ORIGINAL PAPER Balance characteristics of multivariate background error covariance for rainy and dry seasons and their impact on precipitation forecasts of two rainfall events Yaodeng Chen 1,2 • Xue Xia 1,2 • Jinzhong Min 1,2 • Xiang-Yu Huang 3 • Syed R. H. Rizvi 4 Received: 24 June 2015 / Accepted: 14 January 2016 / Published online: 8 February 2016 Ó Springer-Verlag Wien 2016 Abstract Atmospheric moisture content or humidity is an important analysis variable of any meteorological data assimilation system. The humidity analysis can be uni- variate, using humidity background (normally short-range numerical forecasts) and humidity observations. However, more and more data assimilation systems are multivariate, analyzing humidity together with wind, temperature and pressure. Background error covariances, with unbalanced velocity potential and humidity in the multivariate formu- lation, are generated from weather research and forecasting model forecasts, collected over a summer rainy season and a winter dry season. The unbalanced velocity potential and humidity related correlations are shown to be significantly larger, indicating more important roles unbalanced velocity potential and humidity play, in the rainy season than that in the dry season. Three cycling data assimilation experiments of two rainfall events in the middle and lower reaches of the Yangtze River are carried out. The experiments differ in the formulation of the background error covariances. Results indicate that only including unbalanced velocity potential in the multivariate background error covariance improves wind analyses, but has little impact on tempera- ture and humidity analyses. In contrast, further including humidity in the multivariate background error covariance although has a slight negative effect on wind analyses and a neutral effect on temperature analyses, but significantly improves humidity analyses, leading to precipitation fore- casts more consistent with China Hourly Merged Precipi- tation Analysis. 1 Introduction The background error covariance matrix (B) plays a crucial role in meteorological data analysis (Bannister 2008a, b). For operations of meteorological data assimilation, the size of B is very large (typically, *10 7 9 l0 7 ), which could lead to great difficulties in the storage and computations. It is mainly for this reason B has to be simplified with approximations and often modeled using a suitable se- quence of analysis control variable transforms (CVTs) (Parrish and Derber 1992; Courtier et al. 1998; Gustafsson et al. 2001; Barker et al. 2012). Generally, CVTs include horizontal, vertical and physical transforms. The horizontal and vertical transforms handle the error correlations in horizontal and vertical. The physical transform handles error correlations between different meteorological vari- ables. Dynamic balance relations can be imposed through physical transforms. It remains a major challenge for variational data assimilation schemes to derive a reason- able and manageable representation of B (Derber and Bouttier 1999; Gustafsson et al. 2001;Z ˇ agar et al. 2005; Berre et al. 2006; Michel and Auligne´ 2010; Storto and Randriamampianina 2010; Michel et al. 2011; Chen et al. 2013; Wang et al. 2014). Responsible Editor: F. Mesinger. & Yaodeng Chen keyu@nuist.edu.cn 1 Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, NUIST, Nanjing 210044, China 2 Key Laboratory of Meteorological Disaster of Ministry of Education, NUIST, Nanjing 210044, China 3 Meteorological Service Singapore, Centre for Climate Research Singapore, Singapore 537054, Singapore 4 National Center for Atmospheric Research, Boulder, CO, USA 80301 123 Meteorol Atmos Phys (2016) 128:579–600 DOI 10.1007/s00703-016-0434-4