Webinar - February 26, 2014

Leaf Area Index (LAI): Theory, Measurement, & Application

In this webinar, Dr. Steve Garrity discusses Leaf Area Index (LAI).  Topics covered include the theory behind the measurement, direct and indirect methods, variability among those methods, things to consider when choosing a method, and applications of LAI.



Video transcript:

What is LAI?

In this virtual seminar, we’ll be covering leaf area index (LAI) theory, different LAI measurement methods, and some applications for measuring LAI. We’ll start by defining leaf area index. Figure 1 represents two theoretical plots out in the forest or in a crop. 

How to calculate leaf area index (LAI): conceptual diagram of a plant canopy
Figure 1. How to calculate leaf area index. Conceptual diagram of a plant canopy where (a) = 1 (b) = 3


The plot on the left is one meter on each side or one square meter of ground area (brown square). Above that, the entire area is covered by leaf area (green square). Imagine a really big leaf covering the full area above the plot. To calculate LAI in the left example, we know the ground area is equal to one square meter and the leaf area is also equal to one square meter. LAI is calculated as the ratio of leaf area to ground area, in this case, one to one. So in this example, LAI would equal one. 

On the right of Figure 1 is that same plot but this time with three leaf layers. In this case, there is one square meter of ground area and three square meters of leaf area, giving us a leaf area to ground area ratio of three to one. So in this case, LAI would equal three. 

Why measure LAI?

LAI is not a complex concept to understand, and I’d like to discuss why we measure leaf area index or why it’s useful. LAI is one of those variables that is pretty ubiquitous, meaning it’s used everywhere. This is because it’s simple but also extremely descriptive.

This is a map of global LAI derived from satellite data (see webinar timecode: 2:16). High LAI areas are represented by dark green, and low LAI areas are light green. Notice that in the tropics around the equator are some of the densest, highest LAI forests anywhere on earth. And north or south of the equator, where many of our deserts occur there is very low LAI. Then moving further to the north or to the south in the temperate zones (the boreal zones), LAI picks up again. The LAI patterns in this map are reflective of many processes and many variables. Water or light availability may explain some of these patterns, but in this one example, you can see that LAI is very descriptive of world vegetation patterns. 

Here are a few other reasons why LAI is so important:

  1. Canopy light harvest (productivity, biomass accumulation, crop growth)
  2. Phenology
  3. Canopy structure
  4. Transpiration
  5. Scaling processes, and more

LAI is related to light harvesting. The more leaf material in a canopy, the more capacity there is to absorb light energy from the sun. This light energy is then used to drive plant productivity (primary productivity) through the uptake and conversion of carbon dioxide from the atmosphere into carbohydrates. This is related to biomass accumulation and crop and forest growth. 

LAI is also used as an indicator of phenology where phenology is simply describing the lifecycle events of plants. For example in deciduous forests, every year leaves flush, grow, expand, mature, and finally senesce. All of these processes can be described by tracking leaf area index through time. 

LAI is also commonly used as a measure of canopy structure or a way to differentiate the structure of one canopy from another. And it’s useful in two related parameters: transpiration and scaling processes. 

Exchange processes occur at the surface of the leaf (LAI, leaf area index)
Figure 2. Exchange processes occur at the surface of the leaf


Consider a leaf for example (Figure 2). In that leaf are many physiological processes that interact with the surrounding atmosphere at the surface of the leaf. And those interactions occur in the exchange of both mass and energy. If we understand these exchange processes at the leaf level and we know how many leaves are in a canopy through LAI, it gives us a convenient method to scale these processes to the canopy level and beyond.

How to measure LAI

There are two major divisions in terms of LAI measurement methods: direct methods and indirect methods. Direct LAI methods typically involve destructively harvesting a canopy: cutting down trees or clipping biomass. One way that’s not as destructive is to use litter traps to capture leaves that senesce and fall off of plants. In contrast, indirect methods don’t measure LAI directly but measure some other related variable(s). The related variable(s) are then used either as proxies for LAI or to directly model what LAI is. The indirect methods I’ll cover in this seminar are hemispherical photography, PAR inversion (which uses measurements of transmitted radiation through the canopy), and spectral reflectance (a top-down approach using sensors above the canopy). 

LAI: direct methods

As mentioned, a destructive harvest is common in direct LAI methods. In a forest, it entails cutting down trees and removing all of the leaf material from those trees: a labor-intensive, tedious process that also removes a significant amount of material from the canopy.

Diagram: Direct destructive method where researchers harvest all leaf material from a plot (LAI, leaf area index)
Figure 3. Direct destructive method where researchers harvest all leaf material from a plot


Figure 3 illustrates a very short canopy where researchers designate a circular plot on the ground and harvest all of the leaf material from that plot. In this case, using a destructive method might be the only way to measure LAI just because the canopy is so short. 

Another way to directly measure LAI is to use litter traps. In a deciduous forest every autumn, leaves senesce and drop to the ground. Litter traps can be placed around the canopy to capture some of these leaves. Researchers can then periodically sample the leaves (i.e., pull them out of the trap and take them to the lab for analysis).

With both destructive harvest and litter trap methods, once the leaf material is extracted from the plant, the amount of collected leaf area must be measured. One common method is the Licor Li 3100 which is essentially an optical scanner. A researcher passes each leaf through the scanner and the leaf area is measured. When all the leaves are scanned, the researcher can sum the area and divide that by the ground area to get a measure of LAI. One of the unique advantages of this method is that it allows species-specific leaf area index. This is helpful in unmanaged systems or mixed-species canopies in order to understand the contribution of each species to the total canopy LAI. A researcher can harvest species A, B, and C and then analyze their leaf area independently using a scanner. 

LAI: Indirect methods

All indirect LAI methods discussed in this webinar rely in some way on measuring how light interacts with the canopy, so first, a brief overview of how light can interact with the canopy. There are three fates for light in a canopy. 

  • Transmission: Sunlight is transmitted all the way through the canopy. 
  • Absorbance: Sunlight absorbed or captured by the canopy and the energy is used in the process of photosynthesis 
  • Reflectance: Sunlight strikes the top of the canopy and is reflected back into the atmosphere and into space

We can measure two of these quantities: transmittance and reflectance. Absorbance is immeasurable because that energy is used by the plant. 

Hemispherical photography

Hemispherical photography is a method that uses the measurement of transmitted light to estimate LAI. It’s a method that’s been around for quite a while and is well established. It entails using a camera with a fisheye lens, attaching that whole camera apparatus to a leveling deck, and then pointing it upward so that it’s beneath the canopy facing the sky.

Hemispherical photography from a mixed deciduous forest using a digital camera fisheye lens (LAI, leaf area index)
Figure 4. Hemispherical photography from a mixed deciduous forest using a digital camera fisheye lens


The camera captures an image of the canopy from below in a hemisphere like the one in Figure 5. So you can see that the seven images along the bottom (see images at timecode 13:08 in the webinar) would be a time sequence of photographs that have been collected from the same location within a deciduous forest canopy from very early spring to about the middle of summer. Visually these photographs demonstrate that in early spring there is little to no leaf material in the canopy. And by the time we get to the mid-summer, the leaves have fully flushed, expanded, and matured. 

Hemispherical photography is unique, as opposed to some of the other methods I’ll talk about because an image of the canopy is an extremely data-rich data set. This is because there is both a spatial component and also a color component. It also provides an archive or a record of data that can then be re-analyzed (i.e. it’s possible to use a different method to analyze the imagery as theory and technology change). Whereas with other methods, you’re measuring some value and you can’t go re-measure that value.

The other advantage of hemispherical photography is that besides LAI, you can also measure a suite of other canopy variables related to canopy structure. For example, I’ve plotted here, a hypothetical solar track: the position or the track that the sun takes across the sky for any given day. You might use that information to plot where the sun is going to be and then estimate when a sun fleck might occur at the sample location and what the duration of that sun fleck might be. That could be important if you’re interested in studying how LAI is related to light transmission and how that affects light availability to the understory species. And researchers have come up with many other ways of extracting information from hemispherical photographs other than just leaf area index.

To analyze hemispherical photos, the raw photo is processed using software in order to get to an estimate of LAi or some other variable. This is done is using thresholding. The idea behind thresholding is distinguishing between pixels that are occupied by leaves versus pixels that are occupied by the sky. Notice in the upper left is the raw image (see webinar timecode 15:14). And the other seven images are of different threshold values that have been applied to that image. This is, in my opinion, the Achilles heel of hemispherical photography because different observers might choose different thresholds based on what their eye is telling them.  Also, different automated methods for detecting the threshold might end up with different results. So there’s quite a bit of subjectivity involved in analyzing hemispherical photographs which can make it difficult to compare photographs acquired at different times or when different people are involved in the data processing.

When using hemispherical photography avoid taking a photograph when the solar disk is peeking through the canopy. This is because right around that solar disk will be a very bright spot, and if you try to threshold the difference between a bright background, a bright sky, and a canopy, you’ll underestimate how much canopy is there because of that bright spot. Also, because the image is collected when the sun is shining directly on the canopy, there will be shadows cast within the canopy which will make it very difficult to distinguish what brightness threshold is related to sky versus canopy. Finally, if there are variable clouds in your picture, areas that are clouded will be extremely bright, whereas the sky background will be quite a bit darker. This makes it very difficult to choose a threshold that distinguishes canopy from non-canopy. For all of these reasons, it’s recommended that hemispherical photographs are only collected under uniformly diffuse conditions or uniformly overcast conditions. The other time of day that works is either very early or very late when the sun is low or below the horizon to eliminate issues with the solar disk contaminating the image. 

So what applications are suitable for hemispherical photography? A wheat field is probably not a great place for hemispherical photography because a wheat canopy is fairly low growing, and it would be difficult to get the camera, lens, leveling deck, and the tripod all fully below the canopy. Hemispherical photography works well ln tall canopies like a forest canopy because it’s easy to fit the equipment under all of the leaf material in the canopy.

LP-80: transmitted light and Beer’s law

From a conceptual standpoint, you can tell if you’re in a sparse canopy because there are very few leaves and it tends to be a lot brighter in the understory of a sparse canopy. Whereas if you were in a very dense canopy, you’d expect a lot of the light to be absorbed or reflected and not transmitted to the understory. 

Diagram of a relationship between light transmission and leaf area (LAI, leaf area index)
Figure 5. There is a relationship between light transmission and leaf area


Using these basic observations you can see there is some relationship between light transmission and leaf area. This is formalized by Beer’s law, and for the purposes of LAI, consider the form of Beer’s law dealing with light energy in the form of photosynthetically active radiation or PAR.

Beer's law equation (LAI, leaf area index)
Equation 1


PARt is transmitted bar which might be measured at the bottom of the canopy. This is going to be a function of incident PAR (PARi) or how much photosynthetically active radiation is incident at the top of the canopy. Two more parameters are k and z, where k is the extinction coefficient and z is the path link through the attenuating medium. In this case, the attenuating medium would be the canopy itself. So Beer’s law in this form is the foundation for the way we use measurements of transmitted light to estimate LAI. Specifically, I’m going to illustrate the mathematical model used by the METER Accupar LP-80 (Equations 2 and 3).

Equation: mathematical model used by the METER Accupar LP-80 (LAI, leaf area index)
Equation 2


In Equation 2 on the top left, L is leaf area index, and the first parameter I’d like to address is the calculation of k, which is the extinction coefficient within the model. The bottom right of Equation 2 is a sub-model with two parameters: chi (X) and theta (𝚹). Theta is simply the solar zenith angle at the time a measurement is taken.

Diagram: Solar zenith angle changes throughout the day (LAI, leaf area index)
Figure 6. Solar zenith angle changes during the day. The observer is facing the equator.


Across the course of a day, solar zenith angle changes. In Figure 6, the sun is at various locations across the sky. Early in the morning (left), the sun is lower in the sky relative to time periods closer to noon. And the same thing happens at the end of the day. Theta is important for describing the path length of the beam radiation (the path of photons directly from the sun to the observer to some point in the canopy). 

Notice that early in the day or late in the day that path length is quite a bit longer than in the middle of the day. Thus, the solar zenith angle is calculated simply using time of day and knowledge of the geographic location. Within the LP-80, these parameters are calculated automatically with user input values of time and location, so it’s critical when setting up an LP-80 that you have both of these values input correctly.

Accurate. Automated. Affordable.

Designed for real time, non-destructive LAI measurements, the LP-80 has you covered when it comes to reliable results

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