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John Lewis and S. Lakshmivarahan

analysis methods that were the standard in the precomputer age. In the late 1970s, the terminology for weather map analysis changed again—from objective analysis to data assimilation or more specifically four-dimensional data assimilation (4DDA), that is, analysis in space and time. 1 Amid the development of the pragmatic and computationally efficient objective analysis schemes, there came a less pragmatic and computationally more demanding methodology based on the calculus of variations—the calculus

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Y. Xie, S. Koch, J. McGinley, S. Albers, P. E. Bieringer, M. Wolfson, and M. Chan

techniques introduce additional uncertainty into maintaining the limited information in the covariance matrix. With the deployment of increasingly high-density, accurate, and advanced operational observation systems, more information is now available in the observations than ever before. We can take advantage of this information for atmospheric data assimilation to retrieve the resolvable information before applying a statistical analysis. A standard single variational approach such as three- or four

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Corey K. Potvin, Alan Shapiro, and Ming Xue

, large errors in w throughout the column will occur in cases where the horizontal divergence field changes rapidly with height near the ground, which is a common scenario with convective storms. In the variational dual-Doppler analysis techniques, the solution for the wind field within the radar data gap can be obtained from mass conservation, smoothness, and background constraints, and so no special treatment of the data gap is required ( Gao et al. 1999 ). However, the w analyzed throughout the

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Alan Shapiro, Corey K. Potvin, and Jidong Gao

hundreds to thousands of meters thick commonly separate the lower surface of data coverage from the earth’s surface, where the impermeability condition could legitimately be applied. The problem of missing low-level data is especially acute for radars operating in mountainous terrain. The analysis technique explored here is similar to the weak-constraint variational procedure of Gao et al. (1999) , although here a vertical vorticity equation is incorporated into the analysis. The vorticity equation

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Jean-Marie Beckers, Alexander Barth, Charles Troupin, and Aida Alvera-Azcárate

called Data Interpolating Variational Analysis (DIVA), whose full description can be found elsewhere ( Brasseur 1994 ; Brasseur et al. 1996 ; Troupin et al. 2012 ) and is not repeated here. Looking at DIVA gridding is not restrictive, as we can later exploit relationships with other formulations to allow for generalizations. In DIVA, the gridded field φ over the two-dimensional domain D is searched as the field that minimizes J , defined as where weights μ i control how the analysis has to

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Yanqiu Zhu, John C. Derber, R. James Purser, Bradley A. Ballish, and Jeffrey Whiting

with different parameters, such as GPSRO data whose accuracy varies with moisture uncertainty, is taken into account by the analysis. When new aircraft start reporting, their bias corrections are also automatically derived. The European Centre for Medium-Range Weather Forecasts (ECMWF) took this route and implemented a variational aircraft temperature bias correction inside their data assimilation system in 2012 ( Isaksen et al. 2012 ). Their results showed that after applying aircraft temperature

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Matthias Grzeschik, Hans-Stefan Bauer, Volker Wulfmeyer, Dirk Engelbart, Ulla Wandinger, Ina Mattis, Dietrich Althausen, Ronny Engelmann, Matthias Tesche, and Andrea Riede

other. This comparison is not the subject of this work, as we are focusing on the assimilation technique, which is expected to provide the most accurate initial water vapor fields combining the analysis and the water vapor Raman lidar data: the four-dimensional variational data analysis (4DVAR). This is due to the fact that 4DVAR takes into account the physically consistent time evolution of the model system, the temporal and spatial resolution of the observations, and the error characteristics of

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S. Mark Leidner, Bachir Annane, Brian McNoldy, Ross Hoffman, and Robert Atlas

accuracy previously impossible in practice. CYGNSS ocean surface wind speed is retrieved along each track of specular reflecting points at an interval of approximately 5 s and 25 km. Note that up to four specular points may be tracked simultaneously by each of the eight CYGNSS spacecraft. In this paper we use a variational analysis method (VAM) that adds information to retrieved CYGNSS scalar wind speeds to estimate what we will term VAM-CYGNSS wind vectors. Vector winds implicitly provide low

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Daryl T. Kleist, David F. Parrish, John C. Derber, Russ Treadon, Ronald M. Errico, and Runhua Yang

beneficial to NWP, they suffer from the fact that they undo part of the work that the assimilation had completed to fit the observational dataset ( Williamson et al. 1981 ; Errico et al. 1993 ). Variational approaches have been used to reduce the damage done by initialization after the analysis by taking into account analysis uncertainty ( Daley 1978 ; Williamson and Daley 1983 ; Fillion and Temperton 1989 ). However, it is to be expected that the best result can be obtained by including an

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Xiang-Yu Huang, Qingnong Xiao, Dale M. Barker, Xin Zhang, John Michalakes, Wei Huang, Tom Henderson, John Bray, Yongsheng Chen, Zaizhong Ma, Jimy Dudhia, Yongrun Guo, Xiaoyan Zhang, Duk-Jin Won, Hui-Chuan Lin, and Ying-Hwa Kuo

.1029/2002GL015311 . Guo , Y. R. , H-C. Lin , X. X. Ma , X-Y. Huang , C. T. Terng , and Y-H. Kuo , 2006 : Impact of WRF-Var (3DVar) background error statistics on typhoon analysis and forecast. Seventh WRF Users’ Workshop, Boulder, CO, NCAR, 7 pp. [Available online at / .] . Gustafsson , N. , 1992 : Use of a digital filter as weak constraint in variational data assimilation. Proc. Workshop on

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