# An assessment of L-band surface soil moisture products from SMOS and SMAP in the tropical areas

Hongliang Ma, Xiaojun Li, Jiangyuan Zeng, Xiang Zhang, Jianzhi Dong, Nengcheng Chen, Lei Fan, Morteza Sadeghi, Frédéric Frappart, Xiangzhuo Liu, et al.

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► To cite this version:

Hongliang Ma, Xiaojun Li, Jiangyuan Zeng, Xiang Zhang, Jianzhi Dong, et al. An assessment of L-band surface soil moisture products from SMOS and SMAP in the tropical areas. Remote Sensing of Environment, 2023, 284, pp.113344. 10.1016/j.rse.2022.113344. hal-03871062

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Distributed under a Creative Commons Attribution 4.0 International License
An assessment of L-band surface soil moisture products
from SMOS and SMAP in the tropical areas

Hongliang Ma<sup>a,b</sup>, Xiaojun Li<sup>b</sup>, Jiangyuan Zeng<sup>c</sup>, Xiang Zhang<sup>a,d,e</sup>, Jianzhi Dong<sup>f,m</sup>, Nengcheng

Chen<sup>a,d,e</sup>, Lei Fan<sup>g</sup>, Morteza Sadeghi<sup>h</sup>, Frédéric Frappart<sup>b</sup>, Xiangzhuo Liu<sup>b</sup>, Mengjia Wang<sup>i</sup>,

Huan Wang<sup>b,j,k</sup>, Zheng Fu<sup>k</sup>, Zanpin Xing<sup>l</sup>, Philippe Ciais<sup>k</sup>, Jean-Pierre Wigneron<sup>b,*</sup>

6

a State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing,

Wuhan University, Wuhan 430079, China

b INRAE, UMR1391 ISPA, Université de Bordeaux, F-33140, Villenave d'Ornon, France

c State Key Laboratory of Remote Sensing Science, Aerospace Information Research Institute,

Chinese Academy of Sciences, Beijing 100101, China

d National Engineering Research Center of Geographic Information System, China University of

Geosciences (Wuhan), Wuhan, 430074, China

e School of Geography and Information Engineering, China University of Geosciences (Wuhan),

Wuhan, 430074, China

f Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of

Technology, Cambridge, MA 02142, USA

g Chongqing Jinfo Mountain Karst Ecosystem National Observation and Research Station, School

of Geographical Sciences, Southwest University, Chongqing 400715, China

h Saint Anthony Falls Laboratory, Department of Civil Environmental and Geo-Engineering,

University of Minnesota, Minneapolis, MN 55414, USA

i State Key Laboratory of Remote Sensing Science, Faculty of Geographical Science, Beijing
23 Normal University, Beijing 100875, China

24 j College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

25 k Laboratoire des Sciences du Climat et de l'Environnement, LSCE/IPSL, CEA-CNRS-UVSQ,
26 Université Paris-Saclay, Gif-sur-Yvette 91191, France

27 l State Key Laboratory of Cryospheric Sciences, Northwest Institute of Eco-Environment and Resources, State Key Laboratory of Cryospheric Sciences, Chinese Academy of Sciences,
28 Lanzhou 730000, China

30 m Institute of Surface-Earth System Science, Tianjin University, Tianjin 300350, China

31

32 *Corresponding Author: J.-P. Wigneron (jean-pierre.wigneron@inrae.fr)

33 Abstract

34 Recently, large efforts have been made to develop surface soil moisture (SSM) products
35 based on observations from passive microwave L-band satellites at the global scale. Despite vast
36 previous efforts to assess satellite SSM products based on *in situ* data, the performance of L-band
37 SSM products remains still little known over the tropical areas including the rainforests. To close
38 this knowledge gap, a comprehensive evaluation of five L-band SSM products from the Soil
39 Moisture and Ocean Salinity (SMOS) and Soil Moisture Active Passive (SMAP) satellites,
40 including SMOS-IC, SMAP SCA-V, DCA, and MTDCA, as well as the recently developed SMAP
41 INRAE-BORDEAUX (SMAP-IB) was conducted in tropical areas from 2015 to 2020. The
42 investigation was implemented by using *in situ* observations, and expanded by the Triple
43 Collocation Analysis (TCA) and double instrumental variable (IVd) methods. The results revealed
that all the five L-band SSM products show a good capacity to estimate SSM in most moderately vegetated areas of the tropical areas while they exhibit some uncertainties in dense vegetation (e.g., rainforests). The SSM climatology of the five L-band products in rainforests agreed generally well with that of *in situ* measurements especially for SMOS-IC (R = 0.75), followed by SMAP-IB (R = 0.72). Notably, the newly developed SMAP-IB generally shows satisfactory performance in the tropics with the highest R of 0.73 and the smallest unbiased root mean square difference (ubRMSD) of 0.041 m³/m³ from the study based on *in situ* SM data, and R of more than 0.81 from the combined TCA/IVd method in most vegetation conditions. SMAP-DCA SSM demonstrates comparable performance to SMAP-SCA-V (R = 0.66) from the *in situ* based analysis. This study is expected to deepen our understanding on the skill of L-band SSM products in tropical areas and further promote possible upgrades in algorithms and applications in these regions.

**Key words:** Assessment, Soil Moisture, SMOS, SMAP, Tropics, Rainforests

## 1. Introduction

Surface soil moisture (SSM) has been recognized as a key parameter in land-atmosphere interactions, as it controls the process of energy, water, and carbon exchange (Humphrey et al., 2021; Seneviratne et al. 2010). Over the past two decades, a lot of efforts have been made in developing/improving satellite SSM products. Passive microwave observations at L-band are expected to provide more accurate SSM information benefiting from their stronger penetration capacity, especially in vegetated areas, compared to those at relatively higher frequencies (e.g., C- or X-band) (Wigneron et al., 2017; Zeng et al., 2022a; Zhao et al., 2021). Dedicated for global SSM mapping at L-band, the Soil Moisture and Ocean Salinity (SMOS) and Soil Moisture Active
Passive (SMAP) missions have been successively launched (Entekhabi et al., 2010a; Kerr et al., 2010). Based on brightness temperature (TB) observations from the two L-band satellites, in parallel to the mission official SSM products (e.g., SMAP DCA and SCA-V, SMOS-L2 and -L3), new L-band SSM products have been developed. For instance, the multi-temporal dual channel algorithm (MTDCA) initially developed for the NASA Aquarius sensor (Konings et al., 2016) has been applied to SMAP (Konings et al., 2017). Wigneron et al. (2021) continuously upgraded the newly developed SMOS-IC SSM product derived from the SMOS observations which is less dependent on auxiliary data (i.e., modelled soil moisture and optical vegetation indices) compared to the official SMOS products (e.g., SMOS-L2 and -L3 algorithms). More recently, based on an algorithm similar to SMOS-IC, a new L-band SSM product named SMAP-IB (SMAP-INRAE-BORDEAUX) was proposed by Li et al. (2022).

The evaluation of satellite SSM products is of great importance for the algorithm/product refinements. Driven by these needs, extensive evaluation or comparison studies of various SSM products have been conducted at both global (Al-Yaari et al., 2014; Chan et al., 2016; Colliander et al., 2017a, 2017b) and regional scales (Chen et al., 2017; Zeng et al., 2015, 2022) by using *in situ* observations (Cui et al., 2017; Dorigo et al., 2015; Zeng et al., 2016) or mathematical approaches (e.g., Triple Collocation Analysis, TCA and Three-Cornered Hat, TCH, etc.) (Stoffelen, 1998; Chen et al., 2018a; Kim et al., 2018; Liu et al., 2021a; Xu et al., 2021a). A brief summary of some recent evaluation studies of satellite SSM products is given in Table 1.
<table><caption>Table 1. Summary of recent (over the last three years) assessment/comparison studies of remotely sensed SSM products, involving assessment methods, study area/scale, satellite frequency of SSM products and key findings.</caption><thead><tr><th>Reference</th><th>Evaluation methods</th><th>Scale</th><th>Satellite frequency</th><th>Key findings</th></tr></thead><tbody><tr><td>Chan et al., 2018, Chen et al., 2018b; Colliander et al., 2021; Wigneron et al., 2021; Zhang et al., 2019, etc.</td><td>In situ/Model</td><td>Global/Regional</td><td>L-band</td><td>SMOS-IC V2 SSM is closer to the reference SSM values (ERA5-Land and ISMN SM) than SMOS-IC V105 SSM; The performance of the enhanced passive SMAP 9 km L2/L3 product is demonstrated to be equivalent to that of the standard 36 km L2/L3 product; The high-resolution (3 km) SMAP SSM combining Sentinel-1 and SMAP Level 4 (9 km) SM with complete spatio-temporal coverage meet the expected accuracies; The underestimation of surface temperature used in the SMAP SSM retrieval algorithm contribute to the bias of SMAP passive, active-passive, and enhanced passive products.</td></tr><tr><td>Al-Yaari et al., 2019; Beck et al., 2021; Gruber et al., 2019; Ma et al., 2019, etc.</td><td>In situ</td><td>Global</td><td>Multiple frequencies</td><td>SMAP, SMOS-IC, ESA CCI products perform slightly better than other satellite SSM products at similar spatial resolution (~25 km), in which SMOS-IC shows improvements compared to SMOS-L3; Soil Wetness Index (SWI) derived from SMAP enhanced product (~9 km) shows promising performance; ESA CCI SSM has a good skill benefiting from blending both active and passive satellite observations.</td></tr><tr><td>Cui et al., 2017; Wang et al., 2021b; Xing et al., 2021; Zeng et al., 2022a, etc.</td><td>In situ</td><td>Regional</td><td>Multiple frequencies</td><td>The bias of temperature adopted in SMAP SSM is consistent with the bias of corresponding SSM products; ESA CCI shows satisfactory accuracy in the Tibetan Plateau, and its bias is dependent on GLDAS Noah SSM; The performances of SMOS-IC/L3 are obviously affected in RFI-contaminated areas; Seasonal SSM variations of newly developed SMAP DCA agree well with ground observations.</td></tr><tr><td>Chen et al., 2018; Kim et al., 2020a; Kim et al., 2018; Wu et al., 2021; Zhang et al., 2021, etc.</td><td>TCA and in situ</td><td>Global</td><td>Multiple frequencies/ L-band</td><td>Most satellite products have difficulties in retrieving SSM over arid and polar regions and ASCAT shows higher R values over tropical, savannas; Precipitation better explains the temporal variability of satellite SSM (ASCAT and SMAP) errors than the vegetation proxy LAI; Over densely vegetated areas, remotely sensed SSM can provide better quality than model-based SSM products, and error metrics derived from TCA are in line with those from in situ; Satellite SSM performs better in moderately vegetated areas than in other vegetation conditions.</td></tr><tr><td>Kumar et al., 2018; Liu et al., 2021a, etc.</td><td>Other mathematical methods</td><td>Global/Regional</td><td>Multiple frequencies</td><td>When evaluating satellite SSM, TCH can be an optional solution compared to TCA although a certain degree of bias exists; Information Theory (IT) can measure the stochasticity, level of regularity and randomness in satellite SSM time series without ancillary data.</td></tr></tbody></table>

GLDAS: Global Land Data Assimilation System.
All the previous evaluation activities contributed to enriching the understanding of current remotely sensed SSM products and provided more robust guidelines for specific applications. It has been clearly indicated that L-band microwave SSM products have stronger capabilities to estimate SSM compared to microwave observations at higher frequencies (Wigneron et al., 2021; Ma et al., 2019).

However, some questions relative to the capabilities of satellite SSM products have not still been fully addressed. First, suffering from scarce ground observations, only a few studies pay particular attention to tropical areas. As one hot-spot area, the tropics include the rainforests which are strongly linked to the global carbon cycle and climate change (Chen et al., 2021; Mitchard, 2018). Moreover, tropical areas are also vulnerable to droughts where applications of SM monitoring are highly significant (Agutu et al., 2017; Zhang et al., 2017; Gu et al., 2019). Thus, it is essential to obtain a comprehensive understanding of current satellite SSM datasets in tropical areas, especially for L-band SSM products, which are supposed to have stronger monitoring capabilities in dense forests compared to higher frequency ones. Second, most existing studies concentrating on L-band SSM products have paid more attention to a few well-known products (e.g., SMOS-IC/L3 and SMAP-SCA-V) (Ma et al., 2019; Zeng et al., 2022a), while the performance of the lately developed SMAP-DCA and SMAP-IB SSM products has not yet been fully investigated. Two recent studies have partially addressed this issue. Wang et al. (2021b) have evaluated SMAP-DCA and SMOS-IC V2 SSM products against *in situ* measurements from three networks in cold and arid regions of China. Li et al. (2022) have made a comprehensive evaluation of several L-band SSM products by comparison with ground measurements from the International Soil Moisture Network (ISMN) at a global scale (Dorigo et al., 2021), and only five *in situ* sites in
tropics are used in their study. Thus, the performance of current L-band SSM products in the
tropical area including rainforests still remains largely unknown and deserves to be further
investigated.

Recently, the L-band SMAP observations were demonstrated to be capable of retrieving SSM
in forest ecosystems with moderate biomass (Ayres et al., 2021; Colliander et al., 2020). But SSM
retrievals from satellite observations are generally considered problematic over dense forest
regions (Kim et al., 2020a), especially for rainforests (e.g., Congo and Amazon basins). However,
investigations of the accuracy of L-band SSM products in tropical rainforests are mainly limited
by the lack of *in situ* observations. To overcome this limitation, we used *in situ* sites from the
FLUXNET network (Pastorello et al., 2020). As the time period of the used FLUXNET SM data
does not correspond well to the availability of the SMOS (since 2010) and SMAP (since 2015)
observations, we considered the climatology (mean seasonal cycle) error of SSM, which generally
dominates the total errors of the SSM products (Dong et al., 2020a). We extended the analysis to
*in situ* tropical ISMN datasets, but the ISMN sites are mostly limited to moderately vegetated
areas.

Nonetheless, both the ISMN data in tropical areas and FLUXNET data in rainforests
correspond to local observations, which may bring some uncertainties in the assessment due to
spatial mismatch between single-point measurement and satellite footprint (Jackson et al., 2010;
Ma et al., 2019; Zeng et al., 2015). On the other hand, as mentioned in Table 1, Triple Collocation
Analysis (Stoffelen, 1998) has been widely adopted to evaluate SSM products at regional or global
scales without requiring ground truth data (Chen et al., 2018; Gruber et al., 2016b; McColl et al.,
2014). Although the potential dependence of the evaluated SSM products may hinder the
reliability of the TCA, this approach may provide estimates of the random error variance and correlations of the SSM products throughout the tropics. In addition, as TCA requires three independent SSM products, hardly being achieved in practice. Su et al (2014) developed a single-instrumental variable (IVs) method which enables a TCA assessment utilizing only two independent products. More recently, Dong et al (2019, 2020) improved IVs by including a second instrument variable and proposed a new ‘double instrumental variable’ (IVd) approach. This approach, which is less sensitive to bias and could reduce sampling errors compared to IVs, has been demonstrated to provide a good performance at the global scale in terms of precipitation products (Dong et al., 2019). This newly proposed method has been rarely tested for satellite SSM products (Kim et al., 2020b). In this context, these mathematical methods (TCA and IVd) may provide opportunities to make a more robust evaluation of the satellite SSM products in the tropical areas.

Motivated by the issues and opportunities concerning data and evaluation approaches mentioned above, five L-band satellite SSM products including SMOS-IC, SMAP-SCA-V, SMAP-DCA, SMAP-MTDCA and SMAP-IB, were evaluated in the tropical areas. This study focuses on the following objectives: 1) assessing five L-band SSM products in tropical areas by considering the inherent skills of the original SSM sequence with respect to *in situ* observations; 2) investigating the climatology of the L-band SSM products in tropical rainforests; 3) analyzing the influence of precipitation, vegetation and soil water holding capacity (SWHC) on the L-band SSM products by using TCA and IVd. In Section 2, a brief description of the study area (i.e., tropical areas) is presented. Section 3 introduces the L-band SSM datasets and the used *in situ* observations and ancillary data. Section 4 covers all the evaluation approaches employed in this
151 study. Results are showed and discussed in Section 5 and Section 6, respectively. Our conclusions
152 are given in Section 7.

153 **2. Study area**

154 This study focused on the tropical area (23° N~23° S) (Figure 1), which covers the main
155 rainforests in the world and is characterized by more precipitation and denser vegetation compared
156 to other areas. In Fig. 1, the spatial distributions of yearly precipitation and SMOS-IC vegetation
157 optical depth (VOD, used here as a vegetation index illustrating the vegetation density) show good
158 consistency in the whole tropical areas. As for the distributions of *in situ* observations, around 60
159 sparse ISMN sites in the tropics and 8 FLUXNET stations in rainforests are presented and more
160 detailed information will be given in Section 3.4.
<figure><img src="image_3.png" /><figcaption>Figure 1. Tropical areas considered in this study and spatial distribution of the ground observations. The legend of the color map was derived from the MODIS IGBP global land cover classes (Friedl et al., 2010).</figcaption></figure>
161 **3. Datasets**

162 **3.1. Passive L-band SSM products**

163 Main information of the five L-band passive SSM products evaluated in this study is
164 summarized in Table 2. Among the five SSM products, one is derived from SMOS, and the other
165 four are from SMAP. For more elaborate information, the reader can refer to the Appendix A.

166 With regard to the retrieval algorithms of these SSM products, an overview of their main
167 differences is given in Table 3. All the listed L-band SSM retrieval algorithms apply the
168 zeroth-order radiative transfer equations (i.e., the so-called τ-ω model) (Mo et al., 1982) as the
169 forward model. The measured passive TB represents the natural microwave emission of the land
170 surfaces (Li et al., 2021a; Wang et al., 2021a; Gao et al., 2021), comprising the emission
171 components of the soil and of the overlying vegetation canopy. As shown in Table 3, the main
172 differences in these SSM retrieval algorithms can be related to (i) the retrieval method and (ii)
173 the parameterization of the soil and vegetation parameters (e.g., soil dielectric constant, soil
174 roughness, effective soil temperature, vegetation temperature, and effective scattering albedo).
175 For instance, in SMAP-DCA, the constraints used in the VOD (referred to as "τ" in the equations)
176 and SSM were improved compared to those used in SMAP-SCA-V. The temporal information
177 has been specifically considered in the SMAP-MTDCA and the SMAP-IB algorithm.

178 The new SMAP-IB algorithm is based on the L-MEB model inversion applied to the SMAP
179 dual-polarized TB. Similar to the SMOS-IC algorithm developed for SMOS, the SMAP-IB
180 algorithm provides a new SSM product which is independent of optical vegetation indices
181 (especially for densely vegetated areas) and of modelled SM data (Li et al., 2022).

182
183

184

<table><caption>Table 2. Key features of the evaluated L-band satellite SSM products</caption><thead><tr><td>SSM Products</td><td>Version</td><td>Sampling</td><td>Period available</td><td>Method/Algorithms</td><td>Reference</td></tr></thead><tbody><tr><td>SMAP-SCA-V</td><td>V7</td><td>36 km, daily</td><td>01/04/2015-present</td><td>SCA-V</td><td>(O'Neill et al., 2015)</td></tr><tr><td>SMOS-IC</td><td>V2</td><td>25 km, daily</td><td>12/01/2010-present</td><td>L-MEB</td><td>(Wigneron et al., 2021)</td></tr><tr><td>SMAP-DCA</td><td>V7</td><td>36 km, daily</td><td>01/04/2015-present</td><td>DCA</td><td>(Chaubell et al., 2020)</td></tr><tr><td>SMAP-MTDCA</td><td>V5</td><td>36 km, daily</td><td>01/04/2015-present</td><td>MTDCA</td><td>(Konings et al., 2017)</td></tr><tr><td>SMAP-IB</td><td>V1</td><td>36 km, daily</td><td>01/04/2015-present</td><td>L-MEB</td><td>(Li et al., 2022)</td></tr></tbody></table>

185
<table><caption>Table 3. Main differences in the retrieval algorithms of the L-band SSM products evaluated in this study</caption><thead><tr><th>Algorithm</th><th>SMAP-SCA-V</th><th>SMOS-IC</th><th>SMAP-DCA</th><th>SMAP-MTDCA</th><th>SMAP-IB</th></tr></thead><tbody><tr><td>TB observations</td><td>SMAP V-pol TB at a fixed incidence angle of 40° (mono-angular)</td><td>Multi-angular and dual-polarized SMOS L3 TB (multi-angular)</td><td>SMAP dual-polarized TB at a fixed incidence angle of 40° (mono-angular)</td><td>SMAP dual-polarized TB at a fixed incidence angle of 40° (mono-angular)</td><td>SMAP dual-polarized TB at a fixed incidence angle of 40° (mono-angular)</td></tr><tr><td>Soil roughness modeling</td><td>Q/H model (Wang and Choudhury, 1981);<br>H<sub>R</sub> = f (IGBP);<br>Q<sub>R</sub> = 0;<br>N<sub>RP</sub> = 2 (P = H, V)</td><td>Q/H model (Wang and Choudhury, 1981);<br>H<sub>R</sub> derived from Parrens et al. (2016)<br>N<sub>RP</sub> = -1 (P = H, V) for low vegetation;<br>N<sub>RV</sub> = -1, N<sub>RH</sub> = 1 for forests;<br>Q<sub>R</sub> = 0</td><td>Q/H model (Wang and Choudhury, 1981);<br>H<sub>R</sub> is firstly retrieved with SSM in the case of MODIS NDVI VWC and SMAP data as input in τ-ω<br>Q<sub>R</sub> = 0.1771 H<sub>R</sub>;<br>N<sub>RP</sub> = 2 (P = H, V)</td><td>Q/H model (Wang and Choudhury, 1981);<br>Temporal constant roughness root-mean-square height of 0.13;<br>N<sub>RP</sub> = 0 (P = H, V);<br>Q<sub>R</sub> = 0</td><td>Q/H model (Wang and Choudhury, 1981);<br>H<sub>R</sub> derived from Parrens et al. (2016)<br>N<sub>RP</sub> = -1 (P = H, V) for low vegetation;<br>N<sub>RV</sub> = -1, N<sub>RH</sub> = 1 for forests;<br>Q<sub>R</sub> = 0</td></tr><tr><td>Effective soil temperature</td><td>T<sub>G</sub> = f (T<sub>soil surfaces</sub>, T<sub>soil depth</sub>), T<sub>soil surfaces</sub>, T<sub>soil depth</sub> from GEOS-5</td><td>T<sub>G</sub> = f (T<sub>soil surfaces</sub>, T<sub>soil depth</sub>), T<sub>soil surfaces</sub>, T<sub>soil depth</sub> from ECMWF</td><td>T<sub>G</sub> = f (T<sub>soil surfaces</sub>, T<sub>soil depth</sub>), T<sub>soil surfaces</sub>, T<sub>soil depth</sub> from GEOS-5</td><td>T<sub>G</sub> = f (T<sub>soil surfaces</sub>, T<sub>soil depth</sub>), T<sub>soil surfaces</sub>, T<sub>soil depth</sub> from GEOS-5</td><td>T<sub>G</sub> = f (T<sub>soil surfaces</sub>, T<sub>soil depth</sub>), T<sub>soil surfaces</sub>, T<sub>soil depth</sub> from ERA5</td></tr><tr><td>Vegetation temperature</td><td>T<sub>C</sub> = T<sub>G</sub></td><td>T<sub>C</sub> = ECMWF skin temperature</td><td>T<sub>C</sub> = T<sub>G</sub></td><td>T<sub>C</sub> = T<sub>G</sub></td><td>T<sub>C</sub> = ERA5 skin temperature</td></tr><tr><td>Vegetation modeling</td><td>τ-ω (Mo et al., 1982);<br>τ = b · VWC, b = f (IGBP),<br>VWC is derived from MODIS NDVI climatology</td><td>τ-ω (Mo et al., 1982);<br>τ is simultaneously retrieved with SSM</td><td>τ-ω (Mo et al., 1982);<br>τ is simultaneously retrieved with SSM</td><td>τ-ω (Mo et al., 1982);<br>τ is simultaneously retrieved with SSM</td><td>τ-ω (Mo et al., 1982);<br>τ is simultaneously retrieved with SSM</td></tr><tr><td>Effective scattering albedo (ω)</td><td>ω<sub>V</sub> = ω<sub>H</sub> = ω;<br>ω = f (IGBP)</td><td>ω is calibrated based on IGBP (Fernandezmoran et al., 2017b)</td><td>ω = f (IGBP)</td><td>ω is simultaneously computed with SSM and VOD</td><td>ω is calibrated based on IGBP (Fernandezmoran et al., 2017b)</td></tr><tr><td>Dielectric mixing model</td><td>Mironov et al. (2009)</td><td>Mironov et al. (2009)</td><td>Mironov et al. (2009)</td><td>Mironov et al. (2009)</td><td>Mironov et al. (2009)</td></tr></tbody></table>

H<sub>R</sub> = roughness parameter; Q<sub>R</sub> = polarization mixing coefficient; N<sub>RP</sub> = roughness parameter accounting for polarization dependency; IGBP: International Geosphere-Biosphere Programme; MODIS: Moderate Resolution Imaging Spectroradiometer; NDVI: Normalized Difference Vegetation Index; T<sub>G</sub> = effective soil temperature; GEOS-5: Goddard Earth Observing System Model, Version 5; ECMWF: European Centre for Medium-Range Weather Forecasts; ERA5: ECMWF Reanalysis version 5; T<sub>C</sub> = vegetation canopy temperature; VWC: vegetation water content.
187 **3.2 Other SSM products**

188 **3.2.1 Model-based SSM products**

189 In this study, two model-based SSM products (i.e., GLDAS Noah and ERA5) were used to
190 support the evaluation work. The GLDAS Noah and ERA5 afford spatially seamless land surface
191 monitoring at a global scale in near-real time (Hersbach et al., 2019; Rodell et al., 2004). Both
192 modelled SSM estimates from the first soil layer (i.e., 0-10 cm for GLDAS Noah, and 0-7 cm for
193 ERA5) at grid resolution of 0.25 degree were selected. Since the two model-based SSM products
194 have diverse temporal samplings (i.e., 3-hour for GLDAS Noah, and 1-hour for ERA5), they were
195 averaged to daily values before being utilized for the evaluation. ERA5 SSM was adopted to
196 analyze the climatology of satellite SSM products in tropical areas because it has higher skills than
197 other four reanalysis SM products (i.e., the Japanese 55-year reanalysis (JRA-55), the National
198 Centers for Environmental Prediction Climate Forecast System Reanalysis (CFSR), the
199 Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) and
200 ERA-Interim) compared to *in situ* measurements (Li et al., 2020a). Considering the independence
201 of TCA triplet (L-band SSM, ASCAT SSM, and model-based SSM) used in our study, it cannot be
202 guaranteed by ERA5 considering that: (i) ASCAT SSM data were assimilated into ERA5 (Kim et
203 al., 2020a; Hersbach et al., 2019); (ii) ECMWF surface temperature was used in SMOS-IC and
204 SMAP-IB. Therefore, GLDAS Noah instead of ERA5 was used to form TCA triplet.

205 **3.2.2 ASCAT SSM**

206 The Advanced SCATterometer (ASCAT) active SSM products were used for the TCA/IVd
207 analysis. ASCAT is a real aperture radar carried on the Meteorological Operational Satellite
208 Program of Europe (Metop) series of satellites (i.e., Metop-A/B/C). It is operated at C-band (5.255
209 GHz) at VV polarization, and scans the Earth in descending (9:30 a.m.) and ascending (9:30 p.m.)
orbits (Wagner et al., 2013). In this study, only ASCAT SSM at descending orbit was selected due to increased thermal equilibrium conditions in night or morning time (Ma et al., 2019). ASCAT SSM data with ‘low quality’ were masked via quality flag (e.g., frozen soil, snow cover, topography and wetland probability) as done in Liu et al (2021b). To make a fair evaluation, the ASCAT relative SSM (degree of saturation) was converted into volumetric SSM by using the soil porosity from the Food and Agriculture Organization (FAO) (Reynolds et al. 2000).

It should be noted that although ASCAT SSM is retrieved from C-band active observations with weaker penetration compared to the L-band observations, ASCAT SSM is derived from time series-based change detection method, which is independent of the τ-ω model adopted for all the selected L-band SSM products. This feature may enhance the independence in TCA/IVd combination and was widely considered in previous studies (Kim et al., 2018; Kim et al., 2020a; Zhang et al., 2021).

## 3.3 Auxiliary datasets

As the uncertainties associated with the satellite SSM products may be related to precipitation forcing (Joetzjer et al., 2014), vegetation density and soil water holding capacity (SWHC), the effects of these parameters on the skill of the five SSM products were investigated. Here it should be noted that SWHC is a key parameter linked to drought monitoring by SSM (Martínez-Fernández et al., 2015). With regard to rainfall, daily GPM (The Global Precipitation Measurement) IMERG Final Precipitation L3 (GPM L3) with grid resolution of 0.1 degree was utilized. This product provides final estimate of the daily accumulated precipitation and has been demonstrated to perform better than other satellite and reanalysis rainfall data (Huffman et al., 2019; Tang et al., 2020). In terms of vegetation effect, the newly developed SMOS-IC V2 L-VOD which can be used to characterize the vegetation density (Wigneron et al., 2021) was adopted. The
soil profile of the available water holding capacity (SWHC) with spatial resolution of 0.25 degree was used in this study, and can be obtained from the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC).

## 3.4 *In situ* observations

*In situ* observations employed in this study were obtained from two sources (Figure 1): one part is derived from ISMN (Table 4), and the other part is obtained from the FLUXNET (i.e., an international “network of networks,” tying together regional networks of earth system scientists, https://fluxnet.org/about/) observations in tropical rainforests (Table 5). ISMN is a centralized soil moisture data hosting facility providing globally available *in situ* SSM measurements (Dorigo et al., 2021). Six sparse networks covering around 60 sites in tropical areas were used here (Table 4).

It can be noticed that most *in situ* observations from ISMN are located in low or moderate vegetated areas and only a few in dense forests. To address this issue, 8 ground-based sites of the top soil SM in tropical rainforests were selected as done in Fu et al. (2018). As shown in Table 5, due to the limitations of some objective conditions, all these stations provide SM observations before the year of 2015, which is partially out of the range of the possible evaluation period of SMOS (2010-now) and SMAP (2015-now). As it is impossible to directly assess the performance of satellite SSM product by using these data over different periods, we inter-compared the climatology of SM from the satellite (2010-2020) and FLUNXET products (1999-2014) (we checked in a preliminary step that the climatology of SM has similar patterns over the last two decades).

253

254

255
<table><caption>Table 4. *In situ* SSM observations in tropical areas from ISMN</caption><thead><tr><th>Network Name</th><th>No. of<br>Station Used</th><th>Observation<br>period used</th><th>Depth Used</th><th>IGBP Land Cover</th><th>Reference</th></tr></thead><tbody><tr><td>DAHRA</td><td>2</td><td>20150401-20160101</td><td>0-5/10 cm</td><td>Grasslands</td><td>(Tagesson et al., 2015)</td></tr><tr><td>SD-DEM</td><td>2</td><td>20150401-20201231</td><td>0-5/10 cm</td><td>Grasslands</td><td>(Jonas et al., 2013)</td></tr><tr><td>AMMA-CATCH</td><td>14</td><td>20150401-20181231</td><td>0-5/10 cm</td><td>Grasslands/Croplands</td><td>(Lebel et al., 2009)</td></tr><tr><td>MySMNet</td><td>7</td><td>20150401-20151231</td><td>0-5 cm</td><td>Forests/Croplands</td><td>(Kang et al., 2019)</td></tr><tr><td>COSMOS</td><td>1</td><td>20150401-20201231</td><td>0-5/10 cm</td><td>Grasslands</td><td>(Zreda et al., 2012)</td></tr><tr><td>TAHMO</td><td>33</td><td>20150617-20201231</td><td>0-5/10 cm</td><td>Savannas/Grasslands</td><td>(van de Giesen de et al., 2014)</td></tr></tbody></table>

<table><caption>Table 5. *In situ* SSM observations in tropical rainforests from the FLUXNET network</caption><thead><tr><th>Site Name</th><th>Lat (degree)</th><th>Lon (degree)</th><th>Observation period</th><th>Depth used</th><th>Canopy height (m)</th><th>Leaf area index(m²/m²)</th><th>Reference</th></tr></thead><tbody><tr><td>BR-Cax</td><td>-1.7197</td><td>-51.459</td><td>1999-2003</td><td>Upper soil layer</td><td>30-35</td><td>5.1</td><td>(Restrepo-Coupe et al., 2013)</td></tr><tr><td>ID-Pag</td><td>-2.345</td><td>114.036</td><td>2002-2003</td><td>Upper soil layer</td><td>26</td><td>5.6</td><td>(Hirano et al., 2007)</td></tr><tr><td>VU-Coc</td><td>-15.4427</td><td>167.192</td><td>2001-2004</td><td>Upper soil layer</td><td>16</td><td>5.6</td><td>(Roupsard et al., 2006)</td></tr><tr><td>AU-Rob</td><td>-17.1175</td><td>145.6301</td><td>2014-2014</td><td>Upper soil layer</td><td>28</td><td>3.2</td><td>(Beringer et al., 2016)</td></tr><tr><td>BR-Sa3</td><td>-3.018</td><td>-54.9714</td><td>2000-2004</td><td>Upper soil layer</td><td>35-40</td><td>4.9</td><td>(Restrepo-Coupe et al., 2013)</td></tr><tr><td>GF-Guy</td><td>5.2777</td><td>-52.9288</td><td>2004-2014</td><td>Upper soil layer</td><td>35-40</td><td>7</td><td>(Bonal et al., 2008)</td></tr><tr><td>GH-Ank</td><td>5.2685</td><td>-2.6942</td><td>2011-2014</td><td>Upper soil layer</td><td>25-30</td><td>5.9</td><td>(Chiti et al., 2010)</td></tr><tr><td>MY-PSO</td><td>2.973</td><td>102.3062</td><td>2003-2009</td><td>Upper soil layer</td><td>35</td><td>6.5</td><td>(Kosugi et al., 2012)</td></tr></tbody></table>

## 4. Methods

The flowchart indicating the logical order of the different evaluation steps in this study is shown in Figure 2. As shown in the figure, the evaluations were conducted considering two main perspectives: (i) the assessment via *in situ* data from ISMN and FLUXNET; (ii) evaluation by mathematical approaches (IVd and TCA).
<figure><img src="image_4.png" /><figcaption>Figure 2. Flowchart of evaluation of five L-band SSM products. Two main parts were comprised in this figure: the input data including passive L-band SSM, model-based SSM, active SSM and in situ SSM observations were represented by light green; the processing were marked as light yellow</figcaption></figure>

## 4.1 Pre-processing

To make a robust assessment of L-band SSM products, both the satellite SSM products and *in situ* data should be pre-processed before the evaluation. Specifically, *in situ* observations from ISMN are variable depending on the used devices, installation depths and available observation periods (Dorigo et al., 2021; Ma et al., 2021). Data filtering was done as follows: (i) *in situ* data from ISMN were collected from April 1st, 2015 to December 31st, 2020 corresponding to the evaluation period of the present study; (ii) taking the penetration depth of L-band into
consideration, only the topsoil SM (0-5 cm or 0-10 cm) were adopted. It should be mentioned that the sampling depth of the L-band observations is generally considered as the 0-3 cm topsoil layer (Wigneron et al., 2017), thus using 0-5 cm and 0-10 cm ground observations from ISMN may lead to depth mismatch between satellite SSM and in situ data. This issue will be cautiously considered by selecting specific error metrics and discussed in the following section; (iii) the validation sites will be filtered by using error metrics as presented in the following Section 4.2 and Section 4.3 (TCA/IVd). The nearest neighbor interpolation approach was applied to resample satellite SSM into the grid resolution of 0.25 degree as done in many SSM comparison studies (Cui et al., 2017; Kim et al., 2018; Ma et al., 2019). Additionally, for the same reason as that considered for selecting descending orbit ASCAT SSM, only SSM products at morning overpass time (i.e., descending for SMAP-SCA-V/DCA/MTDCA/IB and ascending for SMOS-IC) were adopted in this study. The UTC time of the in situ datasets from ISMN were converted into local time and then matched with the satellite overpass time before the evaluation. All the quality flags given in the satellite SSM products were adopted for the data filtering (described in the Appendix. A).

## 4.2 Conventional error metrics

To inter-compare the in situ and satellite SSM datasets, two conventional error metrics were adopted in this study: the unbiased root mean square difference (ubRMSD) and Pearson correlation coefficient (R), defined as following:

$$ubRMSD = \sqrt{E\{[(\theta_{product} - E[\theta_{product}]) - (\theta_{in situ} - E[\theta_{in situ}])]^2\}} \quad (1)$$

$$R = \frac{E[(\theta_{product} - E[\theta_{product}]) (\theta_{in situ} - E[\theta_{in situ}])]}{\sigma_{product} \sigma_{in situ}} \quad (2)$$

where E[•] represents the mean operator, $\theta_{product}$ is the satellite SSM, and $\theta_{in situ}$ is the ground SSM observations. In addition to ubRMSD and R, bias and RMSD are also common error metrics for
evaluating SSM products. However, as the latter two metrics are more easily affected by inconsistency in spatial representativeness and depth mismatch between satellite and in situ SM observations (Entekhabi et al. 2010b), only ubRMSD and R were utilized in this study, as they are generally less impacted by these "representativeness" issues (Wigneron et al., 2021). Moreover, to ensure high-quality inter-comparisons, two additional filtering conditions were used: (i) sites with less than 20 valid points were not considered; and (ii) only R-values with p-value < 0.01 were included for the assessment.

## 4.3 TCA/IVd methods

In this study, both TCA-R and IVd-R (the squared correlations derived from TCA and IVd) were used to guarantee a comprehensive assessment for the five SSM products. In TCA, three independent SSM products (x, y, z) are assumed to be linearly related to ground truth and expressed as (taking x for an instance and similarly hereinafter):

$$x = \alpha_x P + \beta_x + \varepsilon_x \quad (3)$$

where P represents the ground truth; $\alpha_x$ represents the scaling factor; $\beta_x$ denotes the temporal constant bias and $\varepsilon_x$ is the zero-mean random error. Based on Eq. (3) and the assumptions comprising error stationarity, orthogonality and zero error cross-correlation of these SSM products, the truth-correlations can be resolved based on McColl et al. (2014) and presented in Eq. (4):

$$R_{px} = \sqrt{\frac{C_{xy}C_{xz}}{C_{yz}C_{xx}}} \quad (4)$$

where $C_{xy} = \alpha_x \alpha_y C_{pp}$, $C_{xz} = \alpha_x \alpha_z C_{pp}$, $C_{yz} = \alpha_y \alpha_z C_{pp}$, $C_{xx} = \alpha_x^2 C_{pp} + \sigma_x^2$, C represents the covariance operation and $\sigma$ is the error variance. For more details on these assumptions, the readers can refer to Gruber et al., 2016b; Gruber et al., 2020.

To assess the product errors based on a method requiring only two independent products
312 (which is an easier requirement to meet than that in the TCA method), Dong et al. (2019) proposed 313 the IVd method on the basis of IVs (Su et al., 2014). In the newly proposed IVd, two instrumental 314 variables (I and J) derived from time lag -1 time series (i.e., phase shifted by one unit) of the 315 primary x and y variables were introduced (i.e., $I_t = \alpha_x P_{t-1} + \beta_x + \epsilon_{x_{t-1}}, J_t = \alpha_y P_{t-1} + \beta_y + 316 \epsilon_{y_{t-1}}$) for the calculation. The IVd-estimated scaling ratio of the primary two SSM products can be 317 expressed in Eq. (5):

$$S_{ivd} = \sqrt{\frac{c_{Ix}}{c_{Iy}}} \qquad (5)$$

318 where $C_{Ix} = \alpha_x^2 L_{pp}, C_{Iy} = \alpha_y^2 L_{pp}, L_{pp}$ is the time lag-1 auto-covariance of the true signal. Based 319 on Eq. (5), the correlation of SSM truth can be deduced by IVd and shown in Eq. (6):

$$R_{Px} = \sqrt{\frac{C_{xy}S_{ivd}}{C_{xx}}} \qquad (6)$$

320 For more detailed descriptions of TCA and IVd, the readers are referred to Dong et al., 2019; 321 Dong et al., 2020a. One issue for TCA/IVd is to select suitable combinations (e.g., doublet for IVd 322 and triplet for TCA). The combination of TCA (L-band SSM, ASCAT, GLDAS) and IVd (L-band 323 SSM, GLDAS), considering relatively-well independent variables, could guarantee a seamless 324 evaluation over tropical areas, and has shown robust performances in previous studies (Kim et al., 325 2020a). Thus, we utilized the two mentioned combinations for the assessment. To ensure robust 326 calculations of TCA and IVd, a minimum number of 120 doublets/triplets per grid were 327 considered in this study. Compared to TCA, IVd is expected to introduce less uncertainties since it 328 only needs two independent SSM products, which is also demonstrated in this study (Section 329 5.3.1). Nevertheless, as demonstrated in Dong et al (2019), equation (5) implicitly assumes that 330 the errors of the products are serially white or have similar auto-correlation strengths. In contrast, 331 TCA does not use the auto-covariance of the SM datasets. Therefore, TCA is insensitive to
332 auto-correlated errors Based on the map of IVd (Appendix B and not shown here), when the
333 auto-correlation of the satellite SSM product is larger than the one for the model SSM product, the
334 R of L-band SSM derived from IVd was found to be overestimated to some extent. In these IVd
335 “anomaly” areas (e.g., rainforests), spatial maps of TCA-R are found to be much more reasonable
336 (more details on this issue are given in the Appendix B).

337 Therefore, both TCA and IVd may have their own strengths and weaknesses. In other words,
338 and in summary of Appendix B, IVd shows slightly stronger stability in most conditions compared
339 to TCA while the robustness of IVd may be also affected when the input products have contrasting
340 error auto-correlations (e.g., rainforests areas). In contrast, TCA is insensitive to remote sensing
341 error auto-correlation, but requires three independent datasets; an assumption which can be
342 violated in practice. Therefore, to make full use of the merits of both approaches, and to further
343 obtain a more robust evaluation, we consider the combination maps derived from TCA and IVd
344 based on the differences between the auto-correlation of L-band SSM and GLDAS SSM. In other
345 words, our evaluation is mainly based on the IVd estimates, but over regions with strong remote
346 sensing and model error auto-correlation differences (i.e., auto-correlation of satellite SSM is
347 larger than that of model SSM), we use the TCA results instead. The combination strategy is
348 defined in Eq. (7):

$$
R_{\text{combined}} = \begin{cases} R_{\text{IVd}}, & \text{when } \operatorname{corr}(\text{satellite}_t, \text{satellite}_{t-1}) \le \operatorname{corr}(\text{model}_t, \text{model}_{t-1}); \\ R_{\text{TCA}}, & \text{when } \operatorname{corr}(\text{satellite}_t, \text{satellite}_{t-1}) > \operatorname{corr}(\text{model}_t, \text{model}_{t-1}) \end{cases} \tag{7}
$$

349 where corr(satellite_t, satellite_{t-1}) and corr(model_t, model_{t-1}) represent the auto-correlation of
350 L-band SSM and GLDAS SSM (here 't-1' means phase shifted by one unit compared to 't'),
351 respectively. In the areas where the auto-correlation of satellite SSM is larger than that of model
352 SSM, TCA- *R* was adopted and otherwise IVd-*R* was selected.

353 **4.4 SSM climatology**

354 In conventional assessment based on *in situ* and TCA/IVd evaluation, the performances of
355 the satellite SSM products are measured by *R* or ubRMSD derived from the original SSM time
356 series. The SSM climatology is mainly related to the overall temporal consistency of different
357 SSM products, whose errors often result in large differences between diverse SSM products (Dong
358 et al., 2019; Koster et al., 2009). Thus, the assessment on SSM climatology can greatly improve
359 our understanding of current L-band SSM products. However, this issue has received limited
360 attention in the literature on SSM product evaluation. In terms of the calculation of the SSM
361 climatology, a 30-day moving window was adopted for each day of year (DOY) across multiple
362 years (i.e., the evaluation period) as done in Dong et al (2019). As mentioned in Section 3.4, the
363 climatology of SSM in rainforests may slightly change over different periods, thus the ERA5 SSM
364 over four periods ranging over 20 years (i.e., 2001-2005, 2006-2010, 2011-2015 and 2016-2020)
365 were utilized to examine the degree of this variability.

366 **4.5 Pixel category**

367 As noted in Section 3.3, to assess the possible impacts of diverse precipitation regimes,
368 vegetation conditions and SWHC on the SSM products, all the results derived from TCA/IVd
369 were classified into five categories. Table 6 shows the classification criteria, in which the types are
370 categorized from type ‘I’ to type ‘V’ corresponding to increasing values of the impact factors. For
371 instance, for the precipitation factor, ‘P-I’ represents the lowest annual precipitation condition and
372 ‘P-V’ denotes the highest one (similar strategy for VOD and SWHC).

<table><caption>Table 6. Classification principle for satellite pixels concerning precipitation, VOD and SWHC. To guarantee sufficient samplings for each category, the pixels were evenly classified based on the overall spatial variations of each parameters in tropical areas.</caption><thead><tr><td>GPM precipitation</td><td>Pixel types</td><td>SMOS-IC L-VOD</td><td>Pixel types</td></tr></thead></table>
<table><tr><td>&lt;300 mm/year</td><td>P-I</td><td>0-0.08</td><td>VOD-I</td></tr><tr><td>300-800 mm/year</td><td>P-II</td><td>0.08-0.22</td><td>VOD-II</td></tr><tr><td>800-1300 mm/year</td><td>P-III</td><td>0.22-0.36</td><td>VOD-III</td></tr><tr><td>1300-1800 mm/year</td><td>P-IV</td><td>0.36-0.68</td><td>VOD-IV</td></tr><tr><td>&gt;1800 mm/year</td><td>P-V</td><td>&gt;0.68</td><td>VOD-V</td></tr><tr><td>Soil water capacity</td><td>Pixel types</td><td></td><td></td></tr><tr><td>&lt;223 mm</td><td>SWHC-I</td><td></td><td></td></tr><tr><td>223-235 mm</td><td>SWHC-II</td><td></td><td></td></tr><tr><td>235-247 mm</td><td>SWHC-III</td><td></td><td></td></tr><tr><td>247-259 mm</td><td>SWHC-IV</td><td></td><td></td></tr><tr><td>&gt;259 mm</td><td>SWHC-V</td><td></td><td></td></tr></table>

## 5. Results

### 5.1 Evaluation based on ISMN non-rainforest sites

Network averaged evaluation results and the primary error metrics (all validation pixels without average) for the five L-band SSM products with respect to the ISMN tropical sites are shown in Table 7 (Figure 3). With regard to the absolute error of the SSM products, SMAP-IB generally performs better than the other L-band SSM products with the smallest averaged ubRMSD of 0.041 m³/m³, which is very close to the SMAP mission target accuracy (i.e., 0.04 m³/m³). As for SMAP-SCA-V, SMAP-DCA and SMOS-IC, they exhibit a very similar accuracy which is better than that of SMAP-MTDCA. In terms of capturing the temporal trend of *in situ* SSM, in line with the results of ubRMSD, SMAP-IB also shows the highest temporal correlation (*R* = 0.73) in tropical areas while the other four L-band SSM products have comparable performances (*R* ≈0.66).

Table 7. Error Metrics (network averaging of all the error metrics which were calculated based on independent stations) of the five L-band SSM from ISMN ground observations in tropical areas. Bold data in the table represent the best results concerning each error metric. To certificate the 99% confidence interval of calculated *R*, we used here ' p-value<0.01'.

<table><thead><tr><th>Metrics</th><th>Networks</th><th>SMAP-SCA-V</th><th>SMOS-IC</th><th>SMAP-DCA</th><th>SMAP-MTDCA</th><th>SMAP-IB</th></tr></thead><tbody><tr><td>ubRMSD</td><td>DAHRA</td><td>0.044</td><td><strong>0.025</strong></td><td>0.039</td><td>0.044</td><td>0.031</td></tr><tr><td>(m³/m³)</td><td>SD-DEM</td><td>0.040</td><td>0.040</td><td>0.038</td><td>0.045</td><td><strong>0.032</strong></td></tr><tr><td></td><td>AMMA-CATCH</td><td>0.040</td><td><strong>0.039</strong></td><td>0.040</td><td>0.046</td><td>0.045</td></tr></tbody></table>
<table><tbody><tr><td></td><td>MySMNet</td><td>0.076</td><td>0.067</td><td>0.076</td><td>0.062</td><td><strong>0.042</strong></td></tr><tr><td></td><td>COSMOS</td><td><strong>0.043</strong></td><td>0.053</td><td>0.045</td><td>0.062</td><td>0.049</td></tr><tr><td></td><td>TAHMO</td><td>0.054</td><td><strong>0.050</strong></td><td>0.055</td><td>0.062</td><td><strong>0.050</strong></td></tr><tr><td></td><td>Average</td><td>0.049</td><td>0.046</td><td>0.049</td><td>0.054</td><td><strong>0.041</strong></td></tr><tr><td rowspan="7">R<br>(p-value&lt;0.01)</td><td>DAHRA</td><td>0.67</td><td><strong>0.75</strong></td><td>0.66</td><td>0.67</td><td>0.71</td></tr><tr><td>SD-DEM</td><td>0.60</td><td>0.47</td><td>0.59</td><td><strong>0.60</strong></td><td>0.60</td></tr><tr><td>AMMA-CATCH</td><td>0.84</td><td>0.84</td><td>0.84</td><td>0.84</td><td><strong>0.88</strong></td></tr><tr><td>MySMNet</td><td>0.35</td><td>0.46</td><td>0.35</td><td>0.44</td><td>0.59</td></tr><tr><td>COSMOS</td><td>0.79</td><td>0.71</td><td>0.78</td><td>0.77</td><td><strong>0.81</strong></td></tr><tr><td>TAHMO</td><td>0.74</td><td>0.74</td><td>0.76</td><td>0.74</td><td><strong>0.78</strong></td></tr><tr><td>Average</td><td>0.66</td><td>0.66</td><td>0.66</td><td>0.68</td><td><strong>0.73</strong></td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Figure 3. Box plots of ubRMSD and R for L-band SSM derived from all the ISMN tropical observations.</figcaption></figure>

Previous studies (Al-Yaari et al., 2019; Ma et al., 2019) have shown that L-band SSM products, such as SMAP-SCA-V, can achieve a temporal correlation (R) of more than 0.72 at the global scale. Thus, in the tropical areas, the L-band SSM products are found to have slightly higher uncertainties compared to those obtained in other climate zones. Despite this concern, SMAP-IB still shows good performance in the tropical areas, which is consistent with a recent global evaluation work of SMAP-IB by Li et al. (2022). As there are no ground observations in the rainforests from ISMN, the performance of the L-band SSM products is investigated based on the *in situ* FLUXNET data in the following section.

## 5.2 Climatology analysis based on rainforest sites

The observation period of SSM in the FLUXNET and satellite datasets (particularly for SMAP) does not match (see Table 5). Thus, before making an evaluation based on the SSM climatology, we check that SSM presents similar temporal trends over different time periods and
over the different sites based on the long term (2001-2020) ERA5 SSM data for four time periods defined in Section 4.4. As shown in Figure 4 and Table 8, comparable and stable temporal patterns of the SSM climatology in the four time periods can be generally observed in most stations, especially in BRCax (Fig. 4a), Au-Rob (Fig. 4d), GF-Guy (Fig. 4f) and GH-Ank (Fig. 4g). Nevertheless, we can also notice that some variations exist over the four time periods for VUCoc (Fig. 4c), BR-Sa3 (Fig. 4e) and MY-PSO (Fig. 4h) (time lags between different time periods can be seen). We computed the correlation between the climatology of ERA5 SSM over the different time periods (i.e., periods when *in situ* data can be obtained and the evaluation periods) over the eight FLUXNET sites (first column of Table 8). Except for VU-Coc (specificity of this site will be discussed later), the lowest correlation we obtained is 0.85. Therefore, it can be considered that the climatology of SSM is relatively stable over the different time periods during 2001-2020 for the eight FLUXNET sites, which is also evidenced in Dong et al. (2020a) using *in situ* sites in the United States.

<figure><img src="image_6.png" /><figcaption>Figure 4. Climatology analysis for four five-year periods during 2000-2020 in eight FLUXNET rainforest stations (from sub-plots (a) to (h)) based on long term ERA5 SSM.</figcaption></figure>
Table 8. Climatology analysis of ERA5 and five L-band SSM products in tropical rainforests.
For BR-Cax and GF-Guy, as very low or non-significant correlation values (shown as ‘NaN’ in the table) were obtained over those two sites using both (i) moving window averaging and (ii) DOY averaging for the climatology calculation, we considered the neighbor pixel obtaining the highest correlation value with ERA5 (see the first column and after ‘/’), in which we assume that the SSM climatology between the targeted pixel and neighbor pixel with the highest correlation value are consistent. Then the L-band SSM at the selecting neighboring locations were adopted for the correlation calculation (the symbol of ‘/’ separates the primary results and results derived from neighbor pixels). Bold data in the table represent the best results concerning each error metric.

<table><thead><tr><th>Stations</th><th>ERA5 (i)</th><th>SMAP-SCA-V</th><th>SMOS-IC</th><th>SMAP-DCA</th><th>SMAP-MTDCA</th><th>SMAP-IB</th></tr></thead><tbody><tr><td>BR-Cax</td><td>0.97/0.99</td><td>0.14/0.65</td><td><strong>0.65/0.90</strong></td><td>0.14/0.68</td><td>0.88/0.70</td><td>0.20/0.64</td></tr><tr><td>ID-Pag</td><td>0.97</td><td>0.91</td><td><strong>0.94</strong></td><td>0.89</td><td>0.88</td><td>0.92</td></tr><tr><td>VU-Coc</td><td>0.81</td><td>NaN</td><td>NaN</td><td>NaN</td><td>NaN</td><td>NaN</td></tr><tr><td>AU-Rob</td><td>0.97</td><td>0.59</td><td><strong>0.75</strong></td><td>0.56</td><td>0.62</td><td>0.55</td></tr><tr><td>BR-Sa3</td><td>0.85</td><td>0.94</td><td>0.85</td><td>0.92</td><td>0.71</td><td><strong>0.97</strong></td></tr><tr><td>GF-Guy</td><td>0.96/0.86</td><td>NaN/0.79</td><td>NaN/0.68</td><td>NaN/0.79</td><td>-0.55/0.82</td><td>NaN/NaN</td></tr><tr><td>GH-Ank</td><td>0.90</td><td>0.74</td><td>0.58</td><td>0.73</td><td>0.74</td><td><strong>0.96</strong></td></tr><tr><td>MY-PSO</td><td>0.90</td><td>0.75</td><td>0.71</td><td>0.73</td><td>0.72</td><td>0.69</td></tr><tr><td>Average</td><td>0.92</td><td>0.68/0.76</td><td><strong>0.75/0.77</strong></td><td>0.66/0.75</td><td>0.57/0.74</td><td><strong>0.72/0.79</strong></td></tr></tbody></table>

(i) Temporal correlations (R) shown in the first column of the table were calculated between *in situ* SSM climatology derived from *in situ* data of each station and ERA5 over the same time period. For instance, since ID-Pag has *in situ* data from 2002 to 2003, the ERA5 SSM climatology in the first period (2000-2005) was used to compute the time correlation between *in situ* / ERA5. While GH-Ank has data from 2011 to 2014, the period of 2011-2015 was utilized for ERA5, correspondingly.

In general, SMOS-IC shows a good performance with the highest mean correlation (R) value of 0.75, followed by the newly developed SMAP-IB (R= 0.72) and by SMAP-SCA-V and SMAP-DCA (R ≈ 0.66) which show slightly better performances than SMAP-MTDCA (R = 0.57).
Regarding the different sites, the highest R values for SMAP-SCA-V, SMAP-DCA and SMAP-IB are found for the BR-Sa3, while the highest ones for SMOS-IC and SMAP-MTDCA were obtained for the ID-pag station. In contrast, the lowest correlation values for the five SSM products are generally obtained in BR-Cax, except for SMAP-MTDCA and SMOS-IC. Moreover, non-significant correlation values (i.e., no data or less than 0.2) are obtained over VU-Coc and GF-Guy (except for SMAP-MTDCA). For these "anomalous" sites obtaining low (< 0.3) or non-significant R values (i.e., R with p-value>0.01), we considered the contiguous pixels of these
436 L-band SSM products in these "anomalous" sites for the climatology evaluation, which are
437 specifically described below Table 8 and discussed in Section 6. We tried to use contiguous pixels
438 for these two anomalous sites, as we assumed that the very low correlation values obtained from
439 these two sites could be due to specific issues in the retrievals (the most likely issue being the
440 presence of large water bodies, such as large rivers or ocean (based on the checking via Google
441 Earth Map), which strongly affect the SM retrievals from microwave observations) (Ye et al.,
442 2015). As for the selection strategy, based on the ERA5 SSM correlations between the 'in situ
443 corresponding pixel' and diverse contiguous pixels, the contiguous pixel obtaining the highest
444 correlation with ERA5 SSM climatology (extracted over the "anomalous" sites) was selected
445 (results are shown after the symbol "/" in Table 8). After considering the neighboring pixels,
446 improved results could be achieved for all the SSM products, and particularly for SMAP-SCA-V
447 and SMAP-DCA, but the conclusions (i.e., the ranking of these evaluated SSM products) remain
448 unchanged.

449 **5.3 TCA/IVd results**

450 **5.3.1 Reliability tests of TCA and IVd**

451 To deepen and expand the analysis in this study, TCA/IVd approaches independent of ground
452 data were used. Some hypotheses (e.g., orthogonality and zero error correlation assumptions)
453 required in TCA/IVd may not be totally guaranteed in practice (Gruber et al., 2020; 2016a; 2016b).
454 Thus, before conducting assessment based on TCA or IVd, the reliabilities of these two methods
455 were evaluated by using diverse combinations considering active microwave SSM and *in situ*
456 SSM in non-rainforests.

457 As explained in Section 4.3, combinations of *IVd* (*passive*, *model*) (*passive* refers to L-band
458 SSM products and *model* refers to GLDAS Noah, the same below) and *TCA* (*passive*, *model*,
active) (active means ASCAT SSM) were adopted for the final evaluation in this study. We adopted the *R* values based on Eq. (4) and Eq. (6) from the above two combinations as the *x* labels in Figure 5 and Figure 6, respectively. Keeping the member of ‘passive’ as stable, by disrupting other members in the two combinations with *in situ* (from ISMN), active (ASCAT SSM) and model (GLDAS SSM), we could obtain diverse new IVd and TCA combinations, i.e., *IVd (passive, in situ)*, *IVd (passive, active)* for IVd, and *TCA (passive, active, in situ)*, *TCA (passive, model, in situ)* for TCA. Then we can calculate the *R* from these new combinations for the same ‘passive’, which were considered as *y* label in Figure 5 and Figure 6. Through this kind of disrupting aimed at the same ‘passive’, the reliability of IVd and TCA can be checked. It should be noted that the numbers of points in each subplot of Figure 5 and Figure 6 are corresponding to the numbers of *in situ* stations from ISMN in non-rainforests. In this kind of tests, for a given L-band SSM product, if a stable *R* value can be achieved for different combinations in IVd or TCA (more points concentrated in the 1:1 line), a good reliability of the assessment method can be assumed. Similar tests of the IVd method applied to SMAP-L4 SM product have also been done by Reichle et al. (2021).
<figure><img src="image_7.png" /><figcaption>Figure 5. Scatter plots of diverse combinations of IVd for five L-band SSM products. For each subplot, we calculated the *R* from diverse combinations by adopting IVd. Taking SMAP-IB (subplot e) for instance, SMAP-IB *R* by (SMAP-IB, GLDAS Noah) was expressed as the same *x* label corresponding to diverse *y* labels. Then, at the same pixel locations, SMAP-IB *R* by (SMAP-IB, *in situ*) (i.e., y1 label was presented by light green triangle symbol) and (SMAP-IB, ASCAT) (i.e., y2 label was shown as blue plus sign) were calculated over the pixels covering the *in situ* stations, respectively, and then plotted as *y* labels. The same approaches were utilized for the other L-band SSM products.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 6. Scatter plots of diverse combinations of TCA for five L-band SSM products. Similar to Figure 5, also taking SMAP-IB (subplot e) for example, SMAP-IB *R* derived from combinations of (SMAP-IB, GLDAS Noah, ASCAT) by TCA was regarded as the same *x* label corresponding to diverse *y* labels. SMAP-IB *R* derived from combinations of (SMAP-IB, GLDAS, *in situ*) (exhibited as cyan triangle) and combinations of (SMAP-IB, ASCAT, *in situ*) (expressed as red plus sign) were calculated by TCA over the pixels covering the *in situ* stations, and then considered as *y* labels.</figcaption></figure>

In the two figures (Figure 5 and Figure 6), for the five L-band SSM products, we can notice
more concentrated points close to the 1:1 line (Figure 5) can be obtained with IVd, which indicates a more robust performance of IVd in comparison to TCA. In particular, as shown in the two figures, the *R* values derived from the IVd combinations including *in situ* data (i.e., the light green triangle in Figure 5) are much closer to the 1:1 line than those obtained with TCA (i.e., the cyan triangle in Figure 6). The results also suggest the higher reliability of using two independent SSM products as done for IVd in non-rainforests, compared to the use of three independent SSM products for TCA. In terms of the satellite product performances, SMAP-IB shows promising accuracies from results of both IVd and TCA with generally higher *R* values (most values higher than 0.8 for IVd and higher than 0.6 for TCA, respectively) compared to the other L-band SSM products, which is in line with the conventional evaluation work presented in the previous section.

### 5.3.2 Spatial distributions of *R* by TCA/IVd

Based on the methods defined in Section 4.3, the maps of combined *R* were obtained from the TCA-*R* and IVd-*R* maps for the five L-band SSM products (Figure 7). Here we should note that the overall spatial patterns of the original (before combination) TCA and IVd *R* maps for the five L-band SSM products are comparable in spite of some abnormal areas (Appendix B). Therefore, the conclusions obtained from the combined maps will not change much compared to those drawn from the original TCA-*R* and IVd-*R* maps. But after the combination processing, the advantages of the two approaches can be fully adopted for the analysis as mentioned in Section 4.3. As shown in Figure 7, in spite of the fact that the climatology of the L-band SSM products obtain relatively good results in rainforests in Section 5.2, all the L-band products obviously exhibit higher uncertainties over rainforests (e.g., Congo basins, Amazon and southeast Asia). To further explore the uncertainties of the L-band SSM products in rainforests, we analyzed the time lag between five L-band SSM
products and model-based SSM products (i.e., ERA5 SSM) (please kindly see the Appendix C), which was also mentioned in previous study (Sadeghi et al, 2020). With regard to non-rainforest areas, SMAP-IB SSM generally shows promising results in most tropical areas by displaying higher *R* values, which is in line with the ground-based evaluations in Sections 5.1 and 5.2.

503
504

<figure><img src="image_9.png" /><figcaption>Figure 7. Spatial distributions of TCA/IVd combined *R* for five L-band SSM products. In the combination processing, taking SMAP-IB for example, we firstly calculated the temporal auto-correlation (the correlation between original series and time lag-1 series) maps of both SMAP-IB and GLDAS Noah, and then we combined TCA-*R* and IVd-*R* as follows: if the auto-correlation of SMAP-IB is larger than that of GLDAS Noah (occurring usually in tropical rainforests), we consider the TCA-*R* for the combination; otherwise, we select IVd-*R* (Cf Section 4.3). Note that there are many blank areas. This is due to the calculation requirements: for TCA, only pixels containing more than 120 samples for all the three components were considered (otherwise, the pixels were masked); for IVd, (i) same requirement concerning 120 samples as TCA, (ii) the pixels where the correlation between L-band SSM and GLDAS SSM was less than 0.1 were masked.</figcaption></figure>

505
506
### 5.3.3 Uncertainties associated with the SSM products for diverse environmental factors

In this section we further explored the uncertainties associated with the SSM products
under diverse environmental conditions using boxplots (Figures 8 to 10). Due to the different capabilities of the different L-band SSM products, the numbers of effective pixels derived from TCA/IVd vary a lot from one product to the other. To make a fair inter-comparison, the TCA/IVd combined maps of the five SSM products were inter-masked, so that we kept the same number of valid pixels for the five products.

In terms of VOD conditions, all the L-band SSM products display satisfactory performances for moderate VOD conditions (i.e., VOD-II to VOD IV intervals), but their performance worsens for the lowest and the highest vegetation conditions (Figure 8). This finding is consistent with previous regional or global *in situ* observations (Ma et al., 2019; Zeng et al., 2022a). Moreover, we can also notice that all the five L-band SSM products show consistent patterns in diverse rainfall conditions (Figure 9) with VOD conditions (Figure 8) (i.e., all the L-band SSM products show better performances in moderate precipitation conditions than in other conditions). This issue can be reasonably explained by the fact that higher rainfall and VOD conditions are located in rainforests, and lower ones are located in many desert areas, in which the low correlations are highly related to the possible soil volume scattering effects caused by the dry soils and very small SSM dynamics (Burgin et al., 2017; Wagner et al., 2022; Zeng et al., 2022b). With regard to SWHC, comparable and stable performances of the five SSM products can be noted in most SWHC conditions except for the lowest SWHC conditions and the highest SWHC conditions, for which slightly lower *R* values can be noted for all products (Figure 10). This stability is in contrast with results obtained as a function of VOD and rainfall, and the difference may be partially due to the low spatial variations of SWHC over tropical areas compared to VOD and rainfall (noted in Table
6 with shallow range for diverse SWHC categories). This stability may also indicate to some degree that SWHC has less impacts on the performances of L-band SSM compared to the other two variables. In terms of specific SSM products, SMAP-IB SSM exhibits generally the best skill under most precipitation, VOD and SWHC conditions compared to the other four L-band SSM products.

534

<figure><img src="image_10.png" /><figcaption>Figure 8. Box plots of TCA/IVd combined *R* stratified by VOD for five L-band SSM products. The range of the VOD intervals is displayed in Table 6.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 9. Same as Fig. 8, except here stratified by precipitation. The range of the precipitation intervals is displayed in Table 6.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 10. Same as Fig. 8, but here stratified by SWHC. The range of the SWHC intervals is displayed in Table 6.</figcaption></figure>

# 6. Discussion

## 6.1 Reliability and limitations of the climatology analysis

In Section 5.2, we evaluated the climatology of five L-band SSM products in the tropical rainforests by using *in situ* data which are not totally contemporaneous of the satellite observations. We showed that the climatology is stable over different periods based on long term ERA5 SSM in rainforests, in spite of the fact that, the robustness of the conclusions will also be slightly impacted by the accuracy of ERA5 SSM, which may contain some inherent uncertainties due to model structure, model parameter or forcing data. Moreover, this kind of relatively stable patterns of SSM climatology in diverse periods in other non-rainforests has also been demonstrated in the literature (Dong et al., 2020a).

Noting these limitations, we found that all the five L-band SSM products exhibit acceptable performances compared to *in situ* measurements in terms of climatology in rainforests with correlation coefficients larger than 0.6 for most products, and the best results obtained for the SMOS-IC data set. Such a result has also been confirmed by a recent study based on *in situ* sites in the United States (Dong et al., 2020a). In spite of the limited
FLUXNET data set used in this study, our results indicate that the L-band satellite-derived SSM climatology seems to be relatively reasonable in the tropics and can be recommended for related applications. At the same time, given the limitations related to the lack of real-time ground-based SSM measurements, the establishment of more ground stations in tropical rainforests in the future would make the climatology assessment in this study more rigorous.

## 6.2 Comparison of *in situ* data and TCA/IVd methods for SSM evaluation

In this study, we obtained generally consistent results between conventional *in situ* measurements and TCA/IVd methods. Actually, mathematical methods (e.g., TCA and IVs/IVd) have been widely recognized as complementary ways to ground-based approaches for SSM evaluation (Kim et al., 2018; Xu et al., 2021b). While the robustness of these methods may be to some degree impacted from the following perspectives:

(i) The absolute independency of the SSM products in the combinations/triplets used as inputs to the mathematical methods can be hardly satisfied in practice. For instance, in all the current L-band SSM retrieval algorithms as described in Table 3, the effective soil temperature is derived from model/reanalysis products. Such factors may to some extent increase the dependence between satellite SSM and model-based one in the combination, and further impact the applicability of these mathematically-based approaches for the SSM evaluation.

(ii) The soil depth inconsistency between the sensing depth of current satellite observations (e.g., 0-1 cm for C-band and 0-3 cm for L-band, respectively) and the soil depth considered in model assimilation (e.g., 0-7 cm for ERA5 and 0-10 cm for GLDAS at topsoil adopted in this study), will also partially contribute to some uncertainties in our results. Moreover, in a large number of previous studies (Gruber et al., 2020; Kim et al., 2020b;
Zhang et al., 2021) and as well as in this study, TCA/IVd have been demonstrated to overestimate the performance of satellite SSM products. In other words, a higher correlation is generally obtained by these methods compared to that obtained from studies based on *in situ* observations. However, from the perspective of the spatial distributions of the errors, the general patterns obtained from the mathematical methods have generally found to be reliable (Gruber et al., 2020).

As for the comparison between the conventional TCA and the newly proposed IVd, IVd only requires two independent SSM products, which is easier to be satisfied in practice. Moreover, the reliability of IVd was demonstrated to be stronger than that of TCA in this study in non-rainforests. From these two considerations, IVd may provide another feasible solution to evaluate SSM products (Dong et al., 2019; Dong et al., 2020b). However, the higher sensitivity of IVd to high temporal auto-correlation in the input SSM series, as noted mainly in rainforests, should also be taken into consideration. In summary, no single evaluation approach is perfect and it is more reasonable to combine the respective advantages of different methods as done in this study.

## 6.3 Potential suggestions for the SSM improvements

In Section 5.2, we can clearly notice abnormal results were obtained for some sites in the rainforests. To further explain the potential reasons for the issue, the specific environmental conditions of the three mentioned stations were carefully checked (based on the corresponding locations in Google Earth). Both GF-Guy and VU-Coc are very close to ocean, especially VU-Coc which is located in an island of Vanuatu, while BR-Cax is next to an inland lake in Brazil. Thus, it can be deduced that water fraction may be the main potential reason for the anomalies found in the L-band SSM products over these three sites. Actually, as
pointed out in previous studies (Bousquet et al., 2021; Yang et al., 2021; Ye et al., 2015),
water fraction has been found to have significant impacts on L-band SSM retrievals. Thus,
more attention should be paid on water fraction corrections in improving these products.

It has been consistently indicated by several results in Section 5, that in spite of
uncertainties in rainforests, the L-band sensors are capable of retrieving SSM in most
moderately vegetated areas, including forest areas, which is consistent with recent studies
(Ayres et al., 2021; Colliander et al., 2020). With regard to the specific SSM products
considered in this study, the satisfactory performance of SMAP-IB SSM in non-rainforests
may benefit from the following perspectives: (i) Better considering the saturation issues of
optical indices (e.g., the NDVI climatology was used as auxiliary data in SMAP SCA-V
algorithm) in densely vegetated areas. The independent retrieval of τ in the retrieval
algorithms should be helpful for SSM improvements; (ii) SMAP dual-polarized TB with
improved RFI filtering and correction (Rajabi et al., 2019) likely enhanced the SSM retrievals
and contributed to explain the better results of SMAP-IB vs. SMOS-IC in most non-rainforest
areas in this study; (iii) Effective soil temperature correction with high accuracy may
contribute to upgrades in the algorithms. As a key external input for the SSM retrieval
algorithms, model-based soil temperature products are often utilized for temperature
correction. Specifically, ERA5 soil temperature products (adopted for SMAP-IB) which
present some improvements vs. ERA-Interim (utilized for SMOS-IC) (Ma et al., 2021) can
partially help to improve the SSM retrievals of SMAP-IB. Moreover, for the satellite
observation modes used in different SSM algorithms, two consistent results were found in this
study. First, as noted in Section 5, although the multi-angular SMOS-IC SSM product does
not show better performance than the other products in the rainforests from the TCA/IVd analysis, the SSM climatology of SMOS-IC in rainforests obtains the highest correlation of 0.745 vs. the FLUXNET *in situ* sites. Second, SMOS-IC shows slightly better performance concerning the time lag analysis in rainforests as shown in Section 5.4. The two above results consistently suggest the good capability of multi-angular observations compared to mono-angular ones for SSM retrievals in rainforests with high vegetation density.

Reducing the noticed uncertainties of current L-band SSM products could rely on improvements in algorithms and penetration abilities of the satellite sensors in the future. First, in terms of the τ-ω model, the higher-order multiple-scattering effects in the vegetation canopy are assumed to be zero (Zeng et al., 2020), which may be not reasonable in dense forests areas. This defect of the τ-ω model may partially explain the uncertainties in the SM retrievals in the rainforests as observed in this study. Thus, higher order solutions of the radiative transfer equations (e.g., two-stream model or other developed solutions) taking the multiple scattering effects into account may be one possible direction for the satellite SSM improvements in forests (Li et al., 2020b; Schwank et al., 2018). Second, despite the fact that L-band sensors have good performances in penetrating vegetation and topsoil, their capabilities are inevitably reduced in dense forests especially in rainforests. In this case, one possible solution is to integrate further P-band satellite observations with stronger penetration capacity and current L-band observations for SSM retrieval in forests areas (Shen et al., 2021).
638

# 7. Conclusions

639

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642

643

644

645

646

With the continuous development of satellite SSM retrievals from L-band, which has been regarded as the much more promising frequency for global SSM mapping compared to X/C-band, several L-band SSM products have been released to the public. Although extensive evaluation studies of satellite SSM products have been conducted, the performance of current L-band SSM products have still been limitedly investigated in tropical areas. To address this gap, this study evaluated five L-band SSM products in tropical areas, comprising SMOS-IC, SMAP-SCA-V, SMAP-DCA, SMAP-MTDCA and SMAP-IB, by adopting both ground observations and mathematical approaches (i.e., TCA and IVd).

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652

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654

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657

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659

All the selected L-band SSM products show acceptable performances with high TCA/IVd-R values (more than 0.6) in most vegetated conditions of the tropical areas except for the lowest and the highest vegetation conditions. This conclusion confirms the capability of current L-band satellite observations for retrieving SSM in moderate vegetation areas (e.g., moderately vegetated forests) as mentioned in a few recent studies. However, in the densest vegetation areas in tropical areas (e.g., the rainforests), larger uncertainties of all the L-band SSM products were found. The SSM climatology of the L-band SSM products, especially for SMOS-IC and SMAP-IB, seemed to be reasonable and can be recommended for the ecological and hydrological applications. Additionally, the performances of the SSM products in diverse vegetation conditions show analogous patterns compared to those in various precipitation conditions. With regard to the specific L-band SSM products, the newly developed SMAP-IB SSM exhibits a fairly satisfactory performance which is slightly better than that of the other L-band SSM products in tropical areas out of the rainforests. The
660 SMAP-DCA SSM shows comparable or slightly better performance than SMAP-SCA-V SSM.

661 This comprehensive evaluation is expected to provide a full understanding on the progress of
662 current L-band SSM products in tropical areas and further facilitate the refinement and
663 applications of these products.

664

665 Acknowledgements

666 This research was supported by the CNES, France (Centre National d'Etudes Spatiales), the
667 National Key R&D Program (No. 2018YFB2100500), National Natural Science Foundation of
668 China program (No. 41971317, 41801339, 41890822, 42001372), Natural Science Foundation of
669 Hubei Province, China (No. 2020CFB615), the Open Fund of State Key Laboratory of Remote
670 Sensing Science (No. OFSLRSS202114) and the Youth Innovation Promotion Association CAS
671 (No. 2018082), and Hongliang Ma was sponsored by China Scholarship Council (No.
672 202006270077). The authors thank all the experts providing us great help for obtaining *in situ* data
673 in tropical rainforests, including Dr. Eduardo Eiji Maeda of University of Helsinki, Dr. Natalia
674 Restrepo Coupe, Dr. Sebastian Apers, Dr. Antonio Donato Nobre, Dr. Claudio Angelo, Dr.
675 Elisangela Broedel, Dr. Celso Von Randow and Dr. Rafael Oliveira etc.

676 The authors thank Goddard Earth Sciences (GES) Data and Information Services Center
677 (DISC), European Space Agency (ESA), National Aeronautics and Space Administration (NASA)
678 and ECMWF for providing SSM products, and the ISMN for supporting *in situ* SSM datasets
679 **Appendix**

680 **Appendix. A**

681 In this appendix, detailed information on the five L-band SSM products are given in addition
682 to the key information in the retrieval algorithms listed in Table 3.

683 **SMAP SCA-V & DCA**

684 The NASA's SMAP mission, which is the newest L-band satellite dedicated for global SSM
685 monitoring, was launched on January, 2015. It affords both ascending (6:00 P.M.) and descending
686 (6:00 A.M.) radiometer observations at 1.41 GHz. In this study, the SMAP L3 radiometer global
687 daily 36 km SSM products derived from SCA-V and DCA algorithms were freely downloaded
688 from the National Snow and Ice Data Center (NSIDC) (https://nsidc.org/data/SPL3SMP). In the
689 SCA-V algorithm, MODIS NDVI derived VWC has been applied for the correction of vegetation
690 effects. While for the newly developed DCA algorithm, the parameter of τ was simultaneously
691 retrieved with SSM on the premise of that roughness parameter was obtained by using NDVI
692 VWC and SMAP data as input (Chaubell et al., 2020).

693 In this study, satellite SSM out of 0-0.6 m³/m³ were excluded for the evaluation (also done
694 for SMOS-IC, SMAP-MTDCA and SMAP-IB). For more details of the two SSM products, the
695 readers can find in (O'Neill et al., 2015; Chaubell et al., 2020, 2021).

696 **SMAP MTDCA**

697 Based on the SMAP observations of full polarizations at the single incidence angle of 40
698 degree, SMAP MTDCA algorithm assumes that the temporal variations of VOD is more stable
699 than that of SSM, and then the VOD, SSM and the effective scattering albedo were simultaneously
700 retrieved independent of optical indices auxiliary data (Konings et al., 2017). Both 36 km and 9
701 km SMAP-MTDCA VOD and SSM data at a global scale can be freely downloaded from
‘http://afeldman.mit.edu/mt-dca-data’. In this study, SMAP-MTDCA SSM of the newest version 5 ranging from April, 2015 to December, 2020, was adopted for the evaluation. More details of SMAP MTDCA algorithm is in Konings et al. (2017).

705 SMOS-IC

706 The ESA’s SMOS mission launched in November, 2009, is the first L-band (1.4 GHz) 707 satellite carrying the microwave radiometer devoted for global SSM and ocean salinity mapping.
708 It scans the Earth’s surface at a local overpass time of 6:00 A.M. for ascending and 6:00 P.M. for 709 descending. In this study, the SMOS newly derived SSM product, SMOS-IC SSM in the newest 710 version 2 projected on EASE-Grid 2.0 25 km, was selected for the evaluation. This data is freely 711 available at the website of ‘https://ibremote-sensing.inrae.fr/’. 712

712 Based on the TB of multi-angles (i.e., 0-60 degree) and dual polarizations, and the newly 713 calibrated maps of soil roughness and vegetation scattering (Fernandez-Moran et al., 2017b), 714 SMOS-IC SSM and VOD products of the first version 105 were released to the public 715 (Fernandez-Moran et al., 2017a). On the basis of version 105, the lower time variations of VOD 716 compared to that of SSM was specifically taken into account in the newly improved SMOS-IC 717 algorithm (Li et al., 2021a; Wigneron et al., 2021). Specifically, previous 10 days retrieved VOD 718 values were adopted for initializing the first guess in the cost function, which is convinced to be 719 more reasonable for the VOD retrievals and further helps to improve the SSM product. In this 720 study, using the quality flag, SSM values with ‘Scene Flags’ >1 and ‘TB-RMSE’ >8 K were not 721 considered for the assessment as done in Li et al (2022).

722 SMAP-IB

723 SMAP-IB SSM and VOD were concurrently retrieved by L-MEB model using SMAP 724 dual-polarized TB. In the SMAP-IB algorithm, constraint based initial guess values of SSM and
L-VOD, and multi-temporal (MT) information were fully taken into consideration to alleviate ill-posed issue due to high correlations of H and V polarizations (Li et al., 2021). Moreover, the newly developed ERA5 SSM was adopted for the SSM calibration, in which improved retrieved results can be acquired by using a dynamic initialized SM instead of a constant one. Based on the newly proposed algorithm, long term L-band SSM and VOD products are expected to be afforded by combination of SMOS and SMAP satellite observations in the future. Similar to SMOS-IC, the retrievals with ‘Scene flag’>1 were excluded. More details of SMAP-IB algorithm is in Li et al (2022).

## Appendix. B

Primary TCA and IVd results are presented here to supplement the combination results in Section 5.4. As shown in Figures A1 and A2, in spite of some anomalies occurred in dense rainforests for SMAP-IB by IVd mentioned above, the general spatial patterns of diverse SSM products can be consistent by TCA and IVd. With regard to the anomaly areas, it can be seen in Figure A2 (e) that the *R* of SMAP-IB was overestimated by IVd in rainforests (e.g., Southeast Asia, Amazon and Congo basins), which is not reasonable in practice. Moreover, for both TCA and IVd derived results, SMAP-IB in general exhibits satisfactory performances in most tropical areas, which is in line with the combination results in Sections 5.4 and 5.5.
<figure><img src="image_13.png" /><figcaption>Figure A1. Spatial distributions of TCA combined *R* for five L-band SSM products.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure A2. Spatial distributions of IVd combined *R* for five L-band SSM products.</figcaption></figure>

With regard to the auto-correlation issue, taking SMAP-IB for instance (Figure A3), it can be 742 clearly noticed that when the difference between auto-correlation of GLDAS and SMAP-IB is 743 negative (i.e., auto-correlation of SMAP-IB is larger than that of GLDAS), the IVd-*R* is obviously 744 overestimated. This kind of anomaly can be mainly seen in rainforests (Amazon, Congo and 745 South-east Asia, etc.). 746
<figure><img src="image_15.png" /><figcaption>Figure A3. The relationship between the IVd-R and differences between auto-correlation of GLDAS and SMAP-IB.</figcaption></figure>

## 747 Appendix. C. Time lag analysis

748 In this appendix section, time lags (or phase lags) of five L-band SSM products relative to
749 ERA5 SSM were computed. As Jones et al. (2014), time lags where computed as a time delay
750 (referred to as time lag) maximizing correlation between time series ERA5 SSM(t) and time series
751 L-band SSM (t-time lag). As pointed out in previous studies (Sadeghi et al, 2020; Bousquet et al.,
752 2021), time lag issues were found for some L-band SSM products in rainforests; these issues being
753 very problematic for some specific applications (e.g., SSM seasonal variations and phenology
754 monitoring (Gao and Zhang, 2021) in rainforests). To our knowledge, no study has specifically
755 checked this issue and we will evaluate here whether there is a time lag for all the L-band SSM
756 products and what are the differences of diverse products in the tropics. To answer the question
757 and expand this comprehensive assessment, the time lag analysis was included in this appendix
758 section. Similar to previous studies (Bousquet et al., 2021), we averaged the satellite and ERA5
759 SSM time series on a monthly scale before calculating the time lag, so that the phase shifting of
760 the SSM seasonal variations can be better investigated in tropical areas.

761 As shown in Figure A4, We can clearly notice time lags for the five L-band SSM
762 particularly in tropical rainforests (e.g., Amazon, Congo and Southeast Asia), which is
consistent with the larger uncertainties in the same areas found with the TCA/IVd methods. In terms of specific products, SMOS-IC shows slightly better results with smaller areas including time lags and smaller absolute values of time lag, followed by SMAP-IB. To further check this issue, we also selected three representative points (as shown in Figure A4(a), point A, B and C) in the areas with obvious time lags, and drawn the time series of these SSM products (Figure A5). From the results, the L-band SSM products show diverse small peaks and troughs relative to ERA5 SSM for all the three selected points. Moreover, in order to check the robustness of the findings based on ERA5, we did the same comparison based on independent and newly developed Gravity Recovery and Climate Experiment (GRACE)-based SSM product (Sadeghi et al, 2020). Here it should be noted that the GRACE SSM ((i.e., first soil layer with depth of 2.5 cm)) has been obtained using a physically based approach proposed by Sadeghi et al. (2020), which is distinguished from the general cognition that GRACE only represents the variations of groundwater. In other words, here we calculated the time lag of five L-band SSM products relative to both ERA5 and GRACE SSM (i.e., ERA5 SM at the first soil layer and GRACE-derived SSM), and then we obtained the consistent results for the two different and independent SSM. The results confirmed the time lag phenomenon of current L-band SSM and should be taken into account in the further improvements and hydro-ecological applications.

To partially explain this phenomenon, we also checked these rainforest areas occurring time lag relative to ERA5. For instance, obvious negative time lags (i.e., blue block in Figure 11 (a1-e1)) can be seen for most L-band SSM in the south west of Amazon. Based on recent related work (Bousquet et al., 2021), these areas correspond to transboundary flooded areas located
in Bolivia, where current L-band SSM retrieval algorithms can be significantly impacted especially for the vegetation (e.g., VOD) parameterization. As for the specific impacts of flooding areas on time lag issues, further investigation could be done in the future. Another potential reason contributing to this time lag may be the flaw of current retrieval model (i.e., $τ-ω$) neglecting multiple-scattering effects (Zeng et al., 2020), especially for rainforests with high biomass.
<figure><img src="image_16.png" /></figure>

Figure A4. Time lag results relative to ERA5 SSM (a1-e1) and corresponding maximum correlation (a2-e2) results for the five L-band SSM products vs. ERA5 in tropical areas. In all figures, the pixels with non-valid maximum *R* (p-value>0.01) were masked (blank areas) for both time lag maps and correlation maps. In the calculation, the max lag (i.e., maximum phase shifting) was set as +/- 6 months. As presented in a1, we selected three points (point A, point B and point C) for which time series are shown in Fig. A5.
<figure><img src="image_17.png" /><figcaption>Figure A5. Time series of monthly average SSM for three representative points (see Fig. A4) in time lag occurring areas</figcaption></figure>

Time lags of five L-band SSM vs. GRACE SSM and corresponding maximum correlations

are presented in Figure A6. Compared to results of ERA5 (Figure A4), the spatial maps of time lag

are general very similar except for some inconsistencies between maximum correlation of ERA5

and GRACE.
<figure><img src="image_18.png" /><figcaption>Figure A6. Time lag (a1-e1) and maximum correlation (a2-e2) results of five L-band SSM products vs. GRACE in tropical areas. In all figures, the pixels with in-valid maximum *R* (p-value>0.01) were masked (blank areas) for both time lag maps and correlation maps. In the calculation, the max lag (i.e., maximum phase shifting) was set as +/- 6 months.</figcaption></figure>
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