Dynamic simulation of light distribution in the live crown of Larix olgensis trees

ObjectiveExtinction coefficient (k) is an important indicator to simulate the light transmission in the crown. By comparing the different methods to obtain k, this paper aims to select the optimal method to estimate the dynamical PAR in the crown of Larix olgensis trees.

Method (1) The PAR data was divided into fitting data and validation data with a ratio of 3:1 and the k predicting model was developed; (2) artificially setting k with different gradients and using fitting data to estimate crown PAR then selecting the optimal k value; (3) Based on the average leaf inclination data, we calculated k with the average leaf inclination formula. The test data was used as an independent sample to conduct an independent test on the PAR estimated by the above three methods. By comparing the above three method’s estimation effect on PAR in the crown, we selected the optimal k to estimate dynamical PAR with meteorological data.

ResultAccording to the measured PAR data, there was a big difference in the crown’s rotation pseudowhorls k, which ranged from 0.1 to 1.5, and showed an obvious exponential or power function relationship with RDINC. Meanwhile, solar altitude angle (S_a), max cumulative leaf area (MCLA), needle area density (NAD), and crown surface area (CS) also had significant effects on k vertical variation. Therefore, considering the exponential function as basic model, the k predicting model was established with RDINC, Sa, MCLA, NAD, and CS as independent variables, and the fitting result indicated that the k model performed well (R² = 0.736, RMSE = 0.124). PAR was best estimated when k was 0.32. The difference of k values in each pseudowhorl calculated by the average leaf inclination distribution formula was not obvious, which ranged from 0.3 to 0.7. The perform of the above three methods on PAR estimation was tested and the results showed that the Method I performed the best (mean error ME = 2.88, mean absolute error: MAE = 117.4, precision estimation: P = 91.53%), Method II was better (ME = 2.88, MAE = 217.5, P = 88.12%), Method III was the worst (Method III-1 ME = 121.4, MAE = 210.1, P = 55.85%; Method III-2 ME = 226.4, MAE = 259.0, P = 42.93%).

Conclusionk was not a constant value in the case of different trees, different pseudowhorls and different Sa. In this study, the k model was established which fully took Sa, CLA and RDINC into account. The PAR for Larix olgensis trees was well estimated based on the k model. The results will provide a scientific basis for simulating the net photosynthetic rate of live crown with different position for planted Larix olgensis trees.