Forest Model

The forest model provides an option to include the drag from forested regions to be included in the momentum equation. The drag force is calculated as follows:

\[F_i= - C_d L(x,y,z) U_i | U_i |\]

Here \(C_d\) is the coefficient of drag for the forested region and \(L(x,y,z)\) is the leaf area density (LAD) for the forested region. A three-dimensional model for the LAD is usually unavailable and is also cumbersome to use if there are thousands of trees. Two different models are available as an alternative:

\[L=\frac{LAI}{h}\]

\[L(z)=L_m \left(\frac{h - z_m}{h - z}\right)^n exp\left[n \left(1 -\frac{h - z_m}{h - z}\right )\right]\]

Here \(LAI\) is the leaf area index and is available from measurements, \(h\) is the height of the tree, \(z_m\) is the location of the maximum LAD, \(L_m\) is the maximum value of LAD at \(z_m\) and \(n\) is a model constant with values 6 (below \(z_m\)) and 0.5 (above \(z_m\)), respectively. \(L_m\) is computed by integrating the following equation (see Lalic and Mihailovic (2004)):

\[LAI = \int_{0}^{h} L(z) dz\]

The simplified model with uniform LAD is recommended for forested regions with no knowledge of the individual trees. LAI values can be used from climate model look-up tables for different regions around the world if no local remote sensing data is available.