Influence of Forest-Edge Flows on Scalar Transport with Different Vertical Distributions of Foliage and Scalar Sources

Abstract

Forest edges have significant impacts on flow dynamics and mass exchange across the forest–atmosphere interface. A better understanding of edge flows and scalar transport has implications for locating and interpreting eddy-covariance flux measurements over finite-size forests with edges. Here the large-eddy simulation module within the Weather Research and Forecasting model is deployed to study the influence of forest edges on flow dynamics and scalar transport for a range of vertical distributions of foliage and scalar sources/sinks. For plant canopies with a relatively dense trunk space, a strong in-canopy flow convergence develops near the leading edge, which dominates the flow dynamics and leads to distinct scalar concentration and flux patterns not only across edges but also across the forest–atmosphere interface for sources near the ground and lower part of the canopy. For plant canopies with a deep, sparse trunk space, a strong and long sub-canopy jet develops, leading to simpler features in flow dynamics and scalar transfer. A real case with scalar sources/sink distributions as simulated by a newly developed multiple-layer canopy module produces even more complex scalar concentration and flux patterns. The budget equations for scalars are also analyzed to quantify the contributions of different terms to scalar fluxes. Our results demonstrate that both the scalar source distributions and canopy structures should be considered when eddy-covariance flux measurements are made over finite-size forests with edges.

Appendix: Flux Budget Equations Over a Forest Edge

Assuming neutral stratification, steady-state flow, homogeneity in the spanwise direction, and ignoring the subgrid-scale contribution (Stull 2012), the budget equation for the resolved-scale momentum flux $u^{\prime}w^{\prime}$ can be written as

$$ \frac{{\partial u^{\prime}w^{\prime}}}{\partial t} = 0 = - u\frac{{\partial u^{\prime}w^{\prime}}}{\partial x} - w\frac{{\partial u^{\prime}w^{\prime}}}{\partial z} $$

(3a)

$$ - u^{\prime}w^{\prime}\frac{\partial w}{\partial z} - u^{\prime}u^{\prime}\frac{\partial w}{\partial x} - u^{\prime}w^{\prime}\frac{\partial u}{\partial x} - w^{\prime}w^{\prime}\frac{\partial u}{\partial z} $$

(3b)

$$ - \frac{{\partial w^{\prime}u^{\prime}u^{\prime}}}{\partial x} - \frac{{\partial w^{\prime}w^{\prime}u^{\prime}}}{\partial z} $$

(3c)

$$ - \frac{1}{\rho }\left( {w^{\prime}\frac{{\partial p^{\prime}}}{\partial x} + u\frac{{\partial p^{\prime}}}{\partial z}} \right). $$

(3d)

The terms on the right-hand side of Eq. 3 represent, respectively, advection by the mean flow (3a), shear production by the velocity gradient (3b), flux transported by turbulent motions (3c), and pressure re-distribution effect (3d).

Similarly, for any scalar c (e.g., CO₂), the resolved-scale scalar flux $w^{\prime}c^{\prime}$ can be written as

$$ \frac{{\partial w^{\prime}c^{\prime}}}{\partial t} = 0 = - u\frac{{\partial w^{\prime}c^{\prime}}}{\partial x} - w\frac{{\partial w^{\prime}c^{\prime}}}{\partial z} $$

(4a)

$$ - w^{\prime}c^{\prime}\frac{\partial w}{\partial z} - u^{\prime}c^{\prime}\frac{\partial w}{\partial x} $$

(4b)

$$ - w^{\prime}u^{\prime}\frac{\partial c}{\partial x} - w^{\prime}w^{\prime}\frac{\partial c}{\partial z} $$

(4c)

$$ - \frac{{\partial w^{\prime}u^{\prime}c^{\prime}}}{\partial x} - \frac{{\partial w^{\prime}w^{\prime}c^{\prime}}}{\partial z} $$

(4d)

$$ - \frac{1}{\rho }\left( {\frac{{\partial p^{\prime}c^{\prime}}}{\partial z} - p^{\prime}\frac{{\partial c^{\prime}}}{\partial z}} \right). $$

(4e)

The terms on the right-hand side of Eq. 4 represent, respectively, advection by the mean flow (4a), shear production by the velocity gradient (4b), shear production by the scalar gradient (4c), flux transported by turbulent motions (4d), the pressure re-distribution effect (4e).

Figure 12 shows the three terms in the CO₂ and water vapour flux budget for case 1 (uniformly distributed LAI). All the terms are normalized in this figure.