Interrelationships between zero-plane displacement, aerodynamic roughness length and plant canopy height

Assuming the momentum diffusivity above the vegetated canopy is equal to the momentum diffusivity within the canopy at the top level of the canopy, Takeda (1964, 1965 and 1966) proposed the following equation: 1/H-dlnH-d/z0=κ2/αH, where H is the effective plant height, α the empirical constant (=0.0870), d the zero-plane displacement, z0 the aerodynamic roughness length and κ the von Kármán's constant (=0.4). In general, Takeda's equation is coincident with the observation. In conditions of the headed corn and sorgo canopies and the forest canopy, however, the equation does not fit in the observed results. According to the observation, it is found that α is changeable with d, z0 or u (the wind velocity). Specifically, α is in proportion to z0 approximately. Hence, the author has improved Takeda's equation into a new equation as follows: lnh-d/z0=(κ2/c)h-d/z0 where h is the mean plant height and c the empirical constant obtained by the author. The dependences of the aerodynamic characteristics of teosinte, corn, sorgo and Japanese larch canopies, and glass rod model canopy were studied experimentally to verify the new relation. The empirical constant (c) has a range of 0.45 to 0.50, but can be a constant, since the analyses give 0.475 as the mean value of c and 0.465 as the mean value of c except the glass rod model canopy. In the cases of teosinte, corn, sorgo and Japanese larch canopies, and glass rod model canopy, the improved equation is in good agreement with the observation. When the leaf area density of the canopy becomes very large, the relation of (h-d)/z0=2.72 is obtained as a limit solution of the author's equation. This relation agrees well with the relation of Kondo (1971) for dense-tall roughness canopies. The averaged ratios of d and z0 against h calculated from the results of many researchers, approximate both the relation of Kondo (1971) and the author's result in the dense canopy for all the variety of conditions.