Examination of the extinction coefficient in the Beer–Lambert law for an accurate estimation of the forest canopy leaf area index

Leaf area index (LAI) is a crucial ecological parameter that represents canopy structure and controls many ecosystem functions and processes, but direct measurement and long-term monitoring of LAI are difficult, especially in forests. An indirect method to estimate the seasonal pattern of LAI in a given forest is to measure the attenuation of photosynthetically active radiation (PAR) by the canopy and then calculate LAI by the Beer–Lambert law. Use of this method requires an estimate of the PAR extinction coefficient (k), a parameter needed to calculate PAR attenuation. However, the determination of k itself requires direct measurement of LAI over seasons. Our goals were to determine (1) the best way to model k values that may vary seasonally in a forest, and (2) the sensitivity of estimates of canopy ecosystem functions to the errors in estimated LAI. We first analyzed the seasonal pattern of the “true” k (k ₚ) under cloudy and sunny conditions in a Japanese deciduous broadleaved forest by using the inverted form of the Beer–Lambert law with the true LAI and PAR. We next calculated the errors of PAR-based LAIs estimated with an assumed constant k (LAI ₚᵣₑd) and determined under what conditions we should expect k to be approximately constant during the growing period. Finally, we examined the effect of errors in LAI ₚᵣₑd on estimates of gross primary production (GPP), net ecosystem production (NEP), and latent heat flux (LE) calculated with a land-surface model using LAI ₚᵣₑd as an input parameter. During the growing period, cloudy k ₚ varied from 0.47 to 1.12 and sunny k ₚ from 0.45 to 1.59. Results suggest that the value of LAI ₚᵣₑd was adequately estimated with the k ₚ obtained under cloudy conditions during the fully-leaved period (0.53–0.57). However, LAI ₚᵣₑd was overestimated by up to 0.6 m ² m –² in May and November. The errors in LAI ₚᵣₑd propagated to errors in modeled carbon and latent heat fluxes of –0.21 to 0.32 g C m –² day –¹ in GPP, –0.09 to 0.19 g C m –² day –¹ in NEP, and –3.2 to 3.9 W m –² in LE, which is close to the measurement errors recognized in the tower flux measurement. LAI ₚᵣₑd estimated with an assumed constant k can be useful for some ecosystem studies as a second-best alternative if k is equated to the value of k ₚ measured under cloudy conditions especially during the fully-leaved period.