Ames, W. F.: Numerical Methods for Partial Differential Equations, Nelson, London, 1958.
Bannister, R. N.: A review of forecast error covariance statistics in atmospheric variational data assimilation. II: Modelling the forecast error covariance statistics, Q. J. Roy. Meteorol. Soc., 134, 1971–1996, 2008.
Bannister, R. N.: How is the Balance of a Forecast Ensemble Affected by Adaptive and Nonadaptive Localization Schemes?,
Mon. Weather Rev., 143, 3680–3699, 2015.
Bannister, R. N.: A review of operational methods of variational and ensemble-variational data assimilation, Q. J. Roy. Meteorol. Soc., 143, 607–633, https://doi.org/10.1002/qj.2982, 2017.
Bannister, R. N., Migliorini, S., and Dixon, M.: Ensemble prediction for nowcasting with a convection-permitting model – II: forecast error statistics, Tellus A, 63, 497–512, 2011.
Berre, L.: Estimation of synoptic and mesoscale forecast error co-variances in a limited-area model, Mon. Weather Rev., 128, 644–667, 2000.
Boas, M. L.: Mathematical Methods in the Physical Sciences, Wiley, Hoboken, New Jersey, 2006.
Bryan, G., Wyngaard, J., and Fritsch, J.: Resolution requirements for the simulation of deep moist convection, Mon. Weather Rev., 131, 2394–2416, 2003.
Clark, P., Browning, K., and Wang, C.: The sting at the end of the tail: Model diagnostics of fine-scale three-dimensional structure of the cloud head, Q. J. Roy. Meteorol. Soc., 131, 2263–2292, 2005.
Clayton, A., Lorenc, A. C., and Barker, D. M.: Operational implementation of a hybrid ensemble/4D-Var global data assimilation
system at the Met Office, Q. J. Roy. Meteorol. Soc., 139, 1445–1461, 2013.
Cullen, M. J. P.: A mathematical theory of large-scale atmosphere/ocean flow, Imperial College Press, London, UK, 2006.
Cullen, M. J. P. and Davies, T.: A conservative split-explicit integration scheme with fourth-order horizontal advection, Q. J. Roy. Meteorol. Soc., 117, 993–1002, 1991.
Daley, R.: Atmospheric Data Analysis, Cambridge University Press, Cambridge, UK, 1991.
Dance, S.: Issues in high resolution limited area data assimilation for quantitative precipitation forecasting, Physica D, 196, 1–27, 2004.
Davies, T., Cullen, M., Malcolm, A., Mawson, M., Staniforth, A., White, A., and Wood, N.: A new dynamical core for the Met Office’s global and regional modelling of the atmosphere, Q. J. Roy. Meteorol. Soc., 131, 1759–1782, 2005.
Dixon, M., Li, Z., Lean, H., Roberts, N., and Ballard, S.: Impact of data assimilation on forecasting convection over the United Kingdom using a high-resolution version of the Met Office Unified Model, Mon. Weather Rev., 137, 1562–1584, 2009.
Durran, D. R.: Numerical methods for wave equations in geophysical fluid dynamics, Springer, New York, 1999.
Gadd, A. J.: A split explicit integration scheme for numerical weather prediction, Q. J. Roy. Meteorol. Soc., 104, 569–582, 1978.
Golding, B., Ballard, S., Mylne, K., Roberts, N., Saulter, A., Wilson, C., Agnew, P., Davis, L., Trice, J., Jones, C., Simonin, D., Li, Z., Pierce, C., Bennett, A., Weeks, M., and Moseley, S.: Forecasting capabilities for the London 2012 Olympics, B. Am. Meteorol. Soc., 95, 883–896, 2014.
Holton, J.: An Introduction to Dynamic Meteorology, 4th Edn., Academic Press, Burlington, Massachusetts, 2004.
Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, Cambridge, UK, 2002.
Kepert, J. D.: Covariance localisation and balance in an ensemble Kalman filter, Q. J. Roy. Meteorol. Soc., 135, 1157–1176, 2009.
Lean, H. W., Clark, P. A., Dixon, M., Roberts, N. M., Fitch, A., Forbes, R., and Halliwell, C.: Characteristics of high-resolution versions of the Met Office Unified Model for forecasting convection over the United Kingdom, Mon. Weather Rev., 136, 3408–3424, 2008.
Liu, C. and Xue, M.: Relationships among Four-Dimensional Hybrid Ensemble-Variational Data Assimilation Algorithms with Full and Approximate Ensemble Covariance Localization, Mon. Weather Rev., 144, 591–606, 2016.
Lorenc, A., Ballard, S., Bell, R., Ingleby, N., Andrews, P., Barker, D., Bray, J., Clayton, A., Dalby, T., Li, D., Payne, T., and Saunders, F.: The Met Office global three-dimensional variational data assimilation scheme, Q. J. Roy. Meteorol. Soc., 126, 2991–3012, 2000.
Lorenc, A. C.: Recommended nomenclature for EnVar data assimilation methods, Research Activities in Atmospheric and Oceanic Modeling, WGNE, Geneva, Switzerland, 2013.
Lorenc, A. C. and Payne, T.: 4D-Var and the butterfly effect: Statistical four-dimensional data assimilation for a wide range of scales, Q. J. Roy. Meteorol. Soc., 133, 607–614, 2007.
Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130–141, 1963.
Park, S. K., and Županski, D.: Four-dimensional variational data assimilation for mesoscale and storm-scale applications, Meteorol. Atmos. Phys., 82, 173–208, 2003.
Petrie, R. E.: Background error covariance modelling for convective-scale variational data assimilation, PhD thesis, Univ. of Reading, Dept. of Meteorology, Reading, 2012.
Petrie, R. E., Bannister, R. N., and Cullen, M. J. P.: ABC model software, GitHub repository, https://doi.org/10.5281/zenodo.495405, 2017.
Pielke, R.: Mesoscale Meteorological Modeling, Academic Press, San Diego, California, 2001.
Press, W., Teukolsky, S., Vetterling, W., and Flannery, B.: Numerical Recipes, in: 3rd Edn.: The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 2007.
Salby, M. L.: Fundamentals of atmospheric physics, in: vol. 61, Academic Press, San Diego, California, 1996.
Sun, J.: Convective-scale assimilation of radar data: progress and challenges, Q. J. Roy. Meteorol. Soc., 131, 3439–3463, 2005.
Thuburn, J., Wood, N., and Staniforth, A.: Normal modes of deep atmospheres, I: Spherical geometry, Q. J. Roy. Meteorol. Soc., 128, 1771–1792, 2002.
Vallis, G.: Atmospheric and oceanic fluid dynamics, Cambridge University Press, Cambridge, UK, 2006.
Vetra-Carvalho, S., Dixon, M., Migliorini, S., Nichols, N. K., and Ballard, S. P.: Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model, Q. J. Roy. Meteorol. Soc., 138, 1709–1720, 2012.
Würsch, M., and Craig, G. C.: A simple dynamical model of cumulus convection for data assimilation research, Meteorol. Z., 23, 483–490, 2014.