Measurement of relationship between wind profile and stability on cultivated fields

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It is well known that in the adiabatic condition the wind velocity profile is represented by the following equation, U(z)=2.303V*/k0logz-d/z0, (1)and that in the non-adiabatic condition it cannot be represented by (1). Many theoretical or experimental equations for wind profile have been introduced, for examples, Deacon (1949), Lettau (1949), Kawahara (1950), Halstead (1951), Ogura (1952), and Takeda (1953). The auther examins the applicability to the measurement of wind on cultivated field of both Deacon's and Ogura's equation.Deacon's equation is represented byU(z)=v*/k0(1-β)[(z/z0)1-β-1] (2)where β<1 for unstable conditions, β=1 at neutral stability, and β<1 for stable conditions.When this equation is adopted for our observation, the first question given rise to is the determination of β. Although Deacon has investigated β on a short grass surface, which is closely related to Richardson's number, we need the value of β on a long grass surface such as a rice or wheat field. Since β is the function of not only stability but also roughness of ground surface, β obtained at a certain place can not be applied necessarily to other places. The second question is evaluation of Richardson's number for determination of β. As the roughness parameter and the zero-plane displacement on a long grass field both depend upon wind velocity, the determination of a standard height on which Richardson's number much depends is very difficult. Deacon and Rider (1954) have assumed that z0 and d are independent of stability, but this assumption is not yet reliable. Thus Deacon's equation have many questionable assumption. Therefore, in order to investigate the wind profile in more detail, we have to make the measurement not only mean value of wind velocity and temperature but also their turbulent characteristics.Ogura's equation is represented byV(z)=W*/k0lnz+z0/z0-αgLz/2CpρθW*2 (3)where W* is velocity of the coupling turbulon in adiabatic atmosphere coinciding with the frictional velocity√τ/ρ, α is a proportional constant about 6, L is heat flux in cal cm-2sec-1, and θ is the mean temperature of the layers in °K.Putting the measurable values in to this equation and calculate the known constant, eventually we obtain the velocity profile as follows:U(z)=2.303w/klogz-d/z0-5.045×107L(z-d-z0)/θ(w/k) (4)where U(z) is mean wind velocity at height z, w is obtained from the horizontal fluctuation u′ and the vertical w′ of wind velocity as w=‹u′w›′1/2, z is the height above ground, θ is meperature of air layer, L is measurable from the fluctuation in temperature θ′ as L=Cpρ‹w′θ′›. Two quantities d and k are obtained both making use of the equation ‹u′w′›1/2=λ(dU/dZ)2, where λ is the scare of coupling turbulon, and the similtaneous measurents of at two height z1 and z2 asλ1=k(z1-d) λ2=k(z2-d) {d=λ2z1-λ1z2/λ2-λ1 (5)Finally putting the value of obtained above in to equation (4). We can determine the value of z0.The accuracy of anemometers for measurement of mean velocity must be of the error less than ±1%