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云南松林分平均高生长模型及模型参数环境解释

罗恒春 张超 魏安超 陆双飞

罗恒春, 张超, 魏安超, 陆双飞. 云南松林分平均高生长模型及模型参数环境解释[J]. 北京林业大学学报, 2018, 40(4): 67-75. doi: 10.13332/j.1000-1522.20170347
引用本文: 罗恒春, 张超, 魏安超, 陆双飞. 云南松林分平均高生长模型及模型参数环境解释[J]. 北京林业大学学报, 2018, 40(4): 67-75. doi: 10.13332/j.1000-1522.20170347
Luo Hengchun, Zhang Chao, Wei Anchao, Lu Shuangfei. Stand average height growth model and environmental interpretation in model parameter of Pinus yunnanensis[J]. Journal of Beijing Forestry University, 2018, 40(4): 67-75. doi: 10.13332/j.1000-1522.20170347
Citation: Luo Hengchun, Zhang Chao, Wei Anchao, Lu Shuangfei. Stand average height growth model and environmental interpretation in model parameter of Pinus yunnanensis[J]. Journal of Beijing Forestry University, 2018, 40(4): 67-75. doi: 10.13332/j.1000-1522.20170347

云南松林分平均高生长模型及模型参数环境解释

doi: 10.13332/j.1000-1522.20170347
基金项目: 

云南省农业基础研究联合专项 2017FG001(-017)

国家自然科学基金项目 31660236

国家自然科学基金项目 31460195

西南林业大学林学一级学科研究计划项目 216628

详细信息
    作者简介:

    罗恒春。主要研究方向:森林经理学。Email:1739461918@qq.com 地址:650224云南省昆明市盘龙区白龙寺300号西南林业大学林学院

    责任作者:

    张超,博士,副教授。主要研究方向:森林经理学。Email:zhchgis@126.com 地址:同上

  • 中图分类号: S758.5+2

Stand average height growth model and environmental interpretation in model parameter of Pinus yunnanensis

  • 摘要: 目的云南松作为我国西南地区的主要建群树种,在西南地区占有重要地位,研建其林分平均高生长模型以及对模型参数进行环境解释,可为气候变暖背景下研究云南松林分的生长动态提供经验模型。方法基于云南省森林资源连续清查数据和气象数据,以云南松林为研究对象,结合7种理论生长模型,采用非线性回归方法构建林分平均高生长模型,并对最优模型的参数进行环境解释。结果对选定的7种理论生长模型进行拟合,以调整R2和均方根误差(RMSE)为模型拟合精度指标,从中选出林分平均高最优生长模型,将标准化的环境影响因子引入到最优生长模型参数中,对最优模型的参数进行环境解释。经方差分析可知,引入环境影响因子后的模型与基础模型之间有显著差异,研究取得了较好的结果,模型具有一定的适用性。结论(1) 从7个理论生长方程中选定林分平均高最优生长模型为逻辑斯蒂(Logistic)模型,调整R2达到0.616,均方根误差RMSE为2.328 m。(2)将环境影响因子引入到不同参数组合位置时表现最优的模型形式,作为该环境因子对林分平均高生长模型的参数环境解释,各环境因子引入后,模型拟合效果明显提高。调整R2后,提高最显著的是将湿润指数同时引入到参数abc位置上时的模型形式,其拟合效果提高了5.375%;提高最低的是将土壤厚度因子同时引入到参数abc位置上时的模型形式,其拟合效果提高了1.938%。(3)各环境影响因子对林分平均高生长模型的影响程度大小排序为:湿润指数>年均降水量>海拔>潜在蒸散量>年均温度>温暖指数>年均生物学温度>坡度>土壤厚度。(4)地形因子和气候因子与林分平均高生长之间的关系有正有负,地形因子中的海拔因子对林分平均高的影响不大,气象因子中温度对林分平均高生长的影响是通过对降水的制约来实现的。

     

  • 表  1  林分平均高生长模型

    Table  1.   Stand average height growth model

    模型名称Model name 模型形式Model form 参数约束Parameter constraint
    逻辑斯蒂Logistic y=a/(1+b·exp(-c·age)) a, b, c > 0
    理查德Richards y=a(1-exp(-b·age))c a, b, c > 0
    坎派兹Gompertz y=a·exp(-b·exp(-c·age)) a, b, c > 0
    单分子Mitscherlich y=a(1-b·exp(-c·age)) a, b, c > 0
    舒马切尔Schumacher y=a·exp(-b/age) a, b > 0
    威布尔Weibull y=a(1-exp(-b·agec)) a, b, c > 0
    S曲线方程S curve equation y=exp(a+b/age)
    注:式中y代表林分平均高(m);age代表林分平均年龄(a);abc为所需估计的参数。下同。Notes: y represents stand average height (m), age represents stand average age(year), a, b, c are the parameters need to be estimated. Same as below.
    下载: 导出CSV

    表  2  环境因子引入模型参数位置表

    Table  2.   The position table of introducing environmental factors

    海拔因子(ALT)引入参数位置
    Introduced parameter position of altitude
    海拔因子(ALT)引入后模型形式
    Model form after introducing altitude factor
                     a y=aALT·q/(1+b·exp(-c·age))
                    b y=a/(1+bALT·q·exp(-c·age))
                    c y=a/(1+b·exp(-cALT·q·age))
                    ab y=aALT·q/(1+bALT·s·exp(-c·age))
                    ac y=aALT·q/(1+b·exp(-cALT·s·age))
                    bc y=a/(1+bALT·q·exp(-cALT·s·age))
                    abc y=aALT·q/(1+bALT·s·exp(-cALT·f·age))
    注:abcqsf为所需估计的参数。Notes:a, b, c, q, s, f are the parameters need to be estimated.
    下载: 导出CSV

    表  3  林分平均高生长模型拟合结果

    Table  3.   Fitting results of stand height growth model

    模型Model 参数值Parameter value 拟合指标Fitting indicator
    a b c 调整R2
    Adjustment R2
    RMSE
    逻辑斯蒂Logistic 18.928 6.326 0.053 0.616 2.328
    理查德Richards 42.266 0.006 0.854 0.611 2.338
    坎派兹Gompertz 21.267 2.351 0.031 0.614 2.334
    单分子Mitscherlich 33.213 0.979 0.009 0.610 2.344
    舒马切尔Schumacher 18.764 21.946 0.563 2.487
    威布尔Weibull 46.013 0.011 0.873 0.614 2.334
    S曲线方程S curve equation 2.598 -14.632 0.588 2.677
    下载: 导出CSV

    表  4  引入环境因子后模型拟合结果汇总

    Table  4.   Results of the model fitting after introducing environmental factors

    环境因子
    Environmental factor
    引入参数位置
    Introduced parameter position
    参数Parameter 拟合指标
    Fitting indicator
    F
    a b c q s f 调整R2
    Adjusted R2
    RMSE
    海拔Altitude(ALT) b 18.457 0.09 0.054 0.003 0.641 2.251 326.45
    abc 19.876 -0.963 0.039 -1.00×10-3 0.004 7.28×10-6 0.641 2.248 217.98
    坡度Gradient(SLO) bc 18.803 7.177 0.051 -0.051 0.000 1 0.628 2.287 247.61
    abc 22.868 8.195 0.043 -0.159 -0.089 4.23×10-4 0.629 2.284 206.95
    土壤厚度Thickness of soil
    (ST)
    bc 19.403 3.494 0.025 0.042 3.91×10-4 0.628 2.287 247.61
    abc 19.550 3.516 0.024 -0.002 0.041 3.95×10-4 0.628 2.287 206.06
    年均温度Annual average temperature(MAT) ab 28.075 16.638 0.052 -0.519 -0.605 0.631 2.278 250.83
    abc 38.342 18.296 0.017 -1.112 -0.699 0.002 0.634 2.269 211.46
    年均生物学温度Annual average biological temperature(BT) b 18.726 12.541 0.054 -0.373 0.629 2.288 309.94
    abc 2.859 6.303 0.076 0.922 -0.017 -0.001 0.633 2.293 210.54
    温暖指数Warmth index
    (WI)
    b 18.758 10.56 0.053 -0.03 0.631 2.281 312.62
    bc 18.854 11.132 0.058 -0.034 -3.20×10-5 0.631 2.280 250.83
    年均降水量Annual average precipitation(MAP) ab 18.368 15.021 0.052 0.005 -0.129 0.631 2.241 250.83
    bc 18.882 22.863 0.092 -0.239 -0.001 0.643 2.245 263.09
    潜在蒸散量Potential Evapotranspiration(ET0) ac 6.437 6.102 0.266 0.291 -0.005 0.640 2.260 259.67
    abc 27.376 -47.51 -0.072 -0.211 1.32 0.003 0.639 2.237 216.09
    湿润指数Humidity index
    (HI)
    bc 18.864 22.311 0.086 -10.149 -0.021 0.617 2.226 236.25
    abc 8.678 20.63 0.112 6.348 -9.113 -0.037 0.649 2.222 225.76
    下载: 导出CSV

    表  5  引入各环境因子后模型拟合检验结果汇总

    Table  5.   Results of the model testing after introducing environmental factors

    环境因子
    Environmental factor
    引入参数位置Introduced parameter position 检验指标Testing indicator
    rRMSE/% MAE MRAE
    无None 无None 19.136 1.972 0.281
    海拔Altitude(ALT) b 18.503 1.888 0.274
    abc
    坡度Gradient(SLO) bc 18.799 1.889 0.270
    abc 18.774 1.885 0.270
    土壤厚度Thickness of soil(ST) bc 18.799 1.950 0.275
    abc 18.799 1.948 0.276
    年均温度Annual average temperature(MAT) ab 18.725 1.906 0.272
    abc 18.651 1.892 0.275
    年均生物学温度Annual average biological temperature(BT) b 18.807 1.908 0.269
    abc 18.848 1.963 0.257
    温暖指数Warmth index(WI) b 18.749 1.907 0.273
    bc 18.741 1.910 0.270
    年均降水量Annual average precipitation(MAP) ab 18.420 1.899 0.272
    bc 18.453 1.933 0.273
    潜在蒸散量Potential evapotranspiration(ET0) ac 18.577 2.006 0.257
    abc
    湿润指数Humidity index(HI) b, c 18.297 1.878 0.267
    abc 18.264 1.878 0.266
    下载: 导出CSV
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  • 收稿日期:  2017-09-25
  • 修回日期:  2018-01-19
  • 刊出日期:  2018-04-01

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