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Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state-parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model. © 2004 Elsevier Ltd. All rights reserved.

This work tests the hypothesis that jointly assimilating satellite observations of leaf area index and surface soil moisture into a land surface model improves the estimation of land vegetation and water variables. An Ensemble Kalman Filter is used to test this hypothesis across the Contiguous United States from April 2015 to December 2018. The performance of the proposed methodology is assessed for several modeled vegetation and water variables (evapotranspiration, net ecosystem exchange, and soil moisture) in terms of random errors and anomaly correlation coefficients against a set of independent validation datasets (i.e., Global Land Evaporation Amsterdam Model, FLUXCOM, and International Soil Moisture Network). The results show that the assimilation of the leaf area index mostly improves the estimation of evapotranspiration and net ecosystem exchange, whereas the assimilation of surface soil moisture alone improves surface soil moisture content, especially in the western US, in terms of both root mean squared error and anomaly correlation coefficient. The joint assimilation of vegetation and soil moisture information combines the results of individual vegetation and soil moisture assimilations and reduces errors (and increases correlations with the reference datasets) in evapotranspiration, net ecosystem exchange, and surface soil moisture simulated by the land surface model. However, because soil moisture satellite observations only provide information on the water content in the top 5 cm of the soil column, the impact of the proposed data assimilation technique on root zone soil moisture is limited. This work moves one step forward in the direction of improving our estimation and understanding of land surface interactions using a multivariate data assimilation approach, which can be particularly useful in regions of the world where ground observations are sparse or missing altogether. [ABSTRACT FROM AUTHOR]

It is well known that the ensemble Kalman filter (EnKF) requires updating each ensemble member with perturbed observations in order to produce the proper analysis-error covariances. While increased accuracy in a mean square sense may be preferable in many applications, less accuracy might be preferable in other applications, especially if the variables being assimilated obey certain conservation laws. In land data assimilation, for instance, the update in soil moisture often produces a water balance residual, in the sense that the input water is not equal to output water. This study shows that suppressing the perturbation of observations in the EnKF and in the weakly constrained ensemble Kalman filter significantly improves the water balance residuals without significantly increasing the state errors. [ABSTRACT FROM AUTHOR]

A weak constraint is introduced in ensemble Kalman filters to reduce the water budget imbalance that occurs in land data assimilation. Two versions of the weakly constrained filter, called the weakly constrained ensemble Kalman filter (WCEnKF) and the weakly constrained ensemble transform Kalman filter (WCETKF), are proposed. The strength of the weak constraint is adaptive in the sense that it depends on the statistical characteristics of the forecast ensemble. The resulting filters are applied to assimilate synthetic observations generated by the Noah land surface model over the Red Arkansas River basin. The data assimilation experiments demonstrate that, for all tested scenarios, the constrained filters produce analyses with nearly the same accuracy as unconstrained filters, but with much smaller water balance residuals than unconstrained filters. [ABSTRACT FROM AUTHOR]

Four methods based on the ensemble Kalman filter (EnKF) are tested to assimilate coarse-scale (25 km) snow water equivalent (SWE) observations (typical of passive microwave satellite retrievals) into finescale (1 km) land model simulations. Synthetic coarse-scale observations are assimilated directly using an observation operator for mapping between the coarse and fine scales or, alternatively, after disaggregation (regridding) to the finescale model resolution prior to data assimilation. In either case, observations are assimilated either simultaneously or independently for each location. Results indicate that assimilating disaggregated finescale observations independently (method 1D-F1) is less efficient than assimilating a collection of neighboring disaggregated observations (method 3D-Fm). Direct assimilation of coarse-scale observations is superior to a priori disaggregation. Independent assimilation of individual coarse-scale observations (method 3D-C1) can bring the overall mean analyzed field close to the truth, but does not necessarily improve estimates of the finescale structure. There is a clear benefit to simultaneously assimilating multiple coarse-scale observations (method 3D-Cm) even as the entire domain is observed, indicating that underlying spatial error correlations can be exploited to improve SWE estimates. Method 3D-Cm avoids artificial transitions at the coarse observation pixel boundaries and can reduce the RMSE by 60% when compared to the open loop in this study. [ABSTRACT FROM AUTHOR]

Soil moisture satellite mission accuracy, repeat time and spatial resolution requirements are addressed through a numerical twin data assimilation study. Simulated soil moisture profile retrievals were made by assimilating near-surface soil moisture observations with various accuracy (0, 1, 2, 3, 4, 5 and 10%v/v standard deviation) repeat time (1, 2, 3, 5, 10, 15, 20 and 30 days), and spatial resolution (0.5, 6, 12 18, 30, 60 and 120 arc-min). This study found that near-surface soil moisture observation error must be less than the model forecast error required for a specific application when used as data assimilation input, else slight model forecast degradation may result. It also found that near-surface soil moisture observations must have an accuracy better than 5%v/v to positively impact soil moisture forecasts, and that daily near-surface soil moisture observations achieved the best soil moisture and evapotranspiration forecasts for the repeat times assessed, with 1–5 day repeat times having the greatest impact. Near-surface soil moisture observations with a spatial resolution finer than the land surface model resolution (∼30 arc-min) produced the best results, with spatial resolutions coarser than the model resolution yielding only a slight degradation. Observations at half the land surface model spatial resolution were found to be appropriate for our application. Moreover, it was found that satisfying the spatial resolution and accuracy requirements was much more important than repeat time. [Copyright &y& Elsevier]

Snow depletion curves (SDC) are functions that are used to show the relationship between snow covered area and snow depth or water equivalent. Previous snow cover data assimilation (DA) studies have used theoretical SDC models as observation operators to map snow depth to snow cover fraction (SCF). In this study, a new approach is introduced that uses snow water equivalent (SWE) observations and satellite-based SCF retrievals to derive SDC relationships for use in an Ensemble Kalman filter (EnKF) to assimilate snow cover estimates. A histogram analysis is used to bin the SWE observations, which the corresponding SCF observations are then averaged within, helping to constrain the amount of data dispersion across different temporal and regional conditions. Logarithmic functions are linearly regressed with the binned average values, for two U.S. mountainous states: Colorado and Washington. The SDC-based logarithmic functions are used as EnKF observation operators, and the satellite-based SCF estimates are assimilated into a land surface model. Assimilating satellite-based SCF estimates with the observation-based SDC shows a reduction in SWE-related RMSE values compared to the model-based SDC functions. In addition, observation-based SDC functions were derived for different intra-annual and physiographic conditions, and landcover and elevation bands. Lower SWE-based RMSE values are also found with many of these categorical observation-based SDC EnKF experiments. All assimilation experiments perform better than the open-loop runs, except for the Washington region's 2004–2005 snow season, which was a major drought year that was difficult to capture with the ensembles and observations. [ABSTRACT FROM AUTHOR]

Abstract: A three dimensional Ensemble Kalman filter (3-D EnKF) and a one dimensional EnKF (1-D EnKF) are used in this study to assimilate Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E) coarse grid (25km) soil moisture retrievals into the Noah land surface model for fine-scale (1km) surface soil moisture estimation over the Little River Experimental Watershed (LREW), Georgia, USA. For the 1-D EnKF integration, the satellite observations are a priori partitioned to the model fine scale resolution, whereas in the 3-D EnKF integration, the original coarse grid satellite observations are directly used and downscaling is accomplished within the 3-D EnKF update step. In both cases, a first order a priori forecast bias correction is applied. Validation against in situ observations shows that both EnKF algorithms improve the soil moisture estimates, but the 3-D EnKF algorithm better preserves the spatial coherence. It is illustrated how surface soil moisture assimilation affects the deeper layer soil moisture and other water budget variables. Through sensitivity experiments, it is shown that data assimilation accelerates the moisture redistribution compared to the model integrations without assimilation, as surface soil moisture updates are effectively propagated over the entire profile. In the absence of data assimilation, the atmospheric conditions (especially the ratio of evapotranspiration to precipitation) control the model state balancing. [Copyright &y& Elsevier]

Abstract: The Land Information System (LIS) is an established land surface modeling framework that integrates various community land surface models, ground measurements, satellite-based observations, high performance computing and data management tools. The use of advanced software engineering principles in LIS allows interoperability of individual system components and thus enables assessment and prediction of hydrologic conditions at various spatial and temporal scales. In this work, we describe a sequential data assimilation extension of LIS that incorporates multiple observational sources, land surface models and assimilation algorithms. These capabilities are demonstrated here in a suite of experiments that use the ensemble Kalman filter (EnKF) and assimilation through direct insertion. In a soil moisture experiment, we discuss the impact of differences in modeling approaches on assimilation performance. Provided careful choice of model error parameters, we find that two entirely different hydrological modeling approaches offer comparable assimilation results. In a snow assimilation experiment, we investigate the relative merits of assimilating different types of observations (snow cover area and snow water equivalent). The experiments show that data assimilation enhancements in LIS are uniquely suited to compare the assimilation of various data types into different land surface models within a single framework. The high performance infrastructure provides adequate support for efficient data assimilation integrations of high computational granularity. [Copyright &y& Elsevier]