Assimilation of near-surface soil temperature and soil moisture in an unsaturated flow model: State and parameter estimation using synthetic and field experiments

Abstract

Soil moisture is a key variable governing land surface hydrology, agricultural productivity, and climate dynamics, influencing crucial processes such as evapotranspiration, infiltration, and surface runoff. Accurate estimation of soil moisture, particularly at the root zone level, is essential for applications such as irrigation management, drought monitoring, flood forecasting, and climate modeling. However, traditional in situ measurements are spatially limited, expensive, and labor-intensive, while remote sensing techniques, though offering broader spatial coverage, struggle to capture deeper soil moisture profiles due to surface interference from vegetation and soil roughness. Hydrological and land surface models provide an alternative approach for estimating soil moisture and its dynamics, but their accuracy is constrained by uncertainties in model parameters, initial conditions, and external forcing data. These limitations necessitate the use of data assimilation techniques, such as the Ensemble Kalman Filter (EnKF), which optimally integrates observational data with numerical models to enhance soil moisture predictions and reduce parameter uncertainties. A comprehensive sensitivity analysis assesses key EnKF components, including ensemble size, damping factor, initial parameter estimates, observation frequency, and the number of unknown parameters. Results show that increasing ensemble size reduces uncertainty in soil hydraulic parameter (SHP) estimates, improving robustness. However, larger ensembles increase computational cost, necessitating an optimal balance. An ensemble size of 100 realizations was found to provide reliable SHP estimates while maintaining efficiency. Simultaneous state and parameter estimation improves accuracy, particularly in dry conditions, with multivariate assimilation (soil moisture + soil temperature) outperforming univariate approaches. Beyond sensitivity analysis, this study evaluates the data worth of soil moisture and temperature observations across all twelve USDA soil texture classes. Results show that soil temperature assimilation is particularly effective in fine-textured soils (e.g., clay), where temperature variations strongly correlate with hydraulic properties such as saturated hydraulic conductivity. Joint assimilation of soil moisture and temperature significantly reduces root mean square error (RMSE) for both state and parameter estimation. Additionally, temperature assimilation improves latent and sensible heat flux predictions more effectively than soil moisture alone. Climate-based analysis reveals that soil moisture assimilation is more effective in hot semi-arid regions for low-permeability soils, while in sub-humid regions, it performs better for high-permeability soils. These findings underscore the importance of simultaneous assimilation of soil moisture and temperature for wide range of soils and climate. This study also addresses parameter estimation in dual-layered soils, examining the impact of uncertain soil layering on assimilation performance. Results indicate that near-surface soil temperature measurements improve deep soil moisture and hydraulic parameter estimates, often outperforming soil moisture assimilation alone. The simultaneous assimilation of multi-depth soil moisture and temperature provides the most accurate estimates, particularly in soils with contrasting textures. Noon-time soil temperature measurements outperform nighttime observations, given their stronger correlation with soil moisture and hydraulic properties. Assuming a homogeneous soil column in heterogeneous soils introduces significant bias, emphasizing the importance of explicitly accounting for soil layering in data assimilation frameworks. To bridge the gap between synthetic experiments and real-world applications, the study applies the EnKF framework to field data, revealing that a bias-aware EnKF with a two-layer soil profile model consistently outperforms single-layer models, particularly for deeper soil moisture estimates. While near-surface soil moisture assimilation improves deep soil moisture predictions, soil temperature assimilation exhibits greater stability and lower uncertainty. Joint assimilation further reduces uncertainty but only marginally improves soil moisture predictions beyond moisture-only assimilation. Multi-depth assimilation significantly enhances estimation accuracy and reduces uncertainty in soil hydraulic parameters and water balance components, underscoring the importance of multivariate and multi-depth data assimilation in field applications. Future research should expand this approach by incorporating remote sensing data, such as soil moisture products from SMAP, SMOS, and NISAR, and land surface temperature estimates from MODIS, LANDSAT, and TRISHNA. Extending assimilation methods to vegetated surfaces using vegetation indices (LAI, NDVI) will improve soil hydraulic parameter estimation in agricultural and forested regions. Additionally, direct assimilation of raw satellite observations, such as brightness temperature or radar backscatter, could enhance soil moisture retrievals, requiring the development of advanced observation operators and machine learning techniques. Given the computational demands of EnKF, future studies should explore surrogate modeling techniques, such as Gaussian process regression and polynomial chaos expansion, to accelerate data assimilation and facilitate real-time hydrological forecasting.