Modeling the Directional Clumping Index of Crop and Forest
Abstract
:1. Introduction
2. Modeling and Evaluation
2.1. Analytical Method for Crop and Forest
2.1.1. Crop Model
2.1.2. Forest Model
2.2. Simulation Method of Directional Clumping Index
2.2.1. Crop Directional Clumping Index Simulation
2.2.2. Forest Scenario Settings
2.2.3. Forest Directional Clumping Index Simulation
2.3 Forest Ground Measurements
3. Results and Evaluation
3.1. Crop Directional Clumping Index Validation
3.2. Forest Directional Clumping Index Validation
3.3. Assessing the Variation Magnitude of Ω(θ)
4. Sensitivity Analysis
4.1. Factors Influencing Crop Clumping Index Variation
4.1.1. Leaf Area Index
4.1.2. Leaf Angle Distribution
4.1.3. Row Structure
4.2. Factors Influencing Forest Clumping Index Variation
4.2.1. Tree Density
4.2.2. Tree Distribution Pattern
4.2.3. Trunk Height
4.2.4. Crown Shape
5. Conclusions
- (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 McPherson [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.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Symbol | Description | Unit |
---|---|---|
Zenith angle, | degree | |
Azimuth angle | degree | |
Gap fraction | dimensionless | |
Clumping index (Ω) | dimensionless | |
LAI | Leaf area index | dimensionless |
u | Leaf volume density | m−1 |
Mean projection of unit foliage area along the direction of zenith angle | dimensionless | |
Row period width, row width, gap width, and crop height, respectively. for any | m | |
Row width and gap width, respectively, in the direction perpendicular to the row | m | |
R | Radius of the tree crown | m |
H | Height (or depth) of the tree crown | m |
Trunk diameter at breast height, DBH | m | |
Trunk height | m | |
Crown closure, counting overlapped crown projection multiple times | dimensionless | |
Crown closure, counts overlapped crown projection once | dimensionless | |
Probability | dimensionless | |
N | Average number of trees in unit area | dimensionless |
M | Average number of trees in a quadrat defined by the Poisson distribution | dimensionless |
m1 | Average group number of trees in a sample area defined by the Neyman distribution | dimensionless |
m2 | Average number of trees in each group | dimensionless |
Leaf reflectance | dimensionless | |
Leaf transmittance | dimensionless | |
Bi-directional reflectance of soil | dimensionless | |
Directional-hemispherical reflectance of soil | dimensionless |
Column ID | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
Height of trunk (m) | 0.5 | 5 | 0.5 | 0.5 | 0, 0.25, …, 1.75 | 0.5 |
Crown depth (m) | 6.5 | 1.5 | 2.28 | 2.28 | 2.28 | 2.07, 2.76, 3.62, 4.38, 5.09, 5.75, 6.37, 6.96 |
Crown radius (m) | 0.45 | 0.75 | 0.76 | 0.76 | 0.76 | 0.80, 0.69, 0.60, 0.55, 0.51, 0.48, 0.45, 0.43 |
H/2R ([-]) | 7.22 | 1 | 1.5 | 1.5 | 1.5 | 1.3, 2, 3, 4, 5, 6, 7, 8 |
Radius at breast height (m) | 0.16 | 0.15 | 0.16 | 0.16 | 0.16 | 0.16 |
([-]) | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Average LAI ([-]) | 4.5 | 2 | 0.28, 0.84, 1.40, 1.97, 2.53, 3.09, 3.65, 4.22 | 2.25 | 2.25 | 2.25 |
Area of research field (ha) | 1 | 5 | 4 | 4 | 4 | 4 |
Distribution | Neyman m2 = 4 | Poisson | Neyman m2 = 4 | Poisson, Neyman m2 = 1, 3, 5, 7, 10, 15, 20 | Neyman m2 = 4 | Neyman m2 = 4 |
Tree Number (per ha) | 4000 | 1011 | 250, 750, …, 3750 | 2000 | 2000 | 2000 |
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Peng, J.; Fan, W.; Wang, L.; Xu, X.; Li, J.; Zhang, B.; Tian, D. Modeling the Directional Clumping Index of Crop and Forest. Remote Sens. 2018, 10, 1576. https://doi.org/10.3390/rs10101576
Peng J, Fan W, Wang L, Xu X, Li J, Zhang B, Tian D. Modeling the Directional Clumping Index of Crop and Forest. Remote Sensing. 2018; 10(10):1576. https://doi.org/10.3390/rs10101576
Chicago/Turabian StylePeng, Jingjing, Wenjie Fan, Lizhao Wang, Xiru Xu, Jvcai Li, Beitong Zhang, and Dingfang Tian. 2018. "Modeling the Directional Clumping Index of Crop and Forest" Remote Sensing 10, no. 10: 1576. https://doi.org/10.3390/rs10101576