Parameterization of in-cloud vertical velocities for cloud droplet activation calculations in coarse-grid models: Analysis of observations and cloud resolving model results

The activation of aerosol particles to cloud droplets depends on the degree of supersaturation, which in turn is related to the in-cloud (more precisely, cloud base) vertical updraft velocity. Vertical velocity varies significantly in space and time, typically on scales of tens to hundreds of meters. As such, the relevant in-cloud updrafts are unresolved in global models with grid spacings of 100-200km. The prognostic calculation of cloud droplet activation in these models, required for the assessment of global aerosol indirect effects, relies therefore on parameterizations: Either updraft values are prescribed (e.g., Sotiropoulou et al. 2007; Pringle et al. 2009), or the updraft velocity is diagnosed from other simulated parameters, typically the eddy diffusion coefficient (Ghan et al 1997; Morrison & Gettelman 2008), or, if available, turbulent kinetic energy (Lohmann et al 2007). Models use a gaussian distribution of vertical velocities (for which the standard deviation σ_w has to be determined), or one single characteristic updraft value w_char, which yields similar results (Peng et al 2005).

We have analyzed different parameterizations for subgrid vertical velocities (Ghan et al, 1997; Morrison & Gettelman, 2008; Wang & Penner, 2009) in the CAM-Oslo global aerosol-climate model. They are compared to different observations: several ground-based remote sensing instruments at Cabauw, Netherlands during the EUCAARI-IMPACT campaign, anemometers mounted on the 200m-tower at Cabauw, aircraft measurements over the North Sea, and ACTOS helicopter measurements in different locations in Germany. In addition, MESO-NH cloud resolving simulations provided a comprehensive set of cloud-related parameters for a North Sea stratocumulus case. It is found that the tested GCM parameterizations for subgrid vertical velocity compare favourably to the observations in cloud-free conditions, but predict significantly too low updrafts inside clouds. This is because these parameterizations, all based on the boundary layer scheme in CAM-Oslo (Holtslag & Boville, 1993), have the common weakness not to account for turbulence generated by the clouds themselves (e. g. by latent heat release, cloud-top cooling).

Based on an analysis of the available data for different types of boundary layer clouds, we derive a new simple parameterization which relates the in-cloud updraft velocity to liquid water content. This is possible because both the buoyancy generated through latent heat release at cloud base, and the negative buoyany driven by cloud-top cooling, are expected to increase with higher cloud liquid water contents. The suggested empirical parameterization will be compared to theoretical considerations on the turbulent kinetic energy budget equation.

With the new parameterization, CAM-Oslo simulates more realistic in-cloud vertical velocities than with previous approaches, and ad-hoc assumptions on prescribed values can be avoided. We suggest this simple solution for GCMs of the present generation, which often use boundary layer schemes similar to that of Holtslag & Boville (1993) instead of more sophisticated schemes which explicitly account for cloud-generated turbulence (e.g. Bretherton & Park 2009).

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