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Correct Answer : D

They are described by partial differential equations.

Atmospheric variables such as wind, temperature, pressure and humidity vary in three space dimensions and in time. The governing equations of motion, continuity, thermodynamics and moisture therefore contain derivatives with respect to several independent variables, and are partial differential equations. Numerical models solve them on a grid.

Ordinary differential equations handle a single independent variable, such as time alone. Empirical and statistical equations are used for parametrisations and forecasts, but they are not how the space- and time-dependent dynamics are described.

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Correct Answer : D

Convection is parameterized because cloud size is much smaller than the grid size.

Individual convective clouds and their updrafts are a few hundred metres to a few kilometres across. A model with a 50 km grid cannot resolve them, so their collective effect on heating, moistening and rainfall within each grid box must be represented in terms of the resolved variables: a parameterization.

Cloud physics is well understood, and models do handle phase change; the problem is scale, not knowledge. If clouds were larger than the grid they would be resolved explicitly and need no parameterization.