•In this study, we used a canopy photosynthesis model which describes changes in photosynthetic capacity with slow temperature-dependent acclimations.
•A flux-partitioning algorithm was applied to fit the photosynthesis model to net ecosystem exchange data for 12 evergreen coniferous forests from northern temperate and boreal regions.
•The model accounted for much of the variation in photosynthetic production, with modeling efficiencies (mean > 67%) similar to those of more complex models. The parameter describing the rate of acclimation was larger at the northern sites, leading to a slower acclimation of photosynthesis to temperature. The response of the rates of photosynthesis to air temperature in spring was delayed up to several days at the coldest sites. Overall photosynthesis acclimation processes were slower at colder, northern locations than at warmer, more southern, and more maritime sites.
•Consequently, slow changes in photosynthetic capacity were essential to explaining variations of photosynthesis for colder boreal forests (i.e. where acclimation of photosynthesis to temperature was slower), whereas the importance of these processes was minor in warmer conifer evergreen forests.
Climate change will affect northern ecosystems by changes in CO2 concentrations, temperature, and the length of the period when ecosystems are physiologically active. Warmer spring temperatures have advanced the budbreak of many plant species and satellite imagery confirms that northern areas are generally greening earlier (Myneni et al., 1997). However, this is not evident at all locations, and reductions of forest growth as a consequence of water stress and later snow melt have also been reported in some boreal forests (Vaganov et al., 1999; D’Arrigo et al., 2004). These studies shed little light on the possible effects of longer growing seasons on the gross primary productivity and carbon (C) balance of evergreen boreal and coniferous northern temperate forests. At some northern evergreen sites (Hollinger et al., 2004), annual net ecosystem C uptake has been found to increase when springtime air temperatures are warmer than normal. For evergreen species, leaf-out dates and other traditional or remotely sensed phenological variables are only of marginal importance for gross primary productivity and C balance of these systems since leaves persist over several years. Nevertheless, it is well known that the photosynthetic capacity of boreal evergreen conifers is greatly diminished in the winter, and the start of photosynthesis in spring requires a reorganization of the photosynthetic apparatus (Ensminger et al., 2004).
Phenological models have long been used to describe traditional phenological variables such as leaf-out or flowering dates (Linkosalo, 1999). These models, which are frequently built on heat sum and day-length approaches, report reasonable predictions of these events. The nature of the start of the photosynthesis in evergreen trees is, however, quite different. Initial photosynthetic capacity seems to be a reversible process (Pelkonen & Hari, 1980) while budburst and leaf development are typically irreversible, and there seems to be a seasonal behavior of photosynthesis in boreal conifers (Thum et al., 2008). Frost hardening and modeling of forest phenology using temperature indices have been shown to be more effective on colder sites in Scandinavia (Thum et al., 2009). To our knowledge, there are no generally accepted models that describe this recovery process and no large-scale analysis has been carried out to understand how factors such as climate, species, or stand structure affect the recovery of photosynthesis.
Good estimates of photosynthesis are required to improve our understanding of ecosystem production and ecosystem C balances under a changing climate. Global carbon models are important tools for managing and predicting ecosystem behavior under future climate scenarios (e.g. Berninger, 1997; Morales et al., 2005; Friend et al., 2007). These models generally consider photosynthesis to respond directly to temperature. However, it is difficult to find unique factors that explain intersite differences in ecosystem productivity as there are many factors affecting photosynthesis.
In this work, we model the C flux of 12 boreal evergreen needle-leaf forests and study the between-site variability of model parameters as a response to temperature and latitude in several locations comprising different ecological situations. The model used was based on Mäkeläet al. (1996, 2004), a simple photosynthesis model that focuses on the long-term acclimation of leaf photochemistry to fluctuations in temperature. The relationship between the parameters and differences in latitude, continentality, and stand characteristics is discussed. We specifically address the questions of how to describe changes in the photosynthetic capacity during periods when the photosystem is acclimating to temporal changes in temperature; and to what extent differences in climate, species or canopy greenness (as measured by the normalized difference vegetation index (NDVI)) are able to account for differences in the parameters of the photosynthesis model.
Materials and Methods
Study sites and data used
The studied datasets included 12 eddy-covariance stations located in boreal evergreen and northern temperate needle-leaf forests from the Fluxnet-Canada Research Network (http://www.fluxnet-canada.ca), Fluxnet (http://www.fluxnet.ornl.gov/fluxnet/siteplan.cfm), and Ameriflux (http://public.ornl.gov/ameriflux). All the flux sites were located at latitudes > 40° in both North America and Europe, including stations with very different precipitation and temperature regimes. We explicitly tried to minimize the effects of stand age on the model results by choosing mature stands to exclude the effects of stand dynamics on fluxes (Goulden et al., 2006). Their main characteristics are shown in Table 1. Fluxes were measured in all cases using the eddy-covariance method (Baldocchi, 2003). Half- hourly eddy flux data were used to calibrate the model. We used site-specific friction velocity thresholds: only data with good mixing conditions and where friction velocity was not correlated with the flux were used in the analyses (Falge et al., 2001; Reichstein et al., 2005). The primary interest of this study is the modeling of the gross ecosystem exchange (GEE) of our forest stands. However, we derived this variable from measurements of net ecosystem exchange (NEE), which are broken down into GEE and ecosystem respiration (Reco). Since Reco was calculated using different algorithms in different datasets, we decided to estimate it ourselves from the data, using the same algorithm for all sites.
Table 1. Site characteristics of eddy-covariance data sets used
Net ecosystem exchange was modeled using a flux-partitioning algorithm where NEE = Reco– GEE. All C flux estimates are in μmol m−2 s−1 and negative values of NEE correspond to forests acting as C sinks. Reco was modeled following the model of Lloyd & Taylor (1994) assuming an Arrhenius-type relationship with air temperature, using the expression:
where Tair(t) is the measured temperature above the canopy in Celsius at time (t) and R10 is the mean respiration at 10°C. After comparing different means of temporal fitting (monthly, biweekly, annual periods), we decided to fit a single expression per site since the differences in the proportion of explained variance were not very large.
Gross ecosystem exchange was modeled using the photosynthesis models of Mäkeläet al. (1996, 2004). The present version uses the modifications of the model presented by Kolari et al. (2007) (with the exception of the small leaf respiration term, which we omitted). We also used an Arrhenius function for respiration instead of the exponential function used by Kolari et al. (2007). This model was originally developed for individual leaves but it was applied here as a big-leaf model. The use of a big-leaf version of this model is justified for atmospherically well-coupled canopies since responses of photosynthetic production to irradiance and vapor pressure are multiplicative. In the model, the gross photosynthetic rate A(t) (in μmol CO2 m−2 s−1) was modeled as a nonlinear function of stomatal conductance of CO2g(t) (in μmol CO2 m−2 s−1), photosynthetic capacity α(t) (in μmol CO2 m−2 s−1), and a saturation function of light intensity γ(t) (dimensionless):
where the stomatal conductance is expressed as:
with and the light response of biochemical reactions of photosynthesis:
Some of these units are slightly changed compared with the original articles to match units frequently used with eddy-covariance data. Ca is the air CO2 concentration in ppm, Q(t) is the photosynthetically active radiation in μmol m−2 s−1, D(t) is the water vapor pressure deficit in kPa, calculated using temperatures above the tree canopies, δ is the half saturation parameter of the light function (μmol m−2 s−1) and λ is a model parameter expressing the carbon required in the long term to sustain transpiration flow (in kPa) derived from an optimal regulation model of stomatal conductance (Berninger & Hari, 1993).
As mentioned earlier, photosynthetic capacity α(t) was modeled as a lagged function of temperature S(t), following Kolari et al. (2007), which was based on Mäkeläet al. (2004), assuming that α(t) is a sigmoid function of S(t). This can be interpreted as the maximum Rubisco limited rate of carboxylation (Kolari et al., 2007). S(t) is a transformation of temperature. It reflects the fact that the photosystem is likely to respond to increasing daily temperatures in a delayed and smooth way in early spring. After comparing different relationships, we used a sigmoid expression based on the logistic function, following Kolari et al. (2007):
Tair(t), the measured air temperature (°C) at time t, and αmax (μmol m−2 s−1), b (°C−1), Ts (°C) and τ are the model parameters: αmax is the maximum photosynthetic efficiency; b is the curvature of the sigmoid function and Ts is the inflection point of the sigmoid curve, that is, the temperature at which α reaches half of αmax; and τ is the time constant (here shown in d) of photosynthetic acclimation and indicates the time it takes for photosynthetic capacity to acclimatize itself to changing temperature. Higher values correspond to longer periods of acclimation of the photosynthesis response to temperature change in the spring (for more details, see Mäkeläet al., 2004). We solved the differential equation for S using the Euler integration algorithm with the same time step as the meteorological observations.
As already described, the parameter λ regulates the stomatal response to vapor pressure deficit and it would be expected to decrease with increasing soil water deficit. However, in a preliminary analysis (not shown) the model was not particularly sensitive to changes in λ. This parameter proved to be the least influential in the model fit and often it was difficult to estimate λ and the other parameters simultaneously from the CO2 exchange measurements. Thus, to avoid parameter trade-offs in the system of nonlinear equations (Canham & Uriarte, 2006) and since we were most interested in studying the variability of τ and αmax, we fixed λ at 3000 kPa and optimized the model for the other five parameters. Attempts to make stomatal conductance sensitive to soil water contents (by making λ sensitive to soil water content as in Mäkeläet al., 1996 and Berninger et al., 1996) did not improve the model fit (data not shown). Additionally, previous published studies as well as our own parameter estimation attempts (data not shown) showed that, with the soil moisture data available, soil moisture effects were generally not very important when estimating photosynthesis in boreal stands (Hollinger et al., 2004; Mäkeläet al., 2006, 2008a; Luyssaert et al., 2007; Vogel et al., 2008), which supports the assumption of constant λ in our modeling approach. Therefore, we did not include the effects of soil moisture on photosynthesis in the model.
Several types of model, with different parameterization and including different datasets from the 12 sites studied, were compared. First, to study the variability of τ along a latitudinal and temperature gradient, we began by fitting the model to each of the 12 datasets analyzed (Table 1), to estimate the five parameters (τ, δ, αmax, b, Ts) in 12 ‘best-fit models’ (Table 2). We investigated whether trends in latitude, NDVI (mostly as an indirect estimate of leaf area index and chlorophyll content; e.g. Gamon et al., 1995), mean temperature, and maximum and minimum temperatures in April and May (both of the air and the soil) could explain the between-site variation in parameter values. NDVI was calculated for the period 9–25 June, for 2003 and 2004, as the mean pixel value included in the 250 × 250 m MODIS images (http://daac.ornl.gov/cgi-bin/MODIS/GR_col5_1/mod_viz.html).
Table 2. Best-fit model results
No. of observations
Approximate standard errors of parameters are shown in parentheses. Mean bias and root mean square error (RMSE) are in μmol m−2 s−1; τ is in d; δ is in μmol m−2 s−1; αmax in micromols m−2 s−1; b in °C-1; Ts in °C. EF, efficiency.
−0.2016 (< 0.0001)
3.129 (< 0.001)
0.0455 (< 0.0001)
−0.3007 (< 0.0001)
Quebec mature boreal
Sask- old jack pine
4.154 (< 0.001)
−0.2889 (< 0.0001)
Secondly, assuming a direct, rather than a delayed, response of photosynthetic capacity to temperature, the model was fitted to the 12 datasets to study the importance of the time delay in the acclimation of photosynthesis. Therefore, we refitted the model by replacing S in Eqn 5 with the air temperature Tair, as expressed in Eqn 6.
Thirdly, we studied how well the model could predict photosynthetic production of evergreen needle-leaf forest stands without prior knowledge of stand properties. This was done by evaluating the fit of the model after expressing the estimated parameters as a function of remotely sensed or climatically derived covariates (NDVI, mean air temperature, mean precipitation and latitude). We assumed that reorganization of the photosystem driven by temperature is likely to occur mainly during spring. Therefore, we established nonlinear relationships between the values of the parameters of the photosynthesis model and climatic variables both for the whole year and for April and May. More specifically, the variables we considered in spring were the mean daily minimum, the mean daily maximum, the mean daily temperature and the monthly temperature range in April and May. In addition, we fitted models to pooled data grouped in three different clusters of different ecology (see more details in the following sections and in Tables 3, 4).
Table 3. Model parameters for different pooled datasets
Approximate standard error of estimates are shown between parenthesis. Mean bias and root mean square error (RMSE) are in μmol m−2 s−1; τ is in d; δ is in μmol m−2 s−1; αmax in micromols m−2s−1; b in °C-1; Ts in °C. EF, efficiency.
North America, Tmean < 2.5
7.291 (< 0.001)
0.0437 (< 0.0001)
−0.2505 (< 0.0001)
North America, Tmean > 2.5
North America, Tmean > 2.5 (−Wind River)
8.333 (< 0.001)
0.0512 (< 0.0001)
−0.2998 (< 0.0001)
5.206 (< 0.001)
0.0617 (< 0.0001)
−0.3001 (< 0.0001)
Boreal (expanded parameters)a
4.807 (< 0.001)
Table 4. Fit statistics for four scenarios: no delay (i.e. S(t) = Tair); statistics calculated using the parameters fitted for a single model to all datasets (model #5 Table 3, statistics calculated applying the parameters fit in model 5 from Table 3 independently to the datasets, then calculating the fit statistics; this being the reason for the small difference with Table 3); and best fit models (from Table 2) for comparison purposes
Bias and root mean square error (RMSE) are in μmol m−2 s−1. EF, efficiency.
The models were compared by commonly used goodness-of-fit statistics such as bias, absolute bias, root mean square error (RMSE) and the coefficient of determination (R2). To distinguish between nonlinear regressions and linear regressions and the theoretical unsuitability of calculating R2 in nonlinear models, we used the term efficiency (EF) to refer to proportion of explained variance (the analog of R2) calculated for nonlinear models and R2 to that calculated in linear models (e.g. Gea-Izquierdo & Cañellas, 2009).
The mean half-hourly NEE for a site was directly related to site mean annual temperature (EF = 0.865), showing that net forest C fixation increased with increasing air temperature. The 12 single model best fits for the studied datasets are shown in Fig. 1 and Table 2, and an independent fit to show the performance of the respiration submodel to all valid eddy flux data collected when photosynthetic active radiation < 5 μmol m−2 s−1 is shown in Supporting Information, Table S1.
For models fitted individually to each site (Model 1), the model fit was unbiased and EF values were generally above 65% with the exception of the Wind River site. However, when attempting to fit a single model to the whole dataset, the results were not as good (Table 3), showing that we were not able to model interstand variation (see the Discussion section). Additionally, when utilizing the parameters estimated for this single model to fit the different datasets individually, the results were biased (Table 4), even if the average bias in the model fit approached zero. We also fitted models to three different groups with similar ecological conditions, namely North America, Tmean < 2.5°C (continental sites); North America, Tmean > 2.5°C (maritime sites); and the European boreal sites. When grouping, the model results were quite good for the ‘continental’ sites (i.e., using a single equation yielded a good fit, as shown in Table 3), accounting for > 65% of the variance of half-hourly measured C flux, although slightly biased (bias = −0.163 μmol m−2 s−1).
When studying the distribution of the fitted parameters along the cited covariates, we observed that τ (Fig. 2) and αmax (Fig. 3) were negatively correlated with temperature, both with mean annual air temperature and with minimum soil temperature in April. Latitude also showed a positive correlation with τ (R2 =0.314). All parameters included in Table 2 were significant, showing the sigmoid nature of photosynthesis capacity (parameters αmax, b and Ts) and the significance of the delay parameter (τ).
As already stated, photosynthesis was modeled as a sigmoid function of the transformed temperature (Eqns 5, 6) depending on three parameters. The different values of b and Ts in the different best-fit models (Table 2) result in different shapes of the sigmoid response of photosynthetic capacity to temperature. The inflection point (Ts) is the temperature at which photosynthetic capacity reaches 50%, and we observed that this temperature was inversely related to mean temperature (Fig. 3b). Thus, high photosynthesis rates were achieved at higher temperatures at colder sites.
As expected, NDVI was strongly related to Tmean, mean NEE, annual precipitation in mm (Pmm), continentality and minimum soil temperature in April (Fig. 4a, and data not shown). NDVI also had a high correlation with asymptotic photosynthetic capacity (Fig. 4b). The model fit got much worse when we replaced the delayed temperature response with an immediate response (this was done by setting S(t) = Tair(t)) (Table 4). Furthermore, the significant model error increased and efficiency decreased when fixing S(t) = Tair(t)). The importance of the delayed temperature response for the model fit was higher for sites with cold springs, but relatively minor at some of the warmer maritime sites (Fig. 5). The influence of the parameter τ on photosynthetic capacity and NEE estimations can be better observed in Fig. 6. Higher values of τ decrease and smooth the transformed temperature used for NEE calculations. In Fig. 6(d), we illustrate model behavior for different values of τ, showing the response of photosynthetic capacity to a step change in temperature: for a tree with an instantaneous response to temperature (low τ), the response of photosynthesis to temperature changes will be very fast, whereas for a tree with a typical value of τ for a boreal conifer forest (suggested by our results as τ = 6.1 d) it would take > 1 wk for photosynthesis to reach its new value. In reality, when temperature changes more gradually, the results are less dramatic, but important differences in the behavior of photosynthesis existed during springtime (Fig. 6).
Photosynthesis in conifer forests from colder sites responded more slowly to temperature than in warmer forests situated further south. The simple model used explained well the intra- and interannual variation of NEE and photosynthetic capacity in evergreen boreal needle-leaf forests of the northern hemisphere and exhibited a very good fit to the data from 12 different cool temperate and boreal evergreen coniferous forests, as did previous similar approaches (e.g. Mäkeläet al., 2004, 2008a). The goodness-of-fit statistics are similar to those observed in more complex modeling approaches (Yuan et al., 2008). Parsimony is one of the most desirable characteristics in any model. The greater the simplicity of a model, the easier it is to achieve a good comparison of parameters, since trade-offs between parameters (Canham & Uriarte, 2006) are more likely to be avoided.
The use of a time-delayed model improved the fit of the model, particularly for the boreal locations considered. The values of τ increased from warm to cold sites, indicating that the response of photosynthesis to temperature changes in these colder sites is slower. Since, in addition, the growing season in these areas is shorter, the importance of the time constant in the estimation of the whole growing season C balance increased (Figs 2, 5). When we modeled photosynthesis as an instant (with no time delay) response to temperature, the goodness of fit decreased in the northern sites, whereas the fit remained unchanged for warmer maritime sites (Fig. 5). This indicates that, in cold boreal climates, slow changes in photosynthetic capacity must be modeled to correctly estimate forest productivity and C balances. Mäkeläet al. (2008a) obtained similar results on a smaller dataset.
The temperatures at which photosynthetic capacity acclimatizes to 50% of its maximum value at the different sites were between 2 and 8°C (Fig. 3), indicating that photosynthetic capacity increases rapidly above 0°C. Similarly to acclimation temperature, at cold sites the temperature at which photosynthesis was saturating (i.e. approaching αmax) also seemed higher than at warmer sites (Fig. 3). Plant physiologists have argued that photosynthetic responses of C3 plants to temperature should be very similar, although this idea continues to be challenged, since genetically different versions of Rubisco seem to have different temperature responses (Sage, 2002). While low temperatures as such do not necessarily harm the photosystem, conditions that combine high light with cold temperatures are known to be detrimental to the photosynthetic apparatus. High light and low temperature generate an imbalance between the light and the dark reactions of photosynthesis, and excess excitation energy may damage the photosystem. Boreal conifers react to these conditions by disassembling their photosystems and by protecting themselves with the creation of alternative electron sinks, mainly xanthophylls. How strongly the photosystem is disassembled seems to depend on temperature and light availability (Slot et al., 2005; Porcar-Castell et al., 2008).
Most studies modeling the recovery of photosynthesis in the spring have used air temperature as the primary determinant of photosynthetic recovery (Pelkonen & Hari, 1980; Mäkeläet al., 2004). It has been argued that both air and soil temperatures are likely to be major limiting factors that affect the recovery of photosynthetic capacity in the spring, and this also seems to be reflected in our results. Controlled-environment studies have consistently shown that low soil temperatures decrease the rate of photosynthesis of seedlings (Vapaavuori et al., 1992). However, for large trees, the evidence concerning the effects of soil temperature on photosynthetic capacity is less clear. Most recent experimental studies show that photosynthesis of large trees in spring is probably not very sensitive to increases in the soil temperature, although decreases in soil temperature tend to slow down the recovery process (Bergh & Linder, 1999; Strand et al., 2002). Nevertheless, Suni et al. (2003b) showed that some photosynthesis occurs when soils are still at 0°C and the stem contains a large, partially accessible, water reservoir that trees can utilize for photosynthesis in the spring (Running, 1980).
The modeled photosynthetic capacity (αmax) showed a high correlation with NDVI, which is usually a good indicator of the photosynthethic capacity of plant canopies (Gamon et al., 1995) and has been directly related to CO2 flux measurements (Yuan et al., 2007; Lindroth et al., 2008). Using NDVI to expand the photosynthetic capacity improved the goodness in a single model fit for all data (Table 3), although the behavior was significantly worse than fitting the model separately to each of the sites studied. Probably a greater number of locations would help to improve the relationship between parameters and covariates. Factors such as precipitation, temperature and NDVI are correlated among themselves. Thus it is not possible to fully quantify their individual importance. Other studies with different approaches have also reported good fits for pooled expanded models for several locations, especially for daily and monthly time-lags (Bergeron et al., 2007; Mäkeläet al., 2008a). This lack of fit was probably not the result of between-species differences. For example, the North American sites with a mean annual temperature below 2.5°C (as suggested by our data) behaved very similarly (regardless of the species within Picea sp., Pinus sp. and Abies sp. (Table 1)) according to the fitted model (Table 3).
The measured average NEE became more negative with increasing mean site temperature, similar to previous studies (e.g. Valentini et al., 2000; Lindroth et al., 2008). The northernmost forests were almost C-neutral, while more southern forests were C sinks (Table 1). The modeled photosynthetic capacity increased with site mean temperature and minimum temperatures in early April (Figs 3, 4). The model fit was the poorest at the Wind River site, the oldest, rainiest and second warmest forest, and hence with different ecology (maritime humid conifer forest with summer drought (Falk et al., 2005, 2008)). This could be related to estimation of respiration in an old stand (Table S1; Falk et al., 2005, 2008; Lindroth et al., 2008) as well as moisture limitations not included in the model and likely to be more influential in that site compared with pure boreal stands (Reichstein et al., 2007; Falk et al., 2008). Respiration is not a straightforward process to estimate, since it is known to be influenced by several different factors difficult to quantify, such as climate or forest stand attributes, that will affect future flux estimations (e.g. Lloyd & Taylor, 1994; Xu et al., 2004).
Further extensions of this analysis could be in studying the effect of foliar nitrogen concentrations on net C exchange (Mäkeläet al., 2008a; Ollinger et al., 2008) or examining the influence of some other factors that were not included in the present model, such as shading, and by including absorbed radiation rather than incoming photosynthetic active radiation as drivers of the model. It would also be interesting to expand the model to nonboreal forests where soil moisture is more limiting, as this has been shown to affect photosynthesis and C allocation in some ecosytems (e.g. Reichstein et al., 2007; Falk et al., 2008).
The temporal and spatial variability of photosynthetic production and C exchange over large areas is important for global models of the C cycle and the prediction of the impacts of climate change. The length of the photosynthetically active period is an important determinant of annual photosynthetic production in boreal, alpine and temperate ecosystems (e.g. Suni et al., 2003a; Baldocchi et al., 2005). Forests in colder northern areas seem to be slower in adapting their photosynthetic capacity to changes in air temperature. We do not know if these differences between sites are genetically or environmentally determined. In this paper, we show that a simple temperature-driven model of the phenology of photosynthesis predicts well the development of photosynthetic capacity through time. Failure to do so will lead to important overestimations of photosynthetic production (Berninger, 1997; Bergh & Linder 1999).
This contribution was partly funded by a NSERC strategic grant held by Y.B. and F.B. We thank the participants and supporters of Ameriflux, Fluxnet and the Canadian Carbon Program (CFCAS, NSERC, NRCan, Environment Canada) for providing the flux and meteorological data. The Howland research was supported by the Office of Science (BER), US Department of Energy, Interagency Agreement No. DE-AI02-07ER64355.