Assimilation of Simulated Doppler Radar Observations with an Ensemble Kalman Filter*

2003 ◽  
Vol 131 (8) ◽  
pp. 1663-1677 ◽  
Author(s):  
Chris Snyder ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Radial Velocity ◽  
Ensemble Kalman Filter ◽  
Doppler Radar ◽  
Weather Prediction ◽  
Forecast Model ◽  
Forecast Errors ◽  
Radar Observations ◽  
Cloud Models ◽  
Reference Simulation

Abstract Assimilation of Doppler radar data into cloud models is an important obstacle to routine numerical weather prediction for convective-scale motions; the difficulty lies in initializing fields of wind, temperature, moisture, and condensate given only observations of radial velocity and reflectivity from the radar. This paper investigates the potential of the ensemble Kalman filter (EnKF), which estimates the covariances between observed variables and the state through an ensemble of forecasts, to assimilate radar observations at convective scales. In the basic experiment, simulated observations are extracted from a reference simulation of a splitting supercell and assimilated using the EnKF and the same numerical model that produced the reference simulation. The EnKF produces accurate analyses, including the unobserved variables, after roughly 30 min (or six scans) of radial velocity observations. Additional experiments, in which forecasts are made from the ensemble-mean analysis, reveal that forecast errors grow significantly in this simple system, so that the ability of the EnKF to track the reference solution is not simply because of stable system dynamics. It is also found that the covariances between radial velocity and temperature, moisture, and condensate are important to the quality of the analyses, as is the initialization chosen for the ensemble members prior to assimilating the first observations. These results are promising, especially given the ease of implementing the EnKF. A number of important issues remain, however, including the initialization of the ensemble prior to the first observation, the treatment of uncertainty in the environmental sounding, the role of error in the forecast model (particularly the microphysical parameterizations), and the treatment of lateral boundary conditions.

Cloud-Resolving Hurricane Initialization and Prediction through Assimilation of Doppler Radar Observations with an Ensemble Kalman Filter

2009 ◽  
Vol 137 (7) ◽  
pp. 2105-2125 ◽  
Author(s):  
Fuqing Zhang ◽  
Yonghui Weng ◽  
Jason A. Sippel ◽  
Zhiyong Meng ◽  
Craig H. Bishop
Keyword(s):  
Kalman Filter ◽  
Radial Velocity ◽  
Ensemble Kalman Filter ◽  
Doppler Radar ◽  
Gulf Coast ◽  
Radar Data ◽  
The United States ◽  
Radar Observations ◽  
Probabilistic Forecasts ◽  
Rapid Formation

This study explores the assimilation of Doppler radar radial velocity observations for cloud-resolving hurricane analysis, initialization, and prediction with an ensemble Kalman filter (EnKF). The case studied is Hurricane Humberto (2007), the first landfalling hurricane in the United States since the end of the 2005 hurricane season and the most rapidly intensifying near-landfall storm in U.S. history. The storm caused extensive damage along the southeast Texas coast but was poorly predicted by operational models and forecasters. It is found that the EnKF analysis, after assimilating radial velocity observations from three Weather Surveillance Radars-1988 Doppler (WSR-88Ds) along the Gulf coast, closely represents the best-track position and intensity of Humberto. Deterministic forecasts initialized from the EnKF analysis, despite displaying considerable variability with different lead times, are also capable of predicting the rapid formation and intensification of the hurricane. These forecasts are also superior to simulations without radar data assimilation or with a three-dimensional variational scheme assimilating the same radar observations. Moreover, nearly all members from the ensemble forecasts initialized with EnKF analysis perturbations predict rapid formation and intensification of the storm. However, the large ensemble spread of peak intensity, which ranges from a tropical storm to a category 2 hurricane, echoes limited predictability in deterministic forecasts of the storm and the potential of using ensembles for probabilistic forecasts of hurricanes.

scholarly journals Ensemble Kalman Filter Assimilation of Doppler Radar Data with a Compressible Nonhydrostatic Model: OSS Experiments

2005 ◽  
Vol 133 (7) ◽  
pp. 1789-1807 ◽  
Author(s):  
Mingjing Tong ◽  
Ming Xue
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Radial Velocity ◽  
Ensemble Kalman Filter ◽  
Doppler Radar ◽  
Radar Data ◽  
Relative Role ◽  
Doppler Radar Data ◽  
Ice Microphysics ◽  
Reflectivity Data

Abstract A Doppler radar data assimilation system is developed based on an ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, it is assumed that the forward models are perfect and that the radar data are sampled at the analysis grid points. A general purpose nonhydrostatic compressible model is used with the inclusion of complex multiclass ice microphysics. New aspects of this study compared to previous work include the demonstration of the ability of the EnKF method to retrieve multiple microphysical species associated with a multiclass ice microphysics scheme, and to accurately retrieve the wind and thermodynamic variables. Also new are the inclusion of reflectivity observations and the determination of the relative role of the radial velocity and reflectivity data as well as their spatial coverage in recovering the full-flow and cloud fields. In general, the system is able to reestablish the model storm extremely well after a number of assimilation cycles, and best results are obtained when both radial velocity and reflectivity data, including reflectivity information outside of the precipitation regions, are used. Significant positive impact of the reflectivity assimilation is found even though the observation operator involved is nonlinear. The results also show that a compressible model that contains acoustic modes, hence the associated error growth, performs at least as well as an anelastic model used in previous EnKF studies at the cloud scale. Flow-dependent and dynamically consistent background error covariances estimated from the forecast ensemble play a critical role in successful assimilation and retrieval. When the assimilation cycles start from random initial perturbations, better results are obtained when the updating of the fields that are not directly related to radar reflectivity is withheld during the first few cycles. In fact, during the first few cycles, the updating of the variables indirectly related to reflectivity hurts the analysis. This is so because the estimated background covariances are unreliable at this stage of the data assimilation process, which is related to the way the forecast ensemble is initialized. Forecasts of supercell storms starting from the best-assimilated initial conditions are shown to remain very good for at least 2 h.

Assimilating Airborne Doppler Radar Observations with an Ensemble Kalman Filter for Convection-Permitting Hurricane Initialization and Prediction: Katrina (2005)

2012 ◽  
Vol 140 (3) ◽  
pp. 841-859 ◽  
Author(s):  
Yonghui Weng ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Hurricane Katrina ◽  
Ensemble Kalman Filter ◽  
Airborne Radar ◽  
Track Forecast ◽  
Forecast Errors ◽  
Radar Observations ◽  
Uncertainty Estimates ◽  
Hurricane Track ◽  
The Impact

Abstract Through a Weather Research and Forecasting model (WRF)-based ensemble Kalman filter (EnKF) data assimilation system, the impact of assimilating airborne radar observations for the convection-permitting analysis and prediction of Hurricane Katrina (2005) is examined in this study. A forecast initialized from EnKF analyses of airborne radar observations had substantially smaller hurricane track forecast errors than NOAA’s operational forecasts and a control forecast initialized from NCEP analysis data for lead times up to 120 h. Verifications against independent in situ and remotely sensed observations show that EnKF analyses successfully depict the inner-core structure of the hurricane vortex in terms of both dynamic (wind) and thermodynamic (temperature and moisture) fields. In addition to the improved analyses and deterministic forecast, an ensemble of forecasts initiated from the EnKF analyses also provided forecast uncertainty estimates for the hurricane track and intensity. Also documented here are the details of a series of data thinning and quality control procedures that were developed to generate superobservations from large volumes of airborne radial velocity measurements. These procedures have since been implemented operationally on the NOAA hurricane reconnaissance aircraft that allows for more efficient real-time transmission of airborne radar observations to the ground.

scholarly journals A Comparison between the 4DVAR and the Ensemble Kalman Filter Techniques for Radar Data Assimilation

2005 ◽  
Vol 133 (11) ◽  
pp. 3081-3094 ◽  
Author(s):  
A. Caya ◽  
J. Sun ◽  
C. Snyder
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Forecast Model ◽  
Radar Data ◽  
Forecast Errors ◽  
Error Covariance ◽  
Convective Scale ◽  
Cloud Resolving Model ◽  
Comparable Accuracy

Abstract A four-dimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloud-resolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assumption of a perfect forecast model. Overall, both assimilation schemes perform well and are able to recover the supercell with comparable accuracy, given radial-velocity and reflectivity observations where rain was present. 4DVAR produces generally better analyses than the EnKF given observations limited to a period of 10 min (or three volume scans), particularly for the wind components. In contrast, the EnKF typically produces better analyses than 4DVAR after several assimilation cycles, especially for model variables not functionally related to the observations. The advantages of the EnKF in later cycles arise at least in part from the fact that the 4DVAR scheme implemented here does not use a forecast from a previous cycle as background or evolve its error covariance. Possible reasons for the initial advantage of 4DVAR are deficiencies in the initial ensemble used by the EnKF, the temporal smoothness constraint used in 4DVAR, and nonlinearities in the evolution of forecast errors over the assimilation window.

scholarly journals Examination of Analysis and Forecast Errors of High-Resolution Assimilation, Bias Removal, and Digital Filter Initialization with an Ensemble Kalman Filter

2012 ◽  
Vol 140 (12) ◽  
pp. 3992-4004 ◽  
Author(s):  
Brian C. Ancell
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Digital Filter ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Surface Wind ◽  
Forecast Errors ◽  
Temperature Bias ◽  
High Resolution Analysis ◽  
Bias Removal

Abstract Mesoscale atmospheric data assimilation is becoming an integral part of numerical weather prediction. Modern computational resources now allow assimilation and subsequent forecasting experiments ranging from resolutions of tens of kilometers over regional domains to smaller grids that employ storm-scale assimilation. To assess the value of the high-resolution capabilities involved with assimilation and forecasting at different scales, analyses and forecasts must be carefully evaluated to understand 1) whether analysis benefits gained at finer scales persist into the forecast relative to downscaled runs begun from lower-resolution analyses, 2) how the positive analysis effects of bias removal evolve into the forecast, and 3) how digital filter initialization affects analyses and forecasts. This study applies a 36- and 4-km ensemble Kalman filter over 112 assimilation cycles to address these important issues, which could all be relevant to a variety of short-term, high-resolution, real-time forecasting applications. It is found that with regard to surface wind and temperature, analysis improvements gained at higher resolution persist throughout the 12-h forecast window relative to downscaled, high-resolution forecasts begun from analyses on the coarser grid. Aloft, however, no forecast improvements were found with the high-resolution analysis/forecast runs. Surface wind and temperature bias removal, while clearly improving surface analyses, degraded surface forecasts and showed little forecast influence aloft. Digital filter initialization degraded temperature analyses with or without bias removal, degraded wind analyses when bias removal was used, but improved wind analyses when bias removal was absent. No forecast improvements were found with digital filter initialization. The consequences of these results with regard to operational assimilation/forecasting systems on nested grids are discussed.

scholarly journals Determining Key Model Parameters of Rapidly Intensifying Hurricane Guillermo (1997) Using the Ensemble Kalman Filter

2012 ◽  
Vol 69 (11) ◽  
pp. 3147-3171 ◽  
Author(s):  
Humberto C. Godinez ◽  
Jon M. Reisner ◽  
Alexandre O. Fierro ◽  
Stephen R. Guimond ◽  
Jim Kao
Keyword(s):  
Kalman Filter ◽  
Latent Heat ◽  
Ensemble Kalman Filter ◽  
Wind Shear ◽  
Doppler Radar ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Radar Observations ◽  
The Impact ◽  
Dual Doppler Radar

Abstract In this work the authors determine key model parameters for rapidly intensifying Hurricane Guillermo (1997) using the ensemble Kalman filter (EnKF). The approach is to utilize the EnKF as a tool only to estimate the parameter values of the model for a particular dataset. The assimilation is performed using dual-Doppler radar observations obtained during the period of rapid intensification of Hurricane Guillermo. A unique aspect of Guillermo was that during the period of radar observations strong convective bursts, attributable to wind shear, formed primarily within the eastern semicircle of the eyewall. To reproduce this observed structure within a hurricane model, background wind shear of some magnitude must be specified and turbulence and surface parameters appropriately specified so that the impact of the shear on the simulated hurricane vortex can be realized. To identify the complex nonlinear interactions induced by changes in these parameters, an ensemble of model simulations have been conducted in which individual members were formulated by sampling the parameters within a certain range via a Latin hypercube approach. The ensemble and the data, derived latent heat and horizontal winds from the dual-Doppler radar observations, are utilized in the EnKF to obtain varying estimates of the model parameters. The parameters are estimated at each time instance, and a final parameter value is obtained by computing the average over time. Individual simulations were conducted using the estimates, with the simulation using latent heat parameter estimates producing the lowest overall model forecast error.

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 A Global Carbon Assimilation System using a modified EnKF assimilation method

2014 ◽  
Vol 7 (5) ◽  
pp. 6519-6547
Author(s):  
S. Zhang ◽  
X. Zheng ◽  
Z. Chen ◽  
B. Dan ◽  
J. M. Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Carbon Assimilation ◽  
Terrestrial Ecosystem ◽  
Carbon Fluxes ◽  
Ecosystem Model ◽  
Atmospheric Co2 ◽  
Forecast Errors ◽  
Global Carbon ◽  
Assimilation System

Abstract. A Global Carbon Assimilation System based on Ensemble Kalman filter (GCAS-EK) is developed for assimilating atmospheric CO2 abundance data into an ecosystem model to simultaneously estimate the surface carbon fluxes and atmospheric CO2 distribution. This assimilation approach is based on the ensemble Kalman filter (EnKF), but with several new developments, including using analysis states to iteratively estimate ensemble forecast errors, and a maximum likelihood estimation of the inflation factors of the forecast and observation errors. The proposed assimilation approach is tested in observing system simulation experiments and then used to estimate the terrestrial ecosystem carbon fluxes and atmospheric CO2 distributions from 2002 to 2008. The results showed that this assimilation approach can effectively reduce the biases and uncertainties of the carbon fluxes simulated by the ecosystem model.

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