Newtonian nudging for a Richards equation-based distributed hydrological model

The objective of data assimilation is to provide physically consistent estimates of spatially distributed environmental variables. In this study a relatively simple data assimilation method has been implemented in a relatively complex hydrological model. The data assimilation technique is Newtonian relaxation or nudging, in which model variables are driven towards observations by a forcing term added to the model equations. The forcing term is proportional to the difference between simulation and observation (relaxation component) and contains four-dimensional weighting functions that can incorporate prior knowledge about the spatial and temporal variability and characteristic scales of the state variable(s) being assimilated. The numerical model couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on digital elevation data for surface water dynamics. We describe the implementation of the data assimilation algorithm for the coupled model and report on the numerical and hydrological performance of the resulting assimilation scheme. Nudging is shown to be successful in improving the hydrological simulation results, and it introduces little computational cost, in terms of CPU and other numerical aspects of the model’s behavior, in some cases even improving numerical performance compared to model runs without nudging. We also examine the sensitivity of the model to nudging term parameters including the spatio-temporal influence coefficients in the weighting functions. Overall the nudging algorithm is quite flexible, for instance in dealing with concurrent observation datasets, gridded or scattered data, and different state variables, and the implementation presented here can be readily extended to any of these features not already incorporated. Moreover the nudging code and tests can serve as a basis for implementation of more sophisticated data assimilation techniques in a Richards equation-based hydrological model.     

Real-time assimilation of streamflow observations into a hydrological routing model: effects of model structures and updating methods

This paper comparatively assesses the performance of five data assimilation techniques for three-parameter Muskingum routing with a spatially lumped or distributed model structure. The assimilation techniques used include direct insertion (DI), nudging scheme (NS), Kalman filter (KF), ensemble Kalman filter (EnKF) and asynchronous ensemble Kalman filter (AEnKF), which are applied to river reaches in Texas and Louisiana, USA. For both lumped and distributed routing, results from KF, EnKF and AEnKF are sensitive to the error specification. As expected, DI outperformed the other models in the case of lumped modelling, while in distributed routing, KF approaches, particularly AEnKF and EnKF, performed better than DI or nudging, reflecting the benefit of updating distributed states through error covariance modelling in KF approaches. The results of this work would be useful in setting up data assimilation systems that employ increasingly abundant real-time observations using distributed hydrological routing models.     

Dual states estimation of a subsurface flow-transport coupled model using ensemble Kalman filtering

Modeling the spread of subsurface contaminants requires coupling a groundwater flow model with a contaminant transport model. Such coupling may provide accurate estimates of future subsurface hydrologic states if essential flow and contaminant data are assimilated in the model. Assuming perfect flow, an ensemble Kalman filter (EnKF) can be used for direct data assimilation into the transport model. This is, however, a crude assumption as flow models can be subject to many sources of uncertainty. If the flow is not accurately simulated, contaminant predictions will likely be inaccurate even after successive Kalman updates of the contaminant model with the data. The problem is better handled when both flow and contaminant states are concurrently estimated using the traditional joint state augmentation approach. In this paper, we introduce a dual estimation strategy for data assimilation into a one-way coupled system by treating the flow and the contaminant models separately while intertwining a pair of distinct EnKFs, one for each model. The presented strategy only deals with the estimation of state variables but it can also be used for state and parameter estimation problems. This EnKF-based dual state-state estimation procedure presents a number of novel features: (i) it allows for simultaneous estimation of both flow and contaminant states in parallel; (ii) it provides a time consistent sequential updating scheme between the two models (first flow, then transport); (iii) it simplifies the implementation of the filtering system; and (iv) it yields more stable and accurate solutions than does the standard joint approach. We conducted synthetic numerical experiments based on various time stepping and observation strategies to evaluate the dual EnKF approach and compare its performance with the joint state augmentation approach. Experimental results show that on average, the dual strategy could reduce the estimation error of the coupled states by 15% compared with the joint approach. Furthermore, the dual estimation is proven to be very effective computationally, recovering accurate estimates at a reasonable cost.     

Uncertainty forecast from 3-D super-ensemble multi-model combination: validation and calibration

Measurements collected during the Recognized Environmental Picture 2010 experiment (REP10) in the Ligurian Sea are used to evaluate 3-D super-ensemble (3DSE) 72-hour temperature predictions and their associated uncertainty. The 3DSE reduces the total Root-Mean-Square Difference by 12 and 32% respectively with reference to the ensemble mean and the most accurate of the models when comparing to regularly distributed surface temperature data. When validating against irregularly distributed in situ observations, the 3DSE, ensemble mean and most accurate model lead to similar scores. The 3DSE temperature uncertainty estimate is obtained from the product of a posteriori model weight error covariances by an operator containing model forecast values. This uncertainty prediction is evaluated using a criterion based on the 2.5th and 97.5th percentiles of the error distribution. The 3DSE error is found to be on average underestimated during the forecast period, reflecting (i) the influence of ocean dynamics and (ii) inaccuracies in the a priori weight error correlations. A calibration of the theoretical 3DSE uncertainty is proposed for the REP10 scenario, based on a time-evolving amplification coefficient applied to the a posteriori weight error covariance matrix. This calibration allows the end-user to be confident that, on average, the true ocean state lies in the −2/+2 3DSE uncertainty range in 95% of the cases.     

Parameter estimation in ensemble based snow data assimilation: A synthetic study

Estimating erroneous parameters in ensemble based snow data assimilation system has been given little attention in the literature. Little is known about the related methods’ effectiveness, performance, and sensitivity to other error sources such as model structural error. This research tackles these questions by running synthetic one-dimensional snow data assimilation with the ensemble Kalman filter (EnKF), in which both state and parameter are simultaneously updated. The first part of the paper investigates the effectiveness of this parameter estimation approach in a perfect-model-structure scenario, and the second part focuses on its dependence on model structure error. The results from first part research demonstrate the advantages of this parameter estimation approach in reducing the systematic error of snow water equivalent (SWE) estimates, and retrieving the correct parameter value. The second part results indicate that, at least in our experiment, there is an evident dependence of parameter search convergence on model structural error. In the imperfect-model-structure run, the parameter search diverges, although it can simulate the state variable well. This result suggest that, good data assimilation performance in estimating state variables is not a sufficient indicator of reliable parameter retrieval in the presence of model structural error. The generality of this conclusion needs to be tested by data assimilation experiments with more complex structural error configurations.     

Error covariance calculation for forecast bias estimation in hydrologic data assimilation

To date, an outstanding issue in hydrologic data assimilation is a proper way of dealing with forecast bias. A frequently used method to bypass this problem is to rescale the observations to the model climatology. While this approach improves the variability in the modeled soil wetness and discharge, it is not designed to correct the results for any bias. Alternatively, attempts have been made towards incorporating dynamic bias estimates into the assimilation algorithm. Persistent bias models are most often used to propagate the bias estimate, where the a priori forecast bias error covariance is calculated as a constant fraction of the unbiased a priori state error covariance. The latter approach is a simplification to the explicit propagation of the bias error covariance. The objective of this paper is to examine to which extent the choice for the propagation of the bias estimate and its error covariance influence the filter performance. An Observation System Simulation Experiment (OSSE) has been performed, in which ground water storage observations are assimilated into a biased conceptual hydrologic model. The magnitudes of the forecast bias and state error covariances are calibrated by optimizing the innovation statistics of groundwater storage. The obtained bias propagation models are found to be identical to persistent bias models. After calibration, both approaches for the estimation of the forecast bias error covariance lead to similar results, with a realistic attribution of error variances to the bias and state estimate, and significant reductions of the bias in both the estimates of groundwater storage and discharge. Overall, the results in this paper justify the use of the traditional approach for online bias estimation with a persistent bias model and a simplified forecast bias error covariance estimation.     

Evolutionary assimilation of streamflow in distributed hydrologic modeling using in-situ soil moisture data

This study has applied evolutionary algorithm to address the data assimilation problem in a distributed hydrological model. The evolutionary data assimilation (EDA) method uses multi-objective evolutionary strategy to continuously evolve ensemble of model states and parameter sets where it adaptively determines the model error and the penalty function for different assimilation time steps. The assimilation was determined by applying the penalty function to merge background information (i.e., model forecast) with perturbed observation data. The assimilation was based on updated estimates of the model state and its parameterizations, and was complemented by a continuous evolution of competitive solutions.The EDA was illustrated in an integrated assimilation approach to estimate model state using soil moisture, which in turn was incorporated into the soil and water assessment tool (SWAT) to assimilate streamflow. Soil moisture was independently assimilated to allow estimation of its model error, where the estimated model state was integrated into SWAT to determine background streamflow information before they are merged with perturbed observation data. Application of the EDA in Spencer Creek watershed in southern Ontario, Canada generates a time series of soil moisture and streamflow. Evaluation of soil moisture and streamflow assimilation results demonstrates the capability of the EDA to simultaneously estimate model state and parameterizations for real-time forecasting operations. The results show improvement in both streamflow and soil moisture estimates when compared to open-loop simulation, and a close matching between the background and the assimilation illustrates the forecasting performance of the EDA approach.     

Developing configuration of WRF model for long-term high-resolution wind wave hindcast over the North Atlantic with WAVEWATCH III

The spatial resolution of wind forcing fields is critical for modeling ocean surface waves. We analyze here the performance of the non-hydrostatic numerical weather prediction system WRF-ARW (Weather Research and Forecasting) run with a 14-km resolution for hindcasting wind waves in the North Atlantic. The regional atmospheric model was run in the domain from 20° N to 70° N in the North Atlantic and was forced with ERA-Interim reanalysis as initial and boundary conditions in a spectral nudging mode. Here, we present the analysis of the impact of spectral nudging formulation (cutoff wavelengths and depth through which full weighting from reanalysis data is applied) onto the performance of the modeled 10-m wind speed and wind wave fields for 1 year (2010). For modeling waves, we use the third-generation spectral wave model WAVEWATCH III. The sensitivity of the atmospheric and wave models to the spectral nudging formulation is investigated via the comparison with reanalysis and observational data. The results reveal strong and persistent agreement with reanalysis data during all seasons within the year with well-simulated annual cycle and regional patterns independently of the nudging parameters that were tested. Thus, the proposed formulation of the nudging provides a reliable framework for future long-term experiments aiming at hindcasting climate variability in the North Atlantic wave field. At the same time, dynamical downscaling allows for simulation of higher waves in coastal regions, specifically near the Greenland east coast likely due to a better representation of the mesoscale atmospheric dynamics in this area.     

Data assimilation for distributed hydrological catchment modeling via ensemble Kalman filter

Catchment scale hydrological models are critical decision support tools for water resources management and environment remediation. However, the reliability of hydrological models is inevitably affected by limited measurements and imperfect models. Data assimilation techniques combine complementary information from measurements and models to enhance the model reliability and reduce predictive uncertainties. As a sequential data assimilation technique, the ensemble Kalman filter (EnKF) has been extensively studied in the earth sciences for assimilating in-situ measurements and remote sensing data. Although the EnKF has been demonstrated in land surface data assimilations, there are no systematic studies to investigate its performance in distributed modeling with high dimensional states and parameters. In this paper, we present an assessment on the EnKF with state augmentation for combined state-parameter estimation on the basis of a physical-based hydrological model, Soil and Water Assessment Tool (SWAT). Through synthetic simulation experiments, the capability of the EnKF is demonstrated by assimilating the runoff and other measurements, and its sensitivities are analyzed with respect to the error specification, the initial realization and the ensemble size. It is found that the EnKF provides an efficient approach for obtaining a set of acceptable model parameters and satisfactory runoff, soil water content and evapotranspiration estimations. The EnKF performance could be improved after augmenting with other complementary data, such as soil water content and evapotranspiration from remote sensing retrieval. Sensitivity studies demonstrate the importance of consistent error specification and the potential with small ensemble size in the data assimilation system.     

An effective method based on dynamic sampling for data assimilation in a global wave model

The ensemble Kalman filter (EnKF) performs well because that the covariance of background error is varying along time. It provides a dynamic estimate of background error and represents the reasonable statistic characters of background error. However, high computational cost due to model ensemble in EnKF is employed. In this study, two methods referred as static and dynamic sampling methods are proposed to obtain a good performance and reduce the computation cost. Ensemble adjustment Kalman filter (EAKF) method is used in a global surface wave model to examine the performance of EnKF. The 24-h interval difference of simulated significant wave height (SWH) within 1 year is used to compose the static samples for ensemble errors, and these errors are used to construct the ensemble states at each time the observations are available. And then, the same method of updating the model states in the EAKF is applied for the ensemble states constructed by a static sampling method. The dynamic sampling method employs a similar method to construct the ensemble states, but the period of the simulated SWH is changing with time. Here, 7 days before and after the observation time is used as this period. To examine the performance of three schemes, EAKF, static, or dynamic sampling method, observations from satellite Jason-2 in 2014 are assimilated into a global wave model, and observations from satellite Saral are used for validation. The results indicate that the EAKF performs best, while the static sampling method is relatively worse. The dynamic sampling method improves an assimilation effect dramatically compared to the static sampling method, and its overall performance is closed to the EAKF. In low latitudes, the dynamic sampling method has a slight advantage over the EAKF. In the dynamic or static sampling methods, only one wave model is required to run and their computational cost is reduced sharply. According to the performance of these three methods, the dynamic sampling method can treated as an effective alternative of EnKF, which could reduce the computational cost and provide a good performance of data assimilation.     

Hydrological data assimilation with the Ensemble Square-Root-Filter: Use of streamflow observations to update model states for real-time flash flood forecasting

The objective of the study is to evaluate the potential of a data assimilation system for real-time flash flood forecasting over small watersheds by updating model states. To this end, the Ensemble Square-Root-Filter (EnSRF) based on the Ensemble Kalman Filter (EnKF) technique was coupled to a widely used conceptual rainfall-runoff model called HyMOD. Two small watersheds susceptible to flash flooding from America and China were selected in this study. The modeling and observational errors were considered in the framework of data assimilation, followed by an ensemble size sensitivity experiment. Once the appropriate model error and ensemble size was determined, a simulation study focused on the performance of a data assimilation system, based on the correlation between streamflow observation and model states, was conducted. The EnSRF method was implemented within HyMOD and results for flash flood forecasting were analyzed, where the calibrated streamflow simulation without state updating was treated as the benchmark or nature run. Results for twenty-four flash-flood events in total from the two watersheds indicated that the data assimilation approach effectively improved the predictions of peak flows and the hydrographs in general. This study demonstrated the benefit and efficiency of implementing data assimilation into a hydrological model to improve flash flood forecasting over small, instrumented basins with potential application to real-time alert systems.     

Coupled assimilation for an intermediated coupled ENSO prediction model

The value of coupled assimilation is discussed using an intermediate coupled model in which the wind stress is the only atmospheric state which is slavery to model sea surface temperature (SST). In the coupled assimilation analysis, based on the coupled wind–ocean state covariance calculated from the coupled state ensemble, the ocean state is adjusted by assimilating wind data using the ensemble Kalman filter. As revealed by a series of assimilation experiments using simulated observations, the coupled assimilation of wind observations yields better results than the assimilation of SST observations. Specifically, the coupled assimilation of wind observations can help to improve the accuracy of the surface and subsurface currents because the correlation between the wind and ocean currents is stronger than that between SST and ocean currents in the equatorial Pacific. Thus, the coupled assimilation of wind data can decrease the initial condition errors in the surface/subsurface currents that can significantly contribute to SST forecast errors. The value of the coupled assimilation of wind observations is further demonstrated by comparing the prediction skills of three 12-year (1997–2008) hindcast experiments initialized by the ocean-only assimilation scheme that assimilates SST observations, the coupled assimilation scheme that assimilates wind observations, and a nudging scheme that nudges the observed wind stress data, respectively. The prediction skills of two assimilation schemes are significantly better than those of the nudging scheme. The prediction skills of assimilating wind observations are better than assimilating SST observations. Assimilating wind observations for the 2007/2008 La Niña event triggers better predictions, while assimilating SST observations fails to provide an early warning for that event.     

Eddy-permitting simulations of the sub-polar North Atlantic: impact of the model bias on water mass properties and circulation

Some previous studies demonstrated that model bias has a strong impact on the quality of long-term prognostic model simulations of the sub-polar North Atlantic Ocean. Relatively strong bias of water mass characteristics is observed in both eddy-permitting and eddy-resolving simulations, suggesting that an increase of model resolution does not reduce significantly the model bias. This study is an attempt to quantify the impact of model bias on the simulated water mass and circulation characteristics in an eddy-permitting model of the sub-polar ocean. This is done through comparison of eddy-permitting prognostic model simulations with the results from two other runs in which the bias is constrained by using spectral nudging. In the first run, the temperature and salinity are nudged towards climatology in the whole column. In the second run, the spectral nudging is applied in the surface 30 m layer and at depths below 560 m only. The biases of the model characteristics of the unconstrained run are similar to those reported in previous eddy-permitting and eddy-resolving studies. The salinity in the surface and intermediate waters of the Labrador Sea waters increases with respect to the climatology, which reduces the stability of the water column. The deep convection in the unconstrained run is artificially intensified and the transport in the sub-polar gyre stronger than in the observations. In particular, the transport of relatively salty and warm Irminger waters into the Labrador Sea is unrealistically high. While the water mass temperature and salinity in the run with spectral nudging in the whole column are closest to the observations, the depth of the winter convection is underestimated in the model. The water mass characteristics and water transport in the run with spectral nudging in the surface and deep layers only are close to observations and at the same time represent well the deep convection in terms of its intensity and position. The source of the bias in the prognostic model run is discussed.     

基于电磁探测数据的时序分析模型研究

针对电磁探测数据交叉检验时对不同卫星探测数据的时间匹配需求,本文基于DEMETER卫星时序探测数据,分析了国际参考电离层(IRI)模型模拟电子浓度(N_e)数据在不同纬度区域的误差分布特征; 同时,基于自回归移动平均(ARIMA)模型构建了N_e数据时序预测模型. 在此基础上,分析比较IRI模型与ARIMA模型在N_e数据时序预测中的优缺点,结果表明: ARIMA模型模拟预测N_e数据时间序列的相对误差在短期内较低(小于10%),且随着预测时间的增长而增大; 而IRI模型模拟预测N_e数据时间序列的相对误差不会随着预测时间的增长而增大,且在高纬度地区的预测相对误差比在中低纬度地区低.      

Errors and uncertainty in physically-based rainfall-runoff modelling of catchment change effects

The error in physically-based rainfall-runoff modelling is broken into components, and these components are assigned to three groups: (1) model structure error, associated with the model’s equations; (2) parameter error, associated with the parameter values used in the equations; and (3) run time error, associated with rainfall and other forcing data. The error components all contribute to “integrated” errors, such as the difference between simulated and observed runoff, but their individual contributions cannot usually be isolated because the modelling process is complex and there is a lack of knowledge about the catchment and its hydrological responses. A simple model of the Slapton Wood Catchment is developed within a theoretical framework in which the catchment and its responses are assumed to be known perfectly. This makes it possible to analyse the contributions of the error components when predicting the effects of a physical change in the catchment. The standard approach to predicting change effects involves: (1) running “unchanged” simulations using current parameter sets; (2) making adjustments to the sets to allow for physical change; and (3) running “changed” simulations. Calibration or uncertainty-handling methods such as GLUE are used to obtain the current sets based on forcing and runoff data for a calibration period, by minimising or creating statistical bounds for the “integrated” errors in simulations of runoff. It is shown that current parameter sets derived in this fashion are unreliable for predicting change effects, because of model structure error and its interaction with parameter error, so caution is needed if the standard approach is to be used when making management decisions about change in catchments.     

浅水湖泊水质系统滤波模型研究

本文建立了浅水湖泊水质系统滤波模型和相应算法,根据滇池流场比较稳定等特点,对湖泊进行单元分区,考虑模型误差扰动和观测误差扰动的存在,建立系统的状态方程和观测方程,然后采用吉尔（Gill)算法求解微分方程,进行系统多点连续模拟和实时预报,用此法对1988年滇池BOD,COD时空变化进行连续预报,取得满意结果。     

基于置信区间的地震压埋人员实时伤亡状态预估模型

在震后应急救援宏观决策中,地震压埋人员的实时伤亡状态是最重要的定量指标和参考依据。因此,以置信度区间为工具,对影响伤亡状态的参数即初始伤亡指数Co、囤陷环境S和体质综合指数B进行了区间分析,建立了实时伤亡状态模型,并以汶川地震灾区为例,对不同人员的伤亡状态进行了预估,预估值与实际情况的误差为10%左右,表明该模型可供震后应急救援工作参考。     

Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea

Coastal management and maritime safety strongly rely on accurate representations of the sea state. Both dynamical models and observations provide abundant pieces of information. However, none of them provides the complete picture. The assimilation of observations into models is one way to improve our knowledge of the ocean state. Its application in coastal models remains challenging because of the wide range of temporal and spatial variabilities of the processes involved. This study investigates the assimilation of temperature profiles with the ensemble Kalman filter in 3-D North Sea simulations. The model error is represented by the standard deviation of an ensemble of model states. Parameters’ values for the ensemble generation are first computed from the misfit between the data and the model results without assimilation. Then, two square root algorithms are applied to assimilate the data. The impact of data assimilation on the simulated temperature is assessed. Results show that the ensemble Kalman filter is adequate for improving temperature forecasts in coastal areas, under adequate model error specification.     

Wave data assimilation using a hybrid approach in the Persian Gulf

The main goal of this study is to develop an efficient approach for the assimilation of the hindcasted wave parameters in the Persian Gulf. Hence, the third generation SWAN model was employed for wave modeling forced by the 6-h ECMWF wind data with a resolution of 0.5°. In situ wave measurements at two stations were utilized to evaluate the assimilation approaches. It was found that since the model errors are not the same for wave height and period, adaptation of model parameter does not result in simultaneous and comprehensive improvement of them. Therefore, an approach based on the error prediction and updating of output variables was employed to modify wave height and period. In this approach, artificial neural networks (ANNs) were used to estimate the deviations between the simulated and measured wave parameters. The results showed that updating of output variables leads to significant improvement in a wide range of the predicted wave characteristics. It was revealed that the best input parameters for error prediction networks are mean wind speed, mean wind direction, wind duration, and the wave parameters. In addition, combination of the ANN estimated error with numerically modeled wave parameters leads to further improvement in the predicted wave parameters in contrast to direct estimation of the parameters by ANN.     

Sensitivity of the French Alps snow cover to the variation of climatic variables

In order to study the sensitivity of snow cover to changes in meteorological variables at a regional scale, a numerical snow model and an analysis system of the meteorological conditions adapted to relief were used. This approach has been successfully tested by comparing simulated and measured snow depth at 37 sites in the French Alps during a ten year data period. Then, the sensitivity of the snow cover to a variation in climatic conditions was tested by two different methods, which led to very similar results. To assess the impact of a particular “doubled CO₂” scenario, coherent perturbations were introduced in the input data of the snow model. It was found that although the impact would be very pronounced, it would also be extremely differentiated, dependent on the internal state of the snow cover. The most sensitive areas are the elevations below 2400 m, especially in the southern part of the French Alps.