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1.
Evaluating the utility of the ensemble transform Kalman filter for adaptive sampling when updating a hydrodynamic model 总被引：1，自引：0，他引：1
This paper compares two Monte Carlo sequential data assimilation methods based on the Kalman filter, for estimating the effect of measurements on simulations of state error variance made by a one-dimensional hydrodynamic model. The first method used an ensemble Kalman filter (EnKF) to update state estimates, which were then used as initial conditions for further simulations. The second method used an ensemble transform Kalman filter (ETKF) to quickly estimate the effect of measurement error covariance on forecast error covariance without the need to re-run the simulation model. The ETKF gave an unbiased estimate of EnKF analysed error variance, although differences in the treatment of measurement errors meant the results were not identical. Estimates of forecast error variance could also be made, but their accuracy deteriorated as the time from measurements increased due in part to model non-linearity and the decreasing signal variance. The motivation behind the study was to assess the ability of the ETKF to target possible measurements, as part of an adaptive sampling framework, before they are assimilated by an EnKF-based forecasting model on the River Crouch, Essex, UK. The ETKF was found to be a useful tool for quickly estimating the error covariance expected after assimilating measurements into the hydrodynamic model. It, thus, provided a means of quantifying the ‘usefulness’ (in terms of error variance) of possible sampling schemes. 相似文献
2.
Real-time assimilation of streamflow observations into a hydrological routing model: effects of model structures and updating methods 总被引：1，自引：1，他引：0
Maurizio Mazzoleni Haksu Lee Yuqiong Liu Dong-Jun Seo Alessandro Amaranto 《水文科学杂志》2018,63(3):386-407
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. 相似文献
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An implementation of the Ensemble Kalman filter (EnKF) with a coupled ice–ocean model is presented. The model system consists of a dynamic–thermodynamic ice model using the elastic-viscous-plastic (EVP) rheology coupled with the HYbrid Coordinate Ocean Model (HYCOM). The observed variable is ice concentration from passive microwave sensor data (SSM/I). The assimilation of ice concentration has the desired effect of reducing the difference between observations and model. Comparison of the assimilation experiment with a free-run experiment shows that there are large differences, especially in summer. In winter the differences are relatively small, partly because the atmospheric forcing used to run the model depends upon SSM/I data. The assimilation has the strongest impact close to the ice edge, where it ensures a correct location of the ice edge throughout the simulation. An inspection of the model ensemble statistics reveals that the error estimates of the model are too small in winter, partly a result of too low model ice-concentration variance in the central ice pack. It is found that the ensemble covariance between ice concentration and sea-surface temperature in the same grid cell is of the same sign (negative) throughout the year. The ensemble covariance between ice concentration and salinity is more dependent upon the physical mechanisms involved, with ice transport and freeze/melt giving different signs of the covariances. The ice-transport and ice-melt mechanisms also impact the ice-concentration variance and the covariance between ice concentration and ice thickness. The ensemble statistics show a high degree of complexity, which to some extent merits the use of computationally expensive assimilation methods, such as the Ensemble Kalman filter. The present study focuses on the assimilation of ice concentration, but it is understood that assimilation of other datasets, such as sea-surface temperature, would be beneficial.Responsible Editor: Jin-Song von Storch 相似文献
5.
Groundwater models are critical decision support tools for water resources management and environmental remediation. However, limitations in site characterization data and conceptual models can adversely affect the reliability of groundwater models. Therefore, there is a strong need for continuous model uncertainty reduction. Ensemble filters have recently emerged as promising high-dimensional data assimilation techniques. Two general categories of ensemble filters exist in the literature: perturbation-based and deterministic. Deterministic ensemble filters have been extensively studied for their better performance and robustness in assimilating oceanographic and atmospheric data. In hydrogeology, while a number of previous studies demonstrated the usefulness of the perturbation-based ensemble Kalman filter (EnKF) for joint parameter and state estimation, there have been few systematic studies investigating the performance of deterministic ensemble filters. This paper presents a comparative study of four commonly used deterministic ensemble filters for sequentially estimating the hydraulic conductivity parameter in low- and moderately high-dimensional groundwater models. The performance of the filters is assessed on the basis of twin experiments in which the true hydraulic conductivity field is assumed known. The test results indicate that the deterministic ensemble Kalman filter (DEnKF) is the most robust filter and achieves the best performance at relatively small ensemble sizes. Deterministic ensemble filters often make use of covariance inflation and localization to stabilize filter performance. Sensitivity studies demonstrate the effects of covariance inflation, localization, observation density, and conditioning on filter performance. 相似文献
6.
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. 相似文献
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《Advances in water resources》2003,26(1):79-93
In order to improve the soil temperature profile predictions in land-surface models, an assimilation scheme using the extended Kalman filter is developed. This formulation is based on the discretized diffusion equation of heat transfer through the soil column. The scheme is designed to incorporate the knowledge of the uncertainties in both the model and the measurement. Model uncertainty is estimated by quantifying the model drift from observations when the model is initialized using the observed values. Furthermore, the initial error covariance has a significant influence on the performance of the assimilation scheme. It is shown that an inaccurate initial value for the error covariance can actually diminish the predictive capabilities of the model. When an appropriate initial error covariance is specified, using the top layer soil temperature observations in the assimilation scheme allows for improved predictive capabilities in lower layers. Observations at 30 min intervals have a significant effect on the model predictions in the lower layers. Assimilation of observations at 24 h intervals also has an effect on the lower layer predictive capability of the model, albeit more slowly than the 30 min assimilation scenario. 相似文献
8.
An effective method based on dynamic sampling for data assimilation in a global wave model 总被引：3，自引：2，他引：1
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. 相似文献
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Ensemble Kalman filter, EnKF, as a Monte Carlo sequential data assimilation method has emerged promisingly for subsurface media characterization during past decade. Due to high computational cost of large ensemble size, EnKF is limited to small ensemble set in practice. This results in appearance of spurious correlation in covariance structure leading to incorrect or probable divergence of updated realizations. In this paper, a universal/adaptive thresholding method is presented to remove and/or mitigate spurious correlation problem in the forecast covariance matrix. This method is, then, extended to regularize Kalman gain directly. Four different thresholding functions have been considered to threshold forecast covariance and gain matrices. These include hard, soft, lasso and Smoothly Clipped Absolute Deviation (SCAD) functions. Three benchmarks are used to evaluate the performances of these methods. These benchmarks include a small 1D linear model and two 2D water flooding (in petroleum reservoirs) cases whose levels of heterogeneity/nonlinearity are different. It should be noted that beside the adaptive thresholding, the standard distance dependant localization and bootstrap Kalman gain are also implemented for comparison purposes. We assessed each setup with different ensemble sets to investigate the sensitivity of each method on ensemble size. The results indicate that thresholding of forecast covariance yields more reliable performance than Kalman gain. Among thresholding function, SCAD is more robust for both covariance and gain estimation. Our analyses emphasize that not all assimilation cycles do require thresholding and it should be performed wisely during the early assimilation cycles. The proposed scheme of adaptive thresholding outperforms other methods for subsurface characterization of underlying benchmarks. 相似文献
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The local ensemble transform Kalman filter (LETKF) is implemented with the Weather Research and Forecasting (WRF) model, and
real observations are assimilated to assess the newly-developed WRF-LETKF system. The WRF model is a widely-used mesoscale
numerical weather prediction model, and the LETKF is an ensemble Kalman filter (EnKF) algorithm particularly efficient in
parallel computer architecture. This study aims to provide the basis of future research on mesoscale data assimilation using
the WRF-LETKF system, an additional testbed to the existing EnKF systems with the WRF model used in the previous studies.
The particular LETKF system adopted in this study is based on the system initially developed in 2004 and has been continuously
improved through theoretical studies and wide applications to many kinds of dynamical models including realistic geophysical
models. Most recent and important improvements include an adaptive covariance inflation scheme which considers the spatial
and temporal inhomogeneity of inflation parameters. Experiments show that the LETKF successfully assimilates real observations
and that adaptive inflation is advantageous. Additional experiments with various ensemble sizes show that using more ensemble
members improves the analyses consistently. 相似文献
11.
The application of interferometric synthetic aperture radar (InSAR) has been increasingly used to improve capabilities to model land subsidence in hydrogeologic studies. A number of investigations over the last decade show how spatially detailed time‐lapse images of ground displacements could be utilized to advance our understanding for better predictions. In this work, we use simulated land subsidences as observed measurements, mimicking InSAR data to inversely infer inelastic specific storage in a stochastic framework. The inelastic specific storage is assumed as a random variable and modeled using a geostatistical method such that the detailed variations in space could be represented and also that the uncertainties of both characterization of specific storage and prediction of land subsidence can be assessed. The ensemble Kalman filter (EnKF), a real‐time data assimilation algorithm, is used to inversely calibrate a land subsidence model by matching simulated subsidences with InSAR data. The performance of the EnKF is demonstrated in a synthetic example in which simulated surface deformations using a reference field are assumed as InSAR data for inverse modeling. The results indicate: (1) the EnKF can be used successfully to calibrate a land subsidence model with InSAR data; the estimation of inelastic specific storage is improved, and uncertainty of prediction is reduced, when all the data are accounted for; and (2) if the same ensemble is used to estimate Kalman gain, the analysis errors could cause filter divergence; thus, it is essential to include localization in the EnKF for InSAR data assimilation. 相似文献
12.
Variational data assimilation for parameter estimation: application to a simple morphodynamic model 总被引：2，自引：1，他引：1
Polly J. Smith Sarah L. Dance Michael J. Baines Nancy K. Nichols Tania R. Scott 《Ocean Dynamics》2009,59(5):697-708
Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce
state and parameter estimates that most accurately approximate the current and future states of the true system. The technique
is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce
more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe
how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved
using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var,
Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var
scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation
is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves
the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more
complex morphodynamic models. 相似文献
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Annette Eicker Maike Schumacher Jürgen Kusche Petra Döll Hannes Müller Schmied 《Surveys in Geophysics》2014,35(6):1285-1309
We introduce a new ensemble-based Kalman filter approach to assimilate GRACE satellite gravity data into the WaterGAP Global Hydrology Model. The approach (1) enables the use of the spatial resolution provided by GRACE by including the satellite observations as a gridded data product, (2) accounts for the complex spatial GRACE error correlation pattern by rigorous error propagation from the monthly GRACE solutions, and (3) allows us to integrate model parameter calibration and data assimilation within a unified framework. We investigate the formal contribution of GRACE observations to the Kalman filter update by analysis of the Kalman gain matrix. We then present first model runs, calibrated via data assimilation, for two different experiments: the first one assimilates GRACE basin averages of total water storage and the second one introduces gridded GRACE data at \(5^\circ\) resolution into the assimilation. We finally validate the assimilated model by running it in free mode (i.e., without adding any further GRACE information) for a period of 3 years following the assimilation phase and comparing the results to the GRACE observations available for this period. 相似文献
16.
Assimilating transient groundwater flow data via a localized ensemble Kalman filter to calibrate a heterogeneous conductivity field 总被引：2，自引：2，他引：0
Juxiu Tong Bill X. Hu Jinzhong Yang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(3):467-478
A localized ensemble Kalman filter (EnKF) method is developed to assimilate transient flow data to calibrate a heterogeneous
conductivity field. To update conductivity value at a point in a study domain, instead of assimilating all the measurements
in the study domain, only limited measurement data in an area around the point are used for the conductivity updating in the
localized EnKF method. The localized EnKF is proposed to solve the problems of the filter divergence usually existing in a
data assimilation method without localization. The developed method is applied, in a synthetical two dimensional case, to
calibrate a heterogeneous conductivity field by assimilating transient hydraulic head data. The simulations by the data assimilation
with and without localized EnKF are compared. The study results indicate that the hydraulic conductivity field can be updated
efficiently by the localized EnKF, while it cannot be by the EnKF. The covariance inflation and localization are found to
solve the problem of the filter divergence efficiently. In comparison with the EnKF method without localization, the localized
EnKF method needs smaller ensemble size to achieve stabilized results. The simulation results by the localized EnKF method
are much more sensitive to conductivity correlation length than to the localization radius. The developed localized EnKF method
provides an approach to improve EnKF method in conductivity calibration. 相似文献
17.
Tidal flow forecasting using reduced rank square root filters 总被引：1，自引：0，他引：1
M. Verlaan A. W. Heemink 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(5):349-368
The Kalman filter algorithm can be used for many data assimilation problems. For large systems, that arise from discretizing
partial differential equations, the standard algorithm has huge computational and storage requirements. This makes direct
use infeasible for many applications. In addition numerical difficulties may arise if due to finite precision computations
or approximations of the error covariance the requirement that the error covariance should be positive semi-definite is violated.
In this paper an approximation to the Kalman filter algorithm is suggested that solves these problems for many applications.
The algorithm is based on a reduced rank approximation of the error covariance using a square root factorization. The use
of the factorization ensures that the error covariance matrix remains positive semi-definite at all times, while the smaller
rank reduces the number of computations and storage requirements. The number of computations and storage required depend on
the problem at hand, but will typically be orders of magnitude smaller than for the full Kalman filter without significant
loss of accuracy.
The algorithm is applied to a model based on a linearized version of the two-dimensional shallow water equations for the prediction
of tides and storm surges.
For non-linear models the reduced rank square root algorithm can be extended in a similar way as the extended Kalman filter
approach. Moreover, by introducing a finite difference approximation to the Reduced Rank Square Root algorithm it is possible
to prevent the use of a tangent linear model for the propagation of the error covariance, which poses a large implementational
effort in case an extended kalman filter is used. 相似文献
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The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a sufficiently large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos expansion (PCE) to represent and propagate the uncertainties in parameters and states. However, PCKF suffers from the so-called “curse of dimensionality”. Its computational cost increases drastically with the increasing number of parameters and system nonlinearity. Furthermore, PCKF may fail to provide accurate estimations due to the joint updating scheme for strongly nonlinear models. Motivated by recent developments in uncertainty quantification and EnKF, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected at each assimilation step; the “restart” scheme is utilized to eliminate the inconsistency between updated model parameters and states variables. The performance of RAPCKF is systematically tested with numerical cases of unsaturated flow models. It is shown that the adaptive approach and restart scheme can significantly improve the performance of PCKF. Moreover, RAPCKF has been demonstrated to be more efficient than EnKF with the same computational cost. 相似文献
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An ensemble Kalman filter (EnKF) is developed to identify a hydraulic conductivity distribution in a heterogeneous medium by assimilating solute concentration measurements of solute transport in the field with a steady‐state flow. A synthetic case with the mixed Neumann/Dirichlet boundary conditions is designed to investigate the capacity of the data assimilation methods to identify a conductivity distribution. The developed method is demonstrated in 2‐D transient solute transport with two different initial instant solute injection areas. The influences of the observation error and model error on the updated results are considered in this study. The study results indicate that the EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating solute concentration measurements. The larger area of the initial distribution and the more observed data obtained, the better the calculation results. When the standard deviation of the observation error varies from 1% to 30% of the solute concentration measurements, the simulated results by the data assimilation method do not change much, which indicates that assimilation results are not very sensitive to the standard deviation of the observation error in this study. When the inflation factor is more than 1.0 to enlarge the model error by increasing the forecast error covariance matrix, the updated results of the hydraulic conductivity by the data assimilation method are not good at all. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献