A diagnostic pressure equation constraint has been incorporated into a storm-scale three-dimensional variational (3DVAR) data assimilation system. This diagnostic pressure equation constraint (DPEC) is aimed to improve dynamic consistency among different model variables so as to produce better data assimilation results and improve the subsequent forecasts. Ge et al. (2012) described the development of DPEC and testing of it with idealized experiments. DPEC was also applied to a real supercell case, but only radial velocity was assimilated. In this paper, DPEC is further applied to two real tornadic supercell thunderstorm cases, where both radial velocity and radar reflectivity data are assimilated. The impact of DPEC on radar data assimilation is examined mainly based on the storm forecasts. It is found that the experiments using DPEC generally predict higher low-level vertical vorticity than the experiments not using DPEC near the time of observed tornadoes. Therefore, it is concluded that the use of DPEC improves the forecast of mesocyclone rotation within supercell thunderstorms. The experiments using different weighting coefficients generate similar results. This suggests that DPEC is not very sensitive to the weighting coefficients. 1. Introduction A dynamic consistent initial condition is very important for making a quality storm-scale numerical weather prediction (NWP) forecast. For this purpose, a large number of studies have been focused on utilizing high-resolution radar data to provide better storm-scale initial conditions (e.g., [1–7]). Since radars primarily observe the radial velocity and reflectivity, most state variables have to be “retrieved” in the data assimilation (DA) process. This makes the assimilation of radar data a very challenging problem. Three-dimensional variational (3DVAR), four-dimensional variational (4DVAR), and ensemble Kalman filter (EnKF) methods have been applied to the previously mentioned radar DA problem. The 4DVAR method uses a NWP model as a strong constraint and hence naturally produces a dynamically consistent analysis. Sun and Crook [8, 9] and Sun [10] have shown encouraging results using a 4DVAR cloud model. However, it is very difficult to develop and maintain complex adjoint codes for NWP models. Complex ice microphysics, which are important for storm-scale applications but contain discontinuities and strong nonlinearities, introduce more difficulties in this situation. All of these difficulties limit the adoption of the 4DVAR method in storm-scale NWP operations. The EnKF technique is expected to
References
[1]
A. Crook and J. D. Tuttle, “Numerical simulations initialized with radar-derived winds—part II: forecasts of three gust-front cases,” Monthly Weather Review, vol. 122, no. 6, pp. 1204–1217, 1994.
[2]
J. Sun and N. A. Crook, “Comparison of thermodynamic retrieval by the adjoint method with the traditional retrieval method,” Monthly Weather Review, vol. 124, no. 2, pp. 308–324, 1996.
[3]
J. Sun and N. A. Crook, “Real-time low-level wind and temperature analysis using single WSR-88D data,” Weather and Forecasting, vol. 16, no. 1, pp. 117–132, 2001.
[4]
M. Hu, M. Xue, and K. Brewster, “3DVAR and cloud analysis with WSR-88D level-II data for the prediction of the Fort Worth, Texas, tornadic thunderstorms—part I: cloud analysis and its impact,” Monthly Weather Review, vol. 134, no. 2, pp. 675–698, 2006.
[5]
M. Hu, M. Xue, J. Gao, and K. Brewster, “3DVAR and cloud analysis with WSR-88D level-II data for the prediction of the Fort Worth, Texas, tornadic thunderstorms—part II: impact of radial velocity analysis via 3DVAR,” Monthly Weather Review, vol. 134, no. 2, pp. 699–721, 2006.
[6]
D. J. Stensrud and J. Gao, “Importance of horizontally inhomogeneous environmental initial conditions to ensemble storm-scale radar data assimilation and very short-range forecasts,” Monthly Weather Review, vol. 138, no. 4, pp. 1250–1272, 2010.
[7]
G. Ge, J. Gao, and M. Xue, “Diagnostic pressure equation as a weak constraint in a storm-scale three-dimensional variational radar data assimilation system,” Journal of Atmospheric and Oceanic Technology, vol. 29, pp. 1075–1092, 2012.
[8]
J. Sun and N. A. Crook, “Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint—part I: model development and simulated data experiments,” Journal of the Atmospheric Sciences, vol. 54, no. 12, pp. 1642–1661, 1997.
[9]
J. Sun and N. A. Crook, “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,” Journal of the Atmospheric Sciences, vol. 55, no. 5, pp. 835–852, 1998.
[10]
J. Sun, “Initialization and numerical forecasting of a supercell storm observed during STEPS,” Monthly Weather Review, vol. 133, no. 4, pp. 793–813, 2005.
[11]
C. Snyder and F. Zhang, “Assimilation of simulated Doppler radar observations with an ensemble Kalman filter,” Monthly Weather Review, vol. 131, no. 8, pp. 1663–1677, 2003.
[12]
F. Zhang, C. Snyder, and J. Sun, “Impacts of initial estimate and observations on the convective-scale data assimilation with an ensemble Kalman filter,” Monthly Weather Review, vol. 132, pp. 1238–1253, 2004.
[13]
A. Caya, J. Sun, and C. Snyder, “A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation,” Monthly Weather Review, vol. 133, no. 11, pp. 3081–3094, 2005.
[14]
M. Tong and M. Xue, “Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments,” Monthly Weather Review, vol. 133, no. 7, pp. 1789–1807, 2005.
[15]
M. Xue, M. Tong, and K. K. Droegemeier, “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,” Journal of Atmospheric and Oceanic Technology, vol. 23, no. 1, pp. 46–66, 2006.
[16]
A. Aksoy, D. C. Dowell, and C. Snyder, “A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations—part I: storm-scale analyses,” Monthly Weather Review, vol. 137, no. 6, pp. 1805–1824, 2009.
[17]
F. Zhang, Y. Weng, J. A. Sippel, Z. Meng, and C. H. Bishop, “Cloud-resolving hurricane initialization and prediction through assimilation of doppler radar observations with an ensemble Kalman filter,” Monthly Weather Review, vol. 137, no. 7, pp. 2105–2125, 2009.
[18]
A. Aksoy, D. C. Dowell, and C. Snyder, “A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations—part II: short-range ensemble forecasts,” Monthly Weather Review, vol. 138, no. 4, pp. 1273–1292, 2010.
[19]
D. C. Dowell, L. J. Wicker, and C. Snyder, “Ensemble kalman filter assimilation of radar observations of the 8 may 2003 oklahoma city supercell: influences of reflectivity observations on storm-scale analyses,” Monthly Weather Review, vol. 139, no. 1, pp. 272–294, 2011.
[20]
N. Snook, M. Xue, and Y. Jung, “Analysis of a tornadic mesoscale convective vortex based on ensemble kalman filter assimilation of CASA X-band and WSR-88D radar data,” Monthly Weather Review, vol. 139, no. 11, pp. 3446–3468, 2011.
[21]
D. T. Dawson, L. J. Wicker, E. R. Mansell, and R. L. Tanamachi, “Impact of the environmental low-level wind profile on ensemble forecasts of the 4 may 2007 Greensburg, Kansas, tornadic storm and associated mesocyclones,” Monthly Weather Review, vol. 140, no. 2, pp. 696–716, 2012.
[22]
J. Marquis, Y. Richardson, P. Markowski, D. Dowell, and J. Wurman, “Tornado maintenance investigated with high-resolution dual-doppler and EnKF analysis,” Monthly Weather Review, vol. 140, no. 1, pp. 3–27, 2012.
[23]
R. L. Tanamachi, L. J. Wicker, D. C. Dowell, H. B. Bluestein, D. T. Dawson, and M. Xue, “EnKF assimilation of high-resolution, mobile Doppler radar data of the 4 May 2007 Greensburg, Kansas, supercell into a numerical cloud model,” Monthly Weather Review, vol. 141, pp. 625–648, 2012.
[24]
C. K. Potvin and L. J. Wicker, “Assessing ensemble forecasts of low-level supercell rotation within an OSSE framework,” Weather and Forecasting, 2013.
[25]
M. Hu and M. Xue, “Analysis and prediction of 8 May 2003 Oklahoma City tornadic thunderstorm and embedded tornado using ARPS with assimilation of WSR-88D radar data,” in Proceedings of the 22nd Conference on Weather Analysis and Forecasting/18th Conference on Numerical Weather Prediction, American Meteorological Society, Salt Lake City, Utah, USA, 2007.
[26]
M. Xue, K. K. Droegemeier, and V. Wong, “The Advanced Regional Prediction System (ARPS)—a multi-scale nonhydrostatic atmospheric simulation and prediction model—part I: model dynamics and verification,” Meteorology and Atmospheric Physics, vol. 75, no. 3-4, pp. 161–193, 2000.
[27]
M. Xue, K. K. Droegemeier, V. Wong et al., “The Advanced Regional Prediction System (ARPS)—a multi-scale nonhydrostatic atmospheric simulation and prediction tool—part II: model physics and applications,” Meteorology and Atmospheric Physics, vol. 76, no. 3-4, pp. 143–165, 2001.
[28]
M. Xue, D. Wang, J. Gao, K. Brewster, and K. K. Droegemeier, “The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation,” Meteorology and Atmospheric Physics, vol. 82, no. 1–4, pp. 139–170, 2003.
[29]
M. Xue, “CAPS realtime storm-scale ensemble and high-resolution forecasts as part of the NOAA Hazardous Weather Testbed 2008 Spring Experiment,” in Proceedings of the 24th Conference on Several Local Storms, American Meteorological Society, Savannah, Ga, USA, 2008.
[30]
M. Xue, “CAPS realtime storm scale ensemble and high resolution forecasts for the NOAA hazardous weather testbed,” in Proceedings of the 25th Conference on Severe Local Storms, American Meteorological Society, Seattle, Wash, USA, 2011.
[31]
T. M. Hamill and C. Snyder, “A hybrid ensemble Kalman filter-3D variational analysis scheme,” Monthly Weather Review, vol. 128, no. 8, pp. 2905–2919, 2000.
[32]
A. C. Lorenc, “The potential of the ensemble Kalman filter for NWP—a comparison with 4D-Var,” Quarterly Journal of the Royal Meteorological Society, vol. 129, no. 595, pp. 3183–3203, 2003.
[33]
M. Buehner, “Ensemble-derived stationary and flow-dependent background-error covariances: evaluation in a quasi-operational NWP setting,” Quarterly Journal of the Royal Meteorological Society, vol. 131, no. 607, pp. 1013–1043, 2005.
[34]
X. Wang, D. M. Barker, C. Snyder, and T. M. Hamill, “A hybrid ETKF-3DVAR data assimilation scheme for the WRF model—part II: real observing experiments,” Monthly Weather Review, vol. 136, no. 12, pp. 5132–5147, 2008.
[35]
X. Wang, D. M. Barker, C. Snyder, and T. M. Hamill, “A hybrid ETKF-3DVAR data assimilation scheme for the WRF model—part I: observation system simulation experiment,” Monthly Weather Review, vol. 136, no. 12, pp. 5116–5131, 2008.
[36]
J. Gao, M. Xue, A. Shapiro, and K. K. Droegemeier, “A variational method for the analysis of three-dimensional wind fields from two Doppler radars,” Monthly Weather Review, vol. 127, no. 9, pp. 2128–2142, 1999.
[37]
J. Gao, M. Xue, A. Shapiro, Q. Xu, and K. K. Droegemeier, “Three-dimensional simple adjoint velocity retrievals from single-Doppler radar,” Journal of Atmospheric and Oceanic Technology, vol. 18, no. 1, pp. 26–38, 2001.
[38]
J. Gao, M. Xue, K. Brewster, and K. K. Droegemeier, “A three-dimensional variational data analysis method with recursive filter for Doppler radars,” Journal of Atmospheric and Oceanic Technology, vol. 21, no. 3, pp. 457–469, 2004.
[39]
M. Hu and M. Xue, “Impact of configurations of rapid intermittent assimilation of WSR-88D radar data for the 8 May 2003 Oklahoma City tornadic thunderstorm case,” Monthly Weather Review, vol. 135, no. 2, pp. 507–525, 2007.
[40]
K. Ide, P. Courtier, M. Ghil, and A. C. Lorenc, “Unified notation for data assimilation: operational, sequential and variational,” Journal of the Meteorological Society of Japan, vol. 75, no. 1 B, pp. 181–189, 1997.
[41]
R. J. Purser, W.-S. Wu, D. F. Parrish, and N. M. Roberts, “Numerical aspects of the application of recursive filters to variational statistical analysis—part I: spatially homogeneous and isotropic Gaussian covariances,” Monthly Weather Review, vol. 131, pp. 1524–1535, 2003.
[42]
R. J. Purser, W.-S. Wu, D. F. Parrish, and N. M. Roberts, “Numerical aspects of the application of recursive filters to variational statistical analysis—part II: spatially inhomogeneous and anisotropic general covariances,” Monthly Weather Review, vol. 131, no. 8, pp. 1536–1548, 2003.
[43]
S. C. Albers, J. A. McGinley, D. L. Birkenheuer, and J. R. Smart, “The local analysis and prediction system (LAPS): analyses of clouds, precipitation, and temperature,” Weather and Forecasting, vol. 11, no. 3, pp. 273–287, 1996.
[44]
J. Zhang, F. Carr, and K. Brewster, “ADAS cloud analysis,” in Proceedings of the Conference on Numerical Weather Prediction, pp. 185–188, American Meteorological Society, Phoenix, Ariz, USA, 1998.
[45]
K. Brewster, “Recent advances in the diabatic initialization of a non-hydrostatic numerical model,” in Proceedings of the 15th Conference on Numerical Weather Prediction and 21st Conference on Severe Local Storms, American Meteorological Society, San Antonio, Tex, USA, 2002.
[46]
D. McCarthy, L. Ruthi, and J. Hutton, “The greensburg, KS tornado,” in Proceedings of the 22nd Conference on Weather Analysis and Forecasting/18th Conference on Numerical Weather Prediction, American Meteorological Society, Park City, Utah, USA, 2007.
[47]
H. B. Bluestein, “The formation and early evolution of the Greensburg, Kansas, tornadic supercell on 4 May 2007,” Weather and Forecasting, vol. 24, no. 4, pp. 899–920, 2009.
[48]
Y.-L. Lin, R. D. Farley, and H. D. Orville, “Bulk parameterization of the snow field in a cloud model,” Journal of Climate & Applied Meteorology, vol. 22, no. 6, pp. 1065–1092, 1983.
[49]
G. S. Romine, D. W. Burgess, and R. B. Wilhelmson, “A dual-polarization-radar-based assessment of the 8 May 2003 Oklahoma City Area tornadic supercell,” Monthly Weather Review, vol. 136, no. 8, pp. 2849–2870, 2008.
