Clouds form an intriguing visual manifestion of the rich structure of atmospheric turbulence in which they live and that they modify.
Excellent examples of this rich structure include the fractal dimension of the cloud boundaries and the power law behaviour of the the cloud size distributions. Perhaps the largest relevance of the geometrical structure of clouds for the climate models are related to the cloud-radiation interaction.
Since most clouds are unresolved in climate models, assumptions need to be made on the so called cloud overlap functions. Virtually all climate models assume a so called maximum-random overlap, implying that consecutive vertical layers in a climate model with non-zero cloud fractions have a maximum overlap.
It will be shown for shallow cumulus cloud fields this assumption gives rise to a systematic underestimation of the projected cloud fraction, leading to a systematic positive bias for the 2-meter temperature.
Analyses of Large Eddy Simulation results for shallow cumulus fields will be used how we can remove these biases.