# Modeling the Directional Clumping Index of Crop and Forest
## 5 Conclusions  
This study investigated the directional clumping effects from typical discontinuous vegetation canopies, including crop and forest. The results verified that the angular variation of the clumping index not only exists, but also reaches notable magnitude for practical cases. We proposed analytical models to predict the \(\Omega(\theta)\) of crop and forest using structural parameters. The models were validated using simulations for near real cases, and also compared with several sets of ground measurements collected from field experiments and literature. The comparisons provide confidence that the calculated and simulated gap fractions fit ground measurements well. The analytical model derived from the definition shows that crop \(\Omega(\theta)\) is mainly determined by the row structures, LAI and leaf angle distribution. The effect of these parameters on \(\Omega(\theta)\) will decrease at large view zenith angles. In contrast, forest \(\Omega(\theta)\) is dominated by tree density, tree distribution pattern, crown shape, and trunk size. Their influence on the variation magnitude of \(\Omega(\theta)\) are all not negligible. Is it necessary to introduce \(\Omega(\theta)\)? In most practical applications of vegetation remote sensing, average clumping index \(\widehat{\Omega}\) has played the leading role and provided the bridge from effective LAI to actual LAI. Since \(\Omega\) has integrated the overall hemispherical influence, it could be conveniently rendered as a unified global map. However, the large \(\Omega(\theta)\) variation in the angular dimension and the influence of clumping index on LAI and GPP prompt us to study \(\Omega(\theta)\) systematically. We intend to investigate the proposed approach to further assess the difference between LAI and GPP products that are derived using \(\widehat{\Omega}\) or \(\Omega(\theta)\), and validate the results using abundant ground measurements. This expansion will be useful to judge whether \(\Omega(\theta)\) should be introduced for standard LAI and GPP production. Another potential option is to apply \(\Omega(\theta)\), as the reference to select an optimal average \(\widehat{\Omega}\). The current research still suffers from many problems and limitations. 1. The crop model was developed for row structure with homogenous plant elements within the hedgerow. It is not suited for other structures or intercropping of multiple crops. The forest model has not considered the complementary tree species. The tree distribution pattern, LAI, and gap fraction will be quite different in a scenario with the mixture of complementary trees [53]. 2. The influence of the crown shape model needs further investigation. Currently, we have assumed the tree crown as vertical ellipsoid. For most species, the crowns can quite well be represented by ellipsoids; however, some exceptions, such as the boreal needle forest, can be fit better by cones [PERSON] [54] stated that the mean difference between the crown volume measures from the assumptions of crown shape as paraboloids, vertical ellipsoids, and horizontal ellipsoids are 10%. In tropical forest, the multi-stem trees are very common. The current crown shape model might be not valid for them. The further effect of crown shape model on the clumping index needs to be discussed for different species. 3. Further comprehensive sensitivity analysis is expected. The analysis in this paper is restricted to be a mono parameter analysis and the variation range of all the parameters is independent. This is only the first step to observe the influence of each single parameter under specific conditions. In the natural environment, there is a size-density allometry of plants under self-thinning as the resources for growing are limited. The crown projection area scales to stem diameter [53]. Besides, LAI and LAD many vary simultaneously. Therefore, a multiple simultaneous analysis is needed to avoid the risk to misconstrue simple size effects as changes in the crown morphology. Further research is required to refine this analysis.