Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model

Abstract

For data assimilation in numerical weather prediction, the initial forecast-error covariance matrix P f is required. For variational assimilation it is particularly important to prescribe an accurate initial matrix P f , since P f is either static (in the 3D-Var case) or constant at the beginning of each assimilation window (in the 4D-Var case). At large scales the atmospheric flow is well approximated by hydrostatic balance and this balance is strongly enforced in the initial matrix P f used in operational variational assimilation systems such as that of the Met Office. However, at convective scales this balance does not necessarily hold any more. Here we examine the extent to which hydrostatic balance is valid in the vertical forecast-error covariances for highresolution models in order to determine whether there is a need to relax this balance constraint in convective-scale data assimilation. We use the Met Office Global and Regional Ensemble Prediction System (MOGREPS) and a 1.5 km resolution version of the Unified Model for a case study characterized by the presence of convective activity. An ensemble of high-resolution forecasts valid up to three hours after the onset of convection is produced. We show that at 1.5 km resolution hydrostatic balance does not hold for forecast errors in regions of convection. This indicates that in the presence of convection hydrostatic balance should not be enforced in the covariance matrix used for variational data assimilation at this scale. The results show the need to investigate covariance models that may be better suited for convective-scale data assimilation. Finally, we give a measure of the balance present in the forecast perturbations as a function of the horizontal scale (from 3-90 km) using a set of diagnostics.

The ABC model: a non-hydrostatic toy model for use in convective-scale data assimilation investigations

“…The B matrix is normally modelled with guidance from large-scale dynamics, namely that geostrophic balance is dominant, and hydrostatic balance is exact. These assumptions are probably not applicable at convective scales (as shown by Berre, 2000, Bannister et al, 2011, Vetra-Carvalho et al, 2012, Bannister, 2015, and as we have seen here, where more imbalance is present at the smaller scales). A key idea which will be explored in a forthcoming paper is to use the normal mode structure of the linearised equations to define the B matrix rather than relying on imposed balances.…”

“…In regions of convection, the aspect ratio increases, and thus hydrostatic balance may no longer be a good approximation. Vetra-Carvalho et al (2012) demonstrated that hydrostatic balance breaks down in the UM when it is run at 1.5 km horizontal resolution in regions of convection. At midlatitudes and high latitudes, the geostrophic assumption is accurate for large-scale flows where the Rossby number is small (e.g.…”

Ensemble prediction for nowcasting with a convection-permitting model – II: forecast error statistics

“…This happens at about 25 grid lengths (35 km) inside this convecting region. Vetra-Carvalho et al (2010) compared the vertical correlations of potential temperature perturbations, θ -θ , with those of the 'hydrostatic potential temperature (found from pressure perturbations through (2)), θ H -θ H after degrading the resolution of the fields in a similar way as is done here. For their case study they found that the θ -θ and θ H -θ H correlation matrices differ at horizontal lengthscales below 20 km in convecting regions.…”

Characteristics of Initial Perturbations in the Ensemble Prediction System of the Korea Meteorological Administration

“…The hydrostatic balance of the initial ensemble perturbations is necessary because the imbalanced initial ensemble perturbations grow during the model integration and degrade the quality of the ensemble forecasts. To measure how this balance is maintained with the initial ensemble perturbations, hydrostatically balanced potential temperature perturbations were calculated using the initial ensemble perturbations from the KMA EPS and UM analyses (see Vetra-Carvalho et al 2012):…”