From e62a057588bc5e73577fb9d9513ab797eb8f81fd Mon Sep 17 00:00:00 2001 From: Harish Date: Sat, 23 Nov 2024 11:27:53 -0700 Subject: [PATCH] Added documentation --- Docs/sphinx_doc/index.rst | 1 + Docs/sphinx_doc/theory/Forest.rst | 31 +++++++++++++++++++++++++++++++ 2 files changed, 32 insertions(+) create mode 100644 Docs/sphinx_doc/theory/Forest.rst diff --git a/Docs/sphinx_doc/index.rst b/Docs/sphinx_doc/index.rst index aefbf3798..7633ba5cf 100644 --- a/Docs/sphinx_doc/index.rst +++ b/Docs/sphinx_doc/index.rst @@ -57,6 +57,7 @@ In addition to this documentation, there is API documentation for ERF generated theory/Forcings.rst Particles.rst theory/WindFarmModels.rst + theory/Forest.rst theory/UnitsAndConstants.rst .. toctree:: diff --git a/Docs/sphinx_doc/theory/Forest.rst b/Docs/sphinx_doc/theory/Forest.rst new file mode 100644 index 000000000..6cece77f2 --- /dev/null +++ b/Docs/sphinx_doc/theory/Forest.rst @@ -0,0 +1,31 @@ +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: + +.. math:: + + F_i= - C_d L(x,y,z) U_i | U_i | + + +Here :math:`C_d` is the coefficient of drag for the forested region and :math:`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: + +.. math:: + L=\frac{LAI}{h} + +.. math:: + 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 :math:`LAI` is the leaf area index and is available from measurements, :math:`h` is the height of the tree, :math:`z_m` is the location +of the maximum LAD, :math:`L_m` is the maximum value of LAD at :math:`z_m` and :math:`n` is a model constant with values 6 (below :math:`z_m`) and 0.5 +(above :math:`z_m`), respectively. :math:`L_m` is computed by integrating the following equation (see `Lalic and Mihailovic (2004) +2.0.CO;2>`_): + +.. math:: + 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. \ No newline at end of file