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Evaluation of Two Momentum Control Variable Schemes and Their Impact on the Variational Assimilation of Radar Wind Data: Case Study of a Squall Line


doi: 10.1007/s00376-016-5255-3

  • Different choices of control variables in variational assimilation can bring about different influences on the analyzed atmospheric state. Based on the WRF model's three-dimensional variational assimilation system, this study compares the behavior of two momentum control variable options——streamfunction velocity potential (ψ-χ) and horizontal wind components (U-V)——in radar wind data assimilation for a squall line case that occurred in Jiangsu Province on 24 August 2014. The wind increment from the single observation test shows that the ψ-χ control variable scheme produces negative increments in the neighborhood around the observation point because streamfunction and velocity potential preserve integrals of velocity. On the contrary, the U-V control variable scheme objectively reflects the information of the observation itself. Furthermore, radial velocity data from 17 Doppler radars in eastern China are assimilated. As compared to the impact of conventional observation, the assimilation of radar radial velocity based on the U-V control variable scheme significantly improves the mesoscale dynamic field in the initial condition. The enhanced low-level jet stream, water vapor convergence and low-level wind shear result in better squall line forecasting. However, the ψ-χ control variable scheme generates a discontinuous wind field and unrealistic convergence/divergence in the analyzed field, which lead to a degraded precipitation forecast.
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  • Barker D. M., W. Huang, Y. R. Guo, A. J. Bourgeois, and Q. N. Xiao, 2004: A three-dimensional variational data assimilation system for MM5: Implementation and initial results. Mon. Wea. Rev., 132, 897- 914.92a4e98a8f7f6f7ea591bb40cdf39af0http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D2004MWRv..132..897B%26db_key%3DPHY%26link_type%3DABSTRACT%26high%3D20143http://xueshu.baidu.com/s?wd=paperuri%3A%28123ab87ad8ac6211f664815678d7fa67%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D2004MWRv..132..897B%26db_key%3DPHY%26link_type%3DABSTRACT%26high%3D20143&ie=utf-8&sc_us=41340900915828137
    Benjamin S.G., Coauthors, 2004: An hourly assimilation-forecast cycle: The RUC. Mon. Wea. Rev., 132, 495- 518.10.1175/1520-0493(2004)1322.0.CO;299e98620a0eb9aac9822fca6d5c3a124http%3A%2F%2Fci.nii.ac.jp%2Fnaid%2F10013126454%2Fhttp://ci.nii.ac.jp/naid/10013126454/The Rapid Update Cycle (RUC), an operational regional analysis09“forecast system among the suite of models at the National Centers for Environmental Prediction (NCEP), is distinctive in two primary aspects: its hourly assimilation cycle and its use of a hybrid isentropic09“sigma vertical coordinate. The use of a quasi-isentropic coordinate for the analysis increment allows the influence of observations to be adaptively shaped by the potential temperature structure around the observation, while the hourly update cycle allows for a very current analysis and short-range forecast. Herein, the RUC analysis framework in the hybrid coordinate is described, and some considerations for high-frequency cycling are discussed. A 20-km 50-level hourly version of the RUC was implemented into operations at NCEP in April 2002. This followed an initial implementation with 60-km horizontal grid spacing and a 3-h cycle in 1994 and a major upgrade including 40-km horizontal grid spacing in 1998. Verification of forecasts from the latest 20-km version is presented using rawinsonde and surface observations. These verification statistics show that the hourly RUC assimilation cycle improves short-range forecasts (compared to longer-range forecasts valid at the same time) even down to the 1-h projection.
    Bluestein H. B., M. H. Jain, 1985: Formation of mesoscale lines of precipitation: Severe squall lines in Oklahoma during the spring. J. Atmos. Sci., 42( 16), 1711- 1732.10.1175/1520-0469(1985)0422.0.CO;2fd1696dce164effb0b7fd0536596551dhttp%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1985JAtS...42.1711Bhttp://adsabs.harvard.edu/abs/1985JAtS...42.1711BFour distinct kinds of severe, mesoscale convective-line development are identified in Oklahoma during the spring based on the analysis of an 11-year period of reflectivity data from the National Severe Storms Laboratory's 10-cm radar in Norman, Oklahoma. The primary classes of fine formation are broken line, back building, broken areal and embedded areal. Each is described in detail, along with illustrative examples. Comparisons are made with other observations and with numerical model simulations. The former two classes of line formation have been previously documented, while the latter two have not. Only the broken-areal squall line has been realistically simulated numerically.The environment for each of the types of line development was determined from data from the standard National Weather Service surface and upper-air networks and from special rawinsonde launches. It was found that broken-line formation tends to occur along cold fronts in a multicell environment, while back building occurs along any boundary in a supercell environment. The former formation is associated with a steering level with respect to cell motion, while the others are not. A steering level with respect to line motion exists around 6 or 7 km MSL in all cases. Cells within back-building squall lines have high relative helicity, like supercells, while cells within broken-line squall lines have low relative helicity. Most lines were oriented approximately 40掳 to the left of the pressure-weighted vertical shear vector in the troposphere, along the pressure-weighted vertical shear vector in the lowest 1 km and at a large angle to the shear somewhere in the lower portion of the middle troposphere.
    Brand es, E. A., R. P. Davies-Jones, B. C. Johnson, 1988: Streamwise vorticity effects on supercell morphology and persistence. J. Atmos. Sci., 45, 947- 963.10.1175/1520-0469(1988)0452.0.CO;24838a2b4fdbe905a848ab45814b6d0bchttp%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1988JAtS...45..947Bhttp://adsabs.harvard.edu/abs/1988JAtS...45..947BAbstract The structure and steadiness of radar-observed supercell thunderstorms are examined in terms of their particular distribution of vorticity. The data confirm that the vorticity vector in supercells points in the direction of the storm-relative velocity vector and that supercell updrafts contain large positive helicity (V路蠅). The alignment of vorticity and velocity vectors dictates that low pressure associates not only with vorticity but also with helicity. Accelerating pressure gradients and helicity, both thought important for suppressing small-scale features within supercells, may combine with shear-induced vertical pressure gradient forces to organize and maintain the large-scale persistent background updrafts that characterize supercells. Rear downdrafts possess weak positive or negative helicity. Thus, the decline of storm circulation may be hastened by turbulent dissipation when the downdraft air eventually mixes into supercell updrafts.
    Chen, D. H., Coauthors, 2008: New generation of multi-scale NWP system (GRAPES): General scientific design. Chin. Sci. Bull., 53( 22), 3433- 3445.10.1007/s11434-008-0494-z426cc55bf84622f194822ec3b646ebafhttp%3A%2F%2Fwww.cqvip.com%2FMain%2FDetail.aspx%3Fid%3D28719473http://www.cnki.com.cn/Article/CJFDTotal-JXTW200822003.htmA new generation of numerical prediction system GRAPES (a short form of Global/Regional Assimilation and PrEdiction System) was set up in China Meteorological Administration (CMA). This paper focuses on the scientific design and preliminary results of the numerical prediction model in GRAPES, including basic idea and strategy of the general scientific design, multi-scale dynamic core, physical package configuration, architecture and parallelization of the codes. A series of numerical experiments using the real data with horizontal resolutions from 10 to 280 km and idealized experiments with very high resolution up to 100 m are conducted, giving encouraging results supporting the multi-scale application of GRAPES. The results of operational implementation of GRAPES model in some NWP centers are also presented with stress at evaluations of the capability to predict the main features of precipitation in China. Finally the issues to be dealt with for further development are discussed.
    Davies-Jones R., D. W. Burgess, and M. Foster, 1990: Test of helicity as a forecast parameter. Preprints, 16th Conf. on Severe Local Storms, Kananaskis Park, AB, Canada, Amer. Meteor. Soc., 588- 592.
    Dong J. L., M. Xue, 2013: Assimilation of radial velocity and reflectivity data from coastal WSR-88D radars using an ensemble Kalman filter for the analysis and forecast of landfalling hurricane Ike (2008). Quart. J. Roy. Meteor. Soc., 139, 467- 487.10.1002/qj.1970acbe85ed-91aa-4fd0-94e2-c56e7e95ac8e7b14981f348ad8c9788bcca5bc82fe93http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fqj.1970%2Fpdfrefpaperuri:(4e0e18a174b14cb917a4a998c3d35d82)http://onlinelibrary.wiley.com/doi/10.1002/qj.1970/pdfNot Available
    Fujita T., 1955: Results of detailed synoptic studies of squall lines. Tellus, 7( 4), 405- 436.10.1111/j.2153-3490.1955.tb01181.xc27d66c549df976ef6fcd1be26e06b0bhttp%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1111%2Fj.2153-3490.1955.tb01181.x%2Fcitedbyhttp://onlinelibrary.wiley.com/doi/10.1111/j.2153-3490.1955.tb01181.x/citedbyNot Available
    Gao J. D., M. Xue, K. Brewster, and K. K. Droegemeier, 2004: A three-dimensional variational data analysis method with recursive filter for Doppler radars. J. Atmos. Oceanic Technol., 21, 457- 469.e485d4c3dc07366bc3f77e8a55f22a67http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D2004JAtOT..21..457G%26db_key%3DPHY%26link_type%3DABSTRACThttp://xueshu.baidu.com/s?wd=paperuri%3A%28bea7369f63db7495437d458da988726a%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D2004JAtOT..21..457G%26db_key%3DPHY%26link_type%3DABSTRACT&ie=utf-8&sc_us=13188604239151258641
    Hu M., M. Xue, J. D. Gao, and K. Brewster, 2006: 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. Mon. Wea. Rev., 134, 699- 721.10.1175/MWR3092.15985d2c8-06ac-4764-97ef-5b98d592928197de4b71474781242f9bc2176f727b52http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2006MWRv..134..675Hrefpaperuri:(2a1b9c7a13ebb23ea77ced12a2fbf3d1)http://adsabs.harvard.edu/abs/2006MWRv..134..675HIn this two-part paper, the impact of level-II Weather Surveillance Radar-1988 Doppler (WSR-88D) reflectivity and radial velocity data on the prediction of a cluster of tornadic thunderstorms in the Advanced Regional Prediction System (ARPS) model are studied. Radar reflectivity data are used primarily in a cloud analysis procedure that retrieves the amount of hydrometeors and adjusts in-cloud temperature, moisture, and cloud fields, while radial velocity data are analyzed through a three-dimensional variational (3DVAR) scheme that contains a mass divergence constraint in the cost function. In Part I, the impact of the cloud analysis and modifications to the scheme are examined while Part II focuses on the impact of radial velocity and the mass divergence constraint. The case studied is that of the 28 March 2000 Fort Worth, Texas, tornado outbreaks. The same case was studied by Xue et al. using the ARPS Data Analysis System (ADAS) and an earlier version of the cloud analysis procedure with WSR-88D level-III data. Since then, several modifications to the cloud analysis procedure, including those to the in-cloud temperature adjustment and the analysis of precipitation species, have been made. They are described in detail with examples. The assimilation and predictions use a 3-km grid nested inside a 9-km one. The level-II reflectivity data are assimilated, through the cloud analysis, at 10-min intervals in a 1-h period that ends a little over 1 h preceding the first tornado outbreak. Experiments with different settings within the cloud analysis procedure are examined. It is found that the experiment using the improved cloud analysis procedure with reflectivity data can capture the important characteristics of the main tornadic thunderstorm more accurately than the experiment using the early version of cloud analysis. The contributions of different modifications to the above improvements are investigated.
    Joyce R. J., J. E. Janowiak, P. A. Arkin, and P. P. Xie, 2004: CMORPH: A method that produces global precipitation estimates from passive microwave and infrared data at high spatial and temporal resolution. Journal of Hydrometeorology, 5( 3), 487- 503.4a3fc2d0005c7912545a662c4155d55ahttp%3A%2F%2Fwww.bioone.org%2Fservlet%2Flinkout%3Fsuffix%3Dbibr19%26dbid%3D16%26doi%3D10.1603%252FME14015%26key%3D10.1175%252F1525-7541%282004%29005%3C0487%253ACAMTPG%3E2.0.CO%253B2http://xueshu.baidu.com/s?wd=paperuri%3A%28aca48978d7ce0f0aaef86f9b0a951a4d%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fwww.bioone.org%2Fservlet%2Flinkout%3Fsuffix%3Dbibr19%26dbid%3D16%26doi%3D10.1603%252FME14015%26key%3D10.1175%252F1525-7541%282004%29005%253C0487%253ACAMTPG%253E2.0.CO%253B2&ie=utf-8&sc_us=14659918988861497797
    Li X., J. Ming, Y. Wang, K. Zhao, and M. Xue, 2013: Assimilation of T-TREC-retrieved wind data with WRF 3DVAR for the short-term forecasting of Typhoon Meranti (2010) near landfall. J. Geophys. Res., 118, 10 361- 10 375.10.1002/jgrd.5081590f01285b704be32a129061cd6171f05http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fjgrd.50815%2Ffullhttp://onlinelibrary.wiley.com/doi/10.1002/jgrd.50815/fullFor most operational radar,such as the WSR-88D of the U.S.,and WSR-98D of China,the maximum Doppler velocity range is about 150 km,far less than the maximum range of reflectivity,Z data,typically 460 km.It would thus be advantageous if the reflectivity data could be used to estimate the wind field to alleviate the limitations of wind data from single Doppler radar.An extended Tracking Radar Echo by Correlation (TREC) technique,called T-TREC technique,has been developed recently to retrieve horizontal circulations within tropical cyclones (TCs) from single Doppler radar reflectivity (Z) and radial velocity (V r,when available) data.This study explores,for the first time,the assimilation of T-TREC-retrieved winds for a landfalling typhoon,Meranti (2010),into a convection-resolving model,the WRF.
    Li X., J. Ming, M. Xue, Y. Wang, and K. Zhao, 2015: Implementation of a dynamic equation constraint based on the steady state momentum equations within the WRF hybrid ensemble-3DVar data assimilation system and test with radar T-TREC wind assimilation for tropical Cyclone Chanthu (2010). J. Geophys. Res., 120, 4017- 4039.10.1002/2014JD02270618d95b0a-7ce3-4b95-bd79-e56af7d760c04ecfdc2c56093598d2e9771bbdaa8b4chttp%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2F2014JD022706%2Fepdfrefpaperuri:(11aca886dd686394db00bd1c7964d561)http://onlinelibrary.wiley.com/doi/10.1002/2014JD022706/epdfProper dynamic equation constraints in data assimilation (DA) systems can help improve balance of analyzed atmospheric state. The formulation of ensemble‐variational DA algorithms allows for easy incorporation of such constraints, but their impacts within such DA systems have been little studied. A dynamic constraint based on the steady momentum equations is incorporated into the WRF (Weather Research and Forecasting) hybrid ensemble‐three‐dimensional variational (3DVar) (En3DVar) DA system as a weak constraint. The constraint aims at improving the coupling and balance among wind and thermodynamic state variables, especially when few state variables are directly observed. The scheme is applied to the assimilation of radar T‐TREC (Typhoon‐Tracking Radar Echo by Correlation) winds at a convection‐allowing resolution, for landfalling typhoon, Chanthu (2010), when it was within the range of a coastal radar. Parallel experiments using the 3DVar and En3DVar with and without the dynamic constraint are run to examine the impact of the constraint. The flow‐dependent ensemble covariance used in En3DVar helps to update unobserved pressure and temperature fields in a dynamically more consistent way compared to the static covariance; the added dynamic constraint produces more accurate pressure within the typhoon. The pressure field improved by the dynamic constraint also leads to better temperature and moisture analyses within the variational minimization through flow‐dependent cross covariance. En3DVar analysis with the dynamic constraint produces the best intensity forecast for the typhoon, in terms of the minimum sea level pressure and maximum surface wind speed. Additional sensitivity experiments examine the impact of the weight of the dynamic constraint.
    Newton C.W., 1950: Structure and mechanism of the prefrontal squall line. J. Atmos. Sci., 7, 210- 222.10.1175/1520-0469(1950)0072.0.CO;26d053f29757bb140bd0f4dbb58b3ce35http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1950JAtS....7..210Nhttp://adsabs.harvard.edu/abs/1950JAtS....7..210NAbstract Using upper-air soundings taken by the Thunderstorm Project and surface and serological data available through teletype distribution, a detailed three-dimensional analysis of a prefrontal squall line is presented and certain new observational features of squall-line structure are shown. It is shown that squall-line thunderstorms appear in some cases to form first over the cold-front surface and subsequently move into the warm sector. Serial ascents taken in such a case show that there is a distinct cold front at the forward edge of the thunderstorm area, which coincides with the squall line observed at the ground. It is suggested that the squall-line activity can be accounted for partly as a result of this front, and partly by the continuous generation of new thunderstorms as a result of convergence-divergence patterns produced by the vertical transfer of horizontal momentum in pre-existent thunderstorms. This is augmented by solenoidal circulations due to unbalance between the “thermal wind” and...
    Newton, C W., 1966: Circulations in large sheared cumulonimbus. Tellus, 18, 699- 713.10.1111/j.2153-3490.1966.tb00291.x1e648a1125b060493414df0d00071a70http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1111%2Fj.2153-3490.1966.tb00291.x%2Fabstracthttp://onlinelibrary.wiley.com/doi/10.1111/j.2153-3490.1966.tb00291.x/abstractABSTRACT The structure of a cumulonimbus cloud subjected to vertical shear is interpreted in light of the horizontal forces acting upon it, and of the varying thermodynamic influences in its different parts. In-cloud horizontal velocities depart greatly from those in the environment, and the forms assumed by draft columns (updrafts typically leaning in a sense opposing the vertical shear) vary with the shear, vertical motion, and speed of storm movement. The cumulonimbus is viewed as an ensemble of air elements which have undergone varying degrees of mixing with the environment, penetrating upward to different heights. Some of the air in the updraft rises into stratospheric towers, then descends as a vigorous downdraft which, because of mixing-in of heat and of air having no initial vertical momentum, dies out in the upper troposphere. This air, together with air reaching the upper troposphere in the less buoyant outskirts of the updraft, feeds the expanding anvil plume. A separate downdraft in the lower part of the cloud, originating from middle levels where the wet-bulb potential temperature is low, continually regenerates the updraft though mechanical lifting. Estimates of the air and water budgets of squall-line thunderstorms are given.
    Parrish D. F., J. C. Derber, 1992: The national meteorological center's spectral statistical-interpolation analysis system. Mon. Wea. Rev., 120, 1747- 1763.10.1175/1520-0493(1992)1202.0.CO;24214772c1895942c49e785d413b108e0http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1992MWRv..120.1747Phttp://adsabs.harvard.edu/abs/1992MWRv..120.1747PAt the National Meteorological Center (NMC), a new analysis system is being extensively tested for possible use in the operational global data assimilation system. This analysis system is called the because the spectral coefficients used in the NMC spectral model are analyzed directly using the same basic equations as statistical (optimal) interpolation. Results from several months of parallel testing with the NMC spectral model have been very encouraging. Favorable features include smoother analysis increments, greatly reduced changes from initialization, and significant improvement of 1-5-day forecasts. Although the analysis is formulated as a variational problem, the objective function being minimized is formally the same one that forms the basis of all existing optimal interpolation schemes. This objective function is a combination of forecast and observation deviations from the desired analysis, weighted by the invent of the corresponding forecast- and observation-error covariance matrices. There are two principal differences in how the SSI implements the minimization of this functional as compared to the current OI used at NMC. First, the analysis variables are spectral coefficients instead of gridpoint values. Second, all observations are used at once to solve a single global problem. No local approximations are made, and there is no special data selection. Because of these differences, it is straightforward to include unconventional data, such as radiances, in the analysis. Currently temperature, wind, surface pressure, mixing, ratio, and Special Sensor Microwave/lmager (SSM/I) total precipitable water can be used as the observation variables. Soon to be added are the scatterometer surface winds. This paper provides a detailed description of the SSI and presents a few results.
    Pu Z. X., X. L. Li, and J. Z. Sun, 2009: Impact of airborne Doppler radar data assimilation on the numerical simulation of intensity changes of Hurricane Dennis near a landfall. J. Atmos. Sci., 66, 3351- 3365.10.1175/2009JAS3121.1d2d5fdcdc56cee83d1ede0841e455b7chttp%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2009JAtS...66.3351Phttp://adsabs.harvard.edu/abs/2009JAtS...66.3351PAccurate forecasting of a hurricane's intensity changes near its landfall is of great importance in making an effective hurricane warning. This study uses airborne Doppler radar data collected during the NASA Tropical Cloud Systems and Processes (TCSP) field experiment in July 2005 to examine the impact of airborne radar observations on the short-range numerical simulation of hurricane track and intensity changes. A series of numerical experiments is conducted for Hurricane Dennis (2005) to study its intensity changes near a landfall. Both radar reflectivity and radial velocity-derived wind fields are assimilated into the Weather Research and Forecasting (WRF) model with its three-dimensional variational data assimilation (3DVAR) system. Numerical results indicate that the radar data assimilation has greatly improved the simulated structure and intensity changes of Hurricane Dennis. Specifically, the assimilation of radar reflectivity data shows a notable influence on the thermal and hydrometeor structures of the initial vortex and the precipitation structure in the subsequent forecasts, although its impact on the intensity and track forecasts is relatively small. In contrast, assimilation of radar wind data results in moderate improvement in the storm-track forecast and significant improvement in the intensity and precipitation forecasts of Hurricane Dennis. The hurricane landfall, intensification, and weakening during the simulation period are well captured by assimilating both radar reflectivity and wind data.
    Rotunno R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong, long-lived squall lines. J.Atmos. Sci., 45, 463- 485.10.1175/1520-0469(1988)0452.0.CO;27340669ce79a156a8c5d08b0f5e87b54http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1988JAtS...45..463Rhttp://adsabs.harvard.edu/abs/1988JAtS...45..463RNot Available
    Sheng C. Y., Y. F. Pu, and S. T. Gao, 2006: Effect of Chinese Doppler radar data on nowcasting output of mesoscale model. Chinese J. Atmos. Sci., 30( 1), 93- 107. (in Chinese)10.1016/S1003-6326(06)60040-X507969e49fb67eac1f8f2e2bdf494e49http%3A%2F%2Fen.cnki.com.cn%2Farticle_en%2Fcjfdtotal-dqxk200601007.htmhttp://en.cnki.com.cn/article_en/cjfdtotal-dqxk200601007.htmThe Advanced Regional Prediction System(ARPS) is a multi-scale model developed by the Center for(Analysis) and Prediction of Storms(CAPS),the complex cloud analysis system in the ARPS data analysis system(ARPSDAS or ADAS) can construct a three-dimensional cloud in the initial field with Doppler radar reflectivity,cloud base and fraction,and satellite image data to adjust the initial cloud and rain water,and ADAS still can adjust the initial wind field directly with radar radial velocity.In order to test the effect of Doppler radar data on mesoscale model,a North China torrential rain event is studied with Chinese Doppler radar data only.Four control experiments are conducted.The 1st experiment is performed without Chinese Doppler radar data analysis,the 2nd is done with Doppler radar reflectivity only to construct a three-dimensional cloud analysis,the 3rd is conducted with radar radial velocity only to adjust the initial wind field,and the last experiment is done with both radar reflectivity and radial velocity.The main results are as follows: 1) The wind components u,v,and w in the initial field adjusted by Doppler radial velocity can be modified under 10 km near the radar observing range,and the most drastic modification of u,v happens in the central troposphere.2) Assimilation of Doppler radar reflectivity can increase the cloud and moisture contents in the strong reflectivity region of the initial field.The adjustment of the water vapor mixture ratio(q_(v)) is mainly below 3 km, the rainfall mixture ratio(q_(r)) below 4 km,cloud vapor mixture ratio(q_(c)) in the troposphere(below 10 km level) and cloud ice(q_(i)) and snow(q_(s)) mixture ratio at around 49 km level in the tro-(posphere.) Diabatic initialization of ADAS will adjust the temperature to balance the cloud microphysical adjustment.3) The comparison between simulated hourly rainfall and observations shows that the assimilation of both reflectivity and radial velocity can improve rainfall forecasting significantly,especially within 3 hours;while the comparison of simulated hourly streamline fields shows that radar radial velocity can increase the mesoscale wind circles in the initial fields and mitigate the model's spin-up time significantly.4) Comparison between radar radial velocity and reflectivity assimilation on the initial field and the simulation shows that Doppler radar radial velocity assimilation can mainly improve the initial wind field while radar reflectivity assimilation can increase the cloud and water contents in the initial field and adjust the temperature.Simulated 6-h rainfall indicates that radar reflectivity assimilation has greater positive effects than radial velocity on the rainfall simulation,although adding radial velocity data results in further improvement in the rain simulation.
    Shi L. J., X. F. Xu, B. Li, H. P. Yang, and F. W. Xu, 2009: Application of Doppler radar data to the landfalling Typhoon Saomai simulation. Journal of Applied Meteorological Science, 20( 3), 257- 266. (in Chinese)33d7cf9879e5fd1f478d66a689f08861http%3A%2F%2Fen.cnki.com.cn%2FArticle_en%2FCJFDTOTAL-YYQX200903002.htmhttp://en.cnki.com.cn/Article_en/CJFDTOTAL-YYQX200903002.htmThe mesoscale model ARPS and its data analyzing system ARPS-3DVar developed by CAPS of Oklahoma university has a good potential to utilize in China.Using ARPS and its 3DVar assimilation system, the Doppler weather radar(CINRAD-SA) reflectivity and radial velocity are assimilated.In order to test the effects of Doppler radar data on the initial field and on the forecast field,numeric study is carried out on super typhoon Saomai(0608) which lands at east China and causes a large damage.Comparison between experiments with and without radar data assimilation shows that Doppler radar assimilation can help obtain more realistic precipitation,wind and reflectivity structures within 6-hour initial time windows.The radar assimilation by ARPS-3DVar has the ability to improve the forecast on the mesoscale rain cell position and intensity.The improvement on typhoon track forecast is due to the effective adjustment of the typhoon vortex and eye structure by radar data assimilation.The result of precipitation forecast is improved significantly,mainly because of the physical quantities in assimilation test displaying typical characteristics of mesoscale system.However,there are some inadequate aspects still needing improvements in the stimulation of typhoon intensity.
    Skamarock, W. C., Coauthors, 2008: Description of the advanced research WRF version 3,Rep. NCAR/TN-475++ STR, Natl. Cent. Atmos. Res., Boulder, Colo., 125 pp.
    Sun J., N. A. Crook, 1997: Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part I: Model development and simulated data experiments. J. Atmos. Sci., 54( 12), 1642- 1661.10.1175/1520-0469(1997)0542.0.CO;2fd50222b-cffe-44b3-98b2-5a4c3f4de7124d65fad43479cedc983061dbc7fe9168http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1997jats...54.1642srefpaperuri:(3442f4439a64c47314ac768eea6c1f42)http://adsabs.harvard.edu/abs/1997jats...54.1642sThe purpose of the research reported in this paper is to develop a variational data analysis system that can be used to assimilate data from one or more Doppler radars. In the first part of this two-part study, the technique used in this analysis system is described and tested using data from a simulated warm rain convective storm. The analysis system applies the 4D variational data assimilation technique to a cloud-scale model with a warm rain parameterization scheme. The 3D wind, thermodynamical, and microphysical fields are determined by minimizing a cost function, defined by the difference between both radar observed radial velocities and reflectivities (or rainwater mixing ratio) and their model predictions. The adjoint of the numerical model is used to provide the sensitivity of the cost function with respect to the control variables.Experiments using data from a simulated convective storm demonstrated that the variational analysis system is able to retrieve the detailed structure of wind, thermodynamics, and microphysics using either dual-Doppler or single-Doppler information. However, less accurate velocity fields are obtained when single-Doppler data were used. In both cases, retrieving the temperature field is more difficult than the retrieval of the other fields. Results also show that assimilating the rainwater mixing ratio obtained from the reflectivity data results in a better performance of the retrieval procedure than directly assimilating the reflectivity. It is also found that the system is robust to variations in the Z-qrelation, but the microphysical retrieval is quite sensitive to parameters in the warm rain scheme. The technique is robust to random errors in radial velocity and calibration errors in reflectivity.
    Sun J., N. A. Crook, 1998: 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. J. Atmos. Sci., 55( 4), 835- 852.10.1175/1520-0469(1998)0552.0.CO;21cebba5079f4d1ed94947fe25caff633http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1998JAtS...55..835Shttp://adsabs.harvard.edu/abs/1998JAtS...55..835SAbstract The variational Doppler radar analysis system developed in part I of this study is tested on a Florida airmass storm observed during the Convection and Precipitation/ Electrification Experiment. The 3D wind, temperature, and microphysical structure of this storm are obtained by minimizing the difference between the radar-observed radial velocities and rainwater mixing ratios (derived from reflectivity) and their model predictions. Retrieval experiments are carried out to assimilate information from one or two radars. The retrieved fields are compared with measurements of two aircraft penetrating the storm at different heights. The retrieved wind, thermodynamical, and microphysical fields indicate that the minimization converges to a solution consistent with the input velocity and rainwater fields. The primary difference between using single-Doppler and dual-Doppler information is the reduction of the peak strength of the storm on the order of 10% when information from only one radar is provided. ...
    Sun J. Z., H. L. Wang, 2013a: Radar data assimilation with WRF 4D-Var. Part II: comparison with 3D-Var for a squall line over the U.S. great plains. Mon. Wea. Rev., 141, 2245- 2264.10.1175/MWR-D-12-00169.1538e5faecb2932e495e33206610790c3http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2013MWRv..141.2245Shttp://adsabs.harvard.edu/abs/2013MWRv..141.2245SNot Available
    Sun J. Z., H. L. Wang, 2013b: WRF-ARW variational storm-scale data assimilation: current capabilities and future developments. Advances in Meteorology, 2013, 81591010.1155/2013/815910113bea3ec9985284346a4beb3c03cfdbhttp%3A%2F%2Fwww.oalib.com%2Fpaper%2F3066673http://www.oalib.com/paper/3066673The variational radar data assimilation system has been developed and tested for the Advanced Research Weather Research and Forecasting (WRF-ARW) model since 2005. Initial efforts focused on the assimilation of the radar observations in the 3-dimensional variational framework, and recently the efforts have been extended to the 4-dimensional system. This article provides a review of the basics of the system and various studies that have been conducted to evaluate and improve the performance of the system. Future activities that are required to further improve the system and to make it operational are also discussed. 1. Introduction In the past two decades active research was conducted on the development of techniques to initialize storm-scale numerical prediction models. It has been recognized that the success will critically depend on the optimal use of the national operational WSR-88D radar network that covers the United States with single Doppler coverage in most areas. Although the network provides observations at a resolution that is able to resolve atmospheric convection, they are only limited to radial wind and reflectivity. Therefore several early studies focused on the feasibility of retrieving meteorological fields from these single Doppler observations. Techniques with different complexities have been developed which aim at obtaining the unobserved meteorological variables such as 3-dimensional (3D) wind, temperature, and microphysical fields from the radar observations of radial velocity and reflectivity (e.g., [1鈥5]). The techniques that make use of a numerical model in a data assimilation (DA) context received particular attention because they combine the retrieval, initialization, and forecast in one system. The first radar DA system for the storm-scale was developed based on the 4-dimensional variational data assimilation (4D-Var) technique and a boundary layer fluid dynamics model for the retrieval of the 3D wind and temperature [1]. This system, known as VDRAS (Variational Doppler Radar Analysis System), was later expanded to include microphysical retrieval, as well as short-term forecasts initialized by these retrieved fields [6鈥9]. Another variational-based radar DA system was developed by Gao et al. [4] using a 3-dimensional variational data assimilation (3D-Var) technique in the framework of the ARPS (Advanced Research and Prediction System [10]) model. A so-called 3.5-dimensional variational radar data assimilation based on Navy鈥檚 COAMPS (The Coupled Ocean/Atmosphere Mesoscale Prediction System) was developed and demonstrated
    Sun J. Z., H. L. Wang, W. X. Tong, Y. Zhang, C.-Y. Lin, and D. M. Xu, 2016: Comparison of the impacts of momentum control variables on high-resolution variational data assimilation and precipitation forecasting. Mon. Wea. Rev., 144, 149- 169.10.1175/MWR-D-14-00205.1d95f35b7ffda06becfffa318c1f65b06http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2016MWRv..144..149Shttp://adsabs.harvard.edu/abs/2016MWRv..144..149SNot Available Not Available
    Wang H. L., J. Z. Sun, X. Zhang, X.-Y. Huang, and T. Auligné, 2013: Radar data assimilation with WRF 4D-Var. Part I: system development and preliminary testing. Mon. Wea. Rev., 141, 2224- 2244.10.1175/MWR-D-12-00168.14a20e2777c23da71385ce70e50cf0025http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2013MWRv..141.2224Whttp://adsabs.harvard.edu/abs/2013MWRv..141.2224WThe major goal of this two-part study is to assimilate radar data into the high-resolution Advanced Research Weather Research and Forecasting Model (ARW-WRF) for the improvement of short-term quantitative precipitation forecasting (QPF) using a four-dimensional variational data assimilation (4D-Var) technique. In Part I the development of a radar data assimilation scheme within the WRF 4D-Var system (WRF 4D-Var) and the preliminary testing of the scheme are described. In Part II the performance of the enhanced WRF 4D-Var system is examined by comparing it with the three-dimensional variational data assimilation system (WRF 3D-Var) for a convective system over the U.S. Great Plains. The WRF 4D-Var radar data assimilation system has been developed with the existing framework of an incremental formulation. The new development for radar data assimilation includes the tangent-linear and adjoint models of a Kessler warm-rain microphysics scheme and the new control variables of cloud water, rainwater, and vertical velocity and their error statistics. An ensemble forecast with 80 members is used to produce background error covariance. The preliminary testing presented in this paper includes single-observation experiments as well as real data assimilation experiments on a squall line with assimilation windows of 5, 15, and 30 min. The results indicate that the system is able to obtain anisotropic multivariate analyses at the convective scale and improve precipitation forecasts. The results also suggest that the incremental approach with successive basic-state updates works well at the convection-permitting scale for radar data assimilation with the selected assimilation windows.
    Xiao Q. N., Y.-H. Kuo, J. Z. Sun, W.-C. Lee, E. Lim, Y.-R. Guo, and D. M. Barker, 2005: Assimilation of Doppler radar observations with a regional 3DVAR system: Impact of Doppler velocities on forecasts of a heavy rainfall case. J. Appl. Meteor., 44, 768- 788.48d2987eb3fdb0b31c810262fbb60553http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D2005JApMe..44..768X%26db_key%3DPHY%26link_type%3DABSTRACThttp://xueshu.baidu.com/s?wd=paperuri%3A%28c07a1e750fc8ddfe5e2c4b8798fda70b%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D2005JApMe..44..768X%26db_key%3DPHY%26link_type%3DABSTRACT&ie=utf-8&sc_us=6356000078318155908
    Xiao Q. N., J. Z. Sun, 2007: Multiple-radar data assimilation and short-range quantitative precipitation forecasting of a squall line observed during IHOP_2002. Mon. Wea. Rev., 135, 3381- 3404.0fc6229af8053a2e010082b72963cea6http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D2007MWRv..135.3381X%26db_key%3DPHY%26link_type%3DABSTRACT%26high%3D19888http://xueshu.baidu.com/s?wd=paperuri%3A%2894178d319f279c20c7f2d7d1ecb57c27%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D2007MWRv..135.3381X%26db_key%3DPHY%26link_type%3DABSTRACT%26high%3D19888&ie=utf-8&sc_us=13718852669626556646
    Xie P. P., A. Y. Xiong, 2011: A conceptual model for constructing high-resolution gauge-satellite merged precipitation analyses. J. Geophys. Res., 116,D21106, doi: 10.1029/2011 JD016118.10.1029/2011JD016118b7a7f803c2139fb3e7756afba19785a6http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F2011JD016118%2Ffullhttp://onlinelibrary.wiley.com/doi/10.1029/2011JD016118/fullAbstract Top of page Abstract 1.Introduction 2.Data 3.Removing Bias in the Satellite Estimates 4.Combining Gauge Data With Bias-Corrected Satellite Estimates 5.Summary and Future Work Acknowledgments References Supporting Information [1] A conceptual model has been developed to create high-resolution precipitation analyses over land by merging gauge-based analysis and CMORPH satellite estimates using data over China for a 5 month period from April to September 2007. A two-step strategy is adopted to remove the bias inherent in the CMORPH satellite precipitation estimates and to combine the bias-corrected satellite estimates with the gauge analysis. First, bias correction is performed for the CMORPH estimates by matching the probability density function (PDF) of the satellite data with that of the gauge analysis using colocated data pairs over a spatial domain of 5lat/lon centering at the target grid box and over a time period of 30 days, ending at the target date. The spatial domain is expanded wherever necessary over gauge-sparse regions to ensure the collection of a sufficient number of gauge-satellite data pairs. The bias-corrected CMORPH precipitation estimates are then combined with the gauge analysis through the optimal interpolation (OI) technique, in which the bias-corrected CMORPH is used as the first guess while the gauge data are used as the observations to modify the first guess over regions with station coverage. Error statistics are computed for the input gauge and satellite data to maximize the performance of the high-resolution merged analysis of daily precipitation. Cross-validation tests and comparisons against independent gauge observations demonstrate feasibility and effectiveness of the conceptual algorithm in constructing merged precipitation analysis with substantially removed bias and significantly improved pattern agreements compared with those of the input gauge and satellite data.
    Xie Y. F., A. E. MacDonald, 2012: Selection of momentum variables for a three-dimensional variational analysis. Pure Appl. Geophys., 169, 335- 351.10.1007/s00024-011-0374-36e32115fc5524abeaa497b2a765926d6http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2012PApGe.169..335Xhttp://adsabs.harvard.edu/abs/2012PApGe.169..335XThree choices of control variables for meteorological variational analysis (3DVAR or 4DVAR) are associated with horizontal wind: (1) streamfunction and velocity potential, (2) eastward and northward velocity, and (3) vorticity and divergence. This study shows theoretical and numerical differences of these variables in practical 3DVAR data assimilation through statistical analysis and numerical experiments. This paper demonstrates that (a) streamfunction and velocity potential could potentially introduce analysis errors; (b) A 3DVAR using velocity or vorticity and divergence provides a natural scale dependent influence radius in addition to the covariance; (c) for a regional analysis, streamfunction and velocity potential are retrieved from the background velocity field with Neumann boundary condition. Improper boundary conditions could result in further analysis errors; (d) a variational data assimilation or an inverse problem using derivatives as control variables yields smoother analyses, for example, a 3DVAR using vorticity and divergence as controls yields smoother wind analyses than those analyses obtained by a 3DVAR using either velocity or streamfunction/velocity potential as control variables; and (e) statistical errors of higher order derivatives of variables are more independent, e.g., the statistical correlation between U and V is smaller than the one between streamfunction and velocity potential, and thus the variables in higher derivatives are more appropriate for a variational system when a cross-correlation between variables is neglected for efficiency or other reasons. In summary, eastward and northward velocity, or vorticity and divergence are preferable control variables for variational systems and the former is more attractive because of its numerical efficiency. Numerical experiments are presented using analytic functions and real atmospheric observations.
    Xue M., D. H. Wang, J. D. Gao, K. Brewster, and K. K. Droegemeier, 2003: The advanced regional prediction system (ARPS), storm-scale numerical weather prediction and data assimilation. Meteor. Atmos. Phys., 82, 139- 170.10.1007/s00703-001-0595-64cab6cb2342b233c1b67deb658994032http%3A%2F%2Fwww.springerlink.com%2Findex%2FCG08L17MKCFAHA14.pdfhttp://www.springerlink.com/index/CG08L17MKCFAHA14.pdfIn this paper, we first describe the current status of the Advanced Regional Prediction System of the Center for Analysis and Prediction of Storms at the University of Oklahoma. A brief outline of future plans is also given. Two rather successful cases of explicit prediction of tornadic thunderstorms are then presented. In the first case, a series of supercell storms that produced a historical number of tornadoes was successfully predicted more than 8 hours in advance, to within tens of kilometers in space with initiation timing errors of less than 2 hours. The general behavior and evolution of the predicted thunderstorms agree very well with radar observations. In the second case, reflectivity and radial velocity observations from Doppler radars were assimilated into the model at 15-minute intervals. The ensuing forecast, covering a period of several hours, accurately reproduced the intensification and evolution of a tornadic supercell that in reality spawned two tornadoes over a major metropolitan area. These results make us optimistic that a model system such as the ARPS will be able to deterministically predict future severe convective events with significant lead time. The paper also includes a brief description of a new 3DVAR system developed in the ARPS framework. The goal is to combine several steps of Doppler radar retrieval with the analysis of other data types into a single 3-D variational framework and later to incorporate the ARPS adjoint to establish a true 4DVAR data assimilation system that is suitable for directly assimilating a wide variety of observations for flows ranging from synoptic down to the small nonhydrostatic scales.
    Yang Y., C. J. Qiu, and J. D. Gong, 2006: Physical initialization applied in WRF-Var for assimilation of Doppler radar data. Geophys. Res. Lett., 33,L22807, doi: 10.1029/2006 GL027656.10.1029/2006GL027656369f029c8383d0d9f2bdf1ccc33eb4edhttp%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F2006GL027656%2Ffullhttp://onlinelibrary.wiley.com/doi/10.1029/2006GL027656/fullWRF-Var is further developed with Physical Initialization (PI) to assimilate Doppler radar radial velocity and reflectivity observations. In this updated 3D-Var, specific humidity and vertical velocity are first derived from reflectivity with PI, and then the model fields of specific humidity are replaced by the modified ones, finally, the estimated vertical velocity is added to the cost-function of the existing WRF-Var (version 2.0) as a new observation type, and radial velocity observations are assimilated directly by the method afforded by WRF-Var. It is tested with a rainfall event that occurred in Hubei province near the Yangtze River on 19 June 2002. Results show that the updated 3D-Var shows better capability to forecast the precipitation than the WRF-Var does, and the forecast reflectivity field correlates well with the observations for about 4-h prediction period.
    Zeng M. J., B. Zhang, J. L. Zhou, W. L. Wang, and H. X. Mei, 2014: Quantitative evaluation for GPS/PWV data assimilation in heavy precipitation events. Journal of the Meteorological Sciences, 34( 1), 77- 86. (in Chinese)3c6edf55e1ea251217d7524f8896d170http%3A%2F%2Fen.cnki.com.cn%2FArticle_en%2FCJFDTotal-QXKX201401012.htmhttp://en.cnki.com.cn/Article_en/CJFDTotal-QXKX201401012.htmBased on WRF model and the three-dimensional variation data assimilation system( WRFDA),using PWV data of Jiangsu GPS observation network,and regional radiosonde and surface data respectively,this paper carried out a series of assimilation experiments of two regional heavy rain events occurred in southern Jiangsu on August 25,2011 and Anhui- Jiangsu on August 1,2008 in order to compare and analyze the quantitative effects of GPS / PWV,sounding and surface data assimilation on heavy precipitation forecast. The results showed that sounding and surface meteorological data assimilation affected the dynamic and thermal field,and formed the strong convergence with upward motion and the thermal instability near the rain center,then improved directly the distribution structure and the intention characteristics of heavy rain,so they played the decisive role in success or failure of numerical simulation. GPS / PWV assimilation enhanced and organized better the water vapor condition on the basis of sounding and surface data assimilation,and provided significant improvements in the intensity and the position of heavy rain center.
    Zhang F. Q., Y. J. Weng, J. A. Sippel, Z. Y. Meng, and C. H. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 137, 2105- 2125.10.1175/2009MWR2645.10936158aba1f1858af596fef36a13452http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2009MWRv..137.2105Zhttp://adsabs.harvard.edu/abs/2009MWRv..137.2105ZThis study explores the assimilation of Doppler radar radial velocity observations for cloud-resolving hurricane analysis, initialization, and prediction with an ensemble Kalman filter (EnKF). The case studied is Hurricane Humberto (2007), the first landfalling hurricane in the United States since the end of the 2005 hurricane season and the most rapidly intensifying near-landfall storm in U.S. history. The storm caused extensive damage along the southeast Texas coast but was poorly predicted by operational models and forecasters. It is found that the EnKF analysis, after assimilating radial velocity observations from three Weather Surveillance Radars-1988 Doppler (WSR-88Ds) along theGulf coast, closely represents the best-track position and intensity of Humberto. Deterministic forecasts initialized from the EnKF analysis, despite displaying considerable variability with different lead times, are also capable of predicting the rapid formation and intensification of the hurricane. These forecasts are also superior to simulations without radar data assimilation or with a threedimensional variational scheme assimilating the same radar observations. Moreover, nearly all members from the ensemble forecasts initialized with EnKF analysis perturbations predict rapid formation and intensification of the storm. However, the large ensemble spread of peak intensity, which ranges from a tropical storm to a category 2 hurricane, echoes limited predictability in deterministic forecasts of the storm and the potential of using ensembles for probabilistic forecasts of hurricanes.
    Zhao K., M. Xue, 2009: Assimilation of coastal Doppler radar data with the ARPS 3DVAR and cloud analysis for the prediction of Hurricane Ike (2008). Geophys. Res. Lett.,36, doi: 10.1029/2009GL038658.10.1029/2009GL038658acd63ea3f0d4c40ae09acd4c77ae2d43http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F2009GL038658%2Ffullhttp://onlinelibrary.wiley.com/doi/10.1029/2009GL038658/fullAbstract Top of page Abstract 1.Introduction 2.Method and Experimental Design 3.Results of Experiments 4.Summary Acknowledgments References [1] The impact of radar data on the analysis and prediction of the structure, intensity, and track of landfalling Hurricane Ike (2008), at a cloud-resolving resolution, is examined. Radial velocity (Vr) and reflectivity (Z) data from coastal radars are assimilated over a 6-h period before Ike landfall, using the ARPS 3DVAR and cloud analysis package through 30-min assimilation cycles. Eighteen-hour predictions were made. All 4 experiments that assimilate radar data produce better structure, intensity and precipitation forecasts than that from operational GFS analysis. The improvement to the track forecast lasts for the entire 18 hours while that to intensity prediction lasts about 12 hours. The Vr data help improve the track forecast more while reflectivity data help improve intensity forecast most. Best results are obtained when both Z and Vr data are assimilated.
    Zhao K., X. F. Li, M. Xue, B. J.-D. Jou, and W.-C. Lee, 2012: Short-term forecasting through intermittent assimilation of data from Taiwan and mainland China coastal radars for Typhoon Meranti (2010) at landfall. J. Geophys. Res., 117,D06108, doi: 10.1029/2011JD017109.10.1029/2011JD017109d0f084bd27db38edfea47485f3c40b9ahttp%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F2011JD017109%2Ffullhttp://onlinelibrary.wiley.com/doi/10.1029/2011JD017109/fullRadial velocity (Vr) and reflectivity (Z) data from eight coastal operational radars of mainland China and Taiwan are assimilated for the first time using the ARPS 3DVAR and cloud analysis package for Pacific Typhoon Meranti of 2010. It is shown that the vortex-scale circulations of Meranti can be adequately established after only 2 hourly assimilation cycles while additional cycles provide more details for subvortex-scale structures. Subsequent 12 h forecasts of typhoon structure, intensity, track, and precipitation are greatly improved over the one without radar data assimilation. Vr data lead to a larger improvement to the intensity and track forecasts than Z data, while additional Z data further improve the precipitation forecast. Overall, assimilating both Vr and Z data from multiple radars gives the best forecasts. In that case, three local rainfall maxima related to typhoon circulations and their interactions with the complex terrain in the southeast China coastal region are also captured. Assimilating radar data at a lower 3 or 6 hourly frequency leads to a weaker typhoon with larger track forecast errors compared to hourly frequency. An attempt to assimilate additional best track minimum sea level pressure data is also made; it results in more accurate surface pressure analyses, but the benefit is mostly lost within the first hour of forecast. Assimilating data from a single Doppler radar with a good coverage of the typhoon inner core region is also quite effective, but it takes one more cycle to establish circulation analyses of similar quality. The forecasts using multiple radars are still the best.
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Manuscript received: 03 December 2015
Manuscript revised: 29 April 2016
Manuscript accepted: 04 May 2016
通讯作者: 陈斌, bchen63@163.com
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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Evaluation of Two Momentum Control Variable Schemes and Their Impact on the Variational Assimilation of Radar Wind Data: Case Study of a Squall Line

  • 1. Jiangsu Research Institute of Meteorological Sciences, Nanjing 210009, China
  • 2. Key Laboratory of Mesoscale Severe Weather/MOE, and School of Atmospheric Sciences, Nanjing University, Nanjing 210023, China
  • 3. Jiangsu Provincial Observatory, Nanjing 210008, China

Abstract: Different choices of control variables in variational assimilation can bring about different influences on the analyzed atmospheric state. Based on the WRF model's three-dimensional variational assimilation system, this study compares the behavior of two momentum control variable options——streamfunction velocity potential (ψ-χ) and horizontal wind components (U-V)——in radar wind data assimilation for a squall line case that occurred in Jiangsu Province on 24 August 2014. The wind increment from the single observation test shows that the ψ-χ control variable scheme produces negative increments in the neighborhood around the observation point because streamfunction and velocity potential preserve integrals of velocity. On the contrary, the U-V control variable scheme objectively reflects the information of the observation itself. Furthermore, radial velocity data from 17 Doppler radars in eastern China are assimilated. As compared to the impact of conventional observation, the assimilation of radar radial velocity based on the U-V control variable scheme significantly improves the mesoscale dynamic field in the initial condition. The enhanced low-level jet stream, water vapor convergence and low-level wind shear result in better squall line forecasting. However, the ψ-χ control variable scheme generates a discontinuous wind field and unrealistic convergence/divergence in the analyzed field, which lead to a degraded precipitation forecast.

1. Introduction
  • Severe convection is among the most common natural hazards in Jiangsu Province, China. Accurate prediction of severe convective weather is crucial for the protection of lives and property. Apart from good prediction models, an accurate initial condition is also a vital factor for improving forecasts, which requires well-performed data assimilation methods. Based on some well-known regional prediction models, such as the WRF model (Skamarock et al., 2008), APRS (Advanced Regional Prediction) (Xue et al., 2003) and GRAPES (Global and Regional Assimilation and Prediction System) (Chen et al., 2008), conventional observations are widely applied in regional operations. For instance, the real-time WRF-RUC (Rapid Update Cycle) (Benjamin et al., 2004) analysis-forecast system is currently used at Jiangsu Meteorological Bureau to assimilate surface synoptic observations, as well as automatic station, radiosonde and wind profiler data. In addition, GPS/MET precipitable water data have been evaluated and introduced into the WRF model for the Jiangsu region (Zeng et al., 2014). However, for the forecasting of severe convection, a better description of three-dimensional dynamic and thermodynamic structures in the initial condition is crucial, which greatly depends on radar data assimilation.

    Many studies have been conducted on radar data assimilation into numerical models. For example, based on the WRF forecasting model, an observation operator for Doppler radial velocity (Sun and Crook, 1997, 1998) was developed within WRF's three-dimensional variational system (WRF-3DVAR) by (Xiao et al., 2005). With the implementation of this operator it was found that radial velocity assimilation was effective in improving the quantitative precipitation forecast for a heavy rainfall case. In addition, a radar reflectivity data assimilation scheme was developed, and the capability of reflectivity assimilation during the landfall of typhoon Rusa (2002) was assessed, in (Xiao and Sun, 2007). Meanwhile, (Pu et al., 2009) explored the impact of airborne Doppler radar wind and reflectivity assimilation using WRF-3DVAR on the forecasting of hurricane Dennis (2005). Broadly speaking, much effort has been applied during the last 10 years in research on various weather systems, including tropical cyclones, heavy rainfall and squall lines (Sheng et al., 2006; Yang et al., 2006; Shi et al., 2009; Zhang et al., 2009; Zhao and Xue, 2009; Zhao et al., 2012; Sun and Wang, 2013a; Wang et al., 2013; Dong and Xue, 2013); and these results suggest——as compared to reflectivity data, which mainly adjust the moisture field——that radial velocity is more effective in improving initial dynamic structures, which are important for the prediction of severe convection.

    Among the various data assimilation methods, 3DVAR is computationally efficient and suitable for operational use. However, the quality of the 3DVAR analyzed field depends on the reasonable construction of the background error covariance (B) matrix used in the variational method. It is well recognized that the B matrix can be approximately generated via the so-called "NMC (National Meteorological Center) method" (Parrish and Derber, 1992) from the statistics of differences between 24-h and 12-h forecasts, typically. Owing to the extremely large dimensions (in excess of 106× 106) of the B matrix, control variable preconditioning is usually applied to avoid the explicit computation of the B matrix. Since different control variables can lead to different B structures, the assimilation results are affected by the choice of control variables. For radar wind assimilation, the behavior of the horizontal wind analysis is mainly determined by the momentum control variables. Two different options are commonly used in regional models (e.g. WRF-3DVAR, ARPS-3DVAR): (1) streamfunction (ψ) and velocity potential (χ); (2) eastward wind (U) and northward wind (V). The former preserves the wind integral values due to the fact that streamfunction and velocity potential are essentially the integration of U and V, while the latter preserves the wind itself (Xie and MacDonald, 2012). In WRF-3DVAR (Barker et al., 2004), before version 3.7 was released, ψ-χ was the only option for momentum control. By contrast, ARPS-3DVAR (Gao et al., 2004) has the ability to use either ψ-χ or U-V as momentum control variables, and the U-V option is used in most ARPS-3DVAR applications (Gao et al., 2004; Hu et al., 2006; Zhao and Xue, 2009).

    Although the ψ-χ control variable option is a popular choice for operational models, recent studies suggest that it may not be suitable for small-scale analysis and forecasts in regional models. Through theoretical investigation, (Xie and MacDonald, 2012) demonstrated that, due to the property of preserving wind integral values possessed by streamfunction and velocity potential, a 3DVAR system using streamfunction and velocity potential (ψ-χ 3DVAR, hereafter) tends to produce nonphysical wind increments with opposite direction to the observed wind in the neighborhood around the observation point. (Sun and Wang, 2013b) reported the same discovery in a review article, and proposed that a 3DVAR system using horizontal wind components (U-V 3DVAR, hereafter) can solve this problem in cases of convective-scale wind assimilation. Besides, in a tropical cyclone case, (Li et al., 2015) described ψ-χ 3DVAR as producing unreasonable circulation around the vortex inner core after radar wind assimilation, and thus the subsequent track forecast was degraded. All these results indicate that comparing ψ-χ 3DVAR and U-V 3DVAR in analyses and forecasts would be useful in identifying the most suitable momentum control variable option for convective-scale wind data assimilation.

    In a recent study, (Sun et al., 2016) compared in detail the behavior of ψ-χ and U-V momentum control in WRF-3DVAR through real-data experiments on seven convective events. In addition to the issues addressed by (Xie and MacDonald, 2012), the characteristics of background error statistics of the two momentum control variable options, which can also impact the quality of the analysis and forecast results, were discussed. It was found that the ψ-χ control variable option tends to increase the length scale and decrease the variance for U and V, which causes a negative impact on the small-scale features of analyzed wind fields, and on precipitation predictions. The assimilation of Doppler radar data was also examined for one of the seven cases in their study. The results suggested that U-V 3DVAR allows a closer fit to radar radial velocity observations, which leads to better short-term precipitation prediction, as compared to ψ-χ 3DVAR.

    The present study examines the behavior of ψ-χ 3DVAR and U-V 3DVAR in the assimilation of radial velocity data from 17 Doppler radars around Jiangsu Province, China, for a squall line case that occurred on 24 August 2014. Based on the WRF-3DVAR data assimilation system, this study focuses on the impact of the two sets of control variables on the dynamic structures of the squall line analyses. Furthermore, the impacts of radar data assimilation on the formation and development of the squall line are also investigated and compared between ψ-χ 3DVAR and U-V 3DVAR. Following this introduction, section 2 describes the WRF-3DVAR system and the modeling process of the two momentum control variable options, the localized Jiangsu WRF-RUC analysis-forecast system, and the radar radial velocity assimilation method. Section 3 examines the squall line case, including an overview of the synoptic situation, a description of the experimental configuration, the performance of the single observation test, the impact of radar data assimilation, and the forecast results. A summary and conclusions are presented in section 4.

2. Method and model description
  • In WRF-3DVAR, the analysis field is obtained via minimizing the cost function as \begin{equation} J({x})=\dfrac{1}{2}({x}-{x}_{\rm b})^{\rm T}{B}^{-1}({x}-{x}_{\rm b})+\dfrac{1}{2}[{y}_{\rm o}-{H}({x})]^{\rm T}{R}^{-1}[{y}_{\rm o}-{H}({x})] . (1)\end{equation}

    Here, x is the analysis vector, x b is the background vector, y o is the observation vector, H stands for the nonlinear observation operator, B is the background error covariance, and R is the observation error covariance.

    In this study, the background error covariance B is derived from a forecast difference ensemble generated by the WRF forecasts during June 2014 using the "NMC method" (Parrish and Derber, 1992), which averages the forecast differences between two forecasts (24-h minus 12-h) valid at the same time over a period of time (one month): \begin{equation} \label{eq1} {B}\equiv\overline{({x}_{\rm b}-{x}_{\rm t})({x}_{\rm b}-{x}_{\rm t})^{\rm T}}\equiv\overline{{\varepsilon}_{\rm b}{\varepsilon}_{\rm b}^{\rm T}} \cong\overline{({x}_{24}-{x}_{12})({x}_{24}-{x}_{12})^{\rm T}} . (2)\end{equation}

    Here, the overbar denotes an average over time and geographical area; x t and x b are the true atmospheric state and background state, respectively; ε b stands for the background error; and x24 and x12 are the 24-h and 12-h forecasts valid at the same time, respectively. In the WRF-3DVAR system, the background error covariance matrix B can be decomposed as B=UU T, with U=U pU vU h, where U h is a horizontal transform, U v is a vertical transform, and U p is a physical variable transform (Barker et al., 2004). By applying the decomposed background matrix U, the analysis increment δ x is obtained through a control variable transform δ x=Uv, where v stands for the control variable.

    In WRFDA v3.7 (DA: data assimilation), two sets of momentum control variables are available, which are named as the CV5 and CV7 options, respectively. The CV5 option employs ψ-χ as the momentum control variables. The five control variables are streamfunction (ψ), unbalanced velocity potential (χ u), unbalanced temperature (T u), relative humidity (RH) and unbalanced surface pressure (P s,u). Through a statistical balance transform, the full variables of χ, T and P are represented by the sum of the balanced parts, which are related to ψ and the unbalanced parts of χ u, T u and P s,u, respectively. The full fields of control variables are then converted to analysis variable increments in the model space through Eq. (3): \begin{equation} \label{eq2} \left( \begin{array}{c} U\\ V\\ T\\ P_{\rm s}\\ q \end{array} \right)_{\rm Analysis}=\left( \begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} {C}_{U,\psi} & {C}_{U,\chi} & {\bf 0} & {\bf 0} & {\bf 0}\\[1mm] {C}_{V,\psi} & {C}_{V,\chi} & {\bf 0} & {\bf 0} & {\bf 0}\\[1mm] {\bf 0} & {\bf 0} & {I} & {\bf 0} & {\bf 0}\\[1mm] {\bf 0} & {\bf 0} & {\bf 0} & {I} & {\bf 0}\\[1mm] {\bf 0} & {\bf 0} & {\bf 0} & {\bf 0} & {C}_{q,{\rm RH}} \end{array} \right)\left( \begin{array}{c} \psi\\ \chi\\ T\\ P_{\rm s}\\ {\rm RH} \end{array} \right)_{\rm Control} . (3)\end{equation}

    Here, CU,ψ=-∂/∂ y, CU,χ=∂/∂ x, CV,ψ=-∂/∂ x and CV,χ=-∂/∂ y represent the relationship between streamfunction/velocity potential and the horizontal wind components U/V; Cq, RH denotes the conversion between RH and the water vapor mixing ratio; and I is the identity matrix.

    The new option, CV7, employs U-V as momentum control variables, and uses a different set of control variables: U, V, temperature (T), RH, and surface pressure (P s). Since the momentum variables have no change through the conversion from control variable space to model space, the transform is more straightforward, as follows in Eq. (4):

    \begin{equation} \left( \begin{array}{c} U\\ V\\ T\\ P_{\rm s}\\ q \end{array} \right)_{\rm Analysis}=\left( \begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} {I} & {\bf 0} & {\bf 0} & {\bf 0} & {\bf 0}\\[0.5mm] {\bf 0} & {I} & {\bf 0} & {\bf 0} & {\bf 0}\\[0.5mm] {\bf 0} & {\bf 0} & {I} & {\bf 0} & {\bf 0}\\[0.5mm] {\bf 0} & {\bf 0} & {\bf 0} & {I} & {\bf 0}\\[0.5mm] {\bf 0} & {\bf 0} & {\bf 0} & {\bf 0} & {C}_{q,{\rm RH}} \end{array} \right)\left( \begin{array}{c} U\\ V\\ T\\ P_{\rm s}\\ {\rm RH} \end{array} \right)_{\rm Control} . (4)\end{equation}

    Note that, in the U-V control variable option, the wind components U and V, the temperature T, and the surface pressure P s, are full variables. These variables are assumed to be analyzed independently. As pointed out by (Sun et al., 2016), the correlation between U and V is not significant, as compared to that between ψ and χ. Therefore, no multivariate correlation between U and V is considered for the U-V control variables in this study. It should also be pointed out that other efforts (e.g. incorporating equation constraint in the cost function) can be made to represent the correlation between wind components. In the ARPS 3DVAR system, a mass continuity constraint is included to couple the three wind components together (Gao et al., 2004; Hu et al., 2006).

  • The operational Jiangsu WRF-RUC analysis-forecast system is used in this study, which includes the WRF model and WRFDA for forecasting and analyzing, respectively. Two one-way nested domains are employed. The domains have horizontal dimensions of 449× 353 and 271× 241, and grid spacings of 15 km and 3 km, respectively. All model domains have 45 vertical levels from the surface to 50 hPa. GFS analyses with 0.5° spacings are used to provide the initial conditions for all DA experiments. The boundary conditions for the coarse domain (D01) and the fine domain (D02) are provided by GFS forecasts and the WRF forecasts from D01, respectively. In real-time forecasting, four cold-start forecasts are conducted every day in D01 with 6-h time intervals. Besides, eight forecasts are carried out in D02 with 3-h time intervals, including six warm-start forecasts and two cold-start forecasts, which start at 0000 UTC and 1200 UTC, respectively (Fig. 1). The physics options include the Thompson microphysics, RRTM longwave radiation, Noah land surface, YSU (Yonsei University) planetary boundary layer, and Kain-Fritsch cumulus (15-km domain only) schemes (Skamarock et al., 2008).

    Figure 1.  Flow chart illustrating the Jiangsu WRF-RUC operational system.

  • Doppler radar data used in this study come from 17 S-band CINRAD WSR-98D (Chinese Next Generation Weather Surveillance Radar 1998 Doppler) radars in Jiangsu Province and surrounding areas (Fig. 2a). During the observation period, all radars used the VCP21 (volume coverage pattern 21), where a volume scan consists of nine elevation angles (0.5°, 1.5°, 2.4°, 3.3°, 4.3°, 6.0°, 9.9°, 14.6°, and 19.5°) and is completed in about 6 min. The maximum Doppler radial velocity range is about 230 km, and the gate spacings and azimuth resolution are 0.25 km and 1°, respectively. After quality control that includes unfolding aliased Doppler velocity and removing noise, the edited data are thinned and interpolated onto WRF grids before assimilation.

    Doppler radial velocity data assimilation in WRF-3DVAR was developed by (Xiao et al., 2005); the observation operator for radial velocity (V r) is \begin{equation} \label{eq3} V_{\rm r}=u\dfrac{x-x_{\rm i}}{r_{\rm i}}+v\dfrac{y-y_{\rm i}}{r_{\rm i}}+(w-v_{\rm T})\dfrac{z-z_{\rm i}}{r_{\rm i}} . (5)\end{equation} Here, (u,v,w) represent wind components; (x,y,z) are the radar location; (x i,y i,z i) are the location of radar observations; r i is the distance between the radar site and the observation; and v T is the terminal velocity, which can be estimated by the rainwater mixing ratio (Sun and Crook, 1997). Since the vertical velocity w is not a control variable, Richardson's equation is used in the WRF-3DVAR physical transform U p to produce the vertical velocity increment (Xiao et al., 2005). The linear and adjoint models of this equation also serve as a bridge between dynamic and thermodynamic fields. A detailed description of WRF-3DVAR radial velocity data assimilation can be found in (Xiao et al., 2005) and (Xiao and Sun, 2007).

    Figure 2.  (a) S-band Doppler radar observation network in Jiangsu Province and surrounding areas. (b, c) Geopotential height (blue solid lines; units: gpm), temperature (red solid lines; units: $^\circ$C) and wind fields (wind barbs) at 500 hPa and 850 hPa, respectively, at 0000 UTC 24 August 2014. (d) Surface pressure (blue solid lines; units: hPa), surface temperature (red solid lines; units: $^\circ$C), and surface wind fields (wind barbs), at 0000 UTC 24 August 2014, and the accumulated precipitation (shaded; units: mm) during 0700-1000 UTC 24 August 2014. In all panels, the borders of Anhui Province and Jiangsu Province are highlighted with thick lines.

3. The 24 August 2014 squall line case
  • On 24 August 2014, under the combined effects of a high-level trough, low-level vortex and surface cyclone, a squall line formed near the border between Anhui and Jiangsu provinces. At 0000 UTC 24 August 2014, Jiangsu Province was affected by southwest flow in front of the westerly trough at 500 hPa (Fig. 2b). In the lower troposphere, a vortex developed near Anhui and Shandong provinces, accompanied by a wind shear line at 850 hPa. An intense southwest jet stream was present to the south of the low-level vortex (Fig. 2c). At the same time, a frontal cyclone occurred (Fig. 2d) and then moved into Jiangsu Province. During the eastward propagation of the surface cyclone, an intense and narrow squall line formed around the cold front and then moved eastward quickly. The maximum hourly rainfall in Jiangsu Province reached 25.1 mm h-1, 27.9 mm h-1, 20.9 mm h-1 and 28.5 mm h-1, respectively, from 0700 UTC to 1000 UTC.

  • In order to evaluate the influence of different momentum control variable schemes on the analysis and forecast of the squall line, three experiments are conducted. A control forecast (CTL), which only assimilates conventional data (surface observations and radiosondes) is performed first. In addition to the conventional data, the experiment RADAR_psichi assimilates radial velocity data from 17 Doppler radar around Jiangsu Province (Fig. 2a) using ψ-χ 3DVAR. For comparison purposes, RADAR_uv assimilates the same data as RADAR_psichi except it uses U-V 3DVAR. In order to make the comparison more clearly, we exclude the reflectivity data assimilation. Furthermore, WRF-RUC analyzed fields valid at 0000 UTC, 0300 UTC and 0600 UTC 24 August (Fig. 1) are chosen as the initial fields for forecasting, respectively, to investigate the impact of a different initial time on the squall line forecast. To better reflect reasonable increments associated with small-scale convection, the default horizontal correlation scales in CV5 and CV7 background error covariances are reduced by a factor of 0.2 and 0.3, respectively, following (Xiao et al., 2005), (Pu et al., 2009) and (Li et al., 2013), resulting in a decorrelation scale of approximate 20 km.

  • In this section, we examine the wind increments using the single observation test in order to clearly understand the influence of different momentum control variable schemes on the wind analysis. Choosing the GFS global analysis field at 0000 UTC 24 August as the background field, a pseudo eastward wind (U wind) observation at the grid point of (i=130, j=130, k=10) [approximately (33°N, 118.8°E), 850 hPa] is assimilated. The innovation (observation minus background) of the single U wind is assigned to be 20 m s-1. Figures 3a and b compare the analysis increments of U wind between ψ-χ 3DVAR and U-V 3DVAR. In Fig. 3a, apart from the eastward wind increments around the observation site, the ψ-χ control variable scheme produces negative increments (westward wind) in the north and south neighboring areas of the observation site, which leads to cyclonic and anticyclonic increments in these areas, respectively. Since streamfunction and velocity potential are essentially the integration of U and V, they possess the property of maintaining the horizontal wind integral values. Therefore, when the velocity changes around the observation site, the velocity adjustment of the opposite direction takes place in its near neighborhood. Owing to the property of streamfunction and velocity potential, this phenomenon cannot be completely avoided in 3DVAR even if the horizontal scale factor of the background error covariance is tuned (Xie and MacDonald, 2012). On the contrary, as shown in Fig. 4b, when the U-V control variable scheme is used, the analysis increments show consistent eastward winds, which reflect the observed wind itself more objectively.

    Figure 3.  The increments of $U$ wind (shaded; units: m s$^-1$) and wind vector at 850 hPa from single observation experiments using the (a) $\psi$-$\chi$ control variable and (b) $U$-$V$ control variable, and the increments of wind speed (shaded; units: m s$^-1$) and wind vector at 850 hPa after the assimilation of NJRD radial velocity using the (c) $\psi$-$\chi$ control variable and (d) $U$-$V$ control variable.

    For further comparing the different behavior of ψ-χ 3DVAR and U-V 3DVAR in wind assimilation, real radial velocity data from Nanjing Doppler radar (NJRD) are assimilated. The background field is also from the GFS global analysis at 0000 UTC 24 August. Figures 3c and d show the increments of wind speed and wind vector after NJRD data assimilation. Remarkable differences can be found between the wind increments from the two momentum control variable schemes. ψ-χ 3DVAR generates some local convergence/divergence and small-scale cyclonic/anticyclonic incremental structures (Fig. 3c) outside the observation region of NJRD, which are nonphysical. This result can be explained by the unrealistic negative wind increments shown by the single observation test (Fig. 3a) when ψ-χ 3DVAR is used. In comparison, the wind increments from U-V 3DVAR reflect the radar observation more objectively. The nonphysical local convergence/divergence increments are avoided (Fig. 4d).

  • The above comparison of wind analysis increments illustrates a significant difference between ψ-χ 3DVAR and U-V 3DVAR in wind assimilation. In this section, the impact of radial velocity data assimilation from 17 radars (Fig. 2) on the forecasting of the squall line is investigated by verifying the analysis and forecast results from WRF-RUC (Fig. 1).

    Figure 4 shows the horizontal wind analyzed fields at 700 hPa for experiments CTL, RADAR_psichi and RADAR_uv at 0600 UTC 24 August. As illustrated in Fig. 1, the analyzed field at 0600 UTC is the final analysis of the three assimilation cycles starting from GFS 0000 UTC with a 3-h time interval. In the analyzed fields at 700 hPa, a low-level vortex can be found in the northern region of Anhui and Jiangsu provinces for each experiment. In CTL, the center of the southwest low-level jet stream is located at approximately (33°N, 118°E), with maximum wind speed of 20 m s-1 (Fig. 4a). In comparison, the two radar assimilation experiments exhibit stronger low-level jet streams with maximum speeds of about 25 m s-1 (Figs. 4b and c), which are also located farther east than in CTL. Comparing the wind analyzed fields between RADAR_psichi and RADAR_uv, it is obvious that the horizontal winds are more continuous (Fig. 4c) when using U-V 3DVAR. Besides, consistent southwest winds appear in the southern area of Jiangsu Province, and northwest flows are found in the northern part of Anhui Province. The confluence of northwest cold flows and southwest warm flows provides potentially favorable conditions for the severe convection. However, when the ψ-χ 3DVAR is employed, the southwest low-level jet is narrower and less well-organized. The wind speeds and wind directions are discontinuous in some areas. The investigations of analyzed horizontal winds show that the assimilation of radar radial velocity data results in enhancement and location adjustment of the low-level jet stream. Similar to the results of analysis increments from single radar assimilation (Fig. 3c), RADAR_psichi generates small-scale convergence/divergence and discontinuous analyzed wind structures.

    Figure 4.  Analyzed wind speed (shaded; units: m s$^-1$) and wind vector at 700 hPa at 0600 UTC 24 August: (a) CTL; (b) RADAR_psichi; (c) RADAR_uv.

    Figure 5.  Composite reflectivity (shaded;units:dB$Z$) predicted by experiment (d-f) CTL, (g-i) RADAR_psichi, and (j-l) RADAR_uv, as compared to (a-c) observed composite reflectivity. The corresponding times are 0600 UTC, 0800 UTC, and 1200 UTC 24 August 2014. The thick solid line in (d, g, j) indicates the vertical cross section location in Fig. 9.

    To assess the impact of radar data assimilation on the analyzed and predicted structures of the squall line, Fig. 5 displays the analyzed and predicted composite radar reflectivity starting from the WRF-RUC analyzed fields at 0600 UTC in each experiment, together with the corresponding observed reflectivity fields. At 0600 UTC, observed reflectivity echoes are found near the border between Anhui and Jiangsu provinces. The structure shows an organized line of multi-cell convections along the southwest-northeast direction, with a maximum reflectivity of about 50 dBZ (Fig. 5a). In CTL (Fig. 5d), the structures of the convective line are captured to some extent. However, the analyzed squall line takes place farther west than observed, with a bias of approximately 0.5° longitude. By contrast, the analyzed squall lines in the other two radar assimilation experiments are better located, matching observations well, and better organized, especially in RADAR_uv (Fig. 5j). However, in RADAR_psichi, an unrealistic rainfall band occurs ahead of the squall line. The echoes of this rainfall band are as large as that of the squall line, while the intensity is relatively weak (Fig. 5g). At 0800 UTC, the observed squall line moves eastward to about 119°E, showing better organized convective-line structures (Fig. 5b). In CTL, the system structure is not well-organized, with scattered convective cells. The location of the predicted squall line still shows westward bias (Fig. 5e), suggesting it moves slower than observed. The unrealistic precipitation band also appears ahead of the predicted squall line in RADAR_psichi (Fig. 5h), the same as that at 0600 UTC. Compared with the other experiments, the squall line in RADAR_uv still shows an organized convective line with better intensity and location, though slightly wider (Fig. 5k) than observed. At 1200 UTC, the observed squall line moves out of Jiangsu Province (Fig. 5c). In CTL (Fig. 5f) and RADAR_psichi (Fig. 5i), the organized structures of squall lines disappear and the eastern region of Jiangsu Province is covered by large-area rainfall. In contrast, although the predicted precipitation appears slightly farther west than observed, RADAR_uv still exhibits the organized structures of the convective line clearly (Fig. 5l).

    To investigate the water vapor condition, the water vapor flux divergences at 700 hPa for all experiments are shown in Fig. 6, along with the horizontal wind vectors. In the analyzed fields at 0600 UTC 24 August, it is obvious that the convergence of the northwest flow associated with the low-level vortex and the southwest warm flow on the south side form a strong moisture convergence zone. The water vapor convergence area in CTL is located near (33.5°N, 117.5°E) (Fig. 6a), matching the precipitation region (Fig. 5d) well. The suggestion, therefore, is that the position bias of the predicted squall line in CTL is mainly caused by the incorrect moisture convergence in the analyzed field. In RADAR_uv, the strong water vapor convergence zone is located near the border between Anhui and Jiangsu provinces, to the east of 118°E, and exhibits several independent structures arranged in a southwest-northeast oriented line (Fig. 6c). The large negative values of water vapor flux divergence reflect the convective precipitation (Fig. 5j) well. In comparison, in RADAR_psichi, apart from the moisture convergence zone that corresponds to the squall line echoes, there is a distinct band of water vapor convergence near 118.2°, from 31.5°N to 32.5°N, caused by the significant horizontal wind shear (Fig. 6b). This unexpected moisture convergence zone is considered to be the main factor for the unrealistic rainfall band ahead of the squall line. The investigation of water vapor flux divergence demonstrates that the assimilation of radar radial velocity through U-V 3DVAR corrects the position of the convergence area by correctly adjusting the wind fields, and thus benefits the forecasting of the subsequent squall line. However, RADAR_psichi produces a problematic analyzed wind field that leads to unexpected moisture convergence.

    Figure 6.  Horizontal wind vector and water vapor flux divergence (shaded; units: 10$^-6$ g cm$^-1$ hPa$^-1$ s$^-1$) at 700 hPa at 0600 UTC 24 August 2014: (a) CTL; (b) RADAR_psichi; (c) RADAR_uv.

    Figure 7.  One-hour ETSs of predicted hourly accumulated precipitation at the 5 mm h$^-1$ threshold for experiment CTL (green lines), RADAR_psichi (blue lines) and RADAR_uv (red lines), from different initial times.

    Figure 8.  Wind field (vectors) at the lowest model level and composite reflectivity (shaded; units: dB$Z$) at 0400 UTC 24 August 2014 in (a) CTL, (b) RADAR_psichi and (c) RADAR_uv, as compared to (d) observed composite reflectivity. The blue curved line in (a-c) indicates the wind convergence line.

    To evaluate the forecasting skill for the heavy rain associated with the squall line, we present in Fig. 7 the equitable threat score (ETS) of the hourly accumulated precipitation for the 5 mm h-1 threshold from 0700 UTC to 1200 UTC. All of the experiments, with their different initial times, are verified against CMORPH analyses (Joyce et al., 2004; Xie and Xiong, 2011) with a resolution of 0.1°× 0.1°. For the forecasts launched at 0000 UTC, the ETSs in the three experiments are all below 0.2, declining as the forecasting time goes on. Since 0000 UTC is four hours earlier than the observed genesis time of the squall line, the improvement brought by radar data assimilation is actually limited. For the forecasts launched at 0300 UTC, the impacts of radar radial velocity data assimilation are obvious. As compared to CTL, RADAR_psichi and RADAR_uv substantially improve the heavy rain forecasting, with ETSs of 0.3 and 0.32 at 0700 UTC, respectively. However, the ETS in RADAR_psichi drops dramatically after 0800 UTC. For the forecasts launched at 0600 UTC, the ETSs in RADAR_psichi and RADAR_uv are much higher than those in CTL throughout the forecasting period. Similar to the results from 0300 UTC, RADAR_uv performs better, with an initial ETS of 0.38 at 0700 UTC——much higher than the value of 0.29 in RADAR_psichi. Overall, it is found that radar data assimilation is able to improve the forecasting of heavy precipitation associated with the squall line; and the forecasting skill improves further with more analysis cycles. Meanwhile, the relatively lower ETSs in RADAR_psichi, as compared to those in RADAR_uv, are probably a result of the unrealistic precipitation forecast (Figs. 5g and h).

  • In the previous section, the influences of radar data assimilation on the squall line forecasts are compared between ψ-χ 3DVAR and U-V 3DVAR. To further illustrate the effects of radar data assimilation on squall line formation and development, this section discusses the dynamic and thermodynamic structures in three experiments in the developing stages.

    Figure 8 shows the predicted wind fields at the lowest model level and the corresponding composite reflectivity at the approximate genesis time of the squall line (0400 UTC 24 August), together with the observed reflectivity fields. All the experiments verified are from the WRF-RUC forecasts initialized from 0300 UTC 24 August. The squall line initially forms in eastern Anhui Province (Fig. 8d). Unlike CTL, which only shows scattered convective cells (Fig. 8a), RADAR_uv preliminarily reflects the convective line to some extent (Fig. 8c), although less well-organized, in the same region as observed. As shown by the predicted winds at the lowest model level, an obvious north-south oriented convergence zone is found in the eastern region of Anhui Province, which provides an important lifting condition for triggering the severe convection. However, RADAR_psichi exhibits an extra convective region near 117°E, to the south of 31.5° (Fig. 8b), as compared with observed radar echoes. The unrealistic convection is probably triggered by the long and narrow convergence line at the low level (Fig. 8b), which has greater north-south span than that in RADAR_uv. This result suggests that the unrealistic convective rainfall band in RADAR_psichi (Figs. 5g and h), which occurs throughout the lifespan of the squall line forecast, is partly attributable to the inaccurate wind fields that lead to incorrect convergence in the near-surface layer during the formation of the squall line.

    To investigate the dynamic and thermodynamic characteristics of the squall line system, we display the vertical cross section of the environmental pseudo-equivalent potential temperature, horizontal wind vectors and reflectivity at 0600 UTC 24 August in Figs. 9a-c, respectively. Besides, the vertical structure of temperature anomalies and velocity vectors along the cross section are presented in Figs. 9d-f. The chosen cross sections of all the experiments are shown in Figs. 5d, g and j. In all three experiments, the environmental pseudo-equivalent potential temperature in the lower levels (below 850 hPa) is higher than that in the middle levels (850-700 hPa) in front of the predicted squall lines. The obvious thermodynamic instability (∂θ/∂ p>0) ahead of the squall line below 700 hPa is conducive to the initiation of single-cell thunderstorms within the squall line, as well as the maintenance of the whole squall line system. Furthermore, low-level wind shear is regarded as a key factor for the maintenance and development of squall lines (Newton, 1950, 1966; Fujita, 1955; Bluestein and Jain, 1985). In front of the squall line in CTL, southeast wind exists near the surface; however, it turns to southwest wind at 850 hPa (Fig. 9a), reflecting wind direction shear at lower levels. In comparison, in RADAR_uv, with the help of radar wind data assimilation, the southwest winds between 850 hPa and 600 hPa are distinctly enhanced in front of the squall line (Fig. 9c), such that the lower-level wind shear is enlarged. Furthermore, the cold pool behind the squall line in RADAR_uv (Fig. 9f) is found to be stronger than that in RADAR_psichi (Fig. 9e), and the lower-level vertical shear ahead of the squall line is also more obvious (Fig. 9f). According to Rotunno-Klemp-Weisman (RKW) theory (Rotunno et al., 1988), the interaction of the cold pool and lower-level vertical shear can produce much deeper and non-inhibited lifting. Thus, the environmental conditions in RADAR_uv are more favorable for the development of the squall line. Nevertheless, note that the minimum temperature anomaly is -4 K and the isoline of -1 K extends to only 850 hPa in RADAR_uv, suggesting the strength of the cold pool is not strong enough at this stage. Therefore, the positive vorticity induced by the wind shear dominates over the negative vorticity caused by the cold pool, and the air ahead of the cold pool is preferentially dragged up and tilted downshear (Fig. 9f). It can be concluded that the successful subsequent forecast for the squall line in RADAR_uv (Figs. 5k and l) relies on the improvement of lower-level wind structures, which leads to a stronger vertical wind shear condition. Besides, note that the upper-level wind speeds of the southwest flows in RADAR_psichi (Fig. 9b) are much larger ahead of the squall line than those in RADAR_uv. The upper-level horizontal wind speed gradient in RADAR_psichi leads to divergence above 300 hPa, which is favorable for the maintenance and development of convective systems. As a result, the vertical cross section of reflectivity in RADAR_psichi shows a broader convective rainfall band than that in RADAR_uv, especially at the high levels above 500 hPa in front of the squall line (Fig. 9b).

    The maintenance and development of squall line systems largely rely on the vorticity transports from the environmental flow. As the storm-relative helicity (SRH) [\(\rm SRH=\int_0^z(\overline V-\overline C)\omega_\rm H\rm dz\); where \(\overline V\) denotes wind speed, \(\overline C\) represents the moving speed of the storm, ω H is vertical vorticity, and z is the height] can reflect the degree of rotation in the environmental flow and the environmental vorticity transported into convective cells (Brandes et al., 1988; Davies-Jones et al., 1990), SRH is considered to be a measure of the potential for updraft rotation in thunderstorm cells. Figure 10 shows the 0-3 km SRH for the three experiments at 0600 UTC 24 August. Large SRH values are obvious in the north-central region of Jiangsu Province in all experiments, corresponding to the convective precipitation (Fig. 5) on the north side of the squall line. Besides, as compared to CTL, RADAR_psichi and RADAR_uv clearly show southwest-northeast oriented large values (in excess of 250 m2 s-2) of SRH to the east of 118°E, from 31°N to 33°N (Figs. 10b and c), indicating the moving trend of the squall line more correctly. Within the region of large SRH values, the horizontal vorticity resulting from vertical wind shear transforms to the vertical vorticity, with the contribution of tilting effects brought by the lower-level inflow. As a result, sustained vertical vorticity ahead of the storm line provides favorable conditions for the development of the squall line system and convective precipitation. Meanwhile, in CTL, the region of large SRH values, which is located to the west of 118°E (Fig. 10a), also explains why the predicted squall line is situated farther west (Fig. 5d) than observed. Through the investigation of the SRH distribution in all experiments, it can be concluded that, as the SRH is diagnosed by lower-level wind structures, the improvement in wind fields brought about by radar wind data assimilation can be ascribed as a main factor for better predicting the squall line.

    Figure 9.  Cross sections of the pseudo-equivalent temperature (shaded; units: K), reflectivity (contours; units: dB$Z$) and horizontal wind (vectors) at 0600 UTC 24 August in (a) CTL, (b) RADAR_psichi and (c) RADAR_uv. Cross sections of temperature anomalies (shaded; units: K), reflectivity (contours; units: dB$Z$) and velocity vectors ($U,W$) ($U$ stands for the wind component along the horizontal axis of the cross section; $W$ is the vertical wind component) in (d) CTL, (e) RADAR_psichi and (f) RADAR_uv at 0600 UTC 24 August 2014.

    Figure 10.  Storm-relative helicity (shaded; units: m$^2$ s$^-2$) in the 0-3 km layer at 0600 UTC 24 August 2014 in (a) CTL, (b) RADAR_psichi and (c) RADAR_uv.

4. Summary and conclusions
  • This study compares the behavior of two momentum control variable options of 3DVAR [stream function-velocity potential (ψ-χ) and horizontal wind components (U-V)] in radar wind data assimilation for a convective case. Based on the Jiangsu WRF-RUC analysis-forecast system, the assimilation of Doppler radar radial velocity data using WRF-3DVAR is explored for the analysis and prediction of a squall line that affected Jiangsu Province and surrounding areas on 24 August 2014. The main conclusions can be summarized as follows:

    A single observation test is performed to evaluate the characteristics of the two momentum control variable options in wind data assimilation. The wind increments show that the ψ-χ control variable scheme produces nonphysical negative increments in the neighborhood around the observation point because streamfunction and velocity potential preserve integrals of velocity. This property results in unrealistic local convergence and divergence when radar wind data is assimilated. On the contrary, the U-V control variable scheme produces consistent wind increments with the same direction as observed, which objectively reflects the observation itself. As a result, the analysis increments from radar wind data assimilation realistically reveal the information of radar observations.

    Three experiments are conducted to evaluate the impact of radar wind data assimilation on the squall line forecast. In addition to CTL, which only assimilates conventional observations, RADAR_psichi and RADAR_uv further assimilate 17 Doppler radars around Jiangsu Province using ψ-χ 3DVAR and U-V 3DVAR, respectively. Compared to the conventional data, the assimilation of Doppler radar winds significantly improves the mesoscale dynamic fields, in terms of enhancing the southwest low-level jet stream and the water vapor convergence. These lead to better location and structure prediction of the squall line, as well as preferable forecasting skill with respect to strong precipitation. Besides, benefiting from the improvement of lower-level wind structures brought about by radar data assimilation, the near-surface wind convergence triggers the convection more effectively, and the enhanced lower-level wind shear provides more favorable conditions for the maintenance of convective cells in the squall line system. During the developing stage, both of the two radar data assimilation experiments (RADAR_psichi and RADAR_uv) exhibit large values of SRH arranged in a line ahead of the moving direction of the squall line, suggesting strong vorticity enters the updraft flow along the storm streamline. The improved wind field caused by radar wind data assimilation is considered to be a key factor for a better squall line forecast.

    The different impacts on the analyzed fields and subsequent squall line predictions are compared between the ψ-χ and U-V momentum control variable options in 3DVAR. When the ψ-χ control variable scheme is applied, RADAR_psichi shows discontinuous wind analyzed fields that generate obvious convergence/divergence in some regions. The strong water vapor convergence resulting from the unrealistic wind fields leads to an unexpected rainfall band forecast, and thus degrades the precipitation forecasting skill. In comparison, using U-V as momentum control variables, RADAR_uv avoids the unrealistic wind convergence in the analyzed fields and more objectively reflects the radar observation itself. The subsequent forecasts of squall line structures and strong precipitation are significantly improved.

    In this study, the appropriate selection of momentum control variables in variational data assimilation is evaluated through numerical research on a squall line case that occurred on 24 August 2014. The impacts of radar wind data assimilation in the regional model are distinctly influenced by the chosen momentum control variables. Consistent with (Sun et al., 2016), our results demonstrate that U-V is more suitable than ψ-χ for small-scale wind assimilation in convective weather cases. The dynamic structures in the analyzed fields of U-V 3DVAR are found to provide more favorable conditions for the development of severe convection. Although the results are encouraging, to make the conclusions more general, investigations into other severe weather systems (e.g. tropical cyclones) should be conducted in future studies.

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