The physical parameterizations of a climate model

Earth system models (ESMs) and regional climate models (RCMs) produce over a hundred variables describing changes in the climate system. Many of these variables, however, can behave differently from one model to the next, particularly those calculated in full or in part based on the physical parameterizations.

To better understand the behaviour of these climate variables, let’s take a look at the physical parameterizations of a climate model.

Physical climate models, such as ESMs and RCMs, have to solve the fundamental equations of fluid mechanics, which govern atmospheric and ocean circulation, transposed onto three-dimensional calculation grids. The horizontal resolution defines the spacing between the points of the calculation grid.

In the jargon of climate and weather modelling, the processes described by the fundamental equations that are compatible with the size of the grid are said to be resolved and part of the model dynamics. However, a host of climate-relevant phenomena occur on a scale too fine for the calculation grid, so they cannot be handled by the fundamental equations. These unresolved processes must nevertheless be included in the model, as they have effects at the grid size scale. Neglecting them would imply an unrealistic simplification of the Earth’s climate. Each phenomenon must therefore be parameterized, i.e. represented by empirical relationships. Together, these empirically formulated processes constitute the physical parameterizations. In other words, if we can’t model the process itself, we can use parameterization to model its effect.

The physical parameters of climate models contain large families of processes, including:

• ultraviolet and infrared radiation transfers,

• cloud formation schemes,

• the microphysics of precipitation formation in clouds,

• deep convection responsible for tropical storms,

• surface schemes for atmosphere-soil-vegetation exchanges,

• photochemistry,

• etc.

The number of processes included in the physical parameterizations and their formulation depend, in particular, on the horizontal resolution chosen for the simulation, the complexity and state of knowledge of a given climate process, the relative importance of the various processes governing the climate, and the computing power available. 

As far as possible, we want the parameterization of a process to be based on physical laws, so that the climate model is as reliable as possible. Fortunately, this is the case for many of them. A good example of this ideal situation would be the condensation of water vapour, which can be described by relatively simple physical laws. However, a number of obstacles can complicate the parameterization of certain processes. For example, if the cost of calculating the process is prohibitive, we often opt for a simplified formulation even if the physical laws are known (e.g. radiation transfer). In cases where the processes are still poorly understood, they need to be parameterized using simple empirical relationships that can contain adjustable coefficients. Some of these simpler relationships are the result of experiments or measurement campaigns of limited duration and geographical representation. Nevertheless, we include them in the model in the hope of improving them with new knowledge.  

As the horizontal resolution of a simulation becomes more refined, certain processes can even be removed from the physical parameterizations. This is the case for atmospheric convection, which has to be parameterized in an ESM with 100 km grid cells, whereas it would be resolved by the equations in an RCM with 2 km grid cells.