Root-Zone Soil Moisture Estimation From Multi-Frequency Radiometry: Inversion and Optimization With a Five-Parameter Profile Model

Abstract

Brightness temperature measured by low-frequency microwave radiometers contains depth-dependent information on soil moisture (SM), which could complement conventional surface-only products for root-zone soil moisture (RZSM) applications. This study is an information-content and algorithmic feasibility analysis to retrieve RZSM using multifrequency microwave radiometers, not an operational retrieval demonstration. Three strategies are evaluated with the same forward model and test profiles: two classical linearized inversions, based on the Method of Moments (MoM) and Nyström quadrature, and a bounded lookup-table (LUT) optimization using a five-parameter SM profile model. The methodological novelty resides in the controlled adaptation of selected classical solvers, and their comparison for multi-frequency radiometry, the explicit peak-position and peak-width parameterization, and the joint assessment of radiometric sensitivity, frequency selection, incidence angle, polarization, profile-shape mismatch, and implementation feasibility. Simulated brightness temperatures are generated for frequencies from 40 to 1400 MHz. For the smooth profiles measured by multi-depth probes near Lleida, the LUT approach provides the most stable retrievals, whereas MoM and Nyström require strong regularization and become unstable below wet layers. A direct profile-representation stress test shows negligible error for an in-family bell-shaped profile, RMSE values of about $0.011~{\mathrm {m^{3}/m^{3}}}$ for smooth monotonic or wet-surface profiles, and 0.028– $0.040~{\mathrm {m^{3}/m^{3}}}$ for sharp fronts, double wet layers, and inverted-bell profiles. These tests also show that a small layer-mean RZSM error can coexist with a biased vertical profile. Five-hundred-run Monte Carlo experiments have been run to quantify the effect of radiometric noise; the remaining uncertainty associated with soil temperature, dielectric properties, vegetation, roughness, radio-frequency interference, and low-frequency antenna constraints is explicitly identified as a prerequisite for future validation with airborne or satellite observations.