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Figure 2.50. Estimated summary of the average energy (boxes) and main conversion processes in the atmosphere, for a vertical column, averaged over place and time. Boxes contain kinetic energy (Wkin) and the amounts of internal and potential energy available for conversion into kinetic energy (Wvmi, "available" refers to energy above the reference state of the atmosphere). The compartments are further divided into the energy of zonally averaged motion and the average deviations from these, denoted eddy energy (based on Oort, 1964; Lorenz, 1967).

Figure 2.50. Estimated summary of the average energy (boxes) and main conversion processes in the atmosphere, for a vertical column, averaged over place and time. Boxes contain kinetic energy (Wkin) and the amounts of internal and potential energy available for conversion into kinetic energy (Wvmi, "available" refers to energy above the reference state of the atmosphere). The compartments are further divided into the energy of zonally averaged motion and the average deviations from these, denoted eddy energy (based on Oort, 1964; Lorenz, 1967).

The process of creating kinetic energy may be intuitively interpreted in terms of air parcels of a temperature different from the ambient temperature. Such air parcels will rise (if they are hotter than the surroundings) or sink (if they are colder) and give rise to a redistribution of the surrounding air (i.e. to kinetic motion), for as long as temperature differences exist at the same altitude. More precisely, the change in kinetic energy is due to movement of the air parcels across horizontal or vertical pressure gradients, as directly implied by the equations given in section 2.C.

Carte Ciel Mai 2019
Figure 2.51a. Calculated (top of each pair) and observed (bottom of each pair) sea-level pressure in mb (1 mb being 102 Nm-2): (a, above) Averaged over the period December-February (for b, see next page).

Models of general atmospheric circulation

Before going into the influence of the oceans and land masses on the atmospheric circulation, examples of early numerical simulation of the atmospheric circulation without including couplings to oceanic circulation will be presented, based on the work of Manabe et al. (1974), Manabe and Holloway

(1975) and Hahn and Manabe (1975). They used a global, horizontal grid of about 250 km latitude and longitude steps and around ten vertical layers extending to a height of about 30 km, including equations of motion for wind, temperature and water vapour, and using the hydrostatic approximation and the ideal gas equation of state. Continental topography is modelled, whereas the oceans are prescribed seasonal temperatures as boundary conditions for the atmospheric integration. The radiation source term is calculated as a function of the seasonal variation in extraterrestrial radiation, the state variables plus ozone and carbon dioxide data. The hydrological cycle includes a model for evaporation, condensation and cloud distribution, as

Figure 2.51b. Averaged over the period June-August. (cf. a on previous page) (From S. Manabe and J. Holloway (1975), J. Geophys. Res. 80, 1617-1649, copyright of American Geophysical Union).

well as the processes involving ice and snow formation and accumulation as terrestrial snow cover or sea ice. Turbulent and sub-grid scale convection and transport of vapour have been modelled.

Figures 2.51a,b compares the average ground-level pressures during the periods December to February and June to August with observed values. Figure 2.52 gives the mean zonal wind for July, as a function of latitude and height. The longitudinal averaging extends only over the interval 80°E to 95°E, whereas the observed distribution is for 100°E. Within the latitudes included in the figure, the agreement is fair, but in general the model is rather poor in predicting the longitude average of zonal winds in all height-latitude regions, in particular the magnitude and position of the strong mid-latitude jets observed at a height of about 12 km (an indication of the sensitivity of these features on the seasonal variation of radiation and on the model grid size may be inferred from a comparison with earlier work, e.g. Holloway and Manabe, 1971).

Figure 2.52. Observed (top) and calculated (bottom) zonal wind for July, in m s-1 (positive eastwards). The lower silhouette represents the mountain topography, an idealised one being assumed in the calculation. The observed wind field is for 100°E, whereas the calculated one has been averaged over the interval 80-95°E (based on Manabe et al., 1974).

Figure 2.52. Observed (top) and calculated (bottom) zonal wind for July, in m s-1 (positive eastwards). The lower silhouette represents the mountain topography, an idealised one being assumed in the calculation. The observed wind field is for 100°E, whereas the calculated one has been averaged over the interval 80-95°E (based on Manabe et al., 1974).

Figure 2.53 gives the streamfunction corresponding to the calculated meridional circulation, for January and for July. Corresponding measured values, averaged over somewhat longer periods (three months) were shown in Fig. 2.46. In this case, the agreement is quite convincing, both in regard to the strength of the Hadley cells near the Equator, and in regard to the distribution of the weaker cells at higher latitudes. Figure 2.54 gives the northward transport of absolute angular momentum by eddies for July and January, averaged over longitudes. The corresponding measured values are found in Fig. 2.47, but averaged over the year. Figure 2.54 shows that the calculated transport is strongest in winter, and the average of January and July generally concur with the value derived from measurements.

In Fig. 2.55, the annual average precipitation rates derived from the model calculation are compared with measured values. Apparently, agreement between the two is very good, over both oceans and continents. A comparison with the earlier efforts by Manabe's group (e.g. those neglecting the seasonal variation in the extraterrestrial radiation), shows that the precipitation rates are very sensitive indicators of the appropriateness of the assumptions regarding the hydrological cycle. The more accurate presentation of measured data in Fig. 2.57 indicates detailed features not captured by the limited early atmospheric model results.

As suggested by Fig. 2.50, the formation of kinetic energy mainly involves the eddy motion (i.e. deviations from zonal mean winds). Figure 2.56 shows the calculated latitude variations of the main conversion branches: the transformation of available eddy energy into eddy kinetic energy and of zonal kinetic energy into eddy kinetic energy (which is mostly negative, i.e. the process goes the opposite way), and the dissipation of eddy kinetic energy through friction (transformation of large-scale eddies into small-scale eddies, cf. section 2.C, and the small-scale eddies eventually into heat).

Figure 2.53. July (top) and January (bottom) streamfunctions of longitude averaged meridional mass transport in units of 109 kg s-1 (based on Manabe and Holloway, 1975).

Figure 2.53. July (top) and January (bottom) streamfunctions of longitude averaged meridional mass transport in units of 109 kg s-1 (based on Manabe and Holloway, 1975).

Figure 2.54. Northward transport of angular momentum by eddies, averaged over longitude, for July (top) and January (bottom), in 1018 kg m2 s-2 per unit of pressure, 104 N m-2 (based on Manabe et al., 1974).

Calculated height distributions indicate that the frictional dissipation is not confined to regions near the ground (Manabe et al., 1974). Comparing the conversion rates with Fig. 2.50, it is evident that the order of magnitude is correct. The formation of eddy kinetic energy from eddy available energy and the frictional dissipation are both about 50% larger than the value deduced from observations, and the zonal to eddy kinetic energy is about three times too small. However, it should be remembered that there are no directly observed values for these conversions.

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