The leaf-level net carbon assimilation of photosynthesis, An, is based on Farquhar et al. (1980) as An=min⁡Ac,Aj,Ap-Respd, where Ac, Aj, and Ap are the enzyme (RuBisCO)-limited, light-limited, and product-limited rates of carboxylation, respectively, and Respd is the leaf-level respiration. The enzyme limited rate is defined as Ac=Vcmax(ci-Γ*)ci+Kc(1+oiKo), where ci is the intercellular leaf partial pressure of CO2, oi = 0.209 Patm, Patm is atmospheric pressure, and Kc, Ko, and Γ* are constants. The maximum rate of carboxylation at 25 ∘C, Vcmax25, is defined as Vcmax25=NaFLNRFNRaR25βt, where Na is the nitrogen concentration per leaf area, FLNR the fraction of leaf nitrogen within the RuBisCO enzyme, FNR the ratio of total RuBisCO molecular mass to nitrogen mass within RuBisCO, and aR25 is the specific activity of RuBisCO at 25 ∘C. The Vcmax25 is adjusted for leaf temperature to provide Vcmax in Eq. (2), used in the final photosynthetic calculation. Both Aj and Ap are functions of Vcmax as well (not shown). The variable βt represents the level of soil moisture availability, which influences both Vcmax (Sellers et al., 1996), and stomatal conductance (Eq. 5). CLM calculates βt as a factor (0–1, high to low stress) by combining soil moisture, the rooting depth profile, and a plant-dependent response to soil water stress as βt=∑iwiri, where wi is a plant wilting factor for soil layer i and ri is the fraction of roots in layer i. The plant wilting factor is scaled according to soil moisture and water potential, depending on plant functional type (PFT). Soil moisture is predicted based upon prescribed precipitation and vertical soil moisture dynamics (Zeng and Decker, 2009). The root fraction in each soil layer depends upon a vertical exponential profile controlled by PFT-dependent root distribution parameters adopted from Zeng (2001).

The carbon and water balance are linked through ci by the stomatal conductance to CO2, gs, following the Ball–Berry model (Ball et al., 1987) as defined by Collatz et al. (1991): gs=mAncs/Patmhs+bβt, where m is the stomatal slope, cs the partial pressure of CO2 at the leaf surface, hs the relative humidity at the leaf surface, and b the minimum stomatal conductance when the leaf stomata are closed.

The version of CLM used here has a two-layer (shaded, sunlit) representation of the vegetation (Oleson et al., 2013). Photosynthesis and stomatal conductance are calculated separately for the shaded and sunlit portion and the total canopy photosynthesis is the potential gross primary productivity (GPP), CFGPPpot: CFGPPpot=[(An+Respd)sunlit(LAI)sunlit+An+RespdshadedLAI)shaded⋅12.011-6, where LAI is the leaf area index and 12.011-6 is a unit conversion factor. The total carbon available for new growth allocation (CFavail_alloc) is defined as CFavail_alloc=CFGPPpot-CFGPP, mr-CFGPP, xs, where the maintenance respiration is derived either from recently assimilated photosynthetic carbon CFGPP, mr or, if photosynthesis is low or zero (e.g., night), the maintenance respiration is drawn from a carbon storage pool (CFGPP, xs). In contrast, CFalloc, is the actual carbon allocated to growth calculated from the available nitrogen and fixed C : N ratios for new growth (e.g., stem, roots, leaves). The downregulation of photosynthesis from nitrogen limitation, fdreg, is given by fdreg=CFavail_alloc-CFallocCFGPPpot. The actual, nitrogen-limited GPP is defined as GPP=CFGPPpot(1-fdreg).

The canopy-level fractionation factor α is defined as the ratio of 13C / 12C within atmospheric CO2 (Ra) and the products of photosynthesis (RGPP) as α=RaRGPP. The preference of C3 vegetation to assimilate the lighter CO2 molecule during photosynthesis is simulated in CLM with two steps: diffusion of CO2 across the leaf boundary layer and into the stomata, followed by enzymatic fixation to give the leaf-level fractionation factor: α=1+4.4+22.6ci*ca1000. where ci* and ca are the intracellular and atmospheric CO2 partial pressure, respectively. The numbers 4.4 and 22.6 represent the diffusional and enzymatic contributions to isotopic discrimination, respectively (Farquhar et al., 1989). The variable ci* (known in CLM as the “revised intracellular CO2 partial pressure”) is marked with an asterisk to indicate the inclusion of nitrogen downregulation defined as ci*=ca-An(1-fdreg)Patm(1.4gs)+(1.6gb)gbgs, where gb is the leaf boundary layer conductance. Equation (11) is a general expression for ci*, where within the model ci* and discrimination are calculated for the sunlit and shaded layer of leaves separately and subject to the local environmental conditions unique to each layer (Oleson et al., 2013). The inclusion of the nitrogen downregulation factor fdreg reflects the two-stage process in which the potential photosynthesis (Eq. 6) and the actual photosynthesis (Eq. 9) are calculated within CLM and prevents a mismatch between the actual photosynthesis and the intracellular CO2. This mismatch is a result of the carbon–water (An-gs) coupling (Eq. 5) being imposed prior to the effect of nitrogen limitation (Eq. 9), and is an artifact of the model implementation. We also test a separate model formulation (described in detail in the next paragraph) specific to this analysis that imposes nitrogen limitation through the Vcmax parameterization and removes the artifact of fdreg.

The sensitivity of preliminary model results to nitrogen limitation led us to test three distinct discrimination formulations (Fig. 1; Table 2). The limited nitrogen formulation was based on the default version of CLM4.5 and included both nitrogen limitation and the nitrogen downregulation factor within the calculation of ci* as given in Eq. (11). The second, unlimited nitrogen formulation, which we created specifically for this analysis, also follows Eq. (11); however, the vegetation is allowed unlimited access to nitrogen (CFGPPpot=GPP,fdreg= 0) which ignores the nitrogen budget within CLM. We account for the increased productivity in the unlimited nitrogen model simulations by calibrating Vcmax (Sect. 2.4). Finally, in the no-downregulation discrimination formulation (also created specifically for this analysis), we included nitrogen limitation, but removed the downregulation factor fdreg within the isotopic discrimination Eq. (11).

In the unlimited nitrogen formulation, we use a different modifier on Vcmax25 (Fig. 1; described in Sect. 2.4 and Figs. S1, S2 in the Supplement) in the calibrated runs to give similar carbon flux, water flux, and biomass as in the other two formulations, such that all three formulations have fluxes and biomass that are similar to what is observed at the site, and which presumably reflect nitrogen limitation. Thus, the distinction between these three formulations can be viewed entirely as when nitrogen limitation is imposed in relation to photosynthesis: (1) after photosynthesis via a downregulation between potential and actual GPP (Eq. 9) that feeds back on the ci*/ca used for isotopic discrimination but not on gs or An in the limited nitrogen formulation; (2) before photosynthesis via Vcmax, which limits photosynthetic capacity affecting both ci*/ca, gs and An in the unlimited nitrogen formulation; and (3) after photosynthesis with no effect on either the ci*/ca for isotopic discrimination or gs or An in the no-downregulation discrimination formulation. The downscaled portion of the carbon during nitrogen limitation (CFGPPpot-GPP) is removed from the system and does not appear as a respired flux (Fig. 1). In summary, the limited nitrogen (post-photosynthetic) formulation adjusts the photosynthetic rate by explicitly tracking N availability, whereas the unlimited nitrogen (pre-photosynthetic) formulation takes into account any N limitation through the Vcmax parameterization. Because the limited nitrogen formulation reduces An during the nitrogen downregulation step without explicitly solving for gs, the carbon–water cycle is partially coupled, whereas the unlimited nitrogen formulation is fully coupled.

Carbon isotope ratios are expressed by standard delta notation: δ13Cx=RxRVPDB-1×1000, where Rx is the isotopic ratio of the sample of interest and RVPDB is the isotopic ratio of the Vienna Pee Dee Belemnite standard. The delta notation is dimensionless but expressed in parts per thousand (‰) where a positive (negative) value refers to a sample that is enriched (depleted) in 13C / 12C relative to the standard. Because this is the only carbon isotope ratio we are concerned with in this paper, the “13” superscript is omitted for brevity in subsequent definitions using the delta notation. The canopy-integrated photosynthetic discrimination, Δcanopy, is defined as the difference between the δ13C of the atmospheric and assimilated carbon, Δcanopy=δatm-δGPP. The difference between δ13C of the total ecosystem respiration (ER) and GPP fluxes, called the isotope disequilibrium (Bowling et al., 2014), is defined as disequilibrium=δER-δGPP. The ecosystem-level water-use efficiency (WUE) is defined as actual carbon assimilated (GPP) per unit water transpired (ET) per unit land surface area: WUE=GPPET. The intrinsic water-use efficiency (iWUE) from leaf-level physiological ecology is defined as iWUE=Angs, where An is the net carbon assimilated per unit leaf area and gs is the stomatal conductance. CLM calculates gs (Eq. 5) for shaded and sunlit portions of the canopy separately, therefore an overall conductance was calculated by weighting the conductance by sunlit and shaded leaf areas.

Global average atmospheric CO2 concentrations increased roughly 40 % from 1850 to 2013 (from 280 to 395 ppm). The standard version of CLM4.5 includes an annually and globally averaged time series of this CO2 increase; however, this does not capture the observed seasonal cycle of ∼ 10 ppm at Niwot Ridge (Trolier et al., 1996). Therefore, we created a site-specific atmospheric CO2 time series (Fig. 2) to provide a seasonally realistic atmosphere at Niwot Ridge. From 1968 to 2013 the CO2 time series was fit to flask observations (Dlugokencky et al., 2015) from Niwot Ridge. Prior to 1968, the CO2 time series was created by combining the average multiyear seasonal cycle based on the Niwot Ridge flask data to the annual CO2 product provided by CLM. More details are located in the Supplement.

As atmospheric CO2 has increased, the δ13C of atmospheric CO2(δatm) has become more depleted (Francey et al., 1999), and this change continues at Niwot Ridge at -0.25 ‰ per decade (Bowling et al., 2014). The δatm also varies seasonally, and depends on latitude (Trolier et al., 1996). However, CLM4.5 as released assigned a constant δ13C of -6 ‰. We therefore created a synthetic time series of δatm from 1850 to 2013 (Fig. 2). From 1990 to 2013, the time series was fit to the flask observations (White et al., 2015) as described in Sect. 2.3.1. Prior to 1990, the interannual variation within the δatm time series was fit to the ice core data from Law Dome (Francey et al., 1999; see also Rubino et al., 2013). This annual data product was then combined with the average seasonal cycle at Niwot Ridge as determined by the flask observations to create the synthetic product from 1850 to 1990. More details about the methods and the site-specific data set of atmospheric CO2 and δ13C of CO2 are located in the Supplement.

We performed an initialization to transition the model from near-bare ground conditions to present-day carbon stocks and LAI that allowed for proper evaluation of isotopic performance. This was implemented in four stages: (1) accelerated decomposition (1000 model years), (2) normal decomposition (1000 model years), (3) parameter calibration (1000 model years), and (4) transient simulation period (1850–2013). The first two stages were preset options within CLM with the first stage used to accelerate the equilibration of the soil carbon pools, which require a long period to reach steady state (Thornton and Rosenbloom, 2005). The parameter calibration stage was not a preset option but designed specifically for our analysis. For this, we introduced a seasonally varying Vcmax that scaled the simulated GPP and ecosystem respiration fluxes to present-day observations (Sect. 2.4). In the transient phase, we introduced time-varying atmospheric conditions from 1850 to 2013 including nitrogen deposition (CLM provided), atmospheric CO2, and δatm (site-specific as described above). Environmental conditions of temperature, precipitation, relative humidity, radiation, and wind speed were taken from the Niwot Ridge flux tower observations from 1998 to 2013 and then cycled continuously for the entirety of the initialization process. We used a scripting framework (PTCLM) that automated much of the workflow required to implement several of these stages in a site-level simulation (Mao et al., 2016; Oleson et al., 2013).

The CLM model (limited nitrogen simulation) was successful at simulating GPP, ER, and latent heat fluxes (Fig. 3), leaf area index (LAI), and aboveground biomass (Fig. 4), but only following site-specific calibration. Similar improvement was observed after calibration for the unlimited nitrogen run (not shown). The calibration also eliminated erroneous winter GPP. In general, terrestrial carbon models tend to overestimate photosynthesis during cold periods for temperate/boreal conifer forests (Kolari et al., 2007), including Niwot Ridge (Thornton et al., 2002). Although our calibration approach forced Vcmax to zero during the winter, it did not solve the underlying mechanistic shortcoming. A more fundamental approach should address either cold inhibition (Zarter et al., 2006) of photosynthesis or soil water availability associated with snowmelt (Monson et al., 2005) to achieve the photosynthetic reduction. Nevertheless, within the confines of our study area, our calibration approach was sufficient to provide a skillful representation of photosynthesis and provided a sufficient testbed for evaluating carbon isotope behavior. We caution that because the fdf parameter (Eq. 17) was calibrated specifically for Niwot Ridge, it would not be applicable outside this study area.

The model performed better at simulating δ13C biomass of bulk needle tissue, roots, and soil carbon (Fig. 5) for the unlimited nitrogen and no downregulation discrimination cases as compared to the limited nitrogen case. When nitrogen limitation was included the model underestimated δ13C of sunlit needle tissue (1.8 ‰), bulk roots (1.0 ‰), and organic soil carbon (0.7 ‰). All simulations fell within the observed range of δ13C in needles that span from -28.7 ‰ (shaded) to -26.7 (sunlit). This vertical pattern in δ13C of leaves is common (Martinelli et al., 1998) and results from vertical differences in nitrogen allocation and photosynthetic capacity. The model results integrated the entire canopy and ideally should be closer to sun leaves (as in Fig. 5) given that the majority of photosynthesis occurs near the top of the canopy.

Model simulations of δ13C of living roots were ∼ 1 ‰ more negative as compared to the structural roots. This range in δ13C results from decreasing δatm with time (Suess effect, Fig. 2). The living roots had a relatively fast turnover time of carbon within the model, whereas the structural roots had a slower turnover time and reflected an older (more enriched δatm) atmosphere. The limited nitrogen simulation was a poor match to observations relative to the others (Fig. 5b).

There was an observed vertical gradient in δ13C of soil carbon (-24.9 to -26 ‰) with more enriched values at greater depth (Fig. 5c). This vertical gradient is commonly observed (Ehleringer et al., 2000). Simulated δ13C of soil carbon was most consistent with the organic horizon observations. There are a wide variety of post-photosynthetic fractionation processes in the soil system (Bowling et al., 2008; Brüggemann et al., 2011) that are not considered in the CLM4.5 model, so the match with observations is perhaps fortuitous.

All modeled carbon pools showed steady depletion in δ13C since 1850 (coinciding with the start of the transient phase of simulations, Fig. 5). For the limited nitrogen run, there was a decrease in δ13C of 2.3 ‰ for needles, 2.3 ‰ for living roots, and 0.1 ‰ for soil carbon. This occurred because of (1) decreased δatm (Suess effect, Fig. 2) and (2) increased photosynthetic discrimination. We quantified the contribution of the Suess effect by performing a control run with constant δatm, and kept other factors the same (Fig. 6). Approximately 70 % of the reduction in δ13C of needles occurred due to the Suess effect, and the remaining 30 % was caused by increased photosynthetic discrimination. This occurred as plants responded to CO2 fertilization as illustrated in Fig. 7. The model indicated that plants responded to increased atmospheric CO2 (∼ 40 % increase) by decreasing stomatal conductance (Eq. 5) by 20 % for the limited nitrogen run and 30 % for the unlimited nitrogen run (Fig. 7b) with associated change in ci*/ca (Fig. 7a). Other influences upon stomatal conductance were less significant, including An (+10 % limited nitrogen, -10 % unlimited nitrogen; Fig. 7d), soil moisture availability (2–3 %; Fig. 7e), and negligible changes in relative humidity (multidecadal climate change effects are neglected due to methodological cycling of weather data). This finding that stomatal conductance responded to atmospheric CO2 is consistent with both tree ring studies (Saurer et al., 2014) and site-level experiments (Ward et al., 2012).

The effect of CO2 fertilization and associated response of stomatal conductance and net assimilation led to a multidecadal increase in ci*/ca for all model formulations (Fig. 7a). The ci*/ca increased from 0.71 to 0.76, 0.67 to 0.71, and 0.66 to 0.68 for the limited nitrogen, unlimited nitrogen, and no-downregulation discrimination formulations, respectively, from 1850 to 2013. All simulations therefore suggested an increase in photosynthetic discrimination. This increase in discrimination falls in between two hypotheses posed by Saurer et al. (2004) regarding stomatal response to increased CO2: (1) reduction in stomatal conductance causes ci to proportionally increase with ca keeping ci/ca constant and (2) minimal stomatal conductance response where ci increases at the same rate as ca (constant ca-ci) causing ci/ca to increase. Our simulation generally agrees with the observed trend in ci/ca as estimated from tree ring isotope measurements from a network of European forests (Frank et al., 2015). When controlled for trends in climate, Frank et al. (2015) found that ci/ca was approximately constant during the last century. If the Niwot Ridge multidecadal warming trends in temperature and humidity (Mitton and Ferrenberg, 2012) were included in the CLM simulations (this analysis did not consider multidecadal climate change) the stomatal response may have been stronger, thereby holding ci/ca constant.

The simulated stomatal closure in response to CO2 fertilization led to an increase in iWUE and WUE of approximately 20 and 10 %, respectively (Fig. 7f), from 1960 to 2000. This simulated increase in iWUE is consistent with the observation-based studies (Ainsworth and Long, 2005; Franks et al., 2013; Peñuelas et al., 2011) which indicate a 15–20 % increase in iWUE for forests during that time. The overall increase in WUE suggests that the vegetation at Niwot Ridge has some ability to maintain net ecosystem productivity when confronted with low soil moisture, low humidity conditions. Ultimately, whether Niwot Ridge maintains the current magnitude of carbon sink (Figs. 3, S1) will depend upon the severity of drought conditions, as improvements in WUE, in general, are only likely to negate weak to moderate levels of drought (Franks et al., 2013).

The limited nitrogen formulation simulated larger values of An and gs, and smaller iWUE as compared to the unlimited nitrogen formulation (Fig. 7). This is because the unlimited nitrogen formulation was fully coupled (i.e., solved simultaneously) between An and gs (Eq. 5). The limited nitrogen formulation, however, was only partially coupled because An and gs were initially solved simultaneously through the potential An (Eq. 1); however, under N limitation, An becomes limited below its potential value (Eq. 9) through fdreg. Therefore, gs is calculated through the potential An (Eq. 5) and not the nitrogen-limited An.

The simultaneous increase in both simulated photosynthetic discrimination and iWUE conflicts with previous literature where increases in iWUE are typically linked with weakening discrimination (e.g., Saurer et al., 2004) using a linear model. In general, an increase in atmospheric CO2 alone tends to increase iWUE because of reduced stomatal conductance; however, the impact upon discrimination is close to neutral because the increased supply of CO2 external to the leaf is offset by reduced stomatal conductance (Saurer et al., 2004). The VPD likely plays an important role in determining the final trends for iWUE and discrimination, where an increasing VPD should further reduce stomatal conductance (VPD α1hs; Eq. 5) thereby promoting the well-established relationship (increasing iWUE, decreasing discrimination). In contrast, a weak or decreasing trend in VPD should promote the opposite relationship (increasing iWUE, increasing discrimination).

The CLM model at present neglects mesophyll conductance (gm). When Seibt et al. (2008) included gm in a model that linked iWUE to discrimination, they found there were certain conditions when iWUE and discrimination increased together. This is in part because mesophyll conductance, unlike stomatal conductance, does not respond as strongly to changes in VPD, yet has a significant impact upon ci/ca and discrimination (Flexas et al., 2006). Harvard Forest is an example of a site that was observed to show simultaneous increase in iWUE and discrimination over the last 2 decades, using data derived from tree rings (Belmecheri et al., 2014). In our model simulation, we do not consider multidecadal trends in climate or mesophyll conductance; therefore, increasing atmospheric CO2 must be the primary driver for the modeled simultaneous increase in discrimination and iWUE at Niwot Ridge (Fig. 7). These trends in iWUE and discrimination have also been found in a fully coupled, isotope enabled, global CESM1.2 model run with climate simulated by CAM5 (Community Atmosphere Model) driven by CO2 emissions (unpublished, K. Lindsay; Fig. S3). Specifically, a random sample of land model grid cells representing conifer species in British Columbia (lat: 52.3∘ N, long: -122.5∘ W) and Quebec (lat: 49.5∘ N, long: -70.0∘ W) all showed an increase in photosynthetic discrimination and a 10 % increase in WUE from 1850 to 2005. These randomly chosen grid cells are likely better analogs to the site-level simulations described here because they represent boreal conifer forests, whereas the grid cells that are in the Niwot Ridge area were heterogeneous in land cover (e.g., tundra, grassland, forest) and a poor representation of conifer forest.

The relationship between iWUE and discrimination in the global CESM1.2 model run (with model-simulated climate) suggest that the site-level trends are not isolated to the specific conditions of Niwot Ridge, but are a function of the model formulation. There is a relationship between iWUE and ci*/ca (discrimination) as derived from Eq. (11) within the CLM model: ci*ca≅1-1.6caiWUE. The full derivation is provided in the Supplement. Note that according to Eq. (19) increasing iWUE can be consistent with weakening discrimination (decreasing ci*/ca (∼ α)) and therefore consistent with established understanding between trends in iWUE and discrimination. However, this can be moderated by increasing ca. During the course of our simulation (1850–2013), iWUE increased between 15 and 20 % (Fig. 7); however, ca increased by 40 %.

The simulated photosynthetic discrimination (Fig. 8) was significantly larger than an estimate derived from observations and an isotopic mixing model (Bowling et al., 2014). For brevity, we refer to the estimates based on the Bowling et al. (2014) method as observed discrimination but highlight that they are derived from observations and not directly measured. On average, the simulated monthly growing season mean canopy discrimination was greater than observed values by 4.0, 2.3, and 1.8 ‰ for the limited nitrogen, unlimited nitrogen, and no-downregulation discrimination formulations, respectively. The model–observation mismatch in discrimination, despite model–observation agreement to biomass, carbon, and latent heat flux tower observations (Fig. 3), highlights the independent and useful constraint isotopic observations provide for evaluating model performance. Specifically, the overestimation of discrimination may suggest the stomatal slope in the Ball–Berry model (m= 9 in Eq. 5) used for these simulations was too high. This is supported by Mao et al. (2016), who found a reduced stomatal slope (m= 5.6) was necessary for CLM4.0 to match observed δ13C in an isotope labeling study of loblolly pine forest in Tennessee. The stomatal slope was also important to match discrimination behavior in the ISOLSM model (Aranibar et al., 2006), a predecessor to CLM. A global analysis of stomatal slope inferred from leaf gas exchange measurements found that evergreen coniferous species, such as those at Niwot Ridge, had near the lowest values compared to other PFTs (Lin et al., 2015). In addition, they found that low stomatal slope values were characteristic of species with low stemwood construction costs per water transpired (high WUE), low soil moisture availability, and cold temperatures.

Alternatively, discrimination may be overestimated because CLM does not consider the resistance to CO2 diffusion into the leaf chloroplast. The ability of CO2 to diffuse across the chloroplast boundary layer, cell wall, and liquid interface is collectively known as the mesophyll conductance (gm) (Flexas et al., 2008). Multiple studies suggest that gm is comparable in magnitude to gs, and responds similarly to environmental conditions (Flexas et al., 2008). CLM does not account for gm, and as a result assumes the intracellular CO2 is the same as intercellular CO2, when it can be significantly lower (Di Marco et al., 1990; Sanchez-Rodriguez et al., 1999). The overestimation of ci* could have two important impacts upon our simulation. First, this may lead to unrealistically low values of Vcmax in order to compensate for the overestimation of ci*. In fact, we reduced the default value of Vcmax as much as 50 % in our simulation to match the eddy covariance flux tower observations (see Sect. 4.1). Second, the overestimation of ci* should cause an overestimation of discrimination (Eq. 10), which is also consistent with our simulations (Fig. 8). To determine whether the simulated discrimination bias is a model parameter calibration issue (gs) or from excluding gm, we recommend a mechanistic representation of mesophyll conductance within CLM.

The mixing model approach estimate of Δcanopy (17 ‰) (Bowling et al., 2014), combined with δatm(-8.25 ‰) implies a δ13C of biomass between -26 and -25 ‰ (Fig. 8). This range is only slightly more enriched than the observed ranges of δ13C of needle and root biomass (-27 to -26 ‰). The fact that the different approaches to measure discrimination differ by only 1 ‰, whereas CLM simulates a Δcanopy that is 1.8 to 4.0 ‰ greater than the mixing model discrimination, strongly suggests that the model has overestimated discrimination from 2006 to 2012. Therefore, what appeared to be a successful match between the simulated and observed δ13C biomass, may in fact have been fortuitous. A multidecadal time series of discrimination inferred from δ13C of tree rings (Saurer et al., 2014; Frank et al., 2015) would be useful to investigate this mismatch as a function of time, but these data are not presently available.

If the overestimation of modeled discrimination originates from a lack of response of stomatal conductance to environmental conditions, this could be a result of one or several of the following within the model: (1) the stomatal slope value is too high, (2) multidecadal trends in climate (e.g., VPD) have not been included in the simulation, (3) the model neglects gm, or (4) the Ball–Berry representation of gs is not sensitive enough to changes in environmental conditions (e.g., humidity, soil moisture). It has been shown that VPD may be an improved predictor of gs (Katul et al., 2000; Leuning, 1995) and discrimination (Ballantyne et al., 2010, 2011) as compared to relative humidity, currently used in CLM4.5. Future work should consider which of these scenarios is responsible for overestimation of discrimination.

The model formulations that did not explicitly consider the influence of nitrogen limitation upon discrimination (unlimited nitrogen, no downregulation discrimination) were most successful at reproducing the seasonality of discrimination (Figs. 8, S4). In general, the observed discrimination was stronger during the spring and fall and weaker during summer. This observed Δcanopy seasonal range (excluding November) varied from 16.5 to 18 ‰ using Reichstein partitioning (Fig. 8), and was more pronounced using Lasslop partitioning (16.5 to 23 ‰) (Fig. S4). The nitrogen-limited simulated Δcanopy had no seasonal trend, whereas the unlimited nitrogen and no-downregulation discrimination simulations ranged from 18.4 to 21.2 and 17.8 to 20.6 ‰, respectively.

The main driver of the seasonality of discrimination was the net assimilation (An) for the unlimited nitrogen formulation (Fig. 9). This was evident given the inversely proportional relationship between the simulated fractionation factor (α) and An, consistent with Eq. (11). Stomatal conductance (gs) also influenced the seasonal pattern. The most direct evidence for this was during the period between days 175 and 200 (Fig. 9), where An descended from its highest value (favoring higher α), and gs abruptly ascended to its highest value (favoring higher α). The α responded to this increase in gs with an abrupt increase by approximately 0.003 (3 ‰). Similarly, the limited nitrogen simulation seasonal discrimination pattern was shaped by both An and gs, although the magnitude for both was approximately 30 % higher during the summer months as compared to the unlimited nitrogen simulation. This was because the calibrated Vcmax value for the limited nitrogen simulation was much higher than for the unlimited nitrogen simulation (Sect. 4.1). The difference in α between the two model formulations coincided with the sharp increase in fdreg between days 125 and 275, providing strong evidence that the downregulation mechanism within the limited nitrogen formulation led to increased discrimination during the summer. Therefore, it follows that the nitrogen downregulation mechanism was the root cause of the small range in simulated seasonal cycle discrimination for the limited nitrogen formulation, which was inconsistent with the observations.

The simulated Δcanopy was driven primarily by net assimilation (An), followed by vapor pressure deficit (VPD) (Fig. 10). The correlation between VPD and Δcanopy was strongest for the unlimited nitrogen simulation, where the range in monthly average Δcanopy spanned values from 18 to 22 ‰ (Fig. 10b, e, and h). This resembled the observed range in response based upon a fitted relationship from Bowling et al. (2014) that spanned from roughly 16 to 19 ‰ (Fig. 10a, b, and c), although with a consistent discrimination bias. The correlation between VPD and Δcanopy, however, does not demonstrate causality. If that were the case, given that gs is a function of VPD (hs term in Eq. 5) and discrimination is a function of gs (Eqs. 10, 11), a similar relationship should have existed between gs and Δcanopy. This, in fact, was not the case. Overall, the influence of gs (responding to VPD) (R value = -0.50) was secondary to An (R value = -0.77) in driving changes in discrimination (Fig. 10). The model suggested that the range in seasonal discrimination (intra-annual variation) was driven by the magnitude of An based on the inverse relationship between An and Δcanopy, (Eq. 11) illustrated by the separation between months of low photosynthesis (October, May) vs. high photosynthesis (June, July, August). During times of relatively low photosynthesis, An also drove the interannual variation in Δcanopy. On the other hand, gs (VPD) was most influential in driving the interannual variation of discrimination during the summer months only, judging by the directly proportional relationship during the months of June, July, and August. Strictly speaking, gs is a function of hs (leaf relative humidity) and not atmospheric VPD in CLM. However, the two are closely related and the relationship between either variable (atmospheric VPD or simulated leaf humidity) to Δcanopy was similar (Fig. S5).

The limited nitrogen formulation did not produce as wide a range in discrimination as compared to the observations (Fig. 10a, d, and g). Part of this result was attributed to the lack of response between An and Δcanopy. In this case, the discrimination did not decrease with increasing An because the signal was muted by the countering effect of fdreg. The limited nitrogen formulation was, however, able to reproduce the same discrimination response to gs as compared to the other model formulations. The tendency for the limited nitrogen model to simulate discrimination response to gs and not to An may negatively impact its ability to simulate multidecadal trends in discrimination. This may not be a major detriment to sites such as Niwot Ridge which have maintained a consistent level of carbon uptake during the last decade, and is likely more susceptible to environmental impact upon stomatal conductance. However, sites that have shown a significant increase in assimilation rate (e.g., Harvard Forest; Keenan et al., 2013) are less likely to be well represented by this model formulation.

Given the dependence of forest productivity at Niwot Ridge on snowmelt (Hu et al., 2010), it was surprising that the model simulated minimal soil moisture stress (Fig. 9e) and therefore minimal discrimination response to soil moisture. However, this finding was consistent with Bowling et al. (2014), who did not find an isotopic response to soil moisture. In addition, lack of response to change in soil moisture may not be indicative of poor performance of the isotopic submodel performance, but rather an effect of the hydrology submodel (Duarte et al., 2016). However, a comparison of observed soil moisture at various depths at Niwot Ridge generally agrees with the CLM-simulated soil moisture (not shown), suggesting the lack of model response to soil moisture was not from biases in the hydrology model.