# Evaluation of Whole Tree Growth Increment Derived from Tree-Ring Series for Use in Assessments of Changes in Forest Productivity across Various Spatial Scales

^{*}

## Abstract

**:**

## 1. Introduction

^{3}) derived from past diameters reconstructed from breast height ring widths compared to the same estimates obtained from full stem analysis data, when both estimates are available for the same tree. We did this using data from five species common in the Western Canadian boreal forest: lodgepole pine (Pinus contorta Dougl. var. latifolia Engelm.) jack pine (Pinus banksiana Lamb.), black spruce (Picea mariana (Mill.) B.S.P.), white spruce (Picea glauca (Moench) Voss.), and trembling aspen (Poplus tremuloides Michx.). The purpose of this evaluation is to determine the potential error associated with measures of volume growth increment, derived from tree ring measurements at breast height only, in terms of the actual value of the growth increment, as well as its pattern of inter-annual variation. We also apply our estimates of error to an example stand where tree-ring data have previously been used to estimate inter-annual variation in growth [2,3], to estimate the potential stand level magnitude of this error.

## 2. Materials and Methods

#### 2.1. Stem Analysis Data Collection and Measurement

#### 2.2. Stem Analysis Growth Estimates

^{3}). Historical tree height (m) was interpolated assuming equal annual height growth within a log section, and assuming that each disk cuts through the middle of a growth cycle, and was referred to as stem analysis height (HTs). Volume was calculated from ring width measurements on each of the disk sections and summed for the entire tree for each year, and referred to as stem analysis volume (Vs). The volume for each log section was calculated using Smalian’s formula, V = (L(Ab + At)/2), for the top section from the volume of a paraboloid, V = (LAb)/2, and for the stump section from the volume of a cylinder V = LAb, where V is the volume of the section (cm

^{3}), L is the length of the section (cm), Ab is the cross-sectional area of the base of the section (cm

^{2}), and At is the cross-sectional area of the top of the section (cm

^{2}). Note that, while the stem analysis-based measurements were taken as the true standard against which alternatives derived from the breast height sample were compared, they are not themselves without uncertainty. For example, estimates derived from stem analysis will differ depending on the method used to interpolate height between cross sections [18], which standard model is used to determine log volume [22,23], the number of cross-cuts sampled, and the number of radii measured along each sample [12], and because trees are not perfectly round in cross section [24,25].

#### 2.3. Model-Based Growth Estimates

#### 2.3.1. Height Estimation

_{ob}is the outside bark diameter (DBH, cm), and a, b, and c are the parameters obtained from published sources for Alberta ([31], Table S1) and Manitoba ([29], Table S1). Trees in Saskatchewan and the Northwest Territories also used the Alberta parameters, as regional parameters were not available for these jurisdictions. We calculated two height increment series from the annually reconstructed DBH, (1) a raw height series (HTr), which used the height estimate directly from Equation (1), as well as (2) a corrected height series (HTc), where a ratio between the final predicted height from the raw height series and the measured tree height was used as a correction factor and applied to the raw height series to scale past predicted heights so that the final height in the corrected series was equal to the measured height at the time the tree was sampled.

#### 2.3.2. Volume Estimation

_{0}, β

_{1}, and β

_{2}are fixed-effect parameters, and δ

_{i}, δ

_{ij}, and δ

_{ijk}are random effects associated with the province, plot, and tree, respectively [26]. We also tested two methods that use both DBH and H as predictors. The first was also a national level taper equation (VNdh) [26]:

_{2}is a fixed-effect parameter, and δ

_{i}, δ

_{ij}, and δ

_{ijk}, are random effects associated with the province, plot, and tree, respectively [26] (Table S2). The second was a different taper equation (VRdh) [27], for which regional parameter estimates were generally available [28,29,30]:

_{i}is $(1-\sqrt{{h}_{i}/H})/\left(1-\sqrt{p}\right)$, where h

_{i}is the cross-section height i, p is the relative height of the inflection point, typically assumed to be 0.25, and z

_{i}is the relative height (h

_{i}/H) [27]. Parameters a

_{0}, a

_{1}, a

_{2}, b

_{1}, b

_{2}, b

_{3}, b

_{4}, and b

_{5}were obtained from published sources Saskatchewan [28], Manitoba [29], and Alberta [30] (Table S3). Regional parameters were not available for the Northwest Territories; therefore, for trees in that jurisdiction, the Alberta parameters were used. Estimates of volume for each of the methods tested were obtained by numerical integration, and the volume increment from the difference in volume between subsequent years.

#### 2.4. Comparison of Estimates

#### 2.5. Inter-Annual Variation

#### 2.6. Stand-Level Example Application

## 3. Results

#### 3.1. Comparison of Estimates

#### 3.2. Inter-Annual Variation

#### 3.3. Example Application

## 4. Discussion

^{3}) derived from past DBH reconstructed from ring widths and compared these to estimates obtained from full stem analysis data, when both estimates are available for the same tree. This was done using data from n = 170 trees for five species common in the Western Canadian boreal forest: lodgepole pine, jack pine, black spruce, white spruce, and trembling aspen. The main results were that relative errors varied by species, diameter class, and the equation used to estimate volume and that the direction of inter-annual variability for whole tree and breast height estimates of volume increment were highly correlated for nearly all trees. In general, when estimates of volume increment are derived from models that use both DBH and HT as predictors, the total range of values spanned by the relative errors is narrower, relative to volume increment derived from a model using DBH only. The range of observed relative errors for national models was similar to that of regional models, at least for the species tested here. When tree-level errors were propagated to estimates of error for volume increment at the stand level, the overall range of errors was narrower, typically ±5% for our example jack pine stand, at least for our simple procedure that assumed the observed errors were independent. The overall range of errors is less than what is currently assumed to be the uncertainty of growth increments applied by Canada’s National Forest Carbon Monitoring, Accounting, and Reporting system to estimate the carbon balance of Canada’s managed forest [32], but it should be kept in mind that additional error would arise from model and measurement errors that were not accounted for, and at young ages from trees that have died and subsequently decayed such that they could not be detected when the stand was sampled [33]. In this analysis, breast height estimates were consistently high relative to whole tree estimates after age 30–40, but this is likely a result specific to this particular combination of tree species and volume estimation method.

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Luo, Y.; Keenan, T.F.; Smith, M. Predictability of the terrestrial carbon cycle. Glob. Chang. Biol.
**2015**, 21, 1737–1751. [Google Scholar] [CrossRef] [PubMed] - Metsaranta, J.M.; Lieffers, V.J. Using dendrochronology to obtain annual data for modelling stand development: A supplement to permanent sample plots. Forestry
**2009**, 82, 163–173. [Google Scholar] [CrossRef] - Metsaranta, J.M.; Kurz, W.A. Inter-annual variability of ecosystem production in boreal jack pine forests (1975–2004) estimated from tree-ring data using CBM-CFS3. Ecol. Mod.
**2012**, 224, 111–123. [Google Scholar] [CrossRef] - Hember, R.A.; Kurz, W.A.; Metsaranta, J.M.; Black, T.A.; Coops, N.C.; Guy, R.D. Accelerated regrowth of temperate-maritime forests due to environmental change. Glob. Chang. Biol.
**2012**, 18, 2026–2040. [Google Scholar] [CrossRef] - Babst, F.; Alexander, M.R.; Szejner, P.; Bouriaud, O.; Klesse, S.; Roden, J.; Ciais, P.; Poulter, B.; Frank, D.; Moore, D.J.P.; et al. A tree-ring perspective on the terrestrial carbon cycle. Oecologia
**2014**, 176, 307–322. [Google Scholar] [CrossRef] [PubMed] - Graumlich, L.J.; Brubaker, L.B.; Grier, C.C. Long-term trends in forest net primary productivity: Cascade Mountains, Washington. Ecology
**1989**, 70, 405–410. [Google Scholar] [CrossRef] - Babst, F.; Bouriaud, O.; Alexander, R.; Trouet, V.; Frank, D. Toward consistent measurement of carbon accumulation: A multi-site assessment of biomass and basal area increment across Europe. Dendrochronologia
**2014**, 32, 153–161. [Google Scholar] [CrossRef] - Fang, O.; Wang, Y.; Shao, X. The effect of climate on the net primary production (NPP) of Pinus koraiensis in the Changbai Mountains over the past 50 years. Trees
**2016**, 30, 281–294. [Google Scholar] [CrossRef] - Bunn, A.G.; Hughes, M.K.; Kirdyanov, A.V.; Losleben, M.; Shishov, V.V.; Berner, L.T.; Oltchev, A.; Vaganov, E.A. Comparing forest measurements from tree rings and a space based index of vegetation activity in Siberia. Environ. Res. Lett.
**2013**, 8, 035034. [Google Scholar] [CrossRef] - Babst, F.; Bouriaud, O.; Papale, D.; Gielen, B.; Jansenns, I.A.; Nikinmaa, E.; Ibrom, A.; Wu, J.; Bernhofer, C.; Köstner, B.; et al. Above-ground woody carbon sequestration measured from tree rings is coherent with net ecosystem productivity at five eddy-covariance sites. New Phytol.
**2014**, 201, 1289–1303. [Google Scholar] [CrossRef] [PubMed] - LeBlanc, D.C. Relationship between breast-height and whole-stem growth indices for red spruce on Whiteface Mountain, New York. Can. J. For. Res.
**1990**, 20, 1399–1407. [Google Scholar] [CrossRef] - Newton, P.F. A stem analysis computational algorithm for estimating volume growth and its empirical evaluation under various sampling strategies. Comput. Electron. Agric.
**2004**, 44, 21–31. [Google Scholar] [CrossRef] - Bouriaud, O.; Breda, N.; Dupouey, J.-L.; Granier, A. Is ring width a reliable proxy for stem-biomass increment? A case study in European beech. Can. J. For. Res.
**2005**, 35, 2920–2933. [Google Scholar] [CrossRef] - Chhin, S.; Hogg, E.H.; Lieffers, V.J.; Huang, S. Growth–climate relationships vary with height along the stem in lodgepole pine. Tree Phys.
**2010**, 30, 335–345. [Google Scholar] [CrossRef] [PubMed] - Van der Maaten-Theunissen, M.; Bouriaud, O. Climate-growth relationships at different stem heights in silver fir and Norway spruce. Can. J. For. Res.
**2012**, 42, 958–969. [Google Scholar] [CrossRef] - Duff, G.H.; Nolan, N.J. Growth and morphogenesis in the Canadian forest species: I. The controls of cambial and apical activity in Pinus resinosa. Can. J. Bot.
**1957**, 31, 471–513. [Google Scholar] [CrossRef] - Shea, S.R.; Armson, K.A. Stem analysis of jack pine (Pinus banksiana Lamb.): Techniques and concepts. Can. J. For. Res.
**1972**, 2, 392–406. [Google Scholar] [CrossRef] - Dyer, M.E.; Bailey, R.L. A test of six methods for estimating true height from stem analysis data. For. Sci.
**1987**, 33, 3–13. [Google Scholar] - Halliwell, D.H.; Apps, M.J. BOReal Ecosystem-Atmosphere Study (BOREAS) Biometry and Auxiliary Sites: Overstory and Understory Data; Natural Resources Canada, Canadian Forest Service, Northern Forestry Centre: Edmonton, AB, Canada, 1997.
- Varem-Sanders, T.M.L.; Cambpell, I.D. BOReal Ecosystem-Atmosphere Study (BOREAS) Biometry and Auxiliary Sites: X-ray Densitometry of Tree Allometry Samples; Natural Resources Canada, Canadian Forest Service, Northern Forestry Centre: Edmonton, AB, Canada, 1998.
- Varem-Sanders, T.M.L.; Cambell, I.D. DendroScan: A Tree-Ring Width and Density Measurement System; UBC Press: Vancouver, BC, Canada, 1996. [Google Scholar]
- Martin, A.J. Testing volume equation accuracy with water displacement techniques. For. Sci.
**1984**, 30, 41–50. [Google Scholar] - Figueiredo-Filho, A.; Schaaf, L.B. Comparison between predicted volumes estimated by taper equations and true volumes obtained by the water displacement technique (xylometer). Can. J. For. Res.
**1999**, 29, 451–461. [Google Scholar] [CrossRef] - Biging, G.S.; Wensel, L.C. The effect of eccentricity on the estimation of basal area and basal area increment of coniferous trees. For. Sci.
**1988**, 34, 621–633. [Google Scholar] - Bakker, J.D. A new, proportional method for reconstructing historical tree diameters. Can. J. For. Res.
**2005**, 35, 2515–2520. [Google Scholar] [CrossRef] - Ung, C.H.; Guo, X.J.; Fortin, M. Canadian national taper models. For. Chron.
**2014**, 89, 211–224. [Google Scholar] [CrossRef] - Kozak, A. A variable-exponent taper equation. Can. J. For. Res.
**1988**, 18, 1362–1368. [Google Scholar] [CrossRef] - Gál, J.; Bella, I.E. New Stem Taper Functions for 12 Saskatchewan Timber Species; Information Report NOR-X-338; Natural Resources Canada, Canadian Forest Service, Northern Forestry Centre: Edmonton, AB, Canada, 1994.
- Klos, R. Ecologically Based Taper Equations for Major Tree Species in Manitoba. Master’s Thesis, Lakehead University, Thunder Bay, ON, Canada, 2004. [Google Scholar]
- Huang, S. Ecologically Based Individual Tree Volume Estimation for Major Alberta Tree Species Report #1 Individual Tree Volume Estimation Procedures for Alberta: Methods of Formulation and Statistical Foundations; Alberta Sustainable Resource Development, Public Lands and Forests Division: Edmonton, AB, Canada, 1994.
- Huang, S. Ecologically Based Individual Tree Volume Estimation for Major Alberta Tree Species Report #2 Ecologically Based Individual Tree Height-Diameter Models for Major Alberta Tree Species; Alberta Sustainable Resource Development, Public Lands and Forests Division: Edmonton, AB, Canada, 1994.
- Metsaranta, J.M.; Shaw, C.H.; Kurz, W.A.; Boisvenue, C.; Morken, S. Uncertainty of inventory-based estimates of the carbon dynamics of Canada’s managed forest (1990–2014). Can. J. For. Res.
**2016**. in review. [Google Scholar] - Metsaranta, J.M.; Lieffers, V.J.; Wein, R.W. Dendrochronological reconstruction of jack pine snag and downed log dynamics in Saskatchewan and Manitoba, Canada. For. Ecol. Manag.
**2008**, 255, 1262–1270. [Google Scholar] [CrossRef] - Hasenauer, H.; Monserud, R.A. Biased predictions for tree height increment models developed from smoothed ‘data’. Ecol. Mod.
**1997**, 98, 13–22. [Google Scholar] [CrossRef] - Sumida, A.; Miyaura, T.; Torii, H. Relationships of tree height and diameter at breast height revisited: Analysis of stem growth using 20-year data of an even-aged Chamaecyparis obtuse stand. Tree Phys.
**2013**, 33, 106–118. [Google Scholar] [CrossRef] [PubMed] - Lambert, M.C.; Ung, C.H.; Raulier, F. Canadian national tree aboveground biomass equations. Can. J. For. Res.
**2005**, 35, 1996–2018. [Google Scholar] [CrossRef] - Ung, C.H.; Bernier, P.; Guo, X.J. Canadian national biomass equations: New parameter estimates that include British Columbia data. Can. J. For. Res.
**2008**, 38, 1123–1132. [Google Scholar] [CrossRef] - Weiskittel, A.R.; MacFarlane, D.W.; Radtke, P.J.; Affleck, D.L.R.; Temesgen, H.; Woodall, C.W.; Westfall, J.A.; Coulston, J.W. A call to improve methods for estimating tree biomass for regional and national assessments. J. For.
**2015**, 113, 414–424. [Google Scholar] [CrossRef] - Garcia, O. Sampling for tree-ring analysis. In Presented at Integrating Forest Information Over Space and Time, Canberra, Australia, 13–17 January 1992; pp. 110–128.
- Osawa, A.; Abaimov, A.P.; Kajimoto, T. Feasibility of estimating total stem volume and aboveground biomass from measurement on the largest trees in even-aged pure stands. Can. J. For. Res.
**2001**, 31, 2042–2048. [Google Scholar] [CrossRef] - Mérian, P.; Bert, D.; Lebourgeois, F. An approach for quantifying and correcting sample size-related bias in population estimates of climate-tree growth relationships. For. Sci.
**2013**, 59, 444–452. [Google Scholar] [CrossRef] - Nehrbass-Ahles, C.; Babst, F.; Klesse, S.; Nöttzli, M.; Bouriaud, O.; Neukom, R.; Dobbertin, M.; Frank, D. The influence of sampling design on tree-ring based quantification of forest growth. Glob. Chang. Biol.
**2014**, 20, 2867–2885. [Google Scholar] [CrossRef] [PubMed] - Sharma, M.; Zhang, S.Y. Height-diameter models using stand characteristics for Pinus banksiana and Picea mariana. Scand. J. For. Res.
**2004**, 19, 442–451. [Google Scholar] [CrossRef] - Sharma, M.; Zhang, S.Y. Variable-exponent taper equations for jack pine, black spruce and balsam fir in eastern Canada. For. Ecol. Manag.
**2004**, 198, 39–53. [Google Scholar] [CrossRef] - Sharma, M.; Parton, J. Modelling stand density effects on taper for jack pine and black spruce plantations using dimensional analysis. For. Sci.
**2009**, 55, 268–282. [Google Scholar] - Almedag, I.S.; Stiell, W.M. Spacing and Age Effects on Biomass Production in Red Pine Plantations. For. Chron.
**1982**, 58, 220–224. [Google Scholar] [CrossRef]

**Figure 1.**Relative error in estimation of volume increment from DBH reconstructed from tree-ring data, in comparison to volume increment derived from whole stem analysis for the same trees. Errors are plotted by species (rows) and 5 cm DBH class. The bars represent the range of the 2.5th and 97.5th percentiles of the relative errors in each class. Bars are plotted in different shades as a function of the percentile location of zero with the distribution of errors in a diameter class, and interpreted as described in the text. The columns represent different potential methods for estimating volume increment, national equations using DBH only (VNd), national equations using DBH and raw HT (VNdh), national equations using DBH and corrected height (VNdhc), regional equations using DBH and raw HT (VRdh), and regional equations using DBH and corrected height (VRdhc).

**Figure 2.**Time series of above ground volume increment (m

^{3}·ha

^{−1}·year

^{−1}) with stand age for a 900 m

^{2}fixed area jack pine plot in Saskatchewan, Canada, for which all live and dead trees present in the stand at age 82 were sampled at breast height for ring width measurement. The line plot represents volume increment derived from these measurements using a regional volume model using corrected height as input. Error bars represent the 2.5th and 97.5th percentiles of stand level estimates of volume increment, derived from diameter class-based relative errors (inset graph) derived from the observed difference in breast height and whole tree-derived growth increment for this species and volume estimation method.

Species | DBH (cm) | Height (m) | Age (Years) | Year Sampled (Year (n)) |
---|---|---|---|---|

White spruce (SW) (Picea glauca) | 23.0 (6.2, 51.4) | 18.7 (6.7, 33.7) | 86 (15, 226) | 1994 (5) |

2005 (4) | ||||

2006 (11) | ||||

2010 (8) | ||||

Black spruce (SB) (Picea mariana) | 11.8 (5.0, 24.6) | 10.8 (6.4, 20.9) | 89 (18, 222) | 1994 (26) |

2005 (19) | ||||

2006 (16) | ||||

2010 (7) | ||||

Trembling aspen (TA) (Populus tremuloides) | 21.4 (5.3, 54.8) | 17.7 (6.5, 35.6) | 69 (19, 176) | 1994 (9) |

2005 (15) | ||||

2010 (7) | ||||

Jack pine (PJ) (Pinus banksiana) | 13.1 (7.0, 18.6) | 12.3 (8.5, 15.8) | 64 (52, 76) | 1994 (15) |

Lodgepole pine (PL) (Pinus contorta) | 15.3 (4.2, 27.0) | 14.7 (5.8, 28.1) | 77 (14, 153) | 2005 (24) |

2006 (6) |

Metric | Comparison | Description | References for Equations and Parameters |
---|---|---|---|

(A) Volume | (1) National DBH | (1.1) Volume is estimated from DBH only, using a national equation | [26] |

(2) National DBH and HT | (2.1) Volume is estimated from DBH and uncorrected height (HTr), using a national equation. | [26]; heights as in B1.1 or B1.2 | |

(2.2) Volume is estimated from DBH and corrected height (HTc) using a national volume equation | |||

(3) Regional DBH and HT | (3.1) Volume is estimated from DBH and uncorrected height (HTr), using a regional equation. | [27] for the equation formulation, Regional parameters from published sources for Saskatchewan [28], Manitoba [29], Alberta [30], and the Northwest Territories [30]. Heights estimated as in B1.1 or B1.2 | |

(3.2) Volume is estimated from DBH and corrected height (HTc) using a regional equation | |||

(B) Tree height | (1) HT DBH model | (1.1) Heights estimated from diameters reconstructed on the breast height sample are compared to heights interpolated between stem analysis sections. | (1.1 and 1.2) Provincial parameter sets for trees in Manitoba [29]. Alberta parameter sets for other provinces (NWT, SK, and AB) [31] |

(1.2) Heights estimated as above, but a correction factor is calculated from the difference between measured and predicted height at time of sampling, and applied to the rest of the height time series. |

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**MDPI and ACS Style**

Metsaranta, J.M.; Bhatti, J.S.
Evaluation of Whole Tree Growth Increment Derived from Tree-Ring Series for Use in Assessments of Changes in Forest Productivity across Various Spatial Scales. *Forests* **2016**, *7*, 303.
https://doi.org/10.3390/f7120303

**AMA Style**

Metsaranta JM, Bhatti JS.
Evaluation of Whole Tree Growth Increment Derived from Tree-Ring Series for Use in Assessments of Changes in Forest Productivity across Various Spatial Scales. *Forests*. 2016; 7(12):303.
https://doi.org/10.3390/f7120303

**Chicago/Turabian Style**

Metsaranta, Juha M., and Jagtar S. Bhatti.
2016. "Evaluation of Whole Tree Growth Increment Derived from Tree-Ring Series for Use in Assessments of Changes in Forest Productivity across Various Spatial Scales" *Forests* 7, no. 12: 303.
https://doi.org/10.3390/f7120303