The Impact of Landscape Fragmentation on Atmospheric Flow: A Wind-Tunnel Study

Abstract

Landscape discontinuities such as forest edges play an important role in determining the characteristics of the atmospheric flow by generating increased turbulence and triggering the formation of coherent tree-scale structures. In a fragmented landscape, consisting of surfaces of different heights and roughness, the multiplicity of edges may lead to complex patterns of flow and turbulence that are potentially difficult to predict. Here, we investigate the effects of different levels of forest fragmentation on the airflow. Five gap spacings (of length approximately 5h, 10h, 15h, 20h, 30h, where h is the canopy height) between forest blocks of length 8.7h, as well as a reference case consisting of a continuous forest after a single edge, were investigated in a wind tunnel. The results reveal a consistent pattern downstream from the first edge of each simulated case, with the streamwise velocity component at tree top increasing and turbulent kinetic energy decreasing as gap size increases, but with overshoots in shear stress and turbulent kinetic energy observed at the forest edges. As the gap spacing increases, the flow appears to change monotonically from a flow over a single edge to a flow over isolated forest blocks. The apparent roughness of the different fragmented configurations also decreases with increasing gap size. No overall enhancement of turbulence is observed at any particular level of fragmentation.

Appendix: Data Analysis Protocol

The data processing steps (1–9) are shown in Fig. 16 and are applied in a consistent way to all configurations.

Fig. 16

Diagram showing the data processing steps

Step 1

The first step consists in collecting the raw data using the LDV system housed on two separate probes mounted at $60^{\circ }$ to each other in a rigid metal housing attached to a traversing system with minimal vertical tilt, and also carefully levelled in the (X, Y) plane. The doppler signal returned from each pair of beams is composed of three vectors: LDA1, LDA2, LDA3.

Step 2

Since air density and air pressure vary the first step is to define a standard reference condition in order to remove variations due to changes in atmospheric conditions. The raw data are brought to a standard pressure and density by dividing measurements by a standard pressure and density factor ($SPD_{ref}$). It is calculated using the formula presented in the diagram in Fig. 16 step 2 using a reference throat pressure of 50 $\hbox {Pa}$ and a reference density of 1.1 kg m$^{-3}$. $\rho$ and $P_{throat}$ are sampled and averaged over time during the acquisition of LDA1, LDA2 and LDA3. An additional correction has to be applied because one of the probes was rotated after laser maintenance. This correction consisted in taking LDA1 (measured by the 1D probe) as the ‘truth’ and correcting LDA2 and LDA3 (measured by the 2D probe) by using multiplication factors $f_{v}$ and $f_{w}$, respectively, which were obtained by measuring the three pairs of probe beam angles very accurately.

Step 3

Step 3 involves converting corrected LDA1, LDA2 and LDA3 signals into a 3D vector in the orthogonal co-ordinate system of the wind tunnel. The exact method to determine the transformation matrix used in this experiment is described in the user guide written by Böhm and Hughes (2004).

Step 4

The next step is to rotate the wind vector into the flow coordinates to remove any possible angle between the probe system and the wind tunnel itself. This consists in rotating the vector by an angle $\phi$ into the streamwise wind direction at each X location where measurements were made. This is done by forcing the V component to zero well above the forest where no surface effect is noticeable. $\phi$ is calculated at each X location using measurements between $z = 3h$ and $z = 4h$ for the Lower and the Upper profiles separately.

Step 5

The next step is to correct for flow distortion due to the presence of the LDV. This is called the ‘blockage effect’. To assess and correct for this effect independent hot-wire anemometry observations were made at the LDV sampling location with and without the LDV apparatus present. As hot-wire anemometry provides good enough measurements of first-order statistics, we are confident about the blockage angles thus deduced. A small, but statistically significant, height dependent rotational deflection in the (X, Z) plane was diagnosed together with a small, statistically insignificant, speed-up of the mean flow. The rotational deflection was nearly constant above the canopy of approximate magnitude $2^{\circ }$, monotonically decreasing to zero at the ground. A correction is therefore applied to the LDV time series to remove the height-dependent rotational deflection.

Step 6

After correcting for blockage, we calculate and apply a second tilt rotation in the (X, Z) plane by an angle $\theta$, for the same reason as in step 4. $\theta$ is calculated from the upstream flow (at $X = -21h$). It is unique for a particular wind-tunnel configuration and is applied to all points in the wind tunnel. Its value ranges between $0^{\circ }$ and $2.8^{\circ }$. $\theta$ represents the angle between the wind-tunnel physical coordinate system represented by the traversing system and the flow coordinate system after correcting for blockage in step 5.

Step 7

A spike filter developed by Højstrup (1993) and adapted by Vickers and Mahrt (1997) is then applied. Any point that is more than 3.5 standard deviations away from the mean is flagged as a possible spike and removed from the dataset. This process is repeated until no more spikes are detected. At each iteration, the factor of 3.5 is increased by 0.3 after the standard deviations are recalculated. This filter is applied in order to remove unphysical velocity component values.

Step 8

A final step is necessary to combine the Lower and Upper profiles as described in Eq. 6. Profiles have to be spatially and temporally averaged in the Y direction to extract U and W, and to determine the matching angle $\beta _{Matching}$. The $\beta$ angles are calculated well above the canopy to avoid surface effects and are averaged from $z = 2.2$ to 4h at each X location. Only the Upper profiles are rotated in order to match the Lower profiles. This is essentially a final small rotation of the upper profile in the (X, Z) plane to get a match with the Lower profile. This rotation differs from one configuration to another but is in a range between $0^{\circ }$ and $-2.5^{\circ }$. This step is necessary due to very minor differences in leveling the LDV with and without the extension.

$$\begin{aligned}&{\left\{ \begin{array}{ll} \beta _{Lower} = \hbox {arctan}(<\overline{W_{Lower}}>/<\overline{U_{Lower}}>)_{averaged\ over\ z = 2.2\ to\ 4h},\\ \beta _{Upper} = \hbox {arctan}(<\overline{W_{Upper}}>/<\overline{U_{Upper}}>)_{averaged\ over\ z= 2.2\ to\ 4h},\\ \beta _{Matching} = \beta _{Upper} - \beta _{Lower},\\ \end{array}\right. }\nonumber \\&\quad {\left\{ \begin{array}{ll} u_{Matching} = u_{Upper}*\hbox {cos}(\beta _{Matching}) + v_{Upper}*\hbox {sin}(\beta _{Matching}),\\ v_{Matching} = v_{Upper},\\ w_{Matching} = -u_{Upper}*\hbox {sin}(\beta _{Matching}) + w_{Upper}*\hbox {cos}(\beta _{Matching}).\\ \end{array}\right. } \end{aligned}$$

(6)

In summary, raw data are first brought to a standard pressure and density, multiplied by $f_{v}$ and $f_{w}$, converted into a tunnel-oriented right-handed Cartesian co-ordinate system (X, Y, Z; U, V, W), rotated using calculated tilt angles at each X location, corrected for blockage due to the LDV and traversing apparatus, and finally rotated with the yaw angle using a unique angle $\theta$ calculated from the upstream flow. After being spatially and temporally averaged, the Lower and Upper profiles are matched through a small rotation in the (X, Z) plane of the Upper profiles. This whole process is applied in a consistent way to all configurations.