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Uncertainty in detecting climate change impact on the projected yield of black spruce (Picea mariana)
Forest Ecology and Management 259 (2010) 730–738
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Forest Ecology and Management journal homepage: www.elsevier.com/locate/foreco
Uncertainty in detecting climate change impact on the projected yield of black spruce (Picea mariana) Se´bastien Coulombe a, Pierre Y. Bernier b,*, Fre´de´ric Raulier a a b
Faculte´ de foresterie et de ge´omatique, Universite´ Laval, Que´bec, QC G1K 7P4, Canada Natural Resources Canada, Canadian Forest Service, P.O. Box 10380, Stn. Sainte-Foy, Quebec, QC G1V 4C7, Canada
A R T I C L E I N F O
A B S T R A C T
Article history: Received 26 January 2009 Received in revised form 2 June 2009 Accepted 21 June 2009
The empirical growth and yield (G&Y) curves used in most timber supply models assume that growth conditions are invariable over time, which may not be correct given the projected future climate. However, errors in G&Y models can be quite large, and we therefore wanted to know the probability of detecting climate change-induced growth anomalies as a departure from current G&Y predictions. The work was carried out in a boreal forest study area in Eastern Canada, where Picea mariana Mill. BSP (black spruce) is the dominant species. Climate change effects were incorporated into G&Y predictions as correction factors obtained from process-based simulations of growth using current or projected climate. Uncertainty in G&Y projections was quantified through the inclusion of sampling and model errors in a bootstrap re-sampling scheme that yielded a percentile distribution of possible differences between G&Y curves that included or did not include climate change effects. Results yielded an average projected increase in productivity of 29% under future climate conditions for the black spruce strata in the study area. The probability of the climate change-modified G&Y predictions being significantly different from the current G&Y projections is 75% when considering the sampling error alone, and of 67% when both the sampling and modelling errors are included. Although incomplete in terms of what sources of error have been included, this study demonstrates the type of information that can be generated on the propagation of uncertainty in G&Y projections and, ultimately, on timber supply. Crown Copyright ß 2009 Published by Elsevier B.V. All rights reserved.
Keywords: Error propagation Timber supply modelling Boreal forest
1. Introduction Timber supply analyses project future harvests and their effects over a long period in order to maintain equilibrium between timber harvest levels and various economic, social and ecological objectives. In boreal forests, the usual horizon for analysis covers 150 years or more, so as to detect and avoid the negative effects of a sustained harvest level over more than one rotation. Timber supply analyses are based on the modelling of changes in standing merchantable timber volumes over time and, in practice, use empirical growth and yield (G&Y) functions that are based solely on observations and thus capture realized growth under past climatic conditions. The use of these models to estimate future timber volumes is therefore based on the implicit assumption that future growth conditions for trees will be similar to past conditions, an assumption that is not likely to hold given the
* Corresponding author. Tel.: +1 418 648 4524; fax: +1 418 648 5849. E-mail address: [email protected] (P.Y. Bernier).
projected future climate (Matala et al., 2003, 2005; Spittlehouse, 2005; Hall et al., 2006). In contrast to traditional G&Y models, process-based growth models can be designed to account for climate effects on physiological or growth processes, and may therefore provide estimates of tree growth response to past or new environmental conditions (Landsberg, 2003; Misson et al., 2004; Girardin et al., 2008). However, timber supply modellers generally consider process-based models as less robust than traditional growth and yield models because they lack the safeguards and general robustness offered by empirical relationships (Mohren and Burkhart, 1994). It is nevertheless possible to reconcile these differences by opting for a complimentary use of both processbased and empirical models. For example, Matala et al. (2005) used a simple transfer function to incorporate the process-based modelled response of tree growth to changes in temperature and CO2 concentration into the growth and yield model currently used in Finland. The resulting model is dynamically coupled to climate, yet still compatible with traditional forest management planning tasks. Although landscape-level processes such as fire or insects strongly affect long-term timber supply (Kurz and Apps,
0378-1127/$ – see front matter . Crown Copyright ß 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2009.06.028
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1999), the incorporation of direct effects of climate change on tree growth could further improve the overall timber supply forecast. The reality, however, is that modelling is inherently imperfect, and that all predictions contain an error term. This notion of error is important because, far from simply being noise, it gives information to both the modeller and the manager. In effect, it is possible that potential climate change effects remain hidden in the noise generated by uncertainty and imprecision factors within the models. Therefore, before deciding on the inclusion of climate change effects in timber supply analyses, it is first necessary to evaluate our actual capacity to distinguish these effects from the uncertainty generated by current procedures. In this study, we propose to investigate the extent to which the error within one component of the timber supply analysis, the G&Y models, may hide the expression of modified stand-level growth due to climate change. As this cannot be done for all growth and yield models, nor can we incorporate all sources of errors, our analysis concentrates on the yield tables currently used in Quebec (Pothier and Savard, 1998), and considers only the uncertainty generated by sampling and growth modelling. The specific objectives of our study are to provide answers to two questions: What is the expected effect of climate change on the yield curves of boreal forest stands? What is the probability that this effect be discernable beyond the current uncertainty associated with longterm volume predictions from growth and yield models? The work focuses on an area of the Canadian boreal forest dominated by Picea mariana Mill. BSP (black spruce) stands. 2. Materials and methods 2.1. Study area The study was carried out in a 65 km2 study area near Chibougamau, Quebec, Canada (Fig. 1). The region is located
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within the ‘‘Black Spruce and Moss’’ bioclimatic domain and part of the Lac Ope´misca regional landscape, characterized by low mean annual temperatures (0.5 8C to 0 8C), flat landscapes, and annual precipitation between 800 mm and 1000 mm (Robitaille and Saucier, 1998). The forest is dominated by black spruce and is quite homogeneous in terms of stand species composition and structure since most of the area was affected by a fire 120 years ago. Deep tills and organic soils account for 44% and 37% of the territory, respectively. This study area is also used as one of two forested landscapes for a modelling comparison project carried out by the Fluxnet-Canada Research Network/Canadian Carbon Program (Trofymow et al., 2008; Margolis et al., 2006). 2.2. Data description Forest stratification was photointerpreted from a mosaic of aerial photos at a scale of 1:20,000. The photointerpretation followed the current provincial norms for areas with a cover density class higher than 25%. Stand polygons were delineated and species composition, cover density, height class, age class, stand origin and year of origin were estimated by experienced photointerpreters. Stand polygons were aggregated into strata on the basis of similarity in photointerpreted attributes. Biometric characterization of the strata followed a method similar to that used by the provincial forest inventory direction, based on the imputation of inventory sample plots located in stands with similar photointerpreted properties, with a minimum target of 15 plots per stratum. Plot selection was done within a plot database of approximately 150,000 temporary sample plots (TSP) established by the Ministe`re des Ressources naturelles et de la faune du Que´bec (MRNFQ) between 1983 and 2001 (second and third forest inventory programs). The study area contains only a few TSPs, and nearly all plots needed for strata characterization are located outside of the study area. Plot selection was done within the constraint of the hierarchical ecological forest classification of Robitaille and Saucier (1998) in order to minimize inherent ecological differences between the selected plots and the target strata. Matching plots were preferentially selected from within the smallest possible ecological landscape unit within which laid the study area, gradually expanding the search through five hierarchical levels. Within the same iterative process, specific photointerpreted attributes were gradually dropped or combined, and strata were aggregated as needed in order to limit the plot search to the closest ecological units. At the end of the aggregation procedure, stands within a stratum had the following attributes in common: species composition, cover density class, height class and age class. For this exercise, we have retained the 10 strata dominated by black spruce out of the 22 strata generated by the exercise for the study area, for a total cover of 34.2 km2 out of the study area’s 56 km2 (Table 1). We use the notion of ‘‘precision’’ in this text to define withinstratum variability, in line with the procedure currently in use by the forest inventory unit of the MRNFQ. This index of variability is defined as the complementary value of the ratio between the confidence interval of a mean and its mean (see footnote of Table 1), as applied to the set of temporary sample plots used to define stratum-level properties. 2.3. The models
Fig. 1. Location of the Chibougamau study area, co-located with a flux tower site of Fluxnet-Canada.
The change in merchantable volume over time within each of the selected plots was first simulated using the G&Y model of Pothier and Savard (1998). This model predicts merchantable volume as a function of stand species composition, stand age, a relative density index and a site index. It is calibrated with the TSP
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Table 1 Strata-level means of initial properties (standard errors in parentheses), modelled effects of climate change (CC effects, in % increase above current growth and yield predictions) and probability to detect the mean effect climate change on growth as a positive deviation from current growth and yield predictions. Strata
Initial properties Volume (m3/ha)
A E F H I J C D G B
21 65 58 101 105 114 5 5 4 60 a
(3) (9) (7) (13) (12) (11) (1) (2) (1) (11)
Precisiona (%)
73 71 75 73 77 81 37 24 45 59
Simulation results Density (stems/ha)
5,030 6,659 5,357 2,525 7,223 4,999 16,197 12,648 28,677 4,223
(699) (746) (774) (276) (1419) (699) (1702) (1755) (4871) (504)
Age (years)
5 69 71 65 61 77 33 31 38 121
(1) (6) (6) (1) (2) (5) (3) (3) (4) (9)
Height (m)
9.4 (0.2) 10.6 (0.5) 10.7 (0.3) 14 (0.4) 11.3 (0.5) 12.9 (0.6) 6.1 (0.4) 5.5 (0.4) 6 (0.2) 12.2 (0.6)
Area (ha)
822 326 291 178 7 7 501 357 183 752
Plots (numbers)
23 29 32 15 24 24 30 12 13 14
CC effects (%)
Probability (%)
Sampling error
Sampling + model errors
60 years
100 years
60 years
100 years
60 years
100 years
27 27 26 19 28 27 31 33 36 29
28 28 27 22 29 28 32 33 37 29
95 90 90 >95 >95 95 80 65 70 75
95 85 90 >95 >95 90 80 65 70 65
80 85 85 90 95 90 70 65 65 70
70 75 80 80 85 80 65 60 60 60
Precision at the 95% probability level on merchantable volume = 100% (t (standard error/mean) 100).
data from the MRNFQ database, using plots located in monospecific (more than 75% in merchantable basal area), undisturbed stands. We followed the operational procedure for deriving curves for multispecies plots by summing the monospecific reference curves of the species found in the plots times a volume adjustment factor corresponding to the ratio of observed to predicted volume. Assessment of climate change effects on forest productivity was done using the process-based model StandLEAP (Raulier et al., 2000; Girardin et al., 2008), which is based on the 3-PG model of Landsberg and Waring (1997). In StandLEAP, photosynthetically active radiation absorbed by the canopy (APAR) is converted into gross primary productivity (GPP, mol m2 month1) with a radiation use efficiency coefficient (RUE): GPP ¼ APAR RUE
(1)
where RUE ¼ RUE f 1 f 2 . . . f n
(2)
RUE represents a species-specific mean value of RUE. Environmental constraints on RUE take on the form of species-specific multipliers (f1. . .fn) with a value close to unity under average conditions, but which can decrease to represent increasing limitations (e.g., soil water deficit) or increase as conditions improve towards optimum (e.g., temperature): f n ¼ 1 þ blx
x x¯ x x¯ 2 þ bqx x¯ x¯
(3)
Parameters blx and bqx represent linear and quadratic effects of the x variable, and x¯ is the mean observed x value over the period of calibration. Multipliers represent the impact of soil drought (fu as in Landsberg and Waring, 1997; Bernier et al., 2002, 2006), frost (fF as in Aber et al., 1996) (both limited to a maximum of 1.0), mean maximum and minimum daily air temperature, vapour pressure deficit (VPD), monthly radiation, and leaf area index (where values greater than 1.0 are possible) on GPP. Respiration is computed as a fixed species-specific proportion of GPP (Malhi et al., 1999; DeLucia et al., 2007), and net primary productivity (NPP; g m2 month1) is computed monthly as GPP minus respiration. As in 3-PG, part of NPP is first allocated to fine roots (Landsberg and Waring, 1997, their Eq. (13)) on a yearly basis and then to replacement of carbon biomass lost to leaf and fine woody litter turnover. The remaining NPP is then allocated to
increments in stand carbon compartments of foliage, branches, coarse roots and stems (Girardin et al., 2008). Canopy light absorption and photosynthesis parameters were adjusted to results obtained with FineLEAP, a detailed multilayer, hourly time step model of canopy photosynthesis and transpiration (Raulier et al., 2000; Bernier et al., 2001). Additional details of the procedure and origin of the basic field measurements can be found in Hall et al. (2006, their Table 2). In particular, data for P. mariana were obtained in part from the BOREAS archives (DAAC database: http://www-eosdis.ornl.gov/NPP/npp_home.html). Required phytometric and soil inputs to StandLEAP were estimated from the inventory data obtained on the selected plots. Plot aboveground biomass was estimated by cumulating individual tree biomasses calculated with national biomass equations of Lambert et al. (2005). Time series of monthly mean daily maximum and minimum temperatures and monthly total precipitation (mm) were generated with the weather generation module in the BIOSIM Pest Management Planning Decision Support program (Re´gnie`re and St-Amant, 2007), using the current (1961–1990) and projected (2041–2070) climate normals. The module interpolates climatic normals of neighbouring weather stations to generate daily series of temperature and precipitation as a function of geographic position, altitude and exposure (a combination of slope and aspect) of individual locations. It also generates between-month variability that is added to the normals in order to produce plausible weather time series. The climatic normals used as references in BIOSIM were generated from the Canadian regional climate model, version ‘‘CRCM4.1.1 acu’’, driven by outputs of the third generation coupled global climate model using the IPCC SRES A2 greenhouse gas and aerosol scenario (Fig. 2; Travis Logan, Ouranos Consortium, pers. comm., 2008). The A2 storyline is one of the most pessimistic of all IPCC storylines in terms of increased greenhouse gas emissions and resulting increases in global temperatures (IPCC, 2001). 2.4. Modelling of plot-level climate change effects Effects of climate change on growth and yield were evaluated for each sample plot by comparing the StandLEAP simulation output obtained using the 1961–1990 climate normals with the output obtained using the projected climate scenario for the 2041– 2070 period. Simulations were done with a continual loop of 12 months for both climate scenarios from stand initiation to 100
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replacement, thus generating a set of n plot yield curves in which the same original curve could be represented more than once. This procedure was repeated 5000 times to generate a population of possible stratum-level yield curves. The exercise was done first without considering the modelling error by equating the random number u of Eq. (4) to zero, and a second time with the modelling error by picking a new random number u in Eq. (4) at every bootstrap repetition. This second percentile distribution of plausible stratum yield curves thus included both the sampling and modelling errors. The exercise was done for current and projected climate scenarios. 2.6. Determination of the uncertainty of detecting climate change effects in future growth
Fig. 2. Current (1961–1990) and projected (2041–2070) climate normals for the Black Spruce–Moss ecological domain of Quebec: current (full lines) and projected (dashed lines) means of monthly minimum (squares) and maximum (triangles) air temperature, and of monthly current (empty bars) and projected (shaded bars) precipitation.
years. No gradual change was modelled from the current scenario to the projected scenario. For each sample plot, adjustment factors were computed by 5-year simulation segments as the ratio of the aboveground biomass estimates from the projected and current climate scenarios. These factors were then applied to the yield curves originating from the Pothier and Savard (1998) model to generate merchantable volume projections under a climate change scenario. 2.5. Characterization of the simulation error We considered two error sources: the error associated with merchantable volume increment predictions (the modelling error) and the error associated with the variability in the properties of plots selected to represent a given stratum (the sampling error). Pothier et al. (2004) have shown that the magnitude of the modelling error on the merchantable volume increment predicted using the Pothier and Savard (1998) model for a specific sample plot tends to stay of similar magnitude and sign over time. Using this observation as basic premise, the evolution of the merchantable volume of a plot at a time (Vt) can thus be represented as: vffiffiffiffiffiffiffiffiffiffiffiffiffi u t1 t1 uX X Vt ¼ Vo þ iv;a þ ut s 2ˆ (4) a¼0
a¼0
iv
where Vo is the initial volume, iv;a represents the vector of predicted net volume increments between times 0 and t 1, u is a random number drawn from a standard normal distribution N(0, 1), and s iv is the root mean square error (RMSE) between observed and predicted plot volume increment estimates. This RMSE for black spruce has previously been evaluated at 1.78 m3 ha1 y1 (Raulier et al., 2004) in a comparison between estimated and measured merchantable volume increments in 209 permanent sample plots located in black spruce-dominated stands in Quebec. We used Eq. (4) to add a modelling error to the yield curve computed for each sample plot within each forest stratum. The expected volume growth of a stratum corresponds to the mean of the expected growth of the set of sample plots selected to represent this stratum. The sampling error affecting a stratum curve can thus be associated with the percentile distribution of plausible stratum yield curves. This distribution was approximated with bootstrap re-sampling of the plot yield curves within a stratum (Manly, 1997). For each stratum, the set of the n individual plot yield curves selected to represent it was re-sampled with
The 5000 bootstrap-generated mean yield curves that included the climate change effect were paired randomly to bootstrapgenerated mean curves that did not include the climate change effect. The difference between the curves within each of the 5000 pairs was then used to produce a percentile distribution of expected differences. The percentile at which the zero difference occurred at a given reference age (60 years and 100 years) was considered to be the detection threshold. The exercise was done by stratum, for simulations with the sampling error only, and for simulation with both the sampling and modelling errors. 3. Results 3.1. Effect of the sampling error For our 10 strata, the precision for initial merchantable volumes varied between 24% and 81% (Table 1). For most inventory strata whose mean stand age exceeded 50 years, the precision for merchantable volume was over 70%, a threshold considered acceptable for timber supply analyses in Quebec. These strata included about 50% of the forested area considered in this study. The other 50% of the forest for which precision was much lower was composed mostly of juvenile strata with a cover height of less than 7 m characterized by low merchantable volumes, with the exception of the B stratum, a low density 90-year-old stratum dominated by black spruce, for which the precision was of 59% (Table 1). Estimated changes in merchantable volume over time varied greatly between plots among individual strata, and these differences were mostly due to initial differences in mean plotlevel tree age and volume as well as, to a lesser extent, differences in tree species composition. Examples of growth trajectories of individual plots within particular strata are given in Fig. 3. Negative growth is generated by the senescence component of the G&Y model, and very early senescence in the figure indicates that the mean plot-level tree age was relatively high at the start of the simulation period. Even with a good within-strata precision for initial mean merchantable volume, yield curves of plots within a given stratum showed an important variability. For instance, stratum A (Fig. 3) had a precision of 73% for the initial volume, and the yield curves for the underlying plots were relatively well grouped. By contrast, the yield curves of plots from the juvenile stratum (stratum G) diverged strongly from their common origin, and produced a highly skewed curve distribution. The plots for the older B and J strata had very different initial mean plot-level tree age that, in turn, generated very different growth trajectories, including strong senescence in some of the plots. 3.2. Effect of the modelling error Inclusion of the modelling error added a large degree of variability to the possible mean yield curves, as illustrated by the
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Fig. 3. Growth trajectories of individual temporary sample plots selected to represent four different strata, as predicted from the Pothier and Savard (1998) growth and yield curves. Starting plot age corresponds to time of inventory. Negative growth indicates a modelled senescence.
difference in the spread of the percentile distribution between the sampling error only and the combination of sampling and modelling errors (Fig. 4a and b). However, the variability introduced by the modelling error was not as large as the initial variability caused by the sampling error. 3.3. Climate change effect on merchantable volume increment Simulation results using StandLEAP suggest that, under the projected climatic scenario, mean merchantable volume of individual strata would be 22–37% greater than under current climatic conditions after 100 years of simulation (Table 1). The mean growth increase in merchantable volume of all the strata dominated by black spruce was calculated to be 29%. The results obtained from StandLEAP simulations for each individual plot were transferred to the plot-level yield curves using simple adjustment factors calculated from the StandLEAP simulations. 3.4. Estimating the probability of detecting a climate change effect The 5000 bootstrap repetitions were sufficient to stabilize the percentile distributions of stratum yield curves, as estimated by the stabilization of the u frequency distribution (Eq. (4)) (data not shown). Fig. 4a shows the distribution of the differences between curves with and without a climate change effect for each of the 10 black spruce-dominated strata within the study area, as a result of the sampling error. The addition of the modelling error to the predictions had no effect on the mean difference of individual strata, but resulted in an expansion of the percentile distribution around this mean. Also, because the error structure often caused a divergence in within-strata plot-level curves to increase with time, the probability of detecting the effect of climate change often decreased with time. The line of no difference between the set of curves with and without climate change at 100 years of simulation was found on average at the 75th percentile when only the sampling error was taken into account, and at the 67th percentile when both the
sampling and modelling errors were included. In other words, in the repeated simulations of strata-level growth using curves that included climate change and curves that did not include climate change, the inclusion of climate change resulted in a greater modelled growth 67% of the time when considering both sources of error. The percent success in detecting the climate change impact on growth was greater at 60 years of simulation. Overall, results for mature strata were more accurate because of the smaller sampling error within these strata. Young and over-mature strata had a greater sampling error, and the probability of detecting the increased growth due to climate change was reduced accordingly. Following the guidance notes on addressing uncertainties from the Intergovernmental Panel on Climate Change (Moss and Schneider, 2000), a likelihood of occurrence above 66% should be translated as ‘‘likely’’. 4. Discussion Consideration of both the sampling and modelling errors provides essential information for evaluating the outcomes derived from the incorporation of climate change effects within growth and yield equations. In our case, within the limits of this study, we found a relatively large potential climate change effect but a moderate capacity to detect this effect beyond the uncertainty inherent to the growth prediction system. The percentage of success in detecting a change in predicted volumes with the inclusion of climate change is far less than the levels of ‘‘type I’’ errors of 1% and 5% generally used by scientists, but may be more in the range of the uncertainties that normally confront decision-makers as part of their decision-making process. Ignoring uncertainty in forest planning leads to non-optimal, overoptimistic, and sometimes unfeasible decisions that may lead to net present value losses mostly because of improper planning of harvest timing (Pukkala and Kangas, 1996; Eid, 2000; Borders et al., 2008). As most black spruce forests in Quebec have an abundance of over-mature stands (Gauthier, 2004), the critical period that
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determines the harvest level under a strict even-flow constraint (sensu Davis et al., 2001) tends to appear late in the planning horizon. The actual harvest level is thus expected to be sensitive to climate change. Consequently, a decision-maker should seriously
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consider including climate change effects, or the uncertainty generated by the range of possible futures, into his yield curves, especially for the youngest strata, at least as an alternative scenario. Furthermore, Gauthier (2004) has shown that timber
Fig. 4. Percentile distribution of differences in mean merchantable volumes between paired bootstrap-generated mean stratum growth trajectories simulated with and without climate change effects. Results are shown with the sampling error only (a) or with the sampling and modelling error combined (b). The upper and lower solid lines represent the 5% and 95% percentiles, while the dashed lines represent the 25% and 75% percentiles. The central solid line represents the mean difference.
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Fig. 4. (Continued ).
supply calculations in black spruce forests are very sensitive to changes in the age at which stands become harvestable. Given the low productivity of the black spruce stands considered in this study, a long-term increase of 30% in volume yield corresponds
approximately to a decrease of 10% in harvest age following the yield tables of Pothier and Savard (1998), and thus to a potential increase of 10% in the harvest level. Such a potentially important increase cannot be neglected and also needs to be weighed against
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the probable impacts of climate change on natural disturbances as fire activity is expected to increase in our study area (Flannigan et al., 2005). The 29% cumulative growth increase modelled over more than half a century with StandLEAP is relatively large compared to similar exercises carried out elsewhere in the Canadian boreal forest. Girardin et al. (2008), also using StandLEAP, came to the conclusion that climate change would actually cause growth to decrease slightly in three boreal forest tree species, including P. mariana, in drier Western Canada forests on account of the effect of increased temperatures on the site-level water budgets. Similar results were obtained with Pinus contorta (Chhin et al., 2008), also as a result of a strong drying trend. An analysis by Bunn et al. (2005) suggests a general lack of response of the North American boreal forest to future climate change. By contrast, growth in European forests has been increasing over the past decades, and further increases are expected as a result of climate change. Kelloma¨ki et al. (2008) suggest a potential increase of 44% in Finnish forests. CO2 growth enhancement (Norby et al., 2005), which is not included in StandLEAP, could also generate additional growth, but nitrogen limitation, common to many boreal forest environments, could dampen this effect (Oren et al., 2001). Overall, given these considerations, a 29% growth increment is at the upper end of possible climate change effects for boreal forests in Eastern Canada. Smaller growth increments would make detection of modelled increases more difficult and would lower the interest of considering them during the planning exercise. The modelled change in black spruce growth depends on the climate anomaly predictions, which are themselves dependant on the choice of the emission scenario and on the choice of the global circulation model used to translate this scenario into climate anomalies. The A2 human development scenario is very carbon intensive and results in some of the more extreme predictions in climate anomalies. The use of a less carbonintensive scenario would have generated a lower growth increment, while the use of the most carbon-intensive A1F1 scenario (IPCC, 2001) could have generated an even greater modelled black spruce growth response under the assumption of an absence of other limiting growth factors. Indeed, Raupach et al. (2007) report global CO2 emissions as far back as 2005 that track or exceed the higher forecasts of the A1F1 scenario, making the use of carbon-intensive scenarios such as the A1F1 or the A2 plausible. Also, we choose to use nearer term climate projections (2041–2070). Use of predictions for the 2021–2100 period, during which climate anomalies are projected to be even greater, would have generated different growth predictions. At a broader level, however, the uncertainty surrounding the choice of scenarios, and even the choice of global circulation models, can be lumped into a broad error term (which was not considered in this analysis) surrounding the modelling of climate change effects on forest productivity. This error is actually a summation of the uncertainties from the human development scenarios, their translation into greenhouse gas (GHG) emission scenarios, the modelling of global climate anomalies based on the additional GHG climate forcing, the downscaling of global climate to regional climate, and the biophysical modelling of tree growth. Research is starting to address the issue of uncertainties in atmospheric GHG projections (van Vuuren et al., 2008) and, more importantly for the problem at hand, in forest-level predictions. Simulations by Xu et al. (2009) suggest that differences among projected climate anomalies from different global circulation models and different GHG emission scenarios are sufficient to generate a large variability in predicted landscape-level forest composition. This
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type of approach could be used to determine an additional error term for the prediction of volume or biomass increment. In the world of statistics, the sampling error is not an inherent property of the population as it can be brought down by an increase in sampling size. In the real world of timber supply modelling, however, there are limits imposed on sample size, especially when dealing with a very large and varied forest area such as Canada’s boreal forest. Budget constraints limit the number of samples that can be dedicated to specific forest types within given ecological regions. Expansion of the imputation exercise to incorporate a larger sample size generates additional variability as plots from different ecological regions or from slightly different forest strata must be included to meet new targets of plot numbers. This increased variability would likely eliminate gains made by the increased sample size. Forest inventory and G&Y models, even without climate change effects, carry forward a significant amount of uncertainty that spills onto timber supply estimates in addition to masking potential climate change effects. Other components such as the modelling of forest succession following different degrees or types of disturbances add to the uncertainty of predictions over multirotations. Of potentially great significance to long-term timber supply predictions are natural disturbances. Incorporation of the impact of natural disturbances into timber supply predictions is still a work in progress because of the complexity associated with the inclusion of stochastic phenomena in real timber supply analyses (Davis et al., 2001). In addition, disturbance regimes must be adjusted to the projected climatic conditions in order to determine which current harvest levels are more robust to unexpected events. 5. Conclusion The underlying question in this work is whether or not the timber supply models that are currently run over long time scales without the inclusion of climate change effects provide valid results. The work shows that the term ‘‘valid’’ is more a matter of degree of comfort with risk than a strict yes or no, but it also shows that the risk must be calculated in order to be considered by forest managers. Nelson (2003) compared a timber supply analysis done without considering uncertainty to ‘‘running your vehicle’s engine at the ‘‘red line’’ for its entire life – hardly a sustainable strategy’’. As errors associated with climatic predictions appear largely irreducible (Dessai et al., 2009), managers will have to adapt to the new reality of an uncertain future. Climate change will likely impact trees and forested landscapes within the current lifespan of most tree species. Treating predictions as deterministic may work over very short time scales, and one strategy may be to proceed in this manner and revisit predictions on a periodic basis in order to account for ongoing changes. However, such an approach pays no attention to the advantages offered by risk analysis, for instance, when dealing with stochastic variations of timber prices (e.g., Zhou et al., 2008). Ideally, models should thus incorporate some degree of uncertainty analysis. Uncertainty is information that helps define the confidence we have in future states on which current actions are based, as is the case in timber supply modelling. It also helps focus research resources on the areas that show the greatest uncertainties. Tracking uncertainty and its reduction through research efforts also provides a measure of advancement in our understanding of forest ecosystems and their interactions with climate. Acknowledgments We thank the personnel from the Canadian Forest Service’s Laurentian Forestry Centre who were involved in the significant
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effort needed to construct and photointerpret the photo mosaics, in particular Luc Guindon, Guy Simard and Philippe Villemaire. Essential statistical support for performing the forest stratification and characterization exercises was provided by Xiaojing Guo, also with CFS. We also thank Travis Logan and the Ouranos Consortium for the provision of climate projections, and acknowledge the use of BOREAS ecophysiological data from the Oak Ridge National Laboratory’s Distributed Active Archive Centre (ORNL DAAC). Funding to SC was provided by Natural Resources Canada’s Program for Energy Research and Development. Comments made by the anonymous reviewers helped improve the manuscript. References Aber, J.D., Reich, P.B., Goulden, M.L., 1996. Extrapolating leaf CO2 exchange to the canopy: a generalized model of forest photosynthesis compared with measurements by Eddy correlation. Oecologia 106, 257–265. Bernier, P.Y., Raulier, F., Stenberg, P., Ung, C.-H., 2001. The importance of needle age and shoot structure on canopy net photosynthesis of balsam fir (Abies balsamea): a spatially inexplicit modelling analysis. Tree Physiol. 21, 815–830. Bernier, P.Y., Bre´da, N., Granier, A., Raulier, F., Mathieu, F., 2002. Validation of a canopy gas exchange model and derivation of a soil water modifier for transpiration for sugar maple (Acer saccharum Marsh.) using sap flow density measurements. For. Ecol. Manag. 163, 185–196. Bernier, P.Y., Bartlett, P., Black, T.A., Barr, A., Kljun, N., McCaughey, J.H., 2006. Drought constraints on transpiration and canopy conductance in mature aspen and jack pine stands. Agric. For. Meteorol. 140, 64–78. Borders, B.E., Harrison, W.M., Clutter, M.L., Shiver, B.D., Souter, R.A., 2008. The value of timber inventory information for management planning. Can. J. For. Res. 38, 2287–2294. Bunn, A.G., Goetz, S.J., Fiske, G.J., 2005. Observed and predicted responses of plant growth to climate across Canada. Geophys. Res. Lett. 32, L1710, doi:10.1029/ 2005GL023646. Chhin, S., Hogg, E.H., Lieffers, V.J., Huang, S., 2008. Potential effects of climate change on the growth of lodgepole pine across diameter size classes and ecological regions. For. Ecol. Manag. 256, 1692–1703. Davis, L.S., Johnson, K.N., Bettinger, P., Howard, T.E., 2001. Forest Management to Sustain Ecological, Economic, and Social Values, 4th ed. McGraw-Hill Publishing Company, New York, NY, USA, 804 pp. DeLucia, E.H., Drake, J.E., Thomas, R.B., Gonzalez-Meler, M., 2007. Forest carbon use efficiency: is respiration a constant fraction of gross primary production? Glob. Change Biol. 13, 1157–1167. Dessai, S., Hulme, M., Lempert, R., Pielke Jr., R., 2009. Do we need better predictions to adapt to a changing climate? EOS 90, 111–112. Eid, T., 2000. Use of uncertain inventory data in forestry scenario models and consequential incorrect harvest decisions. Silva Fenn. 34, 89–100. Flannigan, M.D., Logan, K.A., Amiro, B.D., Skinner, W.R., Stocks, B.J., 2005. Future area burned in Canada. Clim. Change 72, 1–16. Gauthier, G., 2004. Analyse de sensibilite´ d’un calcul de possibilite´ forestie`re aux hypothe`ses d’ame´nagement applicables au mode`le de simulation « par courbe ». In: Rapport de´taille´ du comite´ scientifique charge´ d’examiner le calcul de la possibilite´ forestie`re. Ministe`re des Ressources naturelles, de la Faune et des Parcs, Direction de la recherche forestie`re, Que´bec, pp. 189–262. Girardin, M.P., Raulier, F., Bernier, P.Y., Tardif, J.C., 2008. Response of tree growth to a changing climate in boreal central Canada: a comparison of empirical, processbased, and hybrid modelling approaches. Ecol. Model. 213, 209–228. Hall, R.J., Raulier, F., Price, D.T., Arsenault, E., Bernier, P.Y., Case, B.S., Guo, X., 2006. Integrating remote sensing and climate data with process-based models to map forest productivity within west-central Alberta’s boreal forest: Ecoleap-West. For. Chron. 82, 159–176. IPCC (Intergovernmental Panel on Climate Change), 2001. The IPCC Special Report on Emissions Scenarios. GRID-Arendal, Norway. Available at: http://www. grida.no/publications/other/ipcc-sr/. Kelloma¨ki, S., Peltola, H., Nuutinen, T., Korhonen, K.T., Strandman, H., 2008. Sensitivity of managed boreal forests in Finland to climate change, with implications for adaptive management. Philos. Trans., R. Soc. Land. Serv. B: Biol. Sci. 363, 2339–2349. Kurz, W.A., Apps, M.J., 1999. A 70-year retrospective analysis of carbon fluxes in the Canadian forest sector. Ecol. Appl. 9, 526–547. Lambert, M.-C., Ung, C.-H., Raulier, F., 2005. Canadian national tree aboveground biomass equations. Can. J. For. Res. 35, 1996–2018. Landsberg, J., 2003. Modelling forest ecosystems: state of the art, challenges, and future directions. Can. J. For. Res. 33, 385–397.
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Forest Ecology and Management journal homepage: www.elsevier.com/locate/foreco
Uncertainty in detecting climate change impact on the projected yield of black spruce (Picea mariana) Se´bastien Coulombe a, Pierre Y. Bernier b,*, Fre´de´ric Raulier a a b
Faculte´ de foresterie et de ge´omatique, Universite´ Laval, Que´bec, QC G1K 7P4, Canada Natural Resources Canada, Canadian Forest Service, P.O. Box 10380, Stn. Sainte-Foy, Quebec, QC G1V 4C7, Canada
A R T I C L E I N F O
A B S T R A C T
Article history: Received 26 January 2009 Received in revised form 2 June 2009 Accepted 21 June 2009
The empirical growth and yield (G&Y) curves used in most timber supply models assume that growth conditions are invariable over time, which may not be correct given the projected future climate. However, errors in G&Y models can be quite large, and we therefore wanted to know the probability of detecting climate change-induced growth anomalies as a departure from current G&Y predictions. The work was carried out in a boreal forest study area in Eastern Canada, where Picea mariana Mill. BSP (black spruce) is the dominant species. Climate change effects were incorporated into G&Y predictions as correction factors obtained from process-based simulations of growth using current or projected climate. Uncertainty in G&Y projections was quantified through the inclusion of sampling and model errors in a bootstrap re-sampling scheme that yielded a percentile distribution of possible differences between G&Y curves that included or did not include climate change effects. Results yielded an average projected increase in productivity of 29% under future climate conditions for the black spruce strata in the study area. The probability of the climate change-modified G&Y predictions being significantly different from the current G&Y projections is 75% when considering the sampling error alone, and of 67% when both the sampling and modelling errors are included. Although incomplete in terms of what sources of error have been included, this study demonstrates the type of information that can be generated on the propagation of uncertainty in G&Y projections and, ultimately, on timber supply. Crown Copyright ß 2009 Published by Elsevier B.V. All rights reserved.
Keywords: Error propagation Timber supply modelling Boreal forest
1. Introduction Timber supply analyses project future harvests and their effects over a long period in order to maintain equilibrium between timber harvest levels and various economic, social and ecological objectives. In boreal forests, the usual horizon for analysis covers 150 years or more, so as to detect and avoid the negative effects of a sustained harvest level over more than one rotation. Timber supply analyses are based on the modelling of changes in standing merchantable timber volumes over time and, in practice, use empirical growth and yield (G&Y) functions that are based solely on observations and thus capture realized growth under past climatic conditions. The use of these models to estimate future timber volumes is therefore based on the implicit assumption that future growth conditions for trees will be similar to past conditions, an assumption that is not likely to hold given the
* Corresponding author. Tel.: +1 418 648 4524; fax: +1 418 648 5849. E-mail address: [email protected] (P.Y. Bernier).
projected future climate (Matala et al., 2003, 2005; Spittlehouse, 2005; Hall et al., 2006). In contrast to traditional G&Y models, process-based growth models can be designed to account for climate effects on physiological or growth processes, and may therefore provide estimates of tree growth response to past or new environmental conditions (Landsberg, 2003; Misson et al., 2004; Girardin et al., 2008). However, timber supply modellers generally consider process-based models as less robust than traditional growth and yield models because they lack the safeguards and general robustness offered by empirical relationships (Mohren and Burkhart, 1994). It is nevertheless possible to reconcile these differences by opting for a complimentary use of both processbased and empirical models. For example, Matala et al. (2005) used a simple transfer function to incorporate the process-based modelled response of tree growth to changes in temperature and CO2 concentration into the growth and yield model currently used in Finland. The resulting model is dynamically coupled to climate, yet still compatible with traditional forest management planning tasks. Although landscape-level processes such as fire or insects strongly affect long-term timber supply (Kurz and Apps,
0378-1127/$ – see front matter . Crown Copyright ß 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2009.06.028
S. Coulombe et al. / Forest Ecology and Management 259 (2010) 730–738
1999), the incorporation of direct effects of climate change on tree growth could further improve the overall timber supply forecast. The reality, however, is that modelling is inherently imperfect, and that all predictions contain an error term. This notion of error is important because, far from simply being noise, it gives information to both the modeller and the manager. In effect, it is possible that potential climate change effects remain hidden in the noise generated by uncertainty and imprecision factors within the models. Therefore, before deciding on the inclusion of climate change effects in timber supply analyses, it is first necessary to evaluate our actual capacity to distinguish these effects from the uncertainty generated by current procedures. In this study, we propose to investigate the extent to which the error within one component of the timber supply analysis, the G&Y models, may hide the expression of modified stand-level growth due to climate change. As this cannot be done for all growth and yield models, nor can we incorporate all sources of errors, our analysis concentrates on the yield tables currently used in Quebec (Pothier and Savard, 1998), and considers only the uncertainty generated by sampling and growth modelling. The specific objectives of our study are to provide answers to two questions: What is the expected effect of climate change on the yield curves of boreal forest stands? What is the probability that this effect be discernable beyond the current uncertainty associated with longterm volume predictions from growth and yield models? The work focuses on an area of the Canadian boreal forest dominated by Picea mariana Mill. BSP (black spruce) stands. 2. Materials and methods 2.1. Study area The study was carried out in a 65 km2 study area near Chibougamau, Quebec, Canada (Fig. 1). The region is located
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within the ‘‘Black Spruce and Moss’’ bioclimatic domain and part of the Lac Ope´misca regional landscape, characterized by low mean annual temperatures (0.5 8C to 0 8C), flat landscapes, and annual precipitation between 800 mm and 1000 mm (Robitaille and Saucier, 1998). The forest is dominated by black spruce and is quite homogeneous in terms of stand species composition and structure since most of the area was affected by a fire 120 years ago. Deep tills and organic soils account for 44% and 37% of the territory, respectively. This study area is also used as one of two forested landscapes for a modelling comparison project carried out by the Fluxnet-Canada Research Network/Canadian Carbon Program (Trofymow et al., 2008; Margolis et al., 2006). 2.2. Data description Forest stratification was photointerpreted from a mosaic of aerial photos at a scale of 1:20,000. The photointerpretation followed the current provincial norms for areas with a cover density class higher than 25%. Stand polygons were delineated and species composition, cover density, height class, age class, stand origin and year of origin were estimated by experienced photointerpreters. Stand polygons were aggregated into strata on the basis of similarity in photointerpreted attributes. Biometric characterization of the strata followed a method similar to that used by the provincial forest inventory direction, based on the imputation of inventory sample plots located in stands with similar photointerpreted properties, with a minimum target of 15 plots per stratum. Plot selection was done within a plot database of approximately 150,000 temporary sample plots (TSP) established by the Ministe`re des Ressources naturelles et de la faune du Que´bec (MRNFQ) between 1983 and 2001 (second and third forest inventory programs). The study area contains only a few TSPs, and nearly all plots needed for strata characterization are located outside of the study area. Plot selection was done within the constraint of the hierarchical ecological forest classification of Robitaille and Saucier (1998) in order to minimize inherent ecological differences between the selected plots and the target strata. Matching plots were preferentially selected from within the smallest possible ecological landscape unit within which laid the study area, gradually expanding the search through five hierarchical levels. Within the same iterative process, specific photointerpreted attributes were gradually dropped or combined, and strata were aggregated as needed in order to limit the plot search to the closest ecological units. At the end of the aggregation procedure, stands within a stratum had the following attributes in common: species composition, cover density class, height class and age class. For this exercise, we have retained the 10 strata dominated by black spruce out of the 22 strata generated by the exercise for the study area, for a total cover of 34.2 km2 out of the study area’s 56 km2 (Table 1). We use the notion of ‘‘precision’’ in this text to define withinstratum variability, in line with the procedure currently in use by the forest inventory unit of the MRNFQ. This index of variability is defined as the complementary value of the ratio between the confidence interval of a mean and its mean (see footnote of Table 1), as applied to the set of temporary sample plots used to define stratum-level properties. 2.3. The models
Fig. 1. Location of the Chibougamau study area, co-located with a flux tower site of Fluxnet-Canada.
The change in merchantable volume over time within each of the selected plots was first simulated using the G&Y model of Pothier and Savard (1998). This model predicts merchantable volume as a function of stand species composition, stand age, a relative density index and a site index. It is calibrated with the TSP
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Table 1 Strata-level means of initial properties (standard errors in parentheses), modelled effects of climate change (CC effects, in % increase above current growth and yield predictions) and probability to detect the mean effect climate change on growth as a positive deviation from current growth and yield predictions. Strata
Initial properties Volume (m3/ha)
A E F H I J C D G B
21 65 58 101 105 114 5 5 4 60 a
(3) (9) (7) (13) (12) (11) (1) (2) (1) (11)
Precisiona (%)
73 71 75 73 77 81 37 24 45 59
Simulation results Density (stems/ha)
5,030 6,659 5,357 2,525 7,223 4,999 16,197 12,648 28,677 4,223
(699) (746) (774) (276) (1419) (699) (1702) (1755) (4871) (504)
Age (years)
5 69 71 65 61 77 33 31 38 121
(1) (6) (6) (1) (2) (5) (3) (3) (4) (9)
Height (m)
9.4 (0.2) 10.6 (0.5) 10.7 (0.3) 14 (0.4) 11.3 (0.5) 12.9 (0.6) 6.1 (0.4) 5.5 (0.4) 6 (0.2) 12.2 (0.6)
Area (ha)
822 326 291 178 7 7 501 357 183 752
Plots (numbers)
23 29 32 15 24 24 30 12 13 14
CC effects (%)
Probability (%)
Sampling error
Sampling + model errors
60 years
100 years
60 years
100 years
60 years
100 years
27 27 26 19 28 27 31 33 36 29
28 28 27 22 29 28 32 33 37 29
95 90 90 >95 >95 95 80 65 70 75
95 85 90 >95 >95 90 80 65 70 65
80 85 85 90 95 90 70 65 65 70
70 75 80 80 85 80 65 60 60 60
Precision at the 95% probability level on merchantable volume = 100% (t (standard error/mean) 100).
data from the MRNFQ database, using plots located in monospecific (more than 75% in merchantable basal area), undisturbed stands. We followed the operational procedure for deriving curves for multispecies plots by summing the monospecific reference curves of the species found in the plots times a volume adjustment factor corresponding to the ratio of observed to predicted volume. Assessment of climate change effects on forest productivity was done using the process-based model StandLEAP (Raulier et al., 2000; Girardin et al., 2008), which is based on the 3-PG model of Landsberg and Waring (1997). In StandLEAP, photosynthetically active radiation absorbed by the canopy (APAR) is converted into gross primary productivity (GPP, mol m2 month1) with a radiation use efficiency coefficient (RUE): GPP ¼ APAR RUE
(1)
where RUE ¼ RUE f 1 f 2 . . . f n
(2)
RUE represents a species-specific mean value of RUE. Environmental constraints on RUE take on the form of species-specific multipliers (f1. . .fn) with a value close to unity under average conditions, but which can decrease to represent increasing limitations (e.g., soil water deficit) or increase as conditions improve towards optimum (e.g., temperature): f n ¼ 1 þ blx
x x¯ x x¯ 2 þ bqx x¯ x¯
(3)
Parameters blx and bqx represent linear and quadratic effects of the x variable, and x¯ is the mean observed x value over the period of calibration. Multipliers represent the impact of soil drought (fu as in Landsberg and Waring, 1997; Bernier et al., 2002, 2006), frost (fF as in Aber et al., 1996) (both limited to a maximum of 1.0), mean maximum and minimum daily air temperature, vapour pressure deficit (VPD), monthly radiation, and leaf area index (where values greater than 1.0 are possible) on GPP. Respiration is computed as a fixed species-specific proportion of GPP (Malhi et al., 1999; DeLucia et al., 2007), and net primary productivity (NPP; g m2 month1) is computed monthly as GPP minus respiration. As in 3-PG, part of NPP is first allocated to fine roots (Landsberg and Waring, 1997, their Eq. (13)) on a yearly basis and then to replacement of carbon biomass lost to leaf and fine woody litter turnover. The remaining NPP is then allocated to
increments in stand carbon compartments of foliage, branches, coarse roots and stems (Girardin et al., 2008). Canopy light absorption and photosynthesis parameters were adjusted to results obtained with FineLEAP, a detailed multilayer, hourly time step model of canopy photosynthesis and transpiration (Raulier et al., 2000; Bernier et al., 2001). Additional details of the procedure and origin of the basic field measurements can be found in Hall et al. (2006, their Table 2). In particular, data for P. mariana were obtained in part from the BOREAS archives (DAAC database: http://www-eosdis.ornl.gov/NPP/npp_home.html). Required phytometric and soil inputs to StandLEAP were estimated from the inventory data obtained on the selected plots. Plot aboveground biomass was estimated by cumulating individual tree biomasses calculated with national biomass equations of Lambert et al. (2005). Time series of monthly mean daily maximum and minimum temperatures and monthly total precipitation (mm) were generated with the weather generation module in the BIOSIM Pest Management Planning Decision Support program (Re´gnie`re and St-Amant, 2007), using the current (1961–1990) and projected (2041–2070) climate normals. The module interpolates climatic normals of neighbouring weather stations to generate daily series of temperature and precipitation as a function of geographic position, altitude and exposure (a combination of slope and aspect) of individual locations. It also generates between-month variability that is added to the normals in order to produce plausible weather time series. The climatic normals used as references in BIOSIM were generated from the Canadian regional climate model, version ‘‘CRCM4.1.1 acu’’, driven by outputs of the third generation coupled global climate model using the IPCC SRES A2 greenhouse gas and aerosol scenario (Fig. 2; Travis Logan, Ouranos Consortium, pers. comm., 2008). The A2 storyline is one of the most pessimistic of all IPCC storylines in terms of increased greenhouse gas emissions and resulting increases in global temperatures (IPCC, 2001). 2.4. Modelling of plot-level climate change effects Effects of climate change on growth and yield were evaluated for each sample plot by comparing the StandLEAP simulation output obtained using the 1961–1990 climate normals with the output obtained using the projected climate scenario for the 2041– 2070 period. Simulations were done with a continual loop of 12 months for both climate scenarios from stand initiation to 100
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replacement, thus generating a set of n plot yield curves in which the same original curve could be represented more than once. This procedure was repeated 5000 times to generate a population of possible stratum-level yield curves. The exercise was done first without considering the modelling error by equating the random number u of Eq. (4) to zero, and a second time with the modelling error by picking a new random number u in Eq. (4) at every bootstrap repetition. This second percentile distribution of plausible stratum yield curves thus included both the sampling and modelling errors. The exercise was done for current and projected climate scenarios. 2.6. Determination of the uncertainty of detecting climate change effects in future growth
Fig. 2. Current (1961–1990) and projected (2041–2070) climate normals for the Black Spruce–Moss ecological domain of Quebec: current (full lines) and projected (dashed lines) means of monthly minimum (squares) and maximum (triangles) air temperature, and of monthly current (empty bars) and projected (shaded bars) precipitation.
years. No gradual change was modelled from the current scenario to the projected scenario. For each sample plot, adjustment factors were computed by 5-year simulation segments as the ratio of the aboveground biomass estimates from the projected and current climate scenarios. These factors were then applied to the yield curves originating from the Pothier and Savard (1998) model to generate merchantable volume projections under a climate change scenario. 2.5. Characterization of the simulation error We considered two error sources: the error associated with merchantable volume increment predictions (the modelling error) and the error associated with the variability in the properties of plots selected to represent a given stratum (the sampling error). Pothier et al. (2004) have shown that the magnitude of the modelling error on the merchantable volume increment predicted using the Pothier and Savard (1998) model for a specific sample plot tends to stay of similar magnitude and sign over time. Using this observation as basic premise, the evolution of the merchantable volume of a plot at a time (Vt) can thus be represented as: vffiffiffiffiffiffiffiffiffiffiffiffiffi u t1 t1 uX X Vt ¼ Vo þ iv;a þ ut s 2ˆ (4) a¼0
a¼0
iv
where Vo is the initial volume, iv;a represents the vector of predicted net volume increments between times 0 and t 1, u is a random number drawn from a standard normal distribution N(0, 1), and s iv is the root mean square error (RMSE) between observed and predicted plot volume increment estimates. This RMSE for black spruce has previously been evaluated at 1.78 m3 ha1 y1 (Raulier et al., 2004) in a comparison between estimated and measured merchantable volume increments in 209 permanent sample plots located in black spruce-dominated stands in Quebec. We used Eq. (4) to add a modelling error to the yield curve computed for each sample plot within each forest stratum. The expected volume growth of a stratum corresponds to the mean of the expected growth of the set of sample plots selected to represent this stratum. The sampling error affecting a stratum curve can thus be associated with the percentile distribution of plausible stratum yield curves. This distribution was approximated with bootstrap re-sampling of the plot yield curves within a stratum (Manly, 1997). For each stratum, the set of the n individual plot yield curves selected to represent it was re-sampled with
The 5000 bootstrap-generated mean yield curves that included the climate change effect were paired randomly to bootstrapgenerated mean curves that did not include the climate change effect. The difference between the curves within each of the 5000 pairs was then used to produce a percentile distribution of expected differences. The percentile at which the zero difference occurred at a given reference age (60 years and 100 years) was considered to be the detection threshold. The exercise was done by stratum, for simulations with the sampling error only, and for simulation with both the sampling and modelling errors. 3. Results 3.1. Effect of the sampling error For our 10 strata, the precision for initial merchantable volumes varied between 24% and 81% (Table 1). For most inventory strata whose mean stand age exceeded 50 years, the precision for merchantable volume was over 70%, a threshold considered acceptable for timber supply analyses in Quebec. These strata included about 50% of the forested area considered in this study. The other 50% of the forest for which precision was much lower was composed mostly of juvenile strata with a cover height of less than 7 m characterized by low merchantable volumes, with the exception of the B stratum, a low density 90-year-old stratum dominated by black spruce, for which the precision was of 59% (Table 1). Estimated changes in merchantable volume over time varied greatly between plots among individual strata, and these differences were mostly due to initial differences in mean plotlevel tree age and volume as well as, to a lesser extent, differences in tree species composition. Examples of growth trajectories of individual plots within particular strata are given in Fig. 3. Negative growth is generated by the senescence component of the G&Y model, and very early senescence in the figure indicates that the mean plot-level tree age was relatively high at the start of the simulation period. Even with a good within-strata precision for initial mean merchantable volume, yield curves of plots within a given stratum showed an important variability. For instance, stratum A (Fig. 3) had a precision of 73% for the initial volume, and the yield curves for the underlying plots were relatively well grouped. By contrast, the yield curves of plots from the juvenile stratum (stratum G) diverged strongly from their common origin, and produced a highly skewed curve distribution. The plots for the older B and J strata had very different initial mean plot-level tree age that, in turn, generated very different growth trajectories, including strong senescence in some of the plots. 3.2. Effect of the modelling error Inclusion of the modelling error added a large degree of variability to the possible mean yield curves, as illustrated by the
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Fig. 3. Growth trajectories of individual temporary sample plots selected to represent four different strata, as predicted from the Pothier and Savard (1998) growth and yield curves. Starting plot age corresponds to time of inventory. Negative growth indicates a modelled senescence.
difference in the spread of the percentile distribution between the sampling error only and the combination of sampling and modelling errors (Fig. 4a and b). However, the variability introduced by the modelling error was not as large as the initial variability caused by the sampling error. 3.3. Climate change effect on merchantable volume increment Simulation results using StandLEAP suggest that, under the projected climatic scenario, mean merchantable volume of individual strata would be 22–37% greater than under current climatic conditions after 100 years of simulation (Table 1). The mean growth increase in merchantable volume of all the strata dominated by black spruce was calculated to be 29%. The results obtained from StandLEAP simulations for each individual plot were transferred to the plot-level yield curves using simple adjustment factors calculated from the StandLEAP simulations. 3.4. Estimating the probability of detecting a climate change effect The 5000 bootstrap repetitions were sufficient to stabilize the percentile distributions of stratum yield curves, as estimated by the stabilization of the u frequency distribution (Eq. (4)) (data not shown). Fig. 4a shows the distribution of the differences between curves with and without a climate change effect for each of the 10 black spruce-dominated strata within the study area, as a result of the sampling error. The addition of the modelling error to the predictions had no effect on the mean difference of individual strata, but resulted in an expansion of the percentile distribution around this mean. Also, because the error structure often caused a divergence in within-strata plot-level curves to increase with time, the probability of detecting the effect of climate change often decreased with time. The line of no difference between the set of curves with and without climate change at 100 years of simulation was found on average at the 75th percentile when only the sampling error was taken into account, and at the 67th percentile when both the
sampling and modelling errors were included. In other words, in the repeated simulations of strata-level growth using curves that included climate change and curves that did not include climate change, the inclusion of climate change resulted in a greater modelled growth 67% of the time when considering both sources of error. The percent success in detecting the climate change impact on growth was greater at 60 years of simulation. Overall, results for mature strata were more accurate because of the smaller sampling error within these strata. Young and over-mature strata had a greater sampling error, and the probability of detecting the increased growth due to climate change was reduced accordingly. Following the guidance notes on addressing uncertainties from the Intergovernmental Panel on Climate Change (Moss and Schneider, 2000), a likelihood of occurrence above 66% should be translated as ‘‘likely’’. 4. Discussion Consideration of both the sampling and modelling errors provides essential information for evaluating the outcomes derived from the incorporation of climate change effects within growth and yield equations. In our case, within the limits of this study, we found a relatively large potential climate change effect but a moderate capacity to detect this effect beyond the uncertainty inherent to the growth prediction system. The percentage of success in detecting a change in predicted volumes with the inclusion of climate change is far less than the levels of ‘‘type I’’ errors of 1% and 5% generally used by scientists, but may be more in the range of the uncertainties that normally confront decision-makers as part of their decision-making process. Ignoring uncertainty in forest planning leads to non-optimal, overoptimistic, and sometimes unfeasible decisions that may lead to net present value losses mostly because of improper planning of harvest timing (Pukkala and Kangas, 1996; Eid, 2000; Borders et al., 2008). As most black spruce forests in Quebec have an abundance of over-mature stands (Gauthier, 2004), the critical period that
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determines the harvest level under a strict even-flow constraint (sensu Davis et al., 2001) tends to appear late in the planning horizon. The actual harvest level is thus expected to be sensitive to climate change. Consequently, a decision-maker should seriously
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consider including climate change effects, or the uncertainty generated by the range of possible futures, into his yield curves, especially for the youngest strata, at least as an alternative scenario. Furthermore, Gauthier (2004) has shown that timber
Fig. 4. Percentile distribution of differences in mean merchantable volumes between paired bootstrap-generated mean stratum growth trajectories simulated with and without climate change effects. Results are shown with the sampling error only (a) or with the sampling and modelling error combined (b). The upper and lower solid lines represent the 5% and 95% percentiles, while the dashed lines represent the 25% and 75% percentiles. The central solid line represents the mean difference.
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Fig. 4. (Continued ).
supply calculations in black spruce forests are very sensitive to changes in the age at which stands become harvestable. Given the low productivity of the black spruce stands considered in this study, a long-term increase of 30% in volume yield corresponds
approximately to a decrease of 10% in harvest age following the yield tables of Pothier and Savard (1998), and thus to a potential increase of 10% in the harvest level. Such a potentially important increase cannot be neglected and also needs to be weighed against
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the probable impacts of climate change on natural disturbances as fire activity is expected to increase in our study area (Flannigan et al., 2005). The 29% cumulative growth increase modelled over more than half a century with StandLEAP is relatively large compared to similar exercises carried out elsewhere in the Canadian boreal forest. Girardin et al. (2008), also using StandLEAP, came to the conclusion that climate change would actually cause growth to decrease slightly in three boreal forest tree species, including P. mariana, in drier Western Canada forests on account of the effect of increased temperatures on the site-level water budgets. Similar results were obtained with Pinus contorta (Chhin et al., 2008), also as a result of a strong drying trend. An analysis by Bunn et al. (2005) suggests a general lack of response of the North American boreal forest to future climate change. By contrast, growth in European forests has been increasing over the past decades, and further increases are expected as a result of climate change. Kelloma¨ki et al. (2008) suggest a potential increase of 44% in Finnish forests. CO2 growth enhancement (Norby et al., 2005), which is not included in StandLEAP, could also generate additional growth, but nitrogen limitation, common to many boreal forest environments, could dampen this effect (Oren et al., 2001). Overall, given these considerations, a 29% growth increment is at the upper end of possible climate change effects for boreal forests in Eastern Canada. Smaller growth increments would make detection of modelled increases more difficult and would lower the interest of considering them during the planning exercise. The modelled change in black spruce growth depends on the climate anomaly predictions, which are themselves dependant on the choice of the emission scenario and on the choice of the global circulation model used to translate this scenario into climate anomalies. The A2 human development scenario is very carbon intensive and results in some of the more extreme predictions in climate anomalies. The use of a less carbonintensive scenario would have generated a lower growth increment, while the use of the most carbon-intensive A1F1 scenario (IPCC, 2001) could have generated an even greater modelled black spruce growth response under the assumption of an absence of other limiting growth factors. Indeed, Raupach et al. (2007) report global CO2 emissions as far back as 2005 that track or exceed the higher forecasts of the A1F1 scenario, making the use of carbon-intensive scenarios such as the A1F1 or the A2 plausible. Also, we choose to use nearer term climate projections (2041–2070). Use of predictions for the 2021–2100 period, during which climate anomalies are projected to be even greater, would have generated different growth predictions. At a broader level, however, the uncertainty surrounding the choice of scenarios, and even the choice of global circulation models, can be lumped into a broad error term (which was not considered in this analysis) surrounding the modelling of climate change effects on forest productivity. This error is actually a summation of the uncertainties from the human development scenarios, their translation into greenhouse gas (GHG) emission scenarios, the modelling of global climate anomalies based on the additional GHG climate forcing, the downscaling of global climate to regional climate, and the biophysical modelling of tree growth. Research is starting to address the issue of uncertainties in atmospheric GHG projections (van Vuuren et al., 2008) and, more importantly for the problem at hand, in forest-level predictions. Simulations by Xu et al. (2009) suggest that differences among projected climate anomalies from different global circulation models and different GHG emission scenarios are sufficient to generate a large variability in predicted landscape-level forest composition. This
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type of approach could be used to determine an additional error term for the prediction of volume or biomass increment. In the world of statistics, the sampling error is not an inherent property of the population as it can be brought down by an increase in sampling size. In the real world of timber supply modelling, however, there are limits imposed on sample size, especially when dealing with a very large and varied forest area such as Canada’s boreal forest. Budget constraints limit the number of samples that can be dedicated to specific forest types within given ecological regions. Expansion of the imputation exercise to incorporate a larger sample size generates additional variability as plots from different ecological regions or from slightly different forest strata must be included to meet new targets of plot numbers. This increased variability would likely eliminate gains made by the increased sample size. Forest inventory and G&Y models, even without climate change effects, carry forward a significant amount of uncertainty that spills onto timber supply estimates in addition to masking potential climate change effects. Other components such as the modelling of forest succession following different degrees or types of disturbances add to the uncertainty of predictions over multirotations. Of potentially great significance to long-term timber supply predictions are natural disturbances. Incorporation of the impact of natural disturbances into timber supply predictions is still a work in progress because of the complexity associated with the inclusion of stochastic phenomena in real timber supply analyses (Davis et al., 2001). In addition, disturbance regimes must be adjusted to the projected climatic conditions in order to determine which current harvest levels are more robust to unexpected events. 5. Conclusion The underlying question in this work is whether or not the timber supply models that are currently run over long time scales without the inclusion of climate change effects provide valid results. The work shows that the term ‘‘valid’’ is more a matter of degree of comfort with risk than a strict yes or no, but it also shows that the risk must be calculated in order to be considered by forest managers. Nelson (2003) compared a timber supply analysis done without considering uncertainty to ‘‘running your vehicle’s engine at the ‘‘red line’’ for its entire life – hardly a sustainable strategy’’. As errors associated with climatic predictions appear largely irreducible (Dessai et al., 2009), managers will have to adapt to the new reality of an uncertain future. Climate change will likely impact trees and forested landscapes within the current lifespan of most tree species. Treating predictions as deterministic may work over very short time scales, and one strategy may be to proceed in this manner and revisit predictions on a periodic basis in order to account for ongoing changes. However, such an approach pays no attention to the advantages offered by risk analysis, for instance, when dealing with stochastic variations of timber prices (e.g., Zhou et al., 2008). Ideally, models should thus incorporate some degree of uncertainty analysis. Uncertainty is information that helps define the confidence we have in future states on which current actions are based, as is the case in timber supply modelling. It also helps focus research resources on the areas that show the greatest uncertainties. Tracking uncertainty and its reduction through research efforts also provides a measure of advancement in our understanding of forest ecosystems and their interactions with climate. Acknowledgments We thank the personnel from the Canadian Forest Service’s Laurentian Forestry Centre who were involved in the significant
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effort needed to construct and photointerpret the photo mosaics, in particular Luc Guindon, Guy Simard and Philippe Villemaire. Essential statistical support for performing the forest stratification and characterization exercises was provided by Xiaojing Guo, also with CFS. We also thank Travis Logan and the Ouranos Consortium for the provision of climate projections, and acknowledge the use of BOREAS ecophysiological data from the Oak Ridge National Laboratory’s Distributed Active Archive Centre (ORNL DAAC). Funding to SC was provided by Natural Resources Canada’s Program for Energy Research and Development. Comments made by the anonymous reviewers helped improve the manuscript. References Aber, J.D., Reich, P.B., Goulden, M.L., 1996. Extrapolating leaf CO2 exchange to the canopy: a generalized model of forest photosynthesis compared with measurements by Eddy correlation. Oecologia 106, 257–265. Bernier, P.Y., Raulier, F., Stenberg, P., Ung, C.-H., 2001. The importance of needle age and shoot structure on canopy net photosynthesis of balsam fir (Abies balsamea): a spatially inexplicit modelling analysis. Tree Physiol. 21, 815–830. Bernier, P.Y., Bre´da, N., Granier, A., Raulier, F., Mathieu, F., 2002. Validation of a canopy gas exchange model and derivation of a soil water modifier for transpiration for sugar maple (Acer saccharum Marsh.) using sap flow density measurements. For. Ecol. Manag. 163, 185–196. Bernier, P.Y., Bartlett, P., Black, T.A., Barr, A., Kljun, N., McCaughey, J.H., 2006. Drought constraints on transpiration and canopy conductance in mature aspen and jack pine stands. Agric. For. Meteorol. 140, 64–78. Borders, B.E., Harrison, W.M., Clutter, M.L., Shiver, B.D., Souter, R.A., 2008. The value of timber inventory information for management planning. Can. J. For. Res. 38, 2287–2294. Bunn, A.G., Goetz, S.J., Fiske, G.J., 2005. Observed and predicted responses of plant growth to climate across Canada. Geophys. Res. Lett. 32, L1710, doi:10.1029/ 2005GL023646. Chhin, S., Hogg, E.H., Lieffers, V.J., Huang, S., 2008. Potential effects of climate change on the growth of lodgepole pine across diameter size classes and ecological regions. For. Ecol. Manag. 256, 1692–1703. Davis, L.S., Johnson, K.N., Bettinger, P., Howard, T.E., 2001. Forest Management to Sustain Ecological, Economic, and Social Values, 4th ed. McGraw-Hill Publishing Company, New York, NY, USA, 804 pp. DeLucia, E.H., Drake, J.E., Thomas, R.B., Gonzalez-Meler, M., 2007. Forest carbon use efficiency: is respiration a constant fraction of gross primary production? Glob. Change Biol. 13, 1157–1167. Dessai, S., Hulme, M., Lempert, R., Pielke Jr., R., 2009. Do we need better predictions to adapt to a changing climate? EOS 90, 111–112. Eid, T., 2000. Use of uncertain inventory data in forestry scenario models and consequential incorrect harvest decisions. Silva Fenn. 34, 89–100. Flannigan, M.D., Logan, K.A., Amiro, B.D., Skinner, W.R., Stocks, B.J., 2005. Future area burned in Canada. Clim. Change 72, 1–16. Gauthier, G., 2004. Analyse de sensibilite´ d’un calcul de possibilite´ forestie`re aux hypothe`ses d’ame´nagement applicables au mode`le de simulation « par courbe ». In: Rapport de´taille´ du comite´ scientifique charge´ d’examiner le calcul de la possibilite´ forestie`re. Ministe`re des Ressources naturelles, de la Faune et des Parcs, Direction de la recherche forestie`re, Que´bec, pp. 189–262. Girardin, M.P., Raulier, F., Bernier, P.Y., Tardif, J.C., 2008. Response of tree growth to a changing climate in boreal central Canada: a comparison of empirical, processbased, and hybrid modelling approaches. Ecol. Model. 213, 209–228. Hall, R.J., Raulier, F., Price, D.T., Arsenault, E., Bernier, P.Y., Case, B.S., Guo, X., 2006. Integrating remote sensing and climate data with process-based models to map forest productivity within west-central Alberta’s boreal forest: Ecoleap-West. For. Chron. 82, 159–176. IPCC (Intergovernmental Panel on Climate Change), 2001. The IPCC Special Report on Emissions Scenarios. GRID-Arendal, Norway. Available at: http://www. grida.no/publications/other/ipcc-sr/. Kelloma¨ki, S., Peltola, H., Nuutinen, T., Korhonen, K.T., Strandman, H., 2008. Sensitivity of managed boreal forests in Finland to climate change, with implications for adaptive management. Philos. Trans., R. Soc. Land. Serv. B: Biol. Sci. 363, 2339–2349. Kurz, W.A., Apps, M.J., 1999. A 70-year retrospective analysis of carbon fluxes in the Canadian forest sector. Ecol. Appl. 9, 526–547. Lambert, M.-C., Ung, C.-H., Raulier, F., 2005. Canadian national tree aboveground biomass equations. Can. J. For. Res. 35, 1996–2018. Landsberg, J., 2003. Modelling forest ecosystems: state of the art, challenges, and future directions. Can. J. For. Res. 33, 385–397.
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