Modeling Relative Wind Speed by Optical Stratifi cation Porosity within the Canopy of a Coastal Protective Forest at Different Stem Densities

Wind speed and optical stratifi cation porosity (OSP) were measured at various heights inside a coastal protective forest thinned to different stem densities to assess whether any characteristics of the wind profi le in the coastal protective forest could be predicted from OSP. OSP was defi ned as vertical distribution of the proportion of sky hemisphere not obscured by tree elements inside a forest stand, and was determined for various heights using hemispherical photographic silhouettes on a computer processing system. The distribution of OSP in the coastal forest follows the Lambert-Beer’s law with an extinction coeffi cient (ν). The relative wind speed within the canopy can be described using an exponential form with an attenuation coeffi cient (α). Variation in relative wind speed was very closely correlated with the distribution of OSP within the canopy. While below the canopy, i.e., in the trunk space, relative wind speed was little correlated with the distribution of OSP because the distribution of OSP was relatively constant there. Therefore, the linear relationships between relative wind speed and OSP and between the two coeffi cients ν and α were established within the canopy. The results suggest that OSP can be used to predict the wind profi le in case of the application within the canopy of the coastal forest.


Introduction
Porosity of a windbreak is defi ned as the ratio or percentage of pore space to the space occupied by tree stems, branches, twigs and leaves (Cao 1983, Jiang et al. 1989, Loeffl er et al. 1992).Porosity as the most important characteristic of a windbreak with respect to wind reduction has been recognized (Carborn 1965, Moysey and McPherson 1966, Hagen and Skidmore 1971a, b, Plate 1971, Bean et al. 1975, Zhu and Jiang 1992, Groß 1993).Unfortunately, it is nearly impossible to physically measure the aerodynamic porosity of natural plants because of its three-dimensional nature of the pores through which the wind fl ows.Therefore, efforts have been made to fi nd an alternative measurement (Loeffl er et al. 1992).Optical porosity, a two-dimensional measure of porosity determined from the plant silhouettes, has been proved to be a promising alternative of aerodynamic porosity, especially for the thin windbreaks (Kenney 1987, Heisler and DeWalle 1988, Jiang et al. 1989, 1994, 1999).
Methods for estimating the optical porosity of windbreak have been developed (Bean et al. 1975, Kenney 1987, Jiang et al. 1989, Zhou et al. 1991).Particularly for narrow windbreaks, it can be estimated using digitized photographic silhouettes with very high accuracy (Kenney 1987, Jiang et al. 1989).There are many investigations on the relationships between optical porosity of windbreak and wind reduction (Hagen and Skidmore 1971a, b, Fu et al. 1992, Loeffl er et al. 1992, Groß 1993, Jiang et al. 1994, 1999).
When we consider the atmospheric motion in other forests, i.e. not in the shelterbelt or windbreak, for example, a coastal protective forest, it becomes quite apparent that the relationship between airfl ow and optical porosity in the coastal protective forest is a signifi cant aspect for evaluations of wind reduction, wind damage and other ecological effects of wind (Balckburn and Pett 1988, Peltola and Kellomäki 1993, Ennos 1997, Zhu et al. 1998, Peltola et al. 1999).However, there is little information about porosity for other forests, especially for a coastal protective forest.Obviously, the optical porosity of windbreak does not fi t in with the coastal protective forest.It is fair to say that the relationships between wind speed and the optical porosity have been paid little attention in the coastal protective forests because of the diffi culty and peculiarity.Fortunately, there have been a number of efforts using hemispherical photographs to assess the effect of obstruction on irradiation (Anderson 1964, Koike 1985, Wang et al. 1992, Fournier et al. 1996, Saito 1996).These provide us a method using hemispherical photographic silhouette to estimate the optical porosity in a coastal protective forest, and further to assess the relationships between wind speed and optical porosity within the coastal protective forest (Zhu et al. 2003).
The objective of this study is to establish a relationship between the optical porosity and relative wind speed in a coastal pine forest stand thinned to different stem densities.First, the defi nition of optical stratifi cation porosity (OSP) and the method using hemispherical photographic silhouettes for estimating the OSP are introduced briefl y.Then, the distributions of OSP and relative wind speed are discussed in the coastal pine forest with different stem densities.Finally, the relationship between relative wind speed and the OSP in the coastal pine forest is examined.Such a relationship could be proved useful in prediction of the wind speed profi le within the canopy from relatively simple fi eld measurements of the optical stratifi cation porosity.

Site Description
The experiments were conducted in a coastal pine forest for sand-control with different stem densities, which were produced by thinning.The site is located at Aoyama shore, Niigata prefecture, Japan, at 37º52 41.3"N, 138º56 16.8"E, on a sandy soil with a slope around 4º.The coastal forest was planted about 35 years ago at a spacing of 1.5 × 1.5 m, to give an initial stocking density of approximately 4500 stems ha -1 , and to discourage the development of an understorey.It is composed of Japanese black pine (Pinus thunbergii Parl.) and stretches along a road in about 60º from the true north to several kilometers.
There is a 50 m wide zone of young pine trees behind the sand dune along the seashore.The distance from the shoreline to the road, i.e., the front edge of the coastal forest, is about 120 m.
The coastal forest was thinned with four treatments in December of 1997, i.e., 20%, 30%, 50% thinned and control (unthinned), which are referred to Treatment 1, Treatment 2, Treatment 3 and Treatment 4, respectively.The area of each treatment was 20 × 30 m 2 , surrounded by a buffer zone in the same treatment so that the effective area reached 40 × 50 m 2 .It is about 80 m from the front edge of the coastal forest to the centers of the treatment plots.The stand characteristics before and after thinning are shown in Table 1.

Wind Measurement
Wind data (wind speeds and directions) inside and outside the coastal forest were collected after thinning.One propeller anemometer (Tokyo Ota No. 111-T, Kona Ltd.Japan) with a data logger (Kona DS-64K, Kona Sapporo, Japan) was mounted at a height of 2 m above the ground nearby the sea (about 100 m from the see water) for the purpose of obtaining fundamental data outside the coastal forest.In order to observe the distribution of vertical wind speed inside the coastal forest, two observation towers of 10-m height were established in the control plot (unthinned, treatment 4) and the plot with the most intense thinning (treatment 3, 50% thinned).Two steel pipes fi xed with retractable poles of 10-m height were installed in treatment 1 (20% thinned) and treatment 2 (30% thinned).The collection of vertical wind data in the four treatments was conducted during November of 1999 and January of 2000 using two sets of 4-channel hot-wire anemometers (Rion Tr-Am-11, Rion Ldt.Japan) (Table 2).The observed heights were generally in every 1.0 m up to the forest top, of which one sensor was set just above the forest top (Table 2).
The sensors of the hot wire anemometers were mounted on 1.5 m long arms on the towers and 0.4 m long arms on the 10-m height poles.Simultaneously, two propeller anemometers (Young Model 05103-16B, R. M. Young Company, USA) with data loggers (Kona Kadec-Kaze, Kona Ldt.Japan) were mounted on the top of the two towers in order to get continuous wind data.Intervals of wind data collection were 2 minutes or 10 minutes for the propeller anemometers and 0.5 minute for the hot-wire anemometers.Data runs were irregular in length (between 1 and 6 hours for a run) but generally included the later morning and afternoon.All wind speed data were calibrated according to the hot wire anemometer.
For estimating the atmospheric stability, a three-dimensional sonic anemometer (Kaijo Denki DA-600-3TV, Kaijo Cooperation, Japan) was set on the top of the tower in treatment 4 (unthinned) when vertical wind speeds were measured in each treatment (Table 2).Wind velocity components (longitudinal u, lateral v, and vertical w wind velocity) and temperature (T) were sampled and digitized at a rate of 10 Hz by a data-logging system (TR-62TX, Kaijo Cooperation, Japan) with a data appending system controlled by a computer (PC-9801NS/L, NEC, Japan).Instantaneous data were put onto the hard disk of the computer in the fi eld.The computation was based on a time series of 8192 points over an 819.2 s period.
Wind data obtained inside the coastal forest were selected to meet the following criteria: 1) Wind speed of interval average outside the coastal forest was more than 3.0 m s -1 .2) Wind direction of interval average outside the coastal forest was approximately perpendicular to the coastal forest along the road.
If either of these criteria were not met within the interval, the data obtained inside the coastal forest for the period were discarded.Wind speed data obtained in the coastal forest were sorted by height and wind direction, the mean values were computed with the corresponding wind data outside the coastal forest.Consequently, wind data from ten days were found to meet the criteria (Table 3).Wind data from November 11 in treatment 1, November 22 in treatment 2, November 23 in treatment 3 and December 1 and December 8 of 1999 in treatment 4 were used to develop the related models; other data were used to test the obtained models (Table 3).

Defi nition of the OSP
Stratifi cation porosity is used to describe the distribution of pores of a forest stand on a vertical profi le of forest stand.That is, assuming to cut a forest stand horizontally into many slabs in vertical direction, then the porosity of each slab is recognized as the stratifi cation porosity.However, it is almost impossible to physically measure the aerodynamic porosity (Loeffl er et al. 1992).Therefore, the optical stratifi cation porosity (OSP), a two-dimensional measure of stratifi cation porosity determined from forest silhouettes in vertical direction, is adopted as an alternative of the stratifi cation porosity.The optical stratifi cation porosity is defi ned as the proportion of sky hemisphere not obscured by tree elements downward the horizontal plane at a given height inside a forest stand.An individual OSP can be determined as the ratio of the pore    ), and w' is vertical velocity fl uctuation (m s -1 ).

M
Wind data used for developing the related models, and T Wind data used for testing the related models.
area to the total area using the forest silhouettes in vertical direction on a horizontal plane (Zhu et al. 2003).
The hemispherical photography is a suitable tool for studying the canopy architecture and light regime of forest environments.It has been proven useful in studies requiring fi ne details of canopy structure or the light penetration (Chen and Black 1991).In addition, it combines the advantages of relatively simple procedure for data acquisition, good spatial defi nition of imagery and the easily processing system for the image (Fournier et al. 1996).Therefore, the hemispherical photographic silhouette was used for OSP estimation in this experiment.In fact, the optical porosity is not equal to the effective porosity or aerodynamic porosity because the optical porosity shows only the two dimensional gaps.Nevertheless, the optical porosity has frequently served as a descriptor of natural plants for lack of a practical alternative (Heisler and DeWalle 1988).

Measurement of the OSP
The OSP was measured using a digital hemispherical camera (Nikon, Coolpix 910, Japan, f = 7~21 mm) with a 180º fi sh-eye converter lens (Nikon, FC-E8, Japan, f = 1.7 mm) on calm days soon after the observation of wind in the four treatments.The fi sh-eye lens provided with a simple polar projection of the tree elements.In order to take the photographs at a given height, the camera with the fi sh-eye lens was set into a control-box and fi xed vertically on the top of a retractable pole, which was extendible more than 10 m upward.The observed heights for estimation of OSP were in an interval of 1.0 m from the forest fl oor up to the canopy top and at least three successful images were taken at each height.The images were recorded to a built-in compact fl ash card.Adobe-Photoshop software was chosen as the image processing system.The software provided the total pixels of a given image and the total pixels of tree elements in the same image.Therefore, the value of OSP at a given height can be estimated from Eq. 1.
where P z is optical stratifi cation porosity at height z, which is estimated from the hemispherical image (non-dimension), S z is area of pores in a given image (pixels), S Tz is the total area of the processed image (pixels).Up to three images were available for analysis of OSP for each height, OSP was determined separately for each image and then average value for each height was computed.

Distribution of OSP in Theory
According to the defi nition of OSP, it increases with the increment of height in a forest stand, and attains the maximum 1.0 (the pore proportion is 100%) when it reaches at or over the top of the forest stand.Contrarily, OSP with a value of 1.0 at the top of the forest stand decreases gradually downwards.On the basis of the principle of light attenuation, i.e., the Lambert-Beer's law (Yasugi et al. 1996), the OSP can be obtained under the assumption of homogeneous distributions of branch, leaf and stem in the forest stand (Eq.2).
where d is a distance of the light beam through the homogeneous medium (m), ranging 0 ≤ z ≤ H. H is top height of the forest stand (m).P 0 = 1.0 at or over the forest top.ν is a constant called extinction coeffi cient relating to the change of OSP.Coeffi cient ν should be a constant and independent on distance under the assumption of homogeneous distribution of tree elements.Solving Eq. 2, If the zenith angle of the beam reaching the camera is θ, the distance of a beam light reaching the horizontal plane will become z = d/cos (θ) (4) Combining Eqs. 3 and 4, where P z θ is the OSP related to height and the zenith angle of view.

Determination of Standard OSP
In most of the images taken in the deeply shaded points, the image area above a certain degree of zenith was usually black.In order to compare the OSP among stands with different stem densities, the relationship between OSP and the zenith angle was examined.On the assumption that parameter ν (Eq.5) is constant, the OSP at a given height z is determined only by zenith angle (θ).The OSP decreases with the increment of zenith angle because the silhouette is a polar projection.If the canopy edge of a forest stand is limited to a certain range, the OSP will be changed abruptly when the zenith angle increases to cover the range exceeding the canopy edge.While, if the canopy edge of a forest stand is unlimited, the OSP will decrease with the increasing of zenith angle of the view (θ) as expressed in Eq. 5 (Zhu et al. 2003).
Because the hemispherical photographs were taken in the coastal forest stand with unlimited canopy edge, it is possible to test the effect of the zenith angle (θ) on the estimation of OSP by dividing the image into equiangular circle-belt.
In order to determine the standard or uniform area of image for SOP estimation, the images taken from treatment 1 (20% thinned) at each height were divided into seven equiangular circlebelts.The variation of OSP with zenith angle (θ) from treatment 1 was plotted in Fig. 1 (ln(P θ ) against x).The tested result was listed in Table 4.The result suggests that when the zenith angle (θ) is more than 0.46π, the OSP in the circle-belt was nearly constant to 0. Therefore, the OSP was calculated for a sub-circle 80º of zenith (threequarter area of the hemispherical image) to minimize the infl uence of underexposed areas and to The data used to estimate parameter β s were from the images obtained at each height, which calculated from seven equiangular circle-belts with three repeats.* β s value at height 2.0 m was larger than at 1.0 m may be caused by the errors from the measurement of OSP in the fi eld.allow comparisons among the different thinning treatments.The three-quarter area porosity with excluding the outer one-quarter is determined as the standard OSP.

Distribution of OSP (Standard)
The distributions of OSP measured in the coastal pine forest with different thinning ratios are showed in Fig. 2. The result indicates that OSP is relative stable in the trunk layer and changes greatly within the canopy layer (the trunk layer and canopy layer were divided by bole height, H 0 ).Obvious differences existed across the thinning ratios in the coastal forest.The OSP under the bole height ranged between 0.192~0.213for treatment 4 (unthinned), 0.252~0.315,0.281~0.344and 0.367~0.418for treatment 1 (20% thinned), treatment 2 (30% thinned) and treatment 3 (50% thinned) respectively (Fig. 2).This ranking exactly follows the ranking of stem densities in the four treatments.
It is obvious that in the single-even-aged coastal forest, two layers can be divided by the bole height (H 0 ).If the distribution of OSP is expressed by relative height, according to Eqs. 2 and 3, the distribution of OSP in the coastal forest can be written as, where parameters of ν c (canopy layer) and ν t (trunk layer) are coeffi cients relating to the change of OSP, they should be constant and independent on distance under the assumption of homogeneous distribution of tree elements in each layer.The parameters of ν c and ν t were obtained using the measured OSP (Fig. 2), and their fi tness were tested and listed in Table 5.
The comparison between predicted OSP by the models (Eqs.8 and 9) and the measured in fi eld is showed in Fig. 3.No signifi cant difference has been found between the predicted and the measured OSP for each treatment at p < 0.005 level.

Basic Characteristics of Wind
The fundamental characteristics of the wind data used in this analysis are listed in Table 3.An order-of-magnitude of stability length (Monin-Obukhov length) (L) (see Table 3) was calculated from the measurements of sonic anemometer.Assuming that displacement height of logarithm law was the order of magnitude of tree height, the stability length L was found to be the order of more than 1000 m for most of the measurements, therefore, the atmospheric stability was usually neutral in the experiment.

Distribution of Relative Wind Speed within the Canopy
The analytical model for air movement within plant canopies developed in the literature (Plate 1971, Bergen 1971, Landsberg and James 1971, Konda and Akashi 1976, Ciono 1985) equates the canopy to a two-dimensional distribution of infi nitesimal momentum sinks corresponding to the canopy surfaces (Bergen 1971).The model of airfl ow within canopies was formulated as exponential function of height in Eq. 10.
where z is the interest height within the canopy (m), H is height of top of tree canopy (m), U H is wind speed (m s -1 ) at height H, U in(z) is wind speed (m s -1 ) at height z within the canopy, coefficient α is a constant called attenuation coeffi cient (Amiro 1990) or canopy fl ow index (Cionco 1985, Groß 1993).The coeffi cient α, which is related to drag coeffi cient and average foliage density (Landsberg and James 1971, Kondo and Akashi 1976, Cionco 1985), determines the form of wind profi le within a wide variety of vegetation canopies.The wind profi les within the canopy could be compared quantitatively among the various thinning ratios using the attenuation coeffi cient α.
The mean profi les of relative wind speed obtained from November 11, November 22, November 23 and December 1 and 8 for treatment 1, treatment 2, treatment 3 and treatment 4, respectively were showed in Fig. 4. The regres-  sion statistics for determination of coeffi cient of α in Eq. 10 were shown in Table 6.The exponential relationships were found with α = 3.21 for treatment 4 (unthinned), α = 2.43, 2.05 and 1.77 for treatment 1 (20% thinned), treatment 2 (30% thinned) and treatment 3 (50% thinned), respectively.The reduction of tree density through thinning causes the changes of the vertical forest structure.It is the change that causes the differences of wind profi les within the canopy among the stands with various thinning ratios.Therefore, it can be concluded that greater attenuation of wind speed is related to the canopy density in the various thinning ratios.
The comparison between wind profi les calculated from the model (Eq.10) with the attenuation coeffi cients (Table 6) and that measured in fi eld (wind data measured on January 29 of 2000 for treatment 1, December 10 of 1999 for treatment 2, December 27 of 1999 for treatment 3 and December 9 and 24 of 1999 for treatment 4) is showed in Fig. 5.No signifi cant difference has been found between the wind profi les from predicted and measured for each treatment at p < 0.01 level.

Relative Wind Speed in the Trunk Space
In the trunk layer (under the canopy), the wind profi les were not fi tted the exponential form because of the second maximum appearance of wind speed, i.e., the "blow-through" phenomenon, which may be due to the larger gap, occurring in the trunk layer, especially in treatment 3 (50% thinned).The distributions of the wind profi les (mean values of U in(z) / U H ) for the four treatments were shown in Fig. 4.

Relationship between OSP and Relative Wind Speed
The relationships between the optical stratifi cation porosity and relative wind speed are plotted in Fig. 6.The linear relationships between optical stratifi cation porosity and the relative wind speed (R w = U in(z) / U H ) within the canopy are clearly shown for all the four treatments (Fig. 6A).However, it seems to be little correlated to each other in the trunk layer (Fig. 6B).
As analyzed above, both distributions of wind profi le and the OSP are infl uenced by the tree ele- ments (leaves, branches and stems) in the forest stand, in particular within the canopy (Fig. 6A).Therefore, relative wind speed within the canopy could be predicted from the distribution of OSP.Regression analysis showed that OSP was the independent variable that signifi cantly contributed to predicting the relative wind speed within the canopy.The regression equation obtained as where R w = U in(z) / U H , the relative wind speed, a and b are coeffi cients determined from the measurements of wind and OSP.
The coeffi cients a and b in the linear regression Eq. 11 were determined based on the wind data obtained from November 11, November 22, November 23 and December 1 and 8 for treatment 1, treatment 2, treatment 3 and treatment 4, respectively in Fig. 7.
Comparing the two profi les of OSP and wind velocity within the canopy, we found that they had the same form (Eqs. 8, 10) and they are determined by the coeffi cients α and ν respectively.Therefore, it is signifi cant to check the relationship between the two coeffi cients of wind profi le (α) and the distribution of OSP (ν) within the canopy.The relationship between the two coeffi cients is examined (Fig. 8).A consistent relationship is found between the parameters of α and ν, and can be expressed as (R 2 = 0.98, p < 0.005) Based on this relationship, the attenuation coeffi cient α of wind profi le can be simply estimated from the measurement of OSP.The measurement of OSP is relatively easy because the estimation  of parameter ν within the canopy requires images of photographs at only one position.
In the situation of trunk layer, the distribution of OSP also followed the Lambert-Beer s law although it was relatively constant (Fig. 2).However, the wind profi les were not fi tted the exponential form there because of the "blowthrough" phenomenon.Therefore, relative wind speed was little correlated with the distribution of OSP there, and the relative wind speed in the trunk layer could not be predicted directly from the OSP.

Estimation of Profi les of Relative Wind Speed within the Canopy from OSP
The wind data measured on January 29 of 2000 for treatment 1, December 10 of 1999 for treatment 2, December 27 of 1999 for treatment 3 and December 9 and 24 of 1999 for treatment 4, respectively are showed in Fig. 9.The predicted relative wind speeds using Eq.11 are also showed in Fig. 9 (the solid line, Predicted 1).The differences (mean value ± standard error) between the predicted and measured are 0.0648 ± 0.0331, 0.0656 ± 0.0088, 0.0166 ± 0.0129 and 0.0336 ± 0.0241 for treatments 1, 2, 3 and 4, respectively.It can be concluded that these differences between the predicted and measured values can be ignored when predicting the relative wind speed using the linear relationship between OSP and relative wind speed within the canopy.Fig. 9. Relative wind speeds within the canopy predicted from linear relationships between OSP and relative wind speed and between parameters of α and ν.Solid line, Predicted 1 was predicted from the linear regression in Eq. 11; dash line, Predicted 2 was predicted from the linear regression in Eq. 12.The measured wind data were measured on January 29 of 2000 for treatment 1, December 10 of 1999 for treatment 2, December 27 of 1999 for treatment 3 and December 9 and 24 of 1999 for treatment 4, respectively.The relative wind speeds within the canopy predicted from Eq. 10 by using coeffi cient α, which is estimated from Eq. 12, are also plotted in Fig. 9 (the dash line, Predicted 2).The differences (mean value ± standard error) between the predicted and measured are also examined, i.e., 0.0836 ± 0.0653, 0.0644 ± 0.0072, 0.0058 ± 0.0057 and 0.0169 ± 0.0118 for treatments 1, 2, 3 and 4, respectively.Besides treatment 1, the differences are less than those predicted from Eq. 11.Therefore, Eq. 12 can also provide good fi tness in predicting the relative wind speed within the canopy.

Conclusions
We have adopted this defi nition of optical stratification porosity in developing the models because of the relative easiness and accuracy of the measurement, and it permits comparison among different forest stands.The results suggest that optical stratifi cation porosity can be used to predict the relative wind speed within the canopy of coastal pine forests.Therefore, it may be useful as a guide in the fi eld evaluation of the coastal protective plantation for fi ne-scale ecology study.
The regression results indicate that the higher predictive accuracy could be achieved if enough OSP data were available to develop the prediction equations.However, the relationships derived in this paper should be applied only to the conifer forests.In the case of coniferous forest, the distribution of needles, clusters and branches is relatively homogeneous within the canopy, the linear relationship between the alternative of the aerodynamic porosity, i.e., the OSP, and wind speed has been established successfully.Although it has not been verifi ed for the situation of other tree species in this study, it is possible to obtain the relationships between the OSP and wind speed profi le within the canopy for other tree species using the procedures provided in this paper.
111-T propeller anemometer 2.0 m, outside the forest close to the sea * The eight sensors of the hot wire anemometers were amounted at various heights and the wind data were collected simultaneously in each treatment.Sonic anemometer was set on the top of tower in treatment 4 (unthinned) during the collection of vertical wind data in each treatment.** Nu: Not used.Top The sensor set just on the canopy top.
velocity: the maximum value in the interval.b) Mean velocity: the overall mean value during the period.c) Mean friction velocity: obtained at the top of the tower in treatment 4 (unthinned treatment), z = 10 m. d) H / L : H is mean tree height in treatment 4 (unthinned stand), H = 7.2 m.L is Monin-Obukhov length (m), which was calculated as follows: u' is longitudinal velocity fl uctuation (m s -1

Fig. 1 .
Fig. 1.Relationship between OSP and zenith angle atdifferent heights in treatment 1 (The data were also used inZhu et al. 2003).

Fig. 2 .
Fig. 2. Distribution of optical stratifi cation porosityobtained from the coastal pine forest with different thinning intensities.The legend of bole height mark is in the bracket (Data in this fi gure were also used inZhu et al. 2003).

Fig. 3 .
Fig. 3. Comparison between predicted and measured OSP for the coastal pine forest with different stem densities(Data in this fi gure were also used inZhu et al. 2003).

Fig. 4 .
Fig. 4. Mean wind profi les in the four treatments.The legend of bole height mark is in the bracket.Wind data used in this fi gure were obtained on November 11, November 22, November 23 and December 1 and 8 of 1999 for treatment 1, treatment 2, treatment 3 and treatment 4, respectively.

Fig. 5 .
Fig. 5. Comparison between predicted and measured wind profi les within the canopy for the coastal pine forest with different thinning intensities.Wind data were measured on January 29 of 2000 for treatment 1, December 10 of 1999 for treatment 2, December 27 of 1999 for treatment 3 and December 9 and 24 of 1999 for treatment 4, respectively.

Fig. 8 .
Fig. 8. Relationship between parameters of α and ν used in wind profi les and the distribution of optical stratifi cation porosity within the canopy.

Table 1 .
Mean stand characteristics of the coastal pine forest with four stem densities.

Table 2 .
Instrument types and heights.

Table 3 .
The fundamental characteristics of wind data used to develop and test models.

Table 4 .
Regression statistics for determination of the relationships between zenith angle and OSP in treatment 1 (The same as treatment 2, 3 and 4) (ln(P θ ) = -β s x).

Table 5 .
Regression statistics for determination of the coeffi cient ν in the OSP model by dividing the stand into canopy layer and trunk layer.Parameters of ν c and ν t were determined by data from OSP observations, which were made in an interval of 1.0 m from the forest fl oor up to the canopy top with three repeats.

Table 6 .
Regression statistics for determination of coeffi cient of α in Eq. 10.
Relationships between relative wind speed and OSP for the coastal pine forest with different stem densities.A: within the canopy, B: under the canopy.Regressions of relative wind speed and OSP within the canopy for the coastal pine forest with different stem densities.