Mathematical Modelling of Cloud and Precipitation Processes in Atmosphere

Syllabus

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1. Basic concepts. Time and space scales of cloud and precipitation processes, basic equations in modeling of cloud microphysics and dynamics, types of mathematical models on cloud scale, models of cloud microphysics, cloud models, modeling of cloud systems, transition to the parameterization of cloud and precipitation processes in NWP models. *

2. Explicit modeling of cloud microphysics. Modeling of warm microphysics, time evolution of cloud droplet spectrum, stochastic coalescence, breakup and evaporation. Modeling of ice phase microphysics, primary and secondary ice nucleation, deposition growth, various types of aggregation processes, graupel and hail growth. Effect of microphysics on cloud dynamics. *

3. Parameterization of microphysics in cloud models. Cloud water and ice, precipitation water and ice, source terms describing cloud microphysics, Kessler parameterization, Kessler type parameterization of microphysics, examples of application in cloud models, examples of other cloud microphysics parameterization. *

4. Mathematical modeling of convective clouds. History of convective cloud models from 1D steady state models to 3D nonhydrostatic models of organized convective systems. Modeling of severe storms, influence of vertical wind sheer on storm organization. Non-precipitating cumulus ensemble simulation. *

5. Cumulus parameterization in NWP models. Conception of cumulus parameterization as depending on NWP model scale. Review of convection representation in mesoscale models (Fritsch-Chappel, Kain-Fritch, Perkey-Kreitzberg). *

6. Mathematical modeling of low level stratiform cloudiness Radiative properties of cloudy atmosphere, parameterization of radiative transfer through clouds, effect of radiative processes on the dynamics and precipitation processes in clouds, modeling of fog and stratocumulus clouds. *

7. Middle- and high level clouds Microphysics and dynamics of cloud in middle and high levels, 2D simulation of cirrus cloudiness and altostratus clouds, application of mixed-layer models to middle and high clouds, parameterization in large-scale models. *

8. Orographic clouds and formation of orografic precipitation Wave clouds produced by long ridges, clouds associated with flow over isolated peaks, mechanisms of orographic control over precipitation.

Annotation

Mathematical modeling focused on atmospheric processes that contribute to the evolution of cloud and precipitation systems. Cloud processes on various time scale and space scale.

Techniques applied in objective precipitation forecasting in midlatitudes.