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2006a: 3DVAR and cloud analysis with WSR88D levelII data for the prediction of Fort Worth tornadic thunderstorms. Part I: Cloud analysis and its
 Mon. Wea. Rev
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Simultaneous Estimation of Microphysical Parameters and Atmospheric State with Simulated Radar Data and Ensemble Square Root Kalman Filter. Part I: Sensitivity Analysis and Parameter Identifiability
 1630 MONTHLY WEATHER REVIEW VOLUME
, 2008
"... The possibility of estimating fundamental parameters common in singlemoment ice microphysics schemes using radar observations is investigated for a modelsimulated supercell storm by examining parameter sensitivity and identifiability. These parameters include the intercept parameters for rain, sn ..."
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Cited by 50 (26 self)
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The possibility of estimating fundamental parameters common in singlemoment ice microphysics schemes using radar observations is investigated for a modelsimulated 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 model forecast within data assimilation cycles to the parameter values, and the issue of solution uniqueness of the estimation problem, are examined. The ensemble square root filter (EnSRF) is employed for model state estimation. 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. The model response time to errors in individual parameters are also investigated. The results suggest that radar data should be used at about 5min intervals for parameter estimation. The response functions calculated from ensemble mean forecasts for all five individual parameters show concave shapes, with unique
A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation
 IN REVIEW
, 2005
"... A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assump ..."
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Cited by 49 (4 self)
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A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assumption of a perfect forecast model. Overall, both assimilation schemes perform well and are able to recover the supercell with comparable accuracy, given radialvelocity and reflectivity observations where rain was present. 4DVAR produces generally better analyses than the EnKF given observations limited to a period of 10 min (or three volume scans), particularly for the wind components. In contrast, the EnKF typically produces better analyses than 4DVAR after several assimilation cycles, especially for model variables not functionally related to the observations. The advantages of the EnKF in later cycles arise at least in part from the fact that the 4DVAR scheme implemented here does not use a forecast from a previous cycle as background or evolve its error covariance. Possible reasons for the initial advantage of 4DVAR are deficiencies in the initial ensemble used by the EnKF, the temporal smoothness constraint used in 4DVAR, and nonlinearities in the evolution of forecast errors over the assimilation window.
Tests of an ensemble Kalman filter for mesoscale and regionalscale data assimilation. Part I: Perfect model experiments.
 Mon. Wea. Rev.,
, 2006
"... ABSTRACT In previous works in this series study, an ensemble Kalman filter (EnKF) was demonstrated to be promising for mesoscale and regionalscale data assimilation in increasingly realistic environments. Parts I and II examined the performance of the EnKF by assimilating simulated observations un ..."
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Cited by 44 (8 self)
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ABSTRACT In previous works in this series study, an ensemble Kalman filter (EnKF) was demonstrated to be promising for mesoscale and regionalscale data assimilation in increasingly realistic environments. Parts I and II examined the performance of the EnKF by assimilating simulated observations under both perfectand imperfectmodel assumptions. Part III explored the application of the EnKF to a realdata case study in comparison to a threedimensional variational data assimilation (3DVAR) method in the Weather Research and Forecasting (WRF) model. The current study extends the singlecase realdata experiments over a period of 1 month to examine the longterm performance and comparison of both methods at the regional scales. It is found that the EnKF systematically outperforms 3DVAR for the 1month period of interest in which both methods assimilate the same standard rawinsonde observations every 12 h over the central United States. Consistent with results from the realdata case study of Part III, the EnKF can benefit from using a multischeme ensemble that partially accounts for model errors in physical parameterizations. The benefit of using a multischeme ensemble (over a singlescheme ensemble) is more pronounced in the thermodynamic variables (including temperature and moisture) than in the wind fields. On average, the EnKF analyses lead to more accurate forecasts than the 3DVAR analyses when they are used to initialize 60 consecutive, deterministic 60h forecast experiments for the month. Results also show that deterministic forecasts of up to 60 h initiated from the EnKF analyses consistently outperform the WRF forecasts initiated from the National Centers for Environmental Prediction final analysis field of the Global Forecast System.
Assimilation of Simulated Polarimetric Radar Data for a Convective Storm Using the Ensemble Kalman Filter. Part I: Observation Operators for Reflectivity and Polarimetric Variables // [Mon.
, 2008
"... Abstract A data assimilation system based on the ensemble squareroot Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables. It is used to assess the impact of simulating additional polarimetric observations on convective storm analysis ..."
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Cited by 44 (31 self)
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Abstract A data assimilation system based on the ensemble squareroot Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables. It is used to assess the impact of simulating additional polarimetric observations on convective storm analysis in an OSSE (Observing System Simulation Experiment) framework. The polarimetric variables considered include differential reflectivity Z DR , reflectivity difference Z dp , and specific differential phase K DP . 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 (Z H and Z V ). It is shown that the storm analysis is improved when polarimetric variables are assimilated in addition to Z H or in addition to both Z H and radial velocity V r . Positive impact is largest when Z DR , Z dp , and K DP are assimilated all together. Improvement is generally larger in vertical velocity, water vapor and rainwater mixing ratios. The rain water field benefits the most while the impacts on horizontal wind components and snow mixing ratios are smaller. Improvement is found at all model levels even though the polarimetric data, after the application of thresholds, are mostly limited to the lower levels. Among Z DR , Z dp , and K DP , Z DR is found to produce the largest positive impact on the analysis. It is suggested that Z DR provides more independent information than the other variables. The impact of polarimetric data is also expected to be larger when they are used to retrieve drop size distribution parameters. This study is believed to be the first to directly assimilate (simulated) polarimetric data into a numerical model. 1
Impact of configurations of rapid intermittent assimilation ofWSR88D radar data for the 8 May 2003 Oklahoma city tornadic thunderstorm case
 Monthly Weather Review
, 2007
"... Abstract Various configurations of the intermittent data assimilation procedure for LevelII WSR88D radar data are examined for the analysis and prediction of a tornadic thunderstorm that occurred on 8 May 2003 near Oklahoma City. Several tornadoes were produced by this thunderstorm, causing exten ..."
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Cited by 41 (32 self)
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Abstract Various configurations of the intermittent data assimilation procedure for LevelII WSR88D radar data are examined for the analysis and prediction of a tornadic thunderstorm that occurred on 8 May 2003 near Oklahoma City. Several tornadoes were produced by this thunderstorm, causing extensive damages in south Oklahoma City area. Within our rapidly cycled assimilation system, the ARPS 3DVAR is employed to analyze conventional and radar radial velocity data, while the ARPS complex cloud analysis procedure is used to analyze cloud and hydrometeor fields and adjust incloud temperature and moisture fields based on reflectivity observations and the preliminary analysis of the atmosphere. Forecasts for up to 2.5 hours are made from the assimilated initial conditions. Two oneway nested grids at 9 and 3 km grid spacings are employed although our assimilation configuration experiments are conducted for the 3km grid only while keeping the 9km grid configuration the same. Data from the Oklahoma City radar are used. Different combinations of the assimilation frequency, incloud temperature adjustment schemes, and the length and coverage of the assimilation window are tested, and the results are discussed with respect to the length and evolution stage of the thunderstorm life cycle. It is found that even though the general assimilation method remains the same, the assimilation settings can significantly impact the results of assimilation and the subsequent forecast. For this case, onehour long assimilation window covering the entire initial development stage of the storm together with a 10minute spinup period before storm initiation works best. Assimilation frequency and incloud temperature adjustment scheme should be set carefully to add suitable amount of potential energy during assimilation. High assimilation frequency dose not necessarily lead to a better result because of the significant adjustment during ii the initial forecast period. When a short assimilation window is used, covering the later part of the initial development stage of storm and using a high assimilation frequency and a temperature adjustment scheme based on latent heat release can quickly build up the storm and produce reasonable analysis and forecast. The results also show that when the data from a single Doppler radar is properly assimilated, even with the current relatively inexpensive procedure, the model is able to predict the evolution of the 8 May 2003 Oklahoma City tornadic thunderstorm well for up to 2.5 hours. The implications of the choices of assimilation settings for realtime applications are discussed. 1
A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part I: Stormscale analyses.” Monthly Weather Review
, 2009
"... The effectiveness of the ensemble Kalman filter (EnKF) for assimilating radar observations at convective scales is investigated for cases whose behaviors span supercellular, linear, andmulticellular organization. The parallel EnKF algorithm of the Data Assimilation Research Testbed (DART) is used fo ..."
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Cited by 31 (4 self)
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The effectiveness of the ensemble Kalman filter (EnKF) for assimilating radar observations at convective scales is investigated for cases whose behaviors span supercellular, linear, andmulticellular organization. The parallel EnKF algorithm of the Data Assimilation Research Testbed (DART) is used for data assimilation, while the Weather Research and Forecasting (WRF)Model is employed as a simplified cloud model at 2km horizontal grid spacing. In each case, reflectivity and radial velocity measurements are utilized from a single Weather Surveillance Radar1988 Doppler (WSR88D) within the U.S. operational network. Observations are assimilated every 2 min for a duration of 60 min and correction of folded radial velocities occurs within the EnKF. Initial ensemble uncertainty includes random perturbations to the horizontal wind components of the initial environmental sounding. The EnKF performs effectively and with robust results across all the cases. Over the first 18–30 min of assimilation, the rms and domainaveraged prior fits to observations in each case improve significantly from their initial levels, reaching comparable values of 3–6 m s21 and 7–10 dBZ. Representation of mesoscale uncertainty, albeit in the simplest form of initial sounding perturbations, is a critical part of the assimilation system, as it increases ensemble spread and improves filter performance. In addition, assimilation of ‘‘no precipitation’ ’ observations (i.e., reflectivity observations with values small enough to indicate the absence of precipitation) serves to suppress spurious convection in ensemble members. At the same time, it is clear that the assimilation is far from optimal, as the ensemble spread is consistently smaller than what would be expected from the innovation statistics and the assumed observationerror variance. 1.
2007: Mesoscale Dynamics
"... 13. Numerical modeling of geophysical fluid systems Chapter 13 Numerical modeling of geophysical fluid systems In the previous chapter, we discussed various numerical approximations of the advection equation. However, to simulate a geophysical fluid system, such as the atmosphere and ocean, within a ..."
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Cited by 20 (4 self)
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13. Numerical modeling of geophysical fluid systems Chapter 13 Numerical modeling of geophysical fluid systems In the previous chapter, we discussed various numerical approximations of the advection equation. However, to simulate a geophysical fluid system, such as the atmosphere and ocean, within a finite region, we need to choose the domain size, grid size, time interval, total integration time, and consider other factors, such as the initial condition and boundary conditions. In addition, when we deal with a real fluid system, the governing equations are much more complicated than the onedimensional, linear advection equation, as considered in the previous chapter. For example, we have to integrate threedimensional nonlinear governing equations with several dependent variables, instead of a onedimensional advection equation with only one variable. When a nonlinear equation is being approximated by numerical methods, one may face new problems such as nonlinear computational instability and nonlinear aliasing. Special numerical techniques are required to avoid these types of problems. Once optimal approximate forms of the equations are selected, it is still necessary to define the domain and grid structure over which the partial differential equations will be approximated. In this chapter, we will also briefly describe on how to build a basic numerical model based on a set of partial differential equations governing a shallow water system, and a hydrostatic or nonhydrostatic continuously stratified fluid system.
2005a: Efficient assimilation of radar data at high resolution for shortrange numerical weather prediction
 World Weather Research Program Symposium on Nowcasting and Very ShortRange Forecasting, WSN05, Tolouse, France, WMO, Symposium CD, Paper 3.06
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A comparison of hybrid ensemble transform Kalman filterOptimum Interpolation and ensemble squareroot filter analysis schemes
, 2007
"... A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A twolayer primitive equation model was used under perfectmodel assumptions. A simplified observation network was used ..."
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Cited by 20 (6 self)
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A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A twolayer primitive equation model was used under perfectmodel assumptions. A simplified observation network was used, and the OI method utilized a static background error covariance constructed from a large inventory of historical forecast errors. The hybrid scheme updated the ensemble mean using a hybridized ensemble and static backgrounderror covariance. The ensemble perturbations in the hybrid scheme were updated by the ETKF scheme. The EnSRF ran parallel data assimilation cycles for each member and serially assimilated the observations. The EnSRF backgrounderror covariance was estimated fully from the ensemble. For 50member ensembles, the analyses from the hybrid scheme were as accurate or nearly as accurate as those from the EnSRF, depending on the norm. For 20member ensembles, the analyses from the hybrid scheme were more accurate than analyses from the EnSRF under certain norms. Both hybrid and EnSRF analyses were more accurate than the analyses from the OI. Further reducing the ensemble size to five members, the EnSRF exhibited filter divergence, whereas the analyses from the hybrid scheme were still better than those updated by the OI. Additionally, the hybrid scheme was less prone to spurious gravity