Introduction

The quantitative description of soil water movement faces large uncertainties in all model components - dynamics, material properties, boundary conditions, and states. Data assimilation methods can combine information from imperfect models and uncertain measurements.
The Ensemble Kalman Filter (EnKF) introduced by Evensen [1994] is a data assimilation method widely used in soil hydrology. It can deal with nonlinear models by representing uncertainties with an ensemble. The EnKF is typically used for state estimation, but is also employed to determine soil hydraulic parameters.
In soil hydrology, primarily the parameters, but also the the upper boundary condition face large uncertainties. Especially evaporation fluxes at the soil atmosphere interface are difficult to determine experimentally.

Project

In this project an EnKF for state and parameter estimation was implemented and expanded to simultaneously estimate the upper boundary condition.
This new method is tested on a synthetic 1D test case, where soil water flow is simulated by solving the Richards equation with MuPhi [Ippisch et al., 2006]. States, parameters, and the upper boundary condition are estimated based on subsurface water content measurements, like they are available from time domain reflectometry (TDR) probes.

Results

For this particular test case, the method is able to determine the upper boundary condition well (Figure 1). After a 10 day simulation period, the estimation deviates 11% from the true value.
The results further indicate, that the parameter estimation is not significantly influenced by the additional boundary condition assessment.

Figure 1

  • Integrated boundary condition during the 10 day simulation period. The true value is shown in black, the initial guess in red. The final estimation is shown in blue. The pale blue lines show the ensemble members, the dark blue line the ensemble mean and thus the best guess.