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

Abstract

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

Four-dimensional variational data assimilation for a limited area model

“…Background error statistics for the experiments in this study were derived with the NMCmethod (Parrish and Derber, 1992) and with input of forecast difference data ('36 h and '12 h forecasts valid at the same time) from the RCR domain and from all four seasons. This is certainly not the most optimal choice, since separate studies of moisture background error statistics, for example, have indicated a rather significant seasonal dependency of such background error statistics (Gustafsson et al, 2011). The HIRLAM grid point forecast model applies a twotime level semi-Lagrangian semi-implicit integration scheme (Unde´n et al, 2002).…”

“…For the humidity analysis, a renormalised pseudo-relative humidity assimilation control variable may also be applied (Gustafsson et al, 2011). The renormalisation follows Ho´lm et al (2002), and the purpose is to improve Gaussianity close to zero humidity and saturated model background states.…”

“…The renormalisation follows Ho´lm et al (2002), and the purpose is to improve Gaussianity close to zero humidity and saturated model background states. Since the renormalisation has a non-linear formulation, several outer loop minimisation iterations are required (Gustafsson et al, 2011).…”

Diagnosing non-Gaussianity of forecast and analysis errors in a convective-scale model

“…The asymmetries in PDFs are also accounted for through a nonlinear transformation. This scheme has been implemented through several variants both in global (Holm et al, 2002;Ingleby et al, 2013) and in limited area models (Gustafsson et al, 2011).…”

Modified Relative Humidity Based on the Johnson's S_B Distribution Function

“…Several humidity variables have been proposed for data assimilation, including pseudo relative humidity (PRH; Dee and Da Silva 2002) and its extensions (Gustafssona et al 2011). If a humidity variable is divided into a base state and perturbation, data assimilation mainly controls the perturbation part.…”