Abstract
Abstract. Following the development of the simplified atmospheric convective-scale “toy” model (the ABC model, named after its three key parameters: the pure gravity wave frequency A, the controller of the acoustic wave speed B, and the constant of proportionality between pressure and density perturbations C), this paper introduces its associated variational data assimilation system, ABC-DA. The purpose of ABC-DA is to permit quick and efficient research into data assimilation methods suitable for convective-scale systems. The system can also be used as an aid to teach and demonstrate data assimilation principles. ABC-DA is flexible and configurable, and is efficient enough to be run on a personal computer. The system can run a number of assimilation methods (currently 3DVar and 3DFGAT have been implemented), with user configurable observation networks. Observation operators for direct observations and wind speeds are part of the current system, and these can, for example, be expanded relatively easily to include operators for Doppler winds. A key feature of any data assimilation system is how it specifies the background error covariance matrix. ABC-DA uses a control variable transform method to allow this to be done efficiently. This version of ABC-DA mirrors many operational configurations by modelling multivariate error covariances with uncorrelated control parameters, each with special uncorrelated spatial patterns. The software developed performs (amongst other things) model runs, calibration tasks associated with the background error covariance matrix, testing and diagnostic tasks, single data assimilation runs, and multi-cycle assimilation/forecast experiments, and it also has associated visualisation software. As a demonstration, the system is used to tackle a scientific question concerning the role of geostrophic balance (GB) to model background error covariances between mass and wind fields. This question arises because although GB is a very useful mechanism that is successfully exploited in larger-scale assimilation systems, its use is questionable at convective scales due to the typically larger Rossby numbers where GB is not so relevant. A series of identical twin experiments is done in cycled assimilation configurations. One experiment exploits GB to represent mass–wind covariances in a mirror of an operational set-up (with use of an additional vertical regression (VR) step, as used operationally). This experiment performs badly where error accumulates over time. Two further experiments are done: one that does not use GB and another that does but without the VR step. Turning off GB impairs the performance, and turning off VR improves the performance in general. It is concluded that there is scope to further improve the way that the background error covariance matrices are represented at convective scale. Ideas for further possible developments of ABC-DA are discussed.
Highlights
The grid sizes of limited-area models for operational weather forecasting have become small enough to allow some convective processes to be resolved explicitly (Clark et al, 2016; Yano et al, 2018)
It is common to work backwards here: first a control variable transforms (CVTs) is proposed (based on physical principles such as those discussed in Bannister (2008b) and later in this paper), and its ability to generate reasonable background error covariance structures is studied by looking at the implied covariances
Even though the analyses are closer to the observations than the backgrounds, the errors in the assimilated variables do grow with time and most of the analysis increments do act to increase the rms errors (RMSEs) throughout the experiment
Summary
The grid sizes of limited-area models for operational weather forecasting have become small enough to allow some convective processes to be resolved explicitly (Clark et al, 2016; Yano et al, 2018). N Bannister: ABC-DA system v1.4 clude the COSMO (COnsortium for Small-scale MOdelling) model (Baldauf et al, 2011), used at MeteoSwiss (1.1 km grid size) and at the Deutscher Wetterdienst (DWD) (2.8 km grid size); the AROME (Application of Research to Operations at Mesoscale) model (Brousseau et al, 2016), used at Météo-France (1.3 km grid size); the UKV (UK Variable resolution) model (Tang et al, 2013) (1.5 km grid size); and the WRF (US Weather Research and Forecasting) model (Schwartz and Liu, 2014) (3 km grid size) Each of these systems is invaluable in the forecasting of fine-scale weather, including that associated with convective storms, and has its own data assimilation (DA) system to estimate its initial conditions from new observations and a background state.
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