Estimating the subgrid variance of saturation, and its parametrization for use in a GCM cloud scheme

The prediction of cloud fraction and condensate in the unified weather forecasting/climate prediction model of the UK Meteorological Office, and many other general-circulation models, depends upon a probability distribution of a saturation variable in a grid box. A method of estimating the width of the probability distribution of the saturation variable on the scales of one grid box of the climate configuration (2.5 degrees latitude x 3.75 degrees longitude) has been created, using analyses from the global weather forecasting configuration (0.55 degrees latitude x 0.833 degrees longitude). This width was found to be potentially very variable in time at many locations, therefore the use of climatological values was inappropriate, A parametrization was created to predict the width of the probability distribution of the saturation variable for use in the climate model. The concept of this empirical parametrization was based upon a scaling relationship often observed, and which is present in the global analyses. This new statistically based parametrization replaced the standard approximation used in the Hadley Centre climate model, and significantly reduced the model's biases concerning water vapour, temperature and cloud amount in the upper troposphere.