Examining model error in potential temperature and potential vorticity via weather forecasts at different lead times

The examination of model error is fundamental to improve weather forecasts at any time scale. Here, model errors for two forecast lead times (12, 24 h) at the grid-point level are analysed using (i) the total Eulerian changes in variables, such as potential temperature and potential vorticity (PV), both conserved under adiabatic, frictionless conditions; and (ii) Lagrangian diabatic tracers. The latter refines the Eulerian analysis by decomposing the total Eulerian changes into materially-conserved and diabatically-generated components. For both analyses the behaviour of a theoretical unbiased model, for which the only assumption is that forecast error is zero when averaged over a large number of cases, is used as a reference. Deviations from this theoretical behaviour are used to highlight conditions leading to large errors. The analyses are performed on a set of forecasts produced with the United Kingdom’s Met Office Unified Model for a 25-day period during the NAWDEX (North Atlantic Waveguide and Downstream Impact Experiment) field campaign (16 September--22 October 2016). The Eulerian approach indicates that changes in potential temperature and PV are underestimated with respect to the theoretical behaviour of an unbiased model. The grid points with the largest changes in 12-h forecasts have the largest underestimation in the 24-h forecast, highlighting the importance of the underestimation for the most dynamically and thermodynamically active grid points. The Lagrangian-tracer investigation reveals very large deviations from the theoretical behaviour of an unbiased model regardless of the level of Eulerian change, in particular for PV, and an unrealistic similarity in magnitude between parametrised diabatic changes of PV in the 24-h and 12-h forecasts. This is at odds with what would be otherwise required to obtain unbiased behaviour. Addressing the deviations from the behaviour of a theoretical unbiased model found in this work could be a step forward towards an operational unbiased model.