Large Area Aboveground Biomass and Carbon Stock Mapping in Woodlands in Mozambique with L-Band Radar: Improving Accuracy by Accounting for Soil Moisture Effects Using the Water Cloud Model

: Soil moisture effects limit radar-based aboveground biomass carbon (AGBC) prediction accuracy as well as lead to stripes between adjacent paths in regional mosaics due to varying soil moisture conditions on different acquisition dates. In this study, we utilised the semi-empirical water cloud model (WCM) to account for backscattering from soil moisture in AGBC retrieval from L-band radar imagery in central Mozambique, where woodland ecosystems dominate. Cross-validation results suggest that (1) the standard WCM effectively accounts for soil moisture effects, especially for areas with AGBC ≤ 20 tC/ha, and (2) the standard WCM signiﬁcantly improved the quality of regional AGBC mosaics by reducing the stripes between adjacent paths caused by the difference in soil moisture conditions between different acquisition dates. By applying the standard WCM, the difference in mean predicted AGBC for the tested path with the largest soil moisture difference was reduced by 18.6%. The WCM is a valuable tool for AGBC mapping by reducing prediction uncertainties and striping effects in regional mosaics, especially in low-biomass areas including African woodlands and other woodland and savanna regions. It is repeatable for recent L-band data including ALOS-2 PALSAR-2, and upcoming SAOCOM and NISAR data.


Introduction
Radar remote sensing from a space-borne platform provides the possibility of analysing woody aboveground biomass carbon (AGBC) from the local to global scale in a consistent manner and at high resolution [1]. The ability of radar to estimate AGBC follows from the fundamental physical relationship between the number of woody elements of characteristic size and the amount of energy returned to the radar antennae [2][3][4][5][6][7]. For decades, empirical and semi-empirical relationships between radar cross section and forest canopies have been established for the retrieval of AGBC in varying ecosystems, in particular using long-wavelength radar, for example, from the Japanese Phased Array type L-band Synthetic Aperture Radar instruments aboard the Advanced Land Observing Satellite (ALOS-1/2 PALSAR-1/2) [8][9][10][11][12][13][14][15][16]. In African woodlands, previous work has also shown a strong biomass-backscatter relationship [17].
However, several challenges hinder the application of such methods to large-scale AGBC mapping when applying to open savanna and woodland ecosystems. The AGBC of woodlands varies widely according to the amount and extent of tree cover, from 1.8 tC/ha in the absence of trees [18] to 12-24 tC/ha in dry miombo woodlands [19], and 45 tC/ha in wet miombo woodlands [20]. Unlike other high-biomass ecosystems where the saturation of radar signal is considered as a major limitation for radar-based AGBC retrieval [21], Various studies have discussed the influence of soil moisture in L-band bioma backscatter relationships [13,22,23,25]. A study that modelled the contribution of volu and surface scattering of L-band radar in different forest stands exhibited a reduced v ume scattering (70%) in young forest stands with an AGBC of <25 tC/ha compared t 80%-90% volume scattering contribution when AGBC exceeded 50 tC/ha [7]. This in cates a strong influence of soil in low-biomass regions. In addition, the main source of s moisture variability in African savanna ecosystems is pulsed rainfall, with soil moistu dissipating between 17 and 50 days [26]. Because radar observations are limited by a strictive duty cycle of the imager due to the observation scenario, and, as such, adjac areas are often observed days to weeks apart, introducing variable soil moisture con tions into adjacent scenes. This issue of the soil moisture's influence on AGBC retrie ( Figure A1) becomes important for large area AGBC mapping. A relative correlati method (e.g., polygonal curve approximation) based on the statistics of overlay areas c balance the intensity between neighbouring paths and create a stripe-free mosaic [11,2 29]. However, reducing error propagation and potential bias remains problematic becau either path can be used as a reference. A method that considers the soil moisture differen in intensity balance between neighbouring paths is greatly needed.
The semi-empirical water cloud model (WCM) [30] was formulated to analyse su joint effects of the canopy and soil in scattering radar waves. Although initially intend for use for shorter wavelengths in croplands, the WCM has proven to be robust in descr ing the biomass-backscatter relationship across different forest ecosystems and imagi conditions with L-band radar [11,13,[31][32][33]. In these applications, the scattering comp nents from soil were considered as fixed parameters and fitted empirically alongside oth vegetation parameters. Quantitatively accounting for the soil moisture effect on AG Various studies have discussed the influence of soil moisture in L-band biomassbackscatter relationships [13,22,23,25]. A study that modelled the contribution of volume and surface scattering of L-band radar in different forest stands exhibited a reduced volume scattering (70%) in young forest stands with an AGBC of <25 tC/ha compared to a 80-90% volume scattering contribution when AGBC exceeded 50 tC/ha [7]. This indicates a strong influence of soil in low-biomass regions. In addition, the main source of soil moisture variability in African savanna ecosystems is pulsed rainfall, with soil moisture dissipating between 17 and 50 days [26]. Because radar observations are limited by a restrictive duty cycle of the imager due to the observation scenario, and, as such, adjacent areas are often observed days to weeks apart, introducing variable soil moisture conditions into adjacent scenes. This issue of the soil moisture's influence on AGBC retrieval ( Figure A1) becomes important for large area AGBC mapping. A relative correlation method (e.g., polygonal curve approximation) based on the statistics of overlay areas can balance the intensity between neighbouring paths and create a stripe-free mosaic [11,[27][28][29]. However, reducing error propagation and potential bias remains problematic because either path can be used as a reference. A method that considers the soil moisture difference in intensity balance between neighbouring paths is greatly needed.
The semi-empirical water cloud model (WCM) [30] was formulated to analyse such joint effects of the canopy and soil in scattering radar waves. Although initially intended for use for shorter wavelengths in croplands, the WCM has proven to be robust in describing the biomass-backscatter relationship across different forest ecosystems and imaging conditions with L-band radar [11,13,[31][32][33]. In these applications, the scattering components from soil were considered as fixed parameters and fitted empirically alongside other vegetation parameters. Quantitatively accounting for the soil moisture effect on AGBC retrieval with L-band radar remains problematic. In particular, the relative contributions of canopy volume scattering, double bounces from the interaction of large stems, and the scattering from soil is yet to be resolved, a situation which necessitates an element of trial and error in semi-empirical applications. A global soil moisture product with increasing temporal and spatial resolution [34][35][36][37][38] may serve as a proxy for the soil scattering component in the WCM. It therefore offers a promising approach to improving AGBC estimation in situations of variable soil moisture in African woodlands.
Despite a much lower carbon density compared to closed evergreen forests in tropical regions, accurate estimation of AGBC in African woodlands is of great importance. Over 150 million people inhabit African woodland regions, relying on forest resources for their livelihoods [39]. Characterised by an open tree canopy and a complex mosaic landscape, African woodland are one of the most extensive woody formations in sub-Saharan Africa, covering over 7.5 million km 2 of land [11,40]. It plays a significant role in the assessment of the terrestrial carbon cycle of continental Africa [41] and is one of the major contributors of uncertainties in carbon flux estimation, resulting from its diverse interannual variability, highly varied spatial diversity, and close link to human-induced disturbances [42][43][44]. Accurate and reliable monitoring of stocks in biomass are key parts to sustainable land management [1,45].
The aim of this paper was to assess the potential of using the WCM to improve L-bandbased AGBC retrieval in low-biomass regions in African woodlands. Varying degrees of complexity were introduced to explore which mechanisms needed to be represented in the WCM. We compared a standard WCM (WCM std ) and a complex WCM (WCM k including variables that represent the patchiness of African woodlands) to a simple exponential regression, which has been suggested as a heuristic model in this context (WCM 0 ). The main objectives for this study are to:

1.
Assess whether a semi-empirical WCM can be used to account for soil moisture effects in AGBC retrieval in low-biomass regions; 2.
Assess whether explicit consideration of the patchiness of African woodlands improves the performance of the WCM; and 3.
Create a large-scale moisture-adjusted AGBC map for central Mozambique.

Study Area
The Manica and Sofala Provinces in central Mozambique served as the study area, which covers around 20 million hectares of land and is dominated by woodland ecosystems (Figure 2). The woodland ecosystem in the study site mainly belongs to two classes: the 'drier Zambezian miombo woodland' and 'undifferentiated woodland'. Other woodland classes in this region are 'Colophospermum mopane woodland' and 'scrub woodland'. A small portion of the study site is covered by the 'East African coastal forest mosaic' [40]. The composition and structure of an undisturbed woodland is relatively uniform, with woody plants comprising 95-98% of the AGBC of undisturbed stands [46].
In central Mozambique, the climate typically alternates between a rainy and a dry season, with little rainfall between April to October. Characterised by pulsed rainfall in the wet season, the monthly precipitation estimates range between 0.05 mm/h and 0.65 mm/h in dry and wet season in the study region, respectively ( Figure 3).

In Situ AGBC Data
In situ AGBC data were collected during inventories undertaken between 2006 and 2010 in Manica Province, Mozambique ( Figure 2B). In total, 96 plots (Table 1) were inventoried, recording the diameter at breast height of all trees >5 cm. Plot size ranged between 0.1 and 2.2 ha, with a mean estimated AGBC of 24 tC/ha. The estimated AGBC ranged from 0.39 to 56 tC/ha. The range of AGBC covered the range found by other studies of woodlands [19,20]. A more detailed summary of plot sampling methodology, and an allometric model for AGBC estimation are presented in [47].

ALOS PALSAR-1 Imagery
All available ALOS-1 PALSAR-1 L-band radar images (2007-2011) in fine beam dual mode (FBD) at product level 1.1 (single look complex, SLC) were obtained from the Japan Aerospace Exploration Agency (JAXA) archive to cover the study regions. All images were acquired in ascending orbit, with an incidence angle of 34.3 degrees. Because the WCM is based on a simplified scattering mechanism only involving single scattering from the volumetric content of the soil and vegetation, only HV polarisation was used in this study for its sensitivity to volume scattering [48]. In total, 202 images were acquired, covering nine paths from 575 to 583, 11 frames from 6750 to 6850, and 16 acquisition dates ( Figure 2). The plot data were covered by one frame with 10 time steps (Table A1). The areas of overlap between paths were used to test the effect of the model's de-stripping effects as they represent observations of the same location from different dates and hence soil moisture. These overlap areas covered 26 scenarios with different soil moisture and backscatter combinations (Table A3).

In Situ AGBC Data
In situ AGBC data were collected during inventories undertaken between 2006 and 2010 in Manica Province, Mozambique ( Figure 2B). In total, 96 plots (Table 1) were inventoried, recording the diameter at breast height of all trees >5 cm. Plot size ranged between 0.1 and 2.2 ha, with a mean estimated AGBC of 24 tC/ha. The estimated AGBC ranged from 0.39 to 56 tC/ha. The range of AGBC covered the range found by other studies of woodlands [19,20]. A more detailed summary of plot sampling methodology, and an allometric model for AGBC estimation are presented in [47].

ALOS PALSAR-1 Imagery
All available ALOS-1 PALSAR-1 L-band radar images (2007-2011) in fine beam dual mode (FBD) at product level 1.1 (single look complex, SLC) were obtained from the Japan Aerospace Exploration Agency (JAXA) archive to cover the study regions. All images were acquired in ascending orbit, with an incidence angle of 34.3 degrees. Because the WCM is based on a simplified scattering mechanism only involving single scattering from the volumetric content of the soil and vegetation, only HV polarisation was used in this study for its sensitivity to volume scattering [48]. In total, 202 images were acquired, covering nine paths from 575 to 583, 11 frames from 6750 to 6850, and 16 acquisition dates ( Figure 2). The plot data were covered by one frame with 10 time steps (Table A1). The areas of overlap between paths were used to test the effect of the model's de-stripping effects as they represent observations of the same location from different dates and hence soil moisture. These overlap areas covered 26 scenarios with different soil moisture and backscatter combinations (Table A3).
ALOS PALSAR-1 images were processed using the Mapready Remote Sensing Tool Kit from Alaska Satellite Facility [49] (version 3.1, https://asf.alaska.edu/how-to/data-tools/ data-tools/#mapready accessed on 10 January 2022). Each image was multi-looked with 8 × 2 looks (in range and azimuth, respectively), terrain corrected using the 30 m digital elevation model (DEM) from the Shuttle Radar Topography Mission (SRTM), filtered using an enhanced Lee filter with window size 5 [50], and geocoded to 25 m resolution.

Soil Moisture Datasets
We used globally available daily soil moisture information at a spatial resolution of 0.25 • from the Climate Change Initiative Soil Moisture Product v04.7 (CCI SM) as the soil moisture proxy [37,51]. The CCI SM was demonstrated to have higher accuracies when compared to other satellite-derived soil moisture products [52]. We used CCI SM data from the same acquisition date as the ALOS PALSAR-1 image for model calibration and the analysis of de-striping effects ( Table 1). Missing values in the CCI SM dataset were filled using the mean soil moisture value of the previous and later dates. The dataset was then resampled to 25 m using a mean method to match the resolution of radar data. To illustrate the difference in spatial variation and temporal consistency of the soil moisture datasets in the study region, the soil moisture value was extracted and plotted for three example plots with various AGBC levels ( Figure 3).
Remote Sens. 2022, 14, x FOR PEER REVIEW 5 of 21 with 8 × 2 looks (in range and azimuth, respectively), terrain corrected using the 30 m digital elevation model (DEM) from the Shuttle Radar Topography Mission (SRTM), filtered using an enhanced Lee filter with window size 5 [50], and geocoded to 25 m resolution.

Soil Moisture Datasets
We used globally available daily soil moisture information at a spatial resolution of 0.25° from the Climate Change Initiative Soil Moisture Product v04.7 (CCI SM) as the soil moisture proxy [37,51]. The CCI SM was demonstrated to have higher accuracies when compared to other satellite-derived soil moisture products [52]. We used CCI SM data from the same acquisition date as the ALOS PALSAR-1 image for model calibration and the analysis of de-striping effects ( Table 1). Missing values in the CCI SM dataset were filled using the mean soil moisture value of the previous and later dates. The dataset was then resampled to 25 m using a mean method to match the resolution of radar data. To illustrate the difference in spatial variation and temporal consistency of the soil moisture datasets in the study region, the soil moisture value was extracted and plotted for three example plots with various AGBC levels ( Figure 3).  [53]. Note that monthly precipitation estimates are given in mm/h.   [53]. Note that monthly precipitation estimates are given in mm/h.

Tree Cover Fraction
Tree canopy parameter represents the tree cover fraction at the plot level. This represents the tree canopy parameter (k) used in Equation (8). The Landsat-based Vegetation Continuous Fields (VCF) data from [54] were used to estimate the tree canopy parameter  Table 1). The VCF product was resampled from 30 m Landsat resolution to 25 m resolution to match the spatial resolution of ALOS PALSAR-1 imagery.

Methods
First, the WCM presenting varying degrees of complexity (WCM std Equation (6), WCM k Equation (7), and WCM 0 Equation (9)), were fitted and validated with in situ AGBC data, HV radar backscatter from ALOS PALSAR-1 imagery for 2007-2010, and CCI SM data. Second, the forward WCMs were inverted to express AGBC as a function of soil moisture scattering and total received backscatter. Third, wall-to-wall AGBC maps for the study region were generated. The calibration and validation accuracies of the models within the AGBC range of the training in situ data (0-60 tC/ha) and the models' performance for prediction at a higher AGBC range (0-200 tC/ha) were analysed. The difference in mean predicted AGBC between the overlay areas were used to test the de-striping effects of WCM to generate regional AGBC mosaics. A flowchart of the method is provided in Figure 4. Tree canopy parameter represents the tree cover fraction at the plot level. This represents the tree canopy parameter (k) used in Equation (8). The Landsat-based Vegetation Continuous Fields (VCF) data from [54] were used to estimate the tree canopy parameter for each plot ( Table 1). The VCF product was resampled from 30 m Landsat resolution to 25 m resolution to match the spatial resolution of ALOS PALSAR-1 imagery.

Methods
First, the WCM presenting varying degrees of complexity (WCMstd Equation (6), WCMk Equation (7), and WCM0 Equation (9)), were fitted and validated with in situ AGBC data, HV radar backscatter from ALOS PALSAR-1 imagery for 2007-2010, and CCI SM data. Second, the forward WCMs were inverted to express AGBC as a function of soil moisture scattering and total received backscatter. Third, wall-to-wall AGBC maps for the study region were generated. The calibration and validation accuracies of the models within the AGBC range of the training in situ data (0-60 tC/ha) and the models' performance for prediction at a higher AGBC range (0-200 tC/ha) were analysed. The difference in mean predicted AGBC between the overlay areas were used to test the de-striping effects of WCM to generate regional AGBC mosaics. A flowchart of the method is provided in Figure 4.

Model Formulation
Complex scatter interactions in a vegetated area were simplified into a volume scattering model only involving single scattering of the vegetation and soil, where the reflections from the soil were added incoherently to the vegetation contribution (Equation (1)) [30]. WCM assumes a homogeneous 'slab' of canopy above the soil, which scatters some energy back to the antenna and thus attenuates the signal from the soil:

Model Formulation
Complex scatter interactions in a vegetated area were simplified into a volume scattering model only involving single scattering of the vegetation and soil, where the reflections from the soil were added incoherently to the vegetation contribution (Equation (1)) [30]. WCM assumes a homogeneous 'slab' of canopy above the soil, which scatters some energy back to the antenna and thus attenuates the signal from the soil: where the backscatter coefficient σ 0 (m 2 /m 2 ) is the total power backscattered by the land surface; σ 0 veg is the contribution from vegetation; σ 0 soil is the contribution from the soil; and t 2 is the two-way attenuation of the soil signal through the vegetation canopy. Canopy scattering in the WCM was considered from a collection of identical, randomly distributed scatterers, and expressed as a first-order approximation of the backscattering characteristics from clouds of hydrometeors [30]. Ref. [55] further introduced vegetation descriptors V 1 and V 2 . to characterise σ 0 veg (Equation (2)) and t 2 (Equation (3)). For given incidence angle θ, the scattering by the canopy (σ 0 veg ) is approximated as: Whilst the two-way attenuation by the canopy (t 2 ) is represented as: Ref. [30] suggested a linear relationship between the volumetric soil moisture content m s and scattering coefficient of soil σ 0 soil expressed in dB. Scattering by soil σ 0 soil in the power ratio can be approximated as: Overall, this allows the WCM (Equation (1)) to be described as: where A and B are vegetation parameters and C and D are soil moisture parameters all specific to the incidence angle θ. Parameter A relates to the albedo of the vegetation; B is the canopy attenuation coefficient; C represents a calibration constant for soil/radar backscatter from dry soil; and D relates to the sensitivity of the radar signal to variations in volumetric soil moisture [33,56,57]. m s is the volumetric soil moisture content proxy by soil moisture CCI SM in m 3 /m 3 . σ 0 is the backscatter coefficient in m 2 /m 2 .
Given that there is no general theoretical background allowing us to define the best set of canopy descriptors, Equation (5) can be interpreted in various ways due to the complexity of the vegetation structure and the relative simplicity of the models [55]. Table 2 summarises various remote-sensing-generated indices used in previous studies to represent V 1 and V 2 . To reduce the difficulties in the inversion of WCM for AGBC mapping, following [11,13], V 1 = 1 was used in this study (Equation (6), referred to as the standard WCM (WCM std ) in this paper):  [55], W is the volumetric water content of the vegetation layer [30], LAI is the leaf area index [58], and GSV is the growing stock volume [59]. Even in this case, the heterogeneity of African woodlands may play an important role in the scattering. Most African woodlands violate the 'slab' assumption of the WCM as they are partly composed of tree-free areas where only soil interaction will take place. Following a similar model formulation suggested by [31], such a 'patchy' WCM (WCM k ) can be represented as: where k is the tree canopy parameter that describes the fraction of the plot covered by the tree canopy. We compared WCM std and WCM k to a reduced model of no soil moisture effects ('vegetation-only' model): Forward WCM s were inverted to express vegetation parameter V 2 as a function of soil moisture scattering and total received backscatter. In this study, we considered V 2 to scale linearly with AGBC, while the soil moisture content (m s , kg/m 3 ) scaled with soil moisture estimates from CCI SM. Thus, the forward WCM s (WCM std , WCM k , and WCM 0 ) can be inverted as a function of backscatter and m s to estimate AGBC as follows (referred to as BM-WCM std , BM-WCM k , and BM-WCM 0 , respectively):

Parameterisation
Data described in Section 2.2 were used to fit the forward WCM s (WCM std , WCM k , and WCM 0 ) and the inverted WCM s for AGBC estimation (BM-WCM std , BM-WCM k , and BM-WCM 0 ). We used in situ AGBC data to represent vegetation volume scattering; L-band ALOS PALSAR-1 imagery at HV polarisation to represent the total backscatter σ 0 ; and CCI SM as the soil moisture proxy acquired for each available radar observation. It is worth noting that in situ AGBC data may not be acquired on the same acquisition day as the radar imagery due to the limited amount of field work conducted. Soil moisture and vegetation parameters in the models were estimated simultaneously using the nonlinear least squares model (nls package) in R (version 3.2.3) [63].

Assessing Model Performance
Calibration and validation error were used to assess the forward WCM s (WCM std , WCM k , and WCM 0 ) and the inverted WCM s (BM-WCM std , BM-WCM k , and BM-WCM 0 ) and compared among different AGBC or soil moisture groups. Root mean square error (RMSE) of calibration (Equation (13)) was used to represent the calibration error, which quantifies how well the fit between the data and the calibration model. where n is the number of plots used in the fitting of the model; Y i is the ith observed value; andŶ i is the ith predicted value. The overall uncertainty of the model's prediction was validated with a 5000 crossvalidation with 50:50 split. In each iteration, the training and validation data are selected randomly without any duplicate realisation. Absolute bias (Bias val ) and RMSE (RMSE val ) for each compared model were calculated with Equations (14) and (15), respectively.
where j = 1 . . . 5000 realisation of the 50:50 cross-validation; i = 1 . . . n is the ith validation plot in a total of n points (in a 50:50 split cross-validation, n equals half of the total plots); Y i is the ith validation AGBC value; andŶ i is the ith AGBC prediction from the regression.
To assess how well the model removed the striping effects, we compared the predicted AGBC in overlapping areas between different paths, with radar data acquired at different dates, and thus with different soil moistures. The difference in mean predicted AGBC between the two dates in the overlay areas were used to measure the effectiveness of inverted WCM s in de-striping an AGBC mosaic by correcting the soil moisture effects between adjacent paths.

Prediction Accuracy of the Forward WCM s
Compared to WCM 0 , which does not account for soil moisture scattering, WCM std and WCM k showed improved backscatter estimation accuracy with a reduced cross-validation RMSE val of 26.5% from 0.0083 m 2 /m 2 to 0.0061 m 2 /m 2 . Separating the vegetation and soil contribution in the fitted WCM std and WCM k ( Figure 5) indicated that soil moisture played a more important role than vegetation scattering when AGBC was <16 tC/ha for WCM k , and 12 tC/ha when WCM std was applied. This effect from soil moisture decreased as AGBC increased, but still existed within the entire range of the in situ AGBC values (0-60 tC/ha) observed in this study.
To explore the implications of the fitted model, we extrapolated beyond the range of the calibration data (0-60 tC/ha for AGBC and 0.0077-0.473 m 3 /m 3 for soil moisture) and simulated the model's performance in a higher AGBC (0-200 tC/ha) and soil moisture (0-1 m 3 /m 3 ) range. Figure 6 depicts how the influence of soil moisture is biomassdependent. Backscatter predictions from WCM std varied according to different AGBC or soil moisture levels. When AGBC was ≥140 tC/ha, the predicted backscatter coefficient was almost constant as soil moisture increased, meaning that the soil contribution is negligible. When AGBC was <140 tC/ha, the prevailing phenomenon was attenuation of the soil contribution by the vegetation, and attenuation increased as AGBC increased. The lower the AGBC level, the more the attenuation rate of WCM std was altered by soil moisture proxies.  Table  A2.
To explore the implications of the fitted model, we extrapolated beyond the range of the calibration data (0-60 tC/ha for AGBC and 0.0077-0.473 m 3 /m 3 for soil moisture) and simulated the model's performance in a higher AGBC (0-200 tC/ha) and soil moisture (0-1 m 3 /m 3 ) range. Figure 6 depicts how the influence of soil moisture is biomass-dependent. Backscatter predictions from WCMstd varied according to different AGBC or soil moisture levels. When AGBC was ≥140 tC/ha, the predicted backscatter coefficient was almost constant as soil moisture increased, meaning that the soil contribution is negligible. When AGBC was <140 tC/ha, the prevailing phenomenon was attenuation of the soil contribution by the vegetation, and attenuation increased as AGBC increased. The lower the AGBC level, the more the attenuation rate of WCMstd was altered by soil moisture proxies.  Table A2.

Prediction Accuracy of the Inverted WCM s for AGBC Estimation
Validation error suggests that considering the soil moisture effects and the patchiness of the tree canopy in the model improved AGBC estimation (Table 3), particularly for regions with AGBC ≤20 tC/ha (Figure 7). RMSE val for BM-WCM std and BM-WCM k at the low AGBC range (≤10 tC/ha) was around 15% lower (5% for ≤20 tC/ha AGBC group) than that of BM-WCM 0 whereas at higher AGBC range (>20 tC/ha), the RMSE val was similar among all three models (Figure 7). The overall RMSE val was similar between BM-WCM k (7.70 tC/ha) and BM-WCM std (7.72 tC/ha), which were slightly lower than that of the BM-WCM 0 (8.10 tC/ha) ( Table 3). Parameters for each fitted model are presented in Table A2 with the model's prediction curve presented in Figure A2.

Prediction Accuracy of the Inverted WCMs for AGBC Estimation
Validation error suggests that considering the soil moisture effects and the patchiness of the tree canopy in the model improved AGBC estimation (Table 3), particularly for regions with AGBC ≤20 tC/ha (Figure 7). RMSEval for BM-WCMstd and BM-WCMk at the low AGBC range (≤10 tC/ha) was around 15% lower (5% for ≤20 tC/ha AGBC group) than that of BM-WCM0 whereas at higher AGBC range (>20 tC/ha), the RMSEval was similar among all three models (Figure 7). The overall RMSEval was similar between BM-WCMk (7.70 tC/ha) and BM-WCMstd (7.72 tC/ha), which were slightly lower than that of the BM-WCM0 (8.10 tC/ha) ( Table 3). Parameters for each fitted model are presented in Table A2 with the model's prediction curve presented in Figure A2.

Effects of Inverted WCM on Producing Regional AGBC Mosaics
BM-WCMstd reduced the stripes in the generated regional AGBC mosaic com to when BM-WCM0 was used ( Figure 8B vs. Figure 8C). Among the 26 scenarios the biggest soil moisture difference was 0.21 m 3 /m 3 (Table A3). The biggest de-s effect of BM-WCMstd occurred between path 576/577 (Figures 2 and 8C), where the ence in mean predicted AGBC in the overlay area was reduced by 18.6% from 4.5 to 1.47 tC/ha compared to when the BM-WCM0 was used (Table A3). It was also the biggest soil moisture difference occurred, suggesting that the reduction in the

Effects of Inverted WCM on Producing Regional AGBC Mosaics
BM-WCM std reduced the stripes in the generated regional AGBC mosaic compared to when BM-WCM 0 was used ( Figure 8B vs. Figure 8C). Among the 26 scenarios tested, the biggest soil moisture difference was 0.21 m 3 /m 3 (Table A3). The biggest de-striping effect of BM-WCM std occurred between path 576/577 (Figures 2 and 8C), where the difference in mean predicted AGBC in the overlay area was reduced by 18.6% from 4.52 tC/ha to 1.47 tC/ha compared to when the BM-WCM 0 was used (Table A3). It was also where the biggest soil moisture difference occurred, suggesting that the reduction in the difference in AGBC prediction in the overlay area was mainly the result from the correction of soil moisture effects.

How Much Uncertainty Can Be Reduced in AGBC Estimation When Soil Moisture Is Accounted for?
Compared with BM-WCM0, BM-WCMstd and BM-WCMk exhibited a significant improvement in AGBC estimation for African woodlands with an AGBC <20 tC/ha ( Figure  7). As expected, between 20-60 tC/ha, the calibration and validation accuracy among all models were similar, indicating a less important soil moisture influence compared to other sources of error (such as errors in the field measurement, speckle in the backscatter, and random errors). As AGBC further increased, the scattering from soil moisture was negligible ( Figure 6). The fact that the soil moisture correction effects of BM-WCMstd and BM-WCMk only apply to low-biomass areas, which is a small fraction of the calibration and validation data points, explains a limited reduction in AGBC estimation uncertainties when analysed across an AGBC range of 0-60 tC/ha (Table 3). However, with an average AGBC predicted to be around 20 tC/ha in this and previous studies [19,20,47], adjusting for scattering from soil moisture is crucial for an accurate AGBC estimation in African woodlands.
More analysis is needed to draw concrete conclusions of the model's sensibility to soil moisture in regions with AGBC > 60 tC/ha. This is due to a lack of in situ AGBC data with AGBC >60 tC/ha imported in the model parameterisation and validation processes. Moreover, a large amount of uncertainty remains unquantified (Figure 7). WCM and BM-WCM could benefit from a soil moisture dataset with improved spatial resolution, or a simultaneous field measurement of AGBC and soil moisture with the acquisition date of the radar imagery.
Results from this study also suggested that AGBC is a good proxy for vegetation scattering ( ) in the WCM. This finding is in accordance with previous studies where

How Much Uncertainty Can Be Reduced in AGBC Estimation When Soil Moisture Is Accounted for?
Compared with BM-WCM 0 , BM-WCM std and BM-WCM k exhibited a significant improvement in AGBC estimation for African woodlands with an AGBC <20 tC/ha ( Figure 7). As expected, between 20-60 tC/ha, the calibration and validation accuracy among all models were similar, indicating a less important soil moisture influence compared to other sources of error (such as errors in the field measurement, speckle in the backscatter, and random errors). As AGBC further increased, the scattering from soil moisture was negligible ( Figure 6). The fact that the soil moisture correction effects of BM-WCM std and BM-WCM k only apply to low-biomass areas, which is a small fraction of the calibration and validation data points, explains a limited reduction in AGBC estimation uncertainties when analysed across an AGBC range of 0-60 tC/ha (Table 3). However, with an average AGBC predicted to be around 20 tC/ha in this and previous studies [19,20,47], adjusting for scattering from soil moisture is crucial for an accurate AGBC estimation in African woodlands.
More analysis is needed to draw concrete conclusions of the model's sensibility to soil moisture in regions with AGBC > 60 tC/ha. This is due to a lack of in situ AGBC data with AGBC >60 tC/ha imported in the model parameterisation and validation processes. Moreover, a large amount of uncertainty remains unquantified (Figure 7). WCM and BM-WCM could benefit from a soil moisture dataset with improved spatial resolution, or a Remote Sens. 2022, 14, 404 13 of 20 simultaneous field measurement of AGBC and soil moisture with the acquisition date of the radar imagery.
Results from this study also suggested that AGBC is a good proxy for vegetation scattering (σ 0 veg ) in the WCM. This finding is in accordance with previous studies where a simplified WCM was used in describing the biomass-backscatter relationship across different forest ecosystems [11,13,[31][32][33].

Does Reverted WCM Reduce Stripes in AGBC Mosaics by Accounting for Soil Moisture
Changes between Adjacent Paths?
Regional AGBC mosaics are normally generated based on annual radar backscatter mosaics such as the Global PALSAR-2/PALSAR Yearly Mosaic provided by JAXA. Histogram matching or polygonal curve approximation were normally used to balance the intensity between neighbouring paths to create a stripe-free mosaic [27][28][29], based on which a stripe-free regional biomass map was generated [11]. Although gaps are introduced to reduce error propagation during image balancing [27], bias may still persist. A relative correction algorithm relays statistics from overlay areas and aims to reduce the relative systematic bias between two compared paths, meaning that either path can be used as a reference; however, the resulting mosaic can be biased. Applying inverted WCM could achieve better de-striping results because the correction is biomass-dependent and avoids the potential accumulated bias introduced by applying a relative correction algorithm between adjacent paths. The CCI SM data are provided at a high temporal resolution of one day, meaning that it is possible to capture the difference in bias between AGBC maps produced from ALOS PALSAR-1 imagery with different acquisition dates using inverted WCM. Results from Figure 8 support this conclusion by showing an improved correlation in AGBC estimation for overlay areas from adjacent paths when BM-WCM std was used compared to BM-WCM 0 . Although applying inverted WCM might introduce variation to the prediction due to errors from the soil moisture dataset, the mosaic should be less biased than when using a relative correction algorithm. This de-striping effect is particularly important in African woodlands, which are characterised by pulsed rainfall and open canopy. Changes in soil moisture conditions between different acquisition dates will cause a huge difference in backscatter intensity between adjacent paths [23,27]. When temporally dense time series of radar data become available, accounting for soil moisture effects between images from different acquisition dates will become more and more important in AGBC retrieval. The capacity of the proposed WCM to provide de-striped mosaics can be an important contribution for future large-area studies in global woodland regions.

Does Explicit Consideration of the Patchiness of African Woodlands Improve the Performance of the WCM? Which Other Factors Matter?
Previous studies have shown robust water-cloud types of models that consider the patchiness of the tree canopy in describing the backscatter to AGBC relationship [13,31,64]. In these studies, Light Detection and Ranging (LiDAR) data were used to provide accurate canopy gap information. In this study, BM-WCM k 's performance was only slightly better than BM-WCM std . This is most likely due to uncertainties in the tree cover data used to parameterise the model (Table 3). Due to the lack of LiDAR data, which are rarely available at a large scale, VCF tree cover data at 30 m resolution was used for model parameterisation. Further study incorporating more accurate global tree cover data (e.g., the forest canopy height product from [65]) are needed to prove the efficiency of BM-WCM k in large-scale AGBC mapping.
Compared to a more uniformly planted cropland (for which the WCM used in this study was developed), the backscattering mechanism of a wooded area is more complex. While the theory of the WCM neatly describes total backscatter as the sum of contributions from the vegetation and soil moisture, there is no general theoretical basis to define the best set of canopy or soil moisture descriptors, and consequently, to derive the values of vegetation parameters A and B and soil moisture parameters C and D [57,66]. Applying a comprehensive multi-layer WCM may improve AGBC estimation by describing the scattering mechanism in woodlands more thoroughly. This has a larger effect in areas with more incident angle dependence of backscattering such as mountain areas. Finally, importantly, other land surface conditions such as soil roughness and texture, which were not considered in the WCM, could also play an important role in altering the biomassbackscatter relationship in African woodlands.

Conclusions
A set of semi-empirical WCMs were used to correct the soil moisture effects in AGBC retrieval in African woodlands. In situ AGBC data, L-band ALOS PALSAR radar imagery, and daily soil moisture estimates from CCI SM were used for model parameterisation with thee BM-WCM std yield showing the best result. Soil moisture has a significant impact in AGBC retrieval in low-biomass regions. In this study, correcting soil moisture effects in areas with AGBC ≤20 tC/ha led to a 15% increase in AGBC estimation accuracy. As AGBC increased, the impact of soil moisture was less important, and even negligible. In addition, an improved regional AGBC mosaic was created using BM-WCM std because WCM effectively accounted for the difference in soil moisture conditions between different acquisition dates for adjacent paths. The difference in mean predicted AGBC was reduced by 18.6% in overlay areas for two paths with a large soil moisture difference. Explicitly considering the patchiness of African woodlands in the WCM provided limited improvement in AGBC prediction compared to a standard WCM. Incorporating a more accurate global tree cover data is promising to provide better AGBC estimations. The capacity of the proposed WCM to account for soil-moisture difference and provide de-striped mosaics can be an important contribution for future large-area studies in global woodland regions (e.g., savanna forests in Australia, cerrado in Brazil, and dry forest in Mexico) when dense time series of ALOS PALSAR-2 or NASA-ISRO Synthetic Aperture Radar (NISAR) data become openly available. Data Availability Statement: ALOS PARSAR data were downloaded from JAXA's AUIG2 platform https://auig2.jaxa.jp/openam/UI/Login accessed on 10 January 2022. Registration is required to access the data. The Climate Change Initiative Soil Moisture Product v04.7 was used as the soil moisture proxy and downloaded from https://esa-soilmoisture-cci.org/ accessed on 10 January 2022. The Landsat-based Vegetation Continuous Fields (VCF) data representing tree cover fraction were downloaded from http://www.landcover.org/ accessed on 10 January 2022.

Acknowledgments:
The authors would like to thank JAXA for providing the ALOS PALSAR-1 data through the 4th and 6th RAs agreements. The authors gratefully acknowledge financial support from IIED as part of the Testing REDD+ in the Beira Corridor project, the Chinese Scholarship Council, and the Elizabeth Sinclair Irvine Fund. Sincere gratitude to Sam Bowers and Helen Carter for proofreading the paper.

Conflicts of Interest:
The authors declare no conflict of interest.