A Three-Dimensional Variational Data Analysis Method with Recursive Filter for Doppler Radars

Abstract In this paper, a new method of dual-Doppler radar wind analysis based on a three-dimensional variational data assimilation (3DVAR) approach is proposed. In it, a cost function, including background term and radial observation term, is minimized through a limited memory, quasi-Newton conjugate-gradient algorithm with the mass continuity equation imposed as a weak constraint. In the method, the background error covariance matrix, though simple in this case, is modeled by a recursive filter. Furthermore, the square root of this matrix is used to precondition the minimization problem. The current method is applied to Doppler radar observation of a supercell storm, and the analysis results are compared to a conceptual model and previous research. It is shown that the horizontal circulations, both within and around the storms, as well as the strong updraft and the associated downdraft, are well analyzed. Because no explicit integration of the anelastic mass continuity equation is involved, error accumu...

[1]  R. Purser,et al.  Three-Dimensional Variational Analysis with Spatially Inhomogeneous Covariances , 2002 .

[2]  R. C. Srivastava,et al.  Doppler radar characteristics of precipitation at vertical incidence , 1973 .

[3]  Philip E. Gill,et al.  Practical optimization , 1981 .

[4]  Alan Shapiro,et al.  New Formulations of Dual-Doppler Wind Analysis , 1999 .

[5]  A. Lorenc.  Iterative analysis using covariance functions and filters , 1992 .

[6]  Xiang-Yu Huang,et al.  Variational Analysis Using Spatial Filters , 2000 .

[7]  Juanzhen Sun,et al.  Dynamical and Microphysical Retrieval from Doppler Radar Observations Using a Cloud Model and Its Adjoint. Part I: Model Development and Simulated Data Experiments. , 1997 .

[8]  Juanzhen Sun,et al.  2 B . 2 INITIALIZATION AND FORECASTING OF THUNDERSTORMS : SPECIFICATION OF RADAR MEASUREMENT ERRORS , 2003 .

[9]  Tammy M. Weckwerth,et al.  Observations of the Sea-Breeze Front during CaPE. Part II: Dual-Doppler and Aircraft Analysis , 1995 .

[10]  J. Testud,et al.  Three-Dimensional Wind Field Analysis from Dual-Doppler Radar Data. Part III: The Boundary Condition: An Optimum Determination Based on a Variational Concept , 1983 .

[11]  K. Wieghardt,et al.  LUDWIG PRANDTL AND HIS KAISER-WILHELM -INSTITUT , 1987 .

[12]  R. James Purser,et al.  Recursive Filter Objective Analysis of Meteorological Fields: Applications to NESDIS Operational Processing , 1995 .

[13]  Jidong Gao,et al.  A Variational Method for the Analysis of Three-Dimensional Wind Fields from Two Doppler Radars , 1999 .

[14]  P. Courtier,et al.  A strategy for operational implementation of 4D‐Var, using an incremental approach , 1994 .

[15]  G. Foote,et al.  Terminal Velocity of Raindrops Aloft , 1969 .

[16]  N. Roberts,et al.  Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part II: Spatially Inhomogeneous and Anisotropic General Covariances , 2003 .

[17]  Edward A. Brandes,et al.  Flow in Severe Thunderstorms Observed bu Dual-Doppler Radar , 1977 .

[18]  R. J. Doviak,et al.  Clear-Air Roll Vortices and Turbulent Motions as Detected with an Airborne Gust Probe and Dual-Doppler Radar , 1981 .

[19]  Yu-Chieng Liou,et al.  SINGLE RADAR RECOVERY OF CROSS-BEAM WIND COMPONENTS USING A MODIFIED MOVING FRAME OF REFERENCE TECHNIQUE , 1999 .

[20]  E. Brandes.  Finestructure of the Del City-Edmond Tornadic Mesocirculation , 1981 .

[21]  Conrad L. Ziegler,et al.  Single- and Multiple-Doppler Radar Observations of Tornadic Storms , 1980 .

[22]  Qin Xu,et al.  Background error covariance functions for Doppler radial‐wind analysis , 2003 .

[23]  David C. Dowell,et al.  The Arcadia, Oklahoma, Storm of 17 May 1981: Analysis of a Supercell during Tornadogenesis , 1997 .

[24]  Richard E. Carbone,et al.  A Severe Frontal Rainband. Part II: Tornado Parent Vortex Circulation , 1983 .

[25]  Peter S. Ray,et al.  Initialization of a modeled convective storm using Doppler radar-derived fields , 1992 .

[26]  T. Gal-Chen,et al.  Errors in fixed and moving frame of references - Applications for conventional and Doppler radar analysis , 1982 .

[27]  Juanzhen Sun,et al.  Dynamical and Microphysical Retrieval from Doppler Radar Observations Using a Cloud Model and Its Adjoint. Part II: Retrieval Experiments of an Observed Florida Convective Storm , 1998 .

[28]  K. A. Browning,et al.  The Determination of Kinematic Properties of a Wind Field Using Doppler Radar , 1968 .

[29]  Peter S. Ray,et al.  The Oklahoma Squall Line of 19 May 1977. Part I: A Multiple Doppler Analysis of Convective and Stratiform Structure , 1987 .

[30]  Philippe Courtier,et al.  Dual formulation of four‐dimensional variational assimilation , 1997 .

[31]  David B. Parsons,et al.  Dynamics and Fine Structure of a Microburst , 1990 .

[32]  Richard J. Doviak,et al.  Dual-Doppler Observation of a Tornadic Storm. , 1975 .

[33]  J. Testud,et al.  Three-Dimensional Wind Field Analysis from Doppler Radar Data , 1983 .

[34]  Conrad L. Ziegler,et al.  Hail Growth in an Oklahoma Multicell Storm , 1983 .

[35]  C. Qiu,et al.  Simple Adjoint Methods for Single-Doppler Wind Analysis with a Strong Constraint of Mass Conservation , 1994 .

[36]  P. Hobbs,et al.  Organization and Structure of Precipitating Cloud Systems , 1982 .

[37]  Thomas Matejka,et al.  The accuracy of vertical air velocities from Doppler radar data , 1998 .

[38]  Ionel M. Navon,et al.  Conjugate-Gradient Methods for Large-Scale Minimization in Meteorology , 1987 .

[39]  C. Doswell,et al.  Severe Thunderstorm Evolution and Mesocyclone Structure as Related to Tornadogenesis , 1979 .

[40]  Andrew C. Lorenc,et al.  Analysis methods for numerical weather prediction , 1986 .

[41]  Joseph B. Klemp,et al.  DYNAMICS OF TORNADIC THUNDERSTORMS , 1987 .

[42]  Robert B. Wilhelmson,et al.  The Morphology of Several Tornadic Storms on 20 May 1977 , 1981 .

[43]  J. Testud,et al.  Three-Dimensional Wind Field Analysis from Dual-Doppler Radar Data. Part II: Minimizing the Error due to Temporal Variation , 1983 .

[44]  Richard J. Doviak,et al.  Error Estimation in Wind Fields Derived from Dual-Doppler Radar Measurement , 1976 .

[45]  L. J. Miller,et al.  A dual doppler radar method for the determination of wind velocities within precipitating weather systems , 1974 .