Analysis And Improvement Of The Accuracy Of Bell’s Law In Measuring Leaf Area Index

Leaf area index refers to half of the leaf surface area per unit horizontal forest land.The leaf area index can reflect the growth of vegetation and the information of vegetation canopy structure.At the same time,the leaf area index is also an important parameter in ecology,which can describe the quantitative information of the material and energy exchange on the surface of the vegetation canopy.Therefore,the leaf area index is also very important for studying forest carbon cycle models.Therefore,the accuracy of leaf area index measurement is extremely important.The traditional leaf area index measurement methods include direct measurement method and indirect measurement method.Direct method measurement includes destructive sampling method,litter method and point oblique sampling method,etc.,with high accuracy,but it is a lot of work,time-consuming and labor-intensive.The indirect measurement method uses the optical principle to obtain the leaf area index.Commonly used instruments include LAI-2200,Accu PAR,Sunscan and TRAC,etc.,which are easy to operate.These instruments are also commonly used methods for measuring leaf area index in actual forest surveys,and the theoretical basis for measuring leaf area index using optical principles is Bell’s law,so the accuracy analysis of Bell’s law measuring leaf area index is very important.In this study,three sample plots of 100m*100m were set up in Maoershan Experimental Forest Farm,and each tree was inspected and the position of each tree was located.A leaf collecting device was set up every10 m in the sample plot.The LAI-2200 and TRAC instruments were used to measure the effective leaf area index and leaf clumping index of the plot,and then the true leaf area index measured by the optical instrument was obtained,which was compared with the true leaf area index of the plot measured by the litter method.The applicable conditions of Bell’s law are determined by the methods of theoretical derivation,data simulation and verification of sample survey data.Then the sample plots were divided into five scales:20m×20m,30m×30m,40m×40m,50m×50m and 100m×100m.At each scale,the relationship between the canopy porosity calculated using Bell’s law based on the measured true leaf area index and the background visual probability calculated using the four-scale model was compared,and then the applicable scale of Bell’s law was determined.Finally,on the scale of failure of Bell’s law,that is,when the canopy porosity calculated by Bell’s law and the four-scale model according to the measured true leaf area index is not equal,the canopy scale clumping index,the leaf scale clumping index in the canopy,the coniferous clumping index₀)（needle-to-shoot）between needles within a cluster,and a scaling factor for canopy porosity adjustment between discontinuous vegetation and continuous vegetation(1-₂₈,₂₈ represents the inter-canopy porosity where the crown is a rigid body)were used to correct for canopy porosity measured by Bell’s Law.Until the canopy porosity calculated by the corrected Bell’s law and the four-scale model is equal,then the effective leaf area index and the true leaf area index obtained by the corrected Bell’s law are accurate values.The results showed that:（1）The applicable condition of Bell’s law was that a single tree or pixel（or plot）is infinite;（2）The gap frequency calculated by Bell’s law at each scale was not close to the probability of seeing ground calculated by four-scale model,and the optimal Bell’s law had not been found,that was,the true leaf area index measured by Bell’s law at any finite scale had a large error.（3）Adjusting the effective leaf area index with the clumping index of the three scales was not effective in correcting the canopy porosity calculated by Bell’s law,while the scaling factor(1-₂₈)was used to correct the porosity calculated by Bell’s law.The difference between the porosity corrected by(1-₂₈)and the probability of seeing ground calculated by the four-scale model is less than 0.1.（4）Divided the effective leaf area index measured by Bell’s law corrected by(1-₂₈)by the clumping index between leaves,and divided the coniferous tree species by the needle-to-shoot to obtain the true leaf area index measured by Bell’s law.The accuracy of the real leaf area index measured by Bell’s law after correction with(1-₂₈)was improved by more than 10%in the three plots.In the three plots,the accuracy was improved by more than 10%,and the highest accuracy of the leaf area index improvement in the three plots could reach 39.48%,32.19%and26.73%,respectively.And in the coniferous tree sample plot,the accuracy after correction with the effective leaf area index divided by needle-to-shoot is about 3%higher than that without needle-to-shoot.Therefore,it is feasible to use(1-₂₈)to correct the real leaf area index measured by Bell’s law.