Explicit cloud microphysics in ensemble-average modeling

Marine boundary layer (MBL) stratus and stratocumulus clouds are of great importance for the heat balance of the earth-atmosphere system. The ocean surface has a very low albedo whereas stratus clouds reflect solar radiation efficiently. The temperatures of the ocean surface and the cloud top are similar, which implies that they radiate about equal amounts in the long-wave range of the spectrum. The total radiative forcing of MBL clouds is thus negative. Measurements are never sufficiently dense to determine temporal and spatial variability in cloud depth, cloud droplet number, and effective radius from observations alone, nor can feedback mechanisms be easily quantified solely on the basis of field data. Models based on first-principles allow one to explore phenomena governing MBL clouds over a wide range of conditions.

A number of models of varying complexity have been developed to study different aspects of MBL clouds. They range from mixed-layer models with bulk water schemes to LES with explicit microphysics each having its own advantages and limitations. The most fundamental simulations can be obtained by LES, but they are extremely computer intensive and cannot be used to study a wide range of phenomena and scenarios.

Ensemble-average models are commonly used for simulating boundary layers. A few attempts have been performed to extend such models to include calculations of binned explicit microphysics. However, they have a serious limitation because of omission of important terms in the equations for the time evolution of the spatially averaged droplet spectrum. When deriving the ensemble-averaged equations for the time evolution of the binned cloud droplets, two correlation terms arise from unresolved scale perturbations in supersaturation and droplet number concentration. These two terms, for the condensational growth and collision/coalescence processes, have previously been neglected in ensemble-average models.

An earlier investigation, using LES results, found the collision/coalescence correlation to be negligible. The model presented here is and ensemble-average boundary-layer model with explicit calculations of CCN and cloud droplets/drops, including calculations of condensational growth, collision/coalescence, and gravitational settling. The supersaturation-number concentration correlation term is here parameterized using a traditional boundary-layer flux-gradient relationship. The simulations presented in this paper clearly show the impact of this previously neglected term. The simulated supersaturation exhibits a maximum at cloud base, decreasing to zero at the cloud top, just as is found when conditionally averaging over the up-drafts in a LES. Simulated cloud droplet spectra are realistic in the entire cloud; the cloud droplet number concentration is constant with height in the cloud, and the radius of the mean droplet volume increases with height, as is found in observations of marine stratocumulus.

These results suggest that conclusions drawn from previous studies with ensemble-average models neglecting this term are likely to be influenced by unphysical behavior of the model.