scholarly journals On the Choice of an Optimal Localization Radius in Ensemble Kalman Filter Methods

2014 ◽  
Vol 142 (6) ◽  
pp. 2165-2175 ◽  
Author(s):  
Paul Kirchgessner ◽  
Lars Nerger ◽  
Angelika Bunse-Gerstner
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Degrees Of Freedom ◽  
Localization Length ◽  
Ensemble Size ◽  
Localization Radius ◽  
Filter Methods ◽  
Local Observation ◽  
Optimal Localization ◽  
Analysis Quality

Abstract In data assimilation applications using ensemble Kalman filter methods, localization is necessary to make the method work with high-dimensional geophysical models. For ensemble square root Kalman filters, domain localization (DL) and observation localization (OL) are commonly used. Depending on the localization method, appropriate values have to be chosen for the localization parameters, such as the localization length and the weight function. Although frequently used, the properties of the localization techniques are not fully investigated. Thus, up to now an optimal choice for these parameters is a priori unknown and they are generally found by expensive numerical experiments. In this study, the relationship between the localization length and the ensemble size in DL and OL is studied using twin experiments with the Lorenz-96 model and a two-dimensional shallow-water model. For both models, it is found that the optimal localization length for DL and OL depends linearly on an effective local observation dimension that is given by the sum of the observation weights. In the experiments no influence of the model dynamics on the optimal localization length was observed. The effective observation dimension defines the degrees of freedom that are required for assimilating observations, while the ensemble size defines the available degrees of freedom. Setting the localization radius such that the effective local observation dimension equals the ensemble size yields an adaptive localization radius. Its performance is tested using a global ocean model. The experiments show that the analysis quality using the adaptive localization is similar to the analysis quality of an optimally tuned constant localization radius.

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.

scholarly journals Gain Form of the Ensemble Transform Kalman Filter and Its Relevance to Satellite Data Assimilation with Model Space Ensemble Covariance Localization

2017 ◽  
Vol 145 (11) ◽  
pp. 4575-4592 ◽  
Author(s):  
Craig H. Bishop ◽  
Jeffrey S. Whitaker ◽  
Lili Lei
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Satellite Data ◽  
Localization Length ◽  
Model Space ◽  
Ensemble Size ◽  
Length Scales ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Expanded Ensemble

To ameliorate suboptimality in ensemble data assimilation, methods have been introduced that involve expanding the ensemble size. Such expansions can incorporate model space covariance localization and/or estimates of climatological or model error covariances. Model space covariance localization in the vertical overcomes problematic aspects of ensemble-based satellite data assimilation. In the case of the ensemble transform Kalman filter (ETKF), the expanded ensemble size associated with vertical covariance localization would also enable the simultaneous update of entire vertical columns of model variables from hyperspectral and multispectral satellite sounders. However, if the original formulation of the ETKF were applied to an expanded ensemble, it would produce an analysis ensemble that was the same size as the expanded forecast ensemble. This article describes a variation on the ETKF called the gain ETKF (GETKF) that takes advantage of covariances from the expanded ensemble, while producing an analysis ensemble that has the required size of the unexpanded forecast ensemble. The approach also yields an inflation factor that depends on the localization length scale that causes the GETKF to perform differently to an ensemble square root filter (EnSRF) using the same expanded ensemble. Experimentation described herein shows that the GETKF outperforms a range of alternative ETKF-based solutions to the aforementioned problems. In cycling data assimilation experiments with a newly developed storm-track version of the Lorenz-96 model, the GETKF analysis root-mean-square error (RMSE) matches the EnSRF RMSE at shorter than optimal localization length scales but is superior in that it yields smaller RMSEs for longer localization length scales.

scholarly journals Optimal ensemble size of ensemble Kalman filter in sequential soil moisture data assimilation

2015 ◽  
Vol 42 (16) ◽  
pp. 6710-6715 ◽  
Author(s):  
Jifu Yin ◽  
Xiwu Zhan ◽  
Youfei Zheng ◽  
Christopher R. Hain ◽  
Jicheng Liu ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Ensemble Size ◽  
Soil Moisture Data ◽  
Optimal Ensemble

scholarly journals Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

2015 ◽  
Vol 15 (10) ◽  
pp. 5835-5850 ◽  
Author(s):  
D. R. Allen ◽  
K. W. Hoppel ◽  
D. D. Kuhl
Keyword(s):  
Kalman Filter ◽  
Shallow Water ◽  
Ensemble Kalman Filter ◽  
Stratospheric Ozone ◽  
Localization Length ◽  
Polar Vortex ◽  
Meridional Wind ◽  
Water Model ◽  
Shallow Water Model ◽  
Polar Orbiting Satellite

Abstract. The feasibility of extracting wind information from stratospheric ozone observations is tested using ensemble Kalman filter (EnKF) data assimilation (DA) and a global shallow water model that includes advection of an ozone-like tracer. Simulated observations are created from a truth run (TR) that resembles the Northern Hemisphere winter stratosphere with a polar vortex disturbed by planetary-scale wave forcing. Ozone observations mimic sampling of a polar-orbiting satellite, while geopotential height observations are randomly placed in space and time. EnKF experiments are performed assimilating ozone, height, or both, over a 10-day period. The DA is also implemented using two different pairs of flow variables: zonal and meridional wind (EnKF-uv) and stream function and velocity potential (EnKF-ψχ). Each experiment is tuned for optimal localization length, while the ensemble spread is adaptively inflated using the TR. The experiments are evaluated using the maximum wind extraction potential (WEP). Ozone only assimilation improves winds (WEP = 46% for EnKF-uv, and 58% for EnKF-ψχ), but suffers from spurious gravity wave generation. Application of nonlinear normal mode initialization (NMI) greatly reduces the unwanted imbalance and increases the WEP for EnKF-uv (84%) and EnKF-ψχ (81%). Assimilation of only height observations also improved the winds (WEP = 60% for EnKF-uv, and 69% for EnKF-ψχ), with much less imbalance compared to the ozone experiment. The assimilation of both height and ozone performed the best, with WEP increasing to ~87% (~90% with NMI) for both EnKF-uv and EnKF-ψχ, demonstrating that wind extraction from ozone assimilation can be beneficial even in a data-rich environment. Ozone assimilation particularly improves the tropical winds, which are not well constrained by height observations due to lack of geostrophy.

scholarly journals Sensitivity tests for an ensemble Kalman filter for aerosol assimilation

2010 ◽  
Vol 10 (3) ◽  
pp. 5947-5997
Author(s):  
N. A. J. Schutgens ◽  
T. Miyoshi ◽  
T. Takemura ◽  
T. Nakajima
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Patch Size ◽  
Initial Conditions ◽  
Grid Cell ◽  
Ensemble Size ◽  
Sensitivity Tests ◽  
Local Patch ◽  
The Impact ◽  
Assimilation System

Abstract. We present sensitivity tests for a global aerosol assimilation system utilizing AERONET observations of AOT (aerosol optical thickness) and AAE (aerosol Ångström exponent). The assimilation system employs an ensemble Kalman filter which requires optimization of three numerical parameters: ensemble size nens, local patch size npatch and inflation factor ρ. In addition, experiments are performed to test the impact of various implementations of the system. For instance, we use a different prescription of the emission ensemble or a different combination of observations. The various experiments are compared against one-another and against independent AERONET andMODIS/Aqua observations. The assimilation leads to significant improvements in modelled AOT and AAE fields. Moreover remaining errors are mostly random while they are mostly systematic for an experiment without assimilation. In addition, these results do not depend much on our parameter or design choices. It appears that the value of the local patch size has by far the biggest impact on the assimilation, which has sufficiently converged for an ensemble size of nens=20. Assimilating AOT and AAE is clearly preferential to assimilating AOT at two different wavelengths. In contrast, initial conditions or a description of aerosol beyond two modes (coarse and fine) have only little effect. We also discuss the use of the ensemble spread as an error estimate of the analysed AOT and AAE fields. We show that a very common prescription of the emission ensemble (independent random modification in each grid cell) can have trouble generating sufficient spread in the forecast ensemble.

scholarly journals Assessing the Impact of the Covariance Localization Radius when Assimilating Infrared Brightness Temperature Observations Using an Ensemble Kalman Filter

2012 ◽  
Vol 140 (2) ◽  
pp. 543-561 ◽  
Author(s):  
Jason A. Otkin
Keyword(s):  
Kalman Filter ◽  
Brightness Temperature ◽  
Ensemble Kalman Filter ◽  
Short Range ◽  
Infrared Observations ◽  
Localization Radius ◽  
Temperature Observations ◽  
The Impact ◽  
Infrared Brightness ◽  
Cloud Analysis

A regional-scale Observing System Simulation Experiment is used to examine how changes in the horizontal covariance localization radius employed during the assimilation of infrared brightness temperature observations in an ensemble Kalman filter assimilation system impacts the accuracy of atmospheric analyses and short-range model forecasts. The case study tracks the evolution of several extratropical weather systems that occurred across the contiguous United States during 7–8 January 2008. Overall, the results indicate that assimilating 8.5-μm brightness temperatures improves the cloud analysis and forecast accuracy, but has the tendency to degrade the water vapor mixing ratio and thermodynamic fields unless a small localization radius is used. Vertical cross sections showed that varying the localization radius had a minimal impact on the shape of the analysis increments; however, their magnitude consistently increased with increasing localization radius. By the end of the assimilation period, the moisture, temperature, cloud, and wind errors generally decreased with decreasing localization radius and became similar to the Control case in which only conventional observations were assimilated if the shortest localization radius was used. Short-range ensemble forecasts showed that the large positive impact of the infrared observations on the final cloud analysis diminished rapidly during the forecast period, which indicates that it is difficult to maintain beneficial changes to the cloud analysis if the moisture and thermodynamic forcing controlling the cloud evolution are not simultaneously improved. These results show that although assimilation of infrared observations consistently improves the cloud field regardless of the length of the localization radius, it may be necessary to use a smaller radius to also improve the accuracy of the moisture and thermodynamic fields.

scholarly journals Impact of MPEX Upsonde Observations on Ensemble Analyses and Forecasts of the 31 May 2013 Convective Event over Oklahoma

2016 ◽  
Vol 144 (8) ◽  
pp. 2889-2913 ◽  
Author(s):  
Stacey M. Hitchcock ◽  
Michael C. Coniglio ◽  
Kent H. Knopfmeier
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Mobile Systems ◽  
Observation Error ◽  
Ensemble Spread ◽  
Convective Event ◽  
Localization Radius ◽  
Standard Value ◽  
The Impact ◽  
Vertical Localization

Abstract This study examines the impact of assimilating three radiosonde profiles obtained from ground-based mobile systems during the Mesoscale Predictability Experiment (MPEX) on analyses and convection-permitting model forecasts of the 31 May 2013 convective event over Oklahoma. These radiosonde profiles (in addition to standard observations) are assimilated into a 36-member mesoscale ensemble using an ensemble Kalman filter (EnKF) before embedding a convection-permitting (3 km) grid and running a full ensemble of 9-h forecasts. This set of 3-km forecasts is compared to a control run that does not assimilate the MPEX soundings. The analysis of low- to midlevel moisture is impacted the most by the assimilation, but coherent mesoscale differences in temperature and wind are also seen, primarily downstream of the location of the soundings. The ensemble of forecasts of convection on the 3-km grid are improved the most in the first three hours of the forecast in a region where the analyzed position of low-level frontal convergence and midlevel moisture was improved on the mesoscale grid. Later forecasts of the upscale growth of intense convection over central Oklahoma are improved somewhat, but larger ensemble spread lowers confidence in the significance of the improvements. Changes in the horizontal localization radius from the standard value applied to the MPEX sounding assimilation alters the specific times that the forecasts are improved in the first three hours of the forecasts, while changes to the vertical localization radius and specified temperature and wind observation error result in little to no improvements in the forecasts.

Use of Phase Streamlines for Covariance Localization in Ensemble Kalman Filter for Three-Phase History Matching

2012 ◽  
Vol 15 (03) ◽  
pp. 273-289 ◽  
Author(s):  
Shingo Watanabe ◽  
Akhil Datta-Gupta
Keyword(s):  
Kalman Filter ◽  
Gas Phase ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Model Parameters ◽  
Ensemble Size ◽  
Three Phase ◽  
Cross Covariance ◽  
The Cross ◽  
Water Cut

Summary The ensemble Kalman filter (EnKF) has gained increased popularity for history matching and continuous reservoir-model updating. It is a sequential Monte Carlo approach that works with an ensemble of reservoir models. Specifically, the method uses cross covariance between measurements and model parameters estimated from the ensemble. For practical field applications, the ensemble size needs to be kept small for computational efficiency. However, this leads to poor approximations of the cross covariance and can cause loss of geologic realism from unrealistic model updates outside the region of the data influence and/or loss of variance leading to ensemble collapse. A common approach to remedy the situation is to limit the influence of the data through covariance localization. In this paper, we show that for three-phase-flow conditions, the region of covariance localization strongly depends on the underlying flow dynamics as well as on the particular data type that is being assimilated, for example, water cut or gas/oil ratio (GOR). This makes the traditional distance-based localizations suboptimal and, often, ineffective. Instead, we propose the use of water- and gas-phase streamlines as a means for covariance localization for water-cut- and GOR-data assimilation. The phase streamlines can be computed on the basis of individual-phase velocities which are readily available after flow simulation. Unlike the total velocity streamlines, phase streamlines can be discontinuous. We show that the discontinuities in water-phase and gas-phase streamlines naturally define the region of influence for water-cut and GOR data and provide a flow-relevant covariance localization during EnKF updating. We first demonstrate the validity of the proposed localization approach using a waterflood example in a quarter-five-spot pattern. Specifically, we compare the phase streamline trajectories with cross-covariance maps computed using an ensemble size of 2,000 for both water-cut and GOR data. The results show a close correspondence between the time evolution of phase streamlines and the cross-covariance maps of water-cut and GOR data. A benchmark uncertainty quantification (the PUNQ-S3) (Carter 2007) model application shows that our proposed localization outperforms the distance-based localization method. The updated models show improved forecasts while preserving geologic realism.

scholarly journals Application of Ensemble Kalman Filter to Pedestrian Flow

2020 ◽  
Vol 5 ◽  
pp. A101
Author(s):  
Fumiya Togashi ◽  
Takashi Misaka ◽  
Rainald Löhner ◽  
Shigeru Obayashi
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Computational Simulation ◽  
Atmospheric Condition ◽  
Weather Forecast ◽  
Pedestrian Flow ◽  
Simulation Code ◽  
First Case

We adopted the Ensemble Kalman Filter (EnKF) methodology in our computational simulation code for pedestrian flows. The EnKF, which is a type of data assimilation methodology, has been developed in the field of weather forecast where the atmospheric condition varies hour by hour. The EnKF estimates the parameters or boundary/initial conditions in the numerical model based on the updated measured data. We considered the EnKF a promising tool for the simulation of pedestrian flows, which are notoriously difficult to predict. In this study, two scenarios were conducted to confirm the usefulness of the EnKF. The first case was unidirectional pedestrian flow in straight corridors, and the second case was Mataf scenario at the Kaaba in Mecca. Needless to say, the second scenario was very challenging because of the number of pilgrims and the degrees of freedom. In each scenario, we conducted the numerical simulation using the original parameter set and then applied the EnKF to improve the accuracy of the simulation.

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