (m<sup>3</sup>·m<sup>-3</sup>)</th><th>R</th><th>bias (m<sup>3</sup>·m<sup>-3</sup>)</th><th>ubRMSE (m<sup>3</sup>·m<sup>-3</sup>)</th></tr></thead><tbody><tr><td>(1) Globally-constant values of ω, H<sub>R</sub> and N<sub>R</sub></td><td>0.60</td><td>-0.023</td><td>0.062</td><td>0.59</td><td>-0.022</td><td>0.061</td></tr><tr><td>(2) IGBP-based values of ω, H<sub>R</sub>, N<sub>R</sub></td><td>0.61</td><td>-0.019</td><td>0.062</td><td>0.62</td><td>-0.019</td><td>0.061</td></tr><tr><td>(3) SMOS L3 SM</td><td>0.54</td><td>-0.034</td><td>0.070</td><td>0.54</td><td>-0.037</td><td>0.069</td></tr><tr><td>(4) Homogeneous (SMOS L3 SM ω, H<sub>R</sub>, N<sub>R</sub>)</td><td>0.44</td><td>0.028</td><td>0.086</td><td>0.39</td><td>0.035</td><td>0.089</td></tr></tbody></table>

To better evaluate the improvement obtained from the use of the IGBP-based approach (2) over the SMOS L3 SM product (3), Table 4 shows the percentage of *in situ* stations that performs best in each case in terms of maximum values of R and minimum values of |bias| and ubRMSE. The IGBP-based "optimized" approach is the best option for 84.4%, 57.0% and 86.1% of the *in situ* stations in terms of, respectively R, bias and ubRMSE values.

<table><caption>Table 4: Percentage of *in situ* stations where the best statistical metrics were obtained for each case (considering all stations (a) and all stations except the ones used in the calibration step (b))</caption><thead><tr><th rowspan="2">CASE</th><th colspan="3">a</th><th colspan="3">b</th></tr><tr><th>R</th><th>bias (m<sup>3</sup>·m<sup>-3</sup>)</th><th>ubRMSE (m<sup>3</sup>·m<sup>-3</sup>)</th><th>R</th><th>bias (m<sup>3</sup>·m<sup>-3</sup>)</th><th>ubRMSE (m<sup>3</sup>·m<sup>-3</sup>)</th></tr></thead><tbody><tr><td>(2) IGBP-based values of ω, H<sub>R</sub>, N<sub>R</sub></td><td>84.4%</td><td>57.0%</td><td>86.1%</td><td>79.1%</td><td>56.4%</td><td>85.3%</td></tr><tr><td>(3) SMOS L3 SM</td><td>15.6%</td><td>43.0%</td><td>13.9%</td><td>20.9%</td><td>43.6%</td><td>14.7%</td></tr></tbody></table>

## 4. Conclusions

The main objective of this study was to calibrate the parameters which account for two crucial effects in the SM retrieval at L-band: soil roughness (in terms of H<sub>R</sub>, N<sub>RH</sub> and N<sub>RV</sub> values) and vegetation (in terms of effective scattering albedo, ω). A large range of values of the latter parameters were used in order to retrieve soil moisture (SM) and vegetation optical depth (τ<sub>NAD</sub>) over a large number of sites
543 worldwide. The present study was carried out considering an optimized retrieval approach which is different
544 from that used in the SMOS L3 SM retrieval algorithm. In this approach, pixels were assumed to be
545 homogeneous (SM was retrieved over the whole SMOS pixel), while heterogeneity is accounted for in the
546 SMOS L3 algorithm. The latter accounts for the surface fraction of the main cover types (bare soil and low
547 vegetation, forest, water, urban, etc.) within each SMOS footprint depending on the incidence angles of the
548 observations. However, the retrieval is only made over one fraction: either the nominal or forest fraction in
549 some specific cases.

550 Long term SM retrievals were compared to *in situ* measurements obtained from the International
551 Soil Moisture Network (ISMN) over the period 2011 – 2013, and were evaluated using different metrics
552 (R, bias and ubRMSE). Note that, as the focus of this study was the optimization of the SM retrievals, the
553 retrieval results concerning the τ<sub>NAD</sub> parameter were not analyzed here. They will be presented and
554 discussed in future studies. Some first results are described in Fernandez-Moran et al. (2017).

555 Finding the optimal retrieval values of the vegetation and soil parameters for the SM retrievals
556 requires finding a compromise considering all the statistical metrics, i.e. the optimization of all of them
557 (with a focus on R and ubRMSE). Performances of the SM retrievals, evaluated in terms of R, bias and
558 ubRMSE, showed a high sensitivity of SM to ω and were found optimum for high ω values (ω ~ 0.10). On
559 the contrary, the calibration of H<sub>R</sub> required compromise between the performances obtained in terms of
560 ubRMSE (lower for low H<sub>R</sub> values) and of |bias| (lower for larger H<sub>R</sub> values). It was found that increasing
561 ω and decreasing H<sub>R</sub> values led to drier SM retrievals. However, due to the different sampling depths of the
562 *in situ* measurements (0 - 5 cm) and of the SMOS L-band observations (~ 0 – 3 cm), bias was considered
563 as a second order criterion in the assessment of the results. Globally, a value of ω = 0.10, H<sub>R</sub> = 0.4 and N<sub>R</sub>
564 = -1 (p = H, V) was found optimum at global scale. This finding is consistent with the work of Van der
565 Schalie et al. (2016), who globally obtained ω equal to 0.12 after applying the Land Parameter Retrieval
566 Model (LPRM) and evaluating SM retrievals against model datasets as MERRA-Land (MERRA) and ERA-
567 Interim/Land (ERA). The latter study has also shown the low influence of soil roughness on the correlation
statistics in terms of SM retrievals when $\omega = 0.12$. Furthermore, the global map of the effective scattering albedo provided by the SMAP L4 product is in agreement with the findings of this study ($\omega = 0.09 \pm 0.07$).
On the contrary, studies by Konings et al. (2016) found lower values ($\omega = 0.02 - 0.06$) and the current set of effective scattering albedo in the SMOS L3 SM product is $\omega = 0.06 - 0.08$ for forest and $\omega = 0$ for the rest of the cover types.

All *in situ* sites used in this study were classified using the International Geosphere-Biosphere Programme (IGBP) land cover classification scheme, and then specific calibrated values of $H_R$, $N_{Rp}$ ($p = H$, V) and $\omega$ were proposed for each class. Over the different IGBP classes, it was found that $\omega$ values are in a narrow range, from 0.08 to 0.12, whereas $H_R$ ranged from 0.1 to 0.5. It is noticeable that the low $H_R$ (~ 0.1) was associated to low vegetation cover types (open shrublands and barren or sparsely vegetated covers) whereas higher values, ranging from 0.4 to 0.5, were linked to the rest of IGBP classes. These results are in good agreement with the global map of $H_R$ obtained by Parrens et al. (2017), who calibrated this parameter using SMOS retrievals and Leaf Area Index (LAI) data from MODIS as auxiliary data.

The calibrated soil roughness and effective scattering albedo values were used in an analysis *a posteriori*. This analysis was based on a comparison between the SM retrievals using the calibrated values and the SM data measured at the *in situ* sites. To evaluate the robustness of the calibration step two configurations were considered: a comparison using (a) all *in situ* sites and (b) all sites, excluding the ones (rather homogeneous) considered in the calibration step. Results obtained for both configurations (a) and (b) were generally very similar, which indicates the robustness of the calibrated values.

This analysis exercise confirmed that using either globally-constant or IGBP dependent parameters, there was improvement over the SMOS L3 SM product in terms of SM retrieval accuracies, as compared to the *in situ* SM data ($R = 0.61$, bias = -0.019 m³·m⁻³ and ubRMSE = 0.062 for the IGBP-based calibration; $R = 0.54$, bias = -0.034 m³·m⁻³ and ubRMSE = 0.070 for the SMOS L3 SM product). By comparing results obtained for the SMOS L3 SM product and the SMOS L3 SM product under the homogeneous approach
we could show that this improvement could not be explained by the use of homogeneous pixels, but mainly by the use of the new model parameter calibration that we computed in this study. Nonetheless, the drying effect of the SMOS L3 SM algorithm retrieval due to the "heterogeneity" approach was demonstrated: considering the same model parameter calibration, the bias varied from -0.034 m³·m⁻³ when using the SMOS L3 SM algorithm (heterogeneous pixels) to 0.028 m³·m⁻³ when the homogeneous approach was used.

The findings presented in this study have important implications for the calibration of soil roughness and vegetation in the current Level 2 and 3 algorithms of the SMOS mission with potential implications for SMAP as well. An alternative SMOS product (referred to SMOS-INRA-CESBIO, or SMOS-IC for short) (Fernandez-Moran et al., 2017) based on the homogeneous retrieval approach and the new calibrated parameters presented here has been developed by Institut National de la Recherche Agronomique (INRA) and Centre d'Etudes Spatiales de la BIOsphère (CESBIO). One of the main advantages of this approach is its simplicity leading to the development of an efficient processor, capable of processing one year of data over a few hours. The dependence on the auxiliary data has also been reduced as compared to the L3 algorithm. Specifically, SMOS-IC does not use MODIS LAI and ECMWF SM data, whose tendency to SM overestimation is well-known (Albergel et al., 2012). Consequently, the products from the SMOS-IC approach are more aligned to SM products derived from other space-borne sensors (such as SMAP and AMSR-E), where the retrieval is done under the homogeneity assumption (Entekhabi et al., 2014; Ashcroft & Wentz et al., 2000, Owe et al., 2008). Future studies focusing on the global-scale validation of this product would be helpful to better understand its strengths and possible shortcomings.

## Acknowledgements

The authors would like to thank the Terre Océan Surfaces Continentales et Atmosphère (TOSCA) CNES program and the European Space Agency (ESA) for funding this study. The authors acknowledge CATDS for the SMOSL3 dataset (http://catds.ifremer.fr) and the cooperation of the different soil moisture in situ networks in the International Soil Moisture Network (ISMN) project.
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