Adaptive Localization for Tropical Cyclones With Satellite Radiances in an Ensemble Kalman Filter

2021 ◽  
Author(s):  
Chen Wang ◽  
Lili Lei ◽  
Zhe-Min Tan ◽  
Kekuan Chu
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Adaptive Method ◽  
State Variables ◽  
Localization Algorithm ◽  
Sampling Errors ◽  
Satellite Platform ◽  
Geophysical Application ◽  
Vertical Location ◽  
Radiance Data

<p>One important aspect of successfully implementing an ensemble Kalman filter (EnKF) in a high dimensional geophysical application is covariance localization. But for satellite radiances whose vertical locations are not well defined, covariance localization is not straightforward. The global group filter (GGF) is an adaptive localization algorithm, which can provide adaptively estimated localization parameters including the localization width and vertical location of observations for each channel and every satellite platform of radiance data, and for different regions and times. This adaptive method is based on sample correlations between ensemble priors of observations and state variables, aiming to minimize sampling errors of estimated sample correlations. The adaptively estimated localization parameters are examined here for typhoon Yutu (2018), using the regional model WRF and a cycling EnKF system. The benefits of differentiating the localization parameters for TC and non-TC regions and varying the localization parameters with time are investigated. Results from the 6-h priors verified relative to the conventional and radiance observations show that the adaptively estimated localization parameters generally produce smaller errors than the default Gaspari and Cohn (GC) localization. The adaptively estimated localization parameters better capture the onset of RI and yield improved intensity and structure forecasts for typhoon Yutu (2018) compared to the default GC localization. The time-varying localization parameters have slightly advantages over the time-constant localization parameters. Further improvements are achieved by differentiating the localization parameters for TC and non-TC regions.</p>

scholarly journals Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1520
Author(s):  
Zheng Jiang ◽  
Quanzhong Huang ◽  
Gendong Li ◽  
Guangyong Li
Keyword(s):  
Kalman Filter ◽  
Solute Transport ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Parameters Estimation ◽  
Saturated Soils ◽  
Hydrological Models ◽  
State Variables ◽  
Ensemble Size ◽  
Highly Nonlinear

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

A Probabilistic Collocation-Based Kalman Filter for History Matching

SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 294-306 ◽  
Author(s):  
Lingzao Zeng ◽  
Haibin Chang ◽  
Dongxiao Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Initial Conditions ◽  
Collocation Point ◽  
Computational Effort ◽  
Production Data ◽  
Sampling Errors ◽  
Probabilistic Collocation

Summary The ensemble Kalman filter (EnKF) has been used widely for data assimilation. Because the EnKF is a Monte Carlo-based method, a large ensemble size is required to reduce the sampling errors. In this study, a probabilistic collocation-based Kalman filter (PCKF) is developed to adjust the reservoir parameters to honor the production data. It combines the advantages of the EnKF for dynamic data assimilation and the polynomial chaos expansion (PCE) for efficient uncertainty quantification. In this approach, all the system parameters and states and the production data are approximated by the PCE. The PCE coefficients are solved with the probabilistic collocation method (PCM). Collocation realizations are constructed by choosing collocation point sets in the random space. The simulation for each collocation realization is solved forward in time independently by means of an existing deterministic solver, as in the EnKF method. In the analysis step, the needed covariance is approximated by the PCE coefficients. In this study, a square-root filter is employed to update the PCE coefficients. After the analysis, new collocation realizations are constructed. With the parameter collocation realizations as the inputs and the state collocation realizations as initial conditions, respectively, the simulations are forwarded to the next analysis step. Synthetic 2D water/oil examples are used to demonstrate the applicability of the PCKF in history matching. The results are compared with those from the EnKF on the basis of the same analysis. It is shown that the estimations provided by the PCKF are comparable to those obtained from the EnKF. The biggest improvement of the PCKF comes from the leading PCE approximation, with which the computational burden of the PCKF can be greatly reduced by means of a smaller number of simulation runs, and the PCKF outperforms the EnKF for a similar computational effort. When the correlation ratio is much smaller, the PCKF still provides estimations with a better accuracy for a small computational effort.

scholarly journals Simultaneous estimation of model state variables and observation and forecast biases using a two-stage hybrid Kalman filter

2013 ◽  
Vol 10 (4) ◽  
pp. 5169-5224 ◽  
Author(s):  
V. R. N. Pauwels ◽  
G. J. M. De Lannoy ◽  
H.-J. Hendricks Franssen ◽  
H. Vereecken
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
The State ◽  
Bias Error ◽  
Simultaneous Estimation ◽  
State Variables ◽  
Two Stage ◽  
Forecast Bias ◽  
Error Covariance ◽  
Observation Bias

Abstract. In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the Discrete Kalman Filter, and the state variables using the Ensemble Kalman Filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware Ensemble Kalman Filter. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

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

2020 ◽  
Author(s):  
Yohei Sawada
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Land Surface ◽  
Pressure Head ◽  
Surface Flow ◽  
State Variables ◽  
Background Error ◽  
Water Flows

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 one-dimensional 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 to adjust 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.

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

2020 ◽  
Vol 24 (8) ◽  
pp. 3881-3898
Author(s):  
Yohei Sawada
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Land Surface ◽  
Pressure Head ◽  
Surface Flow ◽  
State Variables ◽  
Background Error ◽  
Water Flows

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.

Hierarchical Ensemble Kalman Filter

SPE Journal ◽  
2010 ◽  
Vol 15 (02) ◽  
pp. 569-580 ◽  
Author(s):  
Inge Myrseth
Keyword(s):  
Kalman Filter ◽  
Parameter Uncertainty ◽  
Ensemble Kalman Filter ◽  
State Variables ◽  
Rank Deficiency ◽  
Robust Estimates ◽  
Estimation Uncertainty ◽  
Model Parameter Uncertainty ◽  
Realistic Prediction ◽  
Family Of Distributions

Summary This paper presents the hierarchical ensemble Kalman filter (HEnKF) as a robust extension of the ensemble Kalman filter (EnKF). The HEnKF is developed to be robust against features like estimation uncertainty and rank deficiency related to covariance estimation in EnKF. The HEnKF imposes a hierarchical model on the state variables and uses prior distributions from the Gauss conjugate family of distributions to obtain more-robust estimates. An empirical study demonstrates that the HEnKF provides more-reliable results than the traditional EnKF approach. Better predictions and more-realistic prediction intervals are provided. The latter is caused by model-parameter uncertainty being an integral part of the HEnKF approach, while this effect is ignored in traditional EnKF. The two versions of the ensemble Kalman filter are also compared on a synthetic-reservoir study. The HEnKF appears as significantly better.

scholarly journals Ensemble Kalman filtering without the intrinsic need for inflation

2011 ◽  
Vol 18 (5) ◽  
pp. 735-750 ◽  
Author(s):  
M. Bocquet
Keyword(s):  
Kalman Filter ◽  
Probability Density Function ◽  
Probability Density ◽  
Ensemble Kalman Filter ◽  
Finite Size ◽  
Ensemble Size ◽  
Sampling Errors ◽  
New Class ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

Abstract. The main intrinsic source of error in the ensemble Kalman filter (EnKF) is sampling error. External sources of error, such as model error or deviations from Gaussianity, depend on the dynamical properties of the model. Sampling errors can lead to instability of the filter which, as a consequence, often requires inflation and localization. The goal of this article is to derive an ensemble Kalman filter which is less sensitive to sampling errors. A prior probability density function conditional on the forecast ensemble is derived using Bayesian principles. Even though this prior is built upon the assumption that the ensemble is Gaussian-distributed, it is different from the Gaussian probability density function defined by the empirical mean and the empirical error covariance matrix of the ensemble, which is implicitly used in traditional EnKFs. This new prior generates a new class of ensemble Kalman filters, called finite-size ensemble Kalman filter (EnKF-N). One deterministic variant, the finite-size ensemble transform Kalman filter (ETKF-N), is derived. It is tested on the Lorenz '63 and Lorenz '95 models. In this context, ETKF-N is shown to be stable without inflation for ensemble size greater than the model unstable subspace dimension, at the same numerical cost as the ensemble transform Kalman filter (ETKF). One variant of ETKF-N seems to systematically outperform the ETKF with optimally tuned inflation. However it is shown that ETKF-N does not account for all sampling errors, and necessitates localization like any EnKF, whenever the ensemble size is too small. In order to explore the need for inflation in this small ensemble size regime, a local version of the new class of filters is defined (LETKF-N) and tested on the Lorenz '95 toy model. Whatever the size of the ensemble, the filter is stable. Its performance without inflation is slightly inferior to that of LETKF with optimally tuned inflation for small interval between updates, and superior to LETKF with optimally tuned inflation for large time interval between updates.

The Ensemble Kalman Filter for Continuous Updating of Reservoir Simulation Models

2005 ◽  
Vol 128 (1) ◽  
pp. 79-87 ◽  
Author(s):  
Yaqing Gu ◽  
Dean S. Oliver
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Water Saturation ◽  
State Variables ◽  
Time Step ◽  
Two Phase ◽  
One Dimensional ◽  
Reservoir State

This paper reports the use of ensemble Kalman filter (EnKF) for automatic history matching. EnKF is a Monte Carlo method, in which an ensemble of reservoir state variables are generated and kept up-to-date as data are assimilated sequentially. The uncertainty of reservoir state variables is estimated from the ensemble at any time step. Two synthetic problems are selected to investigate two primary concerns with the application of the EnKF. The first concern is whether it is possible to use a Kalman filter to make corrections to state variables in a problem for which the covariance matrix almost certainly provides a poor representation of the distribution of variables. It is tested with a one-dimensional, two-phase waterflood problem. The water saturation takes large values behind the flood front, and small values ahead of the front. The saturation distribution is bimodal and is not well modeled by the mean and variance. The second concern is the representation of the covariance via a relatively small ensemble of state vectors may be inadequate. It is tested by a two-dimensional, two-phase problem. The number of ensemble members is kept the same as for the one-dimensional problem. Hence the number of ensemble members used to create the covariance matrix is far less than the number of state variables. We conclude that EnKF can provide satisfactory history matching results while requiring less computation work than traditional history matching methods.

Impact of Assimilating AMSU-A Radiances on Forecasts of 2008 Atlantic Tropical Cyclones Initialized with a Limited-Area Ensemble Kalman Filter

2012 ◽  
Vol 140 (12) ◽  
pp. 4017-4034 ◽  
Author(s):  
Zhiquan Liu ◽  
Craig S. Schwartz ◽  
Chris Snyder ◽  
So-Young Ha
Keyword(s):  
Kalman Filter ◽  
Tropical Cyclones ◽  
Ensemble Kalman Filter ◽  
Bias Correction ◽  
Substantial Improvement ◽  
Limited Area ◽  
Radiance Assimilation ◽  
Vertical Location ◽  
Microwave Sounding ◽  
The Impact

Abstract The impact of assimilating radiance observations from the Advanced Microwave Sounding Unit-A (AMSU-A) on forecasts of several tropical cyclones (TCs) was studied using the Weather Research and Forecasting Model (WRF) and a limited-area ensemble Kalman filter (EnKF). Analysis/forecast cycling experiments with and without AMSU-A radiance assimilation were performed over the Atlantic Ocean for the period 11 August–13 September 2008, when five named storms formed. For convenience, the radiance forward operators and bias-correction coefficients, along with the majority of quality-control decisions, were computed by a separate, preexisting variational assimilation system. The bias-correction coefficients were obtained from 3-month offline statistics and fixed during the EnKF analysis cycles. The vertical location of each radiance observation, which is required for covariance localization in the EnKF, was taken to be the level at which the AMSU-A channels’ weighting functions peaked. Deterministic 72-h WRF forecasts initialized from the ensemble-mean analyses were evaluated with a focus on TC prediction. Assimilating AMSU-A radiances produced better depictions of the environmental fields when compared to reanalyses and dropwindsonde observations. Radiance assimilation also resulted in substantial improvement of TC track and intensity forecasts with track-error reduction up to 16% for forecasts beyond 36 h. Additionally, assimilating both radiances and satellite winds gave markedly more benefit for TC track forecasts than solely assimilating radiances.

scholarly journals Sampling Errors in Ensemble Kalman Filtering. Part I: Theory

2008 ◽  
Vol 136 (8) ◽  
pp. 3035-3049 ◽  
Author(s):  
William Sacher ◽  
Peter Bartello
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Test Case ◽  
Sampling Errors ◽  
Background Error ◽  
Theoretical Understanding ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Filter Divergence

Abstract This paper discusses the quality of the analysis given by the ensemble Kalman filter in a perfect model context when ensemble sizes are limited. The overall goal is to improve the theoretical understanding of the problem of systematic errors in the analysis variance due to the limited size of the ensemble, as well as the potential of the so-called double-ensemble Kalman filter, covariance inflation, and randomly perturbed analysis techniques to produce a stable analysis—that is to say, one not subject to filter divergence. This is achieved by expressing the error of the ensemble mean and the analysis error covariance matrix in terms of the sampling noise in the background error covariance matrix (owing to the finite ensemble estimation) and by comparing these errors for all methods. Theoretical predictions are confirmed with a simple scalar test case. In light of the analytical results obtained, the expression of the optimal covariance inflation factor is proposed in terms of the limited ensemble size and the Kalman gain.

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