Simple hydraulic conductivity estimation by the Kalman filtered double constraint method

This paper presents the Kalman Filtered Double Constraint Method (DCM-KF) as a technique to estimate the hydraulic conductivities in the grid blocks of a groundwater flow model. The DCM is based on two forward runs with the same initial grid block conductivities, but with alternating flux-head conditions specified on parts of the boundary and the wells. These two runs are defined as: (1) the flux run, with specified fluxes (recharge and well abstractions), and (2) the head run, with specified heads (measured in piezometers). Conductivities are then estimated as the initial conductivities multiplied by the fluxes obtained from the flux run and divided by the fluxes obtained from the head run. The DCM is easy to implement in combination with existing models (e.g., MODFLOW). Sufficiently accurate conductivities are obtained after a few iterations. Because of errors in the specified head-flux couples, repeated estimation under varying hydrological conditions results in different conductivities. A time-independent estimate of the conductivities and their inaccuracy can be obtained by a simple linear KF with modest computational requirements. For the Kleine Nete catchment, Belgium, the DCM-KF yields sufficiently accurate calibrated conductivities. The method also results in distinguishing regions where the head-flux observations influence the calibration from areas where it is not able to influence the hydraulic conductivity.