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.

Atmospheric Data Assimilation with an Ensemble Kalman Filter: Results with Real Observations

2005 ◽  
Vol 133 (3) ◽  
pp. 604-620 ◽  
Author(s):  
P. L. Houtekamer ◽  
Herschel L. Mitchell ◽  
Gérard Pellerin ◽  
Mark Buehner ◽  
Martin Charron ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Forecast Error ◽  
Lower Troposphere ◽  
Model Error ◽  
Atmospheric Data ◽  
Ensemble Mean ◽  
Parameterized Model

Abstract An ensemble Kalman filter (EnKF) has been implemented for atmospheric data assimilation. It assimilates observations from a fairly complete observational network with a forecast model that includes a standard operational set of physical parameterizations. To obtain reasonable results with a limited number of ensemble members, severe horizontal and vertical covariance localizations have been used. It is observed that the error growth in the data assimilation cycle is mainly due to model error. An isotropic parameterization, similar to the forecast-error parameterization in variational algorithms, is used to represent model error. After some adjustment, it is possible to obtain innovation statistics that agree with the ensemble-based estimate of the innovation amplitudes for winds and temperature. Currently, no model error is added for the humidity variable, and, consequently, the ensemble spread for humidity is too small. After about 5 days of cycling, fairly stable global filter statistics are obtained with no sign of filter divergence. The quality of the ensemble mean background field, as verified using radiosonde observations, is similar to that obtained using a 3D variational procedure. In part, this is likely due to the form chosen for the parameterized model error. Nevertheless, the degree of similarity is surprising given that the background-error statistics used by the two procedures are rather different, with generally larger background errors being used by the variational scheme. A set of 5-day integrations has been started from the ensemble of initial conditions provided by the EnKF. For the middle and lower troposphere, the growth rates of the perturbations are somewhat smaller than the growth rate of the actual ensemble mean error. For the upper levels, the perturbation patterns decay for about 3 days as a consequence of diffusive model dynamics. These decaying perturbations tend to severely underestimate the actual error that grows rapidly near the model top.

Assessing Predictability with a Local Ensemble Kalman Filter

2007 ◽  
Vol 64 (4) ◽  
pp. 1116-1140 ◽  
Author(s):  
David Kuhl ◽  
Istvan Szunyogh ◽  
Eric J. Kostelich ◽  
Gyorgyi Gyarmati ◽  
D. J. Patil ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Forecast Error ◽  
Weather Prediction ◽  
Forecast Errors ◽  
Data Assimilation Scheme ◽  
Ensemble Mean ◽  
Assimilation Scheme

Abstract In this paper, the spatiotemporally changing nature of predictability is studied in a reduced-resolution version of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS), a state-of-the-art numerical weather prediction model. Atmospheric predictability is assessed in the perfect model scenario for which forecast uncertainties are entirely due to uncertainties in the estimates of the initial states. Uncertain initial conditions (analyses) are obtained by assimilating simulated noisy vertical soundings of the “true” atmospheric states with the local ensemble Kalman filter (LEKF) data assimilation scheme. This data assimilation scheme provides an ensemble of initial conditions. The ensemble mean defines the initial condition of 5-day deterministic model forecasts, while the time-evolved members of the ensemble provide an estimate of the evolving forecast uncertainties. The observations are randomly distributed in space to ensure that the geographical distribution of the analysis and forecast errors reflect predictability limits due to the model dynamics and are not affected by inhomogeneities of the observational coverage. Analysis and forecast error statistics are calculated for the deterministic forecasts. It is found that short-term forecast errors tend to grow exponentially in the extratropics and linearly in the Tropics. The behavior of the ensemble is explained by using the ensemble dimension (E dimension), a spatiotemporally evolving measure of the evenness of the distribution of the variance between the principal components of the ensemble-based forecast error covariance matrix. It is shown that in the extratropics the largest forecast errors occur for the smallest E dimensions. Since a low value of the E dimension guarantees that the ensemble can capture a large portion of the forecast error, the larger the forecast error the more certain that the ensemble can fully capture the forecast error. In particular, in regions of low E dimension, ensemble averaging is an efficient error filter and the ensemble spread provides an accurate prediction of the upper bound of the error in the ensemble-mean forecast.

scholarly journals Handling Nonlinearity in an Ensemble Kalman Filter: Experiments with the Three-Variable Lorenz Model

2012 ◽  
Vol 140 (8) ◽  
pp. 2628-2646 ◽  
Author(s):  
Shu-Chih Yang ◽  
Eugenia Kalnay ◽  
Brian Hunt
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Linear Models ◽  
Low Frequency ◽  
Lorenz Model ◽  
Outer Loop ◽  
Nonlinear Growth ◽  
Ensemble Mean ◽  
Ensemble Transform Kalman Filter ◽  
The One

Abstract An ensemble Kalman filter (EnKF) is optimal only for linear models because it assumes Gaussian distributions. A new type of outer loop, different from the one used in 3D and 4D variational data assimilation (Var), is proposed for EnKF to improve its ability to handle nonlinear dynamics, especially for long assimilation windows. The idea of the “running in place” (RIP) algorithm is to increase the observation influence by reusing observations when there is strong nonlinear error growth, and thus improve the ensemble mean and perturbations within the local ensemble transform Kalman filter (LETKF) framework. The “quasi-outer-loop” (QOL) algorithm, proposed here as a simplified version of RIP, aims to improve the ensemble mean so that ensemble perturbations are centered at a more accurate state. The performances of LETKF–RIP and LETKF–QOL in the presence of nonlinearities are tested with the three-variable Lorenz model. Results show that RIP and QOL allow LETKF to use longer assimilation windows with significant improvement of the analysis accuracy during periods of high nonlinear growth. For low-frequency observations (every 25 time steps, leading to long assimilation windows), and using the optimal inflation, the standard LETKF RMS error is 0.68, whereas for QOL and RIP the RMS errors are 0.47 and 0.35, respectively. This can be compared to the best 4D-Var analysis error of 0.53, obtained by using both the optimal long assimilation windows (75 time steps) and quasi-static variational analysis.

Initial Conditions for Convection-Allowing Ensembles over the Conterminous United States

2020 ◽  
Vol 148 (7) ◽  
pp. 2645-2669
Author(s):  
Craig S. Schwartz ◽  
May Wong ◽  
Glen S. Romine ◽  
Ryan A. Sobash ◽  
Kathryn R. Fossell
Keyword(s):  
United States ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Limited Area ◽  
Grid Spacing ◽  
Forecast System ◽  
Skill Scores ◽  
Ensemble Mean ◽  
Horizontal Grid ◽  
Better Than

Abstract Five sets of 48-h, 10-member, convection-allowing ensemble (CAE) forecasts with 3-km horizontal grid spacing were systematically evaluated over the conterminous United States with a focus on precipitation across 31 cases. The various CAEs solely differed by their initial condition perturbations (ICPs) and central initial states. CAEs initially centered about deterministic Global Forecast System (GFS) analyses were unequivocally better than those initially centered about ensemble mean analyses produced by a limited-area single-physics, single-dynamics 15-km continuously cycling ensemble Kalman filter (EnKF), strongly suggesting relative superiority of the GFS analyses. Additionally, CAEs with flow-dependent ICPs derived from either the EnKF or multimodel 3-h forecasts from the Short-Range Ensemble Forecast (SREF) system had higher fractions skill scores than CAEs with randomly generated mesoscale ICPs. Conversely, due to insufficient spread, CAEs with EnKF ICPs had worse reliability, discrimination, and dispersion than those with random and SREF ICPs. However, members in the CAE with SREF ICPs undesirably clustered by dynamic core represented in the ICPs, and CAEs with random ICPs had poor spinup characteristics. Collectively, these results indicate that continuously cycled EnKF mean analyses were suboptimal for CAE initialization purposes and suggest that further work to improve limited-area continuously cycling EnKFs over large regional domains is warranted. Additionally, the deleterious aspects of using both multimodel and random ICPs suggest efforts toward improving spread in CAEs with single-physics, single-dynamics, flow-dependent ICPs should continue.

The Ensemble Kalman Filter for Groundwater Plume Characterization: A Case Study

Ground Water ◽  
2018 ◽  
Vol 56 (4) ◽  
pp. 571-579 ◽  
Author(s):  
James L. Ross ◽  
Peter F. Andersen
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter

Improving numerical forecast accuracy with ensemble Kalman filter and chaos theory: Case study on Ciliwung river model

2014 ◽  
Vol 512 ◽  
pp. 540-548 ◽  
Author(s):  
Yabin Sun ◽  
Chi Dung Doan ◽  
Anh Tuan Dao ◽  
Jiandong Liu ◽  
Shie-Yui Liong
Keyword(s):  
Kalman Filter ◽  
Chaos Theory ◽  
Ensemble Kalman Filter ◽  
Forecast Accuracy ◽  
Numerical Forecast

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 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.

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