Pan-Arctic modelling of net ecosystem exchange of CO₂

(a) Sites and sources of data

Most of the data used in our analysis have been used previously in different comparisons and for other purposes. Here, we combine these data in a pan-Arctic analysis, adding previously unpublished data from 2009 (table 1). The entire, combined dataset is available from the US Arctic Long-Term Ecological Research (LTER) project at http://dryas.mbl.edu/arc/ITEX/data.html.

All of the data come from surveys of the response of NEE to changes in light (PAR) that were completed in a wide range of subarctic, low Arctic and high Arctic ecosystems during the summers of 2003–2009. The five sites were

At each site, the light response of NEE was described for the widest possible array of locally accessible ecosystem types, selected subjectively and distinguished by vegetation stature and composition. Although most of the plots selected were typical of local vegetation, effort was made to include extreme examples as well (e.g. high or low stature, dense or thin canopies, species-rich, monospecific or species-poor canopies). The dataset includes over 4800 individual measurements of NEE, as part of 448 light response curves from 247 individual plots (table 1). Most (greater than 90%) of the measurements were made within 2–3 h of solar noon, at the highest possible sun angles. We occasionally repeated the light response curves on some plots to help quantify the variability among repeated measurements. At Toolik Lake and Abisko, we also repeated measurements on some plots at different times during the growing season or at different times of day (e.g. every 4 h over 24–28 h). Most of the measurements were made in mid-July through early August, but in the present analysis, all data collected at any time during June–August, at any time of day, are included.

(b) Light response of net ecosystem exchange

At all sites, we measured NEE of CO₂ using a portable cuvette system as described in detail in Williams et al. [8] and Street et al. [13]. A clear Plexiglas cuvette was lowered onto a square aluminium base fitted with legs pushed into the soil to create a level support. The cuvette was sealed to the base by compression of a foam rubber gasket. A clear plastic skirt hung down from the base to the ground surface, and was sealed to the ground by draping a heavy chain on top of the skirt. This created an enclosed volume above each 1 × 1 m plot (at Zackenberg and Longyearbyen, we occasionally used a 30 × 30 cm base). The change in CO₂ concentration during each measurement was determined using a LI-COR 6400 or 6200 Photosynthesis System (LI-COR, Lincoln, NE, USA). NEE was calculated knowing the rate of change in [CO₂], the cuvette and base volumes, air temperature and barometric pressure. We assume that each measurements represents the net flux of CO₂ over the area of each plot (NEE), including GPP (or whole-canopy photosynthesis) and R_E (including both plant and soil respiration), where NEE = R_E − GPP.

We measured the light response of NEE by making a series of measurements on the same plot, starting with one to three measurements at full ambient light, followed by one or two measurements at each of several increasing levels of shading (usually three levels), followed by one to three measurements made in complete darkness. Shading was achieved by covering the cuvette and base with one to three layers of optically neutral shade cloth or mosquito netting, and the dark measurements were made by covering the system with an opaque tarp. Between measurements, the cuvette was ventilated by lifting it from the base and allowing CO₂ concentration to return to approximately the ambient value.

(c) Leaf area, canopy N content and environmental variables

Leaf area and the total amount of N in the canopy were estimated using established relationships with canopy reflectance, using the NDVI as the measure of reflectance [15]. Parameters for these regression relationships were established in separate measurements of NDVI in undisturbed vegetation using a Unispec SC or DC Spectroradiometer (PP Systems, Amesbury, MA, USA), followed by harvest of the entire canopy within the field of view of the instrument (usually a circle approx. 20 cm in diameter) and determination of its leaf area and N content. Samples were collected from representative vegetation at all five sites (table 1). We estimated LAI (m² leaf m⁻² ground) in all plots using the overall regression formula

2.1

2.2

In addition to PAR and air temperature measurements that accompanied each measurement of NEE, for each light response curve, we also made four to six measurements of soil temperature at 5 cm depth using a digital soil thermometer. Additional measurements included estimates of plant cover by species and measurements of soil moisture using a Hydrosense soil moisture probe (Campbell Scientific, Logan, UT, USA); for many plots, we also measured soil temperature at the surface and at 10 cm depth and depth of soil thaw.

(d) Net ecosystem exchange model

The NEE model is identical to the NEE₂ model of Shaver et al. [9], where

2.3

2.4

2.5

The predicted NEE (equation (2.3)) is simply the difference between the R_E and GPP models (NEE = R_E − GPP); thus NEE is a negative value when CO₂ is removed from the atmosphere and positive when CO₂ is added to the atmosphere.

The respiration model (equation (2.4)) assumes that R_E comes from two sources. The first source produces CO₂ as a function of a basal respiration rate, R₀ (µmol CO₂ m⁻² leaf s⁻¹), an exponential temperature response where β is an empirically fit parameter (°C⁻¹) and T is air temperature (°C) and LAI (m² leaf m⁻² ground). This first source is assumed to account for the majority of R_E, including both autotrophic (plant) and heterotrophic (‘soil’) respiration. The Q₁₀ for respiration of this pool can be calculated as

2.6

The GPP model (equation (2.5)) is an adaptation of the aggregated canopy photosynthesis model of Rastetter et al. [22], derived by applying the hyperbolic photosynthesis–light equation at the leaf level, using Beer's light extinction equation and integrating down through the canopy, where P_maxL is the light-saturated photosynthetic rate per unit leaf area (µmol m⁻² leaf s⁻¹), k is Beer's law extinction coefficient (m² ground m⁻² leaf) and E₀ is the initial slope of the light response curve or ‘quantum yield’ at low light (µmol CO₂ fixed µmol⁻¹ photons absorbed).

In the present analysis, we also used canopy N content rather than LAI as a predictor of NEE, R_E and GPP. Doing this required substituting canopy N content (N_T, in units of g N m⁻² ground) for LAI in equations (2.4) and (2.5); this of course caused a change in units of P_maxL (to µmol CO₂ g⁻¹ N s⁻¹), k (to m² ground g⁻¹ N) and R₀ (to µmol CO₂ g⁻¹ N s⁻¹⁾. Units of E₀ and R_x were unaffected. In the following text, we identify the results from the two different formulations (LAI versus canopy N predictors) as the LAI-model and the N-model.

(e) Parameter estimation and model evaluation

The NEE model was fit to the data by nonlinear regression, minimizing the root mean square error (r.m.s.e.) of predictions using the Excel SOLVER tool (Microsoft Office Excel 2010). We used as input data either the complete dataset (4853 simultaneous observations of NEE, air temperature and PAR, and estimates of LAI or N_T), or we used various subsets of the data. In the initial runs, the model-estimated parameters were R₀, β, R_x, P_maxL, k and E₀. However, as with our previous analysis of the 2003–2005 data from Toolik and Abisko [9], after numerous runs using different data subsets, we found that the model-estimated value of the light extinction coefficient, k, was unstable and often unrealistic (e.g. k > 1 or < 0). To eliminate this instability, we fixed the value of k at an ecologically realistic value of 0.5 m² m⁻², leaving only R₀, β, R_x, P_maxL and E₀ to be estimated by the regression. Detailed explanation and justification for this procedure is provided in Shaver et al. [9].

Model parameters were calculated by regression using values of LAI (or N_T) estimated from NDVI measured in each plot, and measured air temperature (or soil temperature), PAR and NEE. The regression was performed on the entire dataset (‘All data’) and on data subsets. Subsets included data collected in all high Arctic sites, all low Arctic sites and individual sites and subsites (table 1). The resulting regression parameters were then used to predict NEE for the whole dataset and for individual sites and subsites. In other words, we used regression parameters derived from surveys of NEE in one part of the Arctic to predict NEE in other parts of the Arctic, and compared the accuracy of those predictions with predictions based on other parameter sets. The fit and accuracy of the model was assessed by comparing per cent variance explained (r²) and r.m.s.e. of measured versus predicted NEE.

(a) Overall and site-by-site regression results

When the entire dataset was used to estimate model parameters, the overall regression explained greater than 75 per cent of the variance in the data (r² = 0.759) with a r.m.s.e. of 1.51 µmol CO₂ m⁻² s⁻¹ (figure 1 and table 2). This result is quite similar to our previous analysis of the smaller dataset from Toolik and Abisko (n = 1444, r² = 0.799, r.m.s.e. = 1.53). For comparison, a r.m.s.e. of 1.5 µmol m⁻² s⁻¹ is approximately two to three times the underlying methodological error associated with each measurement using this method [8], and it is less than 7 per cent of the overall range of measured NEE values.

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The model parameters derived from the entire dataset were also ecologically reasonable. For example, P_maxL was 15.184 µmol CO₂ m⁻² s⁻¹, at the high end of the range of P_max values reported for individual leaves at Toolik Lake and Imnavait Creek [23,24]. The value of β, 0.046°C⁻¹, indicated a Q₁₀ for respiration of approximately 1.58, which is also reasonable for cold, often waterlogged tundra soils and associated vegetation [25,26]. The quantum yield, E₀ = 0.041 µmol CO₂ µmol PAR⁻¹, is consistent with a canopy with generally low leaf area and low sun angle.

When the model parameters were estimated using smaller subsets of the data (table 2), the per cent variance explained was also consistently high (74–93%). R.m.s.e. was often lower for these site-by-site regressions than for the regression using the entire dataset, but r.m.s.e. ranged from 0.42 to 2.14 µmol CO₂ m⁻² s⁻¹ depending on site. Parameter values for the individual site regressions varied considerably, however, especially for the P_maxL and β parameters (table 2). For all three of the high Arctic sites, P_maxL was greater than 20 µmol m⁻² s⁻¹, and for Barrow, P_maxL as estimated by regression was greater than 150 µmol m⁻² s⁻¹. For the AR Burn site, P_maxL was greater than 46 µmol m⁻² s⁻¹. These values for P_maxL are unlikely to be accurate as they are much greater than measured values for leaf-level photosynthesis in the dominant species at these sites [23,24]. Similarly, the range of predicted values for β, and thus Q₁₀, indicated a range of Q₁₀ from less than 1.5 to greater than 3.3, with a maximum of 15.6 in the AR Burn site. Values of Q₁₀ > 3.0 have not been reported before for respiration of Arctic plants or soils during the growing season although very high ‘apparent’ Q₁₀ has been reported for CO₂ releases from under snow cover [25,26]. Thus, although the model fits the data quite well for every data subset, occasionally it did so with biologically unreasonable parameter values. In the most extreme case, the regression using data from the AR Burn site had the highest r² and lowest r.m.s.e. among all regressions, but this was based on completely unreasonable estimates of both P_maxL and β (table 2).

The unreasonable values of P_maxL and β in some of the site-level regressions (table 2) were all found when using data subsets where the overall range of measurements of NEE was narrower than in other data subsets and especially when few measurements were available from high light and/or high temperature conditions. In all four cases where the site-by-site regressions gave values of P_maxL > 20, there were few if any measurements made at PAR values greater than 600 µmol photons m² s⁻¹ and thus there were few if any NEE values less than −7 µmol CO₂ m² s⁻¹ (figure 1). Three of these were at the high Arctic sites, Longyearbyen, Zackenberg and Barrow, where incoming PAR is always low due to low sun angles and frequent cloudiness, and the fourth was at the AR Burn site, where all 3 days of measurement were cloudy. As a result, in these four data subsets, the regression was insufficiently constrained by measurements made at or near light-saturating conditions, and P_maxL is an extrapolated value far outside the range of measurements. Similarly, the high values of β (Q₁₀ > 3.0) were all for data subsets where the overall range of air temperatures and NEE measurements was less than for other data subsets. The highest Q₁₀ values were at the AR Burn site and at Barrow and Longyearbyen where the overall range of observed NEE was only approximately 10 µmol C m² s⁻¹ or less (figure 1).

Although regressions based on the different data subsets produce a wide range of parameter values (table 2), parameters estimated in the regression using the entire dataset can be used to make accurate predictions of NEE at all of the individual sites and subsites. When measured values of NEE for individual sites were compared with predicted NEE using regression parameters derived from the whole dataset, the model did about equally well at predicting NEE at each site (figure 1). Regression slopes of measured versus predicted values were close to 1.0 for all sites, with intercepts not significantly different from zero. Per cent variance explained for data from individual sites ranged from 64 per cent at Zackenberg to 90 per cent at Latnjajaure. R.m.s.e. (not shown in figure 1) varied from approximately 0.9 µmol CO₂ m⁻² s⁻¹ at the AR Burn to 2.2 µmol CO₂ m⁻² s⁻¹ at Paddus.

(b) High Arctic versus low Arctic

When data from the high Arctic were used to estimate model parameters, the regression explained 73.9 per cent of the variance in NEE in the high Arctic dataset, a small improvement over the use of parameters derived from the entire dataset to predict NEE in the high Arctic (70.3% in figure 1 and table 3). The r.m.s.e. for measured versus modelled NEE in the high Arctic data was 1.17 µmol CO₂ m⁻² s⁻¹, also a small improvement over the r.m.s.e. of 1.26 µmol m⁻² s⁻¹ when NEE in the high Arctic was predicted using parameters derived from the entire dataset. The parameter values, though, were considerably different in the regression using high Arctic data only, with a much higher P_maxL (20.53 µmol m⁻² s⁻¹), a higher value of β (0.071, equivalent to a Q₁₀ of 2.03), a slightly lower E₀ (0.037) and higher R₀ and lower R_x (table 2).

When the parameters developed from the high Arctic data were used to predict NEE in the low Arctic, or in the entire dataset, the variance explained in these other datasets was considerably lower, only 62–63 per cent (table 3). R.m.s.e. was also much higher, greater than 2 µmol CO₂ m⁻² s⁻¹. By contrast, when data from the low Arctic were used to estimate model parameters, the parameter values were similar to the values derived using the whole dataset. This result is in part due to the fact that the low Arctic dataset is about three times larger than the high Arctic dataset, comprising about three-fourths of total data available. More importantly, though, parameters derived from the low Arctic data led to predictions of NEE in the high Arctic that explained almost 70 per cent of variation in the high Arctic dataset (table 3). When low Arctic parameters were used to predict high Arctic NEE, the r.m.s.e. was even lower (1.27) than when low Arctic parameters were used to predict low Arctic NEE (r.m.s.e. = 1.58).

The different parameter values derived for the high Arctic data might be explained in part as local adaptations to cooler climate with lower PAR. For example, a higher Q₁₀ might be expected in colder environments of the high Arctic [27], although Q₁₀ values this high have never been reported for Arctic ecosystems. Changes in leaf N and leaf area–leaf N relationships might be partly responsible for the higher P_maxL in the high Arctic [14,28]. However, one key difference between the low and high Arctic datasets is that the high Arctic data include a much narrower range of observed values of NEE, LAI, PAR and air temperature on which the regression is based. For the high Arctic sites, there are very few NEE values greater than 5.0 or less than −6.0 µmol m⁻² s⁻¹ (figure 1), and very few observations when GPP was close to saturation [14]. What this means for the present analysis is that predictions of NEE in the low Arctic based on parameters derived from the high Arctic are extrapolations, whereas predictions of NEE in the high Arctic based on parameters derived from the low Arctic are interpolations.

The main reason for the high values of P_maxL and β in the high Arctic regression (table 2) is the lack of measurements at high light or high temperatures to better constrain the regression at its extremes. One way to achieve this constraint is to fix one or both of these parameters at more reasonable values, letting the regression procedure solve for the remaining parameters as we did in fixing the value of k in table 2. For example, we repeated the analysis in table 3, but with the value of β fixed at 0.046 (the same value calculated for the regression including the whole dataset). The results (table 4) indicate an improvement in variance explained and a further reduction in r.m.s.e. when high Arctic data were used to predict NEE in the low Arctic or in the entire dataset. The value of P_maxL for the high Arctic regression was still higher than expected at almost 20 µmol CO₂ m⁻² s⁻¹, though. It is possible that this high predicted value of P_maxL actually reflects higher leaf level rates of light-saturated photosynthesis in high Arctic plants. However, most Arctic species have leaf-level P_max values less than 20 µmol CO₂ m⁻² s⁻¹ [23,24]. To achieve a canopy-level P_max (=P_maxL in this model) of less than 20 µmol CO₂ m⁻² leaf s⁻¹, the average high Arctic vegetation canopy would have to be composed mostly of species with unusually high leaf-level P_max, and all of the individual leaves in the canopy would have to be arranged so that they are fully illuminated at high incoming PAR; this is extremely unlikely. High Arctic plants do have slightly higher average leaf N content [14], which might support higher potential rates of light-saturated photosynthesis, but in reality, the available light levels in these high latitudes are rarely if ever high enough to achieve these rates. Thus, we interpret these high P_maxL values as artefacts resulting from a lack of observations of NEE at high PAR in these datasets to constrain these regression-derived parameters. Fixing the value of P_maxL at a more reasonable value of 14–15 µmol m⁻² s⁻¹ in regression using the high Arctic dataset results in predictions that are very similar to those using either the low Arctic dataset or the entire dataset (results not shown).

(c) Low Arctic versus high Arctic with net ecosystem exchange as a function of N_T

When NEE was predicted as a function of canopy N content (N_T) rather than LAI, the % variance explained was further increased and the r.m.s.e. was further reduced (r² = 0.770, r.m.s.e. = 1.476 in the ‘all data’ regression; table 5). The N-model parameters indicate a P_maxL of 8–10 µmol CO₂ g⁻¹ canopy N s⁻¹, with a lower quantum yield than in the analyses based on LAI. The R₀ parameter varied from 0.6 to 1.0 µmol CO₂ g⁻¹ canopy N s⁻¹. Although the units of P_maxL and R₀ in these regressions were different when N_T rather than LAI was used, the ratios of these two parameters stayed about the same; P_maxL was always approximately 10–12 times the value of R₀ no matter what the units were (table 4 versus table 5). Similarly, P_maxL and R₀ varied among the various data subsets in about the same way, with higher values when using the high Arctic data and lower values for the low Arctic and for all data. When using N_T to predict NEE, the value of R_x was consistently higher, by approximately 0.2–0.35 µmol CO₂ m⁻² s⁻¹, than when LAI was used although the values of R_x changed in the same way among the data subsets.

The similarities in the relationships among the model parameters using either N_T or LAI to predict NEE for different datasets are almost certainly due to the overall close correlation between N_T and LAI, which appears in all of the individual data subsets as well as the overall dataset [13,29]. We also know that the vertical distribution of N in the canopy differs from the vertical distribution of leaf area (i.e. N concentration is not constant at all canopy heights; [14]), which may explain the relatively small differences in calculated quantum efficiency using N_T versus LAI. The slightly higher values of R_x when using N_T to predict NEE may be due to the functioning of this term as essentially a remainder in the regression calculation [9].

(d) Effect of using soil versus air temperature to predict net ecosystem exchange

Using soil temperature at 5 cm instead of air temperature to predict NEE led to less accurate predictions (larger r.m.s.e.) and poorer fit of predictions to measurements (lower r²) although these regressions still explained at least 67 per cent of the variance in the data in all comparisons, with r.m.s.e. always less than 1.9 µmol CO₂ m⁻² s⁻² (table 5). There are at least two likely reasons for this: first, R₀, the temperature-controlled component of R_E, was assumed to include both above-ground and below-ground plant respiration as well as soil respiration. Although one might expect above-ground plant respiration to be correlated with below-ground soil temperatures, the actual range of above-ground temperatures experienced during the measurement of NEE was much greater than the range of below-ground temperatures. One might expect that above-ground plant respiration would be more closely related to this greater variation in air temperatures than to the variation in soil temperatures. Second, there may be a time lag between the effect of soil temperature variation on soil and root respiration and the measurement of that change in respiration using our cuvette method, due to the time it takes for CO₂ to diffuse through the soil and into the well-mixed air volume of the cuvette. These problems could be solved by increasing the complexity of the model to include separate above-ground and below-ground biomass pools and temperature controls, but this would add at least one new parameter and one more variable to the model; it would require measurement of both soil and air temperature for every measurement of NEE. For the purposes of this study, the remarkable fact is how little difference it makes using either soil or air temperature to predict NEE.