In the study, in order to successfully fit TFRI4 data to Ducey and Knapp’s (2010) model which can have a great performance on estimating SDI for mixed-species forests in the northeastern United State, we added extra steps into the initial process and develop a guideline for establish relative density measurement in the mixed-species forests. The extra steps make the calculation reflecting underlying ecological processes and provide more flexible choices. However, after getting the relative density, how to make a decision on forest management for the stand still need to test which level of stocking the value stands for. Besides, establishing a SDMD for the mixed-species forest is also an important part in order to make the relative density can be used widely and easily.
61
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Figures
Figure 3.1 A map of Taiwan showing the distribution of the 4th National Forest Inventory (TFRI4) plots for cypress and pine forests.
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Figure 3.2 A flowchart summarizing the sequence of steps for determining relative density (RD) as implemented in the study.
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Figure 4.1 Estimated reference maximum stand density index (SDI) for pure cypress forests (plots with more than 80 % cypress BA) by Reineke’s SDI equation (Eq. 13).
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Figure 4.2 Estimated reference maximum stand density index (SDI) for pure pine forests (plots with more than 80 % pine BA) by Reineke’s SDI equation (Eq. 13).
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Figure 4.3 Parameter estimates and asymptotic 95 % confidence limits for cypress (a,b) and pine forests (c,d) by quantile applied to Ducey’s model (Eq. 30).
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Figure 4.4 Coefficient estimates for X0 (b0) by quantiles and level of random noise for cypress forests.
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Figure 4.5 Coefficient estimates for X1 (b1) by quantiles and level of random noise for cypress forests.
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Figure 4.6 Coefficient estimates for X0 (b0) by quantiles and level of random noise for pine forests.
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Figure 4.7 Coefficient estimates for X1 (b1) by quantiles and level of random noise for pine forests.
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Figure 4.8 Estimates of implied maximum additive stand density index (ASDI) by quantiles and level of random noise for cypress forests (ASDI is only calculated when both b0 and b1 are significant).
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Figure 4.9 Estimates of implied maximum additive stand density index (ASDI) by quantiles and level of random noise for pine forests (ASDI is only calculated when both b0 and b1 are significant).
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Figure 4.10 Based on 1 % random noise, estimated implied maximum ASDI by quantiles and level of basal area (BA) threshold for cypress forests.
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Figure 4.11 Based on 1 % random noise, estimated implied maximum ASDI by quantiles and level of basal area (BA) threshold for pine forests.
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Figure 4.12 Implied ASDI for cypress forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 0 % cypress BA.
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Figure 4.13 Implied ASDI for cypress forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 10 % cypress BA.
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Figure 4.14 Implied ASDI for cypress forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 20 % cypress BA.
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Figure 4.15 Implied ASDI for cypress forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 30 % cypress BA.
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Figure 4.16 Implied ASDI for cypress forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 40 % cypress BA.
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Figure 4.17 Implied ASDI for cypress forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 50 % cypress BA.
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Figure 4.18 Implied ASDI for pine forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 0 or 10 % pine BA.
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Figure 4.19 Implied ASDI for pine forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 20 or 30 % pine BA.
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Figure 4.20 Implied ASDI for pine forests as a function of quantile and reference maximum SDI source. Plot selection based on 1 % random noise and 40 or 50 % pine BA.
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Tables
Table 3.1 The number of plots and species observed, and the mean, range and
coefficient of variation (CV, %) for trees/ha (N), quadratic mean diameter (QMD, cm), basal area (BA, m2ha-1), and specific gravity (SG) by forest type.
Forest type
Number of plot and species
Variable Mean Min Max CV
Cypress (215, 254) N 1196 140 3740 57.7
QMD 29.3 10.1 138.2 54.8
BA 3.58 0.43 21.29 86.7
SG 0.587 0.362 0.828 15.3
Pine (199, 246) N 1241 120 3820 56.7
QMD 22.5 8.6 48.4 30.7
BA 2.42 0.09 18.25 71.5
SG 0.585 0.406 0.872 15.1
92
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Table 3.2 The number of plots and species observed, and the mean and range of trees/ha (N), and quadratic mean diameter (QMD, cm) by % BA of target species and forest type.
Percent BA Cypress Forests Pine Forests
of Target Species #Plots #Species N QMD #Plot #Species N QMD
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Table 4.1 The mean, minimum (Min), maximum (Max), and coefficient of variation (CV) of X0, X1, and SG by forest type.
Cypress Forests Pine Forests
Variable Mean Min Max CV Mean Min Max CV
X0 1022.03 175.77 2781.21 44.5 874.64 46.81 2099.52 48.6 X1 540.52 95.78 1556.14 46.6 485.77 26.47 1256.77 51.4 SG 0.587 0.362 0.828 15.2 0.585 0.406 0.872 15.0
Table 4.2 Reference maximum SDIs by equation source for cypress forests.
Equation Source
Intercept Slope SDI Condition
Su.A1a,X 6.315 -2.558 548 Ordinary Least Squares
Su.A2a,X 6.898 -2.558 2099 Corrected Ordinary Least Squares Su.A3a,X 5.055 -1.558 753 Reduced Major Axis
Su.A4a,X 6.328 -2.193 1829 Quantile Regression (99th quantile) Su.A5a,X 6.423 -2.532 765 Stochastic Frontier Function (production) Su.A6a,X 6.603 -2.564 1044 Stochastic Frontier Function (cost) Su.N1a,Y 8.246 -3.968 500 Ordinary Least Squares
Su.N2a,Y 9.119 -3.968 3732 Corrected Ordinary Least Squares Su.N3a,Y 5.073 -1.543 824 Reduced Major Axis
Su.N4a,Y 6.482 -2.294 1884 Quantile Regression (99th quantile) Su.N5a,Y 8.214 -3.559 1733 Stochastic Frontier Function (production) Su.N6a,Y 8.246 -3.968 500 Stochastic Frontier Function (cost) Su.Q1a,Z 5.935 -2.315 500 Ordinary Least Squares
Su.Q2a,Z 6.338 -2.315 1264 Corrected Ordinary Least Squares Su.Q3a,Z 5.238 -1.739 641 Reduced Major Axis
Su.Q4a,Z 6.599 -2.525 1173 Quantile Regression (99th quantile) Su.Q5a,Z 6.778 -2.638 1231 Stochastic Frontier Function (production) Su.Q6a,Z 5.935 -2.315 500 Stochastic Frontier Function (cost)
Yenb 7.002 -1.471 1076 Use volume (500m3) to estimate SDI
X Dataset from both NFI1 to NFI3 and Qilan Mountain
Y Dataset only from NFI1 to NFI3
Z Dataset only from Qilan Mountain
94
Table 4.3 Reference maximum SDIs by equation source for pine forests.
Name Intercept Slope SDI Condition
Rei.80 4.657 -1.118 1242 0.80th quantile
Rei.85 5.124 -1.432 1325 0.85th quantile
Rei.90 5.328 -1.570 1359 0.90th quantile
Rei.95 5.260 -1.505 1433 0.95th quantile
Rei.99 5.236 -1.450 1618 0.99th quantile
Table 4.4 Estimated coefficients for X0 and X1, asymptotic 95 % confidence lower limit (LL) and upper limit (UL) by quantiles and forest type.
Forest
95
Table 4.5 Estimated coefficients for X0 and X1, asymptotic 95 % confidence lower limit (LL) and upper limit (UL) by quantiles and % random noise (RN) for cypress forests.
% RN Quantile b0 b0.LB b0.UB b1 b1.LB b1.UB
96
97
0.90 0.00028 0.00023 0.00035 0.00048 0.00033 0.00057 0.95 0.00038 0.00033 0.00049 0.00021 -0.00003 0.00031 0.99 0.00075 0.00068 0.00087 -0.00071 -0.00096 -0.00055
98
Table 4.6 Estimated coefficients for X0 and X1, asymptotic 95 % confidence lower limit (LL) and upper limit (UL) by quantiles and % random noise (RN) for pine forests.
% RN Quantile b0 b0.LB b0.UB b1 b1.LB b1.UB
99
100
0.90 0.00079 0.00076 0.00082 -0.00031 -0.00039 -0.00025 0.95 0.00078 0.00077 0.00079 -0.00036 -0.00038 -0.00034 0.99 0.00033 0.00032 0.00035 0.00030 0.00027 0.00033
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Table 4.7 Estimations of implied maximum ASDI by quantiles, % random noise and forest type (ASDI is only calculated when both b0 and b1 are significant).
Forest Random noise
102
Table 4.8 Based on 1% random noise, estimated coefficients, average SG, and implied maximum ASDIs by quantiles and % basal area threshold for cypress forests.
Percentage 0% 10% 20%
Quantile b0 b1 SG ASDI b0 b1 SG ASDI b0 b1 SG ASDI
0.50 0.000679 0.000345 0.587 1134 0.000770 0.000167 0.581 1153 0.000883 -0.000108 0.578 1219
0.55 0.000594 0.000421 1189 0.000602 0.000404 1195 0.000750 0.000070 1265
0.60 0.000514 0.000472 1264 0.000480 0.000545 1254 0.000938 -0.000431 1452
0.65 0.000517 0.000415 1315 0.000612 0.000199 1374 0.000831 -0.000276 1488
0.70 0.000615 0.000136 1440 0.000720 -0.000118 1513 0.000723 -0.000112 1519
0.75 0.000644 0.000007 1542 0.000653 -0.000016 1553 0.000700 -0.000141 1618
0.80 0.000636 -0.000029 1616 0.000575 0.000044 1663 0.000517 0.000099 1741
0.85 0.000425 0.000274 1707 0.000319 0.000423 1760 0.000376 0.000294 1831
0.90 0.000254 0.000526 1777 0.000247 0.000529 1790 0.000287 0.000454 1821
0.95 0.000353 0.000273 1948 0.000270 0.000455 1830 0.000353 0.000273 1957
0.99 0.000752 -0.000702 2938 0.000170 0.000560 1991 0.000490 -0.000065 2199
102
103
Percentage 30% 40% 50%
Quantile b0 b1 SG ASDI b0 b1 SG ASDI b0 b1 SG ASDI
0.50 0.001010 -0.000391 0.573 1274 0.000846 -0.000180 0.575 1347 0.000715 0.000162 0.564 1240
0.55 0.000953 -0.000460 1450 0.000965 -0.000489 1464 0.000965 -0.000489 1453
0.60 0.000889 -0.000363 1468 0.000861 -0.000331 1490 0.000735 -0.000507 1415
0.65 0.000762 -0.000171 1506 0.000761 -0.000168 1505 0.000779 - -
0.70 0.000722 -0.000171 1602 0.000766 -0.000220 1563 0.000818 -0.000351 1611
0.75 0.000722 -0.000225 1686 0.000743 -0.000286 1730 0.000883 -0.000630 1897
0.80 0.000482 0.000159 1744 0.000694 -0.000276 1868 0.001014 -0.001000 2237
0.85 0.000261 0.000515 1796 0.000303 0.000424 1827 0.001020 -0.001024 2262
0.90 0.000249 0.000527 1814 0.000263 0.000493 1830 0.000302 0.000421 1851
0.95 0.000253 0.000510 1832 0.000270 0.000475 1840 0.002703 0.000475 1857
0.99 0.000490 -0.000061 2198 0.000490 -0.000061 2199 0.000490 -0.000061 2195
103
104
Table 4.9 Based on 1% random noise, estimated coefficients, average SG, and implied maximum ASDIs by quantiles and % basal area threshold for pine forests.
Percentage 0% 10% 20%
Quantile b0 b1 SG ASDI b0 b1 SG ASDI b0 b1 SG ASDI
0.50 0.000739 0.000347 0.585 1061 0.000541 0.000737 0.581 1033 0.000591 0.000659 0.577 1030
0.55 0.000831 0.000112 1116 0.000462 0.000833 1058 0.000700 0.000412 1066
0.60 0.000742 0.000231 1140 0.000545 0.000622 1103 0.000570 0.000589 1099
0.65 0.000842 - - 0.000548 0.000568 1139 0.000611 0.000475 1129
0.70 0.000828 -0.000060 1261 0.000743 0.000121 1230 0.000589 0.000467 1166
0.75 0.001006 -0.000438 1333 0.001150 -0.000705 1350 0.001111 -0.000618 1325
0.80 0.001149 -0.000759 1417 0.001258 -0.000958 1425 0.001310 -0.001038 1405
0.85 0.000960 -0.000514 1516 0.001305 -0.001094 1494 0.001340 -0.001129 1451
0.90 0.000771 -0.000277 1642 0.000882 -0.000481 1660 0.001343 -0.001174 1502
0.95 0.000781 -0.000359 1751 0.000859 -0.000480 1725 0.000902 -0.000522 1664
0.99 0.000334 0.000299 1964 0.000334 0.000299 1969 0.000529 0.000010 1871
104
105
Percentage 30% 40% 50%
Quantile b0 b1 SG ASDI b0 b1 SG ASDI b0 b1 SG ASDI
0.50 0.000540 0.000775 0.572 1016 0.000336 0.001198 0.565 987 0.000324 0.001222 0.557 996
0.55 0.000557 0.000712 1037 0.000596 0.000648 1038 0.000199 0.001421 1010
0.60 0.000637 0.000505 1080 0.000637 0.000505 1084 -0.000041 0.001802 1039
0.65 0.000545 0.000622 1109 0.000457 0.000793 1104 -0.000135 0.001952 1051
0.70 0.000548 0.000568 1145 0.000548 0.000568 1150 -0.000142 - -
0.75 0.001014 -0.000423 1295 0.000803 -0.000010 1254 0.000148 0.001289 1155
0.80 0.001360 -0.001114 1384 0.001075 -0.000554 1313 0.000511 0.000541 1231
0.85 0.001305 -0.001029 1397 0.001422 -0.001250 1398 0.000989 -0.000404 1309
0.90 0.001325 -0.001104 1443 0.001331 -0.001114 1426 0.001083 -0.000613 1348
0.95 0.001003 -0.000695 1652 0.001304 -0.001093 1458 0.000629 0.000204 1348
0.99 0.000859 -0.000480 1713 0.000905 -0.000527 1648 -0.000297 0.001841 1375
105
106
Table 4.10 Estimated coefficients of intersected quantiles by equation source and % basal area threshold from 0 to 20 % for cypress forests.
% BA 0% 10% 20%
107
Su.Q5a,Z 0.58 0.000502 0.000545 0.58 0.000468 0.000594 0.52 0.000753 0.000111
Su.Q6a,Z - - - -
Yenb - - - -
Rei.80 - - - -
Rei.85 - - - -
Rei.90 0.50 0.000679 0.000345 0.50 0.000770 0.000167 - - -
Rei.95 0.52 0.000606 0.000445 0.50 0.000770 0.000167 - - -
Rei.99 0.52 0.000606 0.000445 0.50 0.000770 0.000167 - - -
107
108
Table 4.11 Estimated coefficients of intersected quantiles by equation source and % basal area threshold from 30 to 50 % for cypress forests.
% BA 30% 40% 50%
109
Su.Q5a,Z - - - -
Su.Q6a,Z - - - -
Yenb - - - -
Rei.80 - - - -
Rei.85 - - - -
Rei.90 - - - -
Rei.95 - - - -
Rei.99 - - - -
109
110
Table 4.12 Estimated coefficients of intersected quantiles by equation source and % basal area threshold from 0 to 20 % for pine forests.
% BA 0% 10% 20%
Table 4.13 Estimated coefficients of intersected quantiles by equation source and % basal area threshold from 30 to 50 % for pine forests.
% BA 30% 40% 50%
Table 4.14 Estimated coefficients for maximum, mean, and minimum of intersected quantile by forest type.
Forest Type % BA Max Min Mean
111