Summary

Author

Niels P. R. Anten

Definition

The leaf area index (LAI) is the amount of leaf area per unit soil area. It can be defined for both individual plants and for whole vegetation stands. There are a number of reasons for why there is increasing interest in quantifying the LAI. First it entails the amount of photosynthesizing leaf and transpiring leaves and is thus an important component of vegetation photosynthesis and the (local) carbon- and hydrological cycles. Second leaves reflect less light than does bare soil and thus the LAI directly impacts surface albedo. Together with the LAI effect on evatranspiration, this phenomenon influences local and regional climate, and current climate models explicitly use LAI as a parameter.

Terminology and equations

Leaf area index – LAI = A_leaf / A_soil

A_leaf: Leaf area (m²)

A_soil: Ground area (m²)

K: Canopy extinction coefficient (dimensionless)

I: Photon flux density below the canopy (umol m^-2 s^-1)

Io: Photon flux density above the canopy (umol m^-2 s^-1)

Measurement approaches

There are roughly three ways to determine LAI: direct leaf area measurements, indirectly using light measurements (including remote sensing) and using modeling techniques.

Direct measurements: LAI can be measured by defining a soil area (A_soil) and measuring the area of all leaves (A_leaf). A_leaf can be measured with a leaf area meter (e.g. LI3100, LiCor) or by scanning leaves and using appropriate software to estimate areas digitally. When plots are small the largest source of error comes from inaccurate definitions of A_soil. This approach is usually is feasible for short vegetation where leaves are accessible and when estimates are needed for small areas (i.e., several m² or so). For larger patches or taller stands (e.g. forests) indirect approaches become necessary.

Light measurements: Leaves capture light and thus reduce the light intensity (I). Light intensity I below a vegetation stand can be quantified as (Monsi & Saeki 2005):

with Io the light intensity above the canopy, K the extinction coefficient which is a function of leaf angle (a) and inclination angle of incident radiation (b, for the sun its known for any time of date, day and location), appropriate formulae can be obtained from the literature (e.g. Goudriaan 1988). I/Io can be obtained from simultaneous measurements below and above the canopy (or in an open space close to stand under analysis). If you know a then LAI can be directly determined from Eq. (2). If not, several measurements need to be taken and the two unknowns a and LAI can be derived as there are two or more equations. The LI2000 meter (LiCor) is based on this concept in that it has a sensor that measures light coming in under different angles. This method works well for tall vegetation and for relatively small areas (at most several hectares). For larger scale estimates remote sensing techniques become necessary.

Remote sensing: Leaves absorb more and reflect less light in the visible range (400-700 nm) than in the near infra-red (800-1100 nm) and thus alter the spectral composition of light. Reflectance in both ranges (VIS and NIR, respectively) can be measured with a spectrophotometer from above the vegetation (in an airplane or satellite). Typically the so called normalized vegetation index (NDVI) is calculated as:

The fraction of soil visible from above is given by:

and if there is no water or snow fleaf = 1 – fsoil. So

where NDVIsoil and NDVIleaf are the NDVI values of pure soil or leaves. Substuting 3b into 3c gives after some rewriting

Evidently separate measurements of NDVIleaf and NDVIsoil need to be taken but this is often on the ground or are already known based on soil and leaf types. Also a would have to be known (though for many studies K[a]*LAI is more important than LAI per se).

Model predictions and application of optimization theory

As LAI is a key parameter in quantifying carbon- and hydrological cycles and is increasingly being used in climate modeling, there is an increasing need for predictions of future LAI values. Evidently this can not be done with measurements alone making model predictions inevitable. One method in this respect is to use optimization theory, which asserts that plants would maximize some performance measure with respect to some plant trait (in this case LAI) under a given set of constraints. Which can be formulated as:

As LAI directly relates to canopy photosynthesis past studies have considered whole-stand photosynthesis as a performance measure (P) and constraints (x’s) as light (Saeki 1960), water (Mc Murtrie et al. 2008) or nitrogen limitations (Anten 2002; 2005). Taking the example of water, if the amount water taken up by the plant is limiting plants can either produce a large LAI but with relatively low stomatal conductance (gs) and thus photosynthesis per unit area or a low LAI with a high gs. Thus there should be an optimal LAI. A similar reasoning applies for N or light.

This approach has proven to be useful for example in qualitatively predicting LAI responses to increasing atmospheric CO₂ levels (Hirose et al. 1997; Anten 2005). But quantitatively, predictions are not always accurate, and alternatives have been proposed including: application of evolutionary game theory which considers competitive interactions between plants (Anten 2002) and maximum entropy that considers optimization of energy fluxes (Dewar 2010).

Ranges of values

LAI typically ranges from close to zero in very open vegetation to > 10 m² m^-2 for example in tropical rain forest.

Health, safety and hazardous waste disposal considerations

None of the techniques described involve hazardous compounds. The greatest danger probably arises from either falling out of a tree or having one land on you if you decide destructively determine a forest LAI.

Literature references

Anten NPR (2002) Evolutionarily stable leaf area production in plant populations. J Theor Biol 217: 15-32.

Anten NPR (2005) Optimal photosynthetic characteristics of individual plants in vegetation stands and implications for species coexistence. Annals of Botany 95:495-506.

Dewar RC (2010) Maximum entropy production and plant optimization theories. Phil Trans Lon Soc BB 365: 1429-1435.

Goudriaan J (1988). The bare bones of leaf-angle distribution in radiation models for canopy photosynthesis and energy exchange. Agric For Meteor 34: 155-169.

Hirose T, Ackerly DD, Traw MB, Ramseier D, Bazzaz FA. (1997) CO2 elevation, canopy photosynthesis and optimal leaf area index in annual plant stands. Ecology 78: 2338-2350.

McMurtrie RE, Norby RJ, Medlyn BE, Dewar RC, Pepper DA, Reich PB, Barton CVM (2008) Why is plant growth response to elevated CO₂ amplified when water is limiting but reduced when nitrogen is limiting Func Plant Biol 35: 521-534.

Monsi M, Saeki T (2005) On the factor light in plant communities and its importance for matter production. Annals of Botany 95: 549-567.

Saeki T, (1960) Interrelationships between leaf amount, light distribution and total photosynthesis in a plant community. Bot Mag 73: 55-63.