Path Length Correction for Improving Leaf Area Index Measurements Over Sloping Terrains: A Deep Analysis Through Computer Simulation

Abstract

The in situ measurement of the leaf area index (LAI) from gap fraction is often affected by terrain slope. Path length correction (PLC) is commonly used to mitigate the topographic effect on the LAI measurements. However, the terrain-induced uncertainty and the accuracy improvement of the PLC for LAI measurements have not been systematically analyzed, hindering the establishment of an appropriate protocol for LAI measurements over mountainous regions. In this article, the above knowledge gap was filled using a computer simulation framework, which enables the estimated LAI before and after PLC to be benchmarked against the known and precise model truth. The simulation was achieved by using CANOPIX software and a dedicatedly designed ray-tracing method for continuous and discrete canopies, respectively. Simulations show that the slope distorts the angular pattern of the gap fraction, i.e., increasing the gap fraction in the down-slope direction and reducing it in the up-slope direction. The horizontally equivalent hemispheric gap fraction from the PLC can reconstruct the azimuthally symmetric angular pattern of the real horizontal surface. The azimuthally averaged gap fraction for sloping terrain can both be underestimated or overestimated depending on the LAI and can be successfully corrected through PLC. The topography-induced uncertainty in LAI measurements is found to be ~14.3% and >20% for continuous and discrete canopies, respectively. This uncertainty can be, respectively, reduced to ~1.8% and <7.3% after PLC, meeting the up-to-date uncertainty threshold of 15% established by the Global Climate Observing System (GCOS). Closer analysis shows that the topographic effect is influenced by fractional crown cover, and the largest uncertainty which corresponds to extensively clumping canopy can reach nearly up to 50%. The accuracy of the estimated LAI after PLC safely meets the GCOS uncertainty threshold even for this extreme case. This study demonstrates the necessity of a topographic correction for LAI measurements and the applicability of PLC for reconstructing the horizontally equivalent gap fraction and improving the LAI measurements over sloping terrains. The results of this article throw light on the design of a protocol for LAI measurements over mountainous regions.