Cramer–Rao Lower Bound for SoOp-R-Based Root-Zone Soil Moisture Remote Sensing

Abstract

Signals of opportunity (SoOp) reflectometry (SoOp-R) is a maturing field for geophysical remote sensing as evidenced by the growing number of airborne and spaceborne experiments. As this approach receives more attention, it is worth analyzing SoOp-R's capabilities to retrieve subsurface soil moisture (SM) by leveraging communication and navigation satellite transmitters. In this research, the CRLB is used to identify the effects of variable SoOp-R parameters on the best achievable estimation error for root-zone soil moisture (RZSM). This study investigates the use of multiple frequency, polarization, and incidence angle measurement configurations on a two-layered dielectric profile. The results also detail the effects of variable SM conditions on the capability of SoOp-R systems to predict subsurface SM. The most prevalent observation is the importance of using at least two frequencies to limit uncertainties from subsurface SM estimates. If at least two frequencies are used, the CRLB of a profile is retrievable within the root-zone depending on the surface SM content as well as the number of independent measurements of the profile. For a depth of 30 cm, it is observed that a CRLB corresponding to 4% RZSM estimation accuracy is achievable with as few as 2 dual-frequency-based SoOp-R measurements. For this depth, increasing number of measurements provided by polarization and incidence angle allow for sensing of increasingly wet SM profile structures. This study, overall, details a methodology by which SoOp-R receiver system can be designed to achieve a desired CRLB using a trade-off study between the available measurements and SM profile.

Retrieval of Subsurface Soil Moisture and Vegetation Water Content from Multi-frequency SoOp-Reflectometry: Sensitivity Analysis

“…The sensitivity of retrieval error of RSZM and VWC has been examined through simulations that vary each of the SoOp-R system parameters, including frequency, polarization, orbital inclination, observation time window, and measurement error. The observations regarding frequency and polarization in our simulation study are in agreement with the results from [17] where the Cramer-Rao lower bound was used to determine the lower bound of the estimation variance for RZSM modeled by two SM slabs. The results presented in this article, however, are useful in that the end-to-end retrieval algorithm is applied to the large set of the actual SM data, which is utilized to develop multilayered SM profiles.…”

“…They can be considered as a "representativeness" error containing contributions from other error sources such as the vegetation model and the inversion algorithm. These linear models were then combined into a bivariate model using the square root of the sum of the squares (RSS) to avoid double counting the representativeness error: (17) where b SM and b VWC were assumed to be b SM,η and b VWC,η , respectively. This model will be validated with the simulation with both errors later in Section IV-H.…”

“…As such, the signals reflected at the specular point will have a large left-hand circular polarization (LHCP) component and the signal-tonoise ratio (SNR) measured by an RHCP antenna in space will be very small compared to the other polarizations. It has also been shown that the RHCP observations do not provide significant benefit in estimating RZSM [17]. Therefore, we selected LHCP for our single-polarization observable and an orthogonal pair of linear polarizations (H&V) for our dualpolarization observable.…”

Optimization of Random Surface Scattering Models for RR Polarization in SoOp-R/GNSS-R Applications

“…Later on, its applications on land surfaces have emerged and become more and more promising. Such as soil moisture or root zone soil moisture estimation [9,10], vegetation water content or biomass retrieval [11,12],and snow water equivalent evaluation [13] by SoOP-R or GNSS-R.…”