Research Article | Open Access
Hong Zhao, Yijian Zeng, Jun Wen, Xin Wang, Zuoliang Wang, Xianhong Meng, Zhongbo Su, "An Air-to-Soil Transition Model for Discrete Scattering-Emission Modelling at L-Band", Journal of Remote Sensing, vol. 2021, Article ID 3962350, 20 pages, 2021. https://doi.org/10.34133/2021/3962350
An Air-to-Soil Transition Model for Discrete Scattering-Emission Modelling at L-Band
Topsoil structures and inhomogeneous distribution of moisture in the soil volume will induce dielectric discontinuities from air to bulk soil, which in turn may induce multiple and volume scattering and affect the microwave surface emission. In situ ELBARA-III L-band radiometer observations of brightness temperature ( =H or V polarization) at the Maqu site on the Eastern Tibetan Plateau are exploited to understand the effect of surface roughness on coherent and incoherent emission processes. Assisted with in situ soil moisture (SM) and temperature profile measurements, this study develops an air-to-soil transition (ATS) model that incorporates the dielectric roughness (i.e., resulted from fine-scale topsoil structures and the soil volume) characterized by SM and geometric roughness effects, and demonstrates the necessity of the ATS model for modelling L-band . The Wilheit (1978) coherent and Lv et al. (2014) incoherent models are compared for determining the dielectric constant of bulk soil in the ATS zone and for calculating soil effective temperature . The Tor Vergata discrete scattering model (TVG) integrated with the advanced integral equation model (AIEM) is used as the baseline model configuration for simulating L-band . Whereafter, the ATS model is integrated with the foregoing model for assessing its performance. Results show the ATS-based models reduce the underestimation of (≈20-50 K) by the baseline simulations. Being dynamic in nature, the proposed dielectric roughness parameterization in the ATS model significantly improves the ability in interpreting dynamics, which is important for improving SM retrieval at the global scale.
Soil moisture (hereafter SM) is of significant importance for weather and climate predictions by controlling the partition of heat and water fluxes on the land-atmosphere interface [1–3]. Passive L-band microwave remote sensing has become the most promising technique for measuring near-surface SM by properly quantifying contributions from vegetation and the ground surface [4–6]. Independent L-band brightness temperature observations and radiative transfer models (e.g., the Community Microwave Emission Model ), if integrated with land surface models in a data assimilation framework, can be used for estimating soil physical properties [8–12], which are crucially important for understanding SM dynamics [13, 14].
The efforts related to microwave remote sensing of the land surface may be traced back to the work of Peake , which demonstrates the complementary relationship between emission and scattering and shows such with data from Straiton . This may be called the scattering-emission radiative transfer approach. The more recent works are those of Fung  and Chen  on an advanced integral equation model (AIEM) for a rough bare soil surface, and Ferrazzoli [19, 20] on a discrete scattering model (Tor Vergata model) for a vegetated surface. These approaches consider a uniform soil moisture and soil temperature (SMST) profile and use a surface value of the dielectric constant with roughness parameters for the calculation of the surface reflectivity, by integrating the bistatic scattering coefficients over the half-space above the surface. The other line of work is that of Njoku and Kong  and Wilheit , which uses the stratified coherent radiative transfer approaches to calculate the microwave emission of a medium with the nonuniform temperature profile to account for the nonuniform SMST profile for natural soil (e.g., coherent model). That is to say, the SMST profile is used to determine the smooth surface reflectivity and soil effective temperature . Due to its simpler formulation, the Wilheit  model is widely used and followed by the simplified semiempirical models [5, 23–26] for applications in airborne and satellite microwave remote sensing. Generally, these models use the Fresnel equations to obtain the surface reflectivity with roughness corrections, and they have continued into the zeroth-order radiative transfer model used for the Soil Moisture and Ocean Salinity (SMOS)  and the Soil Moisture Active Passive (SMAP)  SM retrievals [27, 28]. On the other hand, these models do not retain the coherent character as in the Wilheit model, mainly due to the simplified parameterization scheme [23, 29]. To investigate the impact of on microwave radiometry, Lv  used an analytical formulation to physically explain various schemes, all of which having their roots in the scheme of Choudhury , and proposed the Lv’s scheme (e.g., incoherent model). In this study, we will investigate how Wilheit  coherent and Lv  incoherent models affect and associated brightness temperature (, with = H or V polarization) simulations.
Another research focus of microwave radiometry is the surface roughness effect. The geometric roughness resulting from the variation of surface heights influences surface scattering and is modelled by the physically based AIEM. However, AIEM assumes isotropic roughness properties for a homogenous dielectric half-space and does not account for the dielectric effects due to heterogeneities in the soil characteristics (e.g., composition, moisture content, and bulk density). On the other hand, the fact is that lateral structures (e.g., the unfilled surface composed of organic matter and clods) significantly smaller than the observation wavelength (e.g., , at L-band) influence the manner of wave propagation and induce the impedance mismatch of the rough surface between air and soil. The aforementioned heterogeneities produce dielectric roughness (namely, the large dielectric discontinuities at the soil surface and within the soil volume) and may in turn induce the volume and multiple scattering processes, which will affect the microwave surface emission. The model parameters used in the zeroth-order radiative transfer models may implicitly account for both the geometric and dielectric roughness effects. However, they are site-specific empirical ones, obtained by using the best-fit approaches based on limited field observations and model simulation results. An air-to-soil transition (hereafter ATS) model —an intermediate modelling approach between physical and semiempirical approaches—is suggested to describe the roughness effects from topsoil structures on the L-band radiation as an impedance matching between the dielectric constants of air and bulk soil. In the original ATS model [31, 32], the structured topsoil is taken as a transition layer with a geometric thickness , considering that the volume fraction of soil materials increases with depth in the ATS zone. The is related with (the height standard deviation with Gaussian distribution, centered around lateral separation) by [30, 31]. As the geometric surface roughness (i.e., ) does not experience the pronounced change, is a fixed peak-to-trough transition layer thickness induced by topographical effects and independent of soil moisture. However, regarding to be constant is questionable due to the fact that the dielectric properties of the topsoil and the soil volume may be modulated by inhomogeneity related to moisture. This study will develop an enhanced ATS model with a new parameterization to investigate a soil moisture-dependent dielectric roughness at the topsoil structures and the soil volume on the L-band radiation. The Maqu site (33.91°N, 102.16°E) on the eastern Tibetan Plateau meadows providing comprehensive field observations [33–36] will be taken as the study area to validate the model.
With the ATS dielectric layer obtained, an “equivalent” homogenous dielectric entity that acts as the ground scattering-emission medium can be assumed with a given dielectric constant and surface geometric roughness. The AIEM , which uses a more complete expression of the single scattering terms to keep the acceptable energy conservation for calculating bistatic scattering and emission, will be employed for simulating soil surface scattering. As the research object is a natural grassland, the Tor Vergata model simulating vegetation scattering is coupled with AIEM (TVG+AIEM) for the overall vegetation-soil scattering-emission modelling. The coupled model including the ATS model (TVG+AIEM+ATS) is further used to investigate the impacts on estimations and simulations by adapting Wilheit’s or Lv’s stratified model, or using SM at the single-layer depth of 2.5 cm (in situ measurements) given its topmost role in surface emission [22, 37]. Finally, the applicability and uncertainty of the enhanced ATS model on L-band radiometry modelling are discussed.
This paper is organized as follows. The in situ SMST profiles and the ELBARA-III observed on Maqu site are described in the first part of Section 2. In the second part of Section 2, a brief description of the TVG model is introduced. The improved ATS model is described together with Wilheit  and Lv  models. The configurations of different simulation experiments are also explained. Results about the performance of the enhanced ATS model and seasonal simulations are shown in Section 3, as well as how coherent and incoherent models and SM at 2.5 cm influence simulations. The applicability and uncertainty of ATS models in simulations are discussed in Section 4, as well as the impacts of geometric roughness on the performance of the ATS model. The potential advantage of the ATS model that can be used for improving satellite-based SM retrievals is discussed in Section 4. Conclusions and outlooks are drawn in Section 5.
2. Materials and Methods
2.1. In Situ Measurements at Maqu Site
The Tibetan Plateau observatory for soil moisture and soil temperature (Tibet-Obs) was built and maintained since 2006 onwards [14, 33, 34, 38] to provide comprehensive observations for land surface modelling community and for validating SM retrievals from satellite microwave remote sensing and reanalysis SM datasets [35, 39–41]. In 2016, an in situ Dicke-type radiometer ELBARA-III at L-band (1.4 GHz) has been mounted at the Maqu site (33.91°N, 102.16°E) of the Tibet-Obs, providing observations at different incidence angles (between 40° and 70° in steps of 5°) for investigating L-band microwave radiometry for eastern Tibetan alpine meadows [42–45]. Detailed descriptions of ELBARA-III radiometry setup can be found in , as well as a schematic overview (see Figure 1 in ).
In this study, a dense profile of SMST (at 2.5, 5, 10, 20, 35, 60, and 80 cm below the soil surface) collected from the SMST_LC pit near the ELBARA-III (see Figure 1 in ) in the first period between 08/08/2016 and 30/11/2016 is used. Detailed descriptions of SMST measurements can be found in . The analyses of this study will focus on the in situ observed data and the simulations in the late-monsoon (August to September) and post-monsoon (October to November) periods in 2016. To keep consistent with the SMAP incidence angle, the data analysis is confined to the angle of 40°. Additionally, Leaf Area Index (LAI) is an important input parameter for vegetation modelling in the Tor Vergata model, determining the number of grass as discrete dielectric scatters. Time series of LAI extracted from MCD15A2H-MODIS/Terra+Aqua Leaf Area Index (500 m resolution) (https://lpdaac.usgs.gov/products/mcd15a2hv006/) is processed with the harmonic analysis of the time series (HANTS) algorithm  to remove the cloud contamination. The results in Figure 1 show a reliable interpreted LAI. Furthermore, meteorological observation data in the Maqu site  are used to support the analysis. The data mainly involve precipitation intensity, air temperature, and surface albedo with ground surface temperature deriving from the in situ four components radiation measurement (i.e., up- and down-welling shortwave and longwave radiations).
2.2.1. Tor Vergata Discrete Scattering-Emission Model
The TVG [19, 20] assumes the soil as a homogeneous infinite half-space with a rough interface, and the overlying vegetation is represented as an ensemble of discrete dielectric scatters. The scattering modelled by TVG involves three components: vegetation volume scattering, soil surface scattering, and the component resulted from vegetation-surface interactions. The TVG model has been investigated over the Maqu area [42, 47–49]. As in , the grass leaves at the Maqu site are described by dielectric thin discs with a random distribution of orientation. The bistatic scattering and extinction (absorption plus scattering) cross sections of the dielectric discs are computed by applying the Rayleigh-Gans approximation at L-band  (➀ in Figure 2), in which Mätzler  model is used for calculating vegetation dielectric constant. Subsequently, the contributions from all discs (scatters) are integrated using the matrix doubling algorithm (➁ in Figure 2), thereby the scattering and transmission matrices are computed for the whole vegetation (➂ in Figure 2). Vegetation parameters such as the disc radius, disc thickness, numbers of discs (i.e., the ratio of LAI to the area of the disc), and plant moisture content used in this study are calibrated ones from [47, 48], and they are found insensitive to the emissivity for L-band .
The soil surface scattering is computed by adopting AIEM, in which the soil dielectric constant and surface roughness parameters (i.e., the standard deviation of surface heights , the correlation length of surface height , and the assumed exponential autocorrelation function for natural surface) are needed as inputs. In the previous version of TVG adopted for the Maqu site, the grassland litter component is included . The litter layer, however, is not implemented in this study. One reason is that the grassland on the Tibetan Plateau is grazed by sheep and yaks  and litter in most areas is decomposed (see two snapshots in supplementary materials). On the other hand, for nature land surface, there does exist a soft transition zone of the dielectric constant from air to bulk soil than in a case of an abrupt surface, as for example at calm sea . Therefore, our focus in this paper is to improve air-to-soil dielectric transition (ATS) modelling. Ignoring the litter part in the modelling system is for simplicity but also reduces numerous input parameters that may degrade the performance of the model.
In this study, the enhanced ATS model (see Section 2.2.2) will be used to obtain the effective dielectric constant (➃ in Figure 2). Two components: incoherent bistatic scattering coefficients (computed by the AIEM, ➄ in Figure 2) and coherent specular reflection coefficients (computed by the Fresnel equations corrected by roughness factor, ➄ in Figure 2) are computed for the composite air-to-soil medium scattering. The same matrix doubling algorithm is then used to combine the calculated vegetation contribution with that of the air-soil medium (➅ in Figure 2). Subsequently, the emissivity on polarization (i.e., H or V) at an incidence angle is obtained by applying energy conservation law with integrating the bistatic scattering coefficients over the half-space above the surface (➆-➇ in Figure 2). Due to the low vegetation emission at L-band, the physical temperature of vegetation is assumed the same as that of soil in this study. The soil effective temperature can be estimated using either Wilheit  coherent or Lv  incoherent models (see Section 2.2.3) (➈ in Figure 2). Finally, is computed using the emissivity multiplied by (➉ in Figure 2). Figure 2 shows the flowchart of forward simulations by the coupled TVG and AIEM model including the ATS model. Parameter values used for TVG+AIEM+ATS running are listed in Table 1.
2.2.2. The Air-to-Soil Transition (ATS) Model
Vegetated soil medium is composed of a substantial amount of loose dirt, plant debris, and crumbs scattered on the surface and a much denser soil entity lying beneath (Figure 3(a)). Driven by changing weather systems such as after dry and sunny conditions following rainfall events, wetted plant debris and large clods on the surface dry out more quickly than bulk soil beneath the surface. Affected by roots and air pockets present in the soil volume, it produces an inhomogeneous layer between soil structures near the surface and bulk soil at the bottom. All these effects may lead to a large spatial variability in SM at the soil surface and within the soil volume . Consequently, it induces different (e.g., wet-dry layers) interfaces existing in the soft transition zone of the dielectric constant from air to bulk soil (ATS). The ATS zone may extend over the peak-to-trough geometric thickness for the natural smooth surface, especially when the soil surface is dry and electromagnetic waves from deep layers can transmit towards the surface.
Assuming less than the wavelength in free space, a concept of dielectric roughness (, ) is proposed for the ATS zone, in which is a dielectric roughness thickness characterizing the depth of interfaces, not only resulting from topsoil structures () affected by both irregularities (i.e., geometric roughness) of the soil surface and inhomogeneous distribution of moisture but also due to inhomogeneity within soil volume () that is related to soil porosity and moisture. The dielectric roughness thickness for the ATS zone is assumed as a sum of and (see Figure 3(a)).
Due to the difficulty to have detailed volumetric information on inhomogeneous mediums (e.g., loose dirt, plant debris, and bulk soil mixed with roots) along the ATS zone, the Fermi-Dirac distribution function  is used in this study to construct the dielectric depth profile, given an exponential dependence of the roughness thickness on SM [31, 53]. Subsequently, an “equivalent” homogenous dielectric ATS zone with a given dielectric constant is produced as a consequence of the impedance match over the ATS zone, which is used for calculating scattering of the ATS medium by AIEM (see Section 2.2.1).
In this study, is taken as the SM-dependent roughness parameter. Modulated by SM, varies and the probability density function for dielectric roughness height is assumed to have an exponential distribution with a rate parameter , considering the exponential attenuation with regard to water content and (physical) height on surface emission [30, 31, 54]. is formulated by Equation (2):
As is also affected by geometric roughness, the depth dependence of the volume fraction of soil materials that backbone variations of the dielectric profile is consequently related to the dielectric height distribution and can be described as the cumulative distribution of . Specifically, the integral of over depth — represents the volume fraction of soil materials and 1- for the air volume fraction (Equation (3)):
At the soil surface, is backboned by topographic effects and is related to as the surface geometric height (see Figure 3(a)). in this study is also assumed depending on both incidence angle and polarization reported by previous investigations by [25, 55, 56]. If assuming that the air volume fraction is one at an arbitrary position on the top of the surface structures where ( is away from the average surface geometric height for nadir observation), since more soil particles occupy the hollows of topsoil structures on the lateral scale with increasing depth (), the air volume fraction in the topsoil structures decreases (see Figure 3(a)). The decreased air volume is filled by the increased volume of soil materials, and the resultant effect of moisture on can be described by logarithmic SM (Equation (4)). While decreases when the soil surface is wet, the surface may become “saturated” when it is sufficiently wet, namely, the soil moisture reaches field capacity (FC), at which moves to and makes close to . is then given as follows: where is the incidence angle. is a polarization modulation parameter, and is set at 0 for H polarization and -1 for V polarization. SM is volumetric soil moisture.
With deepening in the ATS zone, when the topsoil structures on the whole lateral scale tend to be fully filled with soil materials (see Figure 3(a)), the soil texture (i.e., porosity) and SM profile become the dominant factors whose effects can be represented by , which is the depth where the air volume fraction of the ATS zone equals to a maximum volume of pore space in the soil (porosity) (Equation (5)).
Affected only by moisture in the soil volume (this is where SM is measured), the parameter of the distribution can be estimated by the power attenuation coefficient as in [23, 57], which is determined by and the complex dielectric constant of bulk soil in the ATS zone as follows: where , is real part, and imaginary part of the soil dielectric constant of the ATS zone. In this study, soil porosity is set of 0.62 according to laboratory measurements , and FC is valued of 0.35 m3/m3 for silt loam soil. The sketch of the improved ATS model is shown in Figure 3(a).
The Fermi-Dirac distribution function  shown in Equation (7) is used to describe the dielectric depth profile for the ATS zone. The steepness parameter in Equation (8) is related to and SM effects.
Figure 3(b) shows two estimated and the correspondingly derived under wet and dry soil conditions. The same temperature can be assumed of all layers in the ATS zone due to small influences from temperature change on the dielectric constant of (organic) soils . As such, a coherent radiative transfer model can be used to compute the overall coherent reflectivity for the ATS zone from , which is based on a matrix formulation of the boundary conditions at dielectric discontinuities derived from Maxwell’s equations . The coherent model is performed for a total depth of with the thickness of each layer set to 1 mm, which is less than one-tenth of the wavelength . This coherent model predicts a trend of reflectivity as a function of layer thickness but is characterized by enhanced oscillations due to coherent interactions among multiple reflected waves, and this process can be smoothed by natural variations of layer thickness around its average value and an averaging procedure . Considering the impacts of both surface geometric roughness and SM at the bottom of the ATS zone, the average dielectric surface ( along , see Figure 3(a)) is assumed varying downward with a depth measured by multiplied by logarithmic SM (Equations (9)–(10)).
Consequently, reflectivities obtained at this layer thickness () are averaged, and the effective dielectric constant of an equivalent homogenous dielectric ATS zone (used for calculating the scattering by AIEM) is computed by minimizing an objective function between the obtained reflectivities and those computed for the ATS zone using Fresnel equations .
The effective roughness parameters obtained from model calibration are recommended to be used in the physically based surface backscatter model [61, 62]. In this study, is taken as 0.9 cm and as 9.0 cm in Maqu case . These two calibrated values consider the high correlation between and roughness slope () [61, 63]. SM of the lower boundary of the ATS zone used for calculating (see Equation (4)), and associated (see Equations (5)–(6)) for L-band is difficult to obtain, but can be regarded as the representative SM. The measured SM at 2.5 cm is considered as the representative SM, because the reflectivity of a stratified dielectric is primarily determined by changes in the real part of the refractive index over a depth of about 1/10 and 1/7 wavelengths (~2.5 cm for L-band) . It is to note that representative SM is also obtained by considering the impact of SMST profile on soil microwave emissions through either Wilheit  or Lv  stratified models (see Section 2.2.3). The Mironov dielectric model  is used to calculate throughout the whole study period, and the soil texture (i.e., clay fraction and bulk density) information is based on laboratory measurements .
2.2.3. Wilheit Coherent Model and Lv Incoherent Model
In this study, we regard the Wilheit  model as coherent because the electromagnetic wave considered in the model is formulated with amplitude and phase, and the electromagnetic energy flow through the plane is given by the Poynting vector with retaining coherent character. In reality, when a rapid drying out of the surface occurs, there are dry and wet layers with the depth. Reflections from the air-soil interface and the dry-wet soil interface may interfere, resulting in the wave from deep layers adding to the surface energy density constructively (in phase) or destructively (out of phase), or in between (i.e., adding of two waves). By contrast, Lv  model is taken as incoherent, because the model derivation is based on radiation intensity (i.e., with only amplitude considerations but without phase) . and associated simulations by these two models are expected to provide physical insights on interactions of microwaves with soil medium. From an application perspective, it can help determine whether coherent and incoherent effects are needed to be considered for modelling emission for natural surface, whose status changes with meteorological and hydrological conditions.
(1) Wilheit Coherent Model. In Wilheit  model, soils are treated as a layered plane dielectric medium. The basic assumption is that there is a reflection for the incident radiation on the air-soil interface and the thermal equilibrium in each following layer (i.e., beneath the interface) of this stratified medium. That is to say, only the absorption and transmission of electromagnetic waves are considered in each layer. The fraction of absorption () can be calculated by solving Maxwell’s equations with the aid of boundary conditions at the interfaces for a coherent electromagnetic wave propagating through the layered soil . If is the temperature of the th layer, under thermodynamic equilibrium, the layer radiates energy equal to the product of the fractional absorption and the temperature . In terms of the conservation of energy, the reflectivity of the smooth air-soil interface is described by Equation (11): where represents the total number of discrete soil layers. As such, the representative SM (SM_Wil) used for determining is the one resulting in a minimum root mean square error difference between the obtained reflectivities and those computed for a set of SM through the Fresnel equations . Wilheit  also defined the thermal sampling depth as the average depth, at which the upwelling thermal radiation from the soil originates. is a function of integrals over the imaginary part of the refraction index but calculated using an approximation (Equation (12)). where is the depth of the th layer and ( = H, V polarization) is the weighting function (e.g., the fraction of absorption) for that layer as previously defined. The average soil temperature over the is regarded as the soil effective temperature and calculated by Equation (13).
(2) Lv Incoherent Model. The soil effective temperature is defined as the net intensity at the soil surface, which is a superposition of intensities emitted at various depths . The formula is as follows: where is the soil temperature at depth . is the attenuation coefficient related to the complex soil dielectric constant at depth . For low-loss dielectric and nonmagnetic soil medium, can be expressed as [23, 64]
Assuming uniform SM and texture in each layer, a discrete formulation of (14) is derived by Lv . where 1, , and represent the soil layers. shares the same meaning as in Equation (11). is soil temperature. is the attenuation coefficient given in Equation (15), and is soil thickness. is defined as the weight function for the layer . By assuming uniform dielectric properties of soils throughout the emitting layer and a linear soil temperature gradient along the soil optical depth, the soil temperature at one time of the soil optical depth is proved equivalent to . The depth corresponding to one soil optical thickness is defined as the penetration depth of soil effective temperature  as follows: where , , and share the same meanings as in Equations (15), (16). The in situ SM at 2.5 cm is used for calculating in this case. Measured SM at depths above are integrated using the weight function (in Equation (16)) for obtaining the representative SM (SM_Lv, Equation (18)) that considers the impacts of profile SMST. The (Lv’s model) and (Wilheit’s model) are referred to as sampling depths of soil effective temperature in the following analysis. where refers to SM at layer. The other symbols in Equation (18) share the same meanings as in Equation (16).
2.2.4. Configuration of Simulation Experiments
To assess the importance of the ATS model in seasonal simulations, five experiments involving Wilheit coherent model and Lv incoherent model for the soil part are carried out. The first two experiments are called “Baseline,” only using the AIEM+TVG without the ATS model integrated. The baseline experiments are configured with both Wilheit’s and Lv’s models, which can reflect the impacts of effective soil temperature and effective soil moisture, respectively, on simulations. Considering the emission is sensitive to SM at top layers , the in situ measured SM at 2.5 cm is used to calculate the dielectric constant of bulk soil for the second experiment, which is equivalent to the concept of representative SM based on Wilheit’s model. Furthermore, a total soil depth of 60 cm is used for these two stratified models, since the in situ measured SM at 60 cm is almost constant during the study periods.
The third and fourth experiments integrate the ATS model with the combination of Wilheit’s and Lv’s models separately (named “ATS-Wil” and “ATS-Lv”) to reflect the effects of the dielectric roughness on simulations. Specifically, the SM_Wil and SM_Lv are used, respectively, to determine the dielectric constant of bulk soil and the (i.e., _Wil and _Lv) (see Figure 2). Furthermore, the fifth experiment is considered with the combination of Lv’s model and the 2.5 cm SM for calculating the dielectric constant of bulk soil, evaluating the effectiveness of Lv’s weighted SM approach (see Figure 2). Table 2 summarizes the configurations of simulation experiments.
With the Wilheit  model, properties such as the layer thickness and the interpolation method to estimate the SMST in each layer from a limited number of observations are noted affecting model simulations. Similar to , the linear interpolation is used in this study. Considering the high sensitivity of coherent models to optical thickness, a preliminary test was carried out to investigate the sensitivity of the Wilheit model to the soil layer thickness . The results confirm the use of 1 mm for in Wilheit model simulations, which is consistent with that in .
3.1. The Late-Monsoon Period
3.1.1. The Dielectric Roughness Thickness () and the Sampling Depths of Soil Effective Temperature ( and )
As a constant difference of the dielectric roughness thickness () between H and V polarizations is assumed (see Equations (1), (4)-(5)), only the estimated for H polarization is analyzed. Figure 4 shows comparisons of from the third (_Wil), fourth (_Lv), and fifth (_Lv_SM2.5 cm) experiments (bottom panel), together with the representative SM derived from Wilheit’s (SM_Wil) and Lv’s (SM_Lv) models and the in situ SM at 2.5 cm (SM_2.5 cm) (upper panel). SM_Wil is found changing coincidently with SM_2.5 cm, and this might be due to the sampling depth of SM determined by Wilheit model being the order of about one-tenth wavelength (approximately 2.5 cm at L-band). SM_Wil is also seen slightly higher than SM_2.5 cm when soils go through the transition of dry-wet-dry during the midmonsoon period. Comparatively, a slight variation of SM_Lv is seen in this period, and this is the consequence of Lv incoherent model with an assumed uniform SM distribution in the profile. Correspondingly, _Lv cannot increase as much as _Wil and _Lv_SM2.5 cm do when soils become drier. The Wilheit model can simulate with obvious variations when soils experience dry and wet conditions, due to its capability of considering the effect of SM profile in calculating the dielectric constant of bulk soil. Compared to _Lv_SM2.5 cm, _Wil is slightly lower in the soil drying process (Figure 4). Wet soils at deep layers considered in the Wilheit model lead to the smooth increase of the when the soil surface becomes drier. is estimated exceeding over 10 cm in dry conditions (e.g., ) (Figure 4). When SM increases and is greater than 0.3 m3/m3, estimated from all schemes decrease (Figure 4).
Figure 5 shows that the sensing depths of effective temperature derived from Lv model () and Wilheit model () have the same variations and approach each other during the whole late-monsoon period. Due to considerations of the coherent effect in the Wilheit model, constructive interference might exist for reflections from the air-soil interface and the dry-wet soil interfaces (drying front), and is found higher (~2.3 cm) than (Figure 5). _Wil is close to _Lv, but both have a phase lag reflecting the propagation of periodic temperature waves from the deep soil, compared to the in situ soil temperature at 2.5 cm (ST_2.5 cm). as a resultant of the superposition of the foregoing waves at various depths within the soil does not show as much variation as ST_2.5 cm, because the latter experiences rapid diurnal variations due to direct solar radiation, and this kind of variation becomes damped with increasing soil depth. As such, ST_2.5 cm is higher than _Wil and _Lv at midday but lower at midnight. _Wil is slightly larger (~0.2 K) than _Lv especially at midday and midnight (Figure 5), whereas their differences reduce when soils are wet following rainfall events (see sharp jumps of SM_2.5 cm in Figure 4). Figure 5 shows a negligible difference (~0.2 K) between _Wil and _Lv, while the varied thermal sampling depth (~2.3 cm) of soil temperature is noted important for determining the optimal mounting depth for observations as claimed by .
3.1.2. The Simulation
Figure 6 shows that the two baseline simulations underestimate in the whole late-monsoon period, signifying that considering only impacts of effective soil temperature and effective soil moisture cannot close the discrepancy between simulations and observations. However, the underestimation of (≈30-50 K) is obviously compensated by integrating the ATS model. simulated by the ATS-based models are close to ELBARA-III observations in magnitude before late August, in which the ATS-Wil and ATS-Lv2.5 simulations match to observation while the ATS-Lv model presents underestimations. simulated by the ATS-based models continue to be consistent with observations in September when the soil surface is wet. This indicates the necessity of the ATS model for surface emission modelling for H polarization during the late-monsoon period.
For V polarization, Figure 6 shows that the two baseline models simulate well in August but underestimate (≈20 K) in September when the soil surface is wet. By integrating the dielectric roughness in the ATS model, the underestimation is reduced, similarly as for H polarization. The ATS-based models show slight underestimations compared to ELBARA-III observations before late August but are closer to observations than baseline simulations. The ATS-Wil model performs better than the ATS-Lv model for modelling in this period. While all ATS-based models have the same performances and capture well during the end-monsoon period (September), despite discrepancies occurring after big rainfall events (e.g., on 25/08/2016). The ATS model is seen improving the modelling of surface emission also for V polarization during the late-monsoon period.
3.2. The Post-Monsoon Period
Due to the page limit, similar analyses for the post-monsoon period are presented in the supplementary materials. Results show that (1) the estimated within 4-6 cm is corresponding to surface SM changes within 0.24-0.32 m3/m3 (Figure S1). The SM_Wil and SM_Lv and associated _Lv and _Wil (Figure S1) are consistent with SM_2.5 cm and _Lv_SM2.5 cm correspondingly during the post-monsoon period before the soil freezing-dominated period, where the surface soil temperature is below 0°C (e.g., from 26/11/2016 to 30/11/2016, see Figure S2). While during the surface freeze-thaw transition period, in which the surface soil temperature changes along the freezing level 0°C (e.g., from 12/11/2016 to 25/11/2016, Figure S2), the SM_Wil and SM_Lv and associated _Lv, _Wil and _Lv_SM2.5 cm (Figure S1) show less diurnal variations than those of SM_2.5 cm. (2) Estimated is higher (~1.6 cm) than most of the time during the post-monsoon period (Figure S3), and values of _Wil and _Lv are almost the same. (3) Two baseline simulations underestimate (≈20-50 K) in the post-monsoon period (Figure S4), while simulated by the ATS-based models are much closer to observations. It is to note that when the weather system changes and soils start to experience freeze-thaw processes, simulated by the ATS-based models deviate from observations.
4.1. Applicability and Uncertainty of the ATS Model
The enhanced ATS model in this study stems from the original ATS model [31, 32, 54], considering the effect of roughness components within the observation and finding the impedance match for the ATS zone . The enhanced ATS model with the new parameterizations of dielectric roughness effects maintains physical considerations and helps improving simulations.
The dielectric roughness thickness is a key parameter in the ATS model, which is parameterized comprising two components. One is dielectric roughness within the soil volume (); the other is dielectric roughness induced by SM from the soil surface and geometric roughness effects (). Figure 7 shows during the study period, with SM decreasing (see SM from 0.2 to 0.1 m3/m3 in Figure 4), the contribution from the soil volume to the dielectric roughness thickness () increases (Figure 7), while that from the surface () decreases, and it is vice versa when SM increases (see SM from 0.15 to 0.3 m3/m3 in Figure 4). This is reasonable because as the soil dries out, emissions originate from the deep layers and the spatial heterogeneity of the dielectric constant within the soil volume becomes much larger and enhances dielectric roughness effects, and it is the other way around when soils are wet. This phenomenon is also reported by [31, 53, 55, 67], in which the site-specific empirical soil roughness parameter [25, 68] is obtained for zeroth-order radiative transfer models.
With SM decreasing, the scattering medium (e.g., loose dirt, plant debris, and crumbs) at the soil surface becomes drier and more transparent for electromagnetic wave transmission, thus, the contribution to the dielectric roughness from the soil surface () decreases as shown in Figure 7. Conversely, with SM increasing, the scattering medium including senescent vegetation (see decreased LAI in Figure 1) lying on soils becomes wet and may trigger litter effects and leads to roughness () increasing (see Figure 7). This is in line with findings from [69, 70], in which higher values of the calibrated are used to account for surface effects related to litter over the grassland. Moreover, given the parameterization of related to both geometric roughness and SM, the scaled (namely, ) can be comparable to , which implicitly accounts for both the geometric and dielectric roughness effects. The is found ranging from 0.31 to 0.42 (see Figure 7), and these values are close to the () from  and () from , with the same and used in this study. In another study over grass in the Goulburn River catchment, Australia , is approximated of 0.4.
Correspondingly, for associated modelling during the late-monsoon period, two baseline simulations have high Pearson correlation coefficients () while consistently underestimated the observation. simulated by the ATS-based model only considering are higher than those from two baseline simulations but still underestimated the observed (see Section 3 in the supplementary materials). However, the ATS-based models by considering the impacts of both and greatly compensate underestimations by the foregoing simulations, with more simulation results closely aligned to 1 : 1 line as shown in Figures 8(a) and 8(b) and Figure S9 (in the supplementary materials). The simulated have similarly high (≥0.85) but much lower root mean square errors ( for and 8.0 K for ) than baseline simulations (RMSEs over 37 K for and 12 K for ). The ATS-Wil and ATS-Lv2.5 models perform better than the ATS-Lv model in this period as more clustered points aligned along 1 : 1 line are seen in Figures 8(a) and 8(b) and better matches to observations shown in Figure 6. This underlines the importance of obtaining the realistic SM that can reflect the moisture status of the ATS zone and implies that the coherent effects can be considered during the late-monsoon season. With changing weather systems in the post-monsoon periods, the ATS-based models maintain the performance with lower RMSEs (≤12.5 K for and 10.9 K for ) than baseline simulations (RMSEs over 39 K for and 18 K for ), in which the ATS-Lv2.5 and ATS-Lv models with lower RMSEs perform better than the ATS-Wil model (Figure S5). This may indicate that the coherent effects occurring in the late-monsoon period may be disrupted due to freeze-thaw processes during this period.
The ATS-based models underestimate for soils undergoing surface freeze-thaw processes, and simulated have weak diurnal variations (see Figure S4). The estimated dielectric roughness derived from the ATS-based models in this period (see Figure S6) is also found having slight variations for the ATS-based models, which the stable and and associated _Wil and _Lv (see Figure S1 and Figure S3) may partially account for. As air temperature and ground surface temperature impose the topmost roles in affecting the soil surface freeze-thaw process, the appropriate temperature information is necessary to refine the estimation for soils during the freeze-thaw transition period. On the other hand, the freeze-thaw processes exaggerate the inhomogeneity in the soil media (e.g., composed of ice in pores mixed with preexisting crack, or melted liquid water mixed with ice, organic matter, and soil solid). The formed ice affects the dielectric constant of bulk soil during the nighttime and early morning, and the melted surface (soil) water does that during the daytime. Without the soil ice content and surface (soil) water information considered in the ATS model parameterizations, the ATS model cannot capture such mixtures and accurately model and associated . If we can further take into account surface (soil) liquid water and ice content for the estimation, the performance of the ATS model for L-band radiometry of the freeze-thawed soil is expected to be improved. It is to note that soil ice content cannot be measured directly in situ but can be retrieved indirectly via assimilating proximal sensing signals . The inclusion of soil ice content, surface liquid water fraction, and ground surface temperature into the ATS model will be explored in further studies. A similar improvement can be expected to implement for modelling with rainfall events, such as by ATS model considering surface water effects when the accumulated intensities of rainfall become greater than soil infiltration capacity of the surface, and the formed surface water may block the soil emission from the deep layers.
Nevertheless, correspondences between estimated by the ATS-based models and the observations indicate that the ATS model is necessary for L-band modelling. The parameterized in this study acting as a dynamic parameter can describe well the dielectric roughness at the soil surface and within the soil volume, which is significant for interpreting the observed dynamics. The in this study is also related to the incidence angle and polarization. The , the same as in the empirical roughness parameterization  is found with of 0 and of -1 for the best simulations at Maqu site. This result supports the demonstration that different values should be used for horizontal and vertical polarizations [55, 71, 74]. The applicability of in other climate regimes needs to be further confirmed, but this is beyond the scope of this study.
4.2. The Impacts of Geometric Roughness on the Performance of the ATS Model
Geometric surface roughness parameters (, ) have great impacts on surface scattering. is considered in the dielectric roughness parameterization and affects the depth that determines variations of the effective dielectric constant of the air-to-soil medium (see Section 2.2.2). Considering the difficulty in determining the “true” values of and for natural grassland and their importance in calculating backscattering coefficients in AIEM , the effective geometric roughness parameters (, ) obtained from satellite measurements in Maqu area  are used in this study as described in Section 2.2.2. To investigate the impacts of varying geometric roughness on the performance of baseline and ATS-based model simulations, the sensitivity analyses by using a varying in the range of (0.75, 0.9, 1.2, 1.5, 2.5 cm) with constant of 9 cm (considering its lower impacts than ) are carried out. of 0.9 cm is regarded for a smooth natural surface and of 2.5 cm for a rough one for L-band in this case. The results shown in Section 3 and the aforementioned discussions have confirmed that both ATS-Wil and ATS-Lv2.5 models outperform in simulations in the late-monsoon period and both ATS-Lv and ATS-Lv2.5 models do so in the post-monsoon periods except for the freeze-thaw transition period. Figures reflecting the impacts of geometric roughness are thus only displayed based on the ATS-Wil and ATS-Lv models together with the corresponding baseline models, and discussions are focused on the whole study period except for the freeze-thaw transition period. The error metrics involving and RMSEs are listed in Table 3 to quantitatively describe the performances of models using varying .
Simulated (especially ) by the baseline models (Figure 9(a), Figure S7A) is very sensitive to variations and simulations with large (e.g., 2.5 cm) are closer to observations compared to those with small during the late-monsoon and post-monsoon periods. Please also see reduced RMSEs with larger in Table 3. However, most simulations cannot capture diurnal variations of compared to observations. With the ATS model integrated, variations of (especially ) can be captured, and the impacts of variations on during the late-monsoon period are reduced (i.e., see a narrow range of variations of with different settings in Figure 9(b, 1)), although this is less apparent for (Figure 9(b, 2), Figure S7B-2). simulations with small (e.g., 0.75 cm) present overestimations (Figure 9(b, 1)), which is opposite from those based on the Base-Wil model. simulations with of 2.5 cm are found consistent with those using of 0.9 cm (similar large R and small RMSEs in Table 3) and match observations except during the soil freeze-thaw transition period (Figures S7A, B). However, the calculated microwave polarization difference index (MPDI=) with of 2.5 cm does not show the observed diurnal variations, while it does with of 0.9 cm (Figure 9(c), Figure S7C). This indicates that the positive effects imposed by large geometric surface roughness (e.g., ) on surface emission may become dominant and balance the negative effects of SM in the ATS model. By contrast, the ATS model with of 0.9 cm can continuously capture dynamic variations of dielectric roughness, not only at the soil surface related to the distribution of water and geometric roughness but also with the soil volume. Based on these analyses, the surface geometric roughness parameters ( and ) used in the ATS model are proved sufficient in this study. Surface geometric roughness may have slight changes due to the soil freeze-thaw processes such as frozen soil water causing volume expansion and melted surface water might smooth the surface, but this is beyond the scope of this study.
4.3. The Impacts of Fixed Analog to Used in SMAP and SMOS-CMEM Systems on Simulations
SMAP and SMOS brightness temperature forward modelling use the fixed soil roughness parameter [25, 68] for SM retrievals at the global scale. Given the similarity between derived from the ATS model and (see Section 4.1), this section attempts to investigate the impacts of fixed roughness parameters analogous to those used in SMAP and SMOS retrievals on modelling. In the SMAP SM retrieval algorithms, the parameter is assumed to be linearly related to by with of 1.56 cm for grassland . The default SMAP of 0.156 is reported too low for modelling on the Tibetan Plateau in comparisons to the recommended Wigneron soil roughness model  ( ) with the same (=1.56 cm) adopted . For SMOS long-term monitoring at ECMWF (European Centre for Medium-Range Weather Forecasts), the simple Wigneron soil roughness model  ( ) with of 2.2 cm and of 6 cm is used in the CMEM (Community Microwave Emission Modelling Platform) . The Choudhury soil roughness model  () used in the SMOS SM retrievals  has if of 2.2 cm is used as in CMEM, and this parameterization is found inferior compared to the simple Wigneron  soil roughness model . It is to note this () is different from the scaled (i.e., ), which has a maximum value of one in this study. An alternative SMOS soil moisture product (SMOS-IC)  uses globally mapped values decoupled from the optimized combined vegetation and roughness parameter TR (= , where is vegetation optical depth at nadir ), by assuming a linear relationship between TR and LAI obtained from MODIS. As such, uncertainties of the obtained are more related to vegetation properties than the surface roughness which is the primary interest of this paper. On the other hand, the obtained is directly applied for SMOS-IC retrieval, and there is no quantified relationship between and geometric roughness parameters (, ). Given the large impact of on ATS+AIEM+TVG modelling (see Section 4.2), SMOS-IC is not a good choice used for comparisons in this study. To facilitate the comparison, is set as constant to match (used in SMOS-CMEM) and (suggested in SMAP over the Tibetan Plateau), respectively, during the study period. The same and adopted in SMOS-CMEM and SMAP are used for ATS-based model simulations. The parameter is set the same as in this study (i.e., 0 for H polarization and -1 for V polarization).
simulated by the ATS-based models with the SMAP setting (i.e., ) are found lower than observations during the late-monsoon (Figure 10, RMSE of 28.7 K in Table 4) and post-monsoon periods (Figure S8, RMSE of 26.9 K in Table 4). By contrast, moderate underestimations are seen for simulations (Figure 10, Figure S8) with RSME of 9.7 K and 13.3 K (Table 4) for the late-monsoon and post-monsoon periods, respectively. This may explain why only is used in SMAP soil moisture retrieval algorithms , which might be due to its less sensitivity to changes of surface roughness (see a narrower dynamic range of simulations than in Figure 9, and (50°) simulation results in Section 4 of the supplementary materials). The similar finding is also reported by . simulated by the ATS-based models with the SMOS-CMEM setting (i.e., =0.77) are found close to observations during the late-monsoon and post-monsoon periods ( in Table 4) but do not have observed strong diurnal variations (Figure 10, Figure S8). Furthermore, the fixed roughness parameter cannot capture temporal variations in roughness characteristics related to changing surface conditions driven by the weather system, especially during the soil freeze-thaw transition period. In contrast, the proposed ATS model in this study (see Section 4.1) has the potential to reflect the dynamics of dielectric roughness related to surface conditions, which is important for improving SM retrievals at the global scale.
In summary, the enhanced ATS model coupled with the AIEM+TVG model is validated for the use for natural grassland. The proposed ATS model, as a physically based one, is expected to be applied once all parameters are available for the area of interest (e.g., bare soil, cropland, and forest). Parameters such as wavelength and polarization are from sensor configuration. The roughness parameters (i.e., , , and ) are very difficult to estimate but effective ones can be obtained by calibration using satellite backscatter and brightness temperature observations and soil moisture measurements as introduced by [47, 61]. When in situ measurements are not available, the most consistent input of profile SMST can be estimated by using land surface models (LSMs), such as Community Land Model (CLM)  and Noah LSM , while the simulation results shall be validated to assure the accuracy. Soil texture information can be obtained from global and regional soil maps, for instance, SoilGrids1km  suggested for the Tibetan Plateau . It is to note that AIEM used in this study only involves single scattering terms . Once the multiple scattering term is incorporated, the ATS model shall be coupled with the updated version to make the calculation of scattering more realistic.
Last but not least, we would like to highlight the potential uses of the ATS model for microwave multifrequency (i.e., commonly used 1-10 GHz) applications, because it considers the wavenumber factor when parameterizing the dielectric roughness induced by inhomogeneity in the soil volume (see Equations (5, 6)) and leads to scaling with wavelength. On the other hand, the developed ATS model can be applied to the active microwave case. As radar backscatter depends not only on soil moisture dynamics but also on the surface roughness, and better quantification of the latter can contribute to substantial improvements of soil moisture retrieval [61, 84, 85]. When the surface roughness issue is better tackled with our proposed method, better understanding of the vegetation scattering-emission can be focused, as that will contribute further to soil moisture retrieval of vegetated regions.
In this study, the Tor Vergata discrete scattering model (TVG) coupled with the advanced integral equation model (AIEM) is used as a basis to investigate the effect of surface roughness on coherent and incoherent emission processes. The developed air-to-soil transition (ATS) model with a proposed dielectric roughness parameterization is integrated with the TVG+AIEM model to investigate seasonal signals as observed by ELBARA-III radiometer on an eastern Tibetan alpine meadow. The Wilheit  coherent and Lv  incoherent models are compared in quantifying the dielectric constant of bulk soil in the ATS zone together with in situ SM at 2.5 cm and in calculating soil effective temperature (_Wil and _Lv). The penetration depths representing the sensing depth of derived from the coherent () and incoherent () models are also compared.
The reduced discrepancy (≈20-50 K) between the modelled and observed demonstrates that the ATS model is a necessity in seasonal L-band simulations. The dielectric roughness thickness parameterized in the ATS model can describe well the surface roughness resulted from fine-scale topsoil structures characterized by SM and geometric roughness effects and from the soil volume that is due to the heterogeneous distribution of SM. The proposed dielectric roughness can replace the fixed roughness parameter and capture dynamics of surface roughness related to hydrometeorological conditions. The consideration of dynamic dielectric roughness is important for improving SM retrievals at the global scale, for which the fixed is used in current state-of-the-art processing. Furthermore, the soil porosity and logarithmic SM considered in the parameterization enhances the physical link between microwave emission models and land surface models, which might improve retrievals of soil physical properties and contribute to developing soil monitoring system utilizing space-based earth observation data with in situ data and modelling, especially for remote areas such as the third pole region.
The ATS model combined with Wilheit’s coherent model (ATS-Wil) can be applied for simulations for soils that are in the quasi-equilibrium condition, such as thawed soils with vegetation cover during the late-monsoon season and the beginning of the post-monsoon period. The ATS model combined with Lv incoherent model (ATS-Lv) is applicable for simulations for soils undergoing complex physical processes driven by rapidly changing weather systems, such as the freeze-thaw processes after heavy rainfall events during the post-monsoon season. The ATS model using the in situ SM at 2.5 cm (ATS-Lv2.5) can be applied during the whole study period except during the soil freeze-thaw transition period. The discrepancy between modelled and observed during the soil freeze-thaw transition period suggests a potential enhancement of the ATS model by considering the effects of ground surface temperature, surface water fraction, and liquid water-ice mixtures in calculating .
Conflicts of Interest
The authors declare no competing interests.
H.Z. proposed the method and wrote the paper. Z.S. and Y.Z. conceptualized the method and revised the paper. J.W., X.W., Z.W., and X.M. provided and investigated data.
ELBARA-III is a European Space Agency (ESA) instrument provided for calibration and validation in the Soil Moisture and Ocean Salinity (SMOS) mission. The authors would like to thank Dr. Xiaojing Bai from Nanjing University of Information Science & Technology for providing the AIEM code. They thank Zoige Plateau Wetlands Ecosystem Research Station, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Science, Lanzhou, China, for providing precipitation data. We thank anonymous reviewers for carefully commenting on this paper. The work of H. Zhao was supported by the Chinese Scholarship Council. This work was supported by the National Natural Science Foundation of China (grant no. 41971033), the Fundamental Research Funds for the Central Universities, CHD (grant no. 300102298307), and the CEOP-AEGIS (Coordinated Asia-European long-term Observing system of Qinghai-Tibet Plateau hydro-meteorological processes and the Asian-monsoon systEm with Ground satellite Image data and numerical Simulations) project (https://www.futurewater.eu/projects/ceop-aegis-2/).
1. Result analyses for the post-monsoon period, including Figures S1-S4. 2. Figures S5-S8 for the post-monsoon period to support Discussions in the text. 3. Comparisons of simulations by considering the impacts of only and , including Figures S9-S10 and Table S1. 4. simulations for incidence angles of 50° and 60°, including Figures S11-S12. 5. Two snapshots of Maqu region in Figure S13. (Supplementary Materials)
- E. Babaeian, M. Sadeghi, S. B. Jones, C. Montzka, H. Vereecken, and M. Tuller, “Ground, proximal and satellite remote sensing of soil moisture,” Reviews of Geophysics, vol. 57, no. 2, pp. 530–616, 2019.
- S. I. Seneviratne, T. Corti, E. L. Davin et al., “Investigating soil moisture–climate interactions in a changing climate: a review,” Earth-Science Reviews, vol. 99, no. 3-4, pp. 125–161, 2010.
- C. M. Taylor, R. A. M. de Jeu, F. Guichard, P. P. Harris, and W. A. Dorigo, “Afternoon rain more likely over drier soils,” Nature, vol. 489, no. 7416, pp. 423–426, 2012.
- Y. H. Kerr, P. Waldteufel, J. P. Wigneron et al., “The Smos mission: new tool for monitoring key elements ofthe global water cycle,” Proceedings of the IEEE, vol. 98, no. 5, pp. 666–687, 2010.
- J. P. Wigneron, T. J. Jackson, P. O'Neill et al., “Modelling the passive microwave signature from land surfaces: a review of recent results and application to the L-band Smos & Smap soil moisture retrieval algorithms,” Remote Sensing of Environment, vol. 192, pp. 238–262, 2017.
- D. Entekhabi, E. G. Njoku, P. E. O'Neill et al., “The soil moisture active passive (Smap) mission,” Proceedings of the IEEE, vol. 98, no. 5, pp. 704–716, 2010.
- P. de Rosnay, M. Drusch, and J. I. M. N. Sabater, “Milestone 1 Tech Note - part 1: Smos global surface emission model,” Progress report for ESA contract 3-11640/06/I-LG, ECMWF, Shinfield Park, Reading, 2009.
- X. Han, H.-J. H. Franssen, C. Montzka, and H. Vereecken, “Soil moisture and soil properties estimation in the community land model with synthetic brightness temperature observations,” Water Resources Research, vol. 50, no. 7, pp. 6081–6105, 2014.
- R. Bandara, J. P. Walker, C. Rüdiger, and O. Merlin, “Towards soil property retrieval from space: an application with disaggregated satellite observations,” Journal of Hydrology, vol. 522, pp. 582–593, 2015.
- M. Dimitrov, J. Vanderborght, K. G. Kostov et al., “Soil hydraulic parameters and surface soil moisture of a tilled bare soil plot inversely derived from L-band brightness temperatures,” Vadose Zone Journal, vol. 13, no. 1, pp. 1–18, 2014.
- C. Montzka, H. Moradkhani, L. Weihermüller, H.-J. H. Franssen, M. Canty, and H. Vereecken, “Hydraulic parameter estimation by remotely-sensed top soil moisture observations with the particle filter,” Journal of Hydrology, vol. 399, no. 3-4, pp. 410–421, 2011.
- K. Yang, L. Zhu, Y. Chen et al., “Land surface model calibration through microwave data assimilation for improving soil moisture simulations,” Journal of Hydrology, vol. 533, pp. 266–276, 2016.
- I. C. Prentice, X. Liang, B. E. Medlyn, and Y.-P. Wang, “Reliable, robust and realistic: the three R's of next-generation land-surface modelling,” Atmospheric Chemistry and Physics, vol. 15, no. 10, pp. 5987–6005, 2015.
- Z. Su, P. de Rosnay, J. Wen, L. Wang, and Y. Zeng, “Evaluation of Ecmwf's soil moisture analyses using observations on the Tibetan Plateau,” Journal of Geophysical Research: Atmospheres, vol. 118, no. 11, pp. 5304–5318, 2013.
- W. Peake, “Interaction of electromagnetic waves with some natural surfaces,” IEEE Transactions on Antennas and Propagation, vol. 7, no. 5, pp. 324–329, 1959.
- A. W. Straiton, C. W. Tolbert, and C. O. Britt, “Apparent temperatures of some terrestrial materials and the sun at 4.3-millimeter wavelengths,” Journal of Applied Physics, vol. 29, no. 5, pp. 776–782, 1958.
- A. K. Fung, Microwave Scattering and Emission Models and Their Applications, Artech House, Boston London, 1994.
- K. S. Chen, Tzong-Dar Wu, Leung Tsang, Qin Li, Jiancheng Shi, and A. K. Fung, “Emission of rough surfaces calculated by the integral equation method with comparison to three-dimensional moment method simulations,” IEEE Transactions on Geoscience and Remote Sensing, vol. 41, no. 1, pp. 90–101, 2003.
- P. Ferrazzoli and L. Guerriero, “Emissivity of vegetation: theory and computational aspects,” Journal of Electromagnetic Waves and Applications, vol. 10, no. 5, pp. 609–628, 1996.
- M. Bracaglia, P. Ferrazzoli, and L. Guerriero, “A fully polarimetric multiple scattering model for crops,” Remote Sensing of Environment, vol. 54, no. 3, pp. 170–179, 1995.
- E. G. Njoku and J.-A. Kong, “Theory for passive microwave remote sensing of near-surface soil moisture,” Journal of Geophysical Research, vol. 82, no. 20, pp. 3108–3118, 1977.
- T. T. Wilheit, “Radiative transfer in a plane stratified dielectric,” IEEE Transactions on Geoscience Electronics, vol. 16, no. 2, pp. 138–143, 1978.
- B. J. Choudhury, T. J. Schmugge, and T. Mo, “A parameterization of effective soil temperature for microwave emission,” Journal of Geophysical Research: Oceans, vol. 87, no. C2, pp. 1301–1304, 1982.
- T. J. Schmugge and B. J. Choudhury, “A comparison of radiative transfer models for predicting the microwave emission from soils,” Radio Science, vol. 16, no. 5, pp. 927–938, 1981.
- J. R. Wang and B. J. Choudhury, “Remote sensing of soil moisture content, over bare field at 1.4 Ghz frequency,” Journal of Geophysical Research: Oceans, vol. 86, no. C6, pp. 5277–5282, 1981.
- M. Parrens, J.-C. Calvet, P. de Rosnay, and B. Decharme, “Benchmarking of L-band soil microwave emission models,” Remote Sensing of Environment, vol. 140, pp. 407–419, 2014.
- Y. H. Kerr, P. Waldteufel, P. Richaume et al., “The Smos soil moisture retrieval algorithm,” IEEE Transactions on Geoscience and Remote Sensing, vol. 50, no. 5, pp. 1384–1403, 2012.
- N. N. Das, D. Entekhabi, and E. G. Njoku, “An algorithm for merging Smap radiometer and radar data for high-resolution soil-moisture retrieval,” IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 5, pp. 1504–1512, 2010.
- S. Lv, J. Wen, Y. Zeng, H. Tian, and Z. Su, “An improved two-layer algorithm for estimating effective soil temperature in microwave radiometry using in situ temperature and soil moisture measurements,” Remote Sensing of Environment, vol. 152, pp. 356–363, 2014.
- C. Mätzler, “Surface emission,” in Thermal Microwave Radiation: Applications for Remote Sensing, E. V. Jull and P. J. B. Clarricoats, Eds., pp. 225–425, The Institution of Engineering and Technology, London, UK, 2006.
- K. Schneeberger, M. Schwank, C. Stamm, P. De Rosnay, C. Mätzler, and H. Flühler, “Topsoil structure influencing soil water retrieval by microwave radiometry,” Vadose Zone Journal, vol. 3, no. 4, pp. 1169–1179, 2004.
- M. Schwank, M. Stahli, H. Wydler, J. Leuenberger, C. Matzler, and H. Fluhler, “Microwave L-band emission of freezing soil,” IEEE Transactions on Geoscience and Remote Sensing, vol. 42, no. 6, pp. 1252–1261, 2004.
- Z. Su, J. Wen, L. Dente et al., “The Tibetan Plateau observatory of plateau scale soil moisture and soil temperature (Tibet-Obs) for quantifying uncertainties in coarse resolution satellite and model products,” Hydrology and Earth System Sciences, vol. 15, no. 7, pp. 2303–2316, 2011.
- Y. Zeng, Z. Su, R. van der Velde et al., “Blending satellite observed, model simulated, and in situ measured soil moisture over Tibetan Plateau,” Remote Sensing, vol. 8, no. 3, p. 268, 2016.
- R. Zhuang, Y. Zeng, S. Manfreda, and Z. Su, “Quantifying long-term land surface and root zone soil moisture over Tibetan Plateau,” Remote Sensing, vol. 12, no. 3, p. 509, 2020.
- Z. Su, J. Wen, Y. Zeng et al., “Multiyear in-situ L-band microwave radiometry of land surface processes on the Tibetan Plateau,” Scientific Data, vol. 7, no. 1, p. 317, 2020.
- M. J. Escorihuela, A. Chanzy, J. P. Wigneron, and Y. H. Kerr, “Effective soil moisture sampling depth of L-band radiometry: a case study,” Remote Sensing of Environment, vol. 114, no. 5, pp. 995–1001, 2010.
- H. Zhao, Y. Zeng, S. Lv, and Z. Su, “Analysis of soil hydraulic and thermal properties for land surface modeling over the Tibetan Plateau,” Earth System Science Data, vol. 10, no. 2, pp. 1031–1061, 2018.
- L. Dente, Z. Vekerdy, J. Wen, and Z. Su, “Maqu network for validation of satellite-derived soil moisture products,” International Journal of Applied Earth Observation and Geoinformation, vol. 17, pp. 55–65, 2012.
- D. Zheng, R. van der Velde, Z. Su et al., “Augmentations to the Noah model physics for application to the Yellow River source area. Part I: soil water flow,” Journal of Hydrometeorology, vol. 16, no. 6, pp. 2659–2676, 2015.
- L. Yu, Y. Zeng, J. Wen, and Z. Su, “Liquid-vapor-air flow in the frozen soil,” Journal of Geophysical Research: Atmospheres, pp. 7393–7415, 2018.
- D. Zheng, X. Wang, R. van der Velde et al., “L-band microwave emission of soil freeze–thaw process in the third pole environment,” IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 9, pp. 5324–5338, 2017.
- D. Zheng, X. Li, X. Wang et al., “Sampling depth of L-band radiometer measurements of soil moisture and freeze-thaw dynamics on the Tibetan Plateau,” Remote Sensing of Environment, vol. 226, pp. 16–25, 2019.
- D. Zheng, R. van der Velde, J. Wen et al., “Assessment of the Smap soil emission model and soil moisture retrieval algorithms for a Tibetan Desert ecosystem,” IEEE Transactions on Geoscience and Remote Sensing, vol. 56, no. 7, pp. 3786–3799, 2018.
- D. Zheng, X. Wang, R. van der Velde et al., “Impact of surface roughness, vegetation opacity and soil permittivity on L-band microwave emission and soil moisture retrieval in the third pole environment,” Remote Sensing of Environment, vol. 209, pp. 633–647, 2018.
- W. Verhoef, “Application of harmonic analysis of Ndvi time series (Hants),” in Fourier Analysis of Temporal NDVI in the Southern African and American Continents, pp. 19–24, SC-DLO, Wageningen, The Netherlands, 1996.
- L. Dente, P. Ferrazzoli, Z. Su, R. van der Velde, and L. Guerriero, “Combined use of active and passive microwave satellite data to constrain a discrete scattering model,” Remote Sensing of Environment, vol. 155, pp. 222–238, 2014.
- Q. Wang, R. van der Velde, and Z. Su, “Use of a discrete electromagnetic model for simulating aquarius L-band active/passive observations and soil moisture retrieval,” Remote Sensing of Environment, vol. 205, pp. 434–452, 2018.
- X. Bai, J. Zeng, K. S. Chen et al., “Parameter optimization of a discrete scattering model by integration of global sensitivity analysis using Smap active and passive observations,” IEEE Transactions on Geoscience and Remote Sensing, vol. 57, no. 2, pp. 1084–1099, 2019.
- H. J. Eom and A. K. Fung, “A scatter model for vegetation up to Ku-band,” Remote Sensing of Environment, vol. 15, no. 3, pp. 185–200, 1984.
- C. Mätzler, “Microwave (1-100 Ghz) dielectric model of leaves,” IEEE Transactions on Geoscience and Remote Sensing, vol. 32, no. 4, pp. 947–949, 1994.
- C. Kittel, Introduction to Solid State Physics, Vol. 8, Wiley, New York, 1976.
- J.-P. Wigneron, L. Laguerre, and Y. H. Kerr, “A simple parameterization of the L-band microwave emission from rough agricultural soils,” IEEE Transactions on Geoscience and Remote Sensing, vol. 39, no. 8, pp. 1697–1707, 2001.
- M. Schwank, M. Guglielmetti, C. Matzler, and H. Fluhler, “Testing a new model for the L-band radiation of moist leaf litter,” IEEE Transactions on Geoscience and Remote Sensing, vol. 46, no. 7, pp. 1982–1994, 2008.
- M. J. Escorihuela, Y. H. Kerr, P. de Rosnay, J. P. Wigneron, J. C. Calvet, and F. Lemaitre, “A simple model of the bare soil microwave emission at L-band,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 7, pp. 1978–1987, 2007.
- S. Bircher, N. Skou, and Y. H. Kerr, “Validation of Smos L1c and L2 products and important parameters of the retrieval algorithm in the Skjern River Catchment, Western Denmark,” IEEE Transactions on Geoscience and Remote Sensing, vol. 51, no. 5, pp. 2969–2985, 2013.
- S. Lv, Y. Zeng, J. Wen, H. Zhao, and Z. Su, “Estimation of penetration depth from soil effective temperature in microwave radiometry,” Remote Sensing, vol. 10, no. 4, p. 519, 2018.
- V. L. Mironov, Y. H. Kerr, L. G. Kosolapova, I. V. Savin, and K. V. Muzalevskiy, “A temperature-dependent dielectric model for thawed and frozen organic soil at 1.4 Ghz,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 8, no. 9, pp. 4470–4477, 2015.
- M. Bass, E. Van Stryland, R. William, and W. Wolfe, “Optical properties of films and coatings,” in Handbook of Optics, pp. 42.9–42.14, McGraw-Hill, NewYork, 1995.
- A. Della Vecchia, Advances in modeling microwave interactions with vegetation for active and passive remote sensing, [Ph.D thesis], University of Rome Tor Vergata, Geoinformation PhD School, 2006.
- Z. Su, P. A. Troch, and F. P. de Troch, “Remote sensing of bare surface soil moisture using Emac/Esar data,” International Journal of Remote Sensing, vol. 18, no. 10, pp. 2105–2124, 1997.
- F. Mattia, G. Satalino, L. Dente, and G. Pasquariello, “Using a priori information to improve soil moisture retrieval from Envisat Asar Ap data in semiarid regions,” IEEE Transactions on Geoscience and Remote Sensing, vol. 44, no. 4, pp. 900–912, 2006.
- H.-J. F. Benninga, R. van der Velde, and Z. Su, “Uncertainty of effective roughness parameters calibrated on bare agricultural land using sentinel-L Sar,” in IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium, Valencia, July 2018.
- F. T. Ulaby, D. G. Long, W. J. Blackwell et al., “Electromagnetic wave propagation and reflection,” in Microwave Radar and Radiometric Remote Sensing, pp. 44–50, University of Michigan Press, Ann Arbor, US, 2014.
- S. Lv, Y. Zeng, J. Wen, D. Zheng, and Z. Su, “Determination of the optimal mounting depth for calculating effective soil temperature at L-band: Maqu case,” Remote Sensing, vol. 8, no. 6, p. 476, 2016.
- S. Raju, A. Chanzy, J.-P. Wigneron, J.-C. Calvet, Y. Kerr, and L. Laguerre, “Soil moisture and temperature profile effects on microwave emission at low frequencies,” Remote Sensing of Environment, vol. 54, no. 2, pp. 85–97, 1995.
- T. Mo and T. J. Schmugge, “A parameterization of the effect of surface roughness on microwave emission,” IEEE Transactions on Geoscience and Remote Sensing, vol. GE-25, no. 4, pp. 481–486, 1987.
- B. J. Choudhury, T. J. Schmugge, A. Chang, and R. W. Newton, “Effect of surface roughness on the microwave emission from soils,” Journal of Geophysical Research: Oceans, vol. 84, no. C9, pp. 5699–5706, 1979.
- J. P. Grant, K. Saleh-Contell, J. P. Wigneron et al., “Calibration of the L-Meb model over a coniferous and a deciduous forest,” IEEE Transactions on Geoscience and Remote Sensing, vol. 46, no. 3, pp. 808–818, 2008.
- K. Saleh, J.-P. Wigneron, P. de Rosnay, J.-C. Calvet, and Y. Kerr, “Semi-empirical regressions at L-band applied to surface soil moisture retrievals over grass,” Remote Sensing of Environment, vol. 101, no. 3, pp. 415–426, 2006.
- J.-P. Wigneron, A. Chanzy, Y. H. Kerr et al., “Evaluating an improved parameterization of the soil emission in L-Meb,” IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 4, pp. 1177–1189, 2011.
- K. Saleh, Y. H. Kerr, P. Richaume et al., “Soil moisture retrievals at L-band using a two-step inversion approach (cosmos/Nafe'05 experiment),” Remote Sensing of Environment, vol. 113, no. 6, pp. 1304–1312, 2009.
- S. Mwangi, Y. Zeng, C. Montzka, L. Yu, and Z. Su, “Assimilation of cosmic-ray neutron counts for the estimation of soil ice content on the eastern Tibetan Plateau,” Journal of Geophysical Research: Atmospheres, vol. 125, no. 3, pp. 1–23, 2020.
- H. Lawrence, J.-P. Wigneron, F. Demontoux, A. Mialon, and Y. H. Kerr, “Evaluating the semiempirical H-Q model used to calculate the L-band emissivity of a rough bare soil,” IEEE Transactions on Geoscience and Remote Sensing, vol. 51, no. 7, pp. 4075–4084, 2013.
- P. O’Neill, E. Njoku, T. Jackson, S. Chan, and R. Bindlish, Smap algorithm theoretical basis document: level 2 & 3 soil moisture (passive) data products, Jet Propulsion Lab., California Inst. Technol., Pasadena, CA, USA, 2015.
- P. de Rosnay, J. Muñoz-Sabater, C. Albergel et al., “Smos brightness temperature forward modelling and long term monitoring at Ecmwf,” Remote Sensing of Environment, vol. 237, article 111424, 2020.
- R. Fernandez-Moran, A. al-Yaari, A. Mialon et al., “Smos-Ic: an alternative Smos soil moisture and vegetation optical depth product,” Remote Sensing, vol. 9, no. 5, p. 457, 2017.
- M. Parrens, J. P. Wigneron, P. Richaume et al., “Global-scale surface roughness effects at L-band as estimated from Smos observations,” Remote Sensing of Environment, vol. 181, pp. 122–136, 2016.
- P. O'Neill, R. Bindlish, S. Chan, E. Njoku, and T. Jackson, Algorithm theoretical basis document. Level 2 & 3 soil moisture (passive) data products, 2020.
- J. Zeng, K.-S. Chen, H. Bi, T. Zhao, and X. Yang, “A comprehensive analysis of rough soil surface scattering and emission predicted by Aiem with comparison to numerical simulations and experimental measurements,” IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 3, pp. 1696–1708, 2017.
- K. Oleson, D. Lawrence, G. Bonan et al., Technical description of version 4.5 of the community land model (Clm), Ncar Tech. Note, NCAR/TN-503+ STR, 2013.
- F. Chen and J. Dudhia, “Coupling an advanced land surface-hydrology model with the Penn State-Ncar Mm5 modeling system. Part I: model implementation and sensitivity,” Monthly Weather Review, vol. 129, no. 4, pp. 569–585, 2001.
- T. Hengl, J. M. de Jesus, R. A. MacMillan et al., “Soilgrids1km--global soil information based on automated mapping,” PLoS One, vol. 9, no. 8, article e105992, 2014.
- M. S. Moran, C. D. Peters-Lidard, J. M. Watts, and S. McElroy, “Estimating soil moisture at the watershed scale with satellite-based radar and land surface models,” Canadian Journal of Remote Sensing, vol. 30, no. 5, pp. 805–826, 2004.
- H. Lievens, N. E. C. Verhoest, E. De Keyser et al., “Effective roughness modelling as a tool for soil moisture retrieval from C- and L-band Sar,” Hydrology and Earth System Sciences, vol. 15, no. 1, pp. 151–162, 2011.
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