The sensitivity of domain-averaged solar fluxes to assumptions about cloud geometry

The effects on domain-averaged broad-band solar fluxes due to assumptions about geometry of convective clouds are explored using a Monte Carlo algorithm and 3D distributions of water generated by a cloud-resolving model (CRM). Domains are (400 km)² with 2 km horizontal grid-spacing, Δx, and 35 layers of varying thickness. Optical properties are computed based on single-scattering parametrizations for hydrometeors and the correlated k-distribution method for gaseous absorption. Benchmark fluxes are established using the CRM fields at Δx = 2 km. Four plane-parallel versions of these fields (affected by letting Δx → ∞) are considered which seimic 1D algorithms: the independent column approximation (ICA) uses the full CRM fields; for the others, mixing ratios of cloudy cells are reset to associated layer-mean values thus conserving water mass and cloud fraction in each layer. For the ICA, errors in reflected flux to space and surface irradiance rarely exceed 20 W m^-2. Total atmospheric absorption and heating rates are almost always within 5 W m^-2 and ~3%, respectively. This demonstrates that cloud sides and horizontal fluxes are unimportant for averages over large domains. However, when clouds are homogenized horizontally yet exact overlap is retained, errors increase by almost an order of magnitude. This demonstrates the importance of horizontal variability. When the same clouds are randomly overlapped, errors in boundary fluxes can exceed 250 W m^-2 at high sun, and heating rates can be off by 50% to 100%. When these clouds follow maximal/random overlap, albedo is often underestimated because overlap of CRM liquid clouds falls between maximal and random. This demonstrates the importance of cloud overlap and ultimately the need for 1D models to account equally well for both subgrid-scale variability in cloud extinction and overlap.