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

How to use PRI and NDVI to monitor environmental conditions that adversely affect plant growth.

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.

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Dr. Steve Garrity, METER Group environmental scientist


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This virtual seminar is about Leaf Area Index. We’ll be covering some of the theory, different methods, and some applications of the different methods for measuring leaf area index. So I’d like to start by defining leaf area index just to get us all on the same page. Imagine, for example, that you have a plot out in the forest or out in your crop. That plot is one meter on each side. So we have one square meter of ground area. And then above that, we have that entire area is covered by leaf area, imagine we have a really big leaf covering that full area of the plot. So to calculate LAI, first, we know that we have ground area is equal to one meter then we have one square meter of leaf area. LAI is then the ratio of leaf area to ground area, in this case, one to one. So LAI would equal one. One more example, imagine that we had that same plot, but this time we had 1,2,3 leaf layers. So in this case, we have one square meter of ground area, three square meters of leaf area, giving us a leaf area to ground area ratio of three to one, meaning that LAI would equal three. So fairly straightforward. LAI is not all that complex of a concept to understand. And this is what we’re working with.

So just really briefly, I’d like to discuss why we would want to measure Leaf Area Index. Why is it useful? LAI is one of those variables that is pretty ubiquitous, it’s used all over the place. And that’s because it’s simple, but it’s also extremely descriptive. So for example, I’ve shown a map of the globe, a map of global LAI that was derived from some satellite data. And you can see that, you know, high LAI areas are represented by dark green areas, whereas low LAI are light green areas. So for example, focus on the tropics around the equator. You can see that that’s where we have some of the densest highest LAI forest, anywhere on Earth. And then as we move either to the north, or to the south of that, you can see where a lot of our deserts occur have very low LAI. And then again, moving further to the north, to the south, as we get into the temperate zones in the boreal zones, you can see that LAI picks up again. And a lot of this is I mean that LAI the patterns that we’re seeing are reflective of many processes and many variables. In this case, we could talk about water, we could talk about light availability, that explains some of these patterns. But you can just see that in this case, LAI is is very descriptive of the patterns of worlds vegetation.

So a few other reasons why LAI is so important, and I’m sure that you can come up with more but just a few that I have listed here. One of the really important things that LAI is related to is light harvesting. So you can imagine that the more leaf material that we have in a canopy, the more capacity there is to absorb light energy from the sun. And that light energy then is used to drive plant productivity, primary productivity, through the uptake of carbon dioxide from the atmosphere and fixing it into carbohydrates. This is related to biomass accumulation, crop and forest growth. Leaf Area Index can also be used as an indicator of phonology, where phonology is simply describing the lifecycle events of plants. And so for example, we have deciduous forests that every year leaves flush, they grow, they expand, they mature. And finally they send nests. And all of that can be described simply 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 to another.

LAI is also commonly used as a measure of canopy structure or a way to differentiate the structure of one canopy to another. So these last two are related transpiration and scaling processes. Just in general, let’s consider a leaf for example. And that leaf there’s a lot of physiology that is occurring within that leaf. And then those processes, those physiological processes then are interacting with the atmosphere, the surrounding atmosphere at the surface of the leaf. And those interactions occur in the exchange of both mass and energy. And so we have a leaf at the surface of the leaf we have these exchange processes. So you can imagine that if we understand these processes at the leaf level, then if we know how many leaves are in a canopy, through LAI then gives us a really convenient method to scale these processes to the canopy level and beyond.

Okay, so for the rest of the talk, we’re really gonna be focusing on methods and how people measure LAI. And there’s two major divisions in terms of the methods and those divisions are there’s direct ways to measure LAI. And there’s indirect ways to measure LAI. So the direct ways essentially involve you know, destructively harvesting a canopy, cutting down trees, clipping biomass. One way around that’s not as destructive is actually to the use litter traps to capture leaves that senescent fall off of plants. In contrast, there’s indirect ways that don’t measure LAI directly, but they measure some other variable that’s related, and those variables then can be used either as proxies for LAI or to directly model what LAI is. And the indirect methods I’ll cover in today’s seminar are hemispherical photography, par inversion, which uses measurements of transmitted radiation through the canopy, and finally, spectral reflectance, so a top down approach

Okay, just a little bit more detail about each of the methods here. So as I said, with the direct methods, destructive harvest is common. So you can see that in a forest that entails cutting down trees, and then removing all of the leaf material from those trees, a very labor intensive tedious process, that also removes significant amount of material from the canopy. You can see in the bottom right there a very different canopy, where some people are out in the field, they have a circular plot on the ground, and then they’re harvesting all of the leaf material from that plot. So I’d argue that in the case in the lower right hand side, it might be the only way to measure LAI is using a destructive method just because the canopy is so short, it’s so small, that it would be difficult to measure the LAI of that canopy using any other method. So in addition to directly harvesting that method, in extracting it from from the canopy, another way to directly measure LAI is to use litter traps.

And so for example, this would work well in a deciduous forest, where every year in the fall, the leaves, the nests, they drop to the ground. So with both destructive harvest, and with litter traps, then once the leaf material has been extracted from the plant, we have to have some way of measuring the amount of leaf area that we collected. And so one common way to do that is using something like the Licor LI-3100, which is essentially an optical scanner. So you pass each of the leaves through this scanner, the leaf area would be measured. And when we’re done scanning all of the leaves, we can sum the area, divide that by whatever ground area we were working with to get a measure of the leaf area index.

One of the unique things about this method, as opposed to the others that I’ll be talking about is that this method does allow you to do species specifically leaf area index. So oftentimes we’re working in at least an unmanaged systems in mixed species canopies. And so if we’re interested in understanding the contribution of each species to the total canopy LAI, this would be one way to do that, where we harvest all of the species of species A, B, and C. And then we’re able to analyze their leaf area independently using a scanner such as is shown here.

So for the remainder of the talk, the remainder of the seminar, I’m going to discuss indirect methods for estimating leaf area index. So just an overview of how light can interact with the canopy, there’s really three fates for light in the canopy. The first is transmission. So we have light coming from the sun, that light can be transmitted all the way through the canopy. Another fate would be that the light is actually absorbed. So it’s captured by the canopy and the energy is used in the process of photosynthesis. So then the last way that light can interact with the canopy is through reflectance. So we have light coming from the sun. It strikes the top of the canopy, and then it’s reflected back into the atmosphere back into space. We can measure two of these quantities. We can measure transmittance, and we can measure reflectance. Absorptance, though that energy is used by the plant and therefore is inmeasurable.

So, you know, hemispherical photography is a method that essentially uses measurement of transmitted light to estimate LAI. It’s a method that’s been around for quite a while, and is fairly well established. And what it consists of is taking a camera using a fisheye lens with that camera, attaching that whole camera apparatus to some sort of a leveling deck, and then pointing it upwards so that it’s facing the sky. So it’s placed beneath the canopy, it’s facing the sky, and then we’re going to image the canopy from below, in a hemisphere. The seven images along the bottom would be a time sequence of photographs that have been collected from the same location within a deciduous forest canopy, basically, from very early spring to about the middle of summer. And you can see just visually those photographs demonstrate that you have to begin with we have little to no material in the canopy leaf material in the canopy. And by the time we get to the mid summer on the far right, the canopy is the leaves that fully flushed expanded and matured.

So one of the things that’s unique about hemispherical photography, as opposed to some of the other methods I’ll talk about is that you’re collecting an image of the canopy, which is an extremely data rich data set, because you have both the spatial component, but then also this color component. It also provides an archive or a record of data that can then be re analyzed or you know, you can use a different method at some different point to analyze the imagery as theory and technology change. Whereas with some of the other methods I’ll describe, you’re measuring some value, and you can’t go re measure that value.

So you can imagine that we could use that information to plot where the sun is going to be, and then estimate when during the day, a sunfleck might occur at the sample location, and what the duration of that sun fleck might be. And that might be very important if what we’re interested in studying is how leaf area index is related to sun fleck is related to light transmission and how that affects light availability to understory species.

And there’s a whole variety of other variables that people have come up with ways of extracting from hemispherical photographs other than just leaf area index. So the way that hemispherical photos are analyzed, once you’ve collected the raw photo, you have to use software then to process the photo in order to get to an estimate of LAI or some other variable. And the way that this is done is using thresholding. And the idea behind thresholding is distinguishing between pixels that are occupied by leaves versus pixels that are occupied by sky. And so you can see here in the upper left is the raw image. And then the other seven images are of different thresholding methods or threshold values that have been applied to that image.

And this is, in my opinion, really the Achilles heel of hemispherical photography, and that, you know, different observers might choose different thresholds based on what their eye is telling them, or you’re employing different automated methods for detecting what the threshold might be. And you’re going to end up with a different result. And so there’s quite a bit of subjectivity involved in analyzing hemispherical photographs, which can make it difficult to compare photographs acquired at one time with photographs acquired at another or when different people are involved in the data processing.

So a couple of other items to be aware of when using hemispherical photography, and this is a nice example image. Well, it shows a lot of interesting features that I’ll run through here. The first thing I like to point out here is that this image was collected on a day where it was partly overcast. But you can see that the solar disk is actually peeking through the canopy here. And that’s something that you typically want to avoid, because right around that solar disk is a very bright spot. And so if we’re trying to threshold the difference between you know, the bright background, the bright sky, and canopy in that particular case, we’re going to underestimate how much canopy is there because it’s a very bright spot within the image. The other thing because this image was collected when the sun was shining directly on the canopy, you can see that there’s been a lot of shadows that are cast within the canopy. So again, when it comes time to choose a threshold, a universal or global threshold for this image, those shadows are going to make it very difficult to distinguish you know what brightness threshold is related to sky versus canopy. Then finally, you can see that with those variable clouds, areas that are actually clouded are extremely bright, whereas the sky background is quite a bit darker. So again, this would make it very difficult to choose a threshold that allows us to distinguish canopy from non canopy.

So for all of these reasons, it’s recommended that hemispherical photographs are only collected under a uniformly diffuse conditions or under a 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 so that you don’t have issues with the solar disk contaminating the image. So where would I apply hemispherical photography, so the top set of images you know represent a weak canopy here on the Palouse.

This is probably not a great place for hemispherical photography for the simple fact that you know, the sweet canopy is fairly low growing and it would be difficult to get the camera the lens and the leveling deck and the tripod all fully below the canopy. In contrast, the very tall canopies like the forest canopy, hemispherical photography can work very well because it’s easy to fit all of the the equipment under all of the leaf material in the canopy. Okay, so moving on to the next indirect method, we’re talking about methods that use transmitted measurements of transmitted light to estimate LAI. And just from a conceptual standpoint or very basically, you know, if we’re in a sparse canopy, we know it’s sparse. Well, for one, we can see that there’s very few leaves there. But it also tends to be a lot brighter in the understory of a sparse canopy. Whereas if it was a very dense canopy, we’d expect a lot of the light to be absorbed or reflected. So there’s not a lot left over for leaf or for transmitted. There’s not a lot of transmitted light leftover. So, using these very basic observations that we can see that there must be some relationship between light transmission and leaf area. And indeed there is and this is formalized in Beer’s law or by Beer’s law.

And so for the purposes of leaf area index, let’s consider this form of Beer’s law where we’re dealing with light energy in the form of photosynthetically active radiation or PAR. And so you can see that PAR sub t is transmitted power. So this might be what we measure at the bottom of the canopy. That’s going to be a function of how much incident PAR we have. So how much photosynthetically active radiation is incident at the top of the canopy?

And then two more parameters here K and z, where k is the extinction coefficient and z is the path link through the attenuating medium. So in this case, the attenuating medium would be the canopy itself. So this really formed through Beer’s law in this form is the foundation for what we’ll talk about next are the way that we use measurements of transmitted light to estimate LAI. So specifically, I’m going to be going through the model, the mathematical model that is used by Decagon’s ACCUPAR LP-80. And that model is shown in the upper left, where L is leaf area index, and then you can see the equation on the right and the different parameters that are used as inputs. The first one I’d like to address is this K calculation of K, which is the extinction coefficient within the model. So it’s a sub model, and it has two parameters Chi and theta, and we’ll go through those and see what they are here next.

So theta is simply the solar zenith angle at the time that a measurement is taken. So you can see across the course of a day the solar zenith angle changes. So for example, in the example given, the sun is at various locations across the sky. You can see that early in the morning, the sun is lower in the sky relative to time periods closer to noon. And then the same thing happens as we go to the other end of the day. What theta is really important for is describing the path length of the beam radiation. So the beam radiation is the path of photons directly from the sun to the observer to some point in the canopy. And so you can see that early in the day or late in the day that path length is quite a bit longer than at the middle of the day. So at the middle of day we have the sun in the highest position in the sky, and the path link between the sun and the bottom of the canopy is shortest at that point. Solar zenith angle is calculated simply using time of day and knowledge of geographic location. And so within the LP 80, these are calculated automatically and behind the scenes using user input values of time and location. So it’s critical that when you’re using an LP 80 and you’re in the setup process, make sure that you have both of these values input correctly.

So the next variable in the extinction coefficient model I’d like to discuss is the chi value and chi value describes the leaf angle distribution of a canopy. So, you know every canopy is a mixture of different leaves and these leaves can be horizontal in their orientation, vertical, or some mix so or somewhere, intermediate to horizontal and vertical. And in reality, you know most canopies are a mixture of different of leaves at different inclination angles. And you can see that in the plot here representing three different canopies. The distribution of the leaf angles within three different canopies. You can see that chi values in vertical canopies are below one, the more vertical the canopy is or the leaf angle distribution is, the closer to zero chi becomes. In horizontal canopies chi actually approaches infinity. Typically you’ll see chi values greater than one in this case, and they have to, you know, values of one to five are common in horizontal canopies. Spherical canopies are canopies that are more of a mixture of both vertical and horizontal distributions. And they have chi values that are right around one. And in fact, this is the most common to spherical canopy is the most common or the spherical chi distribution with chi equal to one is the most commonly encountered distribution of leaf angles that occur in nature. And the LP-80 actually uses a chi value equal to one by default. Now you can change that if you want. But in most cases, you can get away with a default.

So I’d like to consider chi value just a little bit more because this seems to be an area where some people get confused. So you can see I’ve got the same plot that we were just looking at in the upper left hand corner, but if we look at the figure in the lower left corner, is demonstrating how chi value or leaf angle distribution influences the extinction coefficient dependent on the zenith angle of the sun. And so for example, you can see that with a chi equal to zero so a completely vertical canopy, if chi is equal to zero and the sun is directly overhead, so the beam zenith angle is equal to zero, you can see that the extinction coefficient is equal to zero, meaning that all the radiation is passing through the canopy. None of it is being absorbed or reflected, it’s 100% transmitted. Contrast that with the horizontal case, or the case where all the leaves are perfectly horizontal, so that would be the chi equals infinity case. And you can see that, then the extinction coefficient has no dependency on the beam zenith angle. And this makes sense, if you think about a perfectly horizontal leaf, it’s not going to matter what angle the solar radiation is striking. It’s going to have an extinction coefficient that’s invariable.

Let’s also have a look at the figure on the lower right. So this is actually looking at transmission relative to solar zenith angle. And again, you can see for the horizontal canopy transmission is going to be the same no matter what the zenith angle is. In the other extreme, for vertical canopies, transmission is one when the sun is directly overhead. And it is almost complete. Well, it is complete when we have very low sun angle, so the sun angle is on the horizon. And again, you can just imagine this, so you have a vertical leaf profile here, and as the sun is directly overhead, it’s not, you know, there is no shadow being cast by the leaf, whereas if the sun is coming from the side at the horizon, there’s going to be complete absorption, and so no transmission of that radiation. I think the most important thing to take away from all of this is to see that in the upper left, there’s three different canopies with very different leaf angle distributions, and thus different chi values. However, those chi values range from 0.5 to three.

But if you look at both the figure in the lower left and the lower right, there isn’t a huge amount of effect, or a huge amount of difference in either extinction coefficient or transmission amongst those chi values. And so the leaf area index model is not highly sensitive to the chi value, especially when when we’re at chi values ranging from, you know, .5 to two or so somewhere in there. Now, this can be a source of error caught if we miss estimate chi, but only in extreme cases. So if we’re dealing in a canopy that’s extremely horizontal, as a highly horizontal distribution, or highly vertical distribution, I’d say if you’re not working in either of those extremes, that a chi value somewhere around one is going to be adequate for your estimation of LAI.

Okay, so we’ve talked about chi or leaf angle distribution, and then theta or solar zenith angle. So now we’ve got the extinction coefficient model taken care of, there’s a few more terms in the LAI model in the upper portion that I’d like to go through. So the first one is f sub b, and f sub b is beam fraction. And it’s calculated as the ratio between diffuse PAR (photosynthetically active radiation) and direct PAR. And so let’s look at what this is, which is graphically represented here on this slide.

So on the left hand side, we’re representing typical clear sky conditions where we have diffuse radiation, which is radiation that has been scattered in the atmosphere by aerosols in other particles and has scattered to some location down in the canopy where we might be measuring transmitted light. Contrast that with the beam radiation, which is dominating in this clear sky condition. And that beam radiation is the radiation that’s coming directly from the sun. And so on this left hand side, we can see that f sub b would be very low because the direct PAR component dominates. So let’s contrast that with the image on the right hand side where we have some clouds or some heavy aerosols within the atmosphere. And in this case, we can see that there’s a lot more scattering going on. There’s a lot less of that beam radiation that’s penetrating directly through those clouds or aerosols to our observation location below the canopy. So in this case, we have f sub b that would be much higher approaching one as we completely eliminate the beam radiation component.

So the take home here is that this f sub b term is important, because it’s describing how or what the distribution of penetration angles of photons is into the canopy. As you can imagine this f sub b is related or interacts with leaf angle distribution, to describe the probability that a photon is going to penetrate, or be transmitted all the way through a canopy. And if this still isn’t making sense, this concept of f sub b, just think about, you know, when you’re outside on a very sunny day, you tend to see a lot of harsh shadows. Shadows are cast that are extremely deep and dark. Whereas on an overcast day, it’s more difficult to find strong shadowing. And that’s simply because there’s a more even distribution of angles of radiation that are striking any object that might cast a shadow. So it’s the same thing with leaves in a canopy.

Okay, the next term that we’re going to discuss is tau and tau is the ratio of transmitted to incident photosynthetically active radiation. And this tau value is probably the most important component of the LAI model. The LAI model is most sensitive to tau. And this is the component that we actually basically forms the core of the measurement when using this model. And so in the example that I’m showing here, we’re measuring incident radiation at the top of the canopy with a PAR Sensor. And then below the canopy, we’re using an LP-80 to measure how much light is being transmitted by the canopy. So you can see it requires both below canopy and above canopy measurements. Now it might be the case that your canopy is extremely tall and you say, well, I can’t get a PAR sensor up above the canopy. There’s at least one solution for that. You can find a clearing or a large gap where you can place your PAR sensor and use that as a measurement of incident radiation.

Now you can either have a PAR sensor out in the clearing that’s continuously logging, or you can take the LP-80 itself out to the clearing, get an incident reading, and then take it back into the canopy to measure transmitted radiation. One thing to be careful of there is if you’re working in conditions where it’s partly overcast or sky conditions are rapidly changing, then you want to update that incident radiation reading fairly frequently or anytime sky conditions and thus ambient light levels change. For that reason, if you’re really concerned about ambient light levels, if they’re fluctuating quite a bit, I’d really recommend that you independently log both incident radiation and transmitted radiation simultaneously so that you’re always accounting for changes in ambient light level and not introducing any source of error into the LAI calculation.

So the example I just showed was using the LP-80, and that works great for doing spot sampling or periodic sampling. Now if you’re interested in continuously monitoring changes in LAI, another approach would be to use PAR sensors both above and below the canopy. And the PAR sensors below the canopy in this example, basically replaced the LP-80. The difference is that the PAR sensors can be continually logged, so you’re getting a continuous measurement of transmitted radiation for input into the LAI model. Okay, so the last term in the LP-80’s, leaf area index model is A which is leaf absorbed, it’s in the PAR photosynthetically active region of the electromagnetic spectrum. In the LP-80, A is fixed to a value of 0.9. And 0.9 is a very good estimate of absorptance for the majority of canopies out there. Absorptance doesn’t change a lot. Now, this might not be the case in some extreme examples. For example, if leaves are extremely young, their absorptance can be quite a bit lower than 0.9. When they’re senescent that can be lower than 0.9. And certainly if you have very hairy or extremely waxy leaves this absorptance term can be quite a bit lower than 0.9. But other than those cases and maybe some other extreme case, a value of 0.9 is a very good estimate for leaf absorptance. And really, you know values that deviate just slightly from 0.9 are not going to have dramatic impacts on a calculation of LAI.

Okay, so we’ve talked about how to use light transmission to estimate LAI. Now we’re going to talk about how to use reflectance to calculate LAI. And again, just starting simply here in cases where LAI is very low, what we typically see is that there’s an even amount of reflectance in both the visible and the near infrared portion of the spectrum. As LAI increases, what we observe is that there’s a decreasing amount of visible reflectance, whereas near infrared reflectance tends to increase. As you can see, there must be some relationship between visible and near infrared reflectance and LAI that we can use to estimate LAI. So here, I’m just showing some reflectance data. So you can see that reflectance is wavelength dependent.

And the plot in the bottom left is covering both the visible and a good chunk of the near infrared region of the electromagnetic spectrum. So the visible goes from 400 to 700 nanometers, and then everything above 700 nanometers is considered near infrared. And you can see that the spectrum has been collected for the same canopy but at different values of leaf area index. And so what you can see is what I just described is a decrease in visible reflectance with increasing LAI. And an increase in near infrared reflectance with increasing LAI. And it turns out that there’s vegetation indices or combinations of different bands that have been invented that allow us to estimate different biophysical canopy variables.

So one of these that’s pretty ubiquitous is the Normalized Difference Vegetation Index, or NDVI. And if you want to know more about spectral reflectance, and some of these vegetation indices, and the NDVI in particular, I’m not going to get into it here, but I encourage you to view some of our other virtual seminars that do go into depth on these topics. But for here, I think it’s enough to know that NDVI is formulated using reflected values of red radiation and near infrared radiation. And it’s been shown the NDVI is related to leaf area index. And so you can see, in the example, I’ve provided that we might have a spectral reflectance sensor at the top of the canopy that’s continually monitoring reflected radiation in the two bands. So you see the two ports, they’re measuring red and near infrared. But if we want to use that NDVI value as a direct estimate of LAI, or as a way of estimating an absolute value of LAI, then we have to develop some relationship with some independent measure of LAI. So for example, we could have an LP-80 that’s calculating LAI from transmitted radiation measurements. And then co located with that, we have a spectral reflectance sensor collecting NDVI values. And then if we collect enough of those values over time or across space, we could develop something like what I’ve shown here a linear regression relationship. And then we could use the subsequent NDVI values in this empirical equation to calculate leaf area index without having to have the other independent source of LAI for all subsequent measurements. So the other thing to consider is that maybe you don’t need absolute values of LAI.

Maybe you’re interested in some other reason to be measuring LAI. So here, I’ve just shown you a couple of examples of how we can use NDVI, just as a proxy for LAI without actually having to have an absolute value of LAI. So on the left hand side of the slide, I’m showing some data from Ryu, where he was measuring both NDVI and canopy photosynthesis in a grassland and for an entire year. So in the top left panel, you can see that NDVI values are plotted in green and then photosynthesis is in the open circles. And you can see that the temporal trajectory of photosynthesis is very well tracked by NDVI. And he goes ahead and shows how a regression equation can be developed. That relates the NDVI values to canopy photosynthesis. So in this case, it is leaf area index. That’s one of the strong drivers of photosynthesis in this annual grassland. But rather than trying to model canopy photosynthesis from LAI he simply uses NDVI as the proxy. So similarly, we could consider maybe a phonology application in the lower right. So what I’m showing here is some data that was collected from a deciduous forest for seven years, where we have leaf area index measured at various intervals. And then simultaneously, we’re measuring NDVI. And you know, just very qualitatively or subjectively, we can see that NDVI tracks the temporal dynamics of leaf area index very closely. So in this case, we could replace a measure of LAI with a proxy of NDVI. Okay, so we’ve covered the methods, the direct and indirect methods.

A few other considerations I’d like to cover. The first is sampling and scaling. So I don’t want anybody to have the impression that you just go out and you measure LAI in one place, and you get that one value, and that’s representative of the whole canopy. That’s not the way it works. For one, you know, one of the assumptions that we tend to have with LAI type model is that leaves are randomly distributed within a canopy. This is almost never the case. There’s always some degree of clumping that occurs just due to branching pattern and the way that leaves are distributed within the branches. And then how trees and branches are distributed within the canopy. One of the easiest ways of getting around negative effects of clumping or negative effects of spatial variability is simply just to increase your sample size.

And so you can see in the lower left, there’s an aerial image of some different crop fields. And then on the right hand side is just that same image was an imaging system was used to collect NDVI data, and then convert that NDVI data into leaf area index. And so you can see that there’s a wide range of LAI values across different management units within that image. And so, you know, the great thing about imaging is that it gives us a sense of what the spatial heterogeneity is, but the methods we’ve talked about are more discrete in terms of the area that they represent. But we can overcome that simply by collecting multiple samples within our study area to try and capture the spatial variability. And then maybe we’re taking a mean, some sort of a spatial mean to represent what the LAI is across the entire area, or maybe we’re simply interested in understanding what the variability of LAI is across the entire area. You know, a few other things to say about scaling, you know, the image that I showed at the beginning of this seminar about the global distribution of leaf area index, that was derived from satellite data. But how do we trust those values? Well, we have to have some way of ground truthing those values and so you can imagine that maybe we have an NDVI sensor above the canopy. And we’re able to take very a detailed measurement at the local level, check it with what our satellite data are giving us and then assign some level of confidence to what we see outside of our sample area using the satellite data.

The other thing to keep in mind is that not all methods will produce the same results. And what I’m showing here was some data that I collected several years ago, during the spring in a deciduous forest canopy. So you can see I used four different methods, I used hemispherical photography, an LAI 2000, a quantum sensor or PAR Sensor, the same thing. And then I used the MODIS satellite, they provided LAI products, so I co located that with some of my measurements, and then compared all four of them. And what you can see is that on any given day, there’s quite a spread of variability between the estimate provided by any one of these methods. So this can be a challenge when you’re comparing one method to another. Some methods tend to compare better with each other. So for example, I didn’t have an LP-80 for this study, but there’s about three or four different papers that have been published now that show that the LAI 2000 and the LP-80 typically give values that are very similar to each other. And then just theoretically, the quantum sensors should be very close to both the LP-80 and the LAI 2000 as well. And they are fairly close in this particular example. You know, the truth is that none of these methods got the absolute value right. In this case, we were using litter traps, and those litter traps are probably the most direct way to estimate what actual LAI was in this canopy. In this case, it was slightly below four. And so you can see at least that maturity, and so you can see that none of these methods got that exactly right. But just use caution when comparing different methods or just understand that there’s going to be variability from method to method.

So why, you know, one of the sources of variability that I think we can avoid is demonstrated here. So this is a, I think, a fairly nice image that demonstrates a lot of the concepts that we’ve been talking about. We have these nice shafts of light that are penetrating the canopy, contrast that with some shaded areas. And you can see that all of that, all those light dynamics are really controlled by how much leaf material is in the canopy and where that leaf material in the canopy is distributed. And so you can imagine, maybe we have a PAR sensor or a single PAR sensor that’s measuring transmitted radiation in this canopy. And if we place it here, at least at this point in time when the image was taken, we’re going to read very high values of transmitted light. But if we have another PAR sensor over here in the shadow, we’re going to get a very different measurement, we’re going to see very low values of transmitted light. So we have to be cognizant of spatial variability that is in the canopy that we’re measuring. So here, these are some data that demonstrate what this might actually look like when we look at individual PAR sensors. So in this case, I had 30 some PAR sensors distributed below a deciduous forest canopy. And you can see that, you know, over time, they all tend to track each other, but the absolute value of transmitted radiation can be very different from location to location.

And so if we’re gonna use transmitted light as an estimate of LAI, you know, which one of these lines, which one of the sensors do we use to estimate LAI? You know, and the answer really depends on what our objective is. If it’s to give some, you know, if we’re just trying to get an average sense of what LAI is, then maybe we take some spatial average of all these values. So another thing to point out is that, you know, these factors of clumping and spatial variability, you know, they are real sources of error. One of the things that we’ve done with the LP-80 is try and account for that in the way that light measurements or transmitted light measurements are acquired. And so the LP-80 has this wand that comes out of the handheld unit, and that wand is about 80 centimeters long, and there’s 80 independent PAR sensors in that wand. And the readings that you get from the wand are actually a spatial or an average across the readings of all of those sensors in the wand. And this was actually shown by some researchers several years ago that in canopies where clumping is present, if you take an average across a linear transect, you tend to reduce the amount of error associated with the clumping. So that’s already physically built into the LP-80. So the other thing you can do, you know, if you’re not using the LP-80, but you’re using a PAR Sensor approach is just make sure that you’re collecting enough samples that are representing the spatial heterogeneity of light transmission, which of course is related to LAI.

So a few other things to consider in wrapping up here. The first thing I always encourage people to consider is why are you measuring LAI? Are you really interested in Leaf Area Index? Or are you interested in some related variable? So for example, a lot of people they try and estimate LAI so that they can estimate transmitted light or absorbed light more often, because they’re trying to estimate canopy productivity or photosynthesis. So then the question becomes why estimate LAI to estimate light absorption when you can more directly measure light absorption through measurement of transmitted incident light.

So again, just understand why LAI is the variable that you’re interested in. Consider whether or not LAI is the only variable you want to measure. So for example, we saw that hemispherical photography can produce several metrics about the canopy structure in addition to LAI that might be useful. Now, are you working with a taller a short canopy? So if you’re working in an extremely tall canopy, maybe it’s not feasible to put an NDVI sensor up above it, because you just don’t have the infrastructure to reach the top of the canopy. In that case, maybe you’re looking at hemispherical photography or some sort of a light transmission measurement like the LP-80 gets. Do you need to measure species specific LAI? So in this case, direct harvest is probably the only method that’s appropriate there. Do you want to perform continuous versus discrete sampling? So do you want to have transmitted light measurements continually logs so that you can continually estimate changes in LAI? Or are you satisfied in just doing a spot sample? For example, if we want to compare LAI amongst different treatment plots, maybe the spot sampling approach is more appropriate. Do you need to scale the measurements? So consider your sampling protocol and what the sources of data are that you have available to scale from the local level to a broader scale. Consider how spatially heterogeneous LAI is within your canopy. Consider how clumped that LAI is. These are going to have, should have an influence on how many samples you collected and where those samples are distributed spatially. And then finally, do you need absolute values of LAI or just simple? Can you use something else as a proxy? So for example, the proxy side would maybe just be using NDVI.

Everything we’ve talked about today is contained in an LAI Application Guide, which is just a document that goes into some detail about what we talked about today, but it also expounds on some of these concepts and touches some other components to be aware of or to consider when measuring LAI or when choosing a method. That Application Guide is free to download. You can visit www.decagon.com/lai and download it whenever it’s convenient for you.

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