Dhrymes, P. J., E.P. Howrey, S.H. Hymans, J. Kmenta,. E.E. Learner, R.E. Quandt, J.B. Ramsey, H.T. Shap- iro, and V. Zarnowitz. 1972. Criteria for evaluation of.
Biomass Equations for Intensively Managed Douglas-fir Trees David W. Hann, Doug Mainwaring, and Doug Maguire iomass data needed to develop equations are difficult and expensive to col: lect. As a consequence, biomass data sets have been small in size relative to the size of the Douglas-fir population found in the Pacific Northwest. The objective of this study was to create equation forms that would be more likely to accurately and precisely extrapolate to elements of the Douglas-fir population not found in the modeling data set. This study used previous work in geometry and mechanics to develop interpretable nonlinear equation forms for predicting components of Douglas-fir biomass using diameter at breast height (D) in cm, total tree height (H) in m, and crown length (CL) in m as predictor variables. Direct predictors were developed for the following biomass components in kg: biomass in foliage (FOL), living branches (LIVEBR), dead branches (DEADER), bark (BRK), sapwood of the stem (SAP), heartwood of the stem (HRT), and total stem inside bark (TSB ). In addition, indirect predictors, formed from direct predictors of appropriate components, were evaluated for total stem outside bark (TSBob) in kg and total tree living biomass above ground (TTLB) in kg.
Data A total of 200 trees were sampled from 23 stands that covered a range in geography, allometry, and treatment history (thinning, fertilization, and early weed control). The 23 sites included research installations (14) and operational timberland (9), and were distributed from 42.80° to 47.20° N latitude, from 123.98° to 121.67° W longitude, and from 140 to 790 m above sea level. Measurements of FOL, LIVEBR, BRK, SAP, and HRT (TSB.b being calculated by summing SAP and HRT) were made on all 200 trees, while DEADER was measured on a subsample of 55 trees for which 51 were in the 90th percentile of the diameter distribution and the remaining 4 trees were in the 10th percentile of the diameter distribution. Details about sampling, field and lab work are available in Coons et al. (2013). Two independent data sets were used to evaluate the capabilities of alternative model forms to extrapolate to different combinations of D, H, and CL and different geographic locations than found in the modeling data set (therefore, they are not considered validation data sets). The first data comes from a single stand located in the Siskiyou Mountains in southwest Oregon (this will be called the SWO data set in the remainder of this report). Biomass was determined for FOL, LIVEBR, BRK, and TSB.b on 32 trees within the stand using the procedures described in Nay and Bormann (2014). The second data set comes from trees sampled on selected old growth stands around the Shelton Ranger District of the Olympic National Forest in northwest Washington (this will be called the NWW data set in the remainder of this report). In this study, biomass was collected by Snell and Anholt (1981) for FOL, LIVEBR, and DEADER on five trees using essentially the same procedures as Brown (1978).
46
A description of the D, H, and CL measurements found in all four data sets is found in Table 1.
77.0
12.2
Where, LCW = Largest crown width of the tree predicted from the northwest Oregon Douglas-fir equation of Hann (1997) in m PFOL = Predicted foliage weight of the tree from Equation [1] BL = H - CL MBL= BL if BL < b2, = b2 if BL > b2 CR = CL/H
57.36 26.59
8.22
[10] RSAP = 1.0, if(D x H) I CR > 60, otherwise
Table 1. Summary statistics for the Douglas-fir tree-level biomass modeling data set and the two evaluation data sets. Variable
Minimum
Mean
Maximum
Standard Deviation
Modeling Data Set for FOL, LIVEBR, BRK, SAP, and HRT, and TSBib (N = 200) D
7.4
H
8.18
30.5 25.33
CL
3.94
13.18
3.55
^.
RSAP-^xCR + V-Q-btxCRJe*1
Modeling Data Set for DEADER (N = 55) D
13.0
38.7 77.0
14.6
H
11.11
28.51 57.36
9.50
CL
8.83
15.05
3.72
D
5WO Evaluation Data (N = 32) 23.1 45.9 80.3
14.1
H
20.1
29.1 36.0
4.7
CL
8.5
15.8 27.6
4.8
D
NWW Evaluation Data (N = 5) 91.7 147.2 220.7
59.8
H
53.7
61.8 77.7
10.2
CL
25.0
32.3 42.7
7.5
24.56
PLIVEBR = Predicted LIVEBR from Equation [2] PTSB.b = Predicted TSB.b from Equation [4] PBRK = Predicted BRK from Equation [6] Equations [1], [2], [3], [4], [7], and [10] are considered direct estimators of the response variables because their parameters were estimated directly from the data. Equations [5], [6], [8], and [9] are indirect estimators of the response variables because they use only predictions from previously parameterized equations and, therefore, do not involve the direct estimation of parameters.
Estimation and Evaluation
Methods Equation Forms for Predicting Biomass The following equation forms were fashioned from equations developed in geometry and mechanics in order to predict biomass:
[1] n)i. =/?, x j / n r / i o r xi;r/. w) [2] /./r/-.«M= A, x[(LCW/lO)2x(PFOl
'' 10)]'-
[3] DKADHK = h{ x < /> H V' ; *(!.< 'It' 1 0 r x ( Mlil. • 1 0 )
[4] TSH.f, =/\ +/>, x ( / > lOr x(//.' lO)x t .V„ i *, x c / j / i o r x ( / / , n))xi-* 0f [8] l'SHllh = I'HRK + /'/.V% [9] ni.K=!'KRK 4 /'/\/% 4- I'l-'Ot + ri.t\TJiR
47
Table 2. Parameter estimates and associated standard errors of the parameters (in parentheses) for predicting Douglas-fir biomass in Kg.
Table 3. Fit statistics BIAS and UW_y for the modeling data set and the two evaluation data sets. Equation
Parameters (Standard Errors) Equation
b,
NA
38.8305134 (0.9973194)
NA
NA
7.93338518 (0.3471377)
0.804701137 (0.01903674)
[3]
NA
43.2444672 (6.92857)
20.89 (5.169313)
[41
3.61578088 (0.58282)
14.1690124 (0.4942984)
-0.210021548 (0.0658482)
[71
0.318564479 (0.1583753)
2.60600933 (0.1496987)
-0.385623122 (0.1097177)
NA
HO]
NA
0.362790893 (0.0352123)
-0.804811836 (0.02849096)
0.538867365 (0.01619606)
[2]
UT-R42
Modeling Data Set
b0
[1]
b2
BIAS
b, [11 NA
-2.09%
0.8169
[21
-0.56%
0.8928
[3]
+4.95%
0.6894
NA
[4]
+0.41%
0.9920
1.90718673 (0.3402741)
[5]
+0.52%
0.9540
[6]
+2.73%
0.9636
[7]
-2.91%
0.9487
[81
+1.99%
0.9920
[9]
+1.57%
0.9923
NA
ometry (e.g., FOL Equation [1], DEADER Equation [3], BRK Equation [7], and TSB.b Equation [4]) or basic mechanics (LIVEBR Equation f2]). Examination of the fit statistics for the modeling data set shows that the resulting equations explained 69% to 89% of the variation in the crown attributes and 95% to 99% of the variation in the stem attributes (Table 3). Bias ranged from -2% to +5% for the crown attributes and from -3% to +3% for the stem attributes. The lower values of UT — Rad[.2 for the crown attributes is probably due to the larger amount of unexplainable measurement error in those response variables due to within crown sampling. The objective for developing these new equations was to explore model forms that might better characterize the biomass components for combinations of tree attributes not found in the modeling data set. Examination of the fit statistics for the two evaluation data sets is also shown in Table 3. Equations [1] and [2] were developed using the northwest Oregon version of the LCW equation. The results in Table 3 for these two equations applied to the SWO evaluation data set shows that the southwest Oregon version of the LCW equation provided substantially better fit statistics. On the other hand, the northwest Oregon LCW equation provided good fit statistics for the NWW evaluation data. These results seem to imply, therefore, that, for a tree of a given DBH, HT, and CL, both FOL and LIVEBR will vary by location and that the LCW equations of Hann (1997) are a reasonable estimator of that variation. The modeling data set fit statistics for DEADBR (Equation [3]) explained the least amount of variation and
SWO Evaluation Data Set [1]-NWOLCWEq.
+14.9%
+0.6696
[1]-SWOLCWEq.
-9.1%
+0.8006
[21-NWOLCWEq.
+68.5%
-0.8370
[2] -SWO LCW Eq.
+15.5%
+0.6941
-7.0%
+0.9743
-3.7%
+0.9766
BRK TSB,b
NWW Evaluation Data Set l1]-NWOLCWEq.
+1.2%
+0.7410
[2]-NWOLCWEq.
+9.5%
+0.7230
[31-NWOLCWEq.
+578.0%
-54.3159
had the largest amount of bias for the three crown attributes examined in this study (Table 3). Equation [3] also had extremely poor fit statistics when applied to the NWW evaluation data set. Given the small size of the modeling data set and the concentration of that sample in dominant trees, the use of Equation [3] should be restricted to the population found in the modeling data set. The SWO evaluation data set fit statistics for theTSB.ID and BRK equations (Equations [4] and [7]) explained just slightly less variation than the modeling data with slightly increased bias (Table 3). UT_Rad2 is calculated using the mean square of the residuals (MSE) for the evaluation data sets and both Dhrymes et al. (1972) and Hocking (1976) have noted that this value must necessarily be larger for an evaluation data set than the MSE found for the modeling data set. As a result, the UT - R adj,.2 of the evaluation data set must also be necessarily smaller than the UT_Rad 2 of the modeling data set. Therefore, the results for Equations [1], [4], and [7] indicate excellent performance when extrapolated to southwest Oregon.
48
A number of previous biomass studies have expressed concern that the component biomass equations will not sum up to an unbiased predictor of total biomass (e.g., Chiyenda and Kozak 1984, Cunia and Briggs 1985, Carvalho and Parresol 2003). As a result, they have proposed procedures that constrain the parameters of the individual equations in order to assure that they sum up to an unbiased estimator of the total biomass. In these procedures, the optimal properties of the individual equations are sacrificed in order to gain the property of additivity. The results of this study indicate that the indirect estimators of TSBob and TTLB are, for all practical purposes, unbiased (Table 3). Therefore, it is concluded that carefully developed component equations can meet the property of additivity without the need to compromise their individual optimal statistical qualities.
Literature Cited Brown, J.E. 1978. Weight and density of crowns of Rocky Mountain conifers. USDA, Forest Service, Intermountain Forest and Range Experiment Station, Research Paper INT-197. 56p. Carvalho, J.P. and B.R. Parresol. 2003. Additivity in tree biomass components of Pyrenean oak (Quercus pyrenaica Willd.).Forest Ecology and Management 179: 269-276. Chiyenda, S.S. and A. Kozak. 1984. Additivity of component biomass regression equations when the underlying model is linear. Canadian Journal of Forest Research 14: 441-446.
49
Coons, K., D. Maguire, D. Mainwaring, A. Bluhm, R. Harrison, and E. Turnblom. 2013. Allometric relationships and above-ground Douglas-fir biomass and nutrient pools under varying stand density and nitrogen fertilization regimes. Pp. 28-32 in DA. Maguire and D.B. Mainwaring (eds). CIPS 2012 Annual Report. Center for Intensive Planted-forest Silviculture, College of Forestry, Oregon State University, Corvallis, OR, USA. Cunia, T. andR.D. Briggs. 1985. Forcing additivity of biomass tables: use of the generalized least squares method. Canadian Journal of Forest Research 15: 23-28. Dhrymes, P. J., E.P. Howrey, S.H. Hymans, J. Kmenta, E.E. Learner, R.E. Quandt, J.B. Ramsey, H.T. Shapiro, and V. Zarnowitz. 1972. Criteria for evaluation of econometric models. Annuals of Economic and Social Measurements 1: 291-324. Hann, D.W. 1997. Equations for predicting the largest crown width of stand-grown trees in western Oregon. Forest Research Lab., Oregon State University, Corvallis, Oregon. Research Contribution 17. I4p. Hocking, R.R. 1976. The analysis and selection of variables in linear regression. Biometrics 32: 1-49. Nay, S.M. and B.T. Bormann. 2014. Site-specific Douglas-fir biomass equations from the Siskiyou Mountains, Oregon, compared with others from the Pacific Northwest. Forest Science 60: 1140-1147. Snell, J.A.K. and B.F. Anholt. 1981. Predicting crown weight of coast Douglas-fir and western Hemlock. USDA Forest Service, Pacific Northwest Forest and Range Experiment Station, Portland, Oregon, Research Paper PNW-281, 13p.
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Annual Report 2014 •-
