Implementation of Two ‐ Stream Emission Model for L ‐ Band Retrievals on the Tibetan Plateau

: This study assesses the suitability of the two ‐ stream microwave emission model in simulating brightness temperature ( T B p ) and retrieving liquid water content ( θ liq ) at L ‐ band in combination with the four ‐ phase dielectric model for both thawed and frozen soil. Both single (SCA) and double (DCA) channel algorithms are adopted using both ground ‐ based ELBARA ‐ III and spaceborne SMAP measurements conducted in a Tibetan grassland site. The ELBARA ‐ III measured T B p are smaller than the SMAP measurements in the warm season due to a lower value of average θ liq presented within the ELBARA ‐ III footprint. The two ‐ stream emission model configured with SMAP vegetation and surface roughness parameterization underestimates both ELBARA ‐ III and SMAP measured T B p at horizontal polarization in the cold season, and overestimates the vertical polarized measurements ( T BV ) in the warm season. Implementation of a new surface roughness and vegetation parameterization resolves above deficiency, and the simulations capture better large ‐ scale SMAP measurements in comparison to these performed for the ELBARA ‐ III footprint. The dynamics of in situ θ liq are better reproduced by retrievals using the SCA based on T BV measurements (SCA ‐ V), whereby the SCA ‐ V retrievals using the SMAP ascending overpass measurements shows the best results with an unbiased root ‐ mean ‐ square error (ubRMSE) of 0.035 m 3 m − 3 that outperforms the SMAP mission specification. This study investigates the performance of the two ‐ stream microwave emission model in simulating L ‐ band T B p and retrieving θ liq in combination with the four ‐ phase dielectric model for both thawed and frozen soils on the Tibetan Plateau. Both single (SCA) and double (DCA) channel algorithms are adopted using both ground ‐ based ELBARA ‐ III and spaceborne SMAP measurements conducted in a Tibetan grassland site. Intercomparison between the time variations of ELBARA ‐ III and SMAP T B p measurements demonstrates that high correlations (R ≥ 0.87) are found between both measurements, though the footprints are obviously distinct for the and ‐ B p are generally lower between and situ average reveals that ,


Introduction
Passive microwave remote sensing at L-band (1-2 GHz) is recognized as one of the most useful approaches for worldwide monitoring of surface soil moisture and freezethaw state [1,2]. Two currently operating satellite missions, i.e., the SMOS (Soil Moisture and Ocean Salinity) and SMAP (Soil Moisture Active Passive) launched, respectively, in 2009 by the European Space Agency (ESA) and in 2015 by the National Aeronautic and Space Administration (NASA), all use this technology to map global soil moisture. In the meantime, numerous studies have been devoted over the past decade to improve parameterizations of the commonly used τ-ω microwave emission model [3] and retrieval of soil moisture by these two missions [2,4,5].
The τ-ω microwave emission model includes radiative components from both vegetation canopy and soil surface, whereby the vegetation canopy is generally treated as a single homogeneous "soft layer" [6,7]. This model is a zero-order solution of the microwave radiative transfer equations, which generally neglects multiple reflections between vegetation canopy and underground soil surface and does not follow the Kirchhoff's law [8]. In addition, the τ-ω microwave emission model also neglects the multiple scattering processes in the vegetation canopy that is inadequate to represent canopy volume scattering [9][10][11]. To resolve this problem, a common way is to calibrate Tibetan Plateau, and a new parameterization has thus been proposed to address these problems. Similar findings have also been reported by Chaubell et al. [40].
In this study, we expand the application of the two-stream microwave emission model to both thawed and frozen soil conditions by incorporating the four-phase dielectric mixing model. Its performance in simulating L-band TB p and retrieving liquid water content (θliq) has been tested using both spaceborne SMAP and ground-based ELBARA-III radiometry measured TB p conducted in a Tibetan grassland site. The impact of different surface roughness and vegetation parameterizations on the TB p simulation is also assessed, and the θliq is retrieved using both single (SCA) and double (DCA) channel algorithms. In Section 2, we show the simultaneous SMAP and ELBARA-III TB p measurements, and Section 3 outlines the two-stream microwave emission model as well as the thereon-based θliq retrieval algorithms. The comparative analysis of SMAP and ELBARA-III TB p measurements and their relationships with in situ θliq are presented in Section 4. Impacts of surface roughness and vegetation parameterizations on the TB p simulations and θliq retrievals based on SMAP and ELBARA-III measured TB p are investigated in Section 4 as well. The findings are summarized in the Section 5.

Maqu Station
The Maqu soil moisture (SM) monitoring network is located within the Yellow River source region on the northeastern part of the Tibetan Plateau ( Figure 1). The Maqu network is configured with about 30 SM profile monitoring sites, which was chosen as one of the calibration/validation sites by the SMAP scientific team for evaluating the SMAP soil moisture retrievals [41]. The dominant land cover is alpine meadows, and the soil type is generally dominated by silt loam, whereby the average sand and clay percentage are about 30% and 10%, and the average bulk density (ρb) is about 1 g cm −3 [16]. The elevations vary from 3400 to 3800 m.
Each monitoring site records readings of SM at different soil depths ranging from 5 to 80 cm every 15 min using the Decagon 5TM probes. In the air, the 5TM sensors integrate a volume of 715 mL around the prong, with a maximum distance of 6 cm from the center of the sensor. In the soil, the zone of influence ranges from 3 to 4 cm from the middle prong of the 5TM sensors [42]. To further improve the measured accuracy of in situ soil liquid water contents θliq derived from the 5TM capacitance measurements, Dente et al. [43] have developed several calibration functions for specific soil types found across the Maqu area. Detailed description of the Maqu SM network is referred to Zheng et al. [44] and Zhang et al. [45].

ELBARA-III Field Site
For the purpose of evaluating the SMOS and SMAP measurements over the Tibetan Plateau, the L-band ELBARA-III radiometer [46] was setup within the Maqu in situ SM monitoring network ( Figure 1) in January, 2016 [47,48]. The ELBARA-III radiometer has been deployed on a tower with 4.8 m height above the ground, and the beam waist of the antenna is about 6.5 m height. Both horizontal (TB H ) and vertical (TB V ) polarized TB p of ground have been measured for incidence angles ranging from 40° to 70° in steps of 5° every 30 min. Concurrent to the TB p measurements, next to the radiometer tower SM and soil temperature (SMST) profiles have been measured by the 5TM probes as well, and micrometeorological measurements have also been performed in the field site. An additional description of the ELBARA-III observation site and the abovementioned in situ measurements was outlined by Zheng et al. [47,48].

SMAP Products
The SMAP satellite mission led by the NASA has been launched in January 2015, which is configured with an L-band (1.41 GHz) radiometer and an L-band (1.26 GHz) radar. The radar ceased operations in July 2015, while the radiometer continues to work and provides a spatial extent of about 40 km with off-nadir incidence angle ψ  40 o as expected.
Latest versions of Level 1C radiometer product and Level 2 radiometer SM product are utilized in this study, which is gridded on a 36 km Equal-Area Scalable Earth-2 (EASE2) grid and is available at https://nsidc.org/data/smap/smap-data.html (accessed on January 2022). A centered validation grid pixel has been defined by the SMAP scientific team for the Maqu SM monitoring network to address the uncertainties related to the spatial mismatch between the SMAP soil moisture retrievals and the in situ references [41]. In Figure 1, it can be noted that the ELBARA-III monitoring station is placed at the upper right part of the SMAP validation grid. The TB p measurements of SMAP during both ascending (6 PM) and descending (6 AM) overpasses are used in this study, and the data during the period from August 2016 to July 2017 are extracted for the validation grid pixel. There are about 360 SMAP measurements that are available for the presented research.
Both SMAP and ELBARA-III measured TB p and the corresponding footprint average θliq used in this study is provided as Supplementary Material. Please find the supplementary Table S1 for the details.

Two-Stream Microwave Emission Model
The two-stream emission model developed by Schwank et al. [6] is implemented to simulate the land surface emission in this study: where p indicates the polarization of microwave emission (p = H, horizontal; p = V, vertical), Tv and TG are the effective vegetation and soil temperature (K), Tsky represents the sky brightness temperature (K), es p , ev p and esky p are emissivity (-) of soil, vegetation and sky, rv represents the vegetation reflectivity (-), γv represents the transmissivity of vegetation canopy (-), r p represents the rough soil reflectivity (-), ω represents the effective scattering albedo (-), τ represents the vegetation optical depth (-), and ψ is the incidence (observation) angle ( o ). The Tsky can be estimated by an empirical approach using air temperature and elevation as input [49], which is ignored in this study due to the fact that its value is very small at L-band (≈5 K) [6]. The estimation of r p is formulated as [50]: where q indicates the polarization of microwave emission (q = H, horizontal; q = V, vertical), rs p and rs q are the specular reflection coefficients (-), N represents the angular effect on the reflectivity (-), h takes into account the intensity effect (-), and Q refers to the impact of polarization mixing (-). The rs p and rs q are estimated by the Fresnel's equations [33] using the effective soil permittivity εs as input: The soil permittivity εs (εs = ε's + iε''s) of the thawed or frozen soil condition is simulated by the four-phase soil dielectric model as [30,31,51]: where θs represents the porosity (m 3 m −3 ), θ represents the soil total water content (m 3 m −3 ) that derived from the in situ θliq (m 3 m −3 ) as in Zheng et al. [52]. The exponent η is specified as 0.5, and the complex permittivity of ice, dry soil matrix and air are taken from Schwank et al. [30] as εice = 3.2 + i0.1, εmatrix = 5.5 + i0.2 and εair = 1. The complex permittivity of liquid water (εw) is computed using the Dobson et al. [26] model as in Zheng et al. [47]. During the SMAP overpass (6 PM or 6 AM), it's reasonable to assume that the nearsurface, vegetation and air are in thermal equilibrium with Tv  TG, which can be represented by the effective soil temperature Teff. Here, we compute Teff according to Choudhury et al. [53] from available in situ SMST information as: where λ is the vacuum wavelength (cm), Ts(z) is the soil temperature (K), and α(z) is the attenuation coefficient (-) at soil depth z.
In this study, the surface roughness parameter N in Equation (7) and vegetation parameter ω in Equations (5) and (6) are set equal to 2 and 0.05 as the SMAP retrieval algorithm [34] for grassland, and two parameterizations are adopted to estimate the parameters τ in Equations (5) and (6), as well as h and Q in Equation (7). One is to implement the parameterization adopted by the SMAP retrieval algorithm [34] (hereafter "SMAP parameterization") as: where NDVI refers to the normalized difference vegetation index (-), VWC refers to the vegetation water content (-), and s represents the standard deviation of surface roughness height (mm). The parameters b and s are set equal to 0.13 (-) and 15.6 mm as the SMAP retrieval algorithm [34] for grassland, which lead to the value of 0.156 for the h according to Equation (15).
The other is to implement the new vegetation and surface roughness parameterization newly developed by Zheng et al. [16,39] (hereafter "Zheng's parameterization") which showed that the SMAP parameterization underestimates the impact of surface roughness and overestimates the effect of vegetation in the Tibetan grassland and desert ecosystems: where LAI is the leaf are index (m 2 m −2 ), s is also set equal to 15.6 mm as the SMAP retrieval algorithm [34] for grassland, which leads to values of 0.58 and 0.1 for the h and Q according to Equations (18) and (19).
The needed NDVI and LAI in this study are obtained from the MODIS MOD13A2 [54] and MOD15A2 [55] products, respectively. Figure 2 presents the time series of vegetation optical depth τ estimated by the SMAP and Zheng's parameterizations for the SMAP descending overpass from August 2016 and July 2017 that is consistent with both SMAP and ELBARA-III measurements. The τ estimates, based on the SMAP parameterization, are considerably larger than those computed by the new parameterization of Zheng et al. [16]. On the contrary, Zheng's parameterization tends to produce larger values of Q and h in comparison to SMAP parameterization, i.e., 0.1 vs. 0 for the Q, and 0.58 vs. 0.156 for the h.
To help the reader understand how the two-stream emission model is implemented with either SMAP or Zheng's vegetation and surface roughness parameterization to simulate the TB p , a sample computation is provided as Supplementary Material. Please find the supplementary Table S2 for the details. .

Soil Liquid Water Content Retrieval Algorithms
Both the single channel soil moisture retrieval algorithm (SCA) using either the TB H (SCA-H) or TB V (SCA-V) measurements and double channel algorithm (DCA) using both TB V and TB H measurements implemented by the SMAP retrieval algorithm [34] are adopted to retrieve the θliq in this study for both thawed and frozen soil conditions. The two-stream emission model is adopted for the forward land emission modelling with the implementation of the four-phase soil dielectric model (see Section 3.1), whereby the better performance of vegetation and surface roughness parameterization (SMAP or Zheng's parameterization) is implemented to estimate the parameters τ, h, and Q. Additional information about the SCA and DCA retrieval approaches is referred to -O'Neill et al. [34]. Figure 3 presents the time series of TB H and TB V measurements collected by the SMAP and ELBARA-III radiometer at the observation angle ψ of 40°. The SMAP measurements performed between August 2016 and July 2017 during both ascending and descending overpasses are considered, and the ELBARA-III measurements closest to the overpasses of SMAP are extracted for the comparison. The data gap noted for the ELBARA-III measurements is caused by power supply failures. Figure 3 also presents the statistical errors estimated between the SMAP and ELBARA-III measurements, which includes the root-mean-square error (RMSE), bias, unbiased RMSE (ubRMSE) and Pearson product moment correlation coefficient (R). Figure 4 further shows the spatial θliq averages at 5 cm soil depth taken from the in situ data collected within the footprints of ELBARA-III and SMAP measurements (Figure 1). The error statistics estimated between the in situ θliq representative of the ELBARA-III and the SMAP footprints are shown in Figure 4 as well.

Comparisons between SMAP and ELBERA-III TB p Observations
The θliq dynamics of the ELBARA-III and SMAP footprints are comparable to each other ( Figure 4). Pearson's correlation coefficient R between the two in situ θliq averages is high (R ≥ 0.96) during the SMAP overpasses. In general, the soil is unfrozen and wet from May to October (i.e., warm season), while it appears as frozen and dry between November and April (i.e., cold season). In the warm season, the average θliq of the ELBARA-III footprint is generally smaller than that within the SMAP footprint, which is due to the fact that the soil porosity and water holding capacity are higher within the SMAP footprint caused by larger organic matter contents found in the soil [43,44]. Comparison of Figures  3 and 4 shows that both ELBARA-III and SMAP measured dynamics of TB p generally follow the θliq variations in the warm season, whereby the TB p increase with decreasing θliq (e.g., July 2017) and vice versa (e.g., September 2016). In the cold season, the θliq sharply decreases due to soil freezing between November and February that results in the increase in TB p , while thawing of soil ice between February and April leads to increase in θliq and thus a decrease in TB p . Generally, the SMAP and ELBARA-III measured TB p show high correlation as indicated by R ≥ 0.87 except for the TB H during the SMAP descending overpass (Figure 3a). In addition, the ELBARA-III measured TB p are generally larger than the SMAP measurements between June and October due to the fact that θliq of ELBARA-III footprint is smaller than that of SMAP footprint.    Figure  5. Compared to the ELBARA-III measurements, the TB H , TB V and PR obtained from the SMAP measurements show higher correlations with footprint averaged θliq for both cold and warm periods during both SMAP descending and ascending overpasses as indicated by smaller scatters and thus higher R values ( Figure 5).

Relations between TB p and θliq Observations
The correlations between both ELBARA-III and SMAP measured TB V and the footprint averaged θliq in the warm season are best explained by a linear function, with R 2 values larger than 0.81 during both SMAP descending and ascending overpasses. In contrast, the largest scatter is found for the plot with the ELBARA-III derived PR versus the footprint averaged θliq. In the cold season, the SMAP measurements (i.e., TB H , TB V and PR) are better linked to the θliq measurements during the SMAP ascending overpass, while the ELBARA-III measurements show better agreement with the in situ θliq during the SMAP descending overpass. In general, higher R 2 values are found between both SMAP and ELBARA-III measured TB H and the θliq measurements in the cold period, and the relationship between SMAP measured TB V and the in situ θliq shows the highest R 2 value during the SMAP ascending overpass.

Brightness Temperature Simulation
To investigate the performance of the two-stream emission model and its sensitivity to different vegetation and surface roughness parameterizations, two simulations are performed with the two-stream model using either the SMAP (Sim1) or Zheng's (Sim2) parameterization (see Section 3.1). The SMST input data are specified as the arithmetic average of in situ data collected within either the ELBARA-III or the SMAP footprint (Section 2) closest to the SMAP overpasses for matching the TB p simulations with either the SMAP or the ELBARA-III measurements. Figure 6 shows the time series of SMAP TB p measurements and simulations produced from both Sim1 and Sim2 performed for the SMAP footprint between August 2016 and July 2017 for the SMAP descending and ascending overpasses. The corresponding statistical errors estimated between the measured and simulated TB p are provided in Table  1. The SMAP TB H measurements are underestimated by the two-stream microwave emission model configured with the vegetation and surface roughness parameterizations of SMAP mission (Sim1) for the cold season (November-April), and the SMAP measured TB V are overestimated for the warm season (June-October). These discrepancies are strongly reduced when using Zheng's surface roughness and vegetation parameterizations within the two-stream model (Sim2). Particularly, the ubRMSE are reduced by, on average, about 44% and 29% for the TB H and TB V . This demonstrates that the impact of surface roughness is underestimated by the Sim1 based on the SMAP parameterizations with the implementation of lower values of Q and h, and the vegetation effect is overestimated due to the usage of higher τ values (Figure 2) in accordance with the findings of Zheng et al. [16]. In addition, it can be noted that both Sim1 and Sim2 underestimate the SMAP measured TB H and TB V for the transition seasons with soil thawing from March and April and soil freezing between October and November and during the SMAP descending overpass. However, such underestimations disappeared in the SMAP ascending overpass. The SMAP TB V measurements are better captured by both Sim1 and Sim2 in terms of error statistics in comparison to the TB H simulation due to the higher correlation with the measured θliq as shown in Section 4.2. Figure 7 further shows the time series of ELBARA-III TB p measurements and simulations for the off-nadir angle ψ = 40° produced by both Sim1 and Sim2 performed for the ELBARA-III footprint during the SMAP overpasses. The corresponding statistical errors estimated between the ELBARA-III measured and simulated TB p are given in Table  2. Similar to the SMAP case, the Sim2 reduces the TB H underestimation between November and February and the TB V overestimation between June and October noted for the Sim1. In addition, the ELBARA-III measured TB V are better captured in comparison to the TB H simulation. However, it should be noted that both TB H and TB V are still underestimated between January and February, which is most probably due to the fact that the θliq measurement at 5 cm soil depth do not necessarily represent well the ELBARA-III sensing depth as reported by Zheng et al. [47,48]. Such underestimations are not found in the simulations performed with Sim2 for the large-scale SMAP TB p measurements, which is consistent with the better agreements noted between SMAP measurements and the in situ θliq (see Section 4.2).

Soil Liquid Water Content Retrieval
The two-stream emission model configured with the four-phase soil dielectric model (see Section 3.1) is adopted by the SCA-V, SCA-H and DCA algorithms (see Section 3.2) to retrieve the θliq, whereby Zheng's vegetation and surface roughness parameterization is implemented to estimate the parameters τ, h, and Q due to its better performance (see Section 4.3). Both ELBARA-III and SMAP measured TB H and TB V during both ascending and descending overpasses are used to retrieve the θliq for both cold and warm periods, and the in situ θliq representative of both ELBARA-III and SMAP footprints measured at 5 cm depth are utilized to identify the optimum retrievals. Figure 8a,b show the time series of in situ θliq representative of SMAP footprint (black line) and the retrieved θliq obtained by the SCA-V, SCA-H and DCA algorithms (colored lines) based on the SMAP TB p measurements during the period between August 2016 and July 2017 for the descending and ascending overpasses, respectively. Corresponding statistical errors estimated between the θliq measurements and retrievals are given in Table  3. For the comparison purpose, the θliq retrieval derived from the SMAP radiometer soil moisture product (see Section 2.3) is also presented in Figure 8 (orange line). It can be found that the SMAP θliq retrieval is only available for the warm season since the adopted soil dielectric mixing model developed by Mironov et al. [25] is only suitable for thawed soil condition. On the contrary, the SCA-V, SCA-H and DCA approaches configured with the four-phase soil dielectric mixing model are able to retrieve θliq for both cold and warm periods in this study. In general, the retrieved θliq obtained by the SCA-V, SCA-H and DCA approaches based on the SMAP TB p measurements are comparable to each other, which capture well both magnitudes and dynamics of in situ θliq representative of SMAP footprint for both warm and cold seasons during both descending and ascending overpasses. In addition, all the θliq retrievals produced in this study are better than the SMAP θliq product, and the latter tends to underestimate the θliq measurements due to poorer performance of SMAP default vegetation and surface roughness parameterizations (Section 4.3). It can be noted that all the θliq retrievals including SMAP product underestimate the θliq measurements for the transition seasons with soil thawing from March and April and soil freezing between October and November during the descending overpass due to underestimations of both TB H and TB V simulations (see Figure  6). Such underestimations, however, disappeared in the SMAP ascending overpass for the θliq retrievals produced in this study. The reason can be that the spatial heterogeneity of soil freezing is not fully represented by the measured θliq representative of SMAP footprint as also given in Zheng et al. [16]. The error statistics shown in Table 3 reflect the better performance of θliq retrievals obtained with the SCA-V than with SCA-H or DCA especially during the ascending overpass as indicated by lower RMSE and ubRMSE values. This finding supports the use of the SCA-V approach as the baseline soil moisture retrieval algorithm of the SMAP mission [56] for the Tibetan environments. Notably, the SCA-V gives the best θliq retrievals that match the average θliq measurements of the SMAP footprint, especially when the SMAP TB V measured during the ascending overpass are used. For these circumstances, an ubRMSE = 0.035 m 3 m −3 is produced, which outperforms the mission goal of SMAP with an expected ubRMSE of 0.04 m 3 m −3 [4]. This indicates that the SMAP TB V measurements during the ascending overpass can be the better choice to retrieve the θliq for both warm and cold periods using the SCA-V approach. Figure 9 further shows the time series of measured θliq representative of ELBARA-III footprint (black line) and retrieved θliq obtained by the three SM retrieval algorithms (colored lines) using the ELBARA-III measured TB p at the observation angle of 40 o . Corresponding statistical errors estimated between the measured θliq and associated retrievals are also provided in Table 3. As in the case for the retrievals using the SMAP TB p measurements, the SCA-V algorithm also outperforms the two other methods (i.e., DCA and SCA-H) in retrieving the θliq using the ELBARA-III measurements for both warm and cold seasons during both descending and ascending overpasses as indicated by lower values of bias, RMSE and ubRMSE and higher R values. In comparison to the θliq retrievals produced based on the SMAP measured TB p , the retrievals produced using the ELBARA-III measurements show poorer performance during the transition seasons with soil thawing (e.g., March and April) and freezing (e.g., October and November). Particularly, the θliq retrievals tend to largely overestimate the in situ θliq representative of ELBARA-III footprint between March and April, which can be related to the thawing of the snowpack that would affect the ELBARA-III measurements.

Conclusions
This study investigates the performance of the two-stream microwave emission model in simulating L-band TB p and retrieving θliq in combination with the four-phase dielectric model for both thawed and frozen soils on the Tibetan Plateau. Both single (SCA) and double (DCA) channel algorithms are adopted using both ground-based ELBARA-III and spaceborne SMAP measurements conducted in a Tibetan grassland site. Intercomparison between the time variations of ELBARA-III and SMAP TB p measurements demonstrates that high correlations (R ≥ 0.87) are found between both measurements, though the footprints are obviously distinct for the spaceborne SMAP and ground-based ELBARA-III measurements. The SMAP measured TB p are generally lower than the ELBARA-III measurements between June and October, which are associated with the distinct variations of in situ average θliq found across the ELBARA-III and SMAP footprints. In addition, the analysis of relations between the TB p measurements and in situ average θliq reveals that (i) SMAP TB p measurements are better responding to the in situ θliq compared to the ELBARA-III measured TB p , and (ii) the in situ θliq explains better the TB V measurements during the warm period from May to October, while TB H measurements are more consistently varying with the in situ θliq in the cold period between November and April.
It is found that the two-stream microwave emission model configured with the default vegetation and surface roughness parameterization of SMAP mission underestimates both ELBARA-III and SMAP measured TB H in the cold season and overestimates the TB V measurements in the warm season. The above deficiencies are largely reduced by adopting the new parameterization proposed by Zheng et al. [16], which employs higher values for the roughness parameters (Q and h) and lower values for the vegetation parameter τ. It can also be found that the SMAP measured TB p are better reproduced with the new parameterization in comparison to the simulations performed for the ELBARA-III footprint, and the simulation of TB V outperforms that of TB H .
In addition, it is found that all the θliq retrievals produced using the SMAP measured TB p in this study capture well the in situ θliq representative of SMAP footprint and are consistently better than the SMAP product. The θliq retrievals produced using the ELBARA-III measurements show poorer performance in comparison to those generated based on the SMAP measurements. The SCA-V algorithm outperforms both DCA and SCA-H methods in retrieving the θliq, which supports implementing the SCA-V method as the baseline soil moisture retrieval algorithm for the SMAP mission. Notably, the θliq retrievals using the SCA-V based on the SMAP TB V measured during the ascending overpass gives the best results (ubRMSE = 0.035 m 3 m −3 ), which is also better than the specified goal of ubRMSE = 0.04 m 3 m −3 for the SMAP mission.
This study shows the potential of using a two-stream model configured with the four-phase soil dielectric model for simulating L-band TB p and retrieving θliq for both thawed and frozen soil conditions. It's also noted that the SCA-V algorithm configured with the SMAP measured TB V during the ascending overpass is able to produce reliable θliq retrievals in a Tibetan meadow ecosystem. These findings are crucial for improving emission simulation and θliq retrievals at the L-band in cold regions such as the Tibetan Plateau. However, additional work is still needed to investigate and test the performance of the proposed method for its application in other areas. Recently, Li et al. [7] have implemented the two-stream model to simulate the TB p and retrieve soil moisture using SMOS measurements at a global scale, which provides an excellent reference to extend the application of the method proposed in this study. For example, the soil dielectric model, and the adopted vegetation and surface roughness parameterization for grassland used by Li et al. [7] can be directly replaced by the four-phase soil dielectric model and new parameterization proposed in this study to improve its performance in a cold region such as the Tibetan Plateau. The needed SMST data can be taken from the reanalysis data such as the ECMWF model simulations carried out by Li et al. [7].