Hydrological Data Assimilation Research Articles

Ensemble Kalman Inversion for upstream parameter estimation and indirect streamflow correction: A simulation study

Data assimilation (DA) techniques such as the Ensemble Kalman filter (EnKF) and its extensions allow for real-time corrections of state-space models and model parameters based on an assumption of Gaussian error. The hydrological DA literature primarily documents applications of the EnKF to solve sequential state estimation problems. Recent advances in the DA literature demonstrate the potential of applying EnKF-based methods as efficient, derivative-free algorithms to solve various general Bayesian inverse problems, such as parameter estimation, while simultaneously providing Uncertainty Quantification (UQ). In this paper, the authors employ the Ensemble Kalman Inversion (EKI) algorithm to infer the distribution of a set of routing parameters. Through this correction, we improve streamflow at locations upstream of the gauged site in a virtual catchment setting. The algorithm enables learning spatially distributed routing parameters with observations available only at the outlet. The study reveals that this method sufficiently improves model performance throughout the basin. The performance of this method is demonstrated in a virtual catchment for three different model/data configurations. Favorable results, even with model misspecification, indicate that this method holds promise for operational application and more general hydrologic parameter estimation problems.

Assimilation of transformed water surface elevation to improve river discharge estimation in a continental-scale river

Abstract. Quantifying continental-scale river discharge is essential for understanding the terrestrial water cycle, but it is susceptible to errors caused by a lack of observations and the limitations of hydrodynamic modeling. Data assimilation (DA) methods are increasingly used to estimate river discharge in combination with emerging river-related remote sensing products (e.g., water surface elevation (WSE), water surface slope, river width, and flood extent). However, directly comparing simulated WSE to satellite altimetry data remains challenging (e.g., because of large biases between simulations and observations or uncertainties in parameters), and large errors can be introduced when satellite observations are assimilated into hydrodynamic models. In this study we performed direct, anomaly, and normalized value assimilation experiments to investigate the capacity of DA to improve river discharge within the current limitations of hydrodynamic modeling. We performed hydrological DA using a physically based empirical localization method applied to the Amazon basin. We used satellite altimetry data from ENVISAT, Jason 1, and Jason 2. Direct DA was the baseline assimilation method and was subject to errors due to biases in the simulated WSE. To overcome these errors, we used anomaly DA as an alternative to direct DA. We found that the modeled and observed WSE distributions differed considerably (e.g., differences in amplitude, seasonal flow variation, and a skewed distribution due to limitations of the hydrodynamic models). Therefore, normalized value DA was performed to improve discharge estimation. River discharge estimates were improved at 24 %, 38 %, and 62 % of stream gauges in the direct, anomaly, and normalized value assimilations relative to simulations without DA. Normalized value assimilation performed best for estimating river discharge given the current limitations of hydrodynamic models. Most gauges within the river reaches covered by satellite observations accurately estimated river discharge, with the Nash–Sutcliffe efficiency (NSE) > 0.6. The amplitudes of WSE variation were improved in the normalized DA experiment. Furthermore, in the Amazon basin, normalized assimilation (median NSE =0.50) improved river discharge estimation compared to open-loop simulation with the global hydrodynamic model (median NSE =0.42). River discharge estimation using direct DA methods was improved by 7 % with calibration of river bathymetry based on NSE. The direct DA approach outperformed the other DA approaches when runoff was considerably biased, but anomaly DA performed best when the river bathymetry was erroneous. The uncertainties in hydrodynamic modeling (e.g., river bottom elevation, river width, simplified floodplain dynamics, and the rectangular cross-section assumption) should be improved to fully realize the advantages of river discharge DA through the assimilation of satellite altimetry. This study contributes to the development of a global river discharge reanalysis product that is consistent spatially and temporally.

Impacts of Spatiotemporal Gaps in Satellite Soil Moisture Data on Hydrological Data Assimilation

Soil moisture modeling is necessary for many hydrometeorological and agricultural applications. One of the ways in which the modeling of soil moisture (SM) can be improved is by assimilating SM observations to update the model states. Remotely sensed SM observations are prone to being riddled with data discontinuities, namely in the horizontal and vertical spatial, and temporal, dimensions. In this study, a set of synthetic experiments were designed to assess how much impact each of these individual components of spatiotemporal gaps can have on the modeling performance of SM, as well as streamflow. The results show that not having root-zone SM estimates from satellite derived observations is most impactful in terms of the modeling performance. Having temporal gaps and horizontal spatial gaps in the satellite SM data also impacts the modeling performance, but to a lesser degree. Real-data experiments with the remotely sensed Soil Moisture Active Passive (SMAP) product generally brought improvements to the SM modeling performance in the upper soil layers, but to a lesser degree in the bottom soil layer. The updating of the model SM states with observations also resulted in some improvements in the streamflow modeling performance during the synthetic experiments, but not during the real-data experiments.

Towards reliable uncertainty quantification for hydrologic predictions, part II: Characterizing impacts of uncertain factors through an iterative factorial data assimilation framework

In this study, an iterative factorial data assimilation (IFDA) framework is developed to holistically characterize the individual and interactive effects of various uncertain factors on hydrological predictions. The IFDA framework is flexible and is able to reveal the impacts from different numbers of uncertain factors. An iterative factorial analysis (IFA) approach is proposed in IFDA to diminish the biased variance estimation in traditional multilevel factorial designs and provide more reliable impact characterization for the considered factors. The proposed IFDA framework is applied to quantitatively reveal the individual and interactive effects of hydrological models, data assimilation (DA) methods, and uncertainties in inputs, streamflow observations and sample sizes on the deterministic and probabilistic predictions from data assimilation. The results indicate that the hydrological models, DA methods and their interactions would have the most dominant effects on hydrological predictions. This implies that different hydrological models or DA methods would produce significantly distinguishable results. When the hydrological model and DA method have been specified, uncertainties in streamflow observations would more likely have a visible effect on the accuracy of resulting predictions. Moreover, the inherent randomness, mainly caused by the Monte Carlo sampling procedures in data assimilation, would also have noticeable effects on the DA performances, especially when the hydrological model and DA method have been pre-identified. These results suggest that enhancement of hydrological models and data assimilation methods would be the most efficient pathway to generate reliable hydrological predictions.

Development of a disaggregated multi-level factorial hydrologic data assimilation model

A disaggregated multi-level factorial hydrologic data assimilation model (FHDA) is proposed for exploring not only the direct effects from individual uncertainties but also, more importantly, the composite ones from multi-layer and multi-parameter interactions among multiple uncertainties in hydrologic data assimilation systems. Based on a disaggregated multi-level factorial analysis method, the proposed FHDA examined the contributions of multiple uncertainty sources, including data assimilation scheme, sample size, forcing data error, and observed data error. Three parameter assimilation schemes of data assimilation i.e., Ensemble Kalman Filter (EnKF), Standard Kernel Smoother (EnKFSKS), and Kernel Smoother with location shrinkage (EnKFKSLS) are tested. The results indicate that: i) the streamflow observations can be well tracked by 95% prediction intervals. ii) reducing streamflow observation error is the most efficient way to improve both deterministic and probabilistic predictions. iii) data assimilation scheme plays a vital role in hydrological predictions, especially for probabilistic ones (i.e., contributes 22% for the ensemble prediction uncertainty). Therefore, to improve the prediction accuracy, it is necessary to optimize the parameter assimilation schemes in hydrological data assimilation model.

Ensemble streamflow data assimilation using WRF-Hydro and DART: novel localization and inflation techniques applied to Hurricane Florence flooding

Abstract. Predicting major floods during extreme rainfall events remains an important challenge. Rapid changes in flows over short timescales, combined with multiple sources of model error, makes it difficult to accurately simulate intense floods. This study presents a general data assimilation framework that aims to improve flood predictions in channel routing models. Hurricane Florence, which caused catastrophic flooding and damages in the Carolinas in September 2018, is used as a case study. The National Water Model (NWM) configuration of the WRF-Hydro modeling framework is interfaced with the Data Assimilation Research Testbed (DART) to produce ensemble streamflow forecasts and analyses. Instantaneous streamflow observations from 107 United States Geological Survey (USGS) gauges are assimilated for a period of 1 month. The data assimilation (DA) system developed in this paper explores two novel contributions, namely (1) along-the-stream (ATS) covariance localization and (2) spatially and temporally varying adaptive covariance inflation. ATS localization aims to mitigate not only spurious correlations, due to limited ensemble size, but also physically incorrect correlations between unconnected and indirectly connected state variables in the river network. We demonstrate that ATS localization provides improved information propagation during the model update. Adaptive prior inflation is used to tackle errors in the prior, including large model biases which often occur in flooding situations. Analysis errors incurred during the update are addressed using posterior inflation. Results show that ATS localization is a crucial ingredient of our hydrologic DA system, providing at least 40 % more accurate (root mean square error) streamflow estimates than regular, Euclidean distance-based localization. An assessment of hydrographs indicates that adaptive inflation is extremely useful and perhaps indispensable for improving the forecast skill during flooding events with significant model errors. We argue that adaptive prior inflation is able to serve as a vigorous bias correction scheme which varies both spatially and temporally. Major improvements over the model's severely underestimated streamflow estimates are suggested along the Pee Dee River in South Carolina, and many other locations in the domain, where inflation is able to avoid filter divergence and, thereby, assimilate significantly more observations.

Earth data assimilation in hydrologic models: recent advances

ABSTRACT Hydrologic model forecasts have inherent uncertainties from input errors, lack of physical representation, and parameter equifinality. Accurate modelling results with reduced uncertainty are necessary for water resources management and decision-making, especially in a changing climate scenario. To this end, the hydrologic modelling community widely accepts the assimilation of satellite remote sensing data. This paper reviews the recent developments in hydrologic data assimilation (DA) focusing on progress in the role of satellite remote sensing data in reducing model uncertainty.

Do surface lateral flows matter for data assimilation of soil moisture observations into hyperresolution land models?

Abstract. It is expected that hyperresolution land modeling substantially innovates the simulation of terrestrial water, energy, and carbon cycles. The major advantage of hyperresolution land models against conventional 1-D land surface models is that hyperresolution land models can explicitly simulate lateral water flows. Despite many efforts on data assimilation of hydrological observations into those hyperresolution land models, how surface water flows driven by local topography matter for data assimilation of soil moisture observations has not been fully clarified. Here I perform two minimalist synthetic experiments where soil moisture observations are assimilated into an integrated surface–groundwater land model by an ensemble Kalman filter. I discuss how differently the ensemble Kalman filter works when surface lateral flows are switched on and off. A horizontal background error covariance provided by overland flows is important for adjusting the unobserved state variables (pressure head and soil moisture) and parameters (saturated hydraulic conductivity). However, the non-Gaussianity of the background error provided by the nonlinearity of a topography-driven surface flow harms the performance of data assimilation. It is difficult to efficiently constrain model states at the edge of the area where the topography-driven surface flow reaches by linear-Gaussian filters. It brings the new challenge in land data assimilation for hyperresolution land models. This study highlights the importance of surface lateral flows in hydrological data assimilation.

Remote sensing data assimilation

ABSTRACT Data assimilation (DA) offers immense potential for uncertainty identification, improving the initial estimates for hydrological and atmospheric modelling. This paper reviews the studies in hydrological DA using Kalman filters. Recent applications of Kalman filters in hydrological and atmospheric DA are summarized. Existing challenges for DA studies are briefly described. In addition, three case study examples are presented highlighting the effects of: (a) soil moisture DA in the Noah land surface model; (b) variational assimilation for improving precipitation forecasts in the WRF (Weather Research Forecast) model; and (c) simulating AMSR-2 (Advanced Microwave Scanning Radiometer-2) radiances towards DA. Although there are many unresolved issues in DA that warrant further research, it has immense potential for predicting variables at a better lead time for hydrometeorology.

Adaptive multi-fidelity probabilistic collocation-based Kalman filter for subsurface flow data assimilation: numerical modeling and real-world experiment

The ensemble Kalman filter (EnKF) has received substantial attention in hydrologic data assimilation due to its ease of implementation. In EnKF, a large enough ensemble size is often required to ensure accuracy, which may result in considerable computational overhead, especially for large-scale problems. Motivated by recent developments in multi-fidelity simulation, we develop a novel data assimilation method that provides an alternative to EnKF, namely adaptive multi-fidelity probabilistic collocation-based Kalman filter (AMF-PCKF). The appealing feature is to approximate the system response with polynomial chaos expansion (PCE) using the adaptive multi-fidelity probabilistic collocation method, which improves the computational efficiency without sacrificing accuracy. This constitutes the forecast step of AMF-PCKF, while the analysis step is established by sequentially updating the PCE coefficients. As demonstrated by a synthetic numerical case of heat transport in unsaturated flow and a real-world two-phase flow experiment, AMF-PCKF can provide more accurate estimations than EnKF under the same amount of computation, even when the number of unknown parameters is as high as 100.

Assimilating GRACE Into a Land Surface Model in the Presence of an Irrigation‐Induced Groundwater Trend

AbstractAssimilating terrestrial water storage observations from the Gravity Recovery and Climate Experiment (GRACE) mission into land surface models (LSMs) provides an opportunity to disaggregate and downscale GRACE information to finer scales and improve water component estimates in LSMs. However, the performance of GRACE data assimilation (GRACE‐DA) is limited by the lack of representation of human activities in most LSMs. To simultaneously improve GRACE‐DA and reduce the uncertainties in the modeled anthropogenic processes, we assimilate mascon‐based GRACE terrestrial water storage into the Noah‐Multiparameterization LSM that includes groundwater extraction for irrigation. Simulations with and without GRACE‐DA and with and without groundwater pumping for irrigation are performed to study the isolated and combined effects of groundwater irrigation and GRACE‐DA on water and energy fluxes over the High Plains Aquifer (HPA). The results reveal that the DA‐only simulation may erroneously distribute increments across water storage components and affect the related fluxes through biased feedbacks, while the irrigation‐only simulation may overestimate groundwater decline due to shortcomings in the irrigation and groundwater parameterizations. Assimilating GRACE when irrigation is simulated produces the best overall performance for water storage trends over the northern HPA. For the southern HPA, GRACE assimilation with irrigation performs similarly to irrigation‐only simulation for water storage components and evapotranspiration. GRACE assimilation also improves results in nonirrigated regions and can potentially alleviate the overestimation of groundwater trends in regions with greater irrigation uncertainties. This study highlights the potential to advance hydrological data assimilation in the context of anthropogenic water consumption and land‐atmosphere interactions.

An instrument variable based algorithm for estimating cross-correlated hydrological remote sensing errors

Optimally using multi-source remote-sensing (RS) and/or reanalyzed hydrological products requires knowledge of each product’s accuracy and inter-product error cross-correlations. Quadruple collocation (QC) analysis can potentially solve for this error information without the reliance of high-quality ground references. However, QC requires at least three independent products for a variable of interest. At the global scale, obtaining three independent products is often a challenge. To address this issue, this study proposes an extended double instrumental variable algorithm (denoted as EIVD), which can accurately estimate product error and inter-product error cross-correlations using only two independent products – a requirement easier to meet in practice. Synthetic numerical experiments demonstrate that EIVD is robust and unbiased – provided product error auto-correlations are not strongly contrasting. The performance of EIVD is further tested via a (real-data) global precipitation error analysis using traditional QC results as a validation reference. The global consistency (i.e., spatial correlation) of QC- and EIVD-estimated product-truth correlation is above 0.86 [–] for all precipitation products being considered, and the relative mean difference of QC- and EIVD-based correlations is, on average, less than 5%. The spatial consistency of QC- and EIVD-based inter-product error cross-correlation is 0.47 [–] with a relative bias of 8%. A quantitative analysis demonstrates that regions with inconsistent EIVD and QC results are likely attributable to the violation of the QC error independency assumptions. Given the robustness of EIVD in fully parameterizing hydrological product error information, it is expected to improve the accuracy and efficiency of multi-source hydrological data merging and data assimilation.

Development and evaluation of a hydrologic data-assimilation scheme for short-range flow and inflow forecasts in a data-sparse high-latitude region using a distributed model and ensemble Kalman filtering

A forecasting system combining a physically-based distributed hydrological model (HYDROTEL), an Ensemble Kalman Filtering (EnKF) Data Assimilation (DA), and forecasted meteorological data (obtained from the North American Ensemble Forecast System; NAEFS) is developed to forecast short-range (0–14 days lead) flows and inflows in the Aishihik and Mayo basins in Yukon Territory, Canada. The system was assessed at three sites, including at the outlet of the Sekulmun River subbasin of the Aishihik basin for river flow forecasting, as well as at Aishihik Lake and Mayo Lake for reservoir inflow forecasting. To ensure accuracy of forecasting outputs, model development and evaluation was performed systematically by: (i) investigating the use of coupled EnKF and HYDROTEL models for improved flow and inflow estimations, (ii) evaluating NAEFS data for short-range flow and inflow forecasts, and (iii) using probabilistic and deterministic criteria to evaluate the forecast performance of the HYDROTEL-EnKF-NAEFS model at each site. Results illustrate that the DA framework significantly improves flow and inflow forecasts, and raw NAEFS data need to be spatially and temporally corrected to be used for hydrological forecasts. Based on probabilistic and deterministic scores, it was found that the developed forecasting system can provide flow and inflow forecasts at the Sekulmun River subbasin, Mayo Lake, Aishihik Lake sites with high, medium, and low accuracies, respectively. Differences in forecast accuracies at each site are possibly associated with: (i) uncertainties of forecasted meteorological data, (ii) ability of HYDROTEL to capture daily flow and inflow variations, (iii) DA algorithm used, (iv) heterogeneity in basin attributes, and (v) limited data availability particularly in the lake areas.

Using Color Coherence Vectors to Evaluate the Performance of Hydrologic Data Assimilation

AbstractAn inadequate characterization of hydrogeological properties can significantly decrease the trustworthiness of subsurface flow and transport model predictions. A variety of data assimilation methods have been proposed in order to estimate hydrogeological parameters from spatially scarce data by incorporating them into the governing physical models. In order to quantify the accuracy of the estimations, several metrics have been used such as Rank Histograms, root‐mean‐square error (RMSE), and Ensemble Spread. However, these commonly used metrics do not regard the spatial correlation of the aquifer's properties. This can cause permeability fields with very different spatial structures to have similar histograms or RMSE. In this paper, we propose an approach based on color coherence vectors (CCV) for evaluating the performance of these estimation methods. CCV is a histogram‐based technique for comparing images that incorporate spatial information. We represent estimated fields as digital three‐channel images and use CCV to compare and quantify the accuracy of estimations. The appealing feature of this technique is that it considers the spatial structure embedded in the estimated fields. The sensitivity of CCV to spatial information makes it a suitable metric for assessing the performance of data assimilation techniques. Under various factors, such as numbers of measurements and structural parameters of the log conductivity field, we compare the performance of CCV with the RMSE.

全球大気・水文結合データ同化システムの開発： 水文ビッグデータ同化による大気・水文予測の改善に向けて

全球大気・水文結合データ同化システムの開発： 水文ビッグデータ同化による大気・水文予測の改善に向けて

Improved streamflow simulations by coupling soil moisture analytical relationship in EnKF based hydrological data assimilation framework

Abstract The present study investigates the potential of coupled Soil Moisture Analytical Relationship (SMAR) and Ensemble Kalman Filter (EnKF) based surface soil moisture data assimilation for improving the streamflow simulations. For this purpose, synthetic and real data assimilation experiments were carried out using Soil and Water Assessment Tool (SWAT) hydrological model in two different sub-catchments lying in the Krishna River basin, India. Here, the satellite-based surface soil moisture estimates from Soil Moisture and Ocean Salinity (SMOS) and Advanced Scatterometer (ASCAT) are used for assimilation. Results of the synthetic experiment show that the use of physically based SMAR scheme coupled with EnkF for updating profile soil moisture has better ability to improve the surface flow, groundwater flow and consequently streamflow over the covariance-based updates using EnKF only. Likewise, the real data assimilation experiment also shows SMAR-EnKF assimilation strategy performs better than the EnKF only updates for simulating streamflow. However, in both the synthetic as well as real data experiment, the improvements are only moderate. This restricted success in improving streamflow simulations indicate that updating only the soil moisture through any updating scheme adopted here is not sufficient to reduce the effect of the errors in model forcing on subsequent simulation days.

Unsupervised ensemble Kalman filtering with an uncertain constraint for land hydrological data assimilation

The standard ensemble data assimilation schemes often violate the dynamical balances of hydrological models, in particular, the fundamental water balance equation, which relates water storage and water flux changes. The present study aims at extending the recently introduced Weak Constrained Ensemble Kalman Filter (WCEnKF) to a more general framework, namely unsupervised WCEnKF (UWCEnKF), in which the covariance of the water balance model is no longer known, thus requiring its estimation along with the model state variables. This extension is introduced because WCEnKF was found to be strongly sensitive to the (manual) choice of this covariance. The proposed UWCEnKF, on the other hand, provides a more general unsupervised framework that does not impose any (manual, thus heuristic) value of this covariance, but suggests an estimation of it, from the observations, along with the state. The new approach is tested based on numerical experiments of assimilating Terrestrial Water Storage (TWS) from Gravity Recovery and Climate Experiment (GRACE) and remotely sensed soil moisture data into a hydrological model. The experiments are conducted over different river basins, comparing WCEnKF, UWCEnKF, and the standard EnKF. In this setup, the UWCEnKF constrains the system state variables with TWS changes, precipitation, evaporation, and discharge data to balance the summation of water storage simulations. In-situ groundwater and soil moisture measurements are used to validate the results of the UWCEnKF and to evaluate its performances against the EnKF. Our numerical results clearly suggest that the proposed framework provides more accurate estimates of groundwater storage changes and soil moisture than WCEnKF and EnKF over the different studied basins.

Geophysical and hydrological data assimilation to monitor water content dynamics in the rocky unsaturated zone

In recent years, geophysics is increasingly used to study the flow and transport processes in the vadose zone. Particularly, when the vadose zone is made up of rocks, it is difficult to install sensors in the subsurface to measure hydrological state variables directly. In these cases, the electrical resistivity tomography (ERT) represents a useful tool to monitor the hydrodynamics of the infiltration and to estimate hydraulic parameters and state variables, such as hydraulic conductivity and water content. We propose an integrated approach aimed at predicting water content dynamics in calcarenite, a sedimentary carbonatic porous rock. The uncoupled hydrogeophysical approach proposed consists in 4D ERT monitoring conducted during an infiltrometer test under falling head conditions. Capacitance probes were installed to measure water content at different depths to validate the estimations derived from ERT. A numerical procedure, based on a data assimilation technique, was accomplished by combining the model (i.e., Richards' equation) with the observations in order to provide reliable water content estimations. We have used a new data assimilation method that is easy to implement, based on the ensemble Kalman filter coupled with Brownian bridges. This approach is particularly suitable for strongly non-linear models, such as Richards' equation, in order to take into account both the model uncertainty and the observation errors. The proposed data assimilation approach was tested for the first time on field data. A reasonable agreement was found between observations and predictions confirming the ability of the integrated approach to predict water content dynamics in the rocky subsoil.

Insights on the impact of systematic model errors on data assimilation performance in changing catchments

Abstract The global prevalence of rapid and extensive land use change necessitates hydrologic modelling methodologies capable of handling non-stationarity. This is particularly true in the context of Hydrologic Forecasting using Data Assimilation. Data Assimilation has been shown to dramatically improve forecast skill in hydrologic and meteorological applications, although such improvements are conditional on using bias-free observations and model simulations. A hydrologic model calibrated to a particular set of land cover conditions has the potential to produce biased simulations when the catchment is disturbed. This paper sheds new light on the impacts of bias or systematic errors in hydrologic data assimilation, in the context of forecasting in catchments with changing land surface conditions and a model calibrated to pre-change conditions. We posit that in such cases, the impact of systematic model errors on assimilation or forecast quality is dependent on the inherent prediction uncertainty that persists even in pre-change conditions. Through experiments on a range of catchments, we develop a conceptual relationship between total prediction uncertainty and the impacts of land cover changes on the hydrologic regime to demonstrate how forecast quality is affected when using state estimation Data Assimilation with no modifications to account for land cover changes. This work shows that systematic model errors as a result of changing or changed catchment conditions do not always necessitate adjustments to the modelling or assimilation methodology, for instance through re-calibration of the hydrologic model, time varying model parameters or revised offline/online bias estimation.

Bias-aware data assimilation in integrated hydrological modelling

Abstract One of the major challenges in hydrological data assimilation applications is the presence of bias in both models and observations. The present study uses the ensemble transform Kalman filtering (ETKF) method and an observational bias estimation technique to estimate groundwater hydraulic heads. The study was carried out in a relatively complex, groundwater dominated, catchment in Denmark using the MIKE SHE model code. The method is implemented and evaluated using synthetic data and subsequently tested against real observations. The results from the synthetic experiments show that the bias-aware filter outperforms the standard filter, with improved state estimate and correct bias estimate. The assimilation using real observations further demonstrates the robustness of bias-aware ETKF, and the potential improvements using integrated hydrological modelling. Furthermore, the experiments with assimilating over different depths show that the state estimates depend on correlation across layers.