Different parameters that are species dependent and site dependent need to be defined before running MAIDENiso at a particular site. Most of these parameters can be obtained from direct observations at the studied site, such as the characteristics of the soil (composition and depth) or the root–leaf proportions of the tree species. When the values of the parameters are unknown, these are calibrated through a Bayesian optimization algorithm described in detail in . This optimization is based on Markov chain Monte Carlo (MCMC) sampling that retains combinations (blocks) of parameters that satisfy a condition, maximizing the coincidence between a series of observations and the equivalent products simulated by MAIDENiso. Here, we used 50 independent chains of parameter blocks and selected the most optimal block of parameters (called the “plausible block”).

The series of observations used in the MCMC consist of observed time series of snow (depth or mass of the snow pile), GPP and δ18O in tree-ring cellulose (δ18OTRC). The parameters to be determined via MCMC for each component of the model are the following:

Snow pile: one parameter, ra from Eq. (). Calibrated by comparing observed and simulated daily snow depth (SNDP).

Because the new and the original versions of MAIDENiso behave differently, an independent calibration of the parameters is needed to run each of them. Note that the original version of MAIDENiso does not need to be calibrated for the snow parameters as it does not include a snow module.

Some parameters can influence more than one process indirectly; for example, the snow pile affects source water and therefore δ18OTRC, or the GPP parameters control the amount of carbon produced, which in turn affects δ18OTRC. To avoid that the calibration of some processes affects parameters that are already calibrated, the parameter sets need to be calibrated in a specific order: snow first, GPP second and lastly δ18OTRC.

The tree-ring study sites are located in Tungsten, Northwest Territories, Yukon border (61.98∘ N, 128.25∘ W; 1145 m a.s.l.), and in the Caniapiscau basin, Quebec (54.86∘ N, 69.72∘ W; 530 m a.s.l.).

MAIDENiso requires daily meteorological inputs for a continuous period of time overlapping with the period of available observations. Daily CO2 data were obtained from the Mauna Loa Observatory observations corrected with the CarbonTracker measurement and modelling system .

The closest meteorological stations to the study sites were located 100 km away from Tungsten and 186 km from Caniapiscau. Therefore, temperature and precipitation data were taken from the NARR (North American Reanalysis) dataset at the coordinates of the studied sites. The NARR has a spatial resolution of 32.5km×32.5 km and spans the period 1979–2013. Meteorological inputs were also needed at two additional sites to calibrate GPP, which are described in detail in Sect. . During the period 1979–2013 based on NARR, average summer temperatures (June–July–August) ranged 5.4–12.6 ∘C in Tungsten and 8.2–16.2 ∘C in Caniapiscau. Yearly temperatures at Tungsten are stable during the whole period, while at Caniapiscau average temperatures steadily rise after 1990 by 0.1 ∘Cyr-1. Average yearly precipitation values during this period were 584 and 796 mm in Tungsten and Caniapiscau, respectively. In Tungsten, 56 % of the yearly precipitation was snowfall, while in the warmer site of Caniapiscau snow was only 45 %.

MAIDENiso also needs information about δ18OP. Two different approaches can be used to infer δ18OP. The first and most direct way is to use daily values of δ18OP as another meteorological input. However, these values are often not available. The second approach, which we used here, is to use precipitation (P, mm), air temperature (Tair, ∘C) and δ18OP from an observed dataset to obtain a linear regression model for daily values of δ18OP based on temperature and precipitation: 2δ18OP=a⋅Tair+b⋅P+c.

This approach has the advantage that, once the model is obtained, the parameters can be used with a different dataset of air temperature and precipitation to obtain the corresponding δ18OP values. In this paper, we calibrated this regression model using meteorological data from the gridded dataset IsoGSM from the grid points that contain the coordinates of the Tungsten and Caniapiscau sites. We discarded the direct use of the IsoGSM meteorological and δ18OP data for MAIDENiso as the precipitation amounts derived from IsoGSM were too low compared to the amounts from observations recorded in meteorological stations nearby the study sites. However, the IsoGSM meteorological data were still useful to obtain the parameters for our regression model. We obtain different equations for liquid (rainfall: arain, brain, crain) and solid precipitation (snowfall: asnow, bsnow, csnow) using separately data corresponding to temperatures below -4 ∘C for snowfall and higher than 2 ∘C for rainfall (see Table ).

We used published δ18OTRC chronologies for Tungsten and Caniapiscau . These chronologies span between 1900–2003 for Tungsten and 1948–2013 for Caniapiscau; however, for this study we used the isotopic records for periods that overlap with the NARR meteorology: 1979–2003 for Tungsten and 1979–2013 for Caniapiscau.

We used GPP data available from the closest eddy covariance flux stations to estimate the parameters controlling GPP, assuming that the obtained parameters were similar at the studied sites. To calibrate GPP in Tungsten, we used the University of Alaska Fairbanks (Uaf) station from the Ameriflux network (64.87∘ N, 147.85∘ W; data period 2003–2018; ) at 1023 km from our study site. For Caniapiscau, we obtained daily GPP data from an eddy covariance station located in a mature black spruce forest in northern Quebec (“Quebec Eastern Old Black Spruce station” – EOBS; 49.69∘ N, 74.34∘ W; http://fluxnet.ornl.gov/site/269 (last access: 26 January 2016); data period 2003–2010; ) at 650 km from our study site. Although these eddy covariance flux stations are geographically distant from our study sites, they provide GPP data for the same tree species in our sites. Because the parameters used to calibrate GPP are more related to species-specific traits than environmental conditions at a given site, it is a reasonable assumption to calibrate GPP at these stations and use the obtained GPP parameters in our study sites. MAIDENiso simulated GPP at both stations, using the following meteorological inputs. For the Uaf station, we used the meteorological inputs available at the station. For the EOBS site, the meteorological inputs were taken from the gridded interpolated Canadian database of daily minimum–maximum temperature and precipitation for 1950–2015 , used in .

In situ snow-pile data are needed to test the predictive skills of MAIDENiso to simulate the snow pile. The snow water equivalent (SWE) data are the ideal snow-pile data to use, because addition (from precipitation) and removal (from sublimation and melting) of snow to or from the snow pile is calculated in units of mass. Alternatively, snow depth (SNDP) data, most commonly available, can be used as well to compare with observations but requires knowledge about snow density. SWE field measurements were only available for the Caniapiscau site at discrete (biweekly) intervals during winter and early spring between 1971–1993 (data provided by Hydro-Québec, personal communication, 2019). Therefore, in order to make the results from both sites comparable, we used SNDP data to calibrate the snow pile at Tungsten and Caniapiscau and only used the SWE measurements at Caniapiscau to validate the simulations. The SNDP data (1979–2013) were extracted from NARR for Caniapiscau and from observations of a meteorological station for Tungsten.

To evaluate the agreement between observed and simulated δ18OTRC for the two versions of MAIDENiso, we calculated the Pearson correlation coefficient and associated p values (p<0.05 were considered significant). To determine that the simulated δ18O at the leaf and cellulose level were statistically different, we used the Welch t test (which tests the null hypothesis that the difference between the means of two curves is zero).

While MAIDENiso does not calculate river discharge as an output (which would be possible through the implementation of a routing model), water discharge (water leaving the system in liquid form) can be calculated as the addition of runoff (water overflowing the infiltration capacity of the soil) and drainage (downwards water flux from the lowest soil layer) and be compared to measurements of river discharge. For this study, these comparisons were only done for Caniapiscau due to the availability of river discharge observations. To evaluate the coincidence between the observed and simulated water discharge, we used the Nash–Sutcliffe model efficiency (NSE) coefficient , which is equivalent to a coefficient of determination: 3NSE=1-∑t(Qsimt-Qobst)2∑t(Qobst-Q‾obs)2, where Qsimt and Qobst are the simulated and observed discharge at time t, respectively. The NSE ranges between -∞ and +1. To facilitate the interpretation of NSE, we rescaled the NSE within the range of (0,1) with the normalized Nash–Sutcliffe efficiency (NNSE) coefficient : 4NNSE=12-NSE.

Another useful metric is the Kling–Gupta efficiency (KGE) , which addresses several shortcomings of the NSE and is increasingly used for model calibration and evaluation: 5KGE=1-(r-1)2-σsimσobs-12+μsimμobs-12, where r is the linear correlation between observations and simulations, σ is the standard deviation and μ is the mean.

Values of NSE>0 (NNSE>0.5) are typically used as the benchmark to establish a model as a “good” model (NSE=0 indicates that the model is a predictor as good as the mean of the observations). The KGE equivalent values to consider that a model is skilful are KGE>1-2≈-0.41 .

To estimate the effect of the new snow module on predictions of δ18OTRC, we compared the parameters influencing δ18OTRC obtained by independent calibrations.

We also investigated the relative contributions to δ18OTRC of the source (xylem) water and of the fractionation processes during transpiration in the leaf (see the Eqs.  and in Appendix ). Using the same approach as in , we compared the predicted δ18OTRC from the reference simulations with those obtained from two experiments. First, to isolate the contribution of the source water on δ18OTRC, we set the relative humidity (hair) and δ18OV constant using the average values of hair and δ18OV obtained from the reference simulations. Second, to isolate the contribution of the isotopic enrichment of the leaf water during transpiration on δ18OTRC, we set δ18O in xylem water (δ18OXW) constant using the average value of the reference simulation. We then compared the reference and experimental simulations using the coefficient of determination (R2).

The snow module was validated using a split-sample approach. At both of our study sites, we divided the period of SNDP observations (1979–2013) into half-periods: 1979–1996 and 1997–2013. We then used the SNDP observations in each half-period to calibrate the snow module, following the same procedure described in Sect.  for the whole period of observations. Using the snow parameter obtained from each half-period, we simulated the whole period and compared the simulated snow pile with the snow observations using the NNSE and KGE metrics. To account for gaps in the observational record, we performed this comparison on the mean annual cycle of the signal (calculated by averaging the series for every day of the year) which was also smoothed with a 30 d spline.

Using the split-sample calibration method, MAIDENiso was able to simulate SNDP data for the full period that compared well with the SNDP observations at each site, as indicated by the two NNSE and KGE metrics (Table ). The obtained values were well above the thresholds that establish the model as a better predictor than the mean of the observations, with thresholds of NNSE=0.5 and KGE=0.41. In addition, the calibrations using half-periods produced similar results to the calibration using the full period, with the first half-period (1979–1996) producing slightly higher values than the second (1997–2013). The most notorious difference was the KGE obtained for the second half-period in Caniapiscau, which showed lower values (0.49) than the first half-period (0.69) and the full period (0.66), but it was still within the values needed to be considered a good model result.

MAIDENiso simulated SNDP and snow density using NARR meteorological data at our two sites, which we compared with the SNDP product from the NARR dataset. To compare with the direct observations of SWE at the Caniapiscau site, we used the simulated snow density to transform the SNDP (both that simulated by MAIDENiso and the NARR product) into SWE, which are shown in Fig. .

The MAIDENiso simulations reproduced the temporal change of the snow pile and showed a similar pattern to the real SWE observations collected at the Caniapiscau site (Fig. b). In contrast, the NARR-based SWE estimates showed higher values of the snowpack during the winter months and offsets in the timing of snow accumulation and melting. The discrepancies between the NARR-based SWE data and the MAIDENiso SWE simulations could arise from a mismatch between the NARR meteorology (used to drive the model) and the NARR's snow-pile data, where, according to the available documentation, the latter was artificially increased to match other sources . Therefore, our SWE simulations made by MAIDENiso using as inputs NARR meteorological data were in better agreement with the direct observations of SWE at the Caniapiscau site than the SWE data obtained directly from the NARR dataset.

The calibration process converged and constrained the values of ra (resistance to water vapour transfer) well at both sites, as shown in Table . We obtained a value of ra almost twice as large at Tungsten (87.35 sm-1) than at Caniapiscau (47.88 sm-1).

Figure  shows the combined runoff and drainage simulated by MAIDENiso with and without including the snow module and the observations of river discharge in the Caniapiscau basin (scaled by the area of the basin). The observations showed a peak in river discharge between May and July, corresponding to the melting of the snow accumulated during winter. In the simulations computed using the original version of MAIDENiso (without snow module), the outflux of the model resembled the pattern of precipitation during the year, because all incoming precipitation was considered liquid and did not show any peak. Conversely, the simulations produced using our new MAIDENiso version (with snow module) did not have any outflux during winter, when all water is in solid state, and they reproduced more accurately the peak of water outflux during spring melting. Overall, the timing of the spring discharge was well reproduced by the MAIDENiso version with snow, while the original version was unable to simulate this peak. This improvement was confirmed by the NNSE between the observed and modelled river discharge at Caniapiscau, which was lower for the model without snow (NNSE=0.1) than for the new model with snow (NNSE=0.45). The KGE for the observed and modelled river discharge at Caniapiscau improved only from -1.04 (without snow) to -0.57 (with snow), which indicates that our modelled river discharge (instant additions of drainage and runoff from all of the basin) can still be further improved.

GPP was calibrated twice at each station: first for the original version of MAIDENiso and second for the new version with snow. Both versions were able to predict GPP observations in a similar way for both the Uaf and the EOBS stations (Fig. ). The observed and simulated GPP were in good agreement regarding the timing (onset and offset) of the yearly peaks. The maximum of these peaks was higher for the observations, but this is due to exceptional days of very high observed GPP. Overall, the average GPP during the growing season was well reproduced at both GPP stations.

A Welch t test determined that the GPP simulated by both versions of the model were statistically not different at the two sites of EOBS (t=0.04, p value=0.97) and Uaf (t=0.47, p value=0.63). This lack of influence of the snow module in the GPP was expected considering that while the snow module increases the availability of water in spring, the trees in our sites are not limited by water availability. This result also guarantees that the effects of the snow module on the δ18O outputs that we are testing below are not affected by GPP by means of Eq. ().

Both model versions (MAIDENiso with and without snow) reproduced the mean level of the δ18OTRC series (Fig. ). This was expected because (1) the calibration process maximized the coincidence between observed and simulated δ18OTRC, and (2) the biochemical and kinetic fractionation parameters ϵ0 and ϵk could compensate the mean level of δ18OTRC in Eq. () for differences in δ18OXW. Regarding the agreement between inter-annual variations, the observed and simulated δ18OTRC were not significantly correlated when snow was absent in the model (Fig. ), but they were significantly correlated when MAIDENiso included snow (r=0.57 in Tungsten and r=0.52 in Caniapiscau, p<0.01; Fig. ). In the case of Caniapiscau, none of the versions of the model were able to simulate the amplitude of the variability of the observed δ18OTRC, which makes it difficult to appreciate the improvement in the correlation between simulated and observed δ18OTRC when adding snow to the model in Fig. b. To facilitate the interpretation of Fig. a and b, we have standardized the observed and simulated δ18OTRC series (transformed to mean 0 and standard deviation 1) in Fig. c and d.

The distribution of the optimized parameters controlling δ18OTRC can help to assess how the model compensated for the absence of snow (Table  and Fig. ). In our simulations, adding snow induced an increase in the dampening factor f0 at both sites, suggesting that the signal of the source water on δ18OTRC was stronger than without considering snow.

To cast light on the effect of the snow module on δ18O, we compared the δ18O values from various parts of the model (precipitation, xylem water, discharge water, leaf water and TRC) for both versions (with and without snow) of MAIDENiso at the two study sites (Fig. ). The δ18O of the precipitation (δ18OP, Fig. a) is the original source of the isotopic signals in the other parts of the model and it matches well to the IsoGSM data we used for its calibration, although it is consistently lower than the monthly data of the OIPC (Online Isotopes in Precipitation Calculator) at both sites. The snow directly impacted the δ18O of the source (xylem) water, δ18OXW (Fig. b). Without the snow module, δ18OXW followed closely the δ18OP signal shown in Fig. a, with a small delay due to the isotopic mixing in the soil. The δ18OXW signal was slightly enriched with respect to δ18OP due to isotopic fractionation associated with soil and canopy evaporation. In contrast, when snow was present in the model, the soil absorbed melted water from the snow pile in spring, which was enriched due to fractionation during sublimation in winter. The δ18OXW values were higher in the version with snow. The difference in δ18OXW values between the two versions reduced in time due to the infiltration and mixing of the enriched summer precipitation. Isotopic composition of discharge water (δ18Odis, Fig. c) follows a similar pattern to xylem water but with a delay of about 2 months and lower amplitudes in the seasonal variations.

The daily δ18O in the leaf (δ18Oleaf) and the TRC calculated with Eqs. () and () are shown in Fig. d and e. The existence of the snow layer induced a higher δ18O at the leaf level, especially in spring, due to the higher δ18OXW level. The mean level of δ18OTRC did not change after adding snow, despite the enrichment of δ18Oleaf and δ18OXW, because it was compensated by the lower values of the biochemical fractionation ϵ0. A Welch t test was used to test the hypothesis that the curves obtained for two versions of the model were different, which was confirmed in all figures.

Finally, we investigated the relative contributions from the source water through δ18OXW and the leaf transpiration enrichment through δ18Oleaf on the δ18OTRC time series (Fig. , peak values in Table ). At both sites, the leaf water δ18O isotopic enrichment had a stronger influence on δ18OTRC than the δ18O variability of xylem source water, as shown by the higher variance explained by the experiment that simulated δ18OTRC considering only the effect of δ18O leaf water enrichment indicated by a higher coefficient of determination (R2).

The addition of snow increased the R2 for both types of experiments but more importantly for the xylem source water experiment. As a consequence, the difference between the R2 of xylem and leaf experiments became smaller, although leaf transpiration still explained higher R2 at both sites. This was in agreement with the increase in f0 seen in Table  for both sites, pointing to an important influence of snow on the source water and on δ18OTRC.

The calibration of the snow module at our sites yielded a value of ra almost twice as large in Tungsten than in Caniapiscau. Because of the lack of data for daily wind speed, we chose to implement ra as a constant parameter. The higher value of ra at Tungsten implies that snow sublimated at a slower rate, likely associated with the fact that the average wind speed during winter at this site was smaller than at Caniapiscau, in accordance to the interpretation of ra .

The skills of MAIDENiso to reproduce the hydrological cycle improved with the implementation of the snow module. Because of the accumulation and melting of snow, the new version of MAIDENiso is now able to simulate the observed peak of river discharge in early spring, while the previous version without the snow module could not simulate any peak (Fig. ). The magnitude of this peak cannot be compared directly with observations, because downscaling the river discharge by the size of the basin is not enough to make a direct comparison, as we also need to consider the following. (1) The water outflux simulated by MAIDENiso is the surface runoff (which is incorporated immediately to the streams) plus the subterranean drainage (which takes a longer time to reach the stream), which creates a time difference between outflux sources within the same spatial point. (2) The outflux from different points of the basin takes different times to reach the main stream of the basin. (3) The outflux over the whole area of the Caniapiscau basin is not necessarily identical. A routing model could be used to calculate the delay and flow to the main stream from across the whole basin for both types of water outflows. The incorporation of a routing model in MAIDENiso would allow us to produce an estimate of streamflow for a basin, allowing for direct comparison with river discharge observations.

The calibration process yielded two different sets of parameters when using the two versions of the MAIDENiso model but resulted in similar predicted GPP values. The parameters controlling GPP that we obtained showed very similar posterior distributions and values in the plausible block (Table  and Figs.  and ). These similarities indicate that, at our study sites, photosynthesis was not very sensitive to additional water from snowmelt, suggesting that radial tree growth was not limited by water availability. This is in agreement with previous studies showing that in high latitudes soil humidity is not often a major constraint on tree growth, and trees are usually mostly sensitive to temperature . However, different results could be found in sites where trees are more dependent on water derived from snowmelt . Because GPP is not affected by the snow module, our study sites are ideal to investigate the effects of snow on δ18OTRC variations, because it allows us to discard GPP as a possible cause for the differences observed between the two model versions.

Following the approach proposed by , we produced yearly δ18OTRC time series by weighting the daily values with the GPP, assuming that C allocation to the stem is proportional to GPP. MAIDENiso has a module for the allocation of available C to the different parts of the tree, which provides an alternative and more realistic way of calculating yearly δ18OTRC. However, the calibration of this module ideally requires observations of the same units as the product of the allocation module, i.e. C mass per unit of stand basal area allocated to the stem. Although tree-ring width (TRW) data were available for both sites, their use was complicated as TRW observations represent just a portion of the total C allocation of the entire tree and do not offer an intra-annual C allocation resolution to constrain the simulations. Therefore, the use of GPP to weight the daily δ18OTRC was the best option for this particular study. The model without snow produced depleted values of δ18OXW, because it lacked the enrichment effect of evaporative fractionation in snow. This was also reflected in the δ18Odis signal, with depleted values for the model without snow. This contradicts studies that show that stream water does not usually show signs of evaporative fractionation . However, the discharge in MAIDENiso is simply the addition of the runoff and the drainage from the upper soil layers, and this lacks the complexity of interactions with deeper groundwater that the real soil has. Therefore, while orientational, δ18Odis is only useful as a possible input to a more complex groundwater model.

The addition of the snow module corrects for an important overcompensation effect that stemmed from the unrealistic representation of hydrology in the previous version. The model without snow produced depleted values of δ18OXW, which the model had to compensate through the δ18O parameters (higher values of ϵ0 and ϵk and lower contributions of xylem water through lower f0). The calibration of the δ18O processes for the two versions of MAIDENiso and the two sites yielded significant differences in the optimized parameters, both in the distribution of the optimal blocks and the values in the plausible blocks (Fig.  and Table ). The dampening factor f0, which controls the direct contribution of the source water to the δ18OTRC signal, was significantly higher (especially in Tungsten) after adding snow. The calibration of the model without snow converged to a value of f0≈0.32, with the posterior distributions pushing toward the lower prior limit of 0.3 (Table  and Fig. ), which suggests that the calibration procedure would have converged towards a smaller value if it had been allowed. Adding snow increased the dampening factor to f0=0.48 in Tungsten and f0=0.43 in Caniapiscau, in agreement with the range of f0=0.4–0.5 reported in previous studies . obtained a dampening factor of f0=0.41 in Quebec using the original model as the parameters from Eq. () could be calibrated to compensate for the absence of snow. These findings indicate that the addition of snow allows the model to increase the contribution of the source water to δ18OTRC.

The calibrated value for the biochemical fractionation ϵ0 was different at the two sites, ranging with snow to without snow from 27.41 ‰ to 27.85 ‰ in Tungsten and from 24.15 ‰ to 24.48 ‰ in Caniapiscau (Table ). The ϵ0 values were slightly higher at both sites when the model lacked snow, which suggests that the calibration compensates for consistently lower values of δ18OXW and/or δ18Oleaf in Eq. () to adjust the mean δ18OTRC to the observations. The kinetic fractionation ϵk obtained also differed strongly between sites, with snow to without snow from 11.8 ‰ to 13 ‰ at Tungsten and from 22.8 ‰ to 23.4 ‰ at Caniapiscau (Table ). The ϵk was set to 26.5 ‰ by , but it can vary over a larger range . obtained a value of ϵk=17.20‰ for Quebec, with a similar posterior distribution that the one obtained here.

Our results also showed that the leaf 18O enrichment due to transpiration has a stronger influence on δ18OTRC than the isotopic composition of the source (xylem) water, both in Tungsten and Caniapiscau, suggesting that it is the main driver of δ18OTRC variations. These results are in agreement with findings and reflect the strong effect of vapour pressure deficit on δ18Oleaf in Quebec. Nevertheless, the δ18OTRC signature also had a strong imprint of the source water signal as recently reported for the Tungsten δ18OTRC record that shared the same large-scale atmospheric patterns than spring–summer δ18OP .

The addition of the snow module to MAIDENiso therefore frees the calibration process from having to overcompensate for the artificially depleted δ18OXW values during the growing season (Fig. b). As our results have shown, this significantly increased the correlation between the observed and simulated δ18OTRC compared to the version without snow (Fig. ; r=0.52 for Caniapiscau and r=0.57 for Tungsten, p<0.01 versus non-significant, respectively). The improvement of the predictive skill of the model with the snow module reflects the influence of winter precipitation on physiological processes. Without snow, all winter precipitation passes through and out of the hydrological system without affecting the trees. In contrast, including snow allows winter precipitation to affect δ18OTRC indirectly through the source water.

Overall, the improvements found in the δ18OTRC simulations at both sites indicate that snow plays a critical role in δ18O of the source water and thus on the final signature of δ18OTRC. Even if the addition of snow would not had resulted in a significant improvement of the correlation between the simulated and observed δ18OTRC, accounting for snow-related processes along the mechanistic chain is necessary for the application of a process-based model in an environment where snow is present. Process-based models are useful to understand complex processes, and while they may not necessarily produce better simulations (closer to observations) than response functions, they can be calibrated under favourable conditions and then used for different datasets . The incorporation of the snow module in MAIDENiso is therefore required for predicting tree-ring isotopic composition in forests located in cold environments where snow is present.

Based on our results and comparison with other studies, we can conclude that the snow module predicted more realistic and robust fluxes of water within the soil–plant–atmosphere continuum. The improvement of MAIDENiso to disentangle the contribution from the source (xylem) water and the δ18Oleaf enrichment signal on δ18OTRC can help to track the origin of the isotopic signal and eventually improve the interpretations of the climate signal recorded in the tree rings. This is important because tree-ring isotopes are important climate proxies . The inclusion of the new snow module in the model can provide a more accurate representation of the physical and physiological processes taking place than in earlier studies that did not take into account the additional effects of snowpack dynamics on δ18OTRC, e.g. . Now, MAIDENiso can simulate more reliable interactions between the coupled water and carbon cycles and tree physiological mechanisms in cold environments. Our findings will contribute to reduce uncertainties in the predictions of the response of forest productivity to hydrological changes, leading to better forward predictions that can eventually be used to reconstruct seasonal and long-term hydroclimatic variations.

An inverse modelling approach has previously been developed and tested using MAIDENiso to reconstruct paleoclimate from tree-ring data in the Fontainebleau Forest, France . However, this exercise was restricted to the reconstruction of meteorological variables during summer and to regions where the tree-ring proxies were not significantly affected by winter meteorology. The inclusion of snow in the model opens new possibilities for reconstructing hydroclimate in cold regions, considering that the new version of MAIDENiso produces simulation of δ18OTRC that account for snow-related processes.

Suitable regions for the application of MAIDENiso in future studies include high-mountain regions, now that the model has a working snow module. Regions with snow-dominated winters and dry summers, such as the southwestern USA or some Mediterranean sites, can also be of interest for future studies with MAIDENiso, as trees in these sites can be more dependent on water derived from snowmelt than the sites used in the present study. The application of MAIDENiso to any site is possible provided that there is sufficient meteorological data to drive the model and local information to calibrate the model parameters (GPP, snow, TRW and TRC stable isotopes). We expect MAIDENiso to be applied more broadly in high-latitude and high-altitude environments in the near future.