The dendroclimatic model MAIDEN has initially been developed by . It explicitly includes biological processes, namely photosynthesis and carbon allocation to different tree compartments, to simulate an annual tree-growth increment. The model uses daily climatic inputs (i.e. CO2 atmospheric concentration, precipitation, and minimum and maximum air temperature). Up to now, MAIDEN has been applied in the Mediterranean and temperate regions , in the Eastern Canadian taiga , and in Argentina . Currently, there are two versions of the model: from , developed for the Mediterranean forests, and , for boreal tree species. A unified version from those two versions has also been developed by Fabio Gennaretti (unpublished). In this study, all tests have been conducted using the unified version of MAIDEN. This unified version gives the opportunity to choose between the version from or from and, if needed, to test equations from both versions to evaluate their impact. However, here, only the version from is used as it is the most adapted to the selected sites.

MAIDEN simulates photosynthesis on a daily basis and allocates the daily available carbon from photosynthesis and stored non-structural carbohydrates to different pools (leaves, roots, stem and storage). The allocation is based on functional rules defined following the ongoing phenological phase (five phases per year: winter 1 with no accumulation of growing degree-days (GDD), winter 2 with active GDD accumulation, budburst, summer and fall). At the end of the year, the model sums all the daily carbon inputs allocated to the stem to get an annual tree-growth increment (yearly Dstem, hereafter Dstem, in grams of carbon per square metre of stand per year). Dstem is assumed to be proportional to tree-ring growth so that we can build simulated tree-ring index time series and compare it with tree-ring width (hereafter TRW) observations (Sect. ) . The structure of the MAIDEN model is provided online (https://figshare.com/articles/MAIDEN_ecophysiological_forest_model/5446435/1, last access: 17 November 2019; ), and its modules are available upon request.

Tree-ring observation site and climate station (corresponding to a single location or grid cell as a function of the climatic dataset) constants of the MAIDEN model (Table S1) are derived from observations, as far as possible. For practical reasons, we were not able to retrieve slope and aspect information from a digital elevation model, for example, because it requires field knowledge of the site and for each sample, which we cannot systematically obtain given our global-scale goals. Thus, slope and aspect constants are set to zero. The soil is divided into four layers (1–15; 15–30; 30–65; 65–100 cm). Clay and sand fractions are extracted from the Harmonized World Soil Database (hereafter HWSD) v1.2 at 30 arcsec resolution at the nearest cell with observed value, which is always at a distance smaller than 100 km to the site and assigned as follows: 1–30 cm parameters from the HWSD for the two first soil layers in MAIDEN; 30–100 cm parameters from the HWSD for the two deepest soil layers in MAIDEN. Soil layer thickness is fixed at the same value for all sites, as for fine root fractions.

VS-Lite was developed by as a simplified version of the full Vaganov–Shashkin model . The model reproduces the primary response of ring width to climate using an approach based on the limiting factors principle (i.e. temperature and soil moisture) and on threshold growth response functions. It does not model any biological processes explicitly so it cannot be considered fully mechanistic. The model needs monthly climate data (cumulated precipitations and average temperature) as input as well as latitude of the study site. The main output of VS-Lite used here is a unitless annual tree-growth increment .

A network of tree-ring width chronologies of Picea mariana collected in similar conditions is available for the Eastern Canadian taiga (; http://dendro-qc-lab.ca/trw.html, last access: 30 March 2019). We use here the tree-ring series directly derived from this compilation, without any modification. The chronologies have been previously standardized using the age-band regional curve standardization (or RCS) method proposed by and further applied to a similar boreal dataset by . We also use the Eastern Canadian taiga chronology for Picea mariana from (hereafter QC_taiga), standardized using a site-specific RCS . The latter is highly replicated compared to the other Eastern Canadian sites from and , which cover a broader spatial range, and provides additional observations to calibrate the model. From this network, we have only selected sites from and ending at least in 2000, with an expressed population signal (defined as the amount of variance of a population chronology infinitely replicated explained by a finite subsample; ) equal to or above 0.8, and replication equal to or above 15. We have also kept the site from as a control site. At the end of the selection process, we get 21 sites (Fig. a). In order to increase replication, the Canadian sites from and are aggregated based on a 1∘ grid by averaging tree-ring width chronologies (Fig. b). From this, we get five aggregated sites (Table ). Note that QC_taiga is not included into the aggregation process to keep it as a reference. The aggregation allows us to get relatively good intersite correlations inside the same 1∘ grid, ranging from 0.442 to 0.732 with an average of 0.558. This observational network represents an archetypal example of a singular species that covers an important hydroclimatic gradient. Sites located along the western (near James Bay, WNFLV1, Fig. a) and eastern (near Labrador sea, WL32, Fig. a) margins of the study area present the warmest growing seasons in the network (864 growing degree-days above 5 ∘C for the 1976–2005 period; ). Sites located in the centre of the Quebec–Labrador peninsula (WHM2, Fig. a) present a much shorter growing season (692 growing degree-days above 5 ∘C), much like the sites located further north (WLECA, Fig. a, 573 growing degree-days above 5 ∘C). Annual precipitation increases from west to east, passing from 668 mm (WNFLV1, Fig. a) to 907 mm (WL32, Fig. a), and significantly decreases with latitude, reaching only 567 mm at WLECA (Fig. a) for the 1976–2005 period . This makes this network a relevant candidate for our calibration and validation exercises.

Three additional tree-ring width chronologies (hereafter European sites) are used to perform tests on sites with good replication, especially at the European Alps site, and long nearby series from meteorological stations (Fig. ): EALP (47∘ N, 10.7∘ E; 2050 m; European Alps; Pinus cembra and Larix decidua; ; processed data available in the PAGES 2k database; ); SWIT179 (46.77∘ N, 9.82∘ E; 1800 m; Picea abies; standardized with a cubic-smoothing spline with a 50 % frequency cut-off at 35 years; ; unprocessed data archived at the International Tree Ring Data Bank, https://www.ncdc.noaa.gov/data-access/paleoclimatology-data, last access: 12 January 2019) and FINL045 (68.07∘ N, 27.2∘ E; Pinus sylvestris; standardized using a spline with a 50 % frequency cut-off response at 32 years; ; processed data available in the Supplement of ). Similarly to the Eastern Canadian taiga chronologies, the tree-ring series were not modified here. Those three European sites exemplify a situation where we only have access to individual sites with different species and from different environmental conditions that are not part of a larger network of tree-ring width observations.

Daily climatic inputs are needed to run MAIDEN (Sect. ). Monthly climatic inputs for VS-Lite are computed from those daily data. Note that monthly-average temperature has been computed by averaging daily maximum and minimum temperatures, which could lead to a small bias. Three daily climatic datasets with different spatial resolution (Table ) were selected for our analysis on the Eastern Canadian taiga network (Fig. a and b). First, a dataset at a high spatial resolution of 5 min from the gridded interpolated Canadian database of daily minimum–maximum temperature and precipitation (, hereafter NRCAN). The Global Meteorological Forcing Dataset for land surface modeling (v1) (http://hydrology.princeton.edu/data.php, last access: 4 January 2019; ) at 1∘ resolution is used as a mid-resolution climatic dataset (hereafter GMF). The NOAA-CIRES 20th Century Reanalysis V2c (https://www.esrl.noaa.gov/psd/data/gridded/data.20thC_ReanV2c.monolevel.html, last access: 4 January 2019) at 2∘ resolution is used as a low-resolution dataset (hereafter 20CRv2c). Finally, the 20CRv2c dataset was modified to match the monthly-mean seasonal cycle of the high-resolution dataset NRCAN (hereafter 20CRv2c corr.). This simple bias correction and downscaling to the location of the site is done by removing the difference between the monthly-mean seasonal cycle of 20CRv2c (2∘) and NRCAN (5 arcmin) from the maximum and minimum temperature data. In order to avoid negative values, daily precipitations are multiplied by the ratio between the monthly-mean seasonal cycle of NRCAN (5 arcmin) and 20CRv2c (2∘). The time series are extracted from the grid cells nearest to the studied individual sites. The climatic data are averaged over the individual site data for the aggregated Eastern Canadian sites (Table ).

The Global Historical Climate Network Daily (Table ; see Table S2 for details on selected stations; ; hereafter GHCN) is used to perform analysis on the European sites (FINL045, EALP, SWIT179, Fig. ).

Daily atmospheric CO2 concentration data are linearly interpolated from the annual data from Sato and Schmidt (https://data.giss.nasa.gov/modelforce/ghgases/, last access: 3 December 2018).

We have developed a protocol to systematically and automatically calibrate the model through a Bayesian procedure with Markov Chain Monte Carlo sampling carried out using the DREAMzs algorithm . The calibration procedure focusses on the most sensitive parameters of the model identified in : 6 parameters influencing the simulated stand growth primary production and 12 parameters involved in the modelling of the daily quantity of carbon allocated to different tree compartments (Table S3). Those 6+12 parameters are calibrated by comparison between simulated Dstem and tree-ring width observations. The comparison relies on the computation of the model likelihood defined as the sum of the logarithms of the normal probability densities of the residuals between the model simulation and the observations. The prior distributions of the 6+12 parameters are assumed to be uniform over an acceptable range, as in . The calibration procedure is made up of three steps. During the first step, we calibrate the 12 carbon allocation parameters, while fixing the 6 photosynthesis parameters to arbitrary values in their acceptable ranges. We run three Markov chains of 10 000 iterations with a five-iteration thinning (i.e. we only consider one random sample out of five) to calibrate the parameters. During the second step, we fix the 12 carbon allocation parameters at the values obtained from the first step. We calibrate the 6 photosynthesis parameters by also running three Markov chains of 10 000 iterations with a five-iteration thinning. Finally, during the third step, the 6 photosynthesis parameters are fixed at the values obtained from the second step, and the 12 carbon allocation parameters are calibrated, by running three Markov chains of 30 000 iterations, with a five-iteration thinning as well. Each of those nine chains starts from random initial values of the parameters in their acceptable ranges. At the end of each calibration step, we select the set of parameters with the highest posterior (maximum a posteriori value or MAP, ) from all iterations considering a burn-in period (i.e. the number of initial iterations of a chain that are not considered in the calibration) of 1000 iterations (first and second steps) and 3000 iterations (third step). At the end of the calibration process, we thus have 6 calibrated parameters from the second calibration step and 12 carbon allocation parameters from the third one. The calibration method has been tested for convergence of Markov chains with Gelman–Rubin statistical indicators .

The MAIDEN model was calibrated at the 21 Eastern Canadian taiga sites and at the 5 aggregated sites over the 1950–2000 time period using the high- (NRCAN), mid- (GMF) and low-resolution (20CRv2c) datasets as inputs, as well as the bias-corrected low-resolution dataset (20CRv2c corr.), and over the 1900–2000 time period using the 20CRv2c and 20CRv2c corr. datasets as climatic inputs. MAIDEN was also calibrated at the three European sites using GHCN station data over 1950–2000 (FINL045; EALP; SWIT179), 1909–1944 (FINL045) and 1910–1949 (EALP and SWIT179). Calibrated parameters values for the 1950–2000 time period are available in Tables S4–S7. Parameter posterior frequency distributions for the NRCAN (5 arcmin) high-resolution climatic dataset are available in Figs. S1–S58. Pearson correlation coefficients between observed TRW and simulated Dstem were computed, as well as the corresponding confidence level. To compare observed and simulated tree-ring growth data after the optimization of the model parameters, both observed tree-ring width series and simulated time series have been normalized to unitless indexes. Ideally, an exhaustive quantitative evaluation of MAIDEN would require a comparison of the variable simulated by MAIDEN to represent tree-growth directly with observations. However, this would imply the use of other tree-growth observations such as tree-ring density measurements, while tree-ring width represents the most widely available tree-growth observations, which makes it a relevant candidate given our global-scale goals. The disadvantage is that this normalization forbids us to assess error in the variance. This is why we only analyse the correlations for simplicity as using other metrics like the RMSE would not help us in this aspect.

The VS-Lite parameters are calibrated at each location following a Bayesian approach described in . In this study, four VS-Lite parameters, corresponding to the lower and upper temperature (respectively T1 and T2 in ) and soil moisture (respectively M1 and M2 in ) thresholds of the model have been optimized. The other parameters were fixed to default values. The method is based on a standard Markov chain Monte Carlo approach, a Metropolis–Hastings algorithm embedded within a Gibbs sampler. The VS-Lite model was calibrated at the same sites and over the same time periods as MAIDEN, using the same climatic data (Sect. ). Calibrated parameters values for the 1950–2000 period are available in Tables S8–S11. Pearson correlation coefficients between TRW observations and simulated tree-growth indexes were also computed. Observed time series have been normalized to unitless indexes as well.

Running MAIDEN takes around 2.5 s on one CPU for a 50-year time span, while running VS-Lite takes around 0.30 s. Currently, calibrating MAIDEN with our method takes around 18 h on one CPU for a site due to the high number of iterations and calibrated parameters, while the calibration method used for VS-Lite and developed by Tolwinski-Ward et al. (2013) takes only a few seconds.