Figures (5)  Tables (6)

    • Figure 1. 

      Study area map of Qingyuan County, Zhejiang Province. The map is from the 2019 Chinese administrative division vector map (https://download.csdn.net/download/gognzixiaobai666/14033998). (a) represents the vector map of Zhejiang Province, and (b) is the topographic map of Qingyuan County.

    • Figure 2. 

      Stem analysis data of Chinese fir.

    • Figure 3. 

      Optimum stand density under different age and site index.

    • Figure 4. 

      Comparison of stand potential volume and actual volume at different ages and densities. (a) represents comparison of stand potential volume and actual volume at different ages, (b) represents comparison of stand potential volume and actual volume at different densities.

    • Figure 5. 

      Difference between potential and actual volume of stands under different SDI. (a) represents young stand, (b) represents middle-aged stand, (c) represents near-mature stand, (d) represents mature stand, (e) represents over-mature stand.

    • Variables Fitting data Testing data
      Minimum
      value      		 Maximum
      value      		 Mean
      value      		 Standard
      deviation      		 Minimum
      value      		 Maximum
      value      		 Mean
      value      		 Standard
      deviation
      Stand age (year) 6 46 18.2 7.57 6 43 19.4 7.83
      Density (N/hm2) 750 4,800 2,125 654.32 1,200 4,500 2,358 633.24
      Average tree height (H, m) 4.3 21.5 12.0 3.71 4.4 22.0 12.1 4.13
      Dominant tree height (HT, m) 5.1 23.5 13.7 3.60 5.0 23.2 13.8 3.11
      Volume (m3 /ha) 11.3 432.3 100.8 75.9 11.7 429.0 100.9 76.1

      Table 1. 

      Subcompartments data for model fitting and testing.

    • VariablesFitting dataTesting data
      Minimum
      value      		Maximum
      value      		Mean
      value      		Standard
      deviation      		Minimum
      value      		Maximum
      value      		Mean
      value      		Standard
      deviation
      Age (t)13211.87.213211.77.2
      Dominant tree height (HT, m)1.120.69.74.11.320.29.64.2

      Table 2. 

      Stem analysis data for model fitting and testing.

    • Model no. Theoretical equations Elimination parameters Initial solution for $ {X}_{0} $ Difference equations
      M1 Modified Weibull:
      $ {h} ={a}\left(1-{e}^{{{-bt}^{c}}}\right) $      		 $ a={e}^{{{X}_{0}}} $
      $ c={c}_{1}+{c}_{2}{X}_{0} $      		 $ {X}_{0}=\ln {h}_{1}-\ln \left(1-{e}^{{{{{-bt}_{1}}}^{{{c}_{1}}+{{c}_{2}}{{X}_{0}}}}}\right) $ $ {h}_{2}={e}^{{{X}_{0}}}\left(1-{e}^{{{{{-bt}_{2}}}^{{{c}_{1}}+{{c}_{2}}{{X}_{0}}}}}\right) $
      M2 $ a={e}^{{{X}_{0}}} $
      $ c={c}_{1}+{c}_{2}/{X}_{0} $      		 $ {X}_{0}=\ln {h}_{1}-\ln \left(1-{e}^{{{{{-bt}_{1}}}^{{{c}_{1}}+{{c}_{2}}/{{X}_{0}}}}}\right) $ $ {h}_{2}={e}^{{{X}_{0}}}\left(1-{e}^{{{{{-bt}_{2}}}^{{{c}_{1}}+{{c}_{2}}/{{X}_{0}}}}}\right) $
      M3 Korf:
      $ {h} ={a}{e}^{{{-bt}^{-c}}} $      		 $ a={e}^{{{X}_{0}}} $
      $ c={c}_{1}+{c}_{2}{X}_{0} $      		 $ {X}_{0}=\ln {h}_{1}+b{t}^{-\left({c}_{1}+{c}_{2}{X}_{0}\right)} $
      		 $ {h}_{2}={e}^{{{X}_{0}}}{e}^{{{{{-bt}_{2}}}^{-\left({c}_{1}+{c}_{2}{X}_{0}\right)}}} $
      $ {h}_{2}={e}^{{{X}_{0}}}{e}^{{{{{-bt}_{2}}}^{-\left({c}_{1}+{c}_{2}/{X}_{0}\right)}}} $
      M4 $ a={e}^{{{X}_{0}}} $
      $ c={c}_{1}+{c}_{2}/{X}_{0} $      		 $ {X}_{0}=\ln {h}_{1}+b{t}^{-\left({c}_{1}+{c}_{2}/{X}_{0}\right)} $ $ {h}_{2}={e}^{{{X}_{0}}}{e}^{{{{{-bt}_{2}}}^{-\left({c}_{1}+{c}_{2}/{X}_{0}\right)}}} $
      M5 Richards:
      $ {h} = {a}{\left(1-{e}^{-bt}\right)}^{c} $      		 $ a={e}^{{{X}_{0}}} $
      $ \text{c=}{c}_{1}+{c}_{2}{X}_{0} $      		 $ {X}_{0}=\left(\ln {h}_{1}-{c}_{1}{F}_{0}\right)/\left(1+{c}_{2}{F}_{0}\right) $
      $ {F}_{0}=\ln \left(1-{e}^{{{-bt}_{1}}}\right) $      		 $ {h}_{2}={e}^{{{X}_{0}}}{\left(1-{e}^{{{-bt}_{2}}}\right)}^{{{c}_{1}}+{{c}_{2}}{{X}_{0}}} $
      M6 $ a={e}^{{{X}_{0}}} $
      $ c={c}_{1}+{c}_{2}/{X}_{0} $      		 $ {X}_{0}=\dfrac{1}{2}\left[{F}_{0}+\sqrt{{{{F}_{0}}}^{2}-4\times {c}_{2}\ln \left(1-{e}^{{{-bt}_{1}}}\right)}\right] $
      $ {F}_{0}={\ln {h}_{1}-c}_{1}\ln \left(1-{e}^{{{-bt}_{1}}}\right) $      		 $ {h}_{2}={e}^{{{X}_{0}}}{\left(1-{e}^{{{-bt}_{2}}}\right)}^{{{c}_{1}}+{{c}_{2}}/{{X}_{0}}} $
      Note: $ {h}_{1} $ and $ {h}_{2} $ represent the dominant heights of the stand at ages $ {t}_{1} $ and $ {t}_{2} $, respectively.

      Table 3. 

      Different site index equations.

    • Model Parameter value Fitting index Testing index
      a11 b11 a12 b12 R2 RMSE MAE
      Density effect model 1.06E-4 2.724 2.407E-9 3.393 0.839 28.104 20.602

      Table 4. 

      Fitting and testing results of the density effect model.

    • Model no.ParametersEstimated valueStandard errorSignificance testing (p)R2RMSEMAE
      M1b0.4100.1230.002**0.9980.3430.259
      $ {c}_{1} $1.4710.162< 0.001***
      $ {c}_{2} $−0.3950.052< 0.001***
      M2b0.4030.104< 0.001***0.9990.2610.257
      $ {c}_{1} $−0.5800.1990.006**
      $ {c}_{2} $2.6710.401< 0.001***
      M3b1.5830.5680.008**0.9821.3360.409
      $ {c}_{1} $2.803622,6000.999
      $ {c}_{2} $2.799403,8000.999
      M4b1.0740.4080.013*0.9990.1010.232
      $ {c}_{1} $−0.1560.2480.533
      $ {c}_{2} $1.8810.5560.001**
      M5b0.0530.014< 0.001***0.9691.7780.400
      $ {c}_{1} $−0.1740.047< 0.001***
      $ {c}_{2} $0.2220.049< 0.001***
      M6b0.0720.0260.009**0.6066.3710.631
      $ {c}_{1} $1.8651.0250.078
      $ {c}_{2} $−1.7632.8060.534
      Note: * p < 0.05; ** p < 0.01; *** p < 0.001.

      Table 5. 

      Parameter estimates and fitting and testing indicators of site index equations.

    • Stand ageOptimal density
      SI = 20SI = 18SI = 16SI = 14SI = 12SI = 10SI = 8SI = 6
      63,1953,3823,6023,8704,2044,6375,2276,099
      73,0613,2463,4663,7334,0674,5015,0965,980
      82,9513,1353,3533,6203,9544,3894,9885,881
      92,8593,0423,2603,5253,8594,2954,8965,797
      102,7822,9633,1803,4453,7784,2144,8175,724
      112,7152,8953,1113,3753,7084,1444,7495,660
      122,6572,8363,0513,3143,6474,0834,6895,605
      132,6062,7842,9983,2613,5934,0294,6365,555
      142,5602,7382,9513,2133,5443,9814,5885,511
      152,5202,6972,9093,1713,5023,9384,5465,471
      162,4842,6602,8723,1333,4633,8994,5085,435
      172,4522,6272,8383,0983,4283,8644,4735,402
      182,4222,5972,8083,0673,3963,8324,4425,373
      192,3962,5702,7803,0393,3683,8034,4135,346
      202,3712,5452,7553,0133,3413,7764,3875,321
      212,3492,5232,7322,9893,3173,7524,3625,298
      222,3292,5022,7102,9683,2953,7304,3405,277
      232,3102,4832,6912,9483,2753,7094,3205,258
      242,2932,4652,6732,9293,2563,6904,3015,240
      252,2772,4492,6562,9123,2393,6734,2845,223
      262,2632,4342,6412,8973,2233,6564,2675,208
      272,2492,4202,6272,8823,2083,6414,2525,194
      282,2372,4072,6132,8683,1943,6274,2385,180
      292,2252,3952,6012,8563,1813,6144,2255,168
      302,2142,3842,5902,8443,1693,6024,2135,156
      312,2042,3742,5792,8333,1583,5914,2025,146
      322,1952,3642,5692,8233,1483,5804,1915,136
      332,1862,3552,5602,8143,1383,5704,1825,126
      342,1782,3472,5512,8053,1293,5614,1725,117
      352,1702,3392,5432,7963,1213,5534,1645,109
      362,1632,3312,5362,7893,1133,5454,1565,101
      372,1562,3242,5282,7813,1053,5374,1485,094
      382,1502,3182,5222,7753,0983,5304,1415,087
      392,1442,3122,5162,7683,0923,5234,1345,081
      402,1382,3062,5102,7623,0853,5174,1285,075

      Table 6. 

      Optimal density based on maximum stand volume yield with various sites.