Agricultural and Forest Meteorology 103 2000 301–313
A first-order closure model for the wind flow within and above vegetation canopies
Pingtong Zeng
∗
, Hidenori Takahashi
Laboratory of Geoecology, Graduate School of Environmental Earth Science, Hokkaido University, Sapporo 060-0810, Japan Received 18 March 1999; accepted 11 January 2000
Abstract
A first-order closure model that has the general utility for predicting the wind flow within and above vegetation canopies is presented. Parameterization schemes that took into account the influence of large turbulent eddies were developed for the
Reynolds stress and the mixing length in the model. The results predicted by the model were compared with measured data for wind speeds within and above six types of vegetation canopy, including agricultural crops, deciduous and coniferous forests,
and a rubber tree plantation during fully leafed, partially leafed and leafless periods. The predicted results agreed well with the measured data; the root-mean-square errors in the predicted wind speeds non-dimensionalized by the friction velocity
above the canopy were about 0.2 or less for all of the canopies. The secondary wind maxima that occurred in the lower canopies were also correctly predicted. The influence of foliage density on the wind profiles within and above a vegetation
canopy was successfully simulated by the model for a rubber tree plantation during fully leafed, partially leafed and leafless periods. The bulk momentum transfer coefficients C
M
and the values of λ which are defined by z =λh−d, where z
is the roughness and d is the zero-displacement height of the canopy for the vegetation canopies were also studied, and the relationships C
Mh
=0.0618 exp0.792C
F
and λ =0.209 exp0.414C
F
were determined; here, C
Mh
is the bulk momentum transfer coefficient at the canopy top; C
F
=C
d
PAI z
max
h, where C
d
is the effective drag coefficient of the canopy, PAI is the plant area index and z
max
is the height at which the plant area density is maximum. The values of λ ranged from 0.22 to 0.32 for the canopies studied. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Numerical model; Wind velocity; Vegetation canopy; Reynolds stress; Mixing length; Turbulent eddy
1. Introduction
Wind is an important factor for scalar fluxes heat, water vapor, carbon dioxide, etc. and movements of
spores, pollen and particles within a vegetation canopy. Information about the wind flow within the vegeta-
tion canopy is important in meteorological, agricul- tural and ecological studies. A number of numerical
models for predicting the vegetation wind flow have
∗
Corresponding author. Fax: +81-11-706-4867.
E-mail address: shtees.hokudai.ac.jp P. Zeng
been developed. However, accurate prediction of wind flow is difficult due to the complexity in the array of
vegetation elements leaves, branches and so on and the complex process of air momentum transport within
a vegetation canopy. Early modeling studies e.g. In- oue, 1963; Cowan, 1968; Thom, 1971 were based on
the K-theory or gradient-diffusion theory; that is, the momentum flux is equal to the product of an eddy
viscosity and the local gradient of mean wind ve- locity. Wilson and Shaw 1977 hereafter WS point
out that a K-theory model provides little insight into the nature of momentum transport processes within
0168-192300 – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 9 2 3 0 0 0 0 1 3 3 - 7
302 P. Zeng, H. Takahashi Agricultural and Forest Meteorology 103 2000 301–313
the vegetation canopy. Moreover, Pereira and Shaw 1980 and Watanabe and Kondo 1990 hereafter
WK show that such a model can not provide accurate predictions of wind velocity in the lower portion of
a plant canopy, where a near-zero vertical gradient of mean wind velocity or a wind velocity ‘bulge’ is fre-
quently observed Shaw, 1977. In another approach, WS proposed a higher-order second-order closure
model in which turbulent kinetic energy equations and Reynolds stress equation were solved simultaneously
with that for mean momentum. However, WS reported that the calculated velocity profile was sensitive to the
parameterization scheme for the turbulent transport term in their model. In order to avoid the deficiency
in the model of WS, Meyers and Paw 1986 here- after MP developed a third-order closure model using
third-order closure principles. However, the utility of a higher-order closure model is still limited. The model
proposed by MP includes about 10 equations for only a one-dimensional problem, and the computation cost
is therefore high. In addition, their modeled results for the turbulent field have large errors MP; Meyers and
Baldocchi, 1991. The parameterization schemes for higher-order closure models used for predicting veg-
etation wind flow need to be further improved MP; Shaw and Seginer, 1987; Wilson, 1988.
As an alternative approach that does not use higher-order closure principles, Li et al. 1985 pro-
posed a non-local closure scheme for the total mo- mentum flux Reynolds stress and dispersive flux
and developed a first-order closure model that was capable of predicting the wind velocity peaks in lower
canopies. However, several problems in their model have been pointed out by Van Pul and Van Boxel
1990. To correct these problems, Miller et al. 1991 hereafter MLL made some modifications to their
model and applied it to wind flow across an alpine forest clearing. However, the utility of their model for
different types of vegetation canopy was not tested. Over the past few decades, extensive measurements
e.g. Raupach et al., 1986; Shaw et al., 1988; Gao et al., 1989 of turbulent flows within and above vege-
tation canopies have been carried out. On the basis of the results of the previous studies, the purpose of
the present study is to develop a first-order closure model, which is simple in computation and has the
general utility for predicting wind flow within and above vegetation canopies, and to investigate the in-
fluences of canopy structure and foliage density on the wind velocities within and above the canopies.
2. Theory and the model
