Background error statistics in the Tropics: Structures and impact in a convective-scale numerical weather prediction system

The background error covariance matrix plays a vital role in any data assimilation system. Proper specification, which is determined by the forecast system set-up, is often required. Previous studies have investigated its relevance in various global and regional numerical weather prediction (NWP) systems; however, very few have explored it in tropical NWP systems. Here, we present and evaluate the structures of the background error covariance matrix for a tropical convective-scale NWP system. A total of 12 background error covariance matrices are modelled using differences between pairs of forecasts of different lengths but valid at the same time, based on the application of the vertical-first and horizontal-first transform order formulations on six permutations of the training data. Through pseudo-single observation tests, we extract and test the sensitivity of their structures to the training data period (seasons), forecast lag and transform order. The structures typically exhibit more dependence on forecast lag and transform order; horizontal-first transform order covariances had structures with shorter horizontal length-scales for wind and larger wind background error standard deviations. We also note that some covariances had horizontal and vertical structures with stronger mass-wind coupling, closely resembling an equatorial Kelvin wave. To assess the performance of each of the covariances, 12 month-long data assimilation trials in May 2018 (characterised by frequent occurrences of localised thunderstorm events) are performed. We show improved short-range precipitation forecasts in trials using some of the covariances compared to the current operational covariance. These covariances generally have structures with weak mass-wind coupling, shorter horizontal length-scales for wind and larger wind background error standard deviations, compared to other covariances which led to poorer forecasts. These may be desirable factors when modelling the background error covariance matrix for tropical convective-scale data assimilation systems.