| Water vapor, as a greenhouse gas in the atmosphere, plays an important role in the climate system. But its dynamics are extremely complicated because it is controlled by both cloud microphysical processes and large-scale dynamical processes. There will be a broad range of scales that can not be explicitly resolved in modeling but whose aggregate effects on the resolved scales must be accounted for. Water vapor modeling and representation is one of the major uncertainties in general circulation models. Better parameterization scheme for these unresolved processes will improve the prediction of weather and climate. In this thesis, we present an observational data-driven, stochastic analysis-based parameterization method.Firstly, we analyze the mean fields of water vapor from European Center for Medium-range Weather Forecasts 40-year Re-Analysis (ERA-40) 4-time daily observation. Based on ERA-40 daily data and an idealized conceptual moisture model, we estimate the convective moistening which includes the complex unresolved physical processes. Control experiments demonstrate that convective moistening is one of the important factors to determine the distribution of water vapor.Secondly, we have devised an observational data-driven, stochastic analysis-based method to parameterize the estimated convective moistening. A correlated noisy process is used in terms of fractional Brownian motion. Based on convergence theorem of variation and stochastic calculus, parameters are obtained by solving the stochastic optimization problem.Finally, an idealized theoretical stochastic model for water vapor evolution is developed. To test its validation, we reproduce and compare the specific humidity with the ERA-40 observation. Results demonstrate that even though we have simplified treatments for water vapor model, the stochastic model can reproduce not only the first-order moment of water vapor but also its second-order moment and probability distribution. Both mathematical theory and numerical experiments verify that this data-based stochastic parameterization is reasonable. |
