If the transport of sensible or latent energy is governed by the gradients of temperature and humidity, it may be described by the diffusion equation (cf. e.g. Sellers, 1966)5
where k is the diffusion coefficient and the z-axis is in the vertical direction. Considering a quasi-stationary situation (the partial derivatives of T with respect to time t as well as with respect to horizontal directions x and y being considered negligible), (2.27) may be integrated to give dT Esens k-_ constant _ —s-. (2.28)
The change in stored sensible heat in a small volume dx dy dz close to the ground is dWsens/dt = p (0 )dx dy dz cP (dT/dt), and the sensible heat flux per unit area thus dEr _ p(0)cP dz dT.
dx dy dt dt
Insertion of this into (2.27) explains the form of the constant used on the right hand side of (2.28).
The vertical transport of water vapour through the laminar boundary layer may also be taken as a diffusion type process and given by the equation analogous to (2.28), kd-q = (2.29)
where q is the specific humidity. The molecular diffusion coefficient in air is of the order of k = 2x10-5 m2 s-1.
Considering the vertical change in the horizontal velocity u of the air, the expression analogous to (2.28) or (2.29), pk — = t (2.30)
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