Assimilation of Simulated Polarimetric Radar Data for a Convective Storm Using the Ensemble Kalman Filter. Part II: Impact of Polarimetric Data on Storm Analysis
TL;DR: In this paper, a data assimilation system based on the ensemble square-root Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables.
Abstract: A data assimilation system based on the ensemble square-root Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables. It is used to assess the impact of assimilating additional polarimetric observations on convective storm analysis in the Observing System Simulation Experiment (OSSE) framework. The polarimetric variables considered include differential reflectivity ZDR, reflectivity difference Zdp, and specific differential phase KDP. To simulate the observational data more realistically, a new error model is introduced for characterizing the errors of the nonpolarimetric and polarimetric radar variables. The error model includes both correlated and uncorrelated error components for reflectivities at horizontal and vertical polarizations (ZH and ZV, respectively). It is shown that the storm analysis is improved when polarimetric variables are assimilated in addition to ZH or in addition to both ZH and radial velocity Vr. Positive impact ...
Citations
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01 Apr 2003
TL;DR: The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it as mentioned in this paper, and also presents new ideas and alternative interpretations which further explain the success of the EnkF.
Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
2,975 citations
TL;DR: In this article, the authors proposed a new warning paradigm in which numerical model forecasts play a larger role in convective-scale warnings, shifting the warning process from warn on detection to warn on forecast, which has the potential to dramatically increase warning lead times.
Abstract: The National Oceanic and Atmospheric Administration's (NOAA's) National Weather Service (NWS) issues warnings for severe thunderstorms, tornadoes, and flash floods because these phenomena are a threat to life and property. These warnings are presently based upon either visual confirmation of the phenomena or the observational detection of proxy signatures that are largely based upon radar observations. Convective-scale weather warnings are unique in the NWS, having little reliance on direct numerical forecast guidance. Because increasing severe thunderstorm, tornado, and flash-flood warning lead times are a key NOAA strategic mission goal designed to reduce the loss of life, injury, and economic costs of these high-impact weather phenomena, a new warning paradigm is needed in which numerical model forecasts play a larger role in convective-scale warnings. This new paradigm shifts the warning process from warn on detection to warn on forecast, and it has the potential to dramatically increase warning lead ...
306 citations
TL;DR: In this article, a 50-member ensemble was produced by randomly perturbing base-state wind profiles and by regularly adding random local perturbations to the horizontal wind, temperature, and water vapor fields in and near observed precipitation.
Abstract: Ensemble Kalman filter (EnKF) techniques have been proposed for obtaining atmospheric state estimates on the scale of individual convective storms from radar and other observations, but tests of these methods with observations of real convective storms are still very limited. In the current study, radar observations of the 8 May 2003 Oklahoma City tornadic supercell thunderstorm were assimilated into the National Severe Storms Laboratory (NSSL) Collaborative Model for Multiscale Atmospheric Simulation (NCOMMAS) with an EnKF method. The cloud model employed 1-km horizontal grid spacing, a single-moment bulk precipitation-microphysics scheme, and a base state initialized with sounding data. A 50-member ensemble was produced by randomly perturbing base-state wind profiles and by regularly adding random local perturbations to the horizontal wind, temperature, and water vapor fields in and near observed precipitation. In a reference experiment, only Doppler-velocity observations were assimilated into ...
193 citations
TL;DR: In this article, a radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed.
Abstract: A radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed. This simulator serves as a test bed for developing and testing forward observation operators of polarimetric radar variables that are needed when directly assimilating these variables into storm-scale numerical weather prediction (NWP) models, using either variational or ensemble-based assimilation methods. The simulator takes as input the results of high-resolution NWP model simulations with ice microphysics and produces simulated polarimetric radar data that may also contain simulated errors. It is developed based on calculations of electromagnetic wave propagation and scattering at the S band of wavelength 10.7 cm in a hydrometeor-containing atmosphere. The T-matrix method is used for the scattering calculation of raindrops and the Rayleigh scattering approximation is applied to snow and ha...
149 citations
TL;DR: In this paper, an indirect radar reflectivity assimilation scheme has been developed within the Weather Research and Forecasting model three-dimensional data assimilation system (WRF 3D-Var).
Abstract: An indirect radar reflectivity assimilation scheme has been developed within the Weather Research and Forecasting model three-dimensional data assimilation system (WRF 3D-Var). This scheme, instead of assimilating radar reflectivity directly, assimilates retrieved rainwater and estimated in-cloud water vapor. An analysis is provided to show that the assimilation of the retrieved rainwater avoids the linearization error of the Z–qr (reflectivity–rainwater) equation. A new observation operator is introduced to assimilate the estimated in-cloud water vapor. The performance of the scheme is demonstrated by assimilating reflectivity observations into the Rapid Update Cycle data assimilation and forecast system operating at Beijing Meteorology Bureau. Four heavy-rain-producing convective cases that occurred during summer 2009 in Beijing, China, are studied using the newly developed system. Results show that on average the assimilation of reflectivity significantly improves the short-term precipitation f...
147 citations
Cites background or methods from "Assimilation of Simulated Polarimet..."
...…to the convective scale was shown by assimilating simulated or real reflectivity observations (e.g., Dowell et al. 2004, 2011; Tong and Xue 2005, 2008; Xue et al. 2006; Jung et al. 2008; Aksoy et al. * The National Center for Atmospheric Research is sponsored by the National Science Foundation....
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...In EnKF, radar reflectivity is efficient to initialize both model hydrometeors and microphysics parameters associatedwith amicrophysical scheme (Tong andXue 2005, 2008; Jung et al. 2008)....
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References
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TL;DR: In this article, a new sequential data assimilation method is proposed based on Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter.
Abstract: A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble.
4,816 citations
"Assimilation of Simulated Polarimet..." refers methods in this paper
...Currently, the two most promising data assimilation techniques for obtaining the atmospheric initial condition or the best estimate of the atmospheric state are the 4DVAR (Le Dimet and Talagrand 1986; Courtier and Talagrand 1987) and the ensemble Kalman filter (EnKF) method (Evensen 1994; Evensen and Leeuwen 1996; Burgers et al. 1998; Houtekamer and Mitchell 1998; Anderson 2001; Bishop et al. 2001; Whitaker and Hamill 2002; Evensen 2003; Tippett et al. 2003), because of their ability to make effective use of the dynamic model equations and observations distributed in space and time, and to provide the best estimate that is also consistent with the prediction model....
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...…of the atmospheric state are the 4DVAR (Le Dimet and Talagrand 1986; Courtier and Talagrand 1987) and the ensemble Kalman filter (EnKF) method (Evensen 1994; Evensen and Leeuwen 1996; Burgers et al. 1998; Houtekamer and Mitchell 1998; Anderson 2001; Bishop et al. 2001; Whitaker and Hamill…...
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TL;DR: A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias, and an ensemble based optimal interpolation scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications.
Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
3,403 citations
01 Apr 2003
TL;DR: The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it as mentioned in this paper, and also presents new ideas and alternative interpretations which further explain the success of the EnkF.
Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
2,975 citations
Book•
01 Jan 1971
TL;DR: This article reviewed the principles of Doppler radar and emphasized the quantitative measurement of meteorological parameters, and illustrated the relation of radar data and images to atmospheric phenomena such as tornadoes, microbursts, waves, turbulence, density currents, hurricanes, and lightning.
Abstract: This book reviews the principles of Doppler radar and emphasizes the quantitative measurement of meteorological parameters. It illustrates the relation of Doppler radar data and images to atmospheric phenomena such as tornadoes, microbursts, waves, turbulence, density currents, hurricanes, and lightning.
Geared toward upper-level undergraduates and graduate students, this text was written by two scientists at the National Severe Storms Laboratory in Norman, Oklahoma, a division of the National Oceanic and Atmospheric Administration. Topics include electromagnetic waves and propagation, weather signals and their Doppler spectra, weather signal processing, measurements of precipitation and turbulence, and observations of winds and storms as well as fair weather. Radar images and photographs of weather phenomena highlight the text.
2,178 citations
TL;DR: In this article, the authors proposed an ensemble Kalman filter for data assimilation using the flow-dependent statistics calculated from an ensemble of short-range forecasts (a technique referred to as Ensemble Kalman filtering) in an idealized environment.
Abstract: The possibility of performing data assimilation using the flow-dependent statistics calculated from an ensemble of short-range forecasts (a technique referred to as ensemble Kalman filtering) is examined in an idealized environment. Using a three-level, quasigeostrophic, T21 model and simulated observations, experiments are performed in a perfect-model context. By using forward interpolation operators from the model state to the observations, the ensemble Kalman filter is able to utilize nonconventional observations. In order to maintain a representative spread between the ensemble members and avoid a problem of inbreeding, a pair of ensemble Kalman filters is configured so that the assimilation of data using one ensemble of shortrange forecasts as background fields employs the weights calculated from the other ensemble of short-range forecasts. This configuration is found to work well: the spread between the ensemble members resembles the difference between the ensemble mean and the true state, except in the case of the smallest ensembles. A series of 30-day data assimilation cycles is performed using ensembles of different sizes. The results indicate that (i) as the size of the ensembles increases, correlations are estimated more accurately and the root-meansquare analysis error decreases, as expected, and (ii) ensembles having on the order of 100 members are sufficient to accurately describe local anisotropic, baroclinic correlation structures. Due to the difficulty of accurately estimating the small correlations associated with remote observations, a cutoff radius beyond which observations are not used, is implemented. It is found that (a) for a given ensemble size there is an optimal value of this cutoff radius, and (b) the optimal cutoff radius increases as the ensemble size increases.
1,827 citations
"Assimilation of Simulated Polarimet..." refers methods in this paper
...Currently, the two most promising data assimilation techniques for obtaining the atmospheric initial condition or the best estimate of the atmospheric state are the 4DVAR (Le Dimet and Talagrand 1986; Courtier and Talagrand 1987) and the ensemble Kalman filter (EnKF) method (Evensen 1994; Evensen and Leeuwen 1996; Burgers et al. 1998; Houtekamer and Mitchell 1998; Anderson 2001; Bishop et al. 2001; Whitaker and Hamill 2002; Evensen 2003; Tippett et al. 2003), because of their ability to make effective use of the dynamic model equations and observations distributed in space and time, and to provide the best estimate that is also consistent with the prediction model....
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...…1986; Courtier and Talagrand 1987) and the ensemble Kalman filter (EnKF) method (Evensen 1994; Evensen and Leeuwen 1996; Burgers et al. 1998; Houtekamer and Mitchell 1998; Anderson 2001; Bishop et al. 2001; Whitaker and Hamill 2002; Evensen 2003; Tippett et al. 2003), because of their…...
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...The filter uses 40 ensemble members and a covariance inflation factor of 15% and a covariance localization radius of 6 km (Anderson 2001; Xue et al. 2005; Houtekamer and Mitchell 1998, 2001; Hamill et al. 2001)....
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