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This study presents a dual Kalman filter (DSUKF – dual standard-unscented Kalman filter) for retrieving states andparameters controlling the soil water dynamics in a homogeneous soil column,by assimilating near-surface state observations. The DSUKF couples astandard Kalman filter for retrieving the states of a linear solver of theRichards equation, and an unscented Kalman filter for retrieving theparameters of the soil hydraulic functions, which are defined according tothe van Genuchten–Mualem closed-form model. The accuracy and thecomputational expense of the DSUKF are compared with those of the dualensemble Kalman filter (DEnKF) implemented with a nonlinear solver of theRichards equation. Both the DSUKF and the DEnKF are applied with twoalternative state-space formulations of the Richards equation, respectivelydifferentiated by the type of variable employed for representing the states:either the soil water content (θ) or the soil water matric pressurehead (h). The comparison analyses are conducted with reference to synthetictime series of the true states, noise corrupted observations, and synthetictime series of the meteorological forcing. The performance of the retrievalalgorithms are examined accounting for the effects exerted on the output bythe input parameters, the observation depth and assimilation frequency, aswell as by the relationship between retrieved states and assimilatedvariables. The uncertainty of the states retrieved with DSUKF isconsiderably reduced, for any initial wrong parameterization, with similaraccuracy but less computational effort than the DEnKF, when this isimplemented with ensembles of 25 members. For ensemble sizes of the sameorder of those involved in the DSUKF, the DEnKF fails to provide reliableposterior estimates of states and parameters. The retrieval performance ofthe soil hydraulic parameters is strongly affected by several factors, suchas the initial guess of the unknown parameters, the wet or dry range of theretrieved states, the boundary conditions, as well as the form(h-based orθ-based) of the state-space formulation. Several analyses arereported to show that the identifiability of the saturated hydraulicconductivity is hindered by the strong correlation with other parameters ofthe soil hydraulic functions defined according to the van Genuchten–Mualemclosed-form model

hydrology and earth system sciences

Kalman filters for assimilating near-surface observations into the Richards equation – Part 2: A dual filter approach for simultaneous retrieval of states and parameters