年龄无关的生长模型研究—以落叶松平均高为例

目的 构建年龄无关的理论生长模型，用于年龄未知或者年龄不是有效因子的情况下的林分生长模拟。 方法 基于理论模型理查德模型，利用隐含年龄的差分形式，构建年龄无关的生长模型来拟合落叶松林分的平均高，并将自由参数表达为林分相关因子和立地因子的函数。 结果 利用刀切法对模型进行验证，时间无关的模型的修正确定系数在0.92~0.94之间，而时间相关的模型修正确定系数为0.85，时间无关的模型修正确定系数提高了8%~10%；时间无关模型的均方根误差RMSE在1.30~1.59之间，远远小于时间相关模型的20.48。年龄无关的模型之间对比，引入气候因子的模型，修正确定系数均方根误差RMSE和TRE较没有引入的有明显的降低，说明气候因子的引入提高了模型的模拟效果。 结论 可以将年龄无关的理论模型应用于年龄不可用或者不相关的林分中。采用自由参数的方式将与年龄无关的立地因子和气候因子引入模型的拟合中，对比固定参数和自由参数的两类模型，可以发现自由参数的模型表现更好。在平均高生长模型中引入立地因子和气候因子，模型效果更好。

Study on Age-independent Tree Model: Taking the Average Height of Larix gmelinii as an Example

Objective To construct an age-independent theoretical growth model for simulating forest growth. Method The Richards model was used to fit the average height of Larix gmelinii stand in Jilin Province by using the difference form of implicit age. The growth model independent of age was constructed, and the free parameters were expressed as functions of stand correlation factor and site factors. Result The Jackknife method was used to validate the model. The age-independent model correction determination coefficient was between 0.92 and 0.94, while the age-dependent model correction determination coefficient was 0.85, and the age-independent model correction determination coefficient was increased by 8%~10%. The root mean square error (RMSE) of the age-independent model was between 1.30 and 1.59, which was much less than that of the age-dependent model (20.48). Comparing the age-independent models, introducing climate factor model to correct the RMSE and total relative error (TRE) of the determination coefficients was significantly lower than that without introducing, which showed that the introduction of climate factor improved the simulation effect of the model. Conclusion The age-independent theoretical models can be applied to stand where the age is unavailable or unrelated. In this paper, the age-independent site factors and climate factors are introduced into the model fitting in the way of free parameters. By comparing the two kinds of models with fixed parameters and free parameters, it is found that the model with free parameters performs better. This paper argues that the model is more effective by introducing site factors and climate factors into the average height growth model.