# Effective Surface Roughness Impact in Polarimetric GNSS-R Soil Moisture Retrievals
## 1 Introduction  
Global Navigation Satellite System-Reflectometry (GNSS-R) is a well-established technique that enables several Earth remote sensing applications from a diverse set of platforms. The most significant benefits of GNSS-R sensors as compared to traditional microwave remote sensing sensors are their reduced size, mass, and cost, as it does not require using large and high directive antennas, and reduced power consumption as compared with active sensors, such as radars. These characteristics make GNSS-R suitable for small platforms as micro-satellites, as is the case of the Cyclone GNSS (CYGNSS) mission [1; 2; 3] or the BuFeng-1 mission [4; 5], or nano-satellites as the FSSCat mission [6; 7; 8; 9], or Spire Global Inc. GNSS-R constellation [10]. Its suitability for smaller platforms allows for reducing its operational cost and increasing the temporal resolution (i.e., lower revisit time) with respect to L-band synthetic aperture radar (SAR) approaches [11; 12; 13]. The Soil Moisture Active Passive (SMAP) mission was launched in 2015, with the goal of studying the Earth's surface properties, such as soil moisture and freeze/thaw being the main objectives by combining L-band radiometry and L-band SAR data. However, shortly after its launch, the radar stopped its nominal operations, and it was decided to tune the SMAP radar receiver to receive GPS L2 reflected signals. Thanks to the highgain and dual-polarization antenna, SMAP-Reflectometry (SMAP-R) constitutes a unique polarimetric GNSS-R dataset. The SMAP-R polarimetric capabilities have been summarized in several publications [14; 15; 16; 17]. The theoretical basis, absolute signal calibration, and performance metrics of the SMAP-R data have been studied in [18], where the Hybrid Compact Polarimetry (HCP) concept is presented for the SMAP-R case, showing the measured Stokes parameters for the RHCP-transmitted GNSS signal. Among the current and potential GNSS-R applications over land, it is worth highlighting those which are defined as Essential Climate Variables (ECV) by the Global Climate Observing System (GCOS) [19], such as soil moisture [3; 4; 7; 20; 21; 22], above-ground biomass [23; 24], or land cover [25; 26]. A key parameter in soil moisture retrieval is the characterization of the surface roughness, as it affects the electromagnetic signals either emitted, reflected, or scattered from the surface. Better knowledge of surface roughness helps model the soil surface and reduces the error in soil moisture estimates. The surface roughness has a significant effect on soil moisture retrievals, particularly when using radiometric models or when full-polarization radar datasets for variable reduction are not available [27; 28; 29]. Accurately modeling the surface roughness is crucial in soil moisture retrievals since the scattering coefficient of a surface can vary up to tens of dB even when the moisture level is the same, making impossible soil moisture minimization without precise roughness modeling [27; 30]. The surface roughness has been a matter of study for soil moisture retrieval both in the field of L-band radiometry [31] and in the field of GNSS-R [31; 32; 33]. In the GNSS-R field, the ratio between the reflectivity and the theoretical Fresnel reflection coefficient has been modeled following the Physical Optics (PO) approximation using the surface root-mean-square (rms) height [30; 34]. However, results report inaccuracies even using in-situ profilers to estimate the rms height [32]. For this reason, researchers have opted to develop semi-empirical models [33; 35; 36; 37] to estimate the roughness parameter based on the combination of radar and radiometry data. This manuscript aims at studying the effects of the surface roughness on GNSS-R data at multiple polarizations. Soil moisture data derived from the SMAP radiometer [13; 18] and full-Stokes parameters GNSS-R data collected by the SMAP radar received working in reflectometry mode (SMAP-R) are used in two models to estimate the surface roughness effect.