Comparative Assessment of Multimodal Earth Observation Data for Soil Moisture Estimation

Field-scale retrieval of surface soil moisture (SM), leaf area index (LAI), and plant height (PH) is essential for precision agriculture, yet it remains an ill-posed inverse problem. Concurrent variations in soil moisture and canopy density generate substantial ambiguities in radar backscatter and spectral responses, which reduces the effectiveness of traditional feedforward regression models in heterogeneous smallholder cropping systems. This study presents the Iterative Energy-Based Transformer (iEBT) for the joint retrieval of coupled soil-canopy states from Sentinel-1 C-band SAR and Sentinel-2 multispectral time series. Instead of direct regression, iEBT embeds multi-modal predictors within a shared sequence, produces an initial state estimate, and iteratively updates the target [SM, LAI, PH] vector through normalized gradient descent to minimize a learned scalar compatibility energy function. Using 700 quality-controlled field measurements from Varanasi, India, iEBT achieved the highest learned-model performance on the random test split, with a four-seed mean R^2 of 0.854 \pm 0.012 (R_SM^2 = 0.841, R_LAI^2 = 0.905, R_PH^2 = 0.821). WCM and PROSAIL were retained as physically interpretable SAR and optical reference models for comparison. Modality ablations confirmed that Sentinel-1 drives SM retrieval, while Sentinel-2 dominates LAI, whereas PH relies on combined structural-phenological signatures. Crucially, the model's terminal energy functions as an uncalibrated post-retrieval quality diagnostic; screening the 10% highest-energy samples markedly reduced target level root-mean-square errors. While leave-one-campaign-out validation highlights persistent cross-season domain shift challenges due to localized management variations, compatibility-guided multimodal fusion offers a structured self-diagnostic path toward reliable biophysical parameter estimation

Accurate soil moisture estimation in semi-arid agricultural regions requires integrating remote sensing and meteorological information while accounting for the delayed response of soil moisture to atmospheric forcing. This study introduces a Cross-Correlation Function (CCF) methodology to determine optimal temporal lags (0-30 days) between meteorological variables and soil moisture, as well as inter-depth lags (0-15 days) describing vertical moisture propagation from the surface (10 cm) to deeper layers (20-50 cm). The approach was validated across seven agricultural plots in southeastern Spain. Three deep learning architectures, each targeting a distinct prediction granularity, were evaluated under five feature configurations ranging from satellite-only to full satellite-meteorology-depth fusion: a CNN for per-pixel estimation within each plot, an LSTM for frame-level (daily plot-mean) prediction, and a CNN-LSTM hybrid operating on sliding windows with pooled multi-patch training. Models were assessed on held-out data to measure genuine generalisation. Meteorological variables improved performance over the satellite-only baseline, while subsurface depth information proved decisive across all architectures. The per-pixel CNN achieved the strongest single-patch result (R^2 = 0.877, RMSE = 2.28), with a seven-patch average R^2 of 0.535, representing an improvement of +1.00 over the satellite-only baseline. The pooled CNN-LSTM hybrid obtained the highest overall performance (R^2 = 0.930, CVRMSE = 8.0%). These results demonstrate that explicitly modelling atmospheric and vertical subsurface delays substantially improves soil moisture estimation for precision agriculture.

Soil Moisture (SM) modelling constitutes a complex spatiotemporal learning problem characterised by nonlinear environmental interactions, heterogeneous data sources, and limited ground observations. Physics-based approaches, such as water balance models, rely on explicit hydrological equations and high-quality inputs, but their computational cost and scalability limitations restrict large-scale deployment. Data-driven artificial intelligence (AI) methods have emerged as flexible alternatives, enabling the extraction of empirical relationships between soil moisture and environmental variables with reduced modelling assumptions. This work presents a structured survey of AI-based models for soil moisture estimation and classification. Existing approaches are organized into five categories: (a) statistical time-series models, (b) geostatistical methods (c) classical machine learning (ML) models, (d) Deep Learning (DL) models and (e) Probabilistic/Bayesian methods. These models leverage historical soil moisture records, meteorological variables, vegetation indices, topography, soil characteristics, and geolocation data to perform regression or classification tasks.