# Obtaining Leaf Area Density Data

The Leaf Area Density (LAD) is the portion of leaf surface ($m^2$) within a volume of air ($m^3$). The formal unit is $$\frac{ \text{Leaf surface } (m^2)}{ \text {Reference volume } (m^3)}$$

In ENVI-met, like in most other models, the LAD is counted one-sided which means that only one side of the leaf is counted as active surface area. This accounts to the fact, that most plants only have stoma on one side of the leaf, typically on the back (but there are others as well). So for the exchange of latent heat ($LE$) it makes sense to count only one side of the leaf as active surface. Also, for the exchange of sensible heat ($H$), normally only one side is exposed to the wind while the other is in the lee of the leaf so that its exchange coeficient approaches zero. This is - of course- a simplicifcation which can be discussed.

## Objective

One of the most frequently asked questions is “How do I get an LAD profile for my plant?

First, I have to admit that the original LAD profiles provided by ENVI-met are rather hand made and based on only a few reference profiles.
There is a very simple but normally also very reliable way of doing it: If you have an idea of the maximum LAD of your plant, you can model your plant by distributing it over the (normalized) height. If you have information about the Leaf Area Index LAI, you can do the same plus check if your values are realistic by summing up the different LAD levels. However, if you need more accurate values, there are basically two methods to approach the problem: measurements and analytical methods. Still, neither oth these methods really solves the problem of the 3D structure of the tree (or plant in general). Trees are normally complex objects that span over several deca-meters with very individual canopy structures depending on the species of the tree. With the implementation of 3D plants, we have introduced a basic approach of defining plants as 3D objects. Those still require the defintion of the $LAD$ values, but you can at least design your tree crown spaces etc.
Recently we are working on the usage of L-Systems to define complex plants in ENVI-met. However, this work is far from beiing finished and will be a feature of upcoming version of ENVI-met.

Going back to the original issue of determing LAD values, let's have a look at the methods availabe:

### Methodology 1a: Optical Measurements

From ground and from space the Leaf Area Index of the vegetation can be obtained using optical methods. While this methods is relatively simple and fast, it does not provide information about the vertical distribution of the leaf area. To obtain this information empirically, the optical sensor must be placed in different levels inside the vegetation stand. Another method is to pick the leafs from the tree and measure the leaf area based on the collected material. There is an obvious drawback on the second approach related to the tree of interest, but it still is an option.

### Methodology 1b: Leaf collection

This methode is straight forward and has certain drawbacks for the tree. You can define your reference volume (1 cubemeter or less) and then collect all the leafs that are inside this volume. You place them on a sheet of paper as close as you can get them and then calculate the leaf surface area. There are also more sophisticated methods available using digital image processing. But as we talk about rude methods here, we restrict outselves to the very basic approach…

You need to do this on different z-levels to get a vertical profile of the LAD.

### Methodology 2: Analytical Approaches

Analytical approaches can help in obtaining the LAD distribution especially if the LAI is known. There are a few papers worth while reading on that aspect:

Meir et al. (2000) provide some ideas how the LAD profile for a tropical rain forest might look like. Their paper is basically focusing on the measurement of LAD/LAI using a photographic method, but it is also useful for getting some ideas on LAD for tropical situations.
Attention: The profiles shown in their figures are normalized with the LAI. Before using them as profiles in ENVI-met, you have to re-calculate the absolute values.

Ross et al. (2000) present an empirical model which allows to calculate the distribution of LAD and LAI based on different probability functions. First they calculate the stem height of a plant and then the correlation of the stem height with the stem leaf area. Finally, the stem leaf area is distributed over the stem height and the LAD profile is calculated. However, this method requires some input data, namely the distribution coefficients for the leaf area to be known. This approach is especially useful if the effects of the growing period should be included in the model.

Stadt and Lieffers (2000) show in their paper how they get the plant characteristics for light transmission model for forest stands (MIXLIGHT). Especially Tab. 1 is very useful as it provides values for the LAD statistical distribution of different species.

Finally, a useful paper is presented by Lalic and Mihailivic (2004), which fits well with the Stadt and Liefers (2000) paper. Lalic and Mihailivic present a very simple and very general method to obtain an LAD profile from very few parameters: type, height and max LAD (which could be extracted for example from the Stadt and Liefers paper).

#### References

Meir, P., Grace, J. and Miranda, A. C. (2000): Photographic method to measure the vertical distribution of leaf area density in forests, Agri.Forrest Met., 102, 105-111

Lalic, B. and Mihailovic, D. T. (2004): An empirical relation describing leaf-area density inside the forest for environmental modelling, J.Appl. Met. 43(4) 641-645

Stadt, K. J. and Lieffers, V.J (2000): MIXLIGHT: a flexible light transmission model for mixed-species forest stands, Agri. Forrest Met., 102, 235-252

Ross, J., Ross, V. and Koppel, A. (2000): Estimation of leaf area and its vertical distribution during growth period, Agri. Forrest Met. 101, 237-246