Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part I: Spatially Homogeneous and Isotropic Gaussian Covariances

Purser, Robert James; Wu, Wanru; Parrish, David; Roberts, Nigel

doi:10.1175//1520-0493(2003)131<1524:naotao>2.0.co;2

Cited by 216 publications

(143 citation statements)

References 21 publications

Supporting

Mentioning

143

Contrasting

Order By: Relevance

“…The 3DVAR was designed especially for the storm-scale assimilation of radial wind observations from multiple radars for input into the Advanced Regional Prediction System (ARPS; Xue et al 2000Xue et al , 2001Xue et al , 2003. It uses a recursive filter (Purser et al 2003), with a mass continuity equation and other constraints incorporated into a cost function, yielding physically consistent three-dimensional analyses of the wind components and other model variables. However, because model forecasts are not involved in this study, the ARPS model itself is not used.…”

Section: A Brief Description Of the 3dvar System Setupmentioning

confidence: 99%

Examination of a Real-Time 3DVAR Analysis System in the Hazardous Weather Testbed

Smith

Gao

Calhoun

et al. 2014

Weather and Forecasting

View full text Add to dashboard Cite

Forecasters and research meteorologists tested a real-time three-dimensional variational data assimilation (3DVAR) system in the Hazardous Weather Testbed during the springs of 2010-12 to determine its capabilities to assist in the warning process for severe storms. This storm-scale system updates a dynamically consistent three-dimensional wind field every 5 min, with horizontal and average vertical grid spacings of 1 km and 400 m, respectively. The system analyzed the life cycles of 218 supercell thunderstorms on 27 event days during these experiments, producing multiple products such as vertical velocity, vertical vorticity, and updraft helicity. These data are compared to multiradar-multisensor data from the Warning Decision Support System-Integrated Information to document the performance characteristics of the system, such as how vertical vorticity values compare to azimuthal shear fields calculated directly from Doppler radial velocity. Data are stratified by range from the nearest radar, as well as by the number of radars entering into the analysis of a particular storm. The 3DVAR system shows physically realistic trends of updraft speed and vertical vorticity for a majority of cases. Improvements are needed to better estimate the near-surface winds when no radar is nearby and to improve the timeliness of the input data. However, the 3DVAR wind field information provides an integrated look at storm structure that may be of more use to forecasters than traditional radar-based proxies used to infer severe weather potential.

show abstract

Section: A Brief Description Of the 3dvar System Setupmentioning

confidence: 99%

Examination of a Real-Time 3DVAR Analysis System in the Hazardous Weather Testbed

Smith

Gao

Calhoun

et al. 2014

Weather and Forecasting

View full text Add to dashboard Cite

show abstract

“…The full F is too large to compute directly, and assumptions and approximations are made to simplify the calculation of F. Huang (2000) demonstrated that the effects of applying the operator F on the control variable q in (4) can be achieved through the use of equivalent spatial filters. We follow the methodology in Purser et al (2003) by assuming that the error covariance matrix B is isotropic and homogeneous, and recursive filters are applied to the control variables to model the effects of F as…”

Section: A Background Termmentioning

confidence: 99%

Short-Term Forecasting of a Midlatitude Convective Storm by the Assimilation of Single–Doppler Radar Observations

Chung

Zawadzki

Yau

et al. 2009

Monthly Weather Review

View full text Add to dashboard Cite

The McGill University radar data assimilation system is used to initialize a convective storm at high resolution (1 km) from single-Doppler radar observations. In this study, the background term in the assimilation system is improved. Specifically, by assuming the correlation of the errors of the control variables to be isotropic and homogeneous, the background error covariance matrix is modeled by a recursive filter. In addition, a 3-h-prior high-resolution model forecast is used as the background field. The analysis fields from the assimilation system successfully trigger the convective storms in the radar-observed regions from a single assimilation window. Without data assimilation, the modeled storms did not occur at the right time and place. To account for the rapid evolution of the convective storms and to correct the forecast errors with time, a cycling process is applied for a very short-term forecast. It is found that the first assimilation window can maintain the prediction of the storms for less than 1 h. The cycling process helps to maintain the intensity of the storm cells for a longer period of time. However, a comparison of radar observations with the 90-min simulation indicates an error in the position of the convective cells. The error of the radial component of the wind field between the observation and the simulation is larger at the upper levels. A wavelet analysis between the observation and simulated reflectivities indicates that the forecast is able to adequately predict the convective scale (;10-20 km) during the first 20 min, whereas the simulation has more predictability at the longer scale (.30 km) beyond 20 min.

show abstract

“…Here we assume that the background errors in u and v are uncorrelated, and the spatial error covariances are assumed Gaussian and modeled using a recursive spatial filter (Hayden and Purser 1995;Purser et al 2003;Gao et al 2004b;Liu and Xue 2006). The diagonal elements of B are the error variances of the background field.…”

Section: B Variational Wind Analysismentioning

confidence: 99%

Variational Analysis of Oversampled Dual-Doppler Radial Velocity Data and Application to the Analysis of Tornado Circulations

Xue

Liu

2007

Journal of Atmospheric and Oceanic Technology

View full text Add to dashboard Cite

For the detection of severe weather phenomena such as tornados, mesocyclones, and strong wind shear, the azimuthal resolution of radial velocity measurements is more important. The typical azimuthal resolutions of 1°for the Weather Surveillance Radar-1988 Doppler (WSR-88D) radars and of 2°for the planned Center for Collaborative Adaptive Sensing of Atmosphere (CASA) radars are not sufficient for this purpose, especially at far ranges. Oversampling is one strategy that can potentially provide more details about the azimuthal structures of flows, and can be achieved by processing raw data at azimuthal increments smaller than the radar beamwidth. In the presence of dual-Doppler observations, the variational method can be used to effectively recover subbeamwidth structures from these oversampled data, which, combined with the typically higher range resolutions, can provide high-resolution wind analyses that are valuable for, for example, tornado detection. This idea is tested in this paper using simulated data as well as reprocessed level-I data from a research WSR-88D radar, for model-simulated and actually observed tornadoes, respectively. The results confirm that much more detailed, often subbeamwidth, flow structures can indeed be recovered through azimuthal oversampling and a properly configured variational analysis, and the detailed flow analysis is expected to significantly improve one's ability in identifying small-scale features such as tornadoes from radial velocity observations.

show abstract

Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part I: Spatially Homogeneous and Isotropic Gaussian Covariances

Cited by 216 publications

References 21 publications

Examination of a Real-Time 3DVAR Analysis System in the Hazardous Weather Testbed

Examination of a Real-Time 3DVAR Analysis System in the Hazardous Weather Testbed

Short-Term Forecasting of a Midlatitude Convective Storm by the Assimilation of Single–Doppler Radar Observations

Variational Analysis of Oversampled Dual-Doppler Radial Velocity Data and Application to the Analysis of Tornado Circulations

Contact Info

Product

Resources

About