Use of a nonlinear pseudo‐relative humidity variable in a multivariate formulation of moisture analysis

We present a reformulation of the humidity part of the HIRLAM (HIgh-Resolution Limited-Area Model) variational data assimilation. The purpose is to rectify some of the shortcomings of the present formulation which uses specific humidity, q, as an assimilation control variable with homogeneous and static covariances. One problem is that specific humidity forecast errors tend to have a non-Gaussian probability distribution, in particular near saturation and near zero humidity. In addition, the variance of the distribution tends to change in space and time due to the dependency of the water vapour saturation pressure on temperature. A modified pseudo-relative humidity variable has been adapted to the statistical balance background constraint, including the associated moisture balance formulation. Background-error statistics for the new moisture control variable and the moisture-related balances were derived, taking differences between forecasts valid at the same time as a proxy for background forecast errors. The background-error statistics were compared with the corresponding statistics for specific humidity as the moisture assimilation control variable. In connection with the nonlinearity of the change of the variable, it was noted that specified background-error standard deviations were chosen to be substantially reduced for nearly dry and saturated states, which can raise difficulties. The impact of the new moisture assimilation control variable is illustrated with simulated observation experiments as well as data assimilation experiments using real observations, for one summer month and one winter month in a 4D-Var assimilation cycle using two outer loop iterations in the 4D-Var minimization. The impact of the new formulation on forecast verification scores is small and essentially neutral, while using the second outer loop in the old formulation has a small positive impact. Copyright © 2011 Royal Meteorological Society