Evaluating the parameter identifiability and structural validity of a probability-distributed model for soil moisture

The objective of this study is to evaluate the performance of a model that simulates local and spatial average soil moisture in a watershed. The model uses well-known expressions for infiltration, evapotranspiration, and groundwater recharge to describe soil moisture dynamics at the local scale. Then, the spatial mean soil moisture is simulated by integrating the local behavior over a probability density function that characterizes the spatial variability of soil saturation. Ultimately, the model requires input of precipitation and potential evapotranspiration (PET) time series and six parameters to simulate the dynamics of the spatial average soil moisture. The model is applied to the Fort Cobb watershed in Oklahoma using one year of data from September 2005 through August 2006. Model performance is evaluated in three main ways. First, the model’s ability to reproduce observed local and spatial average soil moisture through calibration is examined. Second, the identifiability and stability of the parameter values are considered to assess uncertainty in the parameter values and errors in the model’s mathematical structure. Third, a new method is developed that uses the sensitivities of soil moisture to precipitation and PET to assess the impacts of parameter uncertainty and structural errors on forecasts for unobserved conditions. At the local scale, the model reproduces the soil moisture with a similar degree of accuracy as a more physically-based model (HYDRUS 1D), and both models exhibit some structural errors. The model can also be calibrated to approximately reproduce the spatial average soil moisture observations. However, the model produces a relatively wide range of plausible sensitivities and this range varies depending on the window of time from which the parameters are calibrated. This result implies that parameter uncertainty and model structural errors contribute substantially to model uncertainty for unobserved conditions.