Deriving the conditional distribution of soil moisture and its use in estimating memory in the water-soil system

Soil moisture plays a crucial role in both ecosystems and human activities. It serves as a primary water source for plants and soil microorganisms. People use soil moisture information in irrigation strategies, predicting soil-borne plant diseases, and more. Soil moisture memory (SMM) refers to the soil’s ability to reflect signals of perturbations caused by anomalies such as intense storms or prolonged dry periods, over time. Its significance stems from its direct link to soil moisture dynamics, as understanding SMM characteristics helps predict soil moisture behavior over time. Many studies have investigated SMM, employing various metrics for its measurement, for example, the e-folding autocorrelation timescale. The time scale of SMM ranges from a couple of days to several months, but its duration and seasonality vary by location, depending on soil types, local hydrological settings, climatic regimes, and vegetation ecosystems. This study introduces a novel SMM metric based on the differences between the conditional and marginal distributions of soil moisture. First, a soil moisture simulation model is calibrated using modified ERA5 Potential Evapotranspiration (PET) and NASA’s GPM IMERG precipitation data as inputs, with SMAP soil moisture data as target values on a daily scale. Next, 2,000 years of daily precipitation and minimum/maximum temperature are generated using the stochastic weather generator WeaGETS, driven by GPM IMERG and CPC temperature data. PET is then estimated from the simulated temperature using the temperature-based Hargreaves-Samani equation. Using the generated 2,000-year input data, daily soil moisture is simulated. The simulation bias is then corrected using the CDF-matching method. With the bias-corrected daily soil moisture, the joint, marginal, and conditional probability distributions of soil moisture are analyzed at multiple lead times (3, 7, 14, 21 days) across four seasons and two study sites in Iowa and Ukraine. Results show that conditional distributions converge toward marginal distributions within 7-14 days in Iowa and 14-21 days in Ukraine in most seasons, with winter and spring exhibiting the longest SMM time scale for Iowa and Ukraine, respectively. This study shows how the conditional distributions of soil moisture gradually converge to the marginal distributions as lead prediction time increases. The time to convergence, dependent on soils, climate and season is a measure of the memory of soil moisture in the system. The conditional distributions are key to applications like irrigation scheduling.