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LAI—theory and practice

LAI—theory and practice

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Leaf Area Index (LAI) is one of the most widely used measurements for describing plant canopy structure. LAI is also useful for understanding canopy function because many of the biosphere-atmosphere exchanges of mass and energy occur at the leaf surface. For these reasons, LAI is often a key biophysical variable used in biogeochemical, hydrological, and ecological models. LAI is also commonly used as a measure of crop and forest growth and productivity at spatial scales ranging from the plot to the globe.

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In the past, measuring LAI was difficult and time consuming. However, theory and technology developed in recent years have made measuring LAI much simpler and more feasible for a wide range of canopies. Download this application guide for a brief introduction to the theory and instruments used to measure LAI. Several scenarios and special considerations are discussed, which will help individuals choose and apply the most appropriate method for their research needs.

What is LAI?

Leaf area index (LAI) quantifies the amount of leaf material in a canopy. By definition, it is the ratio of one-sided leaf area per unit ground area. LAI is unitless because it is a ratio of areas. For example, a canopy with an LAI of 1 has a 1:1 ratio of leaf area to ground area (Figure 1a). A canopy with an LAI of 3 would have a 3:1 ratio of leaf area to ground area (Figure 1b).

Globally, LAI is highly variable. Some desert ecosystems have an LAI of less than 1, while the densest tropical forests can have an LAI as high as 9. Mid-latitude forests and shrublands typically have LAI values between 3 and 6.

Seasonally, annual and deciduous canopies and croplands can exhibit large variations in LAI. For example, from seeding to maturity, maize LAI can range from 0 to 6. Obviously, LAI is a useful metric for describing both spatial and temporal patterns of canopy growth and productivity.

Conceptual diagram of a plant canopy where (a) = 1 (b) = 3
Figure 1. Conceptual diagram of a plant canopy where (a) = 1 (b) = 3

 

Measuring LAI

There is no one best way to measure LAI. Each method has advantages and disadvantages. The method you choose will depend largely on your research objectives. The researcher who needs a single estimate of LAI might use a different method than the one who is monitoring changes in LAI over time. For example, the grassland researcher may prefer a different method than the forestry researcher. In this guide, we’ll discuss the theoretical basis of each of the major methods along with key advantages and limitations.

Direct measurement

Traditionally, researchers measured LAI by harvesting all the leaves from a plot and painstakingly measuring the area of each leaf. Modern equipment like flatbed scanners have made this process more efficient, but it is still labor intensive, time consuming, and destructive. In tall forest canopies, it may not even be feasible. It does, however, remain the most accurate method of calculating LAI because each individual leaf is physically measured. Litter traps are another way to directly measure LAI, but they don’t work well in evergreen canopies and can only capture information from leaves that have senesced and abscised from the plant.

Indirect measurement

Several decades ago, canopy researchers began to look for new ways to measure LAI, both to save time and to avoid destroying the ecosystems they were trying to measure. These indirect methods infer LAI from measurements of related variables, such as the amount of light that is transmitted through or reflected by a canopy.

Hemispherical photography

Hemisphere photography was one of the first methods used to indirectly estimate LAI. Researchers would photograph the canopy from the ground using a fisheye lens. Photographs were originally analyzed by researchers themselves. Now, most researchers use specialized software to analyze images and differentiate between vegetated and non-vegetated pixels.

A Hemispheric picture from a mixed deciduous forest using a digital camera fisheye lens
Figure 2. Hemispherical photography from a mixed deciduous forest using a digital camera fisheye lens

 

Advantages. Hemispherical photography has decided advantages. First, it delivers more than just LAI measurements. It can also provide canopy measurements such as gap fraction, sunfleck timing and duration, and other canopy architecture metrics. Second, the canopy images can be archived for later use or for reanalysis as methods change and software programs improve.

Limitations. Hemispherical photography has drawbacks, however. In spite of the fact that the images are now digitally processed, user subjectivity remains a significant issue. Users must select image brightness thresholds that distinguish sky pixels from vegetation pixels, causing LAI values to vary from user to user or when using different image analysis algorithms.

Hemispherical photography also remains time consuming. It takes time to acquire good quality images in the field and more time to analyze the images in the lab. Also, sky conditions must be uniformly overcast when the pictures are taken. Hemispherical photography does not work well for short canopies like wheat and corn since the camera body, lens, and tripod may not physically fit under the canopy.

Note: For some users, instruments that measure PAR offer a shortcut. Some models use LAI values to estimate PAR. In this case, the PAR instrument can be used to directly estimate below-canopy levels of PAR, improving the accuracy of the model.

Radiation transmittance

Several commercially available instruments, including METER’s LP-80 ceptometer, offer an alternative to hemispherical photography. They estimate LAI using the amount of light energy transmitted by a plant canopy. The idea is fairly simple; a very dense canopy will absorb more light than a sparse canopy. This means there must be some relationship between LAI and light interception. Beer’s law provides the theoretical basis for this relationship. For the purposes of environmental biophysics, Beer’s law is formulated as

LAI Equation
Equation 1

 

where PARt is transmitted photosynthetically active radiation (PAR) measured near the ground surface, PARi is PAR that is incident at the top of the canopy, z is the path length of photons through some attenuating medium, and k is the extinction coefficient. In the case of vegetation canopies, z accounts for LAI, since leaves are the medium through which photons are attenuated. You can see that if we know k and measure PARt and PARi, it may be possible to invert Equation 1 to calculate z as an estimate of LAI. This approach is commonly referred to as the PAR inversion technique. The real world is slightly more complex, but as you will see in Section 3, Beer’s law is the foundation for estimating LAI using measurements of incident and transmitted PAR.

Advantages. The PAR inversion technique is non-destructive, one obvious but major advantage that allows a canopy to be sampled extensively and repeatedly through time. The PAR-inversion technique is also attractive because it has a solid foundation in radiative transfer theory and biophysics and is applicable in a wide variety of canopy types. For these reasons, the PAR-inversion technique is currently a standard and well-accepted procedure.

In addition to handheld instruments like the METER LP-80 ceptometer, standard PAR sensors (a.k.a. quantum sensors) can also be used to measure transmitted radiation for a PAR-inversion model. The advantage to using PAR sensors as opposed to a purpose-built, handheld LAI instrument is that PAR sensors can be left in the field to continuously measure changes in PAR transmittance. This may be useful when studying rapid changes in canopy LAI or when it is not feasible to visit a field site frequently enough to capture temporal variability in LAI with a handheld instrument.

Limitations. The PAR inversion technique has a few limitations. It requires measurements of both transmitted (below-canopy) and incident (above-canopy) PAR under identical or very similar light conditions. This can be challenging in very tall forest canopies, although incident PAR measurements can be made in large canopy gaps or clearings. Also, in extremely dense canopies, PAR absorption may be nearly complete, leaving little transmitted light to be measured at the bottom of a canopy. This makes it difficult to distinguish changes or differences in LAI when LAI is very high. Finally, estimates of LAI obtained from measurements of transmitted PAR can be affected by foliage clumping. Errors in LAI estimation associated with clumping can usually be alleviated by collecting numerous spatially distributed samples of transmitted PAR.

Radiation reflectance

Another method for estimating LAI uses reflected rather than transmitted light. Radiation that has been reflected from green, healthy vegetation has a very distinct spectrum (Figure 3). In fact, some scientists have proposed finding potentially habitable planets outside our solar system by looking for this unique spectral signal. A typical vegetation reflectance spectrum has very low reflectance in the visible portion of the electromagnetic spectrum (~400 to 700 nm, which is also the PAR region). However, in the near-infrared (NIR) region (> 700 nm) reflectance can be as high as 50%. The exact amount of reflectance at each wavelength depends on the concentration of various foliar pigments like chlorophyll and canopy structure (e.g., arrangement and number of leaf layers).

Advantages. Early attempts to use spectral reflectance data to quantify canopy properties found that the ratio of red and NIR reflectance could be used to estimate the percent canopy cover for a given area. Later efforts have produced a number of different wavelength combinations that relate to various canopy properties. These wavelength combinations, or spectral vegetation indices, are now routinely used as proxies for LAI or, through empirical modeling, are used to directly estimate LAI.

Until recently, one of the only ways to collect reflectance data was with a handheld spectrometer—an expensive, delicate instrument designed for the lab, not the field. But sensor options have expanded with the development of lightweight multiband radiometers that measure a specific vegetation index. These little sensors are inexpensive and don’t require a lot of power, making them perfect for field monitoring.

This is good news for anyone who wants to monitor changes in LAI over time, including researchers interested in phenology, canopy growth, detecting canopy stress and decline, or detecting diseased plants.

Vegetation indices offer another advantage: many earth-observing satellites like Quickbird, Landsat, and MODIS measure reflectance that can be used to calculate vegetation indices. Since these satellites observe large areas, they may serve as a way of scaling observations made at the local scale to much broader areas. Conversely, measurements made at the local scale with a multiband radiometer can be a useful source of ground-truth data for satellite-derived vegetation indices.

Multiband radiometers also offer a top-down option for extremely short canopies like shortgrass prairie and forbs. It’s difficult, if not impossible, to use most LAI estimation methods with these canopies because the equipment is too big to fully fit beneath the canopy. Vegetation indices are measured using sensors that view the canopy from the top down, making them a great alternative in cases like these.

Graph of the reflectance spectra obtained at different stages of canopy development
Figure 3. Reflectance spectra obtained at different stages of canopy development. Note: There is a distinct difference between visible and nearinfrared (NIR) reflectance that develops as LAI increases.

 

Limitations. One of the biggest limitations of vegetation indices is that they are unitless values and when used alone, do not provide an absolute measure of LAI. If you don’t need absolute LAI values, the vegetation index value can be used as a proxy for LAI. If you need absolute values of LAI, however, you will need to use another method for measuring LAI in conjunction with the vegetation index until enough colocated data has been gathered to produce an empirical model.  This method can also be limited due to the location of sensors. By nature, reflectance must be measured from the top of a plant canopy, which may not be feasible in some tall canopies.

Using the LP-80 ceptometer

The METER LP-80 ceptometer uses the PAR inversion technique for calculating LAI. The LP-80 uses a modified version of the canopy light transmission and scattering model developed by Norman and Jarvis (1975). Five key variables used as inputs are discussed below.

τ (ratio of transmitted and incident PAR): The most influential factor for determining LAI with any PAR inversion model is the ratio of transmitted to incident PAR. This ratio (τ) is calculated using measurements of transmitted PAR near the ground surface and incident PAR above the canopy.

τ is a relatively intuitive variable to understand. When LAI is low, most incident radiation is transmitted through the canopy rather than being absorbed or reflected, thus τ will be close to 1. As the amount of leaf material in the canopy increases, there is a proportional increase in the amount of light absorbed, and a decreasing proportion of light will be transmitted to the ground surface. The LP-80 consists of a light bar, which has 80 linearly spaced PAR sensors and an external PAR sensor. In typical scenarios, the light bar is used to measure PAR under the canopy, whereas the external sensor is meant to quantify incident PAR, either above the canopy or in a clearing.

θ (solar zenith angle): θ is the angular elevation of the sun in the sky with respect to the zenith, or the point directly over your head, at any given time, date, and geographical location (Figure 4). The solar zenith angle is used to describe the path length of photons through the canopy (e.g., in a closed canopy, the path length increases as the sun approaches the horizon) and for determining the interaction between beam radiation and leaf orientation (discussed below).

θ is automatically calculated by the LP-80 using inputs of local time, date, latitude, and longitude. Therefore, it is critical to make sure that these are correctly set in the LP-80 configuration menu.

ƒb (beam fraction): In an outdoor environment, the ultimate source of shortwave radiation is the sun. When the sky is clear, most radiation comes as a beam directly from the sun (Figure 5a). In the presence of clouds or haze, however, some portion of the beam radiation is scattered by water vapor and aerosols in the atmosphere (Figure 5b). This scattered component is referred to as diffuse radiation. ƒb is calculated as the ratio between diffuse and beam radiation. The LP-80 automatically calculates ƒb by comparing measured values of incident PAR to the solar constant, which is a known value of light energy from the sun (assuming clear sky conditions) at any given time and place on earth’s surface.

χ (leaf angle distribution): The leaf angle distribution parameter (χ) describes the projection of leaf area onto a surface. Imagine, for example, a light source directly overhead. The shadow cast by a leaf with a vertical orientation would be much smaller than the shadow cast by a leaf with a horizontal orientation. In nature, canopies are typically composed of leaves with a mixture of orientations. This mixture is often best described by what is known as the spherical leaf distribution with a χ value = 1 (the default in the LP-80). Canopies with predominantly horizontal orientations, such as strawberries, have χ values > 1, whereas canopies with predominantly vertical orientations, like some grasses, have χ values < 1.

In general, χ describes how much light will be absorbed by the leaves in a canopy at different times of day as the sun moves across the sky. The estimation of LAI with the PAR inversion technique is not overly sensitive to the χ value, especially when sampling under uniformly diffuse sky conditions (Garrigues et al., 2008). The χ value is most important when working with canopies displaying extremely vertical or horizontal characteristics and when working under clear sky conditions where fb is less than approximately 0.4. For additional information about leaf angle distribution, refer to Campbell and Norman (1998).

Diagram showing solar zenith angle changes during the day
Figure 4. Solar zenith angle changes during the day. The observer is facing the equator.

 

Diagram showing beam fraction under sunny and overcast sky conditions
Figure 5. Beam fraction under (a) sunny and (b) overcast sky conditions

 

K (extinction coefficient): The canopy extinction coefficient, K, describes how much radiation is absorbed by the canopy at a given solar zenith angle and canopy leaf angle distribution. The concept of an extinction coefficient comes from Beer’s law (Equation 1). A detailed explanation of the extinction coefficient can quickly become complicated. For LAI estimation, it is sufficient to know that the angle of solar beam penetration interacts with leaf angle distribution to determine the probability that a photon will be intercepted by a leaf. For purposes of estimating LAI, K is calculated as

LAI equation
Equation 2

 

From this equation, it should be obvious that, for any given canopy, K only changes as the sun moves across the sky. The LP-80 automatically calculates K each time it measures LAI. Once K is calculated and all other variables quantified, LAI is calculated as

LAI equation
Equation 3

 

where L is LAI and A is leaf absorptivity. By default, A is set to 0.9 in the LP-80. Leaf absorptivity is a highly consistent property for most healthy green foliage, and a value of 0.9 is a good approximation for most situations. In extreme cases (e.g., extremely young leaves, highly pubescent or waxy leaves, senescent leaves), A may deviate from 0.9, leading to errors in estimates of LAI. If you are using the LP-80 in non-typical conditions, you may need to manually combine the outputs from the LP-80 with a modified A value to calculate LAI.

Using the LP-80 in short canopies (cereal crops, grasslands)

In typical scenarios, it is best to hold the ceptometer at a consistent height underneath the canopy, while the attached external PAR sensor is held above the canopy. Use the attached bubble level to ensure that the light bar and external PAR sensor are held level. For row crops or small sample plots, researchers often mount the external sensor on a tripod in between rows or above the canopy. The LP-80 makes simultaneous above- and below-canopy PAR measurements each time the button is pressed, accounting for any changes in light conditions. If the canopy is short enough, an even easier approach is to use the ceptometer to acquire both above- and below-canopy measurements. Simply hold the LP-80 above the canopy to acquire an incident PAR measurement. Update the above-canopy measurement every few minutes or as sky conditions change (e.g., due to variable clouds). In either case, all the other variables are measured and calculated automatically, and LAI is updated with each below-canopy measurement.

Using the LP-80 in tall canopies (forests, riparian areas)

In tall canopies, it is often not practical to measure above- and below-canopy PAR with one instrument. When using the LP-80 in tall canopies, there are a couple of options available for making above- and below-canopy measurements of PAR.

One option is to mount a PAR sensor above the canopy or in a wide clearing with an unobstructed view of the sky. This method requires some additional post-processing of the data but can give good results. The PAR sensor needs to be attached to its own data logger, which should be configured to acquire measurements at regular intervals (e.g., every 1 to 5 minutes) so that any variation in ambient light levels will be captured. Collect below-canopy measurements with the ceptometer, then combine the data in post processing using the timestamps to pair each above- and below-canopy measurement. Calculate τ with each pair, which can then be used as an input to Equation 3.

The second option is useful when it is not feasible to place a PAR sensor above the canopy or when a PAR sensor or data logger is not available. If this is the case, use the LP-80 to measure incident PAR in a location outside the canopy with an unobstructed view of the sky. In measurement mode, choose whether measuring incident or transmitted radiation. When using the LP-80 itself to take above- and below-canopy readings, take the variability of sky conditions into account.

On a clear sky day, it is easiest to acquire samples toward the middle of the day, since the light levels won’t change much over the span of 20 to 30 minutes. When sky conditions are uniformly overcast, PAR conditions can remain for longer periods of time, giving a longer measurement window before needing to reacquire an above-canopy measurement.

If sky conditions are highly variable, however, we do not recommend this method, unless it is possible to constantly update the incident PAR measurement. The LP-80 automatically calculates LAI with each below-canopy measurement using the stored incident PAR measurement. Reacquire an incident PAR measurement any time light conditions change (e.g., when cloud obstructs the solar disk or after ~ 20-30 minutes have passed) to prevent error in the LAI calculation.

Clumping and spatial sampling

In most canopies, LAI is variable across space. For example, in row crops, LAI can range from 0 to 2-3 within a distance of 1 meter. Even in forests and other natural canopies, variable tree spacing, branching characteristics, and leaf arrangement on stems cause clumping. This means that point-based measurements of LAI can be highly biased. Lang and Yueqin (1986) found that averaging several measurements along a horizontal transect helped alleviate biases associated with clumping at fine spatial scales.

The LP-80 uses a similar approach, averaging light measurements across eight groups of ten sensors situated along an 80 cm long probe. Although this approach reduces errors at the local scale, it may not account for variability in LAI at the canopy scale. Researchers must consider spatial variability in canopy LAI when developing a sampling scheme. In general, more heterogeneous canopies will require more LAI measurements across space in order to obtain an LAI value that is representative of the entire canopy.

Atmospheric conditions

The LP-80 is capable of accurately measuring LAI in both clear-sky and overcast conditions. This is because the LAI model used by the LP-80 accounts for changes in diffuse and beam radiation (ƒb), solar zenith angle (θ), and because incident and transmitted radiation are measured simultaneously when using an above-canopy PAR sensor. Errors associated with incorrectly specifying the leaf angle distribution (χ) are most pronounced when sampling under clear-sky conditions (Garrigues et al., 2008). This is because there is a larger proportion of radiation coming from a single angle (the beam radiation directly from the sun). Under these conditions, it is important to correctly model how leaf angle and beam penetration angle interact. So, when sampling under clear-sky conditions, make sure to use an appropriate χ value.

Influence of non-photosynthetic elements

In forests, shrublands, and other areas where woody species are present, LP-80 measurements will be influenced by elements other than leaves. For example, tree boles, branches, and stems will intercept some radiation and thus have an effect on estimates of LAI obtained with the PAR inversion technique. In fact, some researchers refer to the measurement obtained from the LP-80 and similar instruments as plant area index (PAI) rather than LAI, in order to acknowledge the contribution of non-leaf material to the measurement. It should come as no surprise that PAI will be higher than LAI in any given ecosystem. However, values of PAI and LAI are often not too different because leaf area is generally much larger than branch area, and the majority of branches are shaded by leaves (Kucharik et al., 1998). In deciduous ecosystems, the contribution of woody material can be accounted for by acquiring measurements during the leaf-off stage.

Using the SRS-NDVI sensor

The SRS-NDVI sensor measures canopy reflectance in red and NIR wavelengths, which allows for calculation of the Normalized Difference Vegetation Index (NDVI). In turn, NDVI can be used to estimate LAI. We provide a brief overview of the SRS-NDVI operating theory here. The SRS-NDVI measures canopy reflectance in red and NIR wavelengths, and its measurements can be used to calculate or approximate LAI. Red and NIR reflectances are used in the following equation to calculate NDVI

LAI equation
Equation 4

 

where ρ denotes percent reflectance in NIR and red wavelengths. Mathematically, NDVI can range from -1 to 1. As LAI increases, red reflectance will typically decrease due to the increasing canopy chlorophyll content, whereas NIR reflectance increases due to expanding mesophyll cells and increasing canopy structural complexity. So, under typical field conditions, NDVI values range from around 0 to 1, representing low and high LAIs, respectively.

Two graphs showing NDVI closely tracking the year to year seasonal dynamics of LAI in a mixed deciduous forest
Figure 6. NDVI closely tracks the year to year seasonal dynamics of LAI in a mixed deciduous forest

 

In cases like phenology and stay-green phenotyping where absolute values of LAI are not required, NDVI values can be used directly as proxies for LAI. For example, if the objective of a study is to track the temporal patterns of canopy growth and senescence (Figure 6), then it may be adequate to simply use NDVI as the metric. If research objectives require estimates of actual LAI, it is possible to establish a canopy-specific model that will allow NDVI to be converted to LAI. This method is described in the next section.

Developing field-based NDVI-LAI regression models

To directly estimate LAI using NDVI values, develop a site-specific or crop-specific correlative relationship. The best way is to take colocated measurements of NDVI and LAI (e.g., using a LP-80 ceptometer). For example, colocated measurements of LAI and NDVI were acquired during a period of rapid canopy growth. Least squares regression was used to fit a linear model to the data (Figure 7). With this model, it is possible to use NDVI to predict LAI without making independent measurements.

Developing a robust empirical model involves some effort, but once the model is complete, one can continuously monitor changes in LAI with an SRS-NDVI sensor deployed over a plot or canopy long term. This method saves significant effort and time in the long run.

Graph showing the relationship between NDVI and LAI
Figure 7. The relationship between NDVI and LAI. Note: the fitted linear regression model (solid line) can be used to predict LAI from NDVI measurements.

 

SRS-NDVI sampling considerations

The SRS-NDVI is designed to be used as a dual-view sensor. This means that one sensor, having a hemispherical field of view, should be mounted facing toward the sky. The other sensor, having a 36° field of view (18° half angle), should be mounted facing downward at the canopy. Down- and up-looking measurements collected from each sensor are used to calculate percent reflectance in the red and NIR bands. Percent reflectances are used as inputs to the NDVI equation (Equation 4).

The up-looking sensor must be placed above any obstructions that will block the sensor’s view of the sky. The down-looking sensor should be directed at the region of the canopy to be measured. The size of the area measured by the down-looking sensor is dependent on the sensor’s height above the canopy. The spot diameter of the down-looking sensor is calculated as

Spot diameter equation
Equation 5

 

where γ is the half angle of the field of view (18° for the SRS-NDVI), and h is the height of the sensor above the canopy. This is valid for measuring spot diameter when the down-looking sensor is pointed straight down (i.e., nadir view angle). In cases where the down-looking sensor is pointing off-nadir, the spot will be oblique and will be larger than that calculated by Equation 5.

To quantify spatial variability in LAI, several down-looking sensors can be set up to monitor different portions of the canopy. For example, several sensors were mounted above the canopy in a deciduous forest to monitor differences in spring phenology of several trees. Measurements of NDVI revealed differences in the timing and magnitude of leaf growth among the trees that were measured (Figure 8). A similar approach could be used to monitor the response of plants in individual plots subject to experimental manipulation or to monitor growth patterns across different agricultural units.

Graph showing spatial variability of NDVI during spring green up
Figure 8. Spatial variability of NDVI during spring green up. Note: The variability is driven by the differences in the timing of leaf development among tree and tree species.

 

Influence of soil background NDVI measurements

Considerable error in NDVI measurements can occur when soil is in the field of view of the SRS-NDVI sensor or in situations where the amount of soil in the field of view changes due to canopy growth (e.g., from early- to late-growing season). Qi et al. (1994) showed that NDVI is sensitive to both soil texture and soil moisture. This soil sensitivity can make it difficult to compare NDVI values collected at different locations or at different times of the year. It can also make it difficult to establish a reliable NDVI-LAI regression model. The Modified Soil Adjusted Vegetation Index (MSAVI) was developed by Qi et al. (1994) as a vegetation index that has little to no soil sensitivity. MSAVI is calculated as

LAI equation
Equation 6

 

The advantages of MSAVI include: (1) no soil parameter adjustment required, and (2) it uses the exact same inputs as NDVI (red and NIR reflectances), meaning it can be calculated from the outputs of any NDVI sensor.

Graph showing that NDVI has limited sense to LAI values greater than 3 to 4
Figure 9. NDVI has limited sense to LAI values greater than 3 to 4.

 

Dealing with NDVI saturation in high-LAI canopies

In addition to soil sensitivity, NDVI also suffers from a lack of sensitivity to changes in LAI when LAI is greater than approximately 3 to 4, depending on the canopy (Figure 9). Decreased NDVI sensitivity at high LAI is due to the fact that chlorophyll is a highly efficient absorber of red radiation. Thus, at some point, adding more chlorophyll to the canopy (e.g., through the addition of leaf material) will not appreciably change red reflectance (see Figure 3).

Several solutions to NDVI saturation have been developed. One of the simplest solutions uses a weighting factor that is applied to the near infrared reflectance in both the numerator and denominator of Equation 4. The resulting index is called the Wide Dynamic Range Vegetation Index (WDRVI; Gitelson, 2004). The weighting factor can be any number between 0 and 1. As the weighting factor approaches 0, the linearity of the WDRVI-LAI correlation tends to increase at the cost of reducing sensitivity to LAI changes in sparse canopies.

The Enhanced Vegetation Index (EVI) is another vegetation index that has higher sensitivity to high LAI compared to NDVI. EVI was originally designed to be measured from satellites and included a blue band as an input to alleviate problems associated with looking through the atmosphere to earth’s surface from orbit. Recently, a new formulation of EVI has been developed that does not require a blue band. This modified version of EVI is referred to as EVI2 (Jiang et al., 2008). Similar to the MSAVI index, EVI2 uses the exact same inputs as NDVI (red and NIR reflectances) and is calculated as

LAI equation
Equation 7

 

Another advantage of EVI2 also is that it has less soil sensitivity compared to NDVI. Thus, EVI2 is a good all-around vegetation index for estimating LAI since it has low sensitivity to soil and has a linear relationship with LAI.

Learn more about NDVI

In the following webinar, Dr. Steve Garrity discusses NDVI and PRI theory, methods, limitations, applications, and more. He also explains spectral reflectance sensors and their measurement considerations.

Quick LAI Method Comparison Chart

MethodRelative CostTemporal SamplingSuitability for Tall CanopiesSuitability for Short CanopiesSpacial ScalingEase of Collecting SamplesVertical Profiling Samples
Destructive harvestH*SingleLHLVLYes
Litter trapsM*SingleHLL - MMNo
Hemispherical photographyMSingleHLMMNo
PAR inversion (LP-80)MBoth*H*HMHYes
Vegetation indexL - VHContinousM**VHM -HVHNo
*Labor intensive**Single with LP-80

Continuous with subcanopy PAR sensors
*Requires access to top of canopy or large open area

**Requires access to top of canopy
Table 1. KEY: VL = very low, L = low, M = moderate, H = high, VH = very high

 

Instrument specifications

SRS Multiband Radiometer

Accuracy: 10% or better for spectral irradiance and radiance values

Dimensions: 43 x 40 x 27 mm

Calibration: NIST traceable calibration to known spectral irradiance and radiance

Measurement type: < 300 ms

Connector type: 3.5 mm (stereo) plug or stripped and tinned wires

Communication: SDI-12 digital sensor

Data logger compatibility: (not exclusive) METER Em50/60 series, Campbell Scientific

NDVI bands: Centered at 630 nm and 800 nm with 50 nm and 40 nm Full Width Half Maximum (FWHM), respectively

LP-80 CEPTOMETER

Operating environment: 0 to 5°C, 0 to 100% relative humidity

Probe length: 86.5 cm

Number of sensors: 80

Overall length: 102 cm (40.25 in)

Microcontroller dimensions: 15.8 x 9.5 x 3.3 cm (6.2 x 3.75 x 1.3 in)

PAR range: 0 to >2,500 µmol m-2 s-1

Resolution: 1 µmol m-2 s-1

Minimum spatial resolution: 1cm

Data storage capacity: 1MB RAM, 9000 readings

Unattended logging interval: User selectable, between 1 and 60 minutes

Instrument weight: 1.22 kg (2.7 lbs)

Data retrieval: Direct via RS-232 cable

Power: 4 AA alkaline cells

External PAR sensor connector: Locking 3-pin circular connector (2 m cable)

Extension cable option: 7.6 m (25 ft)

References

Campbell, Gaylon S., and John M. Norman. “The light environment of plant canopies.” In An Introduction to Environmental Biophysics, pp. 247-278. Springer New York, 1998.

Garrigues, Sébastien, N. V. Shabanov, K. Swanson, J. T. Morisette, F. Baret, and R. B. Myneni. “Intercomparison and sensitivity analysis of Leaf Area Index retrievals from LAI-2000, AccuPAR, and digital hemispherical photography over croplands.” Agricultural and Forest Meteorology 148, no. 8 (2008): 1193-1209.

Gitelson, Anatoly A. “Wide dynamic range vegetation index for remote quantification of biophysical characteristics of vegetation.” Journal of Plant Physiology 161, no. 2 (2004): 165-173.

Hyer, Edward J., and Scott J. Goetz. “Comparison and sensitivity analysis of instruments and radiometric methods for LAI estimation: assessments from a boreal forest site.” Agricultural and Forest Meteorology 122, no. 3 (2004): 157-174.

Jiang, Zhangyan, Alfredo R. Huete, Kamel Didan, and Tomoaki Miura. “Development of a two-band enhanced vegetation index without a blue band.” Remote Sensing of Environment 112, no. 10 (2008): 3833-3845.

Kucharik, Christopher J., John M. Norman, and Stith T. Gower. “Measurements of branch area and adjusting leaf area index indirect measurements.” Agricultural and Forest Meteorology 91, no. 1 (1998): 69-88.

Lang, A. R. G., and Xiang Yueqin. “Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies.” Agricultural and Forest Meteorology 37, no. 3 (1986): 229-243.

Norman, J. M., and P. G. Jarvis. “Photosynthesis in Sitka spruce (Picea sitchensis (Bong.) Carr.). III. Measurements of canopy structure and interception of radiation.” Journal of Applied Ecology (1974): 375-398.

Rouse Jr, J_W, R. H. Haas, J. A. Schell, and D. W. Deering. “Monitoring vegetation systems in the Great Plains with ERTS.” (1974).

Qi, Jiaguo, Abdelghani Chehbouni, A. R. Huete, Y. H. Kerr, and Soroosh Sorooshian. “A modified soil adjusted vegetation index.” Remote Sensing of Environment 48, no. 2 (1994): 119-126.

APPENDIX: Learn more about LAI

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:

How to calculate 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 to measure 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 for measuring 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 4. 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 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. 

Leaf area index (LAI) equation
Equation 3

 

The next variable in the extinction coefficient model (Equation 2 bottom right) is the chi (X) value. chi describes the leaf angle distribution of a canopy. Every canopy is a mixture of leaves that are horizontal or vertical in their orientation or somewhere in between horizontal and vertical. Figure 7 is a plot representing the distribution of the leaf angles within three different canopies.

Graph: Distribution of the leaf angles within three different canopies.
Figure 7. Distribution of the leaf angles within three different canopies (Campbell and Norman, 1998)

 

Note that chi values in vertical canopies are below one. The more vertical a leaf angle distribution is, the closer to zero chi becomes. In horizontal canopies, chi approaches infinity. Typically, you’ll see chi values greater than one in this case (i.e., values of one to five are common in horizontal canopies). Spherical canopies are canopies with a mixture of both vertical and horizontal distributions. They are the most commonly encountered distribution of leaf angles that occur in nature. They have chi values close to or equal one. The LP-80 uses a chi value equal to one by default. You can change that, but in most cases, you can get away with the default. 

Graphs: How chi value or leaf angle distribution influences the extinction coefficient dependent on the zenith angle of the sun
Figure 8. How chi value or leaf angle distribution influence the extinction coefficient dependent on the zenith angle of the sun (Campbell and Norman, 1998)

 

The graph on the lower left of Figure 8 demonstrates how chi value or leaf angle distribution influences the extinction coefficient dependent on the zenith angle of the sun. For example, notice that with a chi equal to zero (a completely vertical canopy) and the sun directly overhead (beam zenith angle is equal to zero), 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 a case where all the leaves are perfectly horizontal (chi equals infinity). Then the extinction coefficient has no dependency on the beam zenith angle. This makes sense if you think about a perfectly horizontal leaf. It’s not going to matter at what angle the solar radiation is striking it. It’s going to have an extinction coefficient that’s invariable.

The graph on the lower right of Figure 8 looks at transmission relative to solar zenith angle. Note that the horizontal canopy transmission is the same no matter what the zenith angle is. And the other extreme, for vertical canopies, transmission equals one when the sun is directly overhead, and it is complete when we have very low sun angle (sun on the horizon). This makes sense when you think of a vertical leaf and the sun directly overhead. There is no shadow being cast by the leaf, whereas if the sun is coming from the side, there’s complete absorption and no transmission of that radiation. 

What can we learn from this? In the upper left of Figure 8, there are 3 different canopies with very different leaf angle distributions and thus different chi values ranging from 0.5 to three. But if you look at both the figures in the lower left and right, there isn’t a big difference in either extinction coefficient or transmission amongst those chi values. So the leaf area index model is not highly sensitive to the chi value, especially chi values ranging from somewhere between 0.5 to 2. 

So misestimating chi can be a source of error but only in extreme cases—if we’re dealing in a canopy that’s extremely horizontal, or highly vertical. If you’re not working in either of those extremes, then a chi value somewhere around one is going to be adequate for your estimation of LAI. 

Leaf area index (LAI) equation
Equation 4

 

Returning to the LAI model (Equation 4), Fb is beam fraction, and it’s calculated as the ratio between diffuse PAR (photosynthetically active radiation) and direct PAR. 

Diagram: Diffuse PAR vs. direct PAR (Leaf area index, LAI)
Figure 9. Diffuse PAR vs. direct PAR

 

Figure 9 illustrates what this means. On the left is typical clear-sky conditions with white lines representing diffuse radiation (radiation scattered in the atmosphere by aerosols in other particles). This radiation is scattered to some location down in the canopy where we might be measuring transmitted light. Also notice the beam radiation (radiation coming directly from the sun) on the same picture which is dominating in this clear sky condition. So we can see that on the left, Fb would be very low because the direct PAR component dominates. 

Contrast that with the image on the right where there are clouds or heavy aerosols within the atmosphere. There’s more scattering, and less of that beam radiation is penetrating those clouds to the observation location below the canopy. In this case, Fb would be much higher (approaching 1) as we completely eliminate the beam radiation component. 

What does this mean? The Fb term is important because it’s describing the distribution of penetration angles of photons into the canopy. Fb 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. For example, 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. This is because there’s a more even distribution of angles of radiation striking objects that might cast a shadow. It’s the same with leaves in a canopy.

Leaf area index (LAI) diagram: Tau is the ratio of transmitted and incident PAR
Figure 10. Tau is the ratio of transmitted and incident PAR

 

The next term that we’re going to discuss is tau (𝛕) 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. It’s the component that forms the core of the measurement when using this model. In Figure 10, 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. This model requires both above- and below-canopy measurements. 

If your canopy is extremely tall, find a clearing or a large gap where you can place your PAR sensor and use that as a measurement of incident radiation. You can either place a PAR sensor out in a 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. 

If you’re working in partly overcast conditions or sky conditions are rapidly changing, then you want to update that incident radiation reading fairly frequently: basically any time sky conditions (and thus ambient light levels) change. For that reason, if you’re concerned about fluctuating ambient light levels, I recommend that you independently log both incident radiation and transmitted radiation simultaneously, so you’re always accounting for changes in ambient light level and not introducing any source of error into the LAI calculation.

The LP-80 works great for spot sampling or periodic sampling. For continuously monitoring changes in LAI, another approach would be to use PAR sensors both above and below the canopy. PAR sensors below the canopy basically replace the LP-80 in Figure 10. The difference is that PAR sensors can continually log which provides a continuous measurement of transmitted radiation for input into the LAI model. 

Leaf area index (LAI) equation/graph: A is leaf PAR absorptance
Figure 11. A is leaf PAR absorptance (graph: www.photobiology.info)

 

The last term in the LP80’s leaf area index (LAI) model is A which is leaf absorptance in the PAR (photosynthetically active) region of the electromagnetic spectrum. 

In the LP-80, A is fixed to a value of 0.9 which is a very good estimate of absorbtance. 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. And when they’re senescent, they can be lower than 0.9. And certainly, for very hairy or extremely waxy leaves, this absorptance term can be quite a bit lower than 0.9. But other than extreme cases, a value of 0.9 is is a very good estimate for leaf absorptance. Values that deviate just slightly from 0.9 won’t have dramatic impacts on a calculation of LAI.

Reflectance: indirect method for LAI calculation

In cases where LAI is very low, typically there’s an even amount of reflectance in both the visible and the near-infrared portion of the spectrum. As LAI increases, there’s a decreasing amount of visible reflectance whereas near-infrared reflectance tends to increase. So there is a relationship between visible and near-infrared reflectance and LAI that we can use to estimate LAI.

Graphs and diagram: Reflectance data (leaf area index, LAI)
Figure 12. Reflectance data

 

In Figure 12, note that reflectance is wavelength dependent. The plot at the bottom left is covering both visible (400 to 700 nanometers) and some of the near-infrared region (above 700 nanometers) of the electromagnetic spectrum. You can see that the spectrum is being collected for the same canopy but at different values of the leaf area index (LAI). What I’m describing is a decrease in visible reflectance with increasing LAI and an increase in near-infrared reflectance with increasing LAI. 

There’s vegetation indices or combinations of different bands that have been invented that allow us to estimate different biophysical canopy variables. One common index is the Normalized Difference Vegetation Index (NDVI). 

Diagram: Each canopy has a unique NDVI-LAI (Leaf area index) relationship
Figure 13. Each canopy has a unique NDVI-LAI relationship

 

Learn more about NDVI in the webinar: “NDVI and PRI: Measurement, Theory, and Applications “ —>

NDVI is formulated using reflected values of red radiation and near-infrared radiation, and it’s been shown that NDVI is related to leaf area index. Figure 13 shows a spectral reflectance sensor at the top of the canopy that’s continually monitoring reflected radiation in the two bands. The two ports are 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 a relationship with some independent measure of LAI. 

For example, we could use an LP-80 to calculate LAI from transmitted radiation measurements, and then colocate a spectral reflectance sensor collecting NDVI values. If we collect enough of those values over time or across space, we could develop a linear regression relationship (Figure 13, top left). Then, we could use the subsequent NDVI values in this empirical equation to calculate leaf area index without having to use the independent source (LP-80) of LAI for all subsequent measurements. 

Perhaps you don’t need absolute values of LAI and have a different reason to measure LAI. Figure 14 shows some examples of how NDVI can be used as a proxy for LAI without actually needing an absolute value of LAI. 

Graphs/Diagram: NDVI can be used as a proxy for LAI, or for related variables (Leaf area index, LAI article)
Figure 14. NDVI can be used as a proxy for LAI, or for related variables (Ryu et al. (2010) Ag for Met)

 

Here the researcher was measuring both NDVI and canopy photosynthesis in a grassland for an entire year. In the top left panel, NDVI values are plotted in green and then photosynthesis is shown with the open circles. You can see that the temporal trajectory of photosynthesis is very well tracked by NDVI. He shows how a regression equation can be developed that relates the NDVI values to canopy photosynthesis. In this case, leaf area index is 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. 

Similarly, we could consider maybe a phenology application. The graphs on the lower right of Figure 14 are some data that was collected from a deciduous forest for seven years with LAI and NDVI measured at various intervals. 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. 

LAI considerations: sampling and scaling

Don’t think you can measure LAI in one place and get one value that is representative of the whole canopy. That’s not the way it works. One assumption we tend to have with an 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, branches, and trees are distributed within the canopy.

One of the easiest ways of getting around the negative effects of clumping or spatial variability is to increase your sample size. 

A recreation of an aerial image of a field (leaf area index, LAI)
Figure 15. An artist’s recreation of an aerial image of a field (Colombo et al. (2003) Rem. Sens. Env)

 

On the left of Figure 15 is an artist’s recreation of an aerial image of some different crop fields. On the right, is a recreation of an image from an imaging system used to collect NDVI data from that same crop field image and then convert that into NDVI data and then into leaf area index. You can see that there’s a wide range of LAI values across different management units within that image. Imaging 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. We can overcome that simply by collecting multiple samples within our study area to try and capture the spatial variability. Then you can take 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. The image I showed at the beginning of this seminar (Figure 1) about the global distribution of leaf area index was derived from satellite data. But how do we trust those values? We have to have some way of ground-truthing those values. How? You could have an NDVI sensor above the canopy taking a very 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.

Graph showing LAI (leaf area index) in a deciduous forest canopy in spring
Figure 16. LAI in a deciduous forest canopy in spring (Garrity et al. (2008) ESA)

 

Remember that not all methods will produce the same results. Figure 16 shows some data I collected several years ago during the spring in a deciduous forest canopy. I used four different methods: hemispherical photography, the LAI 2000, and a quantum sensor (PAR sensor). Then I used the MODIS satellite (they provide an LAI product) and colocated that with some of my measurements and compared all four of them. Note 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. For example, I didn’t have an LP-80 for this study, but there are about three or four different papers that have been published now that show that the LAI 2000 and LP-80 typically give values that are very similar to each other. And theoretically, the quantum sensors should be very close to both the LP-80 and the LAI 2000 as well. 

The truth is, none of these methods got the absolute value right. In this case, we used litter traps which were the most direct way to estimate what the actual LAI was. In this canopy, it was slightly below 4.0. So you can see at least at maturity that none of these methods got that exactly right. So use caution when comparing different methods or just understand that there’s variability from method to method.

One source of variability we can avoid is demonstrated in this picture (see webinar timecode 46.01). This image demonstrates some concepts we’ve discussed. Shafts of light are penetrating the canopy contrasted with some shaded areas. And you can see that all of that all those light dynamics are controlled by how much leaf material is in the canopy and where that leaf material in the canopy is distributed. So if we have a single PAR sensor that’s measuring transmitted radiation in this canopy. And if we place it on the right, 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’ll see very low values of transmitted light. So we have to be cognizant of spatial variability in the canopy that we’re measuring.

Graph showing PAR data (Leaf area index LAI)
Figure 17. PAR data (Garrity, et al. (2011) Ag For Met)

 

Figure 17 shows some data that demonstrate looks like when we look at individual PAR sensors. Here there were 30+ PAR sensors distributed below a deciduous forest canopy. Over time, they all tend to track each other, but the absolute value of transmitted radiation can be very different from location to location. So if we use transmitted light as an estimate of LAI, which trace do we use to estimate LAI? The answer depends on what our objective is. If we’re just trying to get an average sense of what LAI is, then maybe we take a spatial average of all these values. 

Another thing to point out is that these factors of clumping and spatial variability are real sources of error. However, the LP-80 accounts for that in the way that transmitted light measurements are acquired. It has a wand that comes out of the handheld unit, and that wand is about 80 centimeters long with 80 independent PAR sensors in that wand. So LP-80 readings are a spatial average across all of the sensors in the wand.

Picture of LP80 which measures leaf area index (LAI)
Figure 18. The ACCUPAR LP-80 measures PAR and LAI

 

It was 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, and that strategy is already physically built into the LP-80.

If using a PAR sensor, one approach is to make sure that you’re collecting enough samples that represent the spatial heterogeneity of light transmission, which of course is related to LAI. 

Why are you measuring LAI?

Before you measure, consider why you’re measuring LAI. Are you really interested in leaf area index? Or are you interested in some related variable? For example, some researchers estimate LAI so they can estimate transmitted light or absorbed light more often because they’re trying to estimate canopy productivity or photosynthesis. The question becomes why estimate LAI to estimate light absorption when you can more directly measure light absorption through measurement of transmitted and incident light. So understand why LAI is the variable you’re interested in. 

Also consider whether or not LAI is the only variable you want to measure. We saw that hemispherical photography can produce several metrics about the canopy structure in addition to LAI that might be useful. Are you working with a tall or short canopy? If you’re working in an extremely tall canopy, maybe it’s not feasible to put an NDVI sensor above it, because you just don’t have the infrastructure to reach the top of the canopy. In that case, maybe you need hemispherical photography or a light transmission measurement like the LP-80. 

Do you need to measure species-specific LAI? If so, direct harvest is probably the only method that’s appropriate. Do you want to perform continuous versus discrete sampling? In other words, do you want transmitted light measurements continually logged so that you can continually estimate changes in LAI? Or are you satisfied with a spot sample? Let’s say we want to compare LAI amongst different treatment plots. Maybe the spot sampling approach is more appropriate. 

Do you need to scale the measurements? 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 and how clumped that LAI is.  This will have an influence on how many samples you collect and where those samples are distributed spatially. 

And then finally, do you need absolute values of LAI, or can you use a proxy such as NDVI?

Questions?

Explore questions and ideas with a canopy expert. METER scientists have over 100 years combined experience measuring the soil-plant-atmosphere continuum. 

Get the complete picture

We’ve expanded this guide with even more information. Get everything you need to know about measuring leaf area index, all in one place.

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