## Threedimensional models

In this section we will discuss three-dimensional models of the ocean-atmosphere system occupying the highest position in terms of their complexity in the hierarchy of climatic models. As before, much thought will be given to the principles of construction of these models and to their application to simulation of the present-day climate.

An obvious question arises at this point: why use models to simulate the present-day climate if it is already known from observational data? In other words, why make efforts to solve problems that are already solved (even in the first approximation)? It is both easy and difficult to answer this question. Indeed, no climatic model will completely comply with the actual climatic system so that aspirations to understanding the distinctions and similarities between them is an indispensable condition, if we wish climatic models to have, according to Monin (1982), convincing and predicting strength. On the other hand, what one dreams of and what one can actually do might differ for a number of reasons (say, technical or economic ones). It is essential to understand whether what can be done is useful. As for this question the point is that an answer to it can be given only with precise knowledge about the capability of the models to reproduce the modern climate.

At present, seven global models of the ocean-atmosphere system have been tested and verified. These are the models developed at the Laboratory of Geophysical Fluid Dynamics, Princeton University (GFDL model), at the P. P. Shirshov Institute of Oceanology, the Russian Academy of Sciences (IOAS model), at the Computer Centre of the Siberian Branch of the Russian Academy of Science (CC SBAS model), at the National Centre for Atmospheric Research in the United States (NCAR model), at the Oregon State University (OSU model), at the UK Meteorological Office (UKMO model), and at the Max-Planck-Institut für Meteorologie (MPI model). This list could also include models that either fix the sea surface temperature or present the ocean in the form of a 'swamp' with zero or finite heat capacity. In the latter case, the ocean serves as an infinite source of moisture for the atmosphere but does not provide heat transport in the meridional direction. Many such models exist but here we discuss only those listed, i.e. coupled ocean-atmosphere global circulation models, in the order in which they are mentioned.

### GFDL model

The earlier version of this model and the annual mean state of the ocean-atmosphere system obtained with its help are described in an article by Manabe and Bryan (1969). A generalization of this model version for the case of seasonal variability of the climatic system is presented by Manabe et al. (1979).

The GFDL model has the following structure. It consists of atmospheric and ocean submodels and a general library where data necessary to calculate the characteristics of the ocean- atmosphere interaction are continuously updated. The atmospheric submodel includes hydrothermodynamics equations in which the independent variables are time t, longitude X, latitude (p and non-dimensional pressure a = p/ps. The state of the atmosphere is described by zonal u, meridional v and vertical co (in the cr-system of coordinates) components of wind velocity, as well as by temperature T, specific humidity q and pressure ps at the underlying surface. These variables are described by equations of motion:

Ps"

P."-—--iï + Fx + 9-r, a cos (p oX da a 0(p oa

by the hydrostatic equation

0> = 0>s + R by the equation for surface pressure

H--psv cos cp )d(7 = 0, d(p dt a cos (p and by the equations for the heat and moisture budget

~PsT= —P + ~P(FR + H) + Ps(2c + Qp + Go), di Cp(7 cp da d dE

dt da

Here Fk, Fv, QD and PD are terms describing the horizontal diffusion of momentum, heat and moisture respectively; zz and z<p are components of the vertical eddy momentum flux; H and E are vertical eddy fluxes of heat and moisture; FR is the radiative heat flux; Qc and Pc are normalized heat and moisture influxes of convective origin; QP is the rate of temperature change due to water vapour phase transitions; C is the rate of the moisture content change in the atmosphere due to precipitation:

a cos <p oq> da is the operator of the total time derivative; co and p are analogues of the vertical velocity in a- and p-systems of coordinates defined by the diagnostic relations co = -ps

Gd_h+ \( dPsu , Spsvcos(p dt J o cos (p dX a cos <p d<p/

The calculation scheme for the radiative fluxes includes a description of the absorption by ozone, carbon dioxide and water vapour, and also a description of cloud effects and of their albedo dependence on the height of clouds. The annual mean fields of three-level cloudiness and ozone distribution are prescribed from the climatological data. The C02 concentration is considered to be constant. The albedo of the underlying surface varies depending on the type of surface (water, land surface, snow, sea and continental ice).

The evaporation from land and the moisture content in the soil active layer are found by integration by the prognostic equation for soil moisture, taking into account the precipitation, snow melting, evaporation and run-off. In so doing, it is assumed that the land moisture capacity (that is, maximum amount of moisture which can be retained in the land) does not exceed 15 cm, and the effect of land moisture on evaporation manifests itself only in the case where the land moisture content is less than a certain critical value amounting to 75% of the moisture capacity. In this case the evaporation decreases by a value which is proportional to the ratio of current and critical values of the land moisture content. The thickness of the snow cover is determined from the snow mass budget equation, taking into account accumulation, sublimation and melting of snow.

To calculate the convection and water vapour phase transitions, a convective adjustment scheme is used which provides the vertical redistribution of moisture and heat in the presence of hydrostatic instability. The redistribution is performed with an allowance for the integral conservation of the heat and moisture content, after which the condensed moisture is assumed to be precipitated in the form of rain or snow.

The effects of horizontal mixing are parametrized in the following way. The terms describing the horizontal momentum diffusion are represented in the form of the product of appropriate components of the velocity deformation tensor and the horizontal eddy viscosity coefficient. The latter is obtained from the condition of equality between local generation and dissipation of the turbulent energy, and the mixing length (the turbulence scale) is assumed to be equal to the grid step. The same coefficient is used to determine the horizontal heat and moisture diffusion effect.

The vertical eddy fluxes of momentum, heat and moisture are calculated with the help of a semiempirical model of turbulence where the turbulence scale is prescribed as linear, increasing up to a height of 75 m, and then as linearly decreasing to zero at a height of 2.5 km (the upper boundary of the atmospheric planetary boundary layer). To estimate friction stresses and sensible and latent heat fluxes at the underlying surface, the bulk formulae with fixed values of resistance and heat and moisture exchange coefficients are used. The soil temperature is derived from the heat budget equation on the assumption that the heat flux into soil is equal to zero; the sea surface temperature is found from the ocean submodel.

Equations of the atmospheric submodel are approximated by their difference analogues on the latitude-longitude grid with 64 nodal points along the latitude circle and with 19 nodal points along the meridian (between the equator and the pole). Along the vertical the atmosphere is divided into nine layers with a concentration of levels in the planetary boundary layer and in the low stratosphere. The real topography of the Earth's surface is replaced by a smoothed relief, taking into account the major mountain systems, and also the Antarctic and Greenland ice sheets.

The ocean submodel unites the primitive equations of motion in the Boussinesq approximation dp du ( . tan en

dt; / „ tan a the hydrostatic equation p0a cos cp dX

dp/dz = -gp and the continuity equation du dv cos <p dw

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