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The problem of determining the effect of clouds on the radiative energy balance of the globe is of well-recognized importance. One can in principle solve the problem for any given configuration of clouds using numerical techniques. This knowledge is not useful however, because of the amount of input data and computer resources required. Besides, we need only the average of the resulting solution over the grid scale of a general circulation model (GCM). Therefore, we are interested in estimating the average of the solutions of such fine-grained problems using only coarse grained data, a science or art called stochastic radiation transfer.
Byrne's research, in cooperation with Profs. Somerville (UCSD) and Pomraning (UCLA), has three components. These are the development of models of stochastic radiative transport, comparison of the predictions of such models with those currently used by GCMs, and validation of their applicability to global change problems using results from the ARM program.
This work uses a model radiative transfer system which possesses some of the complexities of the cloud-radiation system yet is still simple enough to be analyzed. It is a binary mixture of two materials, each of which has unique and definite radiative properties. The problem is stochastic in that one prescribes only the statistics of the mixture and then seeks the average of the solution over an ensemble of particular realizations. Byrne and his collaborators have found an exact but unclosed solution to this model and have investigated a whole class of approximate solutions, differing only in their closure assumptions. The accuracy of any proposed closure can be estimated by comparing to known solutions, such as a Markovian assemblage of pure absorbers, or to tendencies in known extreme limits, or by comparison to the average of large ensembles of solutions generated numerically, or potentially by comparison to laboratory experiment. The question at issue here is a mathematical one: the accuracy of the solution of a certain exactly specified model system, so appeal to observation of naturally occurring atmospheric phenomena is probably not useful.
But it is useful to compare the prediction of the model equations to reality, because the system may contain enough of the essentials of the cloud-radiation problem to have predictive power in spite of the simplicity of the underlying model. The ARM site should provide a good data set for this purpose. In practice not all of the planned instruments are in place and reporting, and not all of the needed measurements are even in the plan, so the results to date are only preliminary.
ARM provides some MFRSR radiometer data (one of 25 is now reporting) on the ground, reporting direct and diffuse flux every minute. Additionally, there are site-wide cloud cover estimates from GOES every hour. The theory describes spatial averages at one time, but only one radiometer is available. Therefore, a time series from about a dozen half-days, for which MFRSR and GOES data were both available (figure 1.1), have been analyzed. The results are that the stochastic description (figure 1.2) is a somewhat better fit to the data than is a fractional cloud cover model (figure 1.3), but far more data will be required to settle the issue.
More data will be coming soon, though, and in the next few years it should be possible to measure the performance of existing GCM models as well as stochastic ones put forward by us and others in the community.
Reference
Malvagi, F., R.N. Byrne, G.C. Pomraning, R.C.J. Somerville: Stochastic Radiative Transfer in a Partially Cloudy Atmosphere, J. Atmos. Sci., 50, No. 14 and 15, 15 July 93, American Meterological Society.
