Global atmospheric chemistry: Integrating over fractional cloud cover

A new approach defined here allows for the averaging of photochemistry over complex cloud fields within a grid square and can be readily implemented in current global models. As diagnosed from observations or meteorological models, fractional cloud cover with many overlying cloud layers can generate hundreds to thousands of different cloud profiles per grid square. We define a quadrature-based method, applied here to the problem of averaging photolysis rates over this range of cloud patterns, which opens new opportunities for modeling in-cloud chemistry in global models. We select up to four representative cloud profiles, optimizing the selection and weighting of each to minimize the difference in photolysis rates when compared with the integration over the entire set of cloud distributions. To implement our algorithm, we adapt the UCI fast-JX photolysis code to the cloud statistics from the ECMWF forecast model at T42L40 resolution. For the tropics and midlatitudes, grid-square-averaged photolysis rates for O3, NO2, and NO3 using four representative atmospheres differ by at most 3.2% RMS from rates averaged over the hundreds or more cloudy atmospheres derived from a maximum-random overlap scheme. Further, bias errors in both the free troposphere and the boundary layer are less than 1%. Similar errors are shown to be 10–20% for current approximation methods. Errors in the quadrature method are less than the uncertainty in the choice of maximum-random overlap schemes. We apply the method to the averaging of photochemistry over different cloud profiles and outline extensions to heterogeneous cloud chemistry.