A temporal polarization ratio algorithm for calibration-free retrieval of soil moisture at L-band

Highlights

• A new algorithm is designed for the retrieval of soil moisture at L-band.

• Soil moisture retrievals are independent of surface roughness.

• Soil moisture retrievals are independent of vegetation parameters.

• Soil moisture retrievals are robust to systematical errors in soil temperature.

Abstract

Monitoring of surface soil moisture (SM) through microwave radiometry typically relies on the inversion of a radiative transfer model. Conventional inversion algorithms require proper calibration of surface roughness and radiometric parameters of the overlying canopy, including the scattering albedo and optical depth. However, uncertainty in global characterization of these parameters is one of the main sources of error in satellite SM retrievals. To cope with this uncertainty, this paper presents a new algorithm, called “temporal polarization ratio algorithm” (TPRA), that enables retrieval of SM independent of surface roughness and vegetation parameters. This approach uses the temporal differences of polarized emissivity observations assuming that the surface roughness and vegetation parameters are invariant over a window of time. Unlike the classical dual channel algorithms (DCA), TPRA is not only free of surface calibration but also robust to systematical errors arising from surface soil temperature errors. One caveat is that the algorithm is unable to retrieve SM when surface emissivity does not change appreciably in time. The performance of TPRA is evaluated through several controlled numerical experiments and validated using the Soil Moisture Active Passive (SMAP) satellite retrievals as well as in-situ SM measurements over Australia. The results show improved SM retrievals compared with the DCA and SMAP official products as long as the surface emissivity changes sufficiently over the retrieval time period.

Introduction

Surface soil moisture (SM) is an essential hydrologic state variable in the Earth system as it controls evapotranspiration (Wetzel and Chang, 1987; Vivoni et al., 2008; Jung et al., 2010), affects space-time patterns of mesoscale overland rainfall processes (Guillod et al., 2015; Lin et al., 2017a, Lin et al., 2017b), and thus modulates the global water and energy cycle (Seneviratne et al., 2010; Babaeian et al., 2019). It is shown that surface SM, all by itself, contains adequate information about the land surface net water flux and hence variation of total subsurface water storage (Crow et al., 2017; Sadeghi et al., 2019, Sadeghi et al., 2020).

Today, L-band (1–2 GHz) microwave radiometry offers an all-sky capability for frequent observations of SM on a global scale (Njoku and Li, 1999) and has been the cornerstone of two satellite missions including the ESA's Soil Moisture and Ocean Salinity (SMOS, 2009) (Kerr et al., 2010) and NASA's Soil Moisture Active Passive (SMAP, 2015) (Entekhabi et al., 2014). Both missions have provided new opportunities to measure global SM at the topmost ~5 cm depth with a 3-day maximum revisiting time and have significantly extended our understanding of global water, energy, and carbon cycle (McColl et al., 2017a; Feldman et al., 2018b; Wigneron et al., 2020; Tian et al., 2018).

At L-band, the surface emission, from the top ~5 cm of soil layer and the aboveground vegetation, is often obtained from a zeroth-order approximation of the radiative transfer equation, known as the τ–ω model (Mo et al., 1982; Tsang et al., 1985; Ulaby et al., 2014). This model consists of three components including direct upward soil emission, direct upward vegetation emission, and reflected downward vegetation emission. These emission signals are parameterized by the rough surface reflectivity r, vegetation single scattering albedo ω, and vegetation transmissivity γ.

The single scattering albedo, defined as the ratio of scattering to extinction coefficient (Ulaby et al., 1983; Wigneron et al., 1993), accounts for the lumped contribution of scattering in the total vegetation attenuation and is often called the “effective scattering albedo” (Kurum et al., 2012). The albedo parameter is commonly prespecified in the inversion algorithms through experimental (Wigneron et al., 2004) or numerical (Ferrazzoli et al., 2002) calibrations using ground-based (Wigneron et al., 2007; Saleh et al., 2007; Yan et al., 2015; Fernandez-Moran et al., 2017b) and/or spaceborne (De Lannoy et al., 2013, De Lannoy et al., 2014) observations. In practice, for the SMAP and SMOS official products, the global values are determined empirically as a function of land cover/vegetation types (Wigneron et al., 2017). Nevertheless, comparisons between zeroth- and high-order radiative transfer models demonstrate that the commonly used effective scattering albedo in τ-ω model is generally smaller than its theoretical values because of significant scattering by the canopy trunks and branches (Kurum, 2013; Schwank et al., 2018). More recently, attempts have been made to estimate ω directly in the inversion process (Vittucci et al., 2017), assuming that it remains invariant over a window of time (Konings et al., 2016, Konings et al., 2017; Feldman et al., 2018a; Karthikeyan et al., 2019) or space (Gao et al., 2020b). However, due to the ill-posed nature of the inversion, setting ω as an additional unknown parameter may lead to extra uncertainties in the retrievals.

The slanted vegetation transmissivity γ is directly linked to the vegetation optical depth (VOD), denoted by τ, which is determined differently in the family of single channel algorithms (SCA) (Jackson, 1993; Bindlish et al., 2015) and the dual channel algorithms (DCA) (Njoku and Entekhabi, 1996; Njoku et al., 2003; Shi et al., 2006). In the SCA, currently used to produce the official SMAP products, climatology of the normalized difference vegetation index (NDVI) (Chan et al., 2013) from the Moderate Resolution Imaging Spectroradiometer (MODIS) (Justice et al., 1998) is used to estimate the vegetation water content (VWC) (Jackson et al., 1999). The VOD is then linked to VWC through a set of empirical equations (Jackson and O'Neill, 1989; Jackson and Schmugge, 1991), which paves the way for direct estimation of SM from the τ-ω model. However, DCA attempts to directly retrieve VOD and SM simultaneously using some ancillary a priori data. For example, in the SMOS L-band Microwave Emission of the Biosphere (L-MEB) model (Kerr et al., 2006), the leaf area index (LAI) (Chen and Black, 1992) is utilized to obtain an a priori estimate of the VOD values (Kerr et al., 2012). A quadratic regularization term is then used to regress the retrievals toward this a priori estimate, in a Bayesian setting, for reducing uncertainties in the retrievals of both SM and VOD (Pardé et al., 2004). More recently, a box-constrained DCA inversion paradigm was also introduced indicating that constraining the SM and VOD retrievals to their physical/climatological range of variability not only reduces the uncertainties but also yields higher-resolution retrievals (Ebtehaj and Bras, 2019; Gao et al., 2020a). Although a few new algorithms such as SMOS-IC (Fernandez-Moran et al., 2017a) and multi-temporal DCA (Konings et al., 2016) are able to retrieve both VOD and SM independent of any a priori information, it is still challenging for classical DCA and SCA to properly account for VOD in the inversion process.

Soil moisture is usually obtained from the soil dielectric constant (Mironov et al., 2009) that is related to the smooth surface reflectivity through the Fresnel equations. However, the incoherent surface emission is explained by the rough surface reflectivity, which needs to be linked to the smooth surface reflectivity. This linkage has been explained by physically-based numerical models (Li et al., 2000; Huang et al., 2010; Huang and Tsang, 2012; Tsang et al., 2012), analytical models (Wu et al., 2001; Chen et al., 2003), and semi-empirical models (Choudhury et al., 1979; Wang and Choudhury, 1981; Wigneron et al., 2001). The two former approaches usually require parameterization of surface emissivity via Monte Carlo simulations under various surface characteristics (Shi et al., 2002; Chen et al., 2009; Tsang et al., 2013; Cui et al., 2016) and have not yet been widely used for spaceborne retrievals due to the lack of estimates of geometric roughness parameters at the scale of satellite footprint (Loew, 2008). However, the semi-empirical schemes, such as the Q/H model (Lawrence et al., 2013; Peng et al., 2017; Karthikeyan et al., 2017), are commonly deployed for the L-band SM retrieval owing to their relatively high degree of accuracy, simple structure, and low computational cost.

Despite significant efforts made, there are still discrepancies among the prescribed or estimated values of the vegetation parameters on a global scale (De Lannoy et al., 2014; Konings et al., 2016, Konings et al., 2017) and proper parameterization of surface roughness, over the satellite footprint, is not yet well-understood (Neelam et al., 2020). Consequently, the associated uncertainties will propagate into the SM retrievals (Theis and Blanchard, 1988; Grant et al., 2008). For example, the usage of 13-year VOD climatology from MODIS NDVI observations in SMAP SCA can misrepresent real-time dynamics of VOD and leads to significant errors in the SCA SM retrievals (Dong et al., 2018). Moreover, because ω and surface roughness parameter are commonly obtained as a function of global land cover maps (Wigneron et al., 2007; O'Neill et al., 2017), any uncertainty in land cover classification (Fritz et al., 2011; Congalton et al., 2014) can add additional errors to the SM retrievals.

Besides the vegetation parameters and surface roughness, the quality of SM retrievals is moderately affected by the biases in the effective soil temperature (De Rosnay et al., 2006). An accurate estimation of the effective soil temperature often requires high-quality measurements of soil temperature and moisture profiles (Choudhury et al., 1982). Several simplified schemes have been proposed for estimating the effective temperature at a satellite footprint scale (Choudhury et al., 1982; Wigneron et al., 2001, Wigneron et al., 2008; Holmes et al., 2006; Shaoning et al., 2014). An inter-comparison of these schemes (Lv et al., 2016) based on the soil temperature reanalysis from Modern-Era Retrospective analysis for Research and Applications (MERRA) (Gelaro et al., 2017) indicates an up to 5 K uncertainty in the resulted effective soil temperature data sets. This uncertainty can lead to a non-negligible bias in the satellite SM retrievals.

In this paper, to cope with the above-mentioned uncertainties, a new approach is proposed for calibration-free retrieval of SM at L-band, called the “Temporal Polarization Ratio Algorithm” (TPRA). The term “calibration-free” here means that the TPRA does not depend on any empirical values for vegetation or surface roughness parameters, which are inevitable in the conventional algorithms. The main advantage of the new approach is that its SM retrievals are independent of vegetation parameters, surface roughness, and thus land cover maps. Assuming that the soil roughness and vegetation parameters are time-invariant over a sufficiently short window of time, TPRA uses ratios of temporal differences of polarized emissivity values, which are only a function of temporal changes of surface reflectivity. As a result, TPRA is not only independent of the effective scattering albedo, VOD, and surface roughness but also remains relatively robust to systematic emissivity biases arising from the effective soil temperature errors. Nonetheless, this new algorithm is unable to retrieve SM when the observed emissivity does not change significantly over time.

The organization of the paper is as follows: Section 2 describes TPRA following a brief review of the τ–ω radiative transfer model and lays out the algorithmic steps to implement TPRA for satellite observations. In section 3, we first examine the performance of TPRA through a series of controlled numerical experiments and then implement it using level-III SMAP brightness temperatures over Australia. The results are compared with SMAP official products and validated against in-situ measurements from the OzNet monitoring network. In section 4, we conclude and discuss potential future research directions.