The kinetic rncrgy of horizontal flow in a hydrostatic atmosphere is divided into the kinctir cnxgies of its divergent and nondivergent components. The law of conversion betwoen these two cnergics for large-scale flows in the atmosphere is derived and discussed using balancrtl and unbalanced models of circulations in the atmosphere. It is shown that the total potential energy is converted into the kinetic energy of the divergent flow which, in turn, is convrrted into the kinetic energy of the nondivergent flow. These energy conversions are equal in a so-called balanced model, but may differ in a model based on tho primitivr? equations. The analysis shows that the kinetic enrrgy reservoir of the divergent part of the flow may play a quasi-catalytic role in tha energy ronversion betwwn the total potential energy and the kinetic energy of tho nondivergent flow. Two sets of data, the history data generated by the NCAR GCM of January simulation, and tho NMC wind data and FNWC height field of August 1 to 15 of 1970, wcrc used to evaluate the energies and energy conversions. The computations confirm the direction of energy conversions in the theoretical argurncnt ant1 the quasi-catalytic nature of the kinetic energy of the divergent part of the flow. The energy conversions hctween the total potential energy and the kinetic energy of tho divergent flow occurs mainly in the lower layers of the rttmosphero a t middle latitutics where the baroclinic eddy activities are dominant. The energy conversion between the kinrtic cnergies of the divergent and the nondivergent flows is mostly carried out by t,hc Coriolis effect. In other words, the quasi-geostrophic model explains most of this energy conversion. The introduction of n more sophisticated model gives small improvement as far as t h r magnitude of energy is concerned. 5 Present affiliation: European Center for Medium Range Weather Forecasts, Bracknell, Berkshire,

A study is made of the annual variation of the six components, A,, A,, K,, K,, K,, and K,, of the energy in the atmosphere based on data from a complete year, February 1963-January 1964, and on eight vertical levels. The distribution of the energy with respect to pressure and time of the year is investigated with the result that all forms of energy have a maximum in the beginning of the year and a minimum during the month of July.The energy conversions C ( A , , A , ) , C ( K , , K,) and C(K,, K,) are also investigated during the period. The most remarkable result is the annual variation of C(K,, K,) showing a maximum during the fall, a phenomenon also observed during the previous year.Fourier analysis of the data in time is employed to determine the amplitude and phase of the first few components. The first component contains a considerable fraction of the annual variations, but the second component in in certain cases, as for example C (K,, K,), very important in describing the annual behavior. A similar analysis is niitde of three years of data with essentially the same results. The latter set of energy data is used to determine the annual variation of the generation of available potential energy and the frictional dissipation using the energy equations, while the data for 1!)63 are used to calculate the energy conversion C ( A , K ) and the generation C ( A ) based on the energy equations and an assumption concerning the frictional dissipation.The last section of the paper contains a desrription of the results of an investigation of the energy spectra showing that in the range of wave nuinhers 8 < n . .1R we ran tipproximate the form of the spectra by a power law: E ~~ m'n-'. n and b are determined by regression analysis.W e shall also investigate some propertirs of the spectra, in particular t h e functional relationship between the amorint of energy and t h e wave number.

On the basis of a comparison between the results so far obtained by the usual numerical methods in physical weather prediction and the graphical methods it is likely that certain defects in the present forecast methods are due to the Eulerian technique. The possibilities for the use of a quasi-Lagrangian technique are investigated, and it is found that such a technique is possible and becomes especially simple when combined with a space-smoothing which eliminates the shorter fast moving waves in the spectrum. The Lagrangian method of computation is described in the barotropic case and also for a simplified two-parameter baroclinic model.

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Calculations of nonlinear interaction of available potential energy, kinetic energy, enstrophy, and potential enstrophy have been carried out in the domain of wave numbers. The processes of interest are the interactions among waves, the interactions between a given wave and the zonal average, and interactions due to the beta effect for (potential) enstrophy. Results are presented for a three‐month (February through April 1963) period. It is found that available potential energy is cascaded from small to large wave numbers, while kinetic energy is cascaded from intermediate wave numbers to both small and large wave numbers: the greater amounts go to the small wave numbers. Enstrophy and potential enstrophy are cascaded from small to large wave numbers with relatively little accumulation in the middle range (8≤m≤11, where m is the wave number). Verification of the existence of an inertial subrange is inconclusive, although power spectrum analyses of enstrophy and potential enstrophy yield a −1 power law, combined with a −3 slope for the associated kinetic energy spectrum. A value of 2.5×104 m2 sec−1 is obstained for the coefficient of eddy viscosity by means of Leith's formulation, while the value of the cut‐off wavelength for the −3 range is approximately 420 km by means of the formulation by Kraichnan.