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Xuguang Wang
,
Dale M. Barker
,
Chris Snyder
, and
Thomas M. Hamill

Abstract

A hybrid ensemble transform Kalman filter–three-dimensional variational data assimilation (ETKF–3DVAR) system for the Weather Research and Forecasting (WRF) Model is introduced. The system is based on the existing WRF 3DVAR. Unlike WRF 3DVAR, which utilizes a simple, static covariance model to estimate the forecast-error statistics, the hybrid system combines ensemble covariances with the static covariances to estimate the complex, flow-dependent forecast-error statistics. Ensemble covariances are incorporated by using the extended control variable method during the variational minimization. The ensemble perturbations are maintained by the computationally efficient ETKF. As an initial attempt to test and understand the newly developed system, both an observing system simulation experiment under the perfect model assumption (Part I) and the real observation experiment (Part II) were conducted. In these pilot studies, the WRF was run over the North America domain at a coarse grid spacing (200 km) to emphasize synoptic scales, owing to limited computational resources and the large number of experiments conducted. In Part I, simulated radiosonde wind and temperature observations were assimilated. The results demonstrated that the hybrid data assimilation method provided more accurate analyses than the 3DVAR. The horizontal distributions of the errors demonstrated the hybrid analyses had larger improvements over data-sparse regions than over data-dense regions. It was also found that the ETKF ensemble spread in general agreed with the root-mean-square background forecast error for both the first- and second-order measures. Given the coarse resolution, relatively sparse observation network, and perfect model assumption adopted in this part of the study, caution is warranted when extrapolating the results to operational applications.

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Xuguang Wang
,
Dale M. Barker
,
Chris Snyder
, and
Thomas M. Hamill

Abstract

The hybrid ensemble transform Kalman filter–three-dimensional variational data assimilation (ETKF–3DVAR) system developed for the Weather Research and Forecasting (WRF) Model was further tested with real observations, as a follow-up for the observation system simulation experiment (OSSE) conducted in Part I. A domain encompassing North America was considered. Because of limited computational resources and the large number of experiments conducted, the forecasts and analyses employed relatively coarse grid spacing (200 km) to emphasize synoptic scales. As a first effort to explore the new system with real observations, relatively sparse observation datasets consisting of radiosonde wind and temperature during 4 weeks of January 2003 were assimilated. The 12-h forecasts produced by the hybrid analysis produced less root-mean-square error than the 3DVAR. The hybrid improved the forecast more in the western part of the domain than the eastern part. It also produced larger improvements in the upper troposphere. The overall magnitude of the ETKF ensemble spread agreed with the overall magnitude of the background forecast error. For individual variables and layers, the consistency between the spread and the error was less than the OSSE in Part I. Given the coarse resolution and relatively sparse observation network adopted in this study, caution is warranted when extrapolating these results to operational applications. A case study was also performed to further understand a large forecast improvement of the hybrid during the 4-week period. The flow-dependent adjustments produced by the hybrid extended a large distance into the eastern Pacific data-void region. The much improved analysis and forecast by the hybrid in the data void subsequently improved forecasts downstream in the region of verification. Although no moisture observations were assimilated, the hybrid updated the moisture fields flow dependently through cross-variable covariances defined by the ensemble, which improved the forecasts of cyclone development.

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Soichiro Sugimoto
,
N. Andrew Crook
,
Juanzhen Sun
,
Qingnong Xiao
, and
Dale M. Barker

Abstract

The purpose of this study is to investigate the performance of 3DVAR radar data assimilation in terms of the retrievals of convective fields and their impact on subsequent quantitative precipitation forecasts (QPFs). An assimilation methodology based on the Weather Research and Forecasting (WRF) model three-dimensional variational data assimilation (3DVAR) and a cloud analysis scheme is described. Simulated data from 25 Weather Surveillance Radar-1988 Doppler (WSR-88D) radars are assimilated, and the potential benefits and limitations of the assimilation are quantitatively evaluated through observing system simulation experiments of a dryline that occurred over the southern Great Plains. Results indicate that the 3DVAR system is able to analyze certain mesoscale and convective-scale features through the incorporation of radar observations. The assimilation of all possible data (radial velocity and reflectivity factor data) results in the best performance on short-range precipitation forecasting. The wind retrieval by assimilating radial velocities is of primary importance in the 3DVAR framework and the storm case applied, and the use of multiple-Doppler observations improves the retrieval of the tangential wind component. The reflectivity factor assimilation is also beneficial especially for strong precipitation. It is demonstrated that the improved initial conditions through the 3DVAR analysis lead to improved skills on QPF.

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Mi-Seon Lee
,
Ying-Hwa Kuo
,
Dale M. Barker
, and
Eunha Lim

Abstract

An incremental analysis updates (IAU) technique is implemented for 3-h updates of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) three-dimensional variational data assimilation (3DVAR) and model system with a 10-km resolution to remove spurious gravity waves. By gradually incorporating analysis increments, IAU affects only the removal of high frequencies, leaving the waves related to diurnal processes. IAU appears to be efficient in reducing the moisture spinup problem in the MM5 3DVAR cycling system. The advantage of the IAU is the most significant in improving precipitation forecasts. Rapid update cycle (RUC) with 1- and 2-h intervals in conjunction with the IAU indicates a rapid minimization and less spinup and -down problems because of greater balancing between the moisture and dynamic variables. Impact studies are performed on a heavy rainfall case that occurred in the Korean Peninsula. Verification results with a 3-h cycling system are presented on operational environments.

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Craig H. Bishop
,
Daniel Hodyss
,
Peter Steinle
,
Holly Sims
,
Adam M. Clayton
,
Andrew C. Lorenc
,
Dale M. Barker
, and
Mark Buehner

Abstract

Previous descriptions of how localized ensemble covariances can be incorporated into variational (VAR) data assimilation (DA) schemes provide few clues as to how this might be done in an efficient way. This article serves to remedy this hiatus in the literature by deriving a computationally efficient algorithm for using nonadaptively localized four-dimensional (4D) or three-dimensional (3D) ensemble covariances in variational DA. The algorithm provides computational advantages whenever (i) the localization function is a separable product of a function of the horizontal coordinate and a function of the vertical coordinate, (ii) and/or the localization length scale is much larger than the model grid spacing, (iii) and/or there are many variable types associated with each grid point, (iv) and/or 4D ensemble covariances are employed.

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Qingnong Xiao
,
Ying-Hwa Kuo
,
Zaizhong Ma
,
Wei Huang
,
Xiang-Yu Huang
,
Xiaoyan Zhang
,
Dale M. Barker
,
John Michalakes
, and
Jimy Dudhia

Abstract

The tangent linear and adjoint of an adiabatic version of the Weather Research and Forecasting (WRF) Model with its Advanced Research WRF (ARW) dynamic core have been developed. The source-to-source automatic differentiation tool [i.e., the Transformation of Algorithm (TAF) in FORTRAN] was used in the development. Tangent linear and adjoint checks of the developed adiabatic WRF adjoint modeling system (WAMS) were conducted, and all necessary correctness verification procedures were passed. As the first application, the adiabatic WAMS was used to study the adjoint sensitivity of a severe windstorm in Antarctica. Linearity tests indicated that an adjoint-based sensitivity study with the Antarctic Mesoscale Prediction System (AMPS) 90-km domain configuration for the windstorm is valid up to 24 h. The adjoint-based sensitivity calculation with adiabatic WAMS identified sensitive regions for the improvement of the 24-h forecast of the windstorm. It is indicated that the windstorm forecast largely relies on the model initial conditions in the area from the south part of the Trans-Antarctic Mountains to West Antarctica and between the Ross Ice Shelf and the South Pole. Based on the sensitivity analysis, the southerly or southeasterly wind at lower levels in the sensitivity region should be larger, the cyclone should be stronger, and the atmospheric stratification should be more stable over the north slope of the Trans-Antarctic Mountain to the Ross Ice Shelf, than the AMPS analyses. By constructing pseudo-observations in the sensitivity region using the gradient information of forecast windstorm intensity around McMurdo, the model initial conditions are revised with the WRF three-dimensional variational data assimilation, which leads to significant improvement in the prediction of the windstorm. An adjoint sensitivity study is an efficient way to identify sensitivity regions in order to collect more observations in the region for better forecasts in a specific aspect of interest.

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Xiang-Yu Huang
,
Qingnong Xiao
,
Dale M. Barker
,
Xin Zhang
,
John Michalakes
,
Wei Huang
,
Tom Henderson
,
John Bray
,
Yongsheng Chen
,
Zaizhong Ma
,
Jimy Dudhia
,
Yongrun Guo
,
Xiaoyan Zhang
,
Duk-Jin Won
,
Hui-Chuan Lin
, and
Ying-Hwa Kuo

Abstract

The Weather Research and Forecasting (WRF) model–based variational data assimilation system (WRF-Var) has been extended from three- to four-dimensional variational data assimilation (WRF 4D-Var) to meet the increasing demand for improving initial model states in multiscale numerical simulations and forecasts. The initial goals of this development include operational applications and support to the research community. The formulation of WRF 4D-Var is described in this paper. WRF 4D-Var uses the WRF model as a constraint to impose a dynamic balance on the assimilation. It is shown to implicitly evolve the background error covariance and to produce the flow-dependent nature of the analysis increments. Preliminary results from real-data 4D-Var experiments in a quasi-operational setting are presented and the potential of WRF 4D-Var in research and operational applications are demonstrated. A wider distribution of the system to the research community will further develop its capabilities and to encourage testing under different weather conditions and model configurations.

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