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This study presents a dual Kalman filter (DSUKF – dual standard-unscented Kalman filter) for retrieving states and parameters controlling the soil water dynamics in a homogeneous soil column, by assimilating near-surface state observations. The DSUKF couples a standard Kalman filter for retrieving the states of a linear solver of the Richards equation, and an unscented Kalman filter for retrieving the parameters of the soil hydraulic functions, which are defined according to the van Genuchten–Mualem closed-form model. The accuracy and the computational expense of the DSUKF are compared with those of the dual ensemble Kalman filter (DEnKF) implemented with a nonlinear solver of the Richards equation. Both the DSUKF and the DEnKF are applied with two alternative state-space formulations of the Richards equation, respectively differentiated by the type of variable employed for representing the states: either the soil water content (θ) or the soil water matric pressure head (h). The comparison analyses are conducted with reference to synthetic time series of the true states, noise corrupted observations, and synthetic time series of the meteorological forcing. The performance of the retrieval algorithms are examined accounting for the effects exerted on the output by the input parameters, the observation depth and assimilation frequency, as well as by the relationship between retrieved states and assimilated variables. The uncertainty of the states retrieved with DSUKF is considerably reduced, for any initial wrong parameterization, with similar accuracy but less computational effort than the DEnKF, when this is implemented with ensembles of 25 members. For ensemble sizes of the same order of those involved in the DSUKF, the DEnKF fails to provide reliable posterior estimates of states and parameters. The retrieval performance of the soil hydraulic parameters is strongly affected by several factors, such as the initial guess of the unknown parameters, the wet or dry range of the retrieved states, the boundary conditions, as well as the form (h-based or θ-based) of the state-space formulation. Several analyses are reported to show that the identifiability of the saturated hydraulic conductivity is hindered by the strong correlation with other parameters of the soil hydraulic functions defined according to the van Genuchten–Mualem closed-form model.

This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study.

The purpose of this work is to evaluate the performance of a dual Kalman filter procedure in retrieving states and parameters of a one-dimensional soil water budget model based on the Richards equation, by assimilating near-surface soil water content values during evaporation experiments carried out under laboratory conditions. The experimental data set consists of simultaneously measured evaporation rates, soil water content and matric potential profiles. The parameters identified by assimilating the data measured at 1 and 2 cm soil depths are in very good agreement with those obtained by exploiting the observations carried out in the entire soil profiles. A reasonably good correspondence has been found between the parameter values obtained from the proposed assimilation technique and those identified by applying a non-sequential parameter estimation method. The dual Kalman filter also performs well in retrieving the water state in the porous system. Bias and accuracy of the predicted state profiles are affected by observation depth changes, particularly for the experiments involving low state vertical gradients. The assimilation procedure proved flexible and very stable in both experimental cases, independently from the selected initial conditions and the involved uncertainty.

In practice, the catchment hydrologist is often confronted with the task of predicting discharge without having the needed records for calibration. Here, we report the discharge predictions of 10 modellers – using the model of their choice – for the man-made Chicken Creek catchment (6 ha, northeast Germany, Gerwin et al., 2009b) and we analyse how well they improved their prediction in three steps based on adding information prior to each following step. The modellers predicted the catchment's hydrological response in its initial phase without having access to the observed records. They used conceptually different physically based models and their modelling experience differed largely. Hence, they encountered two problems: (i) to simulate discharge for an ungauged catchment and (ii) using models that were developed for catchments, which are not in a state of landscape transformation. The prediction exercise was organized in three steps: (1) for the first prediction the modellers received a basic data set describing the catchment to a degree somewhat more complete than usually available for a priori predictions of ungauged catchments; they did not obtain information on stream flow, soil moisture, nor groundwater response and had therefore to guess the initial conditions; (2) before the second prediction they inspected the catchment on-site and discussed their first prediction attempt; (3) for their third prediction they were offered additional data by charging them pro forma with the costs for obtaining this additional information. Holländer et al. (2009) discussed the range of predictions obtained in step (1). Here, we detail the modeller's assumptions and decisions in accounting for the various processes. We document the prediction progress as well as the learning process resulting from the availability of added information. For the second and third steps, the progress in prediction quality is evaluated in relation to individual modelling experience and costs of added information. In this qualitative analysis of a statistically small number of predictions we learned (i) that soft information such as the modeller's system understanding is as important as the model itself (hard information), (ii) that the sequence of modelling steps matters (field visit, interactions between differently experienced experts, choice of model, selection of available data, and methods for parameter guessing), and (iii) that added process understanding can be as efficient as adding data for improving parameters needed to satisfy model requirements.

This paper describes a set of spatial rainfall statistics (termed "spatial moments of catchment rainfall") quantifying the dependence existing between spatial rainfall organisation, basin morphology and runoff response. These statistics describe the spatial rainfall organisation in terms of concentration and dispersion statistics as a function of the distance measured along the flow routing coordinate. The introduction of these statistics permits derivation of a simple relationship for the quantification of catchment-scale storm velocity. The concept of the catchment-scale storm velocity takes into account the role of relative catchment orientation and morphology with respect to storm motion and kinematics. The paper illustrates the derivation of the statistics from an analytical framework recently proposed in literature and explains the conceptual meaning of the statistics by applying them to five extreme flash floods occurred in various European regions in the period 2002–2007. High resolution radar rainfall fields and a distributed hydrologic model are employed to examine how effective are these statistics in describing the degree of spatial rainfall organisation which is important for runoff modelling. This is obtained by quantifying the effects of neglecting the spatial rainfall variability on flood modelling, with a focus on runoff timing. The size of the study catchments ranges between 36 to 982 km2. The analysis reported here shows that the spatial moments of catchment rainfall can be effectively employed to isolate and describe the features of rainfall spatial organization which have significant impact on runoff simulation. These statistics provide useful information on what space-time scales rainfall has to be monitored, given certain catchment and flood characteristics, and what are the effects of space-time aggregation on flood response modeling.

We investigate the potential impact of accounting for seasonal variations in the climatic forcing and using different methods to parameterize the soil water content at field capacity on the water balance components computed by a bucket model (BM). The single-layer BM of Guswa et al. (2002) is employed, whereas the Richards equation (RE) based Soil Water Atmosphere Plant (SWAP) model is used as a benchmark model. The results are analyzed for two differently-textured soils and for some synthetic runs under real-like seasonal weather conditions, using stochastically-generated daily rainfall data for a period of 100 years. Since transient soil-moisture dynamics and climatic seasonality play a key role in certain zones of the World, such as in Mediterranean land areas, a specific feature of this study is to test the prediction capability of the bucket model under a condition where seasonal variations in rainfall are not in phase with the variations in plant transpiration. Reference is made to a hydrologic year in which we have a rainy period (starting 1 November and lasting 151 days) where vegetation is basically assumed in a dormant stage, followed by a drier and rainless period with a vegetation regrowth phase. Better agreement between BM and RE-SWAP intercomparison results are obtained when BM is parameterized by a field capacity value determined through the drainage method proposed by Romano and Santini (2002). Depending on the vegetation regrowth or dormant seasons, rainfall variability within a season results in transpiration regimes and soil moisture fluctuations with distinctive features. During the vegetation regrowth season, transpiration exerts a key control on soil water budget with respect to rainfall. During the dormant season of vegetation, the precipitation regime becomes an important climate forcing. Simulations also highlight the occurrence of bimodality in the probability distribution of soil moisture during the season when plants are dormant, reflecting that soil, it being of coarser or finer texture, can be preferentially in either wetter or drier states over this period.

The paper aims at evaluating to what extent the forest cover can explain the component of runoff coefficient as defined in a regional flood frequency analysis based on the application of the rational formula coupled with a regional model of the annual maximum rainfall depths. The analysis is addressed to evaluate the component of the runoff coefficient which cannot be captured by the catchment lithology alone. Data mining is performed on 75 catchments distributed from South to Central Italy. Cluster and correlation structure analyses are conducted for distinguishing forest cover effects within catchments characterized by hydro-morphological similarities. We propose to improve the prediction of the runoff coefficient by a linear regression model, exploiting the ratio of the forest cover to the catchment critical rainfall depth as dependent variable. The proposed regression enables a significant bias correction of the runoff coefficient, particularly for those small mountainous catchments, characterised by larger forest cover fraction and lower critical rainfall depth.

No abstract available.