Site index model for Larix olgensis plantation based on generalized algebraic difference approach derivation

Objective Forest site quality assessment is fundamental to forest management and important for estimating forest growth and yields, evaluating forest potential productivity, and making suitable silviculture practices. In this study, the generalized algebraic difference approach (GADA) method was used to develop the more flexible polymorphic site index model based on 60 stem analysis data of dominant and co-dominant trees. The model will provide basic reference for evaluation of the site quality for Larix olgensis plantation in Heilongjiang Province of northeastern China.

Method By selecting the growth equations of modification of the Weibull equation, Korf equation and Richards function, 6 difference site index models were developed by GADA method based on the stem analysis data collected from 1994 to 2017 in Heilongjiang Province. The parameters of model were fitted with nonlinear least square method. Combined with fitting data and validation data set, the model was preliminarily selected by four indexes, i.e. R², root mean square error (RMSE), modelling efficiency, and average absolute error. The optimal models were further screened by residual plots and site index curve clusters. The optimal model and the model developed from ADA method by the same basic equation were compared and evaluated through site index curve cluster and parameters, ages when annual growth reaching the maximum value (inflection) and the values.

Result The difference model based on the Richards equation $h = a{\left( {1 - {{\rm{e}}^{ - bt}}} \right)^c}$ with free parameters $a = {{\rm{e}}^{{X_0}}}, c = {c_2}/{X_0},$ ${X_0} = \dfrac{1}{2}\left[ {\ln {h_1} + \sqrt {\ln {h_1}^2 - 4{c_2}\ln \left( {1 - {{\rm{e}}^{ - b{t_1}}}} \right)} } \right]$ was selected as the optimal model. The results of its parameter estimations were b = 0.046 8 and c₂ = 4.675 4, respectively. The goodness of fit and validation indicators of model were as follows: R² was 0.987 4, RMSE was 0.749 1, MAE was 0.904 0, and EF was 97.04%. Compared with the model developed by ADA method, the optimal model derived by GADA method can better predict the growth process of dominant trees.

Conclusion In the derivation of the status index model, according to the GADA method, the difference model derived from specifying multiple parameters as free parameters has not only good fitting effect, but also can conform to the properties of multiple asymptotic lines and curve polymorphism at the same time, while the ADA method can only satisfy one of them at the same time. According to the fitting results of the optimal model, the asymptotic value of the high growth curve for the dominant tree increases gradually with the increase of the site index, and the time of inflection position occurs earlier. This shows that the Larix olgensis plantation with better site conditions, the growth rate and maximum value of the dominant tree height increase, and the maximum value of height growth rate occurs earlier.