An empirical expression for aerodynamic resistance in the unstable boundary layer

In unstable conditions, the set of equations defining the aerodynamic resistance to sensible heat transfer, r _a , cannot be solved analytically. An iterative technique must be used to obtain r _a exactly, but this is cumbersome and time consuming. In this paper, a new, empirical equation is presented relating the ratio, Q, of the aerodynamic resistances in neutral and unstable conditions, to the bulk Richardson number, Ri _B . The equation takes the form Q = a + b(–Ri) ^c , where a, b and c are empirical functions of (z – d)/z _om . This model is shown to predict r _awith a mean absolute error of 0.06 s m^–1 over the ranges -15 < Ri _B < 0 and 10 < (z – d)/z _om < 2300. Statistical comparison with other equations that have been proposed for r _a in unstable conditions indicates the superior precision of the model presented here.