Effective leaf area index is routinely quantified with optical instruments that measure gap fraction through the probability of beam penetration of sunlight through the vegetation. However, there have been few efforts to obtain theoretically consistent effective leaf area indices from those measurements. To apply the Beer–Lambert law, multiple gap fraction measurements may be averaged in two ways: (1) by taking the mean of the logarithms of the individual gap fraction values or (2) by taking the logarithm of the mean gap fraction. Based on a theoretical model and gap fraction measurements from 41 sites, we report that effective leaf area index must be quantified using the second approach. The first approach implemented in the LAI-2000 instrument considers clumping effects at scales larger than shoots. Thus, the combination of the first approach with an independent clumping index overestimates leaf area index up to 30% at the investigated sites. Clumping effects accounted for by the LAI-2000 instrument, called the “apparent” clumping index, were dependent on canopy cover, crown shape, and canopy height. A forest gap fraction model showed that short canopy height, vertically prolonged crown shape and higher canopy cover are associated with the lowest apparent clumping indices. We show that the apparent clumping index is a useful quantity to constrain the true clumping index and to investigate spatial and temporal variation of clumping effects. Such information would be useful to evaluate a coarse global clumping index map and improve land surface models.
