## F lYduA2 fdviV dlnS1 AI

Where S is the potential air temperature 6, or water density p2 hi is the thickness of the th PBL s is the average (within the PBL) turbulent energy dissipation rate. We note that in (4.4.8) the diffusive turbulent energy fluxes at the outer boundaries of the PBLs and at the water-air interface are assumed to be equal to zero. Besides the obvious advantages of using this equation to determine the eddy viscosity coefficient, it has its own disadvantages the appearance of two new unknown...

## Similarity theory for global oceanatmosphere interaction

As has been mentioned, the primary cause of atmospheric motions is the flux q (1 otp)(na2 4na2)S0 of the absorbed short-wave solar radiation (here S0 is the solar constant, ap is the planetary albedo, see below). Besides q, a set of the external parameters determining the atmospheric circulation includes the radius a of the planet, the angular velocity Q of its rotation, the mass mA pjg of the atmospheric column of a unit cross-section, the gravity g related to mA and pressure ps at the low...

## A WMM [W W

- ps M + ps MM + * * + ' ' I lptm +-d r- p. ( 0 M + W + 0V ) cos cp + PS ( 0 M + 0*co* + 0'a ) Fr p. M +-d r W(MW + + Iq'vl) cos < p + T- M(MM + lq*Q> * + C 7 ) lFq- . Here O gz co dpjdt is the isobaric vertical velocity a p ps, ps is the surface pressure R is the gas constant for air Fx, F(fn FT and Fq are sources and sinks of momentum, heat and moisture, respectively other symbols are the same. System (5.7.1) contains 20 unknown second moments (additional unknowns appear in zonal...

## Definition of the climatic system

The climatic system ( ) is the totality of the atmosphere, si hydrosphere (Jf), cryosphere ( ), lithosphere < ), and biosphere (J1) interacting and exchanging energy and substance with each other, that is, where by the atmosphere is meant the Earth's gas shell by the hydrosphere - the World Ocean with all marginal and internal seas by the cryosphere -the continental ice sheets, sea ice, and land snow cover by the lithosphere -the active land layer and everything that is on it, including...

## I0

Before starting the discussion of theoretical models of the PBL system we note that the external parameters listed above are determined, in turn, by the processes of interaction between the atmospheric PBL and free atmosphere, and between the ocean PBL and deep ocean. But because the eddy fluxes of various substances decrease as they move away from the interface of two environments and vanish at the outer boundaries of the PBLs, then interaction between the boundary layers, the free atmosphere...

## Mass budget

Let us start by deriving expressions describing the mass budget in separate subsystems of the climatic system. Define the mass mA of the atmospheric column with unit cross-section as where pA is the air density, ps is the surface atmospheric pressure, is the height of the underlying surface elevations, g is gravity and z is the vertical coordinate oriented upward. Let us integrate the continuity equation over the whole thickness of the atmosphere, and take advantage of the condition by which...

## Preface

In 1963 when the principal concepts of the study of ocean-atmosphere interaction had only been outlined, a group of leading American geophysicists (see Benton et ai, 1963) stated 'We are beginning to realize dimly, although our information on this score is far from complete, that the atmosphere and the oceans which together constitute the fluid portions of the Earth actually function as one huge mechanical and thermodynamical system.' And further 'A physical understanding of the processes of...

## A 11 Re A A01

For all complex A and a real constant A0. The solutions to the problems (6.1.18) and (6.1.23) can be written under this condition in the form where T(t) ,> 0 is a family of continuous (over t) operators satisfying the condition In the general case, the operators A and B depend on t, and the solutions to the problems (6.1.17), (6.1.18) and (6.1.23) are determined by the evolution operator V C(i) V(t, t)B(t) dT, (6.1.25) f*(t) -f V*(t, z)zy dz. (6.1.26) The solution of Equation (6.1.1) is...

## Info

The one hand, and the universal functions u, < J> r and < I> 9, on the other. To specify functions < I> U, < hr and < q, one can apply Equations (3.8.11) with < Dr(0) < D9(0) 1 or (at large negative values of x3 L) the KEYPS equation providing proper asymptotics in the regime of strongly unstable stratification. In any case, an application of approximating formulae for functions < DU, < > r and allows us dispense with without measurement data on vertical profiles of...

## Dimensional box models

In Section 1.1 we showed that the evolution of the surface air temperature is determined not only by one (inherent to the atmosphere) time scale but depends crucially on the time scales of the upper mixed layer (UML) and deep ocean layer (DOL) interacting with each other and with the atmosphere. This consideration is the basis of the box thermodynamic model suggested by Kagan et al. (1990) and is intended to simulate the seasonal variability of the climatic system of the Northern Hemisphere....

## Heat budget

Figure 2.2 Annual mean zonally averaged net radiation flux (W m2) at the upper atmospheric boundary (a), and its seasonal variability (b). (After Stephens et al, 1981.) Figure 2.2 Annual mean zonally averaged net radiation flux (W m2) at the upper atmospheric boundary (a), and its seasonal variability (b). (After Stephens et al, 1981.) Figure 2.2 shows the time-space variability of zonally averaged net radiation flux at the upper atmospheric boundary. Note three features asymmetry of seasonal...

## Zerodimensional models

The simplest model is a model with one parameter - the temperature T of the outgoing terrestrial emission. It is defined by the condition of radiative equilibrium of the planet characterizing a balance between the absorbed short-wave solar radiation flux na2S0(l ap) and the outgoing long-wave emission flux 4na2faTr4, that is, *S0(1 < *P) f Tt, (5.3.1) where, along with the known symbols, ap is the mean weighted planetary albedo defined by the expression ap j JLj S(x)a(x) dx x sin (p a(x) is...

## ZrWK Mi TOl Wofo

MWTa -2na cos < p( P - ) , (2.4.10) Figure 2.9 Annual mean zonally averaged moisture content (10 kg m2) in the atmosphere (a) and its seasonal variability (b). (After Oort, 1983.) Figure 2.9 Annual mean zonally averaged moisture content (10 kg m2) in the atmosphere (a) and its seasonal variability (b). (After Oort, 1983.) is the meridional transport of fresh water in the atmosphere. The latter is unambiguously related to the meridional transport of water vapour defined by the division of MWTA...

## Scales of temporal variability and its mechanisms

In the atmosphere and weeks in the ocean. Among these are diurnal and semidiurnal oscillations arising from diurnal changes of insolation and the gravitational forces of the Moon and the Sun. 4. Global variations, with periods ranging from weeks to months. Two-week variations of the circulation index (the mean angular velocity of the atmospheric rotation in temperate latitudes with respect to the Earth's surface) and 30- or 60-day oscillations in the Indian and Pacific sectors of the tropical...