basin. It is also the minimum scale that can resolve weather motions characteristic of the climate being simulated. While it can be questioned whether such high resolution is needed for the climate simulation, it should be noted that the downscaling needed for applications is a one-way process. It uses the large-scale simulation as boundary conditions for smaller-scale simulations, but does not feed back on the larger scales. Thus, the highest resolution possible for the climatic simulation will assure the best possible downscaling. We will not argue that 30 km is the ultimate scale needed in the atmosphere but simply use it as a characteristic desirable scale needed to model the atmosphere for climate simulations. Such definiteness is also needed to estimate the computational resources required in this chapter. This resolution may be insufficient for many hydrological problems where resolution is important to adequately represent the groundwater paths and the many interacting spatial scales that affect water on its path from clouds to land to its ultimate return to the ocean. A land soil moisture and vegetation model must be embedded in the atmospheric model.

The relationship between horizontal and vertical scales is defined by the Rossby radius, such that a 30 km scale in the horizontal gives 300 m scales in the vertical. This implies a need for 50 layers up to the tropical tropopause at a height of 15 km. These layers may be augmented by increased resolution in the surface boundary layer. Including the stratosphere in the model requires additional vertical levels. Any sub-grid scale processes, including clouds, turbulent mixing, and boundary layer processes, not resolved by 30 km resolution, must be parameterized in terms of quantities on the resolved scale.

The ocean model is similarly coded from the equations of motion and the conservation of water and salt. To resolve western boundary currents a resolution of at least 10 km in the horizontal and 100 m in the vertical is required. The resolution in the vertical may be enhanced by extra layers to resolve the surface mixed layer. A sea ice model must be embedded in the ocean model in order to get the surface albedo of Earth correct and to ensure the correct salt balance of the ocean.

Because the ocean heat capacity is large and changes slow, it generally takes about 10,000 model years to spin up a coupled climate model to equilibrium, although acceleration techniques are available to speed the process. The model must be run at least 1,000 years, starting from near this equilibrium state, to diagnose its climatology and variability. Only after these diagnoses are performed is the climate model ready for use.

Ensembles

Because climate models may be sensitive to small changes in initial conditions, ensembles of many runs are made, each with slightly different



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