Effects of Strong Wind and Ozone on Localized Tree Decline in the Tanzawa Mountains of Japan

2. 1 Computational Region

The Tanzawa Mountains of Japan was chosen for the computational region (Fig. 1(a)), because here, localized tree/forest decline is observed and O₃ concentrations are relatively high depending on elevation. In the Tanzawa Mountains located in the western part of Kanagawa Prefecture, declined Japanese beech trees (Fagus crenata) are conspicuous in the southern to southwestern slopes along the ridges and at high peaks. Recent study (Takeda and Aihara, 2005; Aso and Nakashima, 2004) suggested that O₃ may be associated with those declines as previously described.

Fig. 1.

Computational region.

To take the influence of the wind direction into account and to prepare time-averaged distribution maps of wind and O₃ concentration, six main wind directions are chosen using data (Ebina, 2002-2004) obtained by AMeDAS (Automated Meteorological Data Acquisition System) from the Japan Meteorological Agency (Fig. 1(a)). Rectangular computational domains set for each main wind direction are shown in Fig. 1(b).

2. 2 Computational Method

In this study, we assume atmospheric conditions of incompressible dry air under neutral stratification. Wind and O₃ transport above a forest canopy layer are simulated, and those in a canopy layer are not directly solved since they are modeled under the ground boundary condition. In order to accurately predict local wind in complex terrains, the continuity, Navier-Stokes and concentration transport equations described in boundary-fitted coordinates are used as basic equations:

where

• x_i =(x, y, z) : Cartesian coordinates (x : main wind direction, y : horizontal direction perpendicular to x, z : vertical direction) [m],
• ξ^k =(ξ, η, ζ) : boundary-fitted coordinates [m],
• U_i=(U, V, W) : velocity components in (x, y, z) direction [m/s],
• U_c^k=(U_c, V_c, W_c) : contravariant velocity components in (ξ, η, ζ) direction [m/s],
• C :O₃ concentration [kg/m³],
• t : time [s],
• ρ : density of atmosphere [kg/m³],
• h_kl=$$ \frac{\partial {\xi }^k}{\partial x_m}\frac{\partial {\xi }^l}{\partial x_m}$$ : fundamental tensor,
• J : Jacobian,
• ν_t : eddy kinetic viscosity [m²/s],
• D_t : eddy diffusivity of ozone [m²/s].

In this simulation, the standard k-ε model is used in order to deduce the eddy kinetic viscosity, and the turbulent Schmidt number is set to 1. Photochemical reactions are omitted since the time scale of the reaction is larger than that of wind flow, and advection must be dominant in the narrow regions of about 10 km×10 km considered here. The third-order upwind finite difference is applied to the advection terms and the second-order central finite difference is applied to the diffusion terms for the discretization of basic equations. The Crank-Nicholson method is used for time development. On the inlet boundary, the logarithmic profiles are given to both the velocity and the concentration on the basis of the analogy between momentum and mass transfer, and the concentration at the ground level is set at 80 percent of the upper air concentration by referring to observation data (Aso and Nakashima, 2004). The convection condition is applied at the outlet boundary, and the free-slip condition of velocity and the zero-flux condition of concentration are imposed on the upper and side boundaries, respectively. On the ground boundary, we apply the logarithmic law of velocity and the equilibrium condition of the concentration diffusion flux and the deposition flux above a canopy layer,

where V_d is deposition velocity. To take account of the wind velocity dependence of V_d, it is divided into the aerodynamic resistance r_a, the quasi-laminar layer resistance r_b and the surface resistance r_c. Then, r_a and r_b are directly calculated from the wind simulation and r_c is set to be 200 s/m on the basis of existing literatures (Matsuda et al., 2005). This ground boundary condition for O₃ deposition is fundamentally valid for a flat terrain, and the effect of a complex terrain on deposition is elucidated through eddy diffusivity D_t and concentration C, which are spatially varied by local wind. The validity of this model is discussed in section 3.1.

Computational conditions are shown in Table 1. Subscripts ‘0’ and ‘a’ in the table indicate the ground surface (a ground height of 0 m) and the height of the upper wind level (350 m), respectively. Assuming the background O₃ originates from the stratosphere or distant urban centers, the inlet O₃ concentration exhibits a logarithmic profile which has positive gradients in the vertical direction. Grid points are allocated at even intervals in the horizontal (x, y) plane and densely near the ground in the vertical direction.

Table 1.

Computational condition.

3. 1 Evaluation of Deposition Model

The validity of this wind simulation has already been confirmed, by comparisons of the simulation results with the results of wind tunnel experiments and wind observations, to show high performance (Hattori et al., 2003), while the validity of the dry deposition model and the computational method for O₃ transport have not yet been examined. Thus, the O₃ concentration obtained by the simulation was compared with that observed in the Tanzawa Mountains (Aso and Nakashima, 2004).

The observational measurement by Aso and Nakashima (2004) was conducted using an Ogawa passive sampling system from May to September in 2004. The ground height of diffusion samplers was approximately 1.5 m. The exposure time was two weeks. The trapping part (filter paper) of the samplers was impregnated with 50 μg of 1 percent NaNO₂ solution. While the samplers were exposed, NaNO₃ was formed in proportion to O₃ concentration by the reaction ‘NaNO₂+O₃ → NaNO₃+O₂’. After they were removed and NO₃^- was analyzed using ion chromatography, O₃ concentration was deduced using the correlation function between O₃ concentration and the rates of NO₃^- conversion.

Since the observation data were time-averaged concentrations in the period, corresponding averaged values were calculated from the numerical results of the six main wind directions by the time-averaging method described in section 3.2. The locations of eight observation points (O1-O8) are shown in Fig. 2, and numerical results and observation results at those eight points are compared in Fig. 3. The horizontal axis in Fig. 3 is the observation point number arranged in the order of altitude, and the vertical axis is the O₃ concentration, which is normalized by the concentration at point O1 (an altitude of 175 m) and point O8 (an altitude of 1,672 m) in the figure (C**=(C-C_O1)/(C_O8-C_O1)) to verify the relative magnitude between the points. The numerical results agree well with the observation results on the points O1-O4 and O6-O8, while the difference between the two results is comparatively large at point O5. This might be caused by an inappropriate inlet boundary condition of O₃ concentration, because point O5 is near the inlet boundary in the case of a S or SSW wind direction with a high occurrence frequency. Although the validation of the computational method for O₃ transport is insufficient and there is room for improvement of the model and inlet boundary conditions, the results suggested that this simulation could predict the qualitative tendency of the O₃ concentration field. In the following sections, we proceed with the discussion on the relationship between wind, O₃ and localized tree decline.

Fig. 2.

Location of observation points in Tanzawa Mountains.

Fig. 3.

Comparison of O3 concentration between passive sampling data and simulation in Tanzawa Mountains. Vertical scale: O3 concentration normalized by the concentration at the point O1 and the point O8. Locations of the observation points are shown in Fig. 2.

3. 2 Spatial Distributions of Wind and O₃

To investigate the influence of wind and O₃ on trees, attention is paid mainly to wind and O₃ concentration at a ground height of 10 m, which corresponds to the height of trees. Figs. 4, 5 show wind velocity, turbulent energy and O₃ concentration for each of S and N main wind directions with high occurrence frequency, respectively. The presentation of the results of the other main wind directions are omitted, since similar tendencies were found in the examination, as described below. The contours in the figures are normalized by the values at the inlet boundary. Small arrows and black and white lines in these figures show local wind directions, altitude contours and the rough locations of distinctive U-shaped ridges, respectively. Wind velocity increases on the upwind slopes of the U-shaped ridge and its branch lines, while wind weakens on the downwind slopes and valleys. As observed in Fig. 6 showing the amplitude of wind velocity in a vertical section (y=2 km in Fig. 4(a)), such wind variations near the ground are closely related to the variation in the thickness of the atmospheric boundary layer caused by the ground slope and to the separation of high-velocity flow behind mountains. Moreover, turbulent energy increases in the areas with high wind velocity, supporting the fact that the increase in wind velocity on the upwind slopes is caused by enhanced atmospheric shear, which is directly related to turbulent intensity.

Fig. 4.

Distribution at the ground height of 10 m (S main wind direction).

Fig. 5.

Distribution at the ground height of 10 m (N main wind direction).

Fig. 6.

Vertical distribution of wind velocity at Y=2 km (S main wind direction).

The O₃ concentration also show an increasing tendency on the upwind slopes of ridges at high altitude, since the O₃ transport from the upper air to the ground is here promoted by the increase in turbulence (Fig. 7). As a result, the distribution of O₃ concentration is essentially similar to those of wind velocity and turbulent energy, though the spatial variation of the concentration is smaller than that of wind field.

Fig. 7.

Vertical distribution of O3 concentration at Y=2 km (S main wind direction).

Among the results in the cases of S and N main wind directions, the locations with high wind velocity and high O₃ concentration are naturally different. However, they take maximum values near ridge lines in both cases, suggesting that such areas should be potentially affected by strong wind and high O₃ concentration.

3. 3 Advection Flux and Diffusion Flux

Localized tree/forest decline phenomena may be related to the finding that wind velocity and O₃ concentration vary near the ground surface in the complex terrains, as described in the previous section. In this section, attention is paid to the advection flux F_C=U_pC, which shows the amount of a substance transported parallel to the ground surface, and the diffusion flux F_D=-D_t∂C/∂n, which is usually used for the evaluation of the amount of deposition, where ‘p’ and ‘n’ denote the ground-parallel and ground-vertical components of wind velocity. The correlation component of velocity fluctuation and concentration fluctuation in F_C is omitted since it is comparatively small.

Figs. 8 and 9 show the distributions of normalized advection flux and diffusion flux near the ground in the case of S main wind direction. The contour of advection flux is highly similar to that of wind velocity. This is caused by the larger variation of wind velocity than that of O₃ concentration, showing that the wind field substantially dominates the advective transport of O₃. On the other hand, the spatial variation of diffusion flux is quite small.

Fig. 8.

Distribution of advection flux at the ground height of 14 m (S main wind direction).

Fig. 9.

Distribution of diffusion flux at the ground height of 14 m (S main wind direction).

3. 4 Time-averaged Distributions and Localized Tree Decline

Since trees/forests should declined owing to the cumulative influence of strong wind and O₃ for example, time-averaged values of wind velocity, concentration, advection flux and diffusion flux of O₃ are calculated using the following equation so as to evaluate the numerical results in cumulative time:

Here, U_H, WD and R_WD are the velocity of strong wind, the direction of strong wind and the occurrence frequency of WD, respectively. ‘Strong wind’ is here defined as wind with higher velocity than ‘mean wind velocity’+‘standard deviation of fluctuating wind’ in the observation data. R_WD is deduced from observation data. Figs. 10-13 show the time-averaged distributions of wind velocity, O₃ concentration and both the fluxes near the ground, respectively. The ellipses in these figures indicate rough locations of the ascertained tree declined areas (D1-D3) where trees visually recognized to be obviously dead or reduced vitality. Wind velocity and O₃ concentration vary according to the ups and downs of the ground surface and show maximum values near ridge lines and peaks of mountains. Such a variation near the ground surface has a close connection with the variation of the thickness of the velocity boundary layer and the flow separation behind mountains, as mentioned in the section 3.2.

Fig. 10.

Time-averaged wind velocity.

Fig. 11.

Time-averaged O3 concentration.

Fig. 12.

Time-averaged O3 advection flux.

Fig. 13.

Time-averaged O3 diffusion flux.

The ascertained tree decline areas correspond well with high-wind-velocity areas near ridge line and peaks, suggesting that the localization of tree/forest decline is strongly influenced by local wind properties, which probably also are related to the evaporation of moisture from trees. On the other hand, the spatial variation of O₃ concentration is much smaller than that of wind velocity, and no clear relationship between the distribution of O₃ concentration and tree decline is found. The similarity in the velocity field and O₃ concentration field, however, suggests that the concentration itself has the possibility of being a secondary factor in the localized decline phenomena in a region with high O₃ concentration.

Advection flux, which is greatly affected by wind, shows good correspondence with the tree decline areas, while the distribution of diffusion flux is nearly constant and does not show a clear correspondence. When considering the impact of ozone on trees/forest, the advection flux should be regarded as a combined influence of wind and O₃, and it seems to have a closer connection with the localized tree/forest decline than the O₃ concentration itself. However, it is not valid if wind and ozone have compound effects (as on the flux), and further ecophysiological observations, particularly of factors such as stomatal conductance, evapotranspiration, and water conditions, are required to evaluate these numerical results.