The semi-conceptual hydrological model PREVAH in its fully distributed form solves the water balance of each grid cell by calculating evapotranspiration, soil water balance, and runoff generation at a sub-daily time step. The core of PREVAH is based on the structure of the widely used model HBV , combined with a conceptual runoff routing scheme . Successive model developments enabled or improved the treatment of interception , snowpack dynamics , glacier runoff , and groundwater runoff . PREVAH was used, among other applications, to estimate the impact of climate change on discharge . Climate impact studies were also conducted using the distributed outputs of PREVAH .

The spatially explicit forest landscape model TreeMig simulates forest establishment, growth, and mortality, as well as seed dispersal. Originally based on a gap model , TreeMig calculates the number of trees per species and height in each cell and operates at an annual time step. Inter- and intraspecific competition is represented through light distribution within the canopy, which depends on the distribution of trees of different heights within a stand and thus on leaf area . TreeMig was used to predict climate impact on tree species distribution in Switzerland , as well as to simulate forest response to land abandonment and the feedbacks between forests and avalanches . Abiotic drivers of forest dynamics are represented by three bioclimatic indices: mean temperature of the coldest month, degree-day sum, and drought (see Sect.  for the latter).

Leaf area index (LAI) is calculated in TreeMig to account for mutual shading and competition for light . In FORHYCS, LAI is passed to the hydrological model, replacing the land-cover-specific parameterization in PREVAH. The allometric equations of relate leaf area to diameter at breast height (D; in centimeters). As D is allometrically linked to tree height, leaf area is calculated for each group of trees of the same species and height class, then summed to obtain the value for the whole stand as follows: 1Al=∑sp=1nspc∑hc=1nhclSLAsp×a1,sp×Dsp,hca2,sp×pd,sp, where Al is the total all-sided stand leaf area (in square meters), nspc is the number of species (30 in FORHYCS), nhcl is the number of height classes (16), SLAsp is the specific leaf area (in square meters per kilogram), a1,sp (in kilograms per centimeter) and a2,sp (unitless) are species-specific allometric parameters , and pd,sp is a dimensionless reduction term accounting for seasonal variations in leaf area, ranging from 0 to 1 (see below and in the Supplement). The reference area in TreeMig is the size of a forest plot, set to 833 m2 (1/12 ha), which is the reference area in many gap models e.g.,, so that 2LAI=Alkc/833, where kc is a factor to convert from true to projected leaf area, set to 0.5 for broadleaves and 0.4 for conifers following . Fractional canopy cover fc is also calculated from the number of trees per species and height class, using the equation of as follows: 3fc=1-exp⁡-1×∑sp=1nspc∑hc=1nhcl(nsp,hc/833)×CAsp,hc, where CAsp,hc is the total crown area for trees of each species and height class. 4CAsp,hc=ka1,sp×hhc2+ka2,sp×hhc×nsp,hc, where ka1,sp and ka2,sp are species-specific allometric parameters, and hhc is the (upper) height of the height class (hc). Minimum values for LAI and fc are set to 0.2 and 0.1, respectively, to account for a minimal cover by grass and shrubs, as well as bare stems. Annual maximum LAI may be reduced as a function of the drought stress of the previous years, as described below in Sect. . It is worth noting that leaf area and crown area are calculated independently from each other, both using empirical relationships with tree size.

To obtain daily values for LAI and fc, a leaf phenology module has been implemented. The variable pd,sp reflects the phenological status of species “sp” in a given cell and varies between 0 (no leaves) and 1 (full foliage). This module also defines the start and end of the growing season in each cell, which is required to calculate the climatic indices for the rooting depth module (Sect. ). In each cell, the growing season lasts as long as pd,sp is greater than 0.5 for the dominant species. Daily values of pd,sp are simulated in spring with the model of , which depends on the number of chill days in winter and accumulated growing degree days in summer. When pd,sp reaches a value of 1, the foliage is assumed to be fully developed. The onset of leaf senescence in autumn is simulated using the model of , which depends on temperature and photoperiod. For broadleaves, the end of the growing season is set to 14 d after the onset of senescence, and pd,sp is linearly reduced from 1 to 0 during this period. Although the leaf area is not varied throughout the year for evergreen conifers, pd,sp is still simulated to define the start and end of the growing season. For these species (as well as for the deciduous conifer Larix decidua), the development of pd,sp following the onset of senescence is calculated using the formulation of . The parameters for the empirical models of and were calibrated against phenological observations across Switzerland . The species-specific parameters and a description of the calibration procedure are given in the Supplement.

The drought index used in TreeMig is based on the ratio of annual to potential evapotranspiration, as calculated with a module modified from . This scheme requires a monthly precipitation sum and temperature average for each cell, as well as the plant-available water storage capacity. Evaporative demand is calculated using an empirical, temperature-dependent approach, and monthly soil water balance is simulated based on water supply and demand, after accounting for interception seefor a full description of this scheme. This approach has a number of drawbacks. First, it does not consider the effect of variations in vegetation properties on evaporative supply and demand, thus neglecting feedbacks between vegetation density, transpiration, and drought see e.g.,. Also, the Thornthwaite–Mather routine does not account for snow-related processes, which can lead to large errors in the estimation of evapotranspiration, diminishing the representativeness of the index for growth conditions . Furthermore, empirical evapotranspiration formulations such as the Thornthwaite–Mather routine rely to a large extent on calibrated values. These may not be transferrable to climatic conditions that differ from the calibration period , limiting the ability of the model to make predictions under a changing climate. For these reasons, this abiotic drought index was replaced by a relative transpiration index . This index is similar to the evapotranspiration deficit index presented above but is based on transpiration rather than evapotranspiration as follows: 5DI=1-∑d=dedsET,act,d∑d=dedsET,pot,d, where de and ds are the first and last day of the period for which the drought stress is calculated, and ET,pot,d and ET,act,d are modeled daily canopy transpiration sums (in millimeters per day). Here, DI is calculated for the entire year, so that de =1 and ds =365. Furthermore, to account for delayed effects of drought on tree physiology , the average of the last 3 years is used here. Transpiration is reduced from the potential rate through the effect of low soil moisture or high atmospheric vapor pressure deficit (VPD) on stomatal resistance (Eq. 14 in ). The rationale behind this index is based on the fact that stomatal closure is one of the first responses of a plant to water deficit. Therefore, the time during which stomatal resistance is increased due to drought is the time during which adverse physiological effects of water shortage (e.g., cavitation, reduced carbon uptake) are likely to occur, and DI serves as a proxy for all these processes. The effect of VPD was included to account for the effects of high evaporative demand on plant-internal hydraulics . The drought stress function fDS determines the relative drought-induced limitation of annual growth . 6fDS=max⁡0,1-DIkDT, where kDT is a species-specific drought tolerance parameter, indicating the value of DI at which growth is completely suppressed. This growth reduction function can take values between 0 (complete growth suppression) and 1 (unstressed conditions). Annual growth of the trees of the same species and height class is the product of a species-specific maximal growth, an environmental reduction function fenv, and a further reduction term accounting for shading. The environmental reduction function is the geometric mean of fDS and two other stress functions, representing the effects of temperature and nitrogen availability . While the effects of temperature are taken into account in this study, nitrogen availability is kept spatially and temporally constant. These two environment-dependent stress functions are further described in Sect. S1.2 of the Supplement (for a description of the effects of light competition and shading, we refer to . The same reduction function is used to simulate mortality in addition to background mortality and applies if it is more severe than mortality caused by low productivity. parameterized kDT for the 30 tree species represented in TreeMig by overlaying modeled DI with inventory-derived maps of species distribution. The values range between 0.27 and 0.5. However, this parameterization did not lead to satisfactory simulations of species composition in the case study of this paper. Therefore, species-specific kDT was defined based on a combination of the rankings by and . Table S7 in the Supplement lists the kDT values used in this study.

FORHYCS accounts for two additional effects of drought stress: a limitation of maximum height and a reduction of annual maximal LAI. The former is parameterized following ; i.e., species-specific maximum tree height may be reduced as a function of the bioclimatic indices DI and DDEGS (degree-day sum; see Sect. S1.2 of the Supplement). The parameter kredmax, which is also species-specific, indicates the fraction of maximum height that can be attained by trees if one of the environmental vitality functions is at its minimum. The more severe of the two reductions (drought or degree-days) is applied. Unlike in the formulation of , where the reduction is a linear function of the bioclimatic indices, the impact functions (Eq.  for drought and S8 for degree-day sum) are used here.

The LAI reduction function follows the formulation of , where the fraction of carbon allocated to roots increases under stress, whereas allocation to foliage and stem decreases. Since allocation is not explicitly simulated in FORHYCS, the following formulation is purely phenomenological. For all size classes of a given species, leaf area is scaled by the ratio of the foliage allocation coefficient under current ηl and unstressed conditions ηl,u. Eq. (1) is thus modified as follows: 7Al=∑sp=1nspc∑hc=1nhclSLAsp×a1,sp×Dsp,hca2,sp×pd,sp×ηl,sp/ηl,u,sp.

The allocation coefficients for foliage are calculated as follows: 8ηl=1-ηr-ηs,  and  ηl,u=1-ηr,u-ηs,u, where ηr and ηr,u are the allocation coefficients to roots and ηs and ηs,u are the allocation coefficients to the stem under current and unstressed conditions, respectively. Following , ηr,u is set to 0.229, and ηr increases with increasing stress by the following relation: 9ηr=0.81+2.51-fenv, where fenv is the geometrical mean of the drought and low temperature stress functions (Eqs. 6 and S8). The carbon allocated to the stem is related to ηr as follows: 10ηs=1-ηr/pl,s+1,andηs,u=1-ηr,u/pl,s+1, where pl,s is the ratio of the growth rates of leaves and stems, in terms of their change in relation to diameter at breast height D. In FORHYCS, pl,s is calculated using the allometric equations used to calculate leaf and stem biomass: 11pl,s=dwl/dDdws/dD=kl,1Dkl,2ks,1Dks,2, where kl,1 and kl,2 are allometric parameters for leaf biomass, and ks,1 and ks,2 are allometric parameters for stem biomass . It is important to stress that FORHYCS does not explicitly simulate carbon assimilation. Hence, Eqs. () and () are only used to determine a reduction factor for leaf area (Eq. ) and have no direct influence on simulated tree growth, stem biomass, and rooting depth.

The implementation of the new drought index (see Sect.  above) required some changes to the evapotranspiration routine in the hydrological model. While the relative transpiration index is based on estimates of actual and potential transpiration, PREVAH does not explicitly differentiate between transpiration and soil evaporation. Therefore, a new local water balance routine was implemented, based on the standalone model FORHYTM . This module combines the soil water balance formulation of the HBV model , which is also implemented in PREVAH, with the transpiration and evaporation scheme of and a Jarvis-type parameterization of canopy resistance. A full description is given in .

The parameterization of canopy resistance differs from the original formulation in two ways. First, the effect of atmospheric vapor pressure deficit (VPD) on stomatal conductance is represented with a negative exponential function instead of a linear function. Second, an additional canopy resistance modifier (f5) was implemented to account for the effect of atmospheric CO2 concentration (Ca [µmol mol-1]). This function is based on the results of . 12f5=1-jcmin(Ca,700)350-1-1, where jc represents the fractional change in conductance in response to an increase in Ca from 350 to 700 µmol mol-1 and was set to 0.1 for coniferous forests, 0.25 for broadleaf forests, and 0.18 for mixed forests (the forest type in each cell is determined based on the relative share of above-ground biomass belonging to conifers and broadleaves). These values were set based on the results reported by ; coniferous species had a value of jc between 0 and 0.2, whereas broadleaves had values up to 0.4. Therefore, for conifers, a value of 0.1 was selected. For broadleaves, as there seemed to be some acclimation for trees growing in elevated CO2, a more conservative (than 0.4) value of 0.25 was chosen. The value for mixed forests corresponds to the arithmetic mean of the two. This affects both potential and actual transpiration so that, with all other factors kept constant, increases in Ca will reduce the level of drought stress. The rationale for implementing this new water balance scheme is to account for the effect of variations in vegetation properties (e.g., LAI) on physiological drought in forests. As FORHYCS includes the possibility of changing land cover classes in a cell, some non-forested cells may become forested over the course of a simulation. As vegetation parameters (such as LAI and effective rooting depth) are prescribed as a function of land cover for non-forested cells, this shift inevitably introduces an artificial discontinuity in the simulation. To reduce this discontinuity, the new water balance scheme is also used for potentially forested land cover types. On the other hand, for land cover types that cannot become forested, the original water balance scheme of PREVAH is applied.

The rooting zone water holding capacity, SFC, is calculated as the product of effective root depth Ze and soil water holding capacity κ . While κ is assumed to remain constant, Ze is assumed to vary as a function of vegetation characteristics and climate. The approach used to parameterize Ze is the carbon cost–benefit approach of . This approach rests on the assumption that plants dimension their rooting systems in a way that optimizes their carbon budget. The optimal rooting depth is the depth at which the marginal carbon costs of deeper roots (linked to root respiration and construction) starts to outweigh the marginal benefits (i.e., additional carbon uptake due to greater availability of water for transpiration). The implementation of this model in FORHYCS follows the procedure described by . Effective rooting depth, expressed as an average over the whole cell, is calculated for both overstory (trees) and understory (shrubs and non-woody plants). The storage volume SFC for a given cell is defined as the sum of these two area-averaged rooting depths, multiplied with soil water holding capacity κ. A full description of this implementation is given in . The underlying equation is: 13γr×DrLr=wph×fseas×d〈T〉dZe, where γr is root respiration rate (in milligrams of carbon per gram of roots per day), Dr is the root length density (in centimeters of roots per cubic centimeter of soil), Lr is the specific root length (in centimeters of roots per gram of roots), wph is the photosynthetic water use efficiency (in grams of carbon per cubic centimeter of H2O), fseas is the growing season length (fraction of a year), and 〈T〉 is the mean daily transpiration (in millimeters per day) during the growing season. The left hand side represents the marginal cost of deeper roots, and the right hand side the marginal benefits; solving for Ze gives the optimal rooting depth. Any equation can be used to relate d〈T〉 to dZe. In this implementation, the probabilistic models of and are used for the understory and overstory, respectively. These two models reflect the differing water uptake strategies of grasses and trees . Both models estimate transpiration based on soil water holding capacity κ and long-term averages of climatic indices. Evaporative demand is represented by potential transpiration, and rainfall is represented as a marked Poisson process characterized by the frequency (λ; in events per day) and mean intensity (α; in millimeters per event) of events. In FORHYCS, these variables are calculated as rolling means with a window of 30 years, including only the growing seasons. Potential transpiration for the understory and overstory are taken from the calculations of the local water balance module (Sect. ), and the rainfall characteristics are taken from modeled effective precipitation (i.e., after accounting for interception). The start and end of the growing season are determined based on the phenology module (Sect. ). In addition, mean daily air temperature is calculated over the growing season to adjust respiration rate. The plant-specific parameters in Eq.  are summarized in the variable PPo, defined as follows: 14PPo=γr,20DrLrwph, where γr,20 is the root respiration rate at 20 ∘C. The actual root respiration rate is dependent on annually averaged temperature via a Q10 function. For further details, please refer to . A higher value of PPo indicates a greater difficulty for the plant to develop additional roots. In FORHYCS, PPo was set to 1.263×10-4 for conifers and 1.01×10-4 for broadleaved species. At the cell level, PPo was averaged based on the relative share of above-ground biomass belonging to conifers and broadleaves. For the understory, the corresponding parameter PPu is set to 1.512×10-4.

For seedlings of the high-mountain species Larix decidua, Pinus cembra, and P. montana, the model also includes the effect of snow-induced fungal infections via the variable FDSA (final day of snow ablation), as described by . An additional mortality term is calculated as follows: 15μs=a×FDSA2+b×FDSA+c, where a, b, and c are empirical parameters fitted by for Larix decidua and for the two aforementioned Pinus species. If μs is greater than background mortality or the mortality term integrating light, temperature, and water stress, it is applied instead for the seedlings of these species. This aspect of the model was implemented to examine the feedback between forest dynamics and avalanches on a small spatial scale but was never tested on landscape scale. Here, FDSA is defined as the last day of the year with more than 5 mm of snow water equivalent.

The methods have so far described the model FORHYCS in its fully coupled version. It is also possible to run FORHYCS in uncoupled mode (without any information transfer between the hydrological and forest models) or with a one-way coupling (information transfer from the forest model to the hydrological model only). An uncoupled FORHYCS run consists essentially of a PREVAH run and a TreeMig run, happening independently from each other. Uncoupled FORHYCS differs from other PREVAH implementations mainly through the parameterization of soil and surface properties. As mentioned in Sect. 4.2, previous applications of PREVAH in Switzerland have used soil depth and water holding capacity from the agricultural suitability map BEK . Preliminary analyses in this project have shown that this parameterization gave implausible results when used with the newly implemented water balance module (Sect. ). Therefore, to ensure comparability between coupled and uncoupled runs, all FORHYCS runs use the soil parameterization from (see Sect. 2.2.2) in forested cells. In uncoupled runs, it is assumed that the rooting depth of forests is 1 m. As this dataset was developed based on forest soil profiles, values for cells outside currently forested areas are not reliable (Jan Remund, Meteotest, personal communication, 2015). To simulate forest expansion under climate and land-use change scenarios, it was nevertheless assumed that cell values of the RA2015 dataset represent the water storage capacity for 1 m of soil depth. To account for shallower rooting of non-forest vegetation types, a land-cover-dependent rooting depth parameter was introduced. The parameter values for different land cover types are given in Table S6. Non-vegetated land cover classes (e.g., built-up or bare rocks) use the same standard soil parameters as in the original PREVAH . Another difference between FORHYCS and PREVAH is the parameterization of canopy resistance. Whereas PREVAH gives a minimum canopy resistance for each land cover class (i.e., normalized by leaf area index), the new water balance module requires a minimum stomatal resistance. Following , minimum stomatal resistance was set to 180 s m-1 for forests, 130 s m-1 for meadows and grasslands, and 210 m-1 for shrubs.

One-way coupling is similar to the modeling experiment of ; vegetation variables from TreeMig are passed to PREVAH, but there is no feedback from the hydrological to the forest model. This configuration uses the abiotic drought index calculated with FORCLIM-E . In this study, TreeMig was run with two soil datasets (BEK and RA2015; see below). In all cases, the hydrological part of the model uses the RA2015 dataset. In this study, rooting zone storage capacity SFC of the hydrological model was kept constant in one-way coupled mode, assuming a rooting depth of 1 m. Enabling climate-dependent adaptation of SFC in this mode would impact simulation results for the hydrology part but not for the forest.

The Navizence catchment is located in the Swiss Central Alps and covers an area of 255 km2. To enable the future migration of tree species that are currently not represented in the catchment, the modeling area extends beyond the catchment to form the rectangular area shown in Fig.  (1079 km2). The catchment is characterized by a sharp elevational gradient, with elevations ranging from 522 to 4505 m a.s.l. Like in its neighboring valleys, this gradient is reflected in the hydro-climatic conditions. Due to the shielding effect of mountain ranges, the Rhône valley, where the catchment outlet is located, is the driest region of Switzerland, with the mean annual precipitation (MAP; 1981–2010) at Sion totaling 603 mm . However, the valley presents a strong altitudinal precipitation gradient, with MAP exceeding 2500 mm at 3000 m a.s.l., most of it falling as snow .

Tree species composition shows a rather clear altitudinal zonation, with drought-resistant species (Pinus sylvestris and Quercus spp.) dominating at lower elevations, whereas Picea abies, Larix decidua, and Abies alba dominate the subalpine stage, and the treeline is formed by Larix decidua and Pinus cembra. The landscape is heavily influenced by human activity, with a large fraction of land occupied by settlements, cropland, vineyards, and pastures. Furthermore, nearly all forests in the area are subject to management in various forms and degrees of intensity, with a considerable impact on forest dynamics. Specifically, many forests were clear-cut between the Middle Ages and the nineteenth century, mostly for fuel . In the first half of the twentieth century, the quantitatively most important anthropogenic disturbance factors were litter collecting and wood pasture by goats . Nowadays, these practices have been largely abandoned, and timber harvesting plays a limited role in the region. As a result of past and current anthropogenic factors, the main deviations from potential natural forest composition are (1) silvicultural practices favoring certain species, such as Pinus sylvestris and Larix decidua (2) effects of litter removal and grazing, and (3) a replacement of L. decidua and Pinus cembra by mountain pastures and dwarf shrubs near the treeline.

Currently, three major hydropower plants are operational in the valley, with a total installed capacity of 164 MW and a mean net annual production of 570 GWh. The main reservoir is the artificial lake Lac de Moiry, located in a lateral valley, with a storage capacity of 77 million m3. A system of pipelines has been built to divert water from the Navizence, as well as from a neighboring catchment, into the lake.

Three kinds of spatial data are needed to run the model: daily meteorological data, time-invariant physiographic data, and spatially distributed model parameters for PREVAH. These parameters represent environmental factors not related to vegetation, such as snow, glacier, and runoff generation processes. Further information on the parameterization of PREVAH is given in Sect. S1.7 of the Supplement. The model is driven by daily values for precipitation (in millimeters), air temperature (in degrees Celsius), global radiation (in watts per square meter), wind speed (in meters per second), relative air humidity (percent), and sunshine duration SSD (in hours), provided by the Swiss Meteorological Office MeteoSwiss .

Physiographic data consists of information on soil, topography and land cover. Soil is represented in terms of water holding capacity κ (in millimeters of water depth per millimeter of soil depth) and soil depth. Two different datasets are used for soil properties. In previous applications in Switzerland, both PREVAH and TreeMig used grids of κ and soil depth from a countrywide agricultural suitability map (; hereafter referred to as “BEK”). The resulting rooting zone storage capacities (SFC; in millimeters) in the forested cells of the study region range between 3.75 and 110 mm. As this dataset was not specifically developed for use in forests, and some values are implausibly low, generated a new countrywide dataset (RA2015) of rooting zone storage capacity, on the basis 1234 forest soil profiles throughout Switzerland, combined with a lithological map. This dataset gives the volume of water that can be stored in the soil for a depth of up to 1 m, with lower values in cells where soil is assumed to be shallower. SFC in the new dataset ranges from 71 to 223 mm in forested cells of the study region. Figure S1 shows the rooting zone storage capacity in forested cells of the study region for both soil parameterizations. For coupled simulations, only the RA2015 parameterization is used. To facilitate a comparison with results from previous studies, the parent models PREVAH and TreeMig are also run with the BEK parameterization.

This section describes the data against which model outputs were compared, including three datasets of vegetation properties and one dataset of streamflow measurements. These datasets are used to plausibilize model outputs and serve as a basis for the choice of model configuration. Daily streamflow was obtained from the operator of the power plants. These data include an accounting of the amount of water diverted through the different pipelines. From this, time series of natural streamflow were reconstructed, which were used as observations. Further details on the streamflow data are given in Sect. S1.9 of the Supplement.

The simulated stem numbers and above-ground biomass were compared against data from the first Swiss National Forest InventoryNFI;. As the sampling plots of the NFI are distributed on a regular grid, each plot is randomly selected from all forest plots in that region and may not be considered representative for a larger area. It is therefore not sensible to compare simulated and observed biomass at the scale of single inventory plots. Instead, the 245 NFI plots in the study area were aggregated to seven classes based on aspect and elevation, with four elevation bands for north-facing plots and three for south-facing plots. This way, each class has a sample size of at least 30 plots, which ensures that the averages are representative. For comparison with inventory data, simulated biomass was also averaged over the same strata.

Simulated LAI was compared to the remotely sensed LAI dataset provided by Copernicus at 300 m resolution . This dataset uses measurements of the satellite Proba-V and its temporal coverage starts in January 2014. The LAI 300 m rasters were resampled to match the resolution and extent of the model input and output, then stratified as described above. For each cell of the original LAI 300 m grids, the maximum value of the 10 d periods contained between May and July of the years 2014 through 2016 was used as an estimate of maximum LAI, independent of intra-annual fluctuations. As forest properties are also shaped by local processes not represented in the model (e.g., disturbance or forest management), a direct cell-by-cell correspondence of simulated and observed values is not expected. Furthermore, cells of the remote sensing dataset are spatially heterogeneous and may include non-forested parts. However, it was still assumed that over larger domains, a good correspondence between simulated and observed LAI would be indicative of good model performance. Therefore, the simulations and observations were also stratified by elevation and aspect. As the number of cells is relatively large, smaller elevation bands were chosen than for inventory data. The cells are divided between north- and south-facing aspects, then binned into nine elevation bands. These elevation bands have a fixed width of 200 m, except the lowest (<700 m a.s.l.) and highest (>2100 m a.s.l.). Each zone contains between 100 and 714 forested cells. Model outputs and observations are only evaluated over the areas classified as forests or shrubland in the model input.

The recently developed Switzerland-wide vegetation height dataset at 1 m resolution of , derived from stereo aerial images, was compared against simulated canopy structure. To compare the level of agreement between observed and simulated canopy structure, two novel metrics were introduced. The rationale behind these metrics is illustrated in Fig. . Both measures are based on the discrete height classes used in TreeMig and use the cumulative fractional cover of each height class, starting from the highest class. In the illustrative example of Fig. a), the cumulative fractional cover of the height class 5–10 m corresponds to the visible crown area of the height classes 5–10 m and 10–15 m, divided by the potentially vegetated area (i.e., excluding the area occupied by a road, shown in grey). In each cell of the model grid, the fractional cover of each height class is calculated from the simulated species–size distribution using the procedure described in Eqs. () and (). For each height class i, the cumulative fractional cover fc,i is defined as follows: 16fc,i=1-exp⁡-1×∑sp=1nspc∑hc=inhclnsp,hc/833×CAsp,hc.

The procedure used to calculate fractional cover is based on the assumption that trees are randomly distributed in space and accounts for overlap between crowns. For example, applying Eq. () to the upper three height classes will return the fractional cover for the trees belonging to these classes, accounting for overlap between them. This assumes that shading of lower parts of their crowns by smaller trees can be neglected.

As can be seen in the examples in Fig. 3c and d, each cell from the model grid covers 200×200 cells of the observations grid. Therefore, for each model cell, the observed fractional cover is calculated from the relative number of high-resolution cells belonging to each height class. Observed cells with a height of 0 m represent non-vegetated surfaces such as roads, water bodies or buildings and were excluded from the analysis. Indeed, as the model does not contain any land cover information on subgrid level, these elements are an irreducible source of disagreement between observations and simulations. On the other hand, observation cells with a height between 0 and 1.37 m are assumed to be covered by ground vegetation and decrease the total fractional canopy cover in a coarse cell. The first cell-level measure of agreement is the difference in observed and simulated H95, i.e., the lowest height class for which the cumulated fractional cover (starting from 0) equals or exceeds 95 % of the total fractional cover. Fig. 3b shows the H95 of the observations, at the level of model cells. The second measure of agreement is illustrated in Fig. 3e and f. The cumulative fractional cover of each class (starting from the top) is plotted for observations and simulations. The better the agreement, the closer the curves are to each other. Therefore, the second measure of agreement, termed 1-ABC (where ABC stands for “area between the curves”), is defined as the fraction of the plot area not contained between the curves. The plot in Fig. 3e applies this to the cell shown in Fig. 3c and represents a case with a poor agreement between simulations and observations. Indeed, this area was devastated by a wildfire and is thus currently very sparsely forested. As this fire is not represented in the model, the simulations indicate a fully developed forest. Even in this extreme case, the ABC does not exceed 40 % of the plot area. Therefore, a 1-ABC score of 0.6 can be considered a poor fit. On the other hand, the sample cell in Fig. 3d and f show a good agreement between observations and simulations, with 1-ABC exceeding 0.99. These two measures of agreement can be used to evaluate the performance of a model by examining their distribution over the whole simulation domain. A better performing model will have a higher proportion of cells with a ΔH95 (difference of the 95th percentile of tree height between observed and simulated forest structure) close to 0 and a 1-ABC close to one. Furthermore, the spatial distribution of ΔH95 and 1-ABC may give insight into the factors that contribute to agreement or disagreement between simulations and observations.

To evaluate the behavior of the coupled model FORHYCS and the importance of the different forest–hydrology couplings implemented, two series of simulation experiments have been conducted. An overview of the different simulation runs is given in Table 1. In a first series of experiments, the simulations start with no forest, and a full succession is modeled. The names for these simulations start with “S”. The second part of the name indicates whether these experiments were conducted in fully coupled mode “F” or in one-way coupled mode “T”. The next part indicates which couplings are switched on and off, as per Table 1. Finally, for the one-way coupled runs, the fourth part of the name indicates the source of the soil water holding capacity BEK or “RA15”; see the next paragraph. In a second series of experiments, starting with “C”, the model was run with several climate change scenarios (see below). In this set of experiments, the model was run in uncoupled (U), one-way coupled (T) and fully coupled mode (F). In addition, a simulation with standalone PREVAH was run, “P”. For the fully coupled simulations, two additional experiments were run (see below), testing the effect of CO2 on stomatal resistance, “_NCS”, standing for “No CO2 effect on stomatal resistance”, and land cover change “_LC”.

In the succession experiments, the simulations start with no forest, and a full succession is modeled. The simulations span a period of 515 years, where the last 45 years are the years 1971 to 2015. For the first 470 years, the meteorological forcing consists of years bootstrapped from the period 1981 to 2000. In two cases (S_T_BEK and S_T_RA15), the model is run in uncoupled mode, and only the forest output is evaluated. This is equivalent to a standard TreeMig run. The difference between the two runs is the parameterization of the rooting zone storage capacity for the (abiotic) drought stress module (FORCLIM-E; ). In the first case, the storage capacity in each cell is given by the soil depth and water holding capacity given in the Swiss soil map for agricultural suitability (referred to as BEK; ), as in previous TreeMig applications in Switzerland (e.g., ). In the second case, the parameterization of Remund and Augustin (referred to as RA15; 2015) is used. As noted in Sect. 2.2.2, the soil water holding capacity is much larger in the RA2015 dataset for most cells. As a result, the (abiotic) drought index also shows great differences between the two model runs. Figure S1c and d show the difference in mean annual drought index (1971–2015), and maximum annual drought index between the BEK and RA2015 parameterizations. Due to the considerable effect of maximum height reduction (Sect. 2.1.3) on the coupled model, two additional TreeMig runs were performed with this effect enabled, to facilitate the comparison between coupled and uncoupled runs.

In coupled mode, FORHYCS is run with different configurations, with the various couplings described in Sect. 2.1 switched on or off (maximum height reduction, stress-induced leaf area reduction, dynamically varying rooting depth, and snow-induced seedling mortality). Based on pilot study results, the configuration S_F_noLAred (all couplings switched on, except leaf area reduction) was selected as the best configuration, as it produced the most plausible long-term biomass dynamics (see Sect. 3.2.1) and shows a good fit to observed canopy structure (see Sect. 3.2.2), and the other configurations in Table 1 differ from S_F_noLAred by only one process switched on or off.

The configuration S_F_noLAred is also used for the second set of model runs, which start in the year 1971 and end in 2100. In the idealized climate change runs, the sensitivity to a ramp-shaped climate change is evaluated (see Fig. 4). In the period 1971–2015, observed forcing is used. From 2016 to 2100, years are randomly selected from the period 1981–2015 (excluding the abnormally dry and hot year 2003). Furthermore, from 2016 on, daily temperature is incremented by a given number of degrees dT, and daily precipitation is scaled by a given factor dP. The values of these factors are given in Table 1. To emulate a gradual progression of climate change, these factors are scaled linearly between 0 and their full value between 2016 and 2050. The runs C_F_NCS test the impact of the CO2 effect on stomatal closing, implemented through Eq. (). In these runs, the CO2 response function is always set to 1; i.e., stomatal response to high CO2 is switched off, whereas in all other runs, this effect is active. In all the runs presented so far, forest growth is restricted to the currently forested cells. In the C_F_LC runs, forest is allowed to grow in all potentially forested land cover classes. Thus, the potential ecohydrological consequences of land abandonment and rising treelines are examined. In addition to the runs with delta change, three runs were performed with meteorological forcing from downscaled regional climate simulations, generated in the CH2018 project . CH2018 contains the output of climate model runs from the EURO-CORDEX initiative , downscaled to a 2km×2 km grid. While there are 39 climate model chains available in the CH2018 dataset, running FORHYCS with each of them would be beyond the scope of this study. Instead, the three chains selected by to represent dry, intermediate, and wet conditions were used. The characteristics of the three chains are given in Table . For more information on the model chains, we refer to . It is worth noting that precipitation in the GCM-RCM chains is higher than in the observations for this region. Mean annual precipitation differs by 300 to 600 mm yr-1, depending on period and subcatchment (see Fig. S2 in the Supplement). Due to these differences, a comparison of the absolute model outputs between delta change runs and GCM-RCM chain runs is of little value. Therefore, the analysis shall focus on the difference between coupled and uncoupled runs for the different scenarios. Precipitation also differs in terms of event frequency (Fig. S3) and mean intensity (Fig. S4); the latter is consistently higher for the three GCM-RCM chains, whereas for the former, observed values lie between the two extreme values of the model chains. The model chains also differ with regard to temperature; the mean annual and seasonal (May–October) temperatures in two arbitrarily selected grid cells (one in the bottom of the Rhone valley at 667 m a.s.l. and one near the treeline at 2160 m a.s.l.) are shown in Fig. S5.

Figure  shows the above-ground biomass simulated with FORHYCS using the configuration S_F_noLAred (fully coupled succession simulation with all vegetation–water couplings switched on except leaf area reduction; analogous figures for the other configurations are provided in the Supplement; Figs. S9 to S16). In addition, the bar shows the average above-ground biomass of trees in plots of the first Swiss national forest inventory (1982–1986; ). The simulations start in 1500 with no trees. Biomass increases quickly at the beginning, so that in most zones, values close to 100 t ha-1 are reached within the first 40 years. The initial species composition consists of various broadleaf species, among which the maple species Acer campestre and A. pseudoplatanus. After this initial state, Pinus sylvestris (mainly at lower elevations) and Larix decidua (mainly at higher elevations) start developing. Finally, Quercus species (lower elevations, mainly Q. pubescens and Q. petraea), Abies alba (north-facing slopes), and Picea abies develop, with the latter becoming dominant at higher elevations. At the end of the simulation, the forest seems to have reached a state in which the relative importance of species changes little over time. At lower elevations, the state at the end of the simulation is close to that reached after the first 100 or 200 years. By contrast, at high elevations, the replacement of L. decidua by P. abies occurs over a much longer time.

At low elevations, simulated biomass is higher than the inventory value, especially on north-facing slopes. By contrast, simulated biomass is lower than the observed value at intermediate elevations. Unlike in simulations, for slopes reaching below 1346 m, there is almost no Quercus and Acer biomass in the inventory data, and the share of other broadleaves is also much smaller. Also at intermediate elevations, FORHYCS simulates a higher biomass for Acer and other broadleaves. However, L. decidua makes up one-third of observed biomass in that elevation band, while it is practically nonexistent in the simulations. Also at higher elevations, the simulated biomass of L. decidua is much lower than in the inventory data.

The results of S_T_noHmax_BEK (one-way coupled succession simulation with low soil moisture storage capacity; Fig. S9) differ greatly from those in Fig. . Pinus sylvestris is dominant at intermediate elevations, whereas high elevations are dominated by L. decidua. P. abies is hardly represented, and simulated biomass for broadleaves is very low. Fluctuations of simulated biomass are also much higher, with increases or decreases of up to 70 t ha-1 within 20 years. For S_T_noHmax_RA15 (one-way coupled succession simulation with high soil moisture storage capacity; Fig. S10), biomass equals or exceeds 200 t ha-1 in all strata except at the highest elevations. The mesophilous species Abies alba and P. abies dominate at all elevations. For TreeMig runs with maximum height reduction (S_T_Hmax_BEK and S_T_Hmax_BEK; Figs. S11 and S12), species composition is similar to the results of standard TreeMig but with much lower biomass.

The configuration S_F_Full differs from S_F_noLAred in that LAI is reduced as a function of drought or low temperatures. Biomass simulated with this configuration (Fig. S13) is markedly higher than with S_F_noLAred, especially at lower and intermediate elevations, while species composition is similar. Biomass also fluctuates more for S_F_Full at lower and intermediate elevations. For S_F_noHmax (no reduction of maximum tree height due to water availability or temperature; Fig. S14) and S_F_cSFC (constant rooting depth of 1 m; Fig. S15), biomass is also higher than for S_F_noLAred. In the former case, species composition is similar to S_F_noLAred, whereas for S_F_cSFC, the share of relatively drought intolerant species is larger at lower elevations (e.g., higher share of P. abies and lower share of Pinus sylvestris). Biomass simulated with S_F_noSmort (no snow-induced sapling mortality; Fig. S16) shows no apparent difference from S_F_noLAred.

The distribution of the two metrics of agreement between observed and simulated canopy structure is shown in Fig. . The distribution of ΔH95 shows large differences between the model configurations. While S_T_noHmax_RA15 has its maximum count of ΔH95 at 25.2 m and overestimates H95 in almost all cells, S_T_noHmax_BEK shows a much flatter distribution, with a large number of under- and overestimations. By contrast, the TreeMig runs with maximum height limitation have their maximum count at 0 m, suggesting a better fit. Most of the FORHYCS runs show a similar pattern, with a peak close to 0 m, and most values contained between -16.8 and 21 m. S_F_noHmax, however, has its maximum at 16.8 m and overestimates H95 in almost all cells. The distribution of the 1-ABC scores, shown in the lower plot, also sets apart the two configurations with the largest overestimation of H95, S_T_noHmax_RA15, and S_F_noHmax. These runs have their highest density at a lower value than the other configurations. The other FORHYCS runs all have their highest density around 0.95. While S_F_Full shows a distribution of ΔH95 that is very similar to S_F_noLAred and S_F_noSmort, its density distribution for 1-ABC differs from that of the other two configurations. S_F_Full has a lower density around 0.95 but a higher density between 0.7 and 0.85, indicating a lower degree of agreement between observations and simulation for this configuration.

Figure  shows a comparison of the Copernicus 300 m LAI and values simulated with the different TreeMig and FORHYCS configurations listed in Table 1. For the observations, the average forest LAI for the different elevation and aspect classes range approximately between 2 and 4. The lowest values occur on south-facing slopes below 700 m a.s.l. (i.e., close to the bottom of the Rhône valley). LAI of the south-facing slopes increases steadily with elevation up to 1700–1900 m a.s.l., where it reaches a value of 4. For cells over 2100 m a.s.l., LAI is again somewhat smaller. LAI is generally higher on north-facing slopes. There is little difference among the elevation bands between 700 and 2100 m a.s.l. Average LAI is always around 4 in that elevational range. Smaller values occur only in the lowest and highest elevation bands. The TreeMig runs differ greatly in the range and pattern of simulated LAI. For S_T_Hmax_BEK, parameterized with available water capacity (AWC) from the soil suitability map , the values range between 2 and 6. The highest values occur in the lowest elevation band and, for north-facing slopes, at 1700–1900 m a.s.l. Except for the lowest elevation band, LAI on north-facing slopes is markedly higher than on south-facing slopes, with differences of up to 2.5. By contrast, for S_T_Hmax_RA15, which uses the AWC from , the absolute values are much higher and the variability much lower. For all elevation bands, values range between 6.5 and 7.5. The results for TreeMig runs with height limitation are almost equal to the standard version.

There is less difference in patterns and absolute values among the FORHYCS runs. The absolute values range from 4 to 7. Spread is lowest for the two highest elevation bands, where all configurations give a value of approximately 6, for both north- and south-facing slopes. At lower elevations, there is a clear difference between the two aspect classes, with consistently higher values for the north-facing slopes. The difference between configurations increases with decreasing elevation and is somewhat higher on south-facing slopes. The configuration S_F_cSFC consistently returns the largest values. On north-facing slopes, the values are lowest for S_F_noLAred. This is also the case at higher elevations on south-facing slopes, whereas at lower elevations, S_noHmax returns the lowest values. In most cases, the results of S_F_Full and S_F_noLAred are similar. Up to 1300–1500 m a.s.l. on north-facing slopes, S_F_Full gives somewhat higher values, whereas on south-facing slopes, the value for S_F_noLAred is higher. In all cases, the symbols for S_F_noSmort are indistinguishable from S_F_noLAred.

Figure  shows how area-averaged LAI and rooting zone storage capacity SFC change for all future simulations (the results are shown here as rolling means with a 30-year window; a version without smoothing is given in Fig. S17). LAI and SFC are averaged over two of the strata used in Fig. , the lowest stratum of south-facing cells (Fig. a and c) and the highest stratum of north-facing cells (Fig. b and d). Figure a shows the results of the coupled run for the low-elevation south-facing cells. At the end of the succession run, LAI is approximately 6, and over the next century the values range between 3.5 and 6.5 for all runs except the dry GCM-RCM chain. Long-term average LAI is lower for warmer and drier runs. In particular, under the dry GCM-RCM chain, LAI starts to decrease sharply around 2050, with values less than 2 at the end of the simulation (Fig. S17). The plot of annual values (Fig. S17) shows that under warmer scenarios, the variability in LAI is much higher, with LAI decreasing much more in certain years than in less warm scenarios. In other years, annual LAI values strongly converge between scenarios. For SFC, values decrease for drying scenarios and increase for wetting scenarios, with consistently higher values for the GCM-RCM chains than for the delta change runs. The high-elevation north-facing cells (Figs. b, S17b) also show a decrease in long-term average LAI and an increase in variability under drying and warming scenarios. Also here, the dry GCM-RCM chain stands out, with a sharp decrease in LAI from the middle of the century. SFC initially increases in all scenarios. Around 2050 (when the temperature and precipitation modifiers reach their maximum), SFC starts decreasing, with a faster decrease in drying delta change runs.

Due to the similarity of LAI simulated by TreeMig with and without height reduction (cf. Fig. ), only the results for the version without height reduction are shown. LAI differs greatly between the two TreeMig simulations, especially for the low-elevation south-facing cells (Figs. c, S17c). With C_T_BEK (one-way coupling with low soil moisture storage capacity), LAI is approximately at 3.5 at the end of the succession run and decreases to less than 1.5 in the warmest and driest scenario (T6_P-10). Unlike with fully coupled FORHYCS, the dry GCM-RCM chain leads to values within the range of the delta runs at the end of the simulations. By contrast, under C_T_RA15 (one-way coupling with high soil moisture storage capacity), LAI decreases from 6.5 to 5 in the T6_P-10 scenario. Interannual variability increases with C_T_RA15 but not with C_T_BEK (Fig. S17c). Here, as for the fully coupled runs, the dry GCM-RCM chain leads to substantially lower values than the other runs. In the high-elevation north-facing cells, the LAI trajectories diverge between the two TreeMig parameterizations. Under C_T_BEK, as for the lower elevation cells, LAI decreases under the T6_P-10 scenario while interannual variability increases. On the other hand, with C_T_RA15, LAI increases under all warming delta change runs. LAI also decreases noticeably under the dry GCM-RCM chain but remains around 5.5 at the end of the simulation.

Figure a shows simulated annual streamflow (30-year rolling means) for subcatchment 1 (Chippis), as simulated with uncoupled FORHYCS (equivalent graphs for the other subcatchments are provided in Figs. S18 to S21 in the Supplement). From initially 550 mm yr-1, streamflow decreases by about 50 % under the most extreme warming and drying delta scenario (temperature increase of 6 K and precipitation decrease by 10 %). The three GCM-RCM chains show little difference to each other, no clear trends and consistently lead to higher mean annual runoff than all delta change runs. Figure b, c, and d show the difference in annual streamflow to the uncoupled run (Fig. a), for the one-way coupled runs (C_T_BEK and C_T_RA15) and the fully coupled FORHYCS runs (C_F), respectively. In all cases, streamflow is higher in the coupled runs. For C_T_BEK, the difference is approximately 30 mm yr-1 at the end of the succession and increases under idealized climate change. The increase is greater for warmer scenarios, with a difference of 60 mm yr-1 for the warmest delta change scenarios (T6_Py) at the end of the simulation. For the GCM-RCM chains, the difference is usually smaller than for most delta change runs. The difference in annual streamflow is much less for C_T_RA15 and ranges between 5 and 20 mm yr-1. Here, the difference in streamflow decreases with idealized climate change, with a more pronounced decrease for the warmer delta change scenarios. For the fully coupled runs, the initial difference is around 30 mm yr-1, which is similar to the initial difference for C_T_BEK. During idealized climate change, the difference does not increase as much as for C_T_BEK: the largest difference on the order of 40 mm yr-1. The only exception is the dry GCM-RCM chain, where streamflow difference starts increasing sharply around 2050 to reach 60 mm yr-1 at the end of the simulation. Unlike for TM_BEK, the delta change scenarios with the greatest difference by the end of the simulation are the three warming and drying scenarios.

The increase in stomatal resistance due to increased CO2 concentration (Eq. ) has a minimal effect on streamflow and area-averaged forest properties (see Fig. S22 in the Supplement). In C_F_NCS (the runs in which Eq.  is set to one), streamflow is consistently lower than in the C_F runs. The greatest difference occurs towards the end of the simulation period in the Chippis subcatchment, with differences up to 10 mm yr-1. The differences are largest in the simulations with a precipitation increase. Regarding vegetation properties, the differences in LAI and SFC, averaged over the strata used in Fig. , never exceed 0.05 m2 m-2 and 1 mm, respectively.

Figure  shows the difference in annual streamflow (30-year annual means) between a fully coupled run without land-use change (C_F) and a run in which forest is allowed to grow in all cells with a “potentially forested” land cover type (see Fig. ). The three subcatchments shown here differ by elevation and distribution of land cover classes. Chippis is the lowest subcatchment and has few cells belonging to the potentially foreste' land cover classes. By contrast, the high-elevation subcatchments Mottec and Moiry are barely forested (Mottec) or have no forest cells at all (Moiry). In the warmest scenarios, LAI and rooting zone storage capacity reached values of 5.5 and 120 mm, respectively, by the end of the simulation even in the highest elevation band of meadows (cells above 2700 m a.s.l.). In all cases, allowing land cover change leads to a decrease in streamflow. The magnitude of this change depends greatly upon the warming scenario. When no warming is assumed, the difference in streamflow relative to the simulation without land cover change is approximately 10 mm yr-1. In all three subcatchments, the difference is greatest under warmer and wetter scenarios. The difference increases rapidly until 2050 (when the temperature and precipitation modifiers reach their maximum), whereas the increase is slower or partially reversed between 2050 and 2100.

Results of this modeling experiment have shown that an increase in atmospheric CO2 concentration has almost no effect on hydrological processes and vegetation dynamics as modeled by FORHYCS. In this implementation, the physiological effect of elevated CO2 concentration is represented by an additional modifier function to the stomatal resistance parameterization. All else being equal, an increase in Ca leads to an increase in stomatal resistance and thus to a decrease in potential and actual transpiration. This slows down canopy water use and thus leads to lower levels of simulated physiological drought. This formulation does not account for other physiological impacts of elevated Ca, such as enhanced photosynthetic rates or possible acclimation effects. The physiological effect of increased Ca is a source of uncertainty in forest models, due to widely differing process formulations among models . For example, our results contrast with the simulations of , who applied a modified version of LPJ-GUESS and found a crucial influence of Ca on simulated future forest biomass in Switzerland. These differences between models are partly due to the knowledge gaps regarding the underlying processes. According to , models that do not consider the physiological effects of Ca at all are likely to underestimate future forest productivity, whereas some other models are likely to yield overestimates due to an improper representation of other limiting factors. From an ecohydrological point of view, the large-scale effects of increased Ca have been the object of a number of recent studies. For example, ) found that decreases in streamflow in Australian catchments were caused by vegetation greening, which was in turn driven by elevated Ca. These studies suggest that the stomatal effects of increased Ca (transpiration reduction) are more than offset by enhanced vegetation growth. This is not the case in this study, where the only visible effect was an increase in streamflow, whereas vegetation properties were not affected at all.

In this simulation experiment, allowing the forest to grow in areas currently covered by meadows caused a reduction of streamflow of up to 60 mm yr-1 at subcatchment level (Fig. ). This is a substantially greater effect than in the simulation experiment of , who found a change in annual runoff on the order of 10 mm yr-1 in regions currently above the treeline as they become forested under simulated climate change. Under the scenario used in their study, temperature was projected to increase by 3–4 K by the end of the century. A major difference with this study is that they only varied LAI, whereas in this study, the development of both LAI and rooting depth were simulated. Both of these variables probably had a major impact on simulated streamflow. These spectacular results must be considered in the light of several potential sources of uncertainty in the model formulation. First, FORHYCS does not account for competition by other vegetation types, which may slow down the expansion of forests. Also, other factors that make the current treelines an extreme environment are not considered by FORHYCS, such as the steep slopes and shallow soils. For example, it was shown that during the warmest period of the Holocene, only stunted trees were able to establish at high elevations, although the climate would have allowed a forest to grow . Another aspect to consider is that at the beginning of the simulation, meadows and alpine vegetation types were parameterized with a prescribed rooting depth of 22 cm. This value was set arbitrarily, and if it was actually higher for these vegetation types, the hydrological impact of forest expansion would be exaggerated in the simulations.