[1] Laura Baker, Alison Rudd, Stefano Migliorini, and Ross Bannister. Representation of model
error in a convective-scale ensemble prediction system. Nonlinear Processes in Geophysics ,
21:19�39, 2014.
[2] Susan P Ballard, Zhihong Li, David Simonin, and Jean-François Caron. Performance of 4D-
Var NWP-based nowcasting of precipitation at the Met O�ce for summer 2012. Quarterly
Journal of the Royal Meteorological Society , 142(694):472�487, 2016.
[3] Ross N Bannister. Can wavelets improve the representation of forecast error covariances in
variational data assimilation? Monthly Weather Review , 135(2):387�408, 2007.
[4] Ross N Bannister. A review of forecast error covariance statistics in atmospheric variational
data assimilation. II: Modelling the forecast error covariance statistics. Quarterly Journal of
the Royal Meteorological Society , 134(637):1971�1996, 2008.
[5] Ross Noel Bannister. The ABC-DA system (v1.4): a variational data assimilation system
for convective scale assimilation research with a study of the impact of a balance constraint.
Geoscienti�c Model Development , 13:3789�3816, 2020.
[6] Dale M Barker, W Huang, Yong-Run Guo, AJ Bourgeois, and QN Xiao. A three-dimensional
variational data assimilation system for MM5: Implementation and initial results. Monthly
Weather Review , 132(4):897�914, 2004.
[7] Loïk Berre. Estimation of synoptic and mesoscale forecast error covariances in a limited-area
model. Monthly Weather Review , 128(3):644�667, 2000.
[8] Loïk Berre, Simona Ecaterina �tef nescu, and Margarida Belo Pereira. The representation of
the analysis e�ect in three error simulation techniques. Tellus A , 58(2):196�209, 2006.
[9] SC Bloom, LL Takacs, AM Da Silva, and D Ledvina. Data assimilation using incremental
analysis updates. Monthly Weather Review , 124(6):1256�1271, 1996.
[10] Pierre Brousseau, Loïk Berre, François Bouttier, and Gérald Desroziers. Background-error co-
variances for a convective-scale data-assimilation system: AROME�France 3D-Var. Quarterly
Journal of the Royal Meteorological Society , 137(655):409�422, 2011.
[11] Jean-François Caron and Mark Buehner. Scale-dependent background error covariance local-
ization: Evaluation in a global deterministic weather forecasting system. Monthly Weather
Review , 146(5):1367�1381, 2018.
[12] Jean-François Caron and Luc Fillion. An examination of background error correlations
between mass and rotational wind over precipitation regions. Monthly Weather Review ,
138(2):563�578, 2010.
[13] Philippe Courtier and Olivier Talagrand. Variational assimilation of meteorological observa-
tions with the direct and adjoint shallow-water equations. Tellus A , 42(5):531�549, 1990.
[14] MJP Cullen and T Davies. A conservative split-explicit integration scheme with fourth-order
horizontal advection. Quarterly Journal of the Royal Meteorological Society , 117(501):993�
1002, 1991.
[15] Alex Deckmyn and Loïk Berre. A wavelet approach to representing background error covari-
ances in a limited-area model. Monthly Weather Review , 133(5):1279�1294, 2005.
[16] J Derber and F Bouttier. A reformulation of the background error covariance in the ECMWF
global data assimilation system. Tellus A , 51(2):195�221, 1999.
[17] Michael Fisher and Erik Andersson. Developments in 4D-Var and Kalman �ltering . European
Centre for Medium-Range Weather Forecasts, 2001.
[18] Mike Fisher. Background error covariance modelling. In Seminar on Recent Development in
Data Assimilation for Atmosphere and Ocean , pages 45�63, 2003.
[19] Jidong Gao, Ming Xue, Alan Shapiro, and Kelvin K Droegemeier. A variational method
for the analysis of three-dimensional wind �elds from two Doppler radars. Monthly weather
review , 127(9):2128�2142, 1999.
[20] P Gauthier, M Buehner, and L Fillion. Background-error statistics modelling in a 3d varia-
tional data assimilation scheme: Estimation and impact on the analyses. In Proc. ECMWF
Workshop on Diagnosis of Data Assimilation Systems , pages 131�145, 1999.
[21] Guoqing Ge, Jidong Gao, and Ming Xue. Diagnostic pressure equation as a weak constraint
in a storm-scale three-dimensional variational radar data assimilation system. Journal of
Atmospheric and Oceanic Technology , 29(8):1075�1092, 2012.
[22] BC Peter Heng, Robert Tubbs, Xiang-Yu Huang, Bruce Macpherson, Dale M Barker, Dou-
glas FA Boyd, Graeme Kelly, Rachel North, Laura Stewart, Stuart Webster, et al. SINGV-DA:
A data assimilation system for convective-scale numerical weather prediction over Singapore.
Quarterly Journal of the Royal Meteorological Society , 2020.
[23] Daniel Hodyss and Nancy Nichols. The error of representation: Basic understanding. Tellus
A: Dynamic Meteorology and Oceanography , 67(1):24822, 2015.
[24] Y Honda, M Nishijima, K Koizumi, Y Ohta, K Tamiya, T Kawabata, and T Tsuyuki. A
pre-operational variational data assimilation system for a non-hydrostatic model at the Japan
Meteorological Agency: Formulation and preliminary results. Quarterly Journal of the Royal
Meteorological Society , 131(613):3465�3475, 2005.
[25] PL Houtekamer, Louis Lefaivre, Jacques Derome, Harold Ritchie, and Herschel L Mitchell. A
system simulation approach to ensemble prediction. Monthly Weather Review , 124(6):1225�
1242, 1996.
[26] Ming Hu, Ming Xue, and Keith Brewster. 3DVar and cloud analysis with WSR-88D level-
II data for the prediction of the Fort Worth, Texas, tornadic thunderstorms. Part I: Cloud
analysis and its impact. Monthly Weather Review , 134(2):675�698, 2006.
[27] N Bruce Ingleby. The statistical structure of forecast errors and its representation in the
Met. O�ce global 3-D variational data assimilation scheme. Quarterly Journal of the Royal
Meteorological Society , 127(571):209�231, 2001.
[28] Daryl T Kleist, David F Parrish, John C Derber, Russ Treadon, Ronald M Errico, and Runhua
Yang. Improving incremental balance in the GSI 3DVar analysis system. Monthly Weather
Review , 137(3):1046�1060, 2009.
[29] AC Lorenc. A global three-dimensional multivariate statistical interpolation scheme. Monthly
Weather Review , 109(4):701�721, 1981.
[30] AC Lorenc, SP Ballard, RS Bell, NB Ingleby, PLF Andrews, DM Barker, JR Bray, AM Clay-
ton, T Dalby, D Li, T Payne, and F Saunders. The Met. O�ce global three-dimensional
variational data assimilation scheme. Quarterly Journal of the Royal Meteorological Society ,
126(570):2991�3012, 2000.
[31] Peter Lynch and Xiang-Yu Huang. Initialization of the HIRLAM model using a digital �lter.
Monthly Weather Review , 120(6):1019�1034, 1992.
[32] Olivier Pannekoucke, Loïk Berre, and Gerald Desroziers. Filtering properties of wavelets for
local background-error correlations. Quarterly Journal of the Royal Meteorological Society ,
133(623):363�379, 2007.
[33] David F Parrish and John C Derber. The National Meteorological Center's spectral statistical-
interpolation analysis system. Monthly Weather Review , 120(8):1747�1763, 1992.
[34] Ruth Elizabeth Petrie, Ross Noel Bannister, and Michael John Priestley Cullen. The ABC
model: a non-hydrostatic toy model for use in convective-scale data assimilation investigations.
Geoscienti�c Model Development , 10(12):4419, 2017.
[35] Corey K Potvin and Louis J Wicker. Correcting fast-mode pressure errors in storm-scale
ensemble Kalman �lter analyses. Advances in Meteorology , 2013, 2013.
[36] Feifei Shen, Dongmei Xu, and Jinzhong Min. E�ect of momentum control variables on assim-
ilating radar observations for the analysis and forecast for Typhoon Chanthu (2010). Atmo-
spheric Research , 230:104622, 2019.
[37] Hyo-Jong Song and Jeon-Ho Kang. E�ects of the wind�mass balance constraint on ensemble
forecasts in the hybrid-4DEnVar. Quarterly Journal of the Royal Meteorological Society ,
145(719):434�449, 2019.
[38] Juanzhen Sun. Convective-scale assimilation of radar data: progress and challenges. Quarterly
Journal of the Royal Meteorological Society , 131(613):3439�3463, 2005.
[39] Juanzhen Sun, Ming Xue, James W Wilson, Isztar Zawadzki, Sue P Ballard, Jeanette Onvlee-
Hooimeyer, Paul Joe, Dale M Barker, Ping-Wah Li, Brian Golding, et al. Use of NWP for
nowcasting convective precipitation: Recent progress and challenges. Bulletin of the American
Meteorological Society , 95(3):409�426, 2014.
[40] P Thiruvengadam, J Indu, and Subimal Ghosh. Assimilation of Doppler weather radar data
with a regional WRF-3DVar system: Impact of control variables on forecasts of a heavy
rainfall case. Advances in Water Resources , 126:24�39, 2019.
[41] Wenxue Tong, Gang Li, Juanzhen Sun, Xiaowen Tang, and Ying Zhang. Design strategies
of an hourly update 3DVar data assimilation system for improved convective forecasting.
Weather and Forecasting , 31(5):1673�1695, 2016.
[42] Sanita Vetra-Carvalho, Mark Dixon, Stefano Migliorini, Nancy K Nichols, and Susan P Bal-
lard. Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met
O�ce Uni�ed Model. Quarterly Journal of the Royal Meteorological Society , 138(668):1709�
1720, 2012.
[43] Cheng Wang, Yaodeng Chen, Min Chen, and Jie Shen. Data assimilation of a dense wind
pro�ler network and its impact on convective forecasting. Atmospheric Research , 238:104880,
2020.
[44] Yuanfu Xie and Alexander E MacDonald. Selection of momentum variables for a three-
dimensional variational analysis. Pure and Applied Geophysics , 169(3):335�351, 2012.
[45] Dongmei Xu, Feifei Shen, and Jinzhong Min. E�ect of background error tuning on assimi-
lating radar radial velocity observations for the forecast of hurricane tracks and intensities.
Meteorological Applications , 27(1):e1820, 2020.
[46] Jun-Ichi Yano, Michaa Z Ziemia«ski, Mike Cullen, Piet Termonia, Jeanette Onvlee, Lisa
Bengtsson, Alberto Carrassi, Richard Davy, Anna Deluca, Suzanne L Gray, et al. Scien-
ti�c challenges of convective-scale numerical weather prediction. Bulletin of the American
Meteorological Society , 99(4):699�710, 2018.
[47] Xing Yu and Tae-Young Lee. Role of convective parameterization in simulations of a convection
band at grey-zone resolutions. Tellus A: Dynamic Meteorology and Oceanography , 62(5):617�
632, 2010.
[48] Zeinab Zakeri, Majid Azadi, and Sarmad Ghader. The impact of di�erent background errors in the assimilation of satellite radiances and in-situ observational data using WRFDA for three
rainfall events over Iran. Advances in Space Research , 61(1):433�447, 2018.