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SUMMARYSpectra of atmospheric turbulence recently measured at various heights and sites under a variety of stability conditions have been analysed and compared. The results are :(i) In regions over which the spectra obey -5/3 power laws, the ratio of the lateral to the longitudinal spectra shows fair agreement with the 4/3 ratio predicted by the Kolmogorov hypothesis for the inertial sub-range. The vertical-longitudinal ratio has a similar tendency.Dissipation rates computed from the longitudinal spectra seem to be consistent with the hypothesis that dissipation is balanced by the total production of mechanical and convective turbulent energy, provided that the turbulence is in equilibrium. In transition from rough to smooth terrain, dissipation exceeds the other terms.(iii) Vertical-velocity spectra obey Monin-Obukhov similarity theory up to a height of about 50 m. Their shapes are reasonably uniform, the major change with stability being a change of scale of the wave number axis, i.e., any characteristic nondimensional wave number is a function of z / L only. This function appears to be the same as the relation between the normalized dissipation and z/L. These results are consistent with previously measured Kolmogorov constants and with measured ratios of standard deviation of vertical velocity to friction velocity. Up to about a height of 50 m the wavelengths of the maxima of the logarithmic spectra increase linearly with height and more slowly thereafter, up to about 300 m. The spectra in stable air above 50 m suggest the existence of a buoyant sub-range.(iv) Longitudinal spectra do not obey similarity theory in a number of ways. The wavelengths do not scale with height, and there may be differences between sites when the spectra are plotted in similarity coordinates.(v) Spectra over the sea seem to have relatively more energy at low frequencies than those over land.(ii)

SIJMMARYTo describe the distribution of wind with height in hydrostatically-neutral air following a change h terrain roughness, a theory is constructed by assurnin2 that only the air below an internal boundary is affected by the chanxe and that air above the boundary is moving with the speed and Reynolds stress that it had upwind of the change of roughness. Unlike in tlic closely related theory of Elliott, the assumed velocity distribution in the lower layer is consistent, not with stress independent of height, but with continuous variation of stress from the surface to the boundarv \vIicre the stress is that in the original layer. The condition of overall conservation of momentum then leads to relations between surface stress, boundary height and fetch. The theory is compared with observations at a variety of locations, and the agreement with measurements is satisfactory. In particular, a fairly sharp boundary separates the masses of air influenced by the two types of terrain; for micrometeorological distanccs, the slope of this interface is of order 1/10.

SUMMARYAn integrated form of the diabatic wind profile based on similarity theory is used to estimate surface stress from measured winds and temperatures. It is shown that excellent estimates of stress can be made, given the roughness length, an estimate of the Richardson number and an accurate wind at one level. The theory can further be applied to estimate the roughness length from relatively few observations of wind and temperature not necessarily under neutral conditions.Suggestions by Taylor and Deacon for the determination of surface stress from autocovariance functions are tested on O'Neill observations. The results show that fair stress estimates can be made if instrumental response is taken into account. THEORYThe structure of wind and temperature in the surface layer is determined by three parameters which are essentially constant with height : roughness length zo, heat flux H and stress T . Very near the ground, another parameter, the displacement length, may be important. Instead of the three basic parameters above, we may use the three quantities involved in similarity theory : zg,, us = ~/ p and a length defined byHere, p is density, T temperature, k von KArmAn's constant and cp the specific heat at constant pressure.In principle, it should be possible to determine the three parameters zo, H and ue from three good wind observations close to the ground. But Priestley (1959) has pointed out that a small error in one or more of the winds leads to a huge error in the stress, so that this technique is not practical. Priestley further suggests that temperature data be added to the wind data in order that accurate estimates of stress be made. Thz present note considers this possibility in some detail. In order to avoid a discussion of the still controversial question as to the numerical value of the ratio of the exchange coefficients for heat and momentum, Kh/Km, it is convenient to define a length L' by :bV T ** , ,Here z is height, V wind speed and 8 potential temperature. The quantity L' is related to L by : L' = LKh/Km. The length L' will be assumed to be independent of height in the surface boundary layer, which implies similarity of the profiles of wind and temperature. This assumption is based upon recent work by Sheppard, and by Webb, both unpublished, and by Panofsky (1961b), but must be regarded as controversial. Similarity theory then requires 85

'. . ' 1 .2,.3 ' I L. Test No. z (m) Ax (m)-k =. The coherence of winds a t two points separated by a horizontal distance i n the atmos-: ,. A: - .-1. t pheric boundary layer was the subject of two L d-' I c. .-recent papers: Ropelewski, e t al., (1973) and-Panofalry, e t al., (1973). From these papers, it !*-is found that the coherence of wind component , , , variations may be modeled as decaying exponen- , .-. t i a l functions of separation distance accord-&ng t o I I' , .-I-L k J. ;-, v 8 1 *-:#: ;cohii-(n) = exp. (aikn~&/W. , , In (1) Coh refers t o the coherency spectrum, n is frequency, a i s a coherency decay factor, Ax i s a separation distance, and a i s ' the mean wind speed. The subscript i = 1, 2, 3 refers t o the turbulence components u' , v' , and w', while the superscript k = 1, 2, 3 refers t o alongwind, crosswind, and vertical separations.. Thus cohiik(n) i s the coherence between ui measured st eac of two locations separated by a distance 9, and uik i s the associated coher-ency decay factor. A small numerical value of aik indicates high coherence. The above mentioned papers s t a t e that the decw factors a l l and aB1 are increasing functions of stability, roughness and tur-I/ bulence intensity. I'he present paper i s based on data that pruvliicrs comparison of the decay factors for alongwind separations for all three wind components. 2. SITE, llPSTRUMWTATION AND DATA The data were dl taken from sonic and G i l l anemometers mounted on tower arrays a t the Hanford meteorological s i t e , which i s located on a broad level expanse of desert with sege-brush and clump grass vegetation. Data from several t e s t s have been analyzed which include several separation distances established by logarithmic spacing of towers i n an dongwind line. Analyses of two of these t e s t s , for which the azimuth angle between the tower l i n e and the mean wind direction was l e s s than lo0, are presented here. I : ; .-.. :I , &rJmw,,x;,,;-.. 1.1 '1' .I-The separation distances Ax between consecutive towers and the heights a t which the instruments were located were: The separlration distances of t e s t s V-6 and T603 were i n the order shown, with the long separation distances being on the upwind end of the line. A l l the data from t e s t V-6 ware taken by G i l l anemometers. The data from t e s t 6 0 3 were taken by four G i l l anemometers and three sonic anemaeters. The sonic anemom-eters enclosed the 4-and 8-m separation distances. The G i l l anemometers enclosed the larger separation distances. Other sgecifics for these t e s t s are given i n Table 1.