Species-specific, pan-European diameter increment models based on data of 2.3 million trees

Abstract

Background

Over the last decades, many forest simulators have been developed for the forests of individual European countries. The underlying growth models are usually based on national datasets of varying size, obtained from National Forest Inventories or from long-term research plots. Many of these models include country- and location-specific predictors, such as site quality indices that may aggregate climate, soil properties and topography effects. Consequently, it is not sensible to compare such models among countries, and it is often impossible to apply models outside the region or country they were developed for. However, there is a clear need for more generically applicable but still locally accurate and climate sensitive simulators at the European scale, which requires the development of models that are applicable across the European continent. The purpose of this study is to develop tree diameter increment models that are applicable at the European scale, but still locally accurate. We compiled and used a dataset of diameter increment observations of over 2.3 million trees from 10 National Forest Inventories in Europe and a set of 99 potential explanatory variables covering forest structure, weather, climate, soil and nutrient deposition.

Results

Diameter increment models are presented for 20 species/species groups. Selection of explanatory variables was done using a combination of forward and backward selection methods. The explained variance ranged from 10% to 53% depending on the species. Variables related to forest structure (basal area of the stand and relative size of the tree) contributed most to the explained variance, but environmental variables were important to account for spatial patterns. The type of environmental variables included differed greatly among species.

Conclusions

The presented diameter increment models are the first of their kind that are applicable at the European scale. This is an important step towards the development of a new generation of forest development simulators that can be applied at the European scale, but that are sensitive to variations in growing conditions and applicable to a wider range of management systems than before. This allows European scale but detailed analyses concerning topics like CO₂ sequestration, wood mobilisation, long term impact of management, etc.

Background

The EU has a vision of sustainable forestry contributing to the economy of its Member States and to the environment—both regionally and globally. In the latter context, the role of forests in biodiversity conservation and climate change mitigation as well as raw material provision has become increasingly important through the United Nations Convention on Biological Diversity (CBD) and the United Nations Framework Convention on Climate Change (UNFCCC). Forests in the EU’s 28 Member States stretch over a huge variety from the Atlantic in the west to the Black Sea in the east, and from the Mediterranean in the south to the boreal in the north covering 157 million ha (FOREST EUROPE 2015). Forest management has evolved at a national or sub-national level influenced by the quantity and nature of the forest resources available, forecasts on their future development, perceived demand for raw material and services, and local economic and social factors. The management of forest resources has been affected in recent years by substantial shifts in the demands and expectations put on forests, while the forest resource itself is subject to new pressures which are not yet sufficiently taken into account in national or international policies.

These pressures include diseases, invasive species, and the effects of climate change on forests through, e.g. drought, and storms (Lindner et al. 2014). Many forests continue to provide the traditional forest products of timber, pulp, paper, etc., but forested areas are also expected to provide important ecosystem services, including climate change mitigation, conservation of biodiversity, recreation and protection of water and soil (Nabuurs et al. 2006; Verkerk et al. 2011). A key policy issue is how the existing and future forests in the EU, which are limited in size and have a fragmented ownership, should be managed to deliver in a sustainable way an optimal mix of social, environmental (including biodiversity conservation) and economic services. These uncertainties plus a long planning horizon in forestry, require us to predict the long term impacts of management and environmental changes. One avenue is the employment of resource projection models (Barreiro et al. 2017).

Making scenario projections of European forests is a hugely challenging task. Not only do they cover a large range of biotic and abiotic conditions, but they are spread over 46 countries, each with their own (forest) policies, inventory systems (Tomppo et al. 2010) and national forest resource projection systems (Barreiro et al. 2016; Barreiro et al. 2017). National forest inventory systems (NFIs), if existing at all, differ considerably in design, size thresholds, definitions, estimation methods, census interval, and importantly, in data access policy. A few countries have made their raw measurements available on the web (Netherlands, Germany, France, Spain), a few make them available on request (e.g. Norway, Sweden), but still most results are only available in aggregated tables and reports. Even when the data are accessible, standardisation and harmonisation between NFIs remains difficult (Köhl et al. 2000; McRoberts et al. 2009; Dunger et al. 2012). Data collection efforts like FOREST EUROPE (FOREST EUROPE 2015) and the Global Forest Resource Assessments by FAO (FAO 2015) try to improve the harmonisation, but it remains a challenge (COSTE43 2011). National forest resource projection systems show an even larger variety in design, methodologies, processes and update cycles (Barreiro et al. 2016; Barreiro et al. 2017), which makes it almost impossible to compare projections among countries.

Resource projections for Europe show different approaches for handling the harmonisation challenge. For a long time, the European Timber Trend Studies (ETTS) as published by the UNECE/FAO were a collection of nationally executed projections of a set of standardised scenarios (Schelhaas et al. 2017). Nilsson et al. (1992) were the first to use a common, empirical projection tool applied country-wise on aggregated national forest inventory data. Since then, the same age-volume class matrix approach was developed and commonly applied as EFISCEN (European Forest Information Scenario model) in studies down to provincial resolution for the total European scale (Nabuurs et al. 2006; Schelhaas et al. 2015; Verkerk et al. 2016) for carbon balance studies, wood availability and e.g. trade-offs with biodiversity. Also, other models like CBM-CFS3 are being employed for European forest carbon balance assessments (Pilli et al. 2016).

When the first European-scale forest resource models were developed, the approach chosen matched best with the predominant forest management approach in Europe (mostly even-aged management), the data availability (only aggregated data available), the issues to be addressed (large-scale resource availability, Member State level carbon sequestration) and the computing power available. In the meantime, the situation has changed drastically. Forestry is now increasingly incorporating natural processes taking into account effects of climate change on growth (Peng 2000) as well as the fulfilment of forest functions other than wood production (Verkerk 2015). As a consequence, the forests are becoming more heterogeneous in species and structure (Hector and Bagchi 2007; Morin et al. 2011; Zhang et al. 2012), and a larger range of management options need to be considered (Duncker et al. 2012; Hengeveld et al. 2012).

At the same time, the data policies are becoming more open and the computing power has increased dramatically. These developments are reflected in the construction of more complex national projection models, often simulating individual trees, with high geographical detail and usually based on NFI data (Barreiro et al. 2016), sometimes capable of incorporating anticipated future growth changes. These tools are usually not transferable to other countries because they are developed on very specific national conditions and datasets. However, a clear need can be identified for such simulation tools at the European level (Schelhaas et al. 2017). Such a tool should be able to 1) cover a wide range of biotic and abiotic conditions, 2) have growth models sensitive to changing environments, 3) be sensitive to varying forest systems and forest management approaches, and 4) be age-independent and have a high geographical detail. In this paper, we aim to develop a set of empirical individual-tree growth models that could be used in such a model at the European scale.

Methods

National forest inventory data

We collected individual tree measurements from available National Forest Inventories to represent the range in growing conditions in Europe (Fig. 1). We included NFI data from Norway (Tomter et al. 2010), Sweden (Fridman et al. 2014), Netherlands (Schelhaas et al. 2014; Oldenburger and Schoonderwoerd 2016), Germany (Riedel et al. 2016), a part of Ireland (Redmond 2016), Poland (Anonymous 2015), France (Hervé 2016), Switzerland (Lanz et al. 2016), Spain (Alberdi et al. 2016) and the Italian regions Piemonte (Camerano et al. 2008) and Aosta (Camerano et al. 2007). NFI systems differ in terms of inventory cycles, sampling system, plot radius, diameter threshold etc. (Table 1). Germany uses an angle count method (Bitterlich 1952), while other countries use a design with circular plots, either with a variable radius depending on the plot conditions, or with different radii with corresponding diameter thresholds. In total, observations were available for more than 2.3 million trees on over 190,000 plots, from 10 different NFIs. Except for France and the two Italian regions, data consisted of repeated tree diameter observations from permanent sample plots. Tree data included observation of diameter at breast height (DBH, hereafter simply referred to as diameter; all countries use a breast height of 1.3 m) during two consecutive measurements and identification of the tree species, for all trees that were alive both at the first and second observation.

Fig. 1

NFI plot locations

Table 1 Overview of the NFI datasets used and their most important features

In France, increment was recorded as the width of the last 5 tree rings as measured on a core, for all trees on the plot. In the two Italian regions, increment was available as the 10-year radial increment of the tree closest to the plot centre, as measured on a core. Radial increment from tree core data was converted to diameter increment (France, the two Italian regions). For these countries we considered the measured diameter increment in the past as a prediction of the diameter increment in the years after the observation, i.e. we did not reconstruct the diameter 5 or 10 years ago as starting point for the analysis. We chose this approach because plot basal area is one of the potential explanatory variables, and we didn’t have sufficient information to reconstruct plot basal area in the past. Tree circumference as measured in France was converted to diameter. All observations were converted to annual diameter increment by dividing the total diameter increment by the number of years between the measurements, using the YEARFRAC function in Excel. Occasional observations of negative diameter change were assumed to result from unbiased measurement errors, therefore these negative diameter changes were kept to avoid introducing bias.

We grouped the tree species in 20 species groups (Table 2). Minor species or species groups were iteratively merged until sufficiently large groups remained. Species or species groups were retained if they covered at least 5% of the total dataset over all countries, or if they were considered as an important species in a certain region of Europe, either in terms of production (like poplar plantations) or in coverage (like Quercus ilex (L.) and Quercus suber (L.) in the Mediterranean region). The group ‘Populus plantations’ includes only Populus species and hybrids that are commonly used in commercial plantations while other Populus species are included in the category ‘shortlived broadleaves’. For completeness in view of intended model application, ‘rest’ groups were created for broadleaves and conifers. For broadleaves the rest category was split into shortlived and longlived species based on authors’ judgement.

Table 2 Summary of observed characteristics of the species after removing incomplete records

Explanatory variables

We constructed a set of potential explanatory variables, covering information on the forest structure (F), soil (S), climate (C), weather (W) and nutrient deposition (D). Forest structure was represented by stand basal area at the time of first measurement as delivered by the different NFIs, and the variable F-rDiffDq, a proxy for the social position of each tree within the stand defined as:

$$ \mathrm{F}-\mathrm{rDiffDq}= DBH/ DBH\mathrm{q}\hbox{--} 1 $$

(1)

with DBH the diameter of the tree and DBHq the quadratic mean diameter of all trees on the plot at the first observation. Values smaller than zero indicate that the tree is relatively small and more likely to be suppressed, while values larger than zero indicate that the tree is more likely to be dominant.

Soil, climate, weather and nutrient deposition variables were derived from data sets with full European coverage, using the plot coordinates. To derive soil characteristics, we used the 1 km resolution SoilGrids dataset (Hengel et al. 2014). This dataset covers soil pH, sand/silt/clay fraction, depth to bedrock, bulk density, cation exchange capacity (CEC), soil organic fraction and fraction of coarse fragments. The dataset consists of estimates of the respective properties at 7 depths ranging from 0 to 200 cm. We only used the third depth (15 cm), since the values at different depths were highly correlated. We also included a map with natural soil susceptibility to compaction from the European Soil Data Centre (Panagos et al. 2012).

To derive climate characteristics, we used the WorldClim (Hijmans et al. 2005) and the GEnS (Metzger et al. 2013, based on the WorldClim (Hijmans et al. 2005) and CGIAR-CSI data (Trabucco et al. 2008; Zomer et al. 2008)) datasets. Both datasets cover a range of climatic variables and indices (like monthly and annual means and extremes for temperature and precipitation, temperature and precipitation in coldest/warmest/wettest driest quarter or summer/winter, several aridity and humidity indices, etc.), averaged for the period 1950–2000, at 1 km resolution. The datasets partly overlap but each set has some unique variables. Altitude correlates with weather and climate variables and is often included as predictor in similar studies. However, the inclusion of altitude makes it impossible to include climate change effects directly in the model and thus we excluded it from the predictor set. For the same reason, latitude was not included either.

For nutrient deposition we used the EMEP data, containing deposition of oxidised and reduced nitrogen and oxidised sulphur at the 50 km grid (www.emep.int). Average nutrient deposition values were calculated for the period 1990–2010.

For weather, we obtained data from Agri4Cast (http://agri4cast.jrc.ec.europa.eu/), at 25 km resolution for the period 1975–2015. We used this dataset to calculate a range of weather indices (similar to the climate indices) for the actual observation period of each tree in our dataset. See Appendix 1 for more information on weather indices and calculation procedures. In total we included 99 abiotic explanatory variables (for a full list see Appendix 2).

To avoid simultaneous use of explanatory variables with large correlations in the models, we made a selection among variables with correlations greater than 0.8 or smaller than − 0.8. This selection was based on scores that preferred simpler variables over more complicated ones (like average temperature over degree days above a certain threshold), weather variables over climate and easily available ones over those that are usually more difficult to obtain. The full list of variables and their priority in the data preparation is given in Appendix 2. Exclusion of correlated variables was done for each species group separately, since the spatial occurrence pattern of the species influences the observation range of the explanatory variables. Incomplete cases in the remaining dataset were removed.

Diameter increment model

Here, we restrict ourselves to modelling the diameter increment. Of all variables measured in the NFIs across Europe, diameter is probably the most harmonised one, available for the largest number of trees, available as repeated observations on the same tree, and directly measured without further interpretation.

Some authors prefer to use basal area increment models over diameter increment models (Wykoff 1990; Quicke et al. 1994; Monserud and Sterba 1996; Schröder et al. 2002,) but Vanclay (1994) argues that both approaches are essentially the same, since one can be derived from the other. Tree diameter generally develops according to an asymmetric sigmoidal function through time, with a slow, but rapidly increasing growth at establishment, almost constant growth during the mature phase followed by a slow decline in growth during senescence (Tomé et al. 2006). Because creating new tree rings is essential for water transport, diameter increment will theoretically never reach zero, although the rings can be very small at old age.

Although age is known to be one of the best predictors of growth (Pukkala 1989; MacFarlane et al. 2002; Zhao et al. 2006; Tomé et al. 2006), we explicitly aim to exclude it as a predictor since it is not directly measured for all trees in the NFIs and forest situations in Europe. Instead, we selected diameter, which is directly measured, as the predictor.

Modelling of sigmoidal relationships is usually achieved with so-called theoretical growth curves, such as the Lundqvist (Korf 1939; Stage 1963), Gompertz (Winsor 1932) and Chapman-Richards (Richards 1959) functions. Here, we choose the Gompertz function, because it has the following properties:

• 1. The function is right-skewed, with a maximum growth at 1/e times the asymptotic diameter.

• 2. The derivative of the function with respect to time (e.g. growth) can be written in a form only dependent on diameter.

Thus, for estimating diameter increment the derivative of the Gompertz equation is used:

$$ \frac{\mathrm{d} DBH}{\mathrm{d}t}={\beta}_1 DBH+{\beta}_2 DBH\ln DBH+\varepsilon $$

(2)

with dDBH/dt the diameter increment (in mm), DBH the diameter (in mm), β₁ and β₂ parameters and ε is the error term with an assumed distribution N~(0, σ). These parameters are a function of a set of independent variables X _i expressed as:

$$ {\beta}_1={c}_1+\sum \limits_{i=1}^p{\theta}_{i,1}{X}_i $$

(3)

$$ {\beta}_2={c}_2+\sum \limits_{i=1}^p{\theta}_{i,2}{X}_i\kern0.5em $$

(4)

For both β₁ and β₂ the variables X _i used to estimate the parameter vectors are the same. The procedure for the selection of the p variables that best explain the diameter increment is described later. Values for c and θ are estimated using ordinary least squares (OLS) by substituting Eqs. 3 and 4 in Eq. 2.

The diameter when maximum growth occurs is defined by:

$$ {DBH}_{opt}={e}^{-\left(\frac{\beta_1}{\beta_2}+1\right)} $$

(5)

with a maximum growth equal to:

$$ {\frac{\mathrm{d} DBH}{\mathrm{d}t}}_{max}=-{\beta}_2{DBH}_{opt} $$

(6)

The census interval in the datasets is overall either around 5 or 10 years depending on the country. To relate the total diameter increment in this varying period to the diameter using a non-linear model, we use the average between the two measured diameters as a proxy for the diameter.

Figure 2 illustrates the shape of the growth model. A simultaneous increase of β₁ and β₂ by the same percentage increases the maximum diameter increment that can be reached, but leaves the diameter with maximum diameter increment and the maximum diameter unchanged. A small relative decrease of β₁, or the same relative increase in β₂, lowers the curve as a whole, resulting in smaller maximum diameter increment, a smaller diameter of maximum diameter increment and a smaller maximum diameter that can be reached.

Fig. 2

Shape of the growth model with β₁ = 0.1 and β₂ = − 0.014 (base), if β₁ and β₂ are increased by 20% and if β₁ is decreased by 1%

Variable selection and model fitting

The selection of variables to be included in the model was performed in two phases for each species independently. First, a forward selection procedure was used. Given the large number of data points, the dataset was split in a selection-dataset (75%) and an acceptance-dataset (25%). Variables were added one-at-a-time. First, using the selection-dataset the additional variables were ranked based on the Akaike information criterion (AIC, Akaike 1974). Because the large number of observations bias the AIC towards ever decreasing values with increasing numbers of variables, acceptance of the best ranking variable was subsequently based on an F-test performed on the predicted values for the acceptance-dataset (Zar 1996). The variables selected for 10 independent data-splits were combined to obtain a list of candidate variables. Secondly, these candidate variables were used in a backward selection procedure on the full dataset for the final selection of explanatory variables. In this procedure the variable to be excluded was again selected based on AIC and it was actually excluded based on an F-test. The selected variables were used to estimate the full set of coefficients of the final model. The full models (substituting Eqs. 3 and 4 in Eq. 2) were fitted using OLS in the lm function in R (R:stats) (R core team 2014). For all F-tests a conservative α-value of 0.0001 was used to avoid overfitting the data. The average observed diameter increment was used as reference for calculation of F-tests and R^2*, rather than a reference value of 0 as is default when no intercept is included in the model. Model residuals showed some heteroscedasticity at small diameters (Additional file 1), but seemed homoscedastic over a large range of observations. We did not transform our data, which would introduce bias due to the need to exclude negative observations. In view of the intended model application we also calculated the R^2* of the total predicted basal area increment at plot-level for all available plots, including all species.

Results

The number of explanatory variables included in the final diameter increment models ranged between 2 and 25 for all species/species groups (Tables 3 and 4). Variables of forest structure were always included (Table 4), weather and climate were included for 18 species, while soil and nutrient deposition were included for 16 and 13 species, respectively. R^2* ranged from 0.10 for Quercus ilex to 0.53 for other conifers (Table 4). The R^2* for total basal area increment at the plot level was 0.85. Conifers generally had greater R^2* than broadleaves (conifers 0.32 on average over all species and broadleaves 0.22). There was no clear relationship between the number of variables or variable groups selected and the explained variance. We tested the contribution to the explained variance of each group of variables by fitting the full model again, excluding the variables from that group, and recorded the decrease in R^2*. If forest structural variables were left out from the model, the explained variance decreased by 43.9%, on average over all species groups. If weather variables were left out, the explained variance decreased by 8.7% and for climate by 3.8%. Soil and nutrient deposition accounted for respectively 2.2% and 1.4% of the explained variance. The weather variables most often selected were generally related to annual temperature (W-MaT), temperature variations (annual temperature range W-aTR, mean diurnal range W-MaDR) or radiation (W-TaR), while less frequently selected variables tended to include indices and minima and maxima for specific 3-month periods (quarters), related to precipitation and potential evapotranspiration (PET). For the climate variables no clear pattern could be distinguished, but also here annual variables were more often selected than indices and values for specific quarters.

Table 3 Selected variables and parameter estimates per species group. For abbreviations of variables see Appendix 2

Table 4 First column: Number of variables selected per species group and R^2* for the full model. Following columns: Number of variables selected per variable group in the final model, and the relative decrease in R^2* if this variable group is omitted from the model and fitted again

To get an impression of the spatial variability in predicted diameter increment, we calculated the growth of a tree for all locations where a tree of that species was present in our dataset. We assumed the tree had a diameter equal to the average diameter of the species in the full dataset (Table 2), an F-rDiffDq of 0 (i.e. the social position of the tree was neutral) and that it was growing in a stand with a basal area equal to the average basal area listed in Table 2. We used the weather conditions of the period 2000–2014. Species groups show distinctively different spatial growth patterns (Fig. 3; Additional file 2). Some species, like Fagus sylvatica and Abies spp., have slow growth at their southern distribution limit and show good growth towards their northern limit, while other species like Picea abies show the opposite pattern. Many species (Picea abies, P. sitchensis, Populus plantations) show an east-west gradient with better growth along the coast and less growth going east, but Pseudotsuga menziesii and Quercus robur + petraea show the opposite tendency. Only few groups (Pinus sylvestris, Betula spp.) show an optimum in their mid-range and decreased growth towards their distribution limits.

Fig. 3

Predicted diameter increment (mm/yr) of Fagus sylvatica and Picea abies at all sites where it is present, assuming average diameter and basal area (Table 2) and a neutral social position (F-rDiffDq = 0), with weather conditions for the period 2000–2014. Please note that the scale is different between the species. For all maps see Additional file 2

To illustrate the sensitivity of the final models we show the predicted diameter increment for a range of conditions (Fig. 4; Additional file 3). The main curve depicts the median diameter increment as predicted for all sites assuming the median F-BA and a neutral social position (F-rDiffDq = 0). Ranges depict deviations from this median growth for 5th and 95th percentile of increment predicted for all locations, 5th and 95th percentile of F-BA observed in all locations and 5th and 95th percentile of F-rDiffDq observed in all locations. Additional file 4 shows the distribution of the underlying data and the moving average curves of both data and predictions.

Fig. 4

Sensitivity of predicted diameter increment in relation to diameter for Picea abies for a range of site and stand conditions. The maximum value at the x-axis corresponds to the 99th percentile of diameter observed per species (Table 2)

Discussion

Growth of trees is governed by physical processes, plant physiological processes and ecological processes (Muys et al. 2010; Sterck et al. 2010). We have established a general description of the predicted diameter increment of European tree species as a function of the diameter and the biotic and abiotic environment of the tree. Even with the rather crude estimates of weather, climate, soil and nutrient deposition that were used, the strict shape of the growth curve, and the exclusion of the known good predictors age, latitude and altitude, we were able to explain between 10% and 53% of the variation in diameter growth of individual trees of the main European tree species and species groups. This level of explained variation is in line with the values reported by other studies based on country-scale forest inventory datasets (e.g. Andreassen and Tomter 2003; Laubhann et al. 2009; Cienciala et al. 2016; Charru et al. 2017). Much of the unexplained variance seems to be attributable to within-stand variation, given the high R^2* value for total basal area increment at the plot level given in the results section. Further application of the models should give insight in the predictive value at larger scales. Other studies (e.g. Laubhann et al. 2009) already applied regression models on individual-tree measurements for multiple European countries, but these studies were aimed at estimating effect sizes, rather than for predictive purposes. To our knowledge our study is the first to present tree diameter increment models with a European-wide validity.

Apart from the regular measurement errors within an NFI (McRoberts et al. 1994), our dataset may contain extra variability by mixing different NFIs with different designs, measurement methods, protocols and thresholds (Table 1). On first screening of the data, we could not find indications for systematic differences between data from different NFIs, probably because we used the original diameter measurements without any further processing or interpretation. Additional noise is caused by the inclusion of explanatory variables of varying resolution (1–25 km), making it impossible to detect small-scale variation as present for example in mountainous terrain. However, the presented models are designed to be applied on a broad scale for large sets of plots, which will result in averaging out such errors. For studies on smaller scales, local or national diameter increment models might be better suited.

The largest part of the explained variance in the final models is attributed to parameters related to the forest structure, where basal area of the stand seems to be more important than the relative size of the tree (Fig. 4; Additional file 3). This is in line with many other studies that found stand density (Cienciala et al. 2016) or basal area (Hökkä et al. 1997) to be important variables. Despite the relatively low contribution of other variable groups to the explained variance, they are important to explain spatial patterns of diameter increment over Europe (Fig. 3; Additional file 2). The spatial patterns of diameter increment as presented in Additional file 2 seem plausible. Picea abies and Picea sitchensis are known to grow well under wet conditions and moderate temperatures. At higher latitudes and altitudes, growth of Picea abies is limited by a short growing season and low average temperatures, as indicated by declining diameter increment. For Picea abies a similar gradual decline is not visible on the southern edge. This is probably because trees are killed by attacks of bark beetles after drought or heat waves (Seidl et al. 2007). The opposite pattern is found in Fagus sylvatica. At the southern edge, increment slows down as temperatures rise, while there is an abrupt halt at the northern edge. This may be caused by mortality due to cold winters, or because Fagus is still expanding its range northwards (Kramer et al. 2010). Pinus sylvestris is known for its wide ability to survive in a wide range of environmental conditions. This is reflected in the spatial growth pattern with a large distribution over Europe, a moderate to good growth over a large range and declining growth only in harsh environments, such as dry inland Spain and under boreal conditions. Application of the models under climate change scenarios should give more information on the sensitivity of these patterns to climate change.

The diameter increment models presented allow for more detailed and consistent modelling of tree-growth at the European scale. With these models such modelling can take into account differences and changes in weather, climate and soil conditions across the continent and over time. As shown in Additional file 3, the models give realistic predictions over a large range of conditions. We recommend to use the models not further than the 99th percentile of diameter, as indicated in Table 2. Beyond these values the data support is very sparse, and the models may give unreasonable results. Similarly, the user should be aware that the models may predict small negative diameter increments for some species for specific combinations of poor locations, small diameters and high basal areas. The development of diameter increment models is a first step towards a full simulation model of forest development at the European scale. Such a growth model should include a way to estimate individual-tree volume from diameter, either directly (Zianis et al. 2005), via height/diameter ratio models (Mehtätalo 2005), or by inclusion of a height growth model (Ritchie and Hann 1986; Hasenauer and Monserud 1997), preferably climate-dependent. Furthermore, modules are needed to cover other important processes, like establishment of new trees, mortality and forest management.

Conclusions

The presented diameter increment models are the first of their kind that are applicable at the European scale. They are based on a unique dataset that covers the full range of growing conditions in Europe, and are sensitive to forest structure and environmental conditions, showing realistic patterns over their application range. This is an important step towards the development of a new generation of forest development simulators that can be applied at the European scale, but being sensitive to variations in growing conditions and applicable to a wider range of management systems than before.

Appendices

Appendix 1

Calculation of weather indices

Data were downloaded from the Agri4Cast website (http://agri4cast.jrc.ec.europa.eu/). It contains daily data for the period 1975–current, at 25 km resolution. We extracted monthly values for mean temperature, total precipitation, total potential evapotranspiration and total radiation, for the period 1990–2015. For all four variables we then computed for each year the annual total (or mean in the case of temperature), the standard deviation and the maximum and the minimum. For every year, the warmest, the coldest, the wettest and the driest quarter of the year was identified. A quarter was defined as a successive period of 3 months, where the value for the months January–March was assigned to January, February–April to February, etc. For the quarters starting in November and December, the months of the next year were used. For every warmest, coldest, wettest and driest quarter, the mean monthly value of all four variables was computed. The resulting explanatory variables where labelled according to their operator (denoted by M for mean, SD for standard deviation, MAX for maximum and MIN for minimum), their aggregation period (a for annual, m for month, waq for warmest quarter, coq for coldest quarter, weq for wettest quarter and drq for driest quarter) and their variable (T for temperature, P for precipitation, PET for potential evapotranspiration and R for radiation), 32 in total.

In addition we calculated the following indices, all on an annual basis:

• Mean diurnal range (labelled as MaDR) from the difference between the monthly averages of the daily maximum and the daily minimum temperature

• Annual temperature range (aTR) as the difference between MAXmT and MINmT

• Isothermality (ISO) as the ratio between MaDR and aTR

• Annual degree days with thresholds 0, 5 and 10 (labelled respectively as DD0, DD5 and DD10)

• Aridity index (ARi) as TaP/TaPET

• Thornthwaite 1948 humidity index (ThHUi), being the accumulated precipitation surplus divided by PET in those months

• Thornthwaite 1948 aridity index (ThARi), being the accumulated precipitation deficit divided by PET in those months

For every observation of individual tree growth, we calculated the average of each variable for the period of observation, including both full years when the tree was measured. Please note that the order of calculation for some variables may lead to different values as presented in the BIOCLIM dataset. For computational efficiency we first aggregated to annual values before averaging over the years.

Appendix 2

Full list of potential explanatory variables and their scoring

Table 5 List of potential explanatory variables included. When two variables are correlated, the one with the highest score is discarded

Table 6 Scores for elements of explanatory variables