Simultaneous Estimation of Microphysical Parameters and Atmospheric State with Radar Data and Ensemble Square-root Kalman Filter . Part I : Sensitivity Analysis and Parameter

The possibility of estimating fundamental parameters common in single-moment ice microphysics schemes using radar observations is investigated, for a model-simulated supercell storm, by examining parameter sensitivity and identifiability. These parameters include the intercept parameters for rain, snow and hail/graupel, and the bulk densities of snow and hail/graupel. These parameters are closely involved in the definition of drop/particle size distributions of microphysical species but often assume highly uncertain specified values. The sensitivity of pure model forecast as well as model state estimation to the parameter values, and the solution uniqueness of the estimation problem are examined. The ensemble square-root filter (EnSRF) is employed for model state estimation. Both forecast and assimilation sensitivity experiments show that the errors in the microphysical parameters have a larger impact on model microphysical fields than on wind fields; radar reflectivity observations are therefore preferred over those of radial velocity for microphysical parameter estimation. Among the three intercept parameters, the pure forecast is most (least) sensitive to rain (snow) intercept while the sensitivity to hail density is generally lager than that to snow density. The analyzed model state in the assimilation sensitivity experiments is, however, found to be most (least) sensitive to hail (rain) intercept, and there is a larger sensitivity to hail density than to snow density. The time scales of analysis response to errors in individual parameters are also investigated. The results suggest that a successful estimation of the parameters can be expected within the typical lengths of assimilation window needed for state estimation. The response functions calculated for the forecast as well as assimilation sensitivity experiments for all five individual parameters show concave shapes, with unique minima occurring at or very close to the true values; therefore true values of these parameters can be retrieved at least in these cases where only one parameter contains error at a time. The identifiability of multiple parameters together is evaluated from their correlations with forecast reflectivity. Significant levels of correlations are found that can be interpreted physically. As the number of uncertain parameters increases, both the level and the area coverage of significant correlations decrease, implying increased difficulties with multiple-parameter estimation. The details of the estimation procedure and the results of a complete set of estimation experiments will be presented in Part II of this paper. _____________________________

[1]  Peter V. Hobbs,et al.  The Mesoscale and Microscale Structure and Organization of Clouds and Precipitation in Midlatitude Cyclones. XII: A Diagnostic Modeling Study of Precipitation Development in Narrow Cold-Frontal Rainbands , 1984 .

[2]  Craig H. Bishop,et al.  Adaptive sampling with the ensemble transform Kalman filter , 2001 .

[3]  D. Short,et al.  Evidence from Tropical Raindrop Spectra of the Origin of Rain from Stratiform versus Convective Clouds , 1996 .

[4]  S. Rutledge,et al.  The Mesoscale and Microscale Structure and Organization of Clouds and Precipitation in Midlatitude Cyclones. VIII: A Model for the “Seeder-Feeder” Process in Warm-Frontal Rainbands , 1983 .

[5]  Nolan J. Doesken,et al.  Density of Freshly Fallen Snow in the Central Rocky Mountains , 2000 .

[6]  Jean-Pierre Pinty,et al.  A comprehensive two‐moment warm microphysical bulk scheme. I: Description and tests , 2000 .

[7]  G. Evensen Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[8]  William W.-G. Yeh,et al.  Coupled inverse problems in groundwater modeling: 2. Identifiability and experimental design , 1990 .

[9]  Roscoe R. Braham Snow Particle Size Spectra in Lake Effect Snows. , 1990 .

[10]  Mingjing Tong,et al.  An OSSE Framework Based on the Ensemble Square Root Kalman Filter for Evaluating the Impact of Data from Radar Networks on Thunderstorm Analysis and Forecasting , 2006 .

[11]  S. Yakowitz,et al.  Instability in aquifer identification: Theory and case studies , 1980 .

[12]  B. Ferrier,et al.  A Double-Moment Multiple-Phase Four-Class Bulk Ice Scheme. Part I: Description , 1994 .

[13]  Louis J. Wicker,et al.  Wind and Temperature Retrievals in the 17 May 1981 Arcadia, Oklahoma, Supercell: Ensemble Kalman Filter Experiments , 2004 .

[14]  Erik N. Rasmussen,et al.  Precipitation Uncertainty Due to Variations in Precipitation Particle Parameters within a Simple Microphysics Scheme , 2004 .

[15]  Joanne Simpson,et al.  Comparison of Ice-Phase Microphysical Parameterization Schemes Using Numerical Simulations of Tropical Convection , 1991 .

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

[17]  J. Whitaker,et al.  Ensemble Data Assimilation without Perturbed Observations , 2002 .

[18]  Ionel Michael Navon,et al.  Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography , 1998 .

[19]  G. Chavent Identification of Distributed Parameter Systems: About the Output Least Square Method, its Implementation, and Identifiability , 1979 .

[20]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[21]  Conrad L. Ziegler,et al.  Retrieval of Thermal and Microphysical Variables in Observed Convective Storms. , 1985 .

[22]  H. D. Orville,et al.  Bulk Parameterization of the Snow Field in a Cloud Model , 1983 .

[23]  P. Courtier,et al.  Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. Ii: Numerical Results , 2007 .

[24]  E. Mansell,et al.  A Bulk Microphysics Parameterization with Multiple Ice Precipitation Categories , 2005 .

[25]  P. Houtekamer,et al.  Data Assimilation Using an Ensemble Kalman Filter Technique , 1998 .

[26]  Richard E. Passarelli,et al.  Theoretical and Observational Study of Snow-Size Spectra and Snowflake Aggregation Efficiencies , 1978 .

[27]  Juanzhen Sun,et al.  Impacts of Initial Estimate and Observation Availability on Convective-Scale Data Assimilation with an Ensemble Kalman Filter , 2004 .

[28]  J. Marshall,et al.  THE DISTRIBUTION WITH SIZE OF AGGREGATE SNOWFLAKES , 1958 .

[29]  Kenneth S. Gage,et al.  Drop-Size Distribution Characteristics in Tropical Mesoscale Convective Systems , 2000 .

[30]  J. Klett,et al.  Microphysics of Clouds and Precipitation , 1978, Nature.

[31]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[32]  Evolution of Snow-Size Spectra in Cyclonic Storms. Part I: Snow Growth by Vapor Deposition and Aggregation , 1988 .

[33]  K. K. Lo,et al.  The Growth of Snow in Winter Storms:. An Airborne Observational Study , 1982 .

[34]  A. Waldvogel,et al.  Raindrop Size Distribution and Sampling Size Errors , 1969 .

[35]  M. Xue,et al.  The Advanced Regional Prediction System (ARPS) – A multi-scale nonhydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applications , 2001 .

[36]  M. Murakami,et al.  Numerical Modeling of Dynamical and Microphysical Evolution of an Isolated Convective Cloud , 1990 .

[37]  J. Whitaker,et al.  Ensemble Square Root Filters , 2003, Statistical Methods for Climate Scientists.

[38]  Mingjing Tong,et al.  Ensemble kalman filter assimilation of doppler radar data with a compressible nonhydrostatic model : OSS experiments , 2005 .

[39]  G. Chavent Identification of functional parameters in partial differential equations , 1974 .

[40]  Jeffrey L. Anderson An Ensemble Adjustment Kalman Filter for Data Assimilation , 2001 .

[41]  J. Gamache,et al.  Diagnosis of Cloud Mass and Heat Fluxes from Radar and Synoptic Data , 1980 .

[42]  W. Yeh Review of Parameter Identification Procedures in Groundwater Hydrology: The Inverse Problem , 1986 .

[43]  S. Nakagiri,et al.  Identifiability of Spatially-Varying and Constant Parameters in Distributed Systems of Parabolic Type , 1977 .

[44]  D. Parsons,et al.  Size Distributions of Precipitation Particles in Frontal Clouds. , 1979 .

[45]  K. Droegemeier,et al.  The Advanced Regional Prediction System (ARPS) – A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification , 2000 .

[46]  G. Evensen,et al.  Analysis Scheme in the Ensemble Kalman Filter , 1998 .

[47]  M. Yau,et al.  A Multimoment Bulk Microphysics Parameterization. Part II: A Proposed Three-Moment Closure and Scheme Description , 2005 .

[48]  Fuqing Zhang,et al.  Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model , 2006 .

[49]  C. Snyder,et al.  Assimilation of Simulated Doppler Radar Observations with an Ensemble Kalman Filter , 2003 .

[50]  Mingjing Tong,et al.  Simultaneous Estimation of Microphysical Parameters and Atmospheric State with Simulated Radar Data and Ensemble Square Root Kalman Filter. Part II: Parameter Estimation Experiments , 2008 .

[51]  A. Waldvogel,et al.  The N0 Jump of Raindrop Spectra , 1974 .

[52]  G. Evensen,et al.  Assimilation of Geosat altimeter data for the Agulhas current using the ensemble Kalman filter with , 1996 .

[53]  N. A. Crook Sensitivity of Moist Convection Forced by Boundary Layer Processes to Low-Level Thermodynamic Fields , 1996 .

[54]  Joanne Simpson,et al.  A Double-Moment Multiple-Phase Four-Class Bulk Ice Scheme. Part II: Simulations of Convective Storms in Different Large-Scale Environments and Comparisons with other Bulk Parameterizations , 1995 .

[55]  Jidong Gao,et al.  The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation , 2003 .

[56]  William R. Cotton,et al.  The Impact of Hail Size on Simulated Supercell Storms , 2004 .