scholarly journals Ensemble Kalman Filter Assimilation of Fixed Screen-Height Observations in a Parameterized PBL

2005 ◽  
Vol 133 (11) ◽  
pp. 3260-3275 ◽  
Author(s):  
Joshua P. Hacker ◽  
Chris Snyder
Keyword(s):  
Kalman Filter ◽  
Great Plains ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Lower Boundary ◽  
The State ◽  
Convective Initiation ◽  
Rich Data ◽  
Pbl Model ◽  
Surface Observations

Abstract In situ surface layer observations are a rich data source that could be more effectively utilized in NWP applications. If properly assimilated, data from existing mesonets could improve initial conditions and lower boundary conditions, leading to the possibility of improved simulation and short-range forecasts of slope flows, sea breezes, convective initiation, and other PBL circulations. A variance–covariance climatology is constructed by extracting a representative column from real-time mesoscale forecasts over the Southern Great Plains, and used to explore the potential for estimating the state of the PBL by assimilating surface observations. A parameterized 1D PBL model and an ensemble Kalman filter (EnKF) approach to assimilation are used to test this potential. Analysis focuses on understanding how effectively the EnKF can spread the surface observations vertically to constrain the state of the PBL model. Results confirm that assimilating surface observations can substantially improve the state of a modeled PBL. Experiments to estimate the moisture availability parameter through the data assimilation system show that the EnKF is a viable tool for parameter estimation, and may help mitigate model error in forecasting and simulating the PBL.

scholarly journals Covariance Inflation in the Ensemble Kalman Filter: A Residual Nudging Perspective and Some Implications

2013 ◽  
Vol 141 (10) ◽  
pp. 3360-3368 ◽  
Author(s):  
Xiaodong Luo ◽  
Ibrahim Hoteit
Keyword(s):  
Kalman Filter ◽  
Numerical Experiment ◽  
Ensemble Kalman Filter ◽  
Sufficient Conditions ◽  
The State ◽  
State Estimate ◽  
Inflation Factor

Abstract This article examines the influence of covariance inflation on the distance between the measured observation and the simulated (or predicted) observation with respect to the state estimate. In order for the aforementioned distance to be bounded in a certain interval, some sufficient conditions are derived, indicating that the covariance inflation factor should be bounded in a certain interval, and that the inflation bounds are related to the maximum and minimum eigenvalues of certain matrices. Implications of these analytic results are discussed, and a numerical experiment is presented to verify the validity of the analysis conducted.

scholarly journals Operational hydrological data assimilation with the Retrospective Ensemble Kalman Filter: use of observed discharge to update past and present model states for flow forecasts

2012 ◽  
Vol 9 (8) ◽  
pp. 9533-9575 ◽  
Author(s):  
H. K. McMillan ◽  
E. Ö. Hreinsson ◽  
M. P. Clark ◽  
S. K. Singh ◽  
C. Zammit ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Present Model ◽  
Filter Design ◽  
Initial Conditions ◽  
Distributed Model ◽  
Design Parameters ◽  
Improve Model ◽  
Measured Flow ◽  
Forecasting System

Abstract. This paper describes the use of the Retrospective Ensemble Kalman Filter (REnKF) to assimilate streamflow data in an operational flow forecasting system of seven catchments in New Zealand. The REnKF updates past and present model states (soil water, aquifer and surface storages), with lags up to the concentration time of the catchment, to improve model initial conditions and hence flow forecasts. To our knowledge, this is the first time the REnKF has been applied in an operational setting, for a distributed model running over large catchments. We found the REnKF overcame instabilities in the standard EnKF which were associated with the natural lag time between upstream catchment wetness and flow at the gauging locations. The forecast system performance was correspondingly improved in terms of Nash Sutcliffe score and bounding of the measured flow by the model ensemble. We present descriptions of filter design parameters and explanations and examples of filter behaviour. The paper provides information and guidance valuable for other groups wishing to apply the REnKF for operational forecasting.

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 Penalized ensemble Kalman filters for high dimensional non-linear systems

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248046
Author(s):  
Elizabeth Hou ◽  
Earl Lawrence ◽  
Alfred O. Hero
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Estimation Error ◽  
Covariance Structure ◽  
Full Rank ◽  
The State ◽  
High Dimensional ◽  
Ensemble Kalman Filters ◽  
Non Linear ◽  
Non Linear System

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems.

scholarly journals DATA ASSIMILATION BY ENSEMBLE KALMAN FILTER WITH THE LORENZ EQUATIONS

2016 ◽  
Vol 38 ◽  
pp. 190
Author(s):  
Regis Sperotto de Quadros ◽  
Fabrício Pereira Harter ◽  
Daniela Buske ◽  
Larri Silveira Pereira
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Forecasting ◽  
Initial Conditions ◽  
Background Field ◽  
Lorenz Equations ◽  
Integration Period ◽  
Numerical Weather Forecasting ◽  
Chaotic Nature

Data Assimilation is a procedure to get the initial condition as accurately as possible, through the statistical combination of collected observations and a background field, usually a short-range forecast. In this research a complete assimilation system for the Lorenz equations based on Ensemble Kalman Filter is presented and examined. The Lorenz model is chosen for its simplicity in structure and the dynamic similarities with primitive equations models, such as modern numerical weather forecasting. Based on results, was concluded that, in this implementation, 10 members is the best setting, because there is an overfitting for ensembles with 50 and 100 members. It was also examined if the EnKF is effective to track the control for 20% and 40% of error in the initial conditions. The results show a disagreement between the “truth” and the estimation, especially in the end of integration period, due the chaotic nature of the system.  It was also concluded that EnKF have to be performed sufficiently frequently in order to produce desirable results.

scholarly journals Comparison of Ensemble Kalman Filter–Based Forecasts to Traditional Ensemble and Deterministic Forecasts for a Case Study of Banded Snow

2012 ◽  
Vol 27 (1) ◽  
pp. 85-105 ◽  
Author(s):  
Astrid Suarez ◽  
Heather Dawn Reeves ◽  
Dustan Wheatley ◽  
Michael Coniglio
Keyword(s):  
Kalman Filter ◽  
Flow Pattern ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Closed Surface ◽  
Flow Patterns ◽  
Precipitation Forecast ◽  
Ensemble Mean ◽  
Correct Location

Abstract The ensemble Kalman filter (EnKF) technique is compared to other modeling approaches for a case study of banded snow. The forecasts include a 12- and 3-km grid-spaced deterministic forecast (D12 and D3), a 12-km 30-member ensemble (E12), and a 12-km 30-member ensemble with EnKF-based four-dimensional data assimilation (EKF12). In D12 and D3, flow patterns are not ideal for banded snow, but they have similar precipitation accumulations in the correct location. The increased resolution did not improve the quantitative precipitation forecast. The E12 ensemble mean has a flow pattern favorable for banding and precipitation in the approximate correct location, although the magnitudes and probabilities of relevant features are quite low. Six members produced good forecasts of the flow patterns and the precipitation structure. The EKF12 ensemble mean has an ideal flow pattern for banded snow and the mean produces banded precipitation, but relevant features are about 100 km too far north. The EKF12 has a much lower spread than does E12, a consequence of their different initial conditions. Comparison of the initial ensemble means shows that EKF12 has a closed surface low and a region of high low- to midlevel humidity that are not present in E12. These features act in concert to produce a stronger ensemble-mean cyclonic system with heavier precipitation at the time of banding.

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.

Ensemble Kalman Filter estimates shear stress and seismic slip rates in synthetic laboratory experiment

2021 ◽  
Author(s):  
Hamed Ali Diab-Montero ◽  
Meng Li ◽  
Ylona van Dinther ◽  
Femke C Vossepoel
Keyword(s):  
Shear Stress ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Slip Rate ◽  
The State ◽  
Shear Stresses ◽  
Limited Information ◽  
Slip Rates ◽  
Laboratory Setup

<p>Our ability to forecast earthquake events is hampered by limited information of the state of stress and strength of faults and their governing parameters. Ensemble data assimilation methods provide a means to estimate these variables by combining physics-based models and observations taking into account their uncertainties. In this study, we estimate earthquake occurrences in synthetic experiments representing a meter-scale laboratory setup of a straight-fault governed by rate-and-state friction. We test an Ensemble Kalman Filter implemented in the Parallel Data Assimilation Framework, which is connected with a 1D forward model using the numerical library GARNET. A perfect-model test shows that the filter can estimate shear stresses, slip rates and state θ acting on the fault even when simulating slip rates up to m/s and can thus be used for estimating earthquake occurrences. We assimilate shear stress and slip-rate observations, representing measurements obtained from shear strain gauges and piezoelectric transducers sensors, and their uncertainties acquired at a small distance to the fault in the homogeneous elastic medium. In this study we evaluate how the Ensemble Kalman filter estimates the state and strength of the faults using these observations, and assess the relative influence of assimilating various observations. The results suggest that the data assimilation improves the estimated timing of the earthquake occurrences. The assimilation of the shear stress observed in the medium improves in particular the estimates of the state θ and the shear stress on the fault, while assimilating observations of velocity in the medium improves the slip-rate estimation.</p>

scholarly journals Improvement of ozone forecast over Beijing based on ensemble Kalman filter with simultaneous adjustment of initial conditions and emissions

2011 ◽  
Vol 11 (24) ◽  
pp. 12901-12916 ◽  
Author(s):  
X. Tang ◽  
J. Zhu ◽  
Z. F. Wang ◽  
A. Gbaguidi
Keyword(s):  
Kalman Filter ◽  
Air Quality ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Urban Site ◽  
Ozone Forecast ◽  
Regional Air Quality ◽  
Simultaneous Adjustment ◽  
Mean Square Errors

Abstract. In order to improve the surface ozone forecast over Beijing and surrounding regions, data assimilation method integrated into a high-resolution regional air quality model and a regional air quality monitoring network are employed. Several advanced data assimilation strategies based on ensemble Kalman filter are designed to adjust O3 initial conditions, NOx initial conditions and emissions, VOCs initial conditions and emissions separately or jointly through assimilating ozone observations. As a result, adjusting precursor initial conditions demonstrates potential improvement of the 1-h ozone forecast almost as great as shown by adjusting precursor emissions. Nevertheless, either adjusting precursor initial conditions or emissions show deficiency in improving the short-term ozone forecast at suburban areas. Adjusting ozone initial values brings significant improvement to the 1-h ozone forecast, and its limitations lie in the difficulty in improving the 1-h forecast at some urban site. A simultaneous adjustment of the above five variables is found to be able to reduce these limitations and display an overall better performance in improving both the 1-h and 24-h ozone forecast over these areas. The root mean square errors of 1-h ozone forecast at urban sites and suburban sites decrease by 51% and 58% respectively compared with those in free run. Through these experiments, we found that assimilating local ozone observations is determinant for ozone forecast over the observational area, while assimilating remote ozone observations could reduce the uncertainty in regional transport ozone.

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