The importance of numerical aspects of climate models continues to be well recognised and new numerical techniques are beginning to be tested for use in climate simulation. However, there has been very little systematic investigation of the impact of improved numerics for climate simulation and many important questions remain unanswered. The degree of interaction between horizontal and vertical resolution in climate models and the interaction of physical parametrizations at differing resolutions has made it extremely difficult to make general statements about the convergence of model solutions and hence the optimum resolution that should be used. An important question regarding the adequacy of resolution is deciding whether the information produced at finer scales at higher resolution feeds back on the larger scales or do the finer scales simply add to local effects (Williamson, 1999). Insufficient systematic work has been done with coupled models to answer this question. As well as improving numerical accuracy in advection, improved horizontal resolution can also improve the representation of the lower boundary of a model (the mountains) and the land-sea mask; this may improve the regional climate of a model but little systematic work has been carried out to assess this aspect.

A series of experiments that explores convergence characteristics has been conducted with the NCAR Community Climate Model (CCM) by Williamson (1999). In these experiments the grid and scale of the physical parametrizations was held fixed while the horizontal resolution of the dynamical core was increased. As the dynamical resolution was increased, but the parametrization resolution held fixed, the local Hadley circulation in the dual-resolution model simulations converged to a state close to that produced by a standard model at the fixed parametrization resolution. The mid-latitude transient aspects did not converge with increasing resolution when the scale of the physics was held fixed. Williamson (1999) concludes that the physical parametrizations used in climate models should explicitly take into account the scale of the grid on which it is applied. That does not seem to be common in parametrizations for global climate models today.

Pope et al. (1999) have also illustrated the positive impact of increased horizontal resolution on the climate of HADAM3. A number of systematic errors evident at low resolution are reduced as horizontal resolution is increased from 300 to 100 km. Improvements are considered to be mainly associated with better representation of storms. It is apparent that, for some models at least, neither the regional aspects of a climate simulation nor the processes that produce them converge over the range of horizontal resolutions commonly used (e.g., Déqué and Piedelievre, 1995; Stephenson and Royer, 1995; Williamson et al., 1995; Stephenson et al., 1998). As part of a European project (High Resolution Ten-Year Climate Simulations, HIRETYCS, 1998), it was found that increases in horizontal resolution did not produce systematic improvements in model simulations and any improvements found were of modest amplitude.

The need for consistency between horizontal and vertical resolution in atmospheric models was first outlined by Lindzen and Fox-Rabinovitz (1989) but little systematic study has been followed. Experiments with the NCAR CCM3 showed that increased vertical resolution (up to 26 levels) above the standard 18 levels typical of the modest vertical resolutions of climate models is beneficial to the simulations (Williamson et al., 1998). Pope et al. (2000) also considered the impact of increased (up to 30 levels) vertical resolution on simulations with HADAM3. In both cases a number of improvements were noted due mostly to the improved representation of the tropopause as the resolution was increased. However, Bossuet et al. (1998) reached a somewhat different conclusion when they increased the vertical resolution in the ARPEGE model; they concluded that increasing vertical resolution produced little impact on the simulated mean climate of their model. They also found that the physical parametrizations they employed were resolution independent. Increased vertical resolution in the upper troposphere and stratosphere has generally reduced model systematic errors in that region (Pawson et al., 2000).

Enhanced regional resolution within an AGCM is possible through the global variable-resolution stretched-grid approach that has been further developed since the SAR (e.g., Dèquè and Piedelievre, 1995; Fox-Rabinovitz et al., 1997); this is discussed in more detail in Chapter 10.

A number of important oceanic processes are not resolved by the current generation of coupled models, e.g., boundary currents, mesoscale eddy fluxes, sill through flows. Two model studies show an explicit dependence of ocean heat transport on resolution, ranging between 4° and 0.1° (Fanning and Weaver, 1997a; Bryan and Smith, 1998). However, this dependence appears to be much weaker when more advanced sub-grid scale mixing parametrizations are used, at least at resolutions of 0.4° or less (Gent et al., 1999). As previously noted, a number of recent non-flux adjusted models produce acceptable large-scale heat transports. The need for ocean resolution finer than 1° is a matter of continuing scientific debate.

Some ocean models have been configured with increased horizontal resolution (usually specifically in the meridional direction) in the tropics in order to provide a better numerical framework to handle tropical ocean dynamics. Unfortunately at this time, there has been little systematic intercomparison of such model configurations.

The lack of carefully designed systematic intercomparison experiments exploring impacts of resolution is restricting our ability to draw firm conclusions. However, while the horizontal resolution of 2.5° (T42) or better in the atmospheric component of many coupled models is probably adequate to resolve most important features, the typical vertical resolution of around 20 levels is probably too low, particularly in the atmospheric boundary layer and near the tropopause. The potential exists for spurious numerical dispersion, when combined with errors in parametrizations and incompletely modelled processes, to produce erroneous entropy sources. This suggests that further careful investigation of model numerics is required as part of a continuing overall programme of model improvement. The vertical resolution required in the ocean component is still a matter of judgement and tends to be governed by available computing resources. There is still considerable debate on the adequacy of the horizontal resolution in the ocean component of coupled models and it is suggested that some results (those that are reliant on meridional heat transport) from coupled models with coarse (>1°) resolution ocean components should be treated cautiously.

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