A Variance Budget to estimate the Growth and Interaction of Uncertainties on Convective Scales

Convection-permitting ensemble prediction systems (EPS) are often underdispersive. To build a more reliable EPS, it is crucial to represent not only uncertainty in initial and lateral boundary conditions (IBC) but also uncertainty arising from model deficiencies. Uncertainty representations like stochastic parameterizations can add substantial variability to deterministic forecasts. However, it has been shown that when additional model uncertainty representations are implemented into an existing EPS that includes IBC uncertainty, they increase the total ensemble variance only slightly. This study aims to quantify this redundancy in ensemble variance by introducing a new "variability budget" framework. The framework decomposes the total ensemble variance into the sum of individual variances and their correlations, measuring the efficiency in increasing the total variance in relation to pre-existing variance.

The variance budget framework is applied to a convective scale EPS based on operational IBC uncertainties, augmented by two model uncertainty representations, the physically-based stochastic perturbations scheme (PSP) and microphysical parameter perturbations (MPP). By adding these two model uncertainty representations we find a marginal increase in total variance of wind, temperature and humidity at various heights. In particular, PSP introduces variability at convection initiation, while MPP prolongs the lifetime of variance. Both model uncertainties work in sub regions of areas influenced by IBC uncertainty and impact convective activity especially at small scales. Since the impact of PSP and MPP is mostly negatively correlated with the existing impact, this only leads to a slight increase in the total variance. A flow-dependent assessment based on the strength of convective forcing reveals that the model uncertainties show larger variances in weakly-forced conditions but with stronger negative correlations. This negative correlation is primarily attributed to random displacements of convection, with a stronger effect during weak forcing when convection is more intermittent compared to strong forcing.