Scale Dependency of Total Water Variance and Its Implication for Cloud Parameterizations

The scale dependency of variance of total water mixing ratio is explored by analyzing data from a general circulation model (GCM), a numerical weather prediction model (NWP), and large-eddy simulations (LESs). For clarification, direct numerical simulation (DNS) data are additionally included, but the focus is placed on defining a general scaling behavior for scales ranging from global down to cloud resolving. For this, appropriate power-law exponents are determined by calculating and approximating the power density spectrum. The large-scale models (GCM and NWP) show a consistent scaling with a power-law exponent of approximately −2. For the high-resolution LESs, the slope of the power density spectrum shows evidence of being somewhat steeper, although the estimates are more uncertain. Also the transition between resolved and parameterized scales in a current GCM is investigated. Neither a spectral gap nor a strong scale break is found, but a weak scale break at high wavenumbers cannot be excluded. The evaluation of the parameterized total water variance of a state-of-the-art statistical scheme shows that the scale dependency is underestimated by this parameterization. This study and the discovered general scaling behavior emphasize the need for a development of scale-dependent parameterizations.