climate sensitive site index models for norway

Draft

Climate sensitive site index models for Norway

Journal: Canadian Journal of Forest Research

Manuscript ID cjfr-2015-0155.R3

Manuscript Type: Article

Date Submitted by the Author: 02-Feb-2016

Complete List of Authors: Antón-Fernández, Clara; Norwegian Institute of Bioeconomy Research Mola-Yudego, Blas; Norwegian Institute of Bioeconomy Research Dalsgaard, Lise; Norwegian Institute of Bioeconomy Research Astrup, Rasmus; Norwegian Institute of Bioeconomy Research

Keyword: climate change, Picea abies, Pinus sylvestris, boreal forest, productivity

https://mc06.manuscriptcentral.com/cjfr-pubs

Canadian Journal of Forest Research

Draft

1

Climate sensitive site index models for Norway

Clara Antón-Fernández, Blas Mola-Yudego, Lise Dalsgaard, and Rasmus

Astrup

1

Clara Antón-Fernández,1 Blas Mola-Yudego, Lise Dalsgaard, and Rasmus Astrup.Norwegian Institute of Bioeconomy Research

1Corresponding author (e-mail: [email protected]).

Can. J. For. Res. 99: 1–33 (2016) DOI: 10.1139/Zxx-xxx © 2016 NRC Canada

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Abstract: The present study aims to develop biologically sound and parsimonious2

site index models for Norway to predict changes in site index under different climatic3

conditions. The models are constructed using data from the Norwegian national4

forest inventory (NNFI) and climate data from the Norwegian meteorological5

institute. Site index was modeled using the potential modifier funtional form, with6

a potential component (POT) depending on site quality classes, and two modifier7

components (MOD): temperature, and moisture. Each of these modifiers was based8

on a portfolio of candidate variables. The best model for spruce dominated stands9

included temperature as modifier (R2 = 0.56). In the case of pine and deciduous10

dominated stands, the best models included both modifiers (R2 of 0.40 and 0.54,11

for temperature and moisture respectively). We illustrate the use of the models by12

analyzing the possible shift in SI for year 2100 under one (RCP4.5) of the benchmark13

scenarios adopted by the IPCC for its fifth Assessment Report. The models presented14

can be valuable for evaluating the effect of climate change scenarios in Norwegian15

forest.16

Key words: Climate change, Picea abies, Pinus sylvestris, Norway spruce, Scots pine,17

deciduous, boreal forest, productivity.18

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Antón-Fernández, Mola-Yudego, Dalsgaard, Astrup 3

1. Introduction19

Quantification and prediction of stand productivity is a key question in forest research,20

with evident implications in forest planning. The productivity of a given area has traditionally21

been estimated by measuring the height of dominant trees at a given age. This value, known22

as site index (SI), is assumed to be a valid surrogate for the potential productivity of a23

particular site. Site index is widely used as a measure of site quality as it can be estimated24

from direct measurements of height and age, and it is a good predictor of volume growth and25

yield (Weiskittel et al., 2011). Site index is also a prevalent key predictor in most traditional26

growth and yield models.27

The site index reflects inherent site characteristics, such as soil and climate, which are28

directly related to forest productivity. Except in the case of intensively managed stands (e.g.29

plantations subject to irrigation or fertilization) site index is generally assumed to remain30

constant through time (Assmann, 1970), as average soil and climatic variables have been31

assumed to remain stable. Therefore, many approaches oriented towards the estimation of site32

index include topographic or locational variables (e.g. slope, latitude, altitude) that relate to33

climate and soil conditions, providing good accuracy in the estimates.34

However, this static approach does no longer hold in the present context of future climatic35

changes, as it is reasonable to expect changes in site index in parallel to changes in climate36

conditions (e.g. Kauppi et al., 2014). This climatic uncertainty context urges for the devel-37

opment of adequate tools for a more dynamic estimation of site index. This is particularly38

relevant in high latitudes, where current climate change scenarios predict the largest tempera-39

ture increases (Stocker et al., 2013). In these regions, temperature is the main variable driving40

forest productivity, and therefore the expected changes will strongly affect forest productivity41

(Peltola et al., 2010).42

Climatic projections for Norway forecast a generally warmer and wetter climate (Stocker43

et al., 2013). The forecasted conditions for Norway are outside the range of conditions cur-44

rently present in Norway, particularly in the southernmost part. Hence, the importance of45

having a site index model that gives biologically sound estimates outside the range of ob-46

served conditions. Several empirical approaches for predicting SI from biophysical predictors,47

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including climatic variables, have been developed. These approaches range from linear models48

(e.g., Nigh et al., 2004; Sharma et al., 2012) to nonparametric approaches (e.g., Sabatia and49

Burkhart, 2014; Weiskittel et al., 2011). Some nonparametric approaches seem to have gained50

some popularity, e.g. the random forest model (e.g., Crookston et al., 2010; Weiskittel et al.,51

2011), because of their high accuracy and lack of assumptions about how the independent52

variables relate to each other and the dependent variable. This approach has, however, an53

important drawback, that when used outside the range of the training data its predictions are54

unreliable (Sabatia and Burkhart, 2014). Linear regression models and similar approaches like55

generalized additive models, GAM, (e.g., Albert and Schmidt, 2010) or other semiparamet-56

ric additive smoothing approaches (e.g., Nothdurft et al., 2012) share, somehow, a similar57

drawback: since SI has biological constrains that are not directly considered within the linear58

model, linear models could predict unrealistic values when used outside the range of the fitting59

data.60

The present study aims to develop biologically sound and parsimonious models for pre-61

dicting changes in site index under different climatic conditions for the three main species in62

Norway. The models are constructed using data from the Norwegian national forest inventory63

and climate data from the Norwegian meteorological institute. We illustrate how the SI models64

can be used by estimating the SI shift in 2100 under one of the IPCC climate change scenarios.65

2. Material and methods66

2.1. Data sources67

The forest measurements for this study were based on data from the Norwegian National68

Forest Inventory (NNFI) measured during the period 2009-2013. The NNFI consists of perma-69

nent plots laid systematically on a 3x3 km grid, covering an extension from latitude 58.8N up70

to 70.8N. The grid covers the whole country except for the northernmost region (Finnmark).71

Plots with more than 20% of Sitka spruce (Picea sitchensis (Bong.) Carr.) were excluded, due72

to differences in measurement methods, and only plots located in productive forestland were73

considered, resulting in 8943 plots included in the calculations. The main species in Norway74

are, in this order, Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and75

birch (Betula pendula Roth. and Betula pubecens Ehr.).76

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Site index (SI) was defined as the average height of the 100 thickest trees per hectare at77

the reference age of 40 years, and it is estimated at each cycle of the NNFI. At each plot78

the SI was assessed for the main species by selecting at least one dominant tree within a 0.179

ha circle. The selection of the dominant tree was done by visual assessment. The heights of80

the selected trees were measured and their corresponding ages were estimated from increment81

cores. The resulting data was used to estimate the SI according to Tveite and Braastad (1981),82

which places SI in classes: 6 (5-6.5), 8 (6.5-9.5), 11 (9.5-12.5), 14 (12.5-15.5), 17 (15.5-18.5),83

20 (18.55-21.5), 23(21.5-24.5), and 26 (>24.5) m.84

In addition, records of soil depth and understory vegetation class were taken at each plot.85

The understory vegetation classes were grouped into 9 categories (Astrup et al., 2010), accord-86

ing to their position along a gradient in nutrients (poor, moderate, and rich) and moisture87

(wet, moderate, and dry). The soil depth was classified in 4 categories: soil depth below 2588

cm, between 25 and 50 cm, between 50 and 100 cm, and above 100 cm. The resulting com-89

bination of soil richness, moisture, and depth form a total of 36 potential combinations, most90

of which are only represented by a small number of plots. These combinations were the basis91

of a categorical variable that organized richness, moisture and soil depth into five biologically92

meaningful groups. The groups were defined to minimize the SI variability for each species93

within each group. The new site quality variable (SQ) had a value of 1 to indicate the poorest94

sites and 5 to indicate the best sites (Figure 1).95

The location of spruce, pine and deciduous dominated stands in Norway is therefore re-96

flected in their frequency in each of the SQ groups defined (Table 1). Pine dominated stands97

are mostly located on poor sites (SQ1) while they are rare on the best sites (SQ5), whereas98

spruce dominated and deciduous dominated stands were mostly distributed in SQ3 and SQ4.99

The distribution of plots among SI classes is similar for deciduous and pine dominated stands100

(Figure 2). The lower SI classes are most commonly dominated by pine and deciduous species,101

while spruce dominated stands lead SI classes higher than 11m. The highest SI observed, 26m,102

is only found in few (12) spruce dominated stands. With respect to soil wetness, deciduous103

and spruce dominated stands are most common in moderate soils while pine are most common104

in dry soils (Figure 2). Most of the plots classified as wet are dominated by deciduous species,105

and only 18 of the plots classified as wet are dominated by pines.106

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Historical climate data (1900-2008) at the plot level were provided by the Norwegian mete-107

orological institute. Monthly precipitation and temperature were geographically interpolated108

from about 400 weather stations throughout Norway. 30-years averages were calculated us-109

ing data from 1979-2008 (MET7908). We used the multimodel (67) ensemble mean monthly110

temperature and precipitation outcomes from representative concentration pathway (RCPs)111

4.5 (Thomson et al., 2011) from the CMIP5 21st century experiments (Royal Meterological112

Institute of The Netherlands (KNMI), 2014), RCP4.5, for projecting SI changes in 2100 for113

NNFI plots currently on forestland. RCP4.5 is one of the benchmark scenarios adopted by the114

IPCC for its fifth Assessment Report (Moss et al., 2008).115

2.2. Modeling approach116

Since the aim of this study is to predict changes in site index under changing climatic117

conditions it is important that the selected modeling approach produces models that behave118

well beyond the range of current climatic conditions. We use a multiplicative potential (POT)119

modifier (MOD) functional form for the SI model (SI = POT ×MOD) where MOD is scaled to120

only have values between 0 and 1. This functional form has the advantage of being constrained121

and robust since the predicted SI will not exceed the potential even when approaching the122

limits of the empirical data used for model development. In this modelling approach both123

the potential and modifiers are estimated as parameters in a nonlinear regression model. The124

applied modelling approach is equivalent to that frequently applied in studies of tree diameter125

growth where an estimated potential maximum growth rate (estimated as part of a nonlinear126

regression model) is modified according to site factors or competition for light or belowground127

resources (e.g. Lilles and Astrup, 2012; Canham and Uriarte, 2006). The approach applied in128

this analysis is different than the more conventional potential modifier approach (as in Belcher129

and Brand, 1982) where the potential is estimated in a separate analysis, and often using a130

different data set, than the one used for fitting the modifier. It is similar to the conventional131

potential modifier approach in the sense that the modifiers vary between 0 and 1 and modify132

how close to realization of the potential the estimated SI is.133

The SI was, therefore, modeled using the multiplicative potential modifier functional form.134

This functional form has two components: The potential component (POT), which can be135

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interpreted as the mean SI at a given SQ when neither temperature or moisture are limiting,136

and a modifier component (MOD) which reduces the potential site index according to relevant137

variables, in the form SI = POT × MOD. The modifier component can consist of one or138

several multiplicative modifiers, each of them taking values between 0 and 1, e.g. MOD =139

MOD1 · MOD2, which results in MOD varying between 0 and 1, and the model predicting140

values between 0 and POT . The potential modifier functional form is commonly used to model141

growth, where the lower limit of zero makes sense. However, when applied to SI modeling a142

value of zero does not make biological sense. Therefore, to account for a lower SI limit of 6,143

which is the minimum SI measured in the NNFI, we redefined the basic form of the model as:144

6 + (POT − 6) × MOD.145

The candidate modifiers included a temperature effect, MODT , and a moisture surplus146

effect MODM . For each modifier, a simple portfolio of candidate variables was considered.147

The modifier MODT included variables related to temperature that may affect SI, namely the148

number of growing days (GD, number of days with average temperature above 5◦C), and com-149

binations of the 30-year monthly average temperatures, for instance the temperature sum for150

spring and summer months (TSUM). The modifier MODM included variables related to water151

availability that may restrict the SI, and included several combinations of the 30-year monthly152

average precipitation, the Palmer drought severity index (Palmer, 1965), PDSI, for the grow-153

ing season months, the topographic wetness index (Beven and Kirkby, 1979), TWI, and the154

monthly moisture surplus defined as the difference between 30-year monthly average precipita-155

tion and the average monthly potential evapotranspiration (MSJ). We followed Thornthwaite156

(1948) to calculate potential evapotranspiration (PET) using the 30-year monthly average157

temperature:158

PET = 16K

(

10T

I

)m

I =12∑

i=1

(

T

5

)1.514

; m = 6.75 × 10−7I3− 7.71 × 10−5I2 + 1.79 × 10−2 + 0.492

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K =(

N

12

)(

NDM

30

)

; N =(

24π

)

ωs

ωs = arccos (− tan φ tan δ) ; δ = 0.4093 sin(

2πJ

365− 1.405

)

159

Where T is the monthly-mean temperature (°C), I is a heat index, which is calculated as160

the sum of 12 monthly index values i, m is a coefficient depending on I, K is a correction161

coefficient computed as a function of the latitude and month, NDM is the number of days of162

the month, N is the maximum number of sun hours, ωs is the hourly angle of sun rising, φ is163

the latitude in radians, and δ is the solar declination in radians, J is the average Julian day of164

the month.165

The plots were grouped according to dominant species (spruce, pine, and deciduous plots)166

and equations were fit to each of these categories separately. All the candidate variables were167

preliminarily explored by examining graphically and analytically their explanatory power for168

site index, for each modifier and for each species. To explore the strength and shape of the169

relationship between site index and the candidate variables we fitted linear tail-restricted170

cubic splines (5 knots) functions to each candidate variable and species (Harrell, 2001). When171

analyzing the strenght of the association between site index and the candidate variables, cubic172

splines offer the advantage of allowing departures from the assumption of linearity in the173

association. In addition, correlation matrices were computed and examined, to determine the174

degree of intercorrelation among variables.175

The criteria for including the candidate variables in the final version of the models were:176

they had to be significant at the 0.05 level, and they had to provide the highest explanatory177

power of the candidate variables.178

Concerning the model shape of the modifiers, two basic forms were considered. Variables179

increasing with the value of the explanatory variable were modelled using the logistic functions180

1/ (1 + exp(−βX)), where X is a vector of explanatory variables, and β is the vector of param-181

eters to be estimated. Relationships reaching a peak at certain point and decreasing afterwards182

were modelled using the Weibull function γ/α · ((X − µ) /α)γ−1 exp (− ((X − µ) /α)γ), where183

X ≥ µ, and α>0, scaled to be bounded between 0 and 1. The Weibull function is a widely used184

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and flexible function that have a shape parameter (γ), a scale parameter(α), and a location185

parameter (µ). To bound the Weibull function between 0 and 1, we added a scaling factor186

(1/ξ) which multiplied the whole function and was calculated as the maximum value of the187

function, and we redefined X as188

X =

X

µ

X ≥ µ

otherwise.

Thus, (X − µ) will never be negative, and values of X below µ will result in the modifier189

taking a value of 0.190

The basic form of the model was 6+(POT − 6)×MOD, where MOD = MODT ×MODM ,191

resulting in two models, named md1 and md2. Model md1 includes the temperature modifier192

MODT , and model md2 includes both the temperature and the moisture availability modifier193

MODM .194

Finally, the models were assessed in order to identify which modifiers, and in which com-

bination, resulted in a better model. The assessment was based in the Akaike information

criterion, AIC, (Akaike, 1974), and BIC (Schwarz, 1978), and the proportion of variance ex-

plained by the model relative to that explained by the simple mean of the data, adjusted by

the sample size (n) and the number of regressors (p):

R2

adj = 1 −

(

n − 1n − p − 1

)

(

1 − R2)

R2 = 1 −

(

∑

i (yi − fi)2

∑

i (yi − y)2

)

where y is the mean of the observed SI, fi is the ith model predicted SI, and yi is the ith195

observed SI.196

To avoid, as much as possible, problems with convergence we used a simulated annealing197

algorithm (Goffe et al., 1994) implemented in the likelihood package (Murphy, 2015) in R198

(R Core Team, 2015) to fit all models. The likelihood package allows to find the maximum199

likelihood estimates of statistical models using simulated annealing, a global optimization200

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10 Can. J. For. Res. Vol. 99, 2016

algorithm, with or without bounded searches.201

2.3. Projections202

The temperature and precipitation outcomes from the multimodel ensemble for RCP4.5203

have a 0.5 degree spatial resolution. Since the source and resolution of these data are differ-204

ent from the ones used for fitting the models (MET7908), we estimated the 30-years monthly205

average temperature at each plot for the 2071-2100 period as the sum of MET7908 and the pro-206

jected change according to RCP4.5. We calculated the projected change according to RCP4.5207

as the difference between the average monthly temperature for the 1979-2008 period available208

from RCP4.5 and the 2071-2100 monthly average from RCP4.5. We used the estimates of the209

30-years monthly averages for the 2071-2100 period, calculated as the sum of MET7908 and210

the projected change according to RCP4.5, to calculate the variables required by the models,211

TSUM and MSJ.212

3. Results213

3.1. Model fitting214

Several candidate variables for MODT were available. The preliminary correlation matrices215

of the candidate variables showed that temperature and number of growing days were highly216

correlated and that the best temperature-based variable had higher correlation with SI than217

the number of growing days for all species. Among the best temperature variables there was218

little variation in their correlation with SI, and the correlation among them was high (>0.94).219

The graphical evaluation of the residuals of the linear tail-restricted cubic splines revealed220

that April, May, and June monthly temperatures performed best, but different months tended221

to perform better in different regions (e.g. northern region), while the sum of temperature in222

spring and early summer had a more consistent residual pattern. Therefore, we selected tem-223

perature in spring and early summer, defined as the sum of the 30-year average temperatures224

in April, May, and June (TSUM), for MODT . The range and distribution of these variables225

is shown in Figure 3.226

For MODM the correlations among candidate variables and SI were smaller than for227

MODT , but stronger for deciduous than for spruce or pine. Measures of goodness-of-fit (resid-228

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ual standard error and coefficient of determination R2) of the linear tail-restricted cubic splines229

revealed that water surplus in June outperformed all variables. Therefore, we selected moisture230

surplus in June (MSJ), defined as the difference between 30-year average precipitation in June231

and average potential evapotranspiration in June.232

The preliminary analysis determined the parameters that varied with SQ and the most233

adequate functional form for each modifier and for each species. We assessed graphically the234

need to make each parameter dependent on the SQ group. Table 2 shows the two modifiers235

selected for each species. In general, the variability explained by the best models, as measured236

by R2, was highest for spruce dominated plots, followed by deciduous and pine dominated237

plots. For all species the largest variability was explained by temperature.238

Consistently with the limiting factor theory, the sensitivity analyses revealed that the effect239

of temperature on SI was smaller for poorer sites and that this effect increases with site quality240

for all species (Figures 4, 5, and 6)241

In the spruce dominated stands, a large part of the variability was already explained by the242

model including TSUM (md1) in addition to the SQ factor (Table 3). In pine dominated stands243

(Table 3), model md2, with two modifiers, performed best. The full model (md2) improved AIC244

and R2 while keeping the estimates of the parameters within the expected range. A decrease245

in moisture surplus at the wetter sites results in an increase in SI, but once the optimum246

was reached, a drier climate (lower moisture surplus) results in a decrease in SI. The effect of247

temperature was greater at optimal moisture surplus, and it was very limited at the lowest248

and highest moisture surplus limits.249

Thus, we regarded md2 (temperature as modifier), md2 (temperature and moisture surplus250

as modifiers) and md2 (temperature and moisture surplus as modifiers) as the best models251

for spruce, pine and deciduous dominated stands, respectively. The selected models show little252

apparent trend in plots of residual values against either predicted values (Figure 7) or any of253

the indendent variables (data not shown).254

3.2. Projections255

Climatic projections for Norway forecast a generally warmer and wetter climate, which256

results in a similar range of MSJ values, but a generally higher TSUM (Figure 8). Projections257

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for SI in 2100 for the NNFI plots used for fitting the models were calculated by adding the258

expected change to the current SI. That is, we used the best models for each species to estimate259

SI for current conditions and for conditions in 2100, we then calculated the difference between260

these two and applied it to the current SI on each plot. For all species the patterns of SI remain261

similar to the current patterns of SI. The projections show that in most plots there will be an262

increase or no change in SI, with pine being the species less affected by climate change. The263

projections show constant or increasing SI, with very rare occurrences of decreasing SI (Figure264

9). The largest changes in SI are for spruce dominated stands, where the projections show an265

increase in SI of at least 1 meter in most regions, with a higher increase in the central part of266

Norway and plots close to the tree line in the southern part of Norway. For pine dominated267

stands the increase in SI was more moderate, with most of the plots experiencing little change.268

For deciduous dominated stands the change in SI was bellow 3 meters in most plots, with little269

change in the northernmost regions, and only few plots experiencing increases of SI above 3270

meters. The range of MSJ on the original data (-115, 134) does not differ much from the range271

of MSJ on RCP4.5 (-119, 118), being the average change in MSJ -6.5 mm. The average change272

in TSUM in RCP4.5 with respect to MET7908 was 6.5 ◦C. The range of TSUM change from273

(0, 32.5) in MET7908 to (1.6, 38.5) in RCP4.5.274

4. Discussion275

The present paper explains the variations of SI in Norway according to climatic and soil276

conditions by using an empirical approach. The models are fit using an extensive data pool277

resulting from the NNFI and environmental variables from the Norwegian meteorological insti-278

tute. Thus, an application to recent climate conditions becomes straightforward. At the same279

time, the models are biologically sound, and efficiently represent the main limitations to forest280

growth in Norwegian conditions.281

However, there are limitations in the data used for the estimation of the SI: in general,282

the overall estimation of site index based on a reference height is a difficult task subject283

to measurement error and the site classes in Norway are defined in intervals, which reduces284

the precision of the predictions. Despite these limitations, the NNFI is the largest data set285

available for the region and covers systematically a broad geographical region with diverse286

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climate conditions, thus providing a solid empirical basis for the models presented.287

The models presented precision levels similar to other recent studies of SI prediction using288

alternative statistical approaches (e.g. Seynave et al., 2005; Albert and Schmidt, 2010; Aertsen289

et al., 2010). In Norway, Sharma et al. (2012) presented SI models for Norway spruce and Scots290

pine with higher predictive power than the ones presented here. Sharma et al. (2012) used linear291

regression models and the year of stand establishment, the temperature sum (degree days above292

5ºC), location, topography, soil, and understory vegetation variables as explanatory variables.293

Although Sharma’s et al. R2 values may look promising (up to 0.85 for Norway spruce and294

0.72 for Scots pine), their models present several limitations when used for prognoses under295

climate change. They assume a linear relationship between temperature sum and SI, thus296

higher temperatures will always, regardless of precipitation, result in higher SI. The inclusion of297

the year of stand establishment results in a continuous trend of higher SI in newly established298

stands, which may result in illogical SI when used for prediction of long-term prognoses.299

Recent studies on SI prediction have focused on modeling the spatial SI trends. For example,300

Albert and Schmidt (2010) used generalized additive regression models with a two-dimensional301

location component to model the spatial SI trend. We chose not to include location components302

in our models because, in our case, location is correlated with the main variables of interest303

(the correlations between TSUM and latitude and longitude are 0.47, and 0.36 respectively,304

and between MMS and latitude and longitude are 0.47, and 0.72, respectively) and that would305

cause confounding of the effects of changes in the climatic variables. Other options to address306

spatial correlation is that of Nothdurft et al. (2012), who applied a simplified universal kriging307

method using B-spline basis functions to provide spatio-temporal predictions of site index308

for an area of Southwest Germany. The Nothdurft et al. (2012) approach requires that the309

mean function of the spatial site-index process, the one that depends on climatic variables, to310

be linear. Since the relationship between SI and most of the climatic variables is non-linear,311

the relationships are linearized through the B-spline functions. Nothdurft et al. (2012) chose312

the number and location of the B-spline knots heuristically to avoid illogical behavior when313

extrapolating beyond the range of the model data. The strength of the approach selected in the314

present paper is that we ensure biologically sound results beyond the current range of climatic315

conditions, and that behavior is defined by the data and the basic form of the models, avoiding316

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14 Can. J. For. Res. Vol. 99, 2016

having to select heuristically some of the parameters. Other interesting approach to model the317

effects of biophysical factors on tree growth is to model the effect of biophysical factors on the318

potential tree height as it is done in SILVA (Pretzsch et al., 2002). This approach, however,319

requires data on dominant height, which is neither currently recorded by the NNFI nor is320

available from experimental plots in a representative scale for Norwegian conditions.321

Our results show that SI increases with temperature. Due to interaction effects between322

temperature and site quality, the increase becomes more pronounced with increasing site qual-323

ity. This results are congruent with Sigurdsson et al. (2013), who found that the effect of324

increase on temperature or CO2 on mature Norway spruce in the boreal zone was not evident325

unless nutrient availability was improved. Our results are also consistent with Pretzsch et al.326

(2014) findings that growth acceleration, likely due to climate change, for Norway spruce since327

1960 in Central Europe is stronger in more fertile sites.328

The effects of the variables included in the final version of the models were logical and329

in line with previous studies. In Norway, Andreassen et al. (2006) underlined the effect of330

temperature and precipitation on Norway spruce growth based on tree-ring series. Andreassen331

et al. (2006) concluded that, of the variables explored, June temperature and precipitation332

had the largest influence on tree ring increments of the variables explored, which is consistent333

with our results. For all three species, most of the variability was explained by MODT , which334

is also consistent with previous studies on the relationship between climatic factors and tree335

growth in Fennoscandia, which show that growth is mainly determined by summer temperature336

(e.g. Ge et al., 2011; Andreassen et al., 2006). Ge et al. (2011) used a process-based growth337

model to assess the impacts of climate change on stem wood growth. They found that most of338

the variability of annual growth in Norway spruce in Finland was explained by temperature,339

particularly June temperature, while the relationship between annual growth and monthly340

precipitation was more subtle. Andreassen et al. (2006) also found stronger correlations of341

growth with summer temperatures than with monthly precipitation for Norway spruce in342

Norway. The fact that moisture surplus is not included in the final model for spruce is not343

to say that that moisture surplus is not an important factor in spruce dominated stands344

productivity. Rather, it indicates that moisture surplus is not a limiting factor within the345

current range of spruce dominated stands.346

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For pine dominated stands the optimal MSJ is lower than for deciduous dominated stands.347

This is not surprising, since pine dominated stands are already dominating the drier sites in348

Norway (Figure 2).349

One of our main objectives was to make the models biologically sound, which is a require-350

ment when the aim of the models is to forecast the productivity of large non-homogeneous351

areas. To achieve this objective we used empirical data and a modeling approach that bounds352

the response of the model between a maximum, the potential, and a minimum, defined as the353

minimum recorded SI (6m). As a result of this, even if the conditions on a plot for a certain354

species become unsuitable for the survival of the species or the plot becomes unproductive, the355

model will still give an estimate of the SI between the minimum and the maximum. Predict-356

ing the suitability of a site for the survival or establishment of a species should be answered357

separately, and it is not within the scope of this paper.358

There are other considerations that should be taken into account when applying climate359

sensitive SI models. One should be careful when applying these models to already established360

stands, as the climate-growth response of the stands already established might depend on361

the provenance of the trees, their age, and elevation, among other factors (Primicia et al.,362

2015). Productivity might also be affected by other factors that might change with time and363

that are not considered here, like CO2, nitrogen deposition (Sigurdsson et al., 2013), nutrient364

availability, and solar radiation.365

The potential component (POT) is the mean SI index at a given site quality (SQ) when366

neither temperature or moisture are limiting. Even under the best climatic conditions there367

are other factors that limit the growth of trees, such as light and nutrient availability, or me-368

chanical factors (e.g. wind, snow). Since the fit of a model is usually performed by minimizing369

weighted errors, the model will predict the average SI found under certain site conditions,370

temperature, and precipitation, which will never be the maximum SI observed because of the371

imperfect correlation between SI and the variables of the models, and the error implicit in372

the measurements of the variables. Thus, the models correctly predict trends due to a change373

in temperature or precipitation, but they will predict expected SI under given conditions. In374

order to predict future SI under climate change, we suggest that the models should be used375

to predict SI change (predicted SI in future climate - predicted SI in current climate) which376

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16 Can. J. For. Res. Vol. 99, 2016

then is added to the currently observed SI. If no information about the current site index is377

available, the models can be used directly but with an expectation of a larger error than when378

current site index information is available. If there is information about current SI and the379

model is used to predict SI change, the predicted SI can exceed POT.380

Thanks to the broad array of conditions currently present in Norway we have been able to381

use the space-for-time substitution, an approach widely used in other fields such as biodiversity382

modeling (Blois et al., 2013), to predict climate change effects on SI for Norway. The space-for-383

time substitution assumes that spatial and temporal variation are equivalent. This approach is384

commonly used accross fields when long-term time-series data are not available. However, this385

approach has some drawbacks that should be considered. For example, as with any empirical386

model, caution should be used when extrapolating beyond the original range. Also, although387

SI is assessed at each cycle of the NNFI, the observed SI is the result of the stand history and388

climate throughout the life of the trees currently in the stand, and as so, it is an imperfect389

measurement of the current SI if a new stand were to be established. Since the observed SI is390

the result of the compound response over the life span of the trees, we chose to use the average391

of the climatic variables over the last 30-years, instead of using only more recent data, as the392

explanatory variable for our SI models.393

When the best models are applied using climate projections for 2100 (RCP4.5), the patterns394

of change observed in Figure 9 reflect the behavior of the models. The general trend for all plots395

considered and all species is an increase in SI for 2100. For more extreme climate scenarios (e.g.396

RCP8.5) the results may be considerably different than under RCP4.5. The moisture indicator,397

MSJ, does not change dramatically between MET7908 and RCP4.5, which is why there are only398

very few plots with a decrease in SI greater than 1 meter (Figure 9). Contrary to the presented399

results, studies from other parts of the boreal forest indicate reduced forest productivity. For400

example, projections for Canada under climate change indicate a likely decrease in productivity401

in areas with relative high water stress and low water-holding capacity, but an increase on forest402

productivity on sites with high water-holding capacity during the 21st century (Johnston et al.,403

2009). In northern Finland, where soil moisture seldom limits forest growth, stem wood growth404

are expected to be higher under climate change, while in sourthern Finnland stem wood growth405

is, on average, lower under climate change due to limited water availability compared with the406

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current climate (Ge et al., 2011). Climatic projections for Norway forecast a generally warmer407

and wetter climate (Stocker et al., 2013), and at least for RCP4.5, it seems that the higher408

precipitation will, in general, compensate the higher water requirements and result in higher409

productivity for most areas in Norway and mainly for spruce and deciduous dominated stands.410

Finally, despite the restrictions of the modelling approach and the obvious limitations411

in forest growth prognoses, the models presented in this paper present a robust and easily412

applicable basis for SI prediction in boreal conditions.413

5. References414

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SI (m)

num

ber

of o

bser

vatio

ns

0

200

400

600

800

1000

6 8 11 14 17 20 23 26

SprucePine

Deciduous

Soil Wetness

num

ber

of o

bser

vatio

ns

0

500

1000

1500

2000

2500

Wet Mod. Dry

Fig. 2. Site index (left) and soil wetness (right) distribution by species dominating the stand.

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Fig. 3. Maps of the distribution and range of the temperature and moisture variables included in themodels. The maps are interpolations of the climatic data at the plots, masked to show only productiveforest area in Norway. TSUM (in ◦C) is the sum of the 30-year average temperatures in April, May,and June. MSJ (in mm) is the moisture surplus in June, defined as the difference between 30-yearaverage precipitation in June and average potential evapotranspiration in June.

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Fig. 4. Sensitivity graphs for the spruce model (md2).

TSUM (ºC)

SI (

m)

10

15

20

25

10 20 30 40

SQ2

SQ3

SQ4

SQ5

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Fig. 5. Contour plots showing the behavior of md2 for pine dominated stands. Grey rectanglesindicate combinations of MSJ, TSUM and SQ that existed in the fitting dataset.

TSUM (ºC)

MS

J (m

m)

−50

0

50

10 20 30

78

9

SQ1

7

89

1011

1213

SQ2

78

910

1112

1314

SQ3

10 20 30

−50

0

507

8 910

1112

1314

1516

17

SQ4

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Fig. 6. Contour plots showing the behavior of md2 for deciduous dominated stands. Grey rectanglesindicate combinations of MSJ, TSUM and SQ that existed in the fitting dataset.

TSUM (ºC)

MS

J (m

m)

−50

0

50

10 20 30

7

8

9

10 11 12

SQ2

7

89

10 1112 13 14 15 16

SQ3

7

78

910 11 12 13 14 15 16 17 18 19 20

SQ4

10 20 30

−50

0

50

7

7

89

10 111213 14 15 16 17 18 19 20 21 22 23

SQ5

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Fig. 7. Residuals of the best model for each species against the predicted SI. A loess smooth functionwith span smoothing parameter = 2/3 and degree of local polynomial = 1 is shown in black.

Predicted SI (m)

Res

idua

ls (

m)

−10

−5

0

5

10

10 15 20

spruce−10

−5

0

5

10

pine−10

−5

0

5

10

deciduous

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Fig. 8. Distribution of TSUM and MSJ under current climate (C) and RCPs 4.5 projections (F).

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J

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0

50

100

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Table 1. Number of observations by sitequality and species dominating the stand.The + indicates categories aggregatedwith the next closest category.

Spruce Pine Deciduous

SQ1 + 1183 +SQ2 712 927 433SQ3 1697 540 1061SQ4 915 110 928SQ5 172 + 265Total 3496 2760 2687

©2016 NRC Canada

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32 Can. J. For. Res. Vol. 99, 2016

Table 2. Definition of the components for each species group. [SQ] indicates when the parametersvary with the site quality parameter.

spruce dominatedP OT π0[SQ]

MODT (1 + exp (−τ1 [SQ] · T SUM + τ0 [SQ]))−1

MODM (1 + exp (−µ1 · MSJ + µ0))−1

pine dominatedP OT π0[SQ]

MODT (1 + exp (−τ1 · T SUM + τ0 [SQ]))−1

MODM ξ−1· µ1/α · ((MSJ − µ0) /α)µ1−1 exp (− ((MSJ − µ0) /α)µ1 )

deciduousP OT π0[SQ]

MODT (1 + exp (−τ1 · T SUM + τ0))−1

MODM ξ−1· µ1/α · ((MSJ − µ0) /α)µ1−1 exp (− ((MSJ − µ0) /α)µ1 )

©2016 NRC Canada

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Table 3. Parameter estimates and measures of goodness of fit for the twocandidate models for the three species.

spruce pine pine deciduous deciduousParameters md1 md1 md2 md1 md2

π0[SQ1] 9.0797 9.469π0[SQ2] 15.4929 12.7145 13.3917 14.4688 13.041π0[SQ3] 21.7727 13.3343 14.7684 20.1651 18.0119π0[SQ4] 22.9493 16.7999 17.8809 25.3659 22.5634π0[SQ5] 26.1775 29.5949 25.9418τ1 0.1576 0.2068 0.1126 0.1125τ0 3.1924 2.7009τ0[SQ1] 1.8948 2.4028τ0[SQ2] 2.3125 2.9211τ0[SQ3] 1.7933 2.4689τ0[SQ4] 2.5339 3.0053ξ 0.0076 0.0060µ1 1.5042 1.8939µ0 -103.5199 -115.2986α 98.0557 137.4867AIC 17427 13121 12844 12742 12539BIC 17508 13180 12921 12784 12598R2

adj 0.56 0.33 0.40 0.50 0.54RMSE 2.91 2.60 2.47 2.58 2.49

©2016 NRC Canada

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climate sensitive site index models for norway

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