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

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.

Balance conditions in variational data assimilation for a high‐resolution forecast model

“…The associated DA (Bannister, 2020) is an incremental 3D‐Var/3DFGAT‐based variational system. The ‐matrix is modelled with a set of parameter/horizontal/vertical transforms where the model variables are decomposed into balanced and unbalanced components which are assumed to be uncorrelated.…”

“…A strongly imposed hydrostatic balance eliminates vertically propagating acoustic waves. In ABC‐DA though, and unlike other systems, some hydrostatically unbalanced analysis increments are allowed (Bannister, 2020).…”

“…The ABC‐DA variational scheme is documented in Bannister (2020), but the relevant parts of the control variable transform (), which define the ‐matrix, are summarised as follows. As mentioned in Section 2, the control parameters of ABC‐DA are , , , , and .…”

“…Turning off a balance relation may indeed allow a more realistic autocovariance for either or , but this may come at the expense of destroying any multivariate components in the implied ‐matrix. For each combination of and , and for each population of forecast errors described in Section 5, the spatial transforms mentioned in Section 4 are re‐calibrated in the way described in Bannister (2020).…”

“…This paper revisits the problem of the use of geophysical balance to model as used in variational and hybrid schemes when applied to midlatitude flows that contain small scales that are expected to have a considerable amount of unbalanced flow by their nature. The model used for most of this study is a high‐resolution (1.5 km grid length) version of the simplified ABC model (Petrie et al ., 2017), and its variational DA system, ABC‐DA (Bannister, 2020), but some results use ensemble forecasts from a 1.5 km grid length version of the Met Office's Unified Model (UM) for a limited‐area domain over the southern UK.…”