The statistical structure of forecast errors and its representation in The Met. Office Global 3‐D Variational Data Assimilation Scheme

Previous studies and different methods of estimating short‐range forecast errors are summarized. Zonally and temporally averaged statistics based on differences of one‐ and two‐day forecasts valid at the same time are presented and an attempt is made to explain many of the features by reference to dynamical concepts. Vertical correlation length‐scale tends to increase with horizontal correlation scale but to be very short in the Tropics; horizontal scale is longest in the Tropics and in the stratosphere. The variations in vertical correlation are much more pronounced for largely balanced variables such as rotational wind and temperature than they are for divergent wind or humidity. The extratropics are dominated by an equivalent barotropic mode with the level of the maximum wind amplitude (and the zero crossing of the temperature correlation) being determined by the tropopause. Surface pressure is negatively correlated with low‐level temperature as expected (except over the Antarctic plateau where it is positively correlated); it is also negatively correlated with temperatures near/above the tropopause in the extratropics. The covariance model used in The Met. Office Global Three‐Dimensional Variational (3D‐Var) Data Assimilation system represents the variation of vertical covariances with latitude reasonably well, but the longer horizontal scales in the stratosphere are not currently reproduced. The implied covariances used operationally have been modified so that the correlation length‐scales, both horizontal and vertical, are somewhat shorter than those direct from the forecast differences. Recent changes to the representation are briefly described, with an indication of their impact on the forecasts. The impacts are significant relative to other changes tested, and the covariance model has played a major role in the successful implementation and subsequent improvement of our 3D‐Var system.