Functional convergence in regulation of net CO2 flux in heterogeneous tundra landscapes in Alaska and Sweden

Authors

  • G. R. SHAVER,

    1. The Ecosystems Center, Marine Biological Laboratory, Woods Hole, MA 02543, USA, School of GeoSciences, Institute of Atmospheric and Environmental Sciences, University of Edinburgh, Edinburgh EH9 3JN, UK, and
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  • L. E. STREET,

    1. The Ecosystems Center, Marine Biological Laboratory, Woods Hole, MA 02543, USA, School of GeoSciences, Institute of Atmospheric and Environmental Sciences, University of Edinburgh, Edinburgh EH9 3JN, UK, and
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  • E. B. RASTETTER,

    1. The Ecosystems Center, Marine Biological Laboratory, Woods Hole, MA 02543, USA, School of GeoSciences, Institute of Atmospheric and Environmental Sciences, University of Edinburgh, Edinburgh EH9 3JN, UK, and
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  • M. T. VAN WIJK,

    1. Plant Production Systems, Wageningen University, Plant Sciences, Haarweg 333, 6709 RZ Wageningen, The Netherlands
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  • M. WILLIAMS

    1. The Ecosystems Center, Marine Biological Laboratory, Woods Hole, MA 02543, USA, School of GeoSciences, Institute of Atmospheric and Environmental Sciences, University of Edinburgh, Edinburgh EH9 3JN, UK, and
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G. R. Shaver (tel. +1 508 289 7492; fax +1 508 457 1548; e-mail gshaver@mbl.edu).

Summary

  • 1Arctic landscapes are characterized by extreme vegetation patchiness, often with sharply defined borders between very different vegetation types. This patchiness makes it difficult to predict landscape-level C balance and its change in response to environment.
  • 2Here we develop a model of net CO2 flux by arctic landscapes that is independent of vegetation composition, using instead a measure of leaf area derived from NDVI (normalized-difference vegetation index).
  • 3Using the light response of CO2 flux (net ecosystem exchange, NEE) measured in a wide range of vegetation in arctic Alaska and Sweden, we exercise the model using various data subsets for parameter estimation and tests of predictions.
  • 4Overall, the model consistently explains ~80% of the variance in NEE knowing only the estimated leaf area index (LAI), photosynthetically active photon flux density (PPFD) and air temperature.
  • 5Model parameters derived from measurements made in one site or vegetation type can be used to predict NEE in other sites or vegetation types with acceptable accuracy and precision. Further improvements in model prediction may come from incorporating an estimate of moss area in addition to LAI, and from using vegetation-specific estimates of LAI.
  • 6The success of this model at predicting NEE independent of any information on species composition indicates a high level of convergence in canopy structure and function in the arctic landscape.

Introduction

Arctic ecosystems vary by 2–3 orders of magnitude in productivity, in carbon and element stocks, and in element cycling rates (Callaghan et al. 2005). The greatest differences in biogeochemistry occur along the latitudinal gradient from Low- to High Arctic, but differences nearly as large occur along local and regional gradients of topography, snowcover, and exposure to sun and wind (Shaver et al. 1996a,b; Gould et al. 2003). Associated with this variation in biogeochemistry is a similarly dramatic variation in vegetation composition (Walker et al. 2005). Except in the extreme High Arctic, a ‘typical’ arctic vegetation may be dominated by deciduous shrubs, woody evergreens, sedges, forbs, mosses or lichens. Boundaries between these vegetation types are often sharply defined, so arctic vegetation overall appears as a mosaic of distinct patches, with the area and frequency of patch types changing along environmental gradients.

The variability among arctic ecosystems greatly complicates the problem of understanding how their distribution and properties are regulated, and especially complicates the problem of predicting how they might change in a future climate. A vast literature already exists on variation in ecosystem processes in relation to vegetation, particularly in relation to plant ‘functional types’ such as those that differ so dramatically across the arctic landscape (Hobbie 1992; Chapin & Shaver 1996; Callaghan et al. 2005). To develop large-area predictions of change based on functional type composition of arctic vegetation would require detailed knowledge of both species effects on ecosystem processes and the actual distribution of ecosystem types over the landscape. Nonetheless, it is essential to make such predictions because (i) the Arctic climate is changing and (ii) Low Arctic ecosystems in particular contain large C stocks, with potential for significant feedback on climate change if this C is released to the atmosphere (Shaver et al. 1992; Callaghan et al. 2005).

Here we develop a model of net ecosystem exchange of CO2 (NEE; Chapin et al. 2006) by Low Arctic ecosystems that is independent of species or functional type composition of vegetation. Our approach builds on previous research showing consistent relationships between production and biomass (Shaver et al. 1996a,b), N use and allocation (Shaver & Chapin 1991; Shaver et al. 1998, 2001), and especially canopy leaf area and N allocation (Williams & Rastetter 1999; Van Wijk et al. 2005), which suggest similar controls over canopy-level C exchange in a range of arctic ecosystems despite dramatic differences in their composition (Williams & Rastetter 1999; Williams et al. 2000, 2001; Street et al. 2007). This approach contrasts with those studies that view arctic landscapes as a mosaic of patches with models individually developed or calibrated for each patch type (e.g. Williams et al. 2001, 2006). Instead, we develop a single model and single parameterization that applies to all patch types, further demonstrating the strong functional convergence (Field 1991; Goetz & Prince 1999) of diverse arctic vegetation with respect to light use and C exchange.

Research sites and vegetation

We measured CO2 fluxes in 79 1-m2 plots representing the vegetation near Toolik Lake, Alaska, and Abisko, Sweden (Table 1). These areas are similar in latitude (68°10–45′N) and elevation (580–1000 m) but separated by 168° of longitude. Toolik Lake, in the foothills of the Brooks Range, has a continental climate with shorter, warmer and drier summers and longer, colder winters. Annual average temperature is –8.8 °C and the entire area is underlain by permafrost; the average temperature in July is 11.6 °C and in January –24.2 °C (Hobbie et al. 2003). Abisko, by contrast, is strongly influenced by its proximity to the North Atlantic Ocean and by precipitation gradients associated with the coastal mountains. Annual average temperature at Abisko is –0.8 °C and permafrost is generally restricted to low, wet bogs; the July average temperature is 11.0 °C and in January it is –11.9 °C (Anderson et al. 1996).

Table 1.  Summary of sites, plots, vegetation types and sampling dates: CO2 fluxes and light response were measured on a total of 79 plots in 32 different site/vegetation combinations. About half of these were in Sweden and half in Alaska
Abisko & Sweden 2004 (68°10–20′N, 18°45–55′E)
 Latnjajaure (elevation 975–1000 m):
  12 plots in 6 vegetation types (Dryas, heath, mesic meadow, snowbed, tussock, wet meadow)
  Dates of sampling: 3–5 August
 Paddus (elevation 580–600 m):
  13 plots in 6 vegetation types (Betula, wet fen, heath, rocky, Salix, wet sedge)
  Dates of sampling: 28–30 July
 STEPPS site (elevation 725–750 m):
  11 plots in 5 vegetation types (Betula, heath, rocky, Salix, wet sedge)
  Dates of sampling: 22–24 July and 10–12 August
Toolik Lake & Imnavait Creek, Alaska, 2003 and 2004 (68°35–45′N, 149°35–45′W)
 Imnavait Creek 2003 (elevation 875–945 m)
  8 plots in 5 vegetation types (Betula, Salix, tussock, heath, wet sedge)
  Dates of sampling: 5–10 July and 19–24 July
 Imnavait Creek 2004 (elevation 875–945 m):
  15 plots in 5 vegetation types (Betula, Rubus/Sphagnum, wet sedge, tussock, Salix)
  Dates of sampling: 12–17 July and 5–14 August
 Toolik Lake 2004 (elevation 760–800 m):
  20 plots in 5 vegetation types (moist acidic tussock, moist non-acidic tussock, nonacidic non-tussock, heath, wet sedge)
  Dates of sampling: 26 June 8 July and 23 July–4 August

Near Toolik Lake we measured CO2 fluxes in 20 plots within 1 km of the lake, and in 23 plots at Imnavait Creek, about 10 km east and 150 m higher in elevation (Table 1). Plots were representative of the vegetation types in each area, with 2–4 plots of each type. Each plot was classified based on the dominant species or species group (e.g. ‘Betula’ for Betula nana-dominated plots, ‘Salix’ for Salix species, ‘tussock’ for Eriophorum vaginatum, ‘wet sedge’ for rhizomatous sedges, and ‘heath’ for Ericaceae). Detailed analyses of production, biomass and species composition are available from previous research on these sites (e.g. Shaver & Chapin 1986, 1991; Hastings et al. 1989; Hahn et al. 1996; Hobbie et al. 2005).

Near Abisko we measured CO2 fluxes in three areas: (i) Paddus and (ii) the ‘STEPPS’ site (http://www.dur.ac.uk/stepps.project/), on a series of moraines south of the Abisko Scientific Research Station, and (iii) Latnjajaure, in the coastal mountains about 20 km to the south-west. In each area we chose 11–13 plots including 2–3 ‘replicates’ of each of 5–6 vegetation types (Table 1). Vegetation was identified by the dominant species or group, as at the Alaskan sites. Biomass, production and species composition at the Abisko sites have been described previously (e.g. Karlsson & Callaghan 1996; Jonasson et al. 1999; van Wijk & Williams 2005; van Wijk et al. 2005).

Flux measurements were generally made between mid-July and mid-August (Table 1), or after most leaf expansion and before leaf senescence (e.g. Shaver & Kummerow 1992; Jones et al. 1997; Molau 1997; Shaver & Laundre 1997; Stenstrom & Jónsdóttir 1997). In 2003 at Imnavait Creek and in 2004 at Toolik Lake, however, we began measurements on 5 July and 26 June, respectively, while leaves were still expanding. Following the demonstration by Street et al. (2007) that there were no significant changes in photosynthesis per unit leaf area within the period of data collection, all of these data were included in the analysis.

Methods

vegetation and soil properties

In 2003 we used a point frame to describe the vegetation by dropping a rod through a regular grid and identifying each species hit (Williams et al. 2006). In 2004 we used a grid of 20 × 20 cm subplots and estimated cover of each vascular species and of mosses, lichens and bare ground in subplots to calculate average values for the whole plot (Street et al. 2007). In all plots we measured soil temperature at 5 cm with a digital thermometer. In 2004 we estimated soil moisture (volumetric, mL H2O mL−1 soil) in the upper 10 cm using a Hydrosense soil moisture probe (Campbell Scientific, Logan, UT, USA), calibrated for organic soils (J. Powers, unpublished data). Finally, in Alaska in both years we measured thaw depth by pushing a metal rod into the soil until hitting frozen ground.

co2 flux

We completed 125 light response curves including 1410 CO2 flux measurements. Each curve included at least 10 measurements at a minimum of five light levels, including full dark. CO2 flux was measured using a LI-COR 6400 Photosynthesis System (LI-COR Inc., Lincoln, NB, USA) connected to a 1 m × 1 m × 25 cm clear Plexiglas chamber over a 1 × 1 m base (Williams et al. 2006; Street et al. 2007). The base was an aluminium square fitted with legs that were pushed into the soil. A plastic skirt was sealed to the base, hanging down to the ground and sealed to the ground by draping a heavy chain around the perimeter of the plot.

The LI-COR 6400 was operated in closed-system mode, monitoring the increase or decrease in CO2 and water vapour, photosynthetic photon flux density (PPFD) and air temperature. A measurement consisted of lowering the chamber onto the base, ensuring a seal, waiting for a steady rate of change in CO2 and logging the data for (usually) 30 s. Between measurements the chamber was opened and the canopy was ventilated. The typical sequence included 1–3 measurements under ambient light, followed by increasing levels of shade, then a dark measurement. When ambient PPFD was highly variable, we often made 2–4 measurements at each light level. Shading was achieved by covering the chamber with 1–3 thicknesses of mosquito netting, and full dark was achieved under an opaque tarpaulin. After this sequence the chamber was removed and the base volume was estimated by measuring the distance from the base to the ground surface, using a 36-point grid.

flux calculations

We calculated net CO2 flux as in previous research (Williams et al. 2006; Street et al. 2007):

image( eqn 1)

where NEE is net ecosystem exchange (Chapin et al. 2006) or net CO2 flux (µmol m−2 s−1), ρ is air density (mol m−3), V is the volume of the chamber plus base (m3), dC/dt is the rate of change in CO2 concentration (µmol mol−1 s−1), and A is the projected horizontal surface area of the chamber (m2). NEE has two main components: (i) GPP or gross primary production and (ii) ER or ecosystem respiration (Chapin et al. 2006). We calculated GPP by assuming the full-dark measurement was equivalent to ER and that GPP = ER – NEE.

ndvi and leaf area

We measured the normalized difference vegetation index (NDVI) of each plot by two methods. In 2003 we used a two-channel sensor (Skye Instruments Ltd, Llandrindod Wells, UK), in a regular grid of 25 measurements per plot, by pointing the sensor directly down from approximately 1 m, giving a field of view of about 20 cm diameter. In 2004 we used a Unispec Spectral Analysis System (PP Systems, Haverhill, MA, USA). The Unispec has a wider field of view so we used only nine measurements per plot in a 3 × 3 grid. For both instruments NDVI was calculated as:

NDVI = (RIR – RVIS)/(RNIR + RVIS)( eqn 2)

where RNIR is reflectance at 0.725–1.0 µm and RVIS is reflectance at 0.58–0.68 µm. Cross-calibration of the two instruments consistently gave the same NDVI values.

To covert NDVI to estimates of leaf area index (LAI; m2 leaf m−2 ground) we combined the data of van Wijk & Williams (2005), Williams et al. (2006) and Street et al. (2007). These data were collected at Toolik Lake, Imnavait Creek and Abisko by measuring NDVI for individual 20 × 20 cm quadrats, followed by harvesting of each quadrat and separation of leaves by species; leaf area was determined using a scanner and WinRhizo software (Regent Instruments Inc, Ste-Foy, Canada). The combined data set used in this research includes 138 paired observations (90 from Abisko-Paddus, 30 from Imnavait Creek, 18 from Toolik Lake). We estimated leaf area in all plots using the overall regression formula (r2 = 0.736):

LAI = 0.0026e8.0783NDVI( eqn 3)

model formulation

To develop the overall model we first modelled ER and GPP separately. The initial analyses (Williams et al. 2006; Street et al. 2007) of ER and GPP indicated that both were correlated with LAI, that GPP was an asymptotic function of PPFD, and that ER was correlated with temperature, so we included LAI, air temperature and PPFD as controls.

The ER model has three alternative forms. The first assumes that ER comes from a single pool and is a function of a basal respiration rate, a Q10 temperature response and LAI:

ER1=R0× LAI ×eβT( eqn 4)

where R0 is the respiration at 0 °C (µmol m−2 leaf s−1), β is an empirically fit parameter (°C−1) and T is air temperature (°C). The second model is identical to the first except that it assumes an additional source of respiratory CO2 (e.g. from deeper soil horizons) that is independent of LAI and short-term fluctuations in air temperature:

ER2= (R0×eβT× LAI) + Rx( eqn 5)

where the units of Rx are (µmol m−2 ground s−1). The third model assumes that both sources of respiratory CO2 respond to temperature:

ER3= (R0× LAI + Rx) ×eβT( eqn 6)

The GPP model we used was an adaptation of the aggregated canopy photosynthesis model of Rastetter et al. (1992), derived by applying the hyperbolic photosynthesis–light equation at the leaf level, using the Beer's light extinction equation, and integrating down through the canopy:

image( eqn 7)

where PmaxL is the light-saturated photosynthetic rate per unit leaf area (µmol m−2 leaf s−1), k is the Beer's law extinction coefficient (m2 ground m−2 leaf), E0 is the initial slope of the light response curve (µmol CO2µmol−1 photons) and I is the top-of-the-canopy PPFD (µmol photons m−2 ground s−1).

The NEE model was simply the difference between the ER and GPP models (NEE = ER – GPP); thus, NEE was a negative value when CO2 is removed from the atmosphere and positive when CO2 is added to the atmosphere. Because there were three ER models there were three alternative versions of the NEE model (NEE1 = ER1 – GPP, NEE2 = ER2 – GPP and NEE3= ER3 – GPP).

parameter estimation and model evaluation

Each model was fit to the corresponding data by nonlinear regression, minimizing the root-mean-square error (RMSE) of predictions vs. observations using the Excel SOLVER tool (Microsoft Office Excel 2003, version 11, SP2). For the three ER models we used as input data the 378 individual full-dark measurements of NEE, and the corresponding air temperature and LAI values (LAI predicted from NDVI; Street et al. 2007). For the GPP model the input data consisted of 1410 observations of GPP (calculated as the average ER for a given plot minus the measured NEE at each PPFD), and the corresponding air temperature, PPFD and LAI values. For the NEE model there were 1410 observations and the estimated parameters were R0, β, Rx, PmaxL, k and E0.

We evaluated the NEE model by using subsets of the data (based on site or vegetation type) to estimate model parameters. We then used these parameters to simulate NEE within each data subset (i.e. within each site or vegetation type) and to predict NEE within the remainder of the data set. Model performance using these different parameterizations was evaluated by comparing r2, RMSE, and the slope and intercept of observed vs. modelled NEE. We also compared model performance using parameters based on data subsets to the model performance using the parameters based on the entire data set, but applied only to the individual data subsets.

We determined overall variance in model parameters by bootstrapping using the NONLIN procedure in SYSTAT (Systat Software, Inc., versions 10 and 11). Because the confidence limits for the mean value of any parameter are a function of the number of records in the data set, and because the number of records varied widely in our data subsetting procedure, we report the standard deviation for the parameter values in the NEE model using the full data set and 1000 random bootstrap samples of 1410 records each.

Results

plant cover and lai

The cover composition varied widely among the vegetation classes (Table 2), ranging from strong dominance by deciduous shrubs in the ‘Betula’ vegetation to very low deciduous cover in the ‘wet sedge’ vegetation. Evergreens were important components of the vegetation in all but the ‘snowbank’ at Latnjajaure. Mosses averaged at least 23% cover in all vegetation types and were the most abundant cover class overall. Moss cover was never greater than total vascular cover or leaf area but varied from about one third to two thirds of vascular leaf area. Although the average LAI varied only twofold, from 0.48 in ‘tussock’ plots to 1.06 in ‘Betula’ plots, the range in LAI among individual plots was 0.07–2.34, more than 30-fold.

Table 2.  Absolute percentage cover by major cover classes including plant functional types, rock, water, and litter and bare ground in the major vegetation classes used in this research. Each column shows the average cover within each vegetation class, with the averages calculated across all sites (Paddus, Latnjajaure, STEPPS, Toolik, Imnavait). The bottom two lines show average leaf area index (LAI) for each vegetation class, and the ratio of leaf area : moss cover
Cover classVegetation class
BetulaHeathMesicSalixSnowbedTussockWet SedgeAll types
Total vascular105.2789.64106.50127.0391.0664.3575.5189.64
Deciduous61.9923.178.9154.1141.0412.476.9027.33
Evergreen32.6956.3010.4841.720.6022.3412.3128.97
Sedge1.472.1521.604.073.8822.7241.7816.94
Grass4.081.3837.516.325.640.070.114.34
Forb4.416.1625.1015.5536.126.7312.7810.55
Fern0.630.262.895.263.780.031.641.48
Rock0.850.250.000.000.000.000.000.19
Water0.000.000.000.000.000.003.470.78
Litter and bare2.893.106.131.870.0013.1610.366.84
Lichen3.3613.133.580.559.426.281.054.93
Moss32.7722.9133.4736.1245.0033.6348.7435.61
LAI, m2 m−21.060.550.640.990.740.480.730.73
LAI : moss area3.242.411.902.731.651.441.502.05

measured co2 fluxes

NEE consistently showed the expected response to shading, changing from a C sink to a C source as incoming PPFD decreased. Light response curves from Paddus and Latnjajaure were typical (Fig. 1); results from Imnavait Creek (Williams et al. 2006), Toolik Lake (Street et al. 2007) and the Abisko STEPPS site (not shown) were similar. In most cases NEE approached light saturation at PPFD of ~800–1000 µmol photons m−2 s−1, but midday PPFD was usually below 1200–1300 µmol photons m−2 s−1 especially in late July and early August.

Figure 1.

NEE light response curves from the Latnjajaure and Paddus sites at Abisko, illustrating variation among and within contrasting vegetation types. Data points represent individual NEE and PPFD measurements; different symbols and lines represent data from a single plot.

The main reason for differences in NEE (Fig. 1), GPP and ER among plots, both within and among vegetation types, was variation in leaf area. A detailed analysis of GPP at Toolik Lake and Abisko is provided in Street et al. (2007). Overall, the light-saturated rates of GPP (Pmax; µmol CO2 m−2 ground s−1) varied from 3 to 43, and ER varied from 1 to 8 µmol CO2 m−2 s−1; Pmax and ER were positively correlated (r2 = 0.34, P < 0.01). Both Pmax and ER were positively correlated with LAI (r2 = 0.44, 0.46; both P < 0.01), as was the initial slope of the light response curve, E0 (r2 = 0.42, P < 0.01). Plots dominated by dense, deciduous shrub canopies (‘Betula’ and ‘Salix’ vegetation) had the highest Pmax and ER while dry heath and snowbed vegetation had smaller fluxes. Air temperature was not significantly correlated with any of these parameters, although there was a strong tendency for higher ER at higher temperatures (r2 = 0.12, P < 0.1).

er models

The three ER models were similar in their ability to explain overall variance in the ER data set (r2 = 0.46, 0.47 and 0.48, all P < 0.001), but they differed importantly in RMSE, with the RMSE for ER1 about 50% greater than for ER2 and ER3 (Table 3). The underlying methodological measurement error for this measurement is about 0.5 µmol CO2 m−2 s−1 (Williams et al. 2006), compared with the RMSE of 0.9–1.4 µmol CO2 m−2 s−1. The three models also differed in their temperature response (Q10 = e10β), ER1 and ER3 having Q10 values of 1.34–1.36 and ER2 having a Q10 of 1.86. Most studies of arctic soil and plant respiration report Q10 values of 1.8–2.2 within the range of temperatures we observed, closer to that for ER2 (e.g. Nadelhoffer et al. 1991; Schimel et al. 2006). Finally, the slopes and intercepts of the regressions of observed vs. predicted values of ER indicate that, while ER2 and ER3 have slopes near 1.0 and intercepts near 0.0, ER1 has a slope of 0.5 and an intercept of 1.8. This means that the predictions of ER2 and ER3 are relatively unbiased across the entire range of measured values, while ER1 overestimates low values and underestimates high values.

Table 3.  Parameters and statistics of fit for the three ER models (eqns 4–6). R0, β and Rx are parameters estimated by nonlinear regression. Values in parentheses are bootstrap estimates of the standard deviation of parameter values in 1000 random samples of 378 records, using the ER2 model. RMSE is the root mean square error of the predicted ER, in µmol m−2 s−1. Slope and Intercept are the parameters of a linear regression of observed vs. predicted values of ER, r2 is the percentage variance explained by the regression and n is the number of observations. Q10 is the β parameter calculated as a Q10 coefficient [Q10 = exp(β × 10)]
 ER1ER2ER3
R01.7930.435 (0.086)0.893
β0.0310.062 (0.008)0.030
Rx1.886 (0.084)0.993
RMSE1.3880.9240.915
Slope0.5020.9981.003
Intercept1.8370.0040.009
r20.460.4720.483
n378378378
Q101.361.861.34

gpp model

The GPP model explained 76% of the variance in GPP (Table 4, P < 0.001). The RMSE was 1.8 µmol CO2 m−2 s−1, compared with an underlying measurement error of about 0.6 µmol CO2 m−2 s−1 (Williams et al. 2006) and across a range of measured GPP values from zero to > 23 µmol CO2 m−2 s−1. The PmaxL parameter was 17.6 µmol CO2 m−2 s−1, within the range of 6–20 reported by Oberbauer & Oechel (1989) in a survey of leaf-level photosynthesis at Imnavait Creek but higher than typical values of 11–14 µmol CO2 m−2 s−1. This high but not unreasonable estimate of PmaxL is probably due to two factors: first, the contribution of mosses to photosynthetic area is not included in our estimate of LAI, while the contribution of mosses to GPP was included in our measurement of GPP. Mean moss cover in our plots was 0.36 m2 moss m−2 ground and the mean LAI was 0.73 (Table 2). The second factor affecting our estimate of PmaxL is the general lack of measurements of GPP at very high light levels (> 1500 µmol CO2 m−2 s−1 PPFD); extrapolation from measurements at non-saturating PPFD will tend to overestimate PmaxL. The E0 parameter was 0.07 µmol CO2 µmol−1 photons, within the range of 0.05–0.12 reported as typical for vascular plants by Larcher (2003). The slope of the regression of measured vs. modelled GPP was 0.94 (not significantly different from 1.00), indicating consistent lack of bias across the range of measured GPP. The intercept of this regression was 0.39, not significantly different from zero and within the underlying measurement error of ~0.6 (Williams et al. 2006), but may again reflect a consistent contribution of some moss photosynthesis that is independent of vascular LAI.

Table 4.  Parameters and statistics of fit for the GPP model (eqn 7). PmaxL, k and E0 are parameters estimated by nonlinear regression. In the column headed ‘k free’, the k parameter was included in the regression. In the ‘k fixed’ column, k was fixed at a value of 0.5 and only PmaxL and E0 were estimated. Values in parentheses are bootstrap estimates of the standard deviation of parameter values in 1000 samples of 1410 records. RMSE is the root mean square error of the predicted GPP, in µmol m−2 s−1. Slope and Intercept are the parameters of a linear regression of observed vs. predicted values of GPP, r2 is the percentage variance explained by the regression and n is the number of observations. The final row is an estimate of canopy-level quantum yield for a canopy with LAI = 1.0
 k freek fixed
PmaxL17.613 (0.762)16.041 (0.908)
k1.886 (0.173)0.5
E00.069 (0.006)0.03 (0.002)
RMSE1.7991.959
Slope0.9420.874
Intercept0.3900.899
r20.7580.740
n14101410
Ec0.0310.026

The light extinction coefficient, k, was 1.9 when the GPP model parameters were estimated without constraint (Table 4). This is a much higher value than in most temperate or tropical forests, shrublands or herbaceous vegetation (typically 0.3–0.7). The high k value is not, however, unreasonable theoretically and may in fact be appropriate given (i) the extremely short vertical distance over which the leaf area of arctic vegetation is distributed and (ii) the very low sun angles and 24-h photoperiod at 68°30′N. Because the canopies are very short (usually < 15 cm, often < 2 cm), leaf area must be displayed effectively as a single layer, maximizing interception at the top of the canopy. Because the sun angle is always low, light penetration all the way through the canopy is reduced, and hence the effectively larger k value (Sinclair & Knoerr 1982).

To evaluate the implications of a more ‘typical’ canopy light extinction, we fixed the k parameter at a range of values from 0.3 to 2.0 and examined the effect on the other parameters and statistics of fit. Results for a k value of 0.5 (Table 4; full range of results not shown) reflect the general insensitivity of the GPP model to the value of k as the overall r2 for the model declined only slightly, from 0.76 to 0.74, and RMSE increased slightly from 1.80 to 1.96. The model-estimated values of both PmaxL and E0 also changed, indicating a covariance in the parameter estimation. This covariance is illustrated by the calculation of an aggregated canopy quantum yield (Ec), i.e.

image( eqn 8)

For an LAI of 1.0, the canopy-level quantum yield is similar in both parameterizations, Ec = 0.031 vs. 0.026 (Table 4).

nee models

The NEE model was parameterized in three ways. First, we used the parameters determined independently within the ER1, ER2, ER3 and GPP models (Tables 3 & 4) to predict NEE in the combined model (Table 5, section A). In this approach the r2 values for all versions were similarly high (0.77–0.79; P < 0.001), but the RMSE for NEE2 was the smallest of the three (RMSE = 1.59) and the slope and intercept of the measured vs. modelled values were closest to one and zero, indicating least bias. Second, we used regression to estimate all five or six parameters in the NEE models simultaneously (Table 5, section B). This approach produced slightly higher r2 (0.79–0.80), slopes and intercepts very close to one and zero, and much lower RMSE (1.51–1.56) for all three versions of the model. Third, we fixed the value of k at 0.5 and estimated the remaining parameters of the three NEE models (Table 5, section C). In this case the statistics of fit were similar to those using the second approach (k estimated as part of the regression), although the parameter values differed slightly.

Table 5.  Parameters and statistics of fit for the NEE models. In (A) the NEE model parameters were estimated separately in the GPP model (Table 3) and the ER models (ER1, ER2, or ER3; Table 2). In (B) all parameters were estimated by nonlinear regression using the complete NEE models. In (C) the value of k was fixed at 0.5 while the remaining parameters were estimated by regression. RMSE is the root mean square error of the predicted NEE, in µmol m−2 s−1. Slope and Intercept are the parameters of a linear regression of observed vs. predicted values of NEE, r2 is the percentage variance explained by the regression and n is the number of observations. Q10 = e10β. Ec is canopy-level quantum yield with LAI = 1.0. Values in parentheses are bootstrap estimates of the standard deviation of parameter values in 1000 samples of 1410 records, using the NEE2 model
 (A) ER and GPP independent(B) k free(C) k fixed
NEE1NEE2NEE3NEE1NEE2NEE3NEE1NEE2NEE3
PmaxL17.61317.613 (0.762)17.61315.32416.458 (0.810)16.74815.39715.831 (0.676)16.214
k1.8861.886 (0.173)1.8860.3600.896 (0.154)0.9650.50.50.5
E00.0690.069 (0.006)0.0690.0340.0439 (0.003)0.0450.0370.036 (0.002)0.034
R01.1930.435 (0.086)0.8920.9050.453 (0.082)0.7150.9180.602 (0.078)0.901
β0.0300.062 (0.008)0.0300.0630.081 (0.006)0.0600.0620.074 (0.005)0.029
Rx1.886 (0.084)0.9930.901 (0.137)0.2520.547 (0.068)0.996
RMSE2.0911.5861.8011.5551.5191.5131.5581.5291.744
Slope0.9230.9920.9771.0101.0001.0001.0141.0000.925
Intercept1.3080.1290.7490.1330.0000.0020.1740.000–0.432
r20.7740.7850.7740.7930.8010.8030.7930.7990.758
n141014101410141014101410141014101410
Q101.361.861.341.8762.2401.8151.862.091.34
Ec0.0310.0310.0310.0290.0290.0290.0290.0280.027

On the whole the parameter values estimated by regression in the NEE model (Table 5, sections B and C) were within the range of expected values based on species- or process-level measurements. The range in PmaxL (15.3–16.5) was still higher than typical leaf-level values of 11–14 (Oberbauer et al. 1989) but, again, the difference is probably due to the inclusion of moss photosynthesis in the measurement without including moss cover as part of the photosynthetic area. The leaf-level quantum yield (E0) varied from 0.34 to 0.45; when expressed at the canopy level (LAI = 1.0) the canopy quantum yield (Ec) was nearly constant at 0.27–0.29. Predicted Q10 values ranged from 1.8 to 2.2 except for NEE3 with fixed k (Q10 = 1.34).

Examination of predicted vs. measured NEE by site and by vegetation type provides further insight into sources of error. For example, using the NEE2 model with k = 0.5 and identifying the data by site (Fig. 2), it is clear from a plot of measured vs. modelled NEE that most of the few outliers come from the STEPPS and Paddus sites where predicted NEE is less negative than the measured NEE (i.e. GPP at high light is underestimated). The same data can also be identified by vegetation type and plotted as residuals against the driving variables PPFD, air temperature and LAI. In the residual plots (Fig. 3) the same outliers show up as ‘Salix’ vegetation; these are all from just two plots, one at the STEPPS site and one at Paddus. Other than the data from these two plots the only other clear outliers are from wet sedge vegetation, especially at high PPFD (Fig. 3); these are all from a single plot at the Paddus site. The total number of data points that are obvious outliers is thus only about 15–20, less than 2% of the data set. These outliers can be linked to just three of the 79 plots.

Figure 2.

NEE modelled vs. NEE measured, using the parameterization estimated with the NEE2 model and the whole data set with k fixed at 0.5. Units for both axes are µmol CO2 m−2 s−1. In both panels, the regression line is the same and was calculated for all data points (n = 1410). In the upper panel, only the data points from the two Alaska sites are plotted (n = 920). In the lower panel, only the data points for the three Abisko sites are plotted (n = 490).

Figure 3.

Residuals (µmol CO2 m−2 s−1) of the regression of NEE modelled vs. NEE measured using the NEE2 model and the full data set, with k fixed at 0.5 (as in Figure 2). Here, individual data points are identified by vegetation type. Residuals are plotted against the measured photosynthetically active radiation, air temperature and LAI.

nee prediction across sites and regions

When the NEE2 model parameters were estimated using data subsets from individual sites (Latnjajaure, Paddus, STEPPS, Toolik, Imnavait) or regions (Abisko, Alaska), the estimated parameters were quite similar (Table 6, section A). The values of PmaxL, for example, ranged from 13.4 to 17.8 vs. 15.8 when the whole data set was used. Estimated values of E0 ranged from 0.34 to 0.44 (vs. 0.36). For the respiration parameters, at Latnjajaure a low range of air temperatures in the data subset led initially to an anomalously low β value (β = 0.014, or Q10 = 1.16) in the initial regression. This was corrected by fixing the value of β at 0.074, the value obtained in the parameterization using the whole data set (Q10 = 2.09), and recalculating the regression to produce new estimates of PmaxL, E0, R0 and Rx. A similar situation occurred in the Toolik data subset, where the initial estimate of β was anomalously high (β = 0.115, or Q10 = 3.15). At all sites except Paddus, and for the Abisko data combined (three sites) the r2 for measured vs. modelled NEE was larger (r2 = 0.803–0.891; P < 0.001 in all cases) than for the whole data set (r2 = 0.799). The regression slopes were all 1.000 and the intercepts 0.000. RMSE for these parameterizations varied from 1.04 to 2.26 µmol m−2 s−1 vs. 1.53 µmol m−2 s−1 for the whole data set.

Table 6.  Results of the NEE2 model using data subsets by site (‘Abisko’ includes data from Lantja, Paddus and STEPPS; ‘Alaska’ includes data from Imnavait and Toolik). Section (A) shows model parameters and statistics of fit for each data subset. Section (B) shows statistics of fit when parameters developed for one subset are used to predict NEE in the whole data set. Section (C) shows statistics of fit when parameters developed for each subset are applied to the remainder of the records in the data set. Section (D) shows statistics of fit when parameters developed for the entire data set (‘All’) are used to predict NEE in each site
 AllAbiskoAlaskaLatnjajaurePaddusSTEPPSImnavaitToolik
(A) Data subset used for model parameterization
 PmaxL15.83114.82116.57917.84813.38715.41316.03517.764
 k0.50.50.50.50.50.50.50.5
 E00.0360.0380.0350.0300.0340.0440.0350.037
 R00.6020.6080.6140.5280.4950.6860.6260.643
 β0.0740.0730.0750.0740.0760.0710.0740.074
 Rx0.5470.4100.5640.5000.3850.4970.6500.387
 RMSE1.5291.8161.3371.0442.2631.7401.3361.269
 r20.7990.8030.7980.8910.7250.8410.8020.808
 SI
 Intercept0.0000.0000.0000.0000.0000.0000.0000.000
 n1410490920120147223679241
(B) Data subsets used to predict NEE in the whole data set
 RMSE 1.5431.5361.5571.5751.5581.5481.572
 r2 0.7980.7980.7950.7980.7970.7980.798
 Slope 1.0120.9890.9971.1310.9391.0050.924
 Intercept 0.1880.1110.1960.1970.1210.2190.188
 n 1410141014101410141014101410
(C) Data subsets used to predict NEE in the remainder of the data set
 RMSE 1.3761.8541.5961.4751.5221.7221.627
 r2 0.7950.8000.7880.8160.7830.8010.799
 Slope 1.0220.9770.9971.1630.9191.0090.916
 Intercept 0.2910.3150.2140.2250.1410.4220.229
 n 9204901290126311877311169
(D) Parameters for entire data set (‘All’ above) used to predict NEE for each data subset
 RMSE 1.8291.3431.0932.3201.7771.3551.308
 r2 0.8020.7980.8870.7240.8390.8010.807
 Slope 0.9881.0111.0070.8831.0690.9941.082
 Intercept 0.1910.1030.2610.1980.8390.2140.209
 n 490920120147223679241

Parameters developed from individual site or regional data subsets produced equally reliable predictions of NEE in the whole data set (Table 6, section B). The range in r2 was negligible (0.795–0.798), as was the range in RMSE (1.55–1.56). Regression slopes of predicted vs. measured NEE were somewhat more variable but still not significantly different from unity. None of the intercepts was significantly different from zero and all were well within typical measurement error (< 0.22 µmol m−2 s−1). Similarly robust predictions resulted when the site- or region-based parameters were used to predict NEE at sites or regions not included in parameter development (Table 6, section C), although the RMSEs were somewhat more variable (1.38–1.85).

Finally, parameterization of the NEE2 model on individual data subsets did not produce more reliable predictions of NEE for those subsets than when generic parameters developed from the whole data set were used to predict NEE in each subset (Table 6, section D). In fact, variation in RMSE and r2 is correlated across columns in sections A and D of Table 6, suggesting that differences in the variability in NEE among sites are not related to differences in the model parameters but to some other source (Fig. 4). The NEE2 model is extremely robust and one implication of Fig. 4 is that there is little or no additional information to be captured in a larger data set relative to the site-based subsets in predicting NEE using the NEE2 model.

Figure 4.

Root mean square error (RMSE, µmol m−2 s−1) for predictions of NEE in individual sites, regions or vegetation types when the NEE2 model parameters are developed by regression on the same data subsets (horizontal axis) or on the whole data set (vertical axis). Points above the 1 : 1 line indicate larger RMSE, and thus less accuracy, using the whole data set.

nee prediction across vegetation types

Similar results were obtained when the data were subset by vegetation type (Table 7). In this analysis the data subsets were generally smaller and the parameterizations slightly more variable than in the site/region comparison. For two vegetation types, tussock and wet sedge, due to the low temperature range in the original data it was necessary to fix β at 0.074, the value derived from the whole data set (Q10 = 2.2). Without this constraint β was a negative value in wet sedge and was equivalent to Q10 = 4.5 in tussock.

Table 7.  Results of the NEE2 model using data subsets by vegetation type. Section (A) shows model parameters and statistics of fit for each data subset. Section (B) shows statistics of fit when parameters developed for one subset are used to predict NEE in the whole data set. Section (C) shows statistics of fit when parameters developed for each subset are applied to the remainder of the records in the data set. Section (D) shows statistics of fit when parameters developed for the entire data set (‘All’) are used to predict NEE in each vegetation type. In section (A) bold type indicates parameters that had unreasonable values in unconstrained regression and were fixed at values calculated using the whole data set
 AllBetulaHeathMesicSalixSnow bedTussockWet sedge
(A) Data subset used for model parameterization
 PmaxL15.83114.34515.06820.72618.43518.29619.83613.492
 k0.50.50.50.50.50.50.50.5
 E00.0360.0390.0320.0310.0380.0250.0370.030
 R00.6020.5121.6220.8310.5020.9470.6900.533
 β0.0740.0770.0310.0510.0890.0470.0740.074
 Rx0.5470.8350.6911.5810.2110.5540.6390.207
 RMSE1.5291.2540.8090.4862.1820.4481.1311.963
 r20.7990.9100.8750.9630.7620.9810.8450.620
 Slope1.0001.0001.0001.0001.0001.0001.0001.000
 Intercept0.0000.0000.0000.0000.0000.0000.0000.000
 n14102622236019023379273
(B) Above parameters applied to whole data set
 RMSE 1.54811.67021.7201.6181.6121.6071.609
 r2 0.7960.7830.7790.7950.7830.7970.798
 Slope 1.0251.0680.8800.8921.0820.8651.119
 Intercept 0.1500.4720.4940.2060.110-0.0510.017
 n 1410141014101410141014101410
(C) Above parameters applied to rest of data set
 RMSE 1.6081.7861.7541.5111.6241.7501.519
 r2 0.7520.7790.7750.8080.7800.7690.837
 Slope 1.0431.0740.8580.8661.0830.8411.230
 Intercept 0.1860.5610.5080.2380.111–0.0610.230
 n 1148118713501220138710311137
(D) Parameters for whole data set (‘All’ above) used to predict NEE for each data subset
 RMSE 1.2770.9240.7842.2650.6901.1922.026
 r2 0.9080.8570.9500.7600.9740.8440.619
 Slope 0.9740.9201.1201.1120.8881.1590.838
 Intercept 0.0650.2420.4830.2840.2060.0430.149
 n 2622236019023370273

Whether anomalous parameters were fixed or not, all parameterizations based on vegetation type gave robust predictions of NEE within the data subset used to develop those predictions (Table 7, section A), with r2 ranging from 0.62 to 0.98 (P < 0.001 in all cases). RMSE varied from 0.45 to 2.18, and in five out of seven cases was smaller than for the parameterization including the whole data set (RMSE = 1.56); for the mesic and snowbed vegetation the RMSE values were low enough (< 0.5 µmol m−2 s−1) to account for essentially all of the variation in those subsets beyond the underlying methodological error (Williams et al. 2006). Regression slopes were all 1.000 and intercepts were 0.000.

When the parameterizations for single vegetation types were used to predict NEE for the whole data set (Table 7, section B), the range in r2 was again negligible (r2 = 0.779–0.798). The regression slopes ranged from 0.88 to 1.12 and the intercepts were not significantly different from zero. RMSE also varied over a narrow range, 1.55–1.72. When these same parameters were used to predict NEE in those parts of the data set that were not used to develop the parameters (Table 7, section C), the statistics of fit were somewhat more variable (r2 = 0.78–0.82; RMSE = 1.38–1.85) but still extremely robust.

As for the site-based data subsets, prediction of NEE in individual vegetation types using parameters developed from the whole data set did not differ greatly in RMSE and other statistics of fit from predictions using parameters developed from the data subsets (Table 7, section D). For the mesic and snowbed vegetation types where RMSE was particularly low in either case, the fit was slightly better using the subset-based parameters than using the whole data set (Fig. 4). Again, there appears to be little additional information to be captured in a larger data set when vegetation-based subsets are used to predict NEE using the NEE2 model.

Discussion

functional convergence of canopies

To predict NEE of Low Arctic ecosystems, it is not necessary to identify species or describe the vegetation other than to estimate leaf area by measuring NDVI. This is consistent with recent studies showing remarkable convergence in vegetation canopy architecture (Williams & Rastetter 1999; van Wijk et al. 2005), production : biomass relationships (Shaver et al. 1996a,b), and above-ground N use and allocation (Shaver et al. 2001) among diverse Low Arctic ecosystems that differ dramatically in their dominant plant functional types. It is also consistent with widely used global models that predict GPP across biomes based primarily on leaf area and light interception estimated by satellite (e.g. Running & Coughlan 1988; Field et al. 1995, 1998; Ciencialaa et al. 1998; Goetz et al. 2005; Bunn & Goetz 2006). Clearly, variation in leaf area is much more important to NEE than any variation among species or functional types in leaf-level photosynthesis. Control of NEE by leaf area may be particularly important in arctic ecosystems, where canopies are often discontinuous and LAI is usually below 1.0.

To test the model's usefulness in predicting NEE, we completed two sensitivity exercises using different data subsets. The first exercise (Table 6), in which we subdivided the data by site or region and used model parameters developed for one site or region to predict NEE in other sites or regions, produced robust and consistent predictions among the different data subsets. The reason for this success was probably that the data from every site included multiple vegetation types, spanning a range of canopies and flux rates nearly as broad as the range within the whole data set. Thus, one conclusion from this exercise is that local surveys of CO2 flux including multiple vegetation types can be used successfully to predict mid-summer NEE throughout the Arctic, at least in those parts of the Low Arctic that contain a similar array of vegetation types.

In the second exercise (Table 7) we subdivided the data by vegetation type, lumping the data across sites and regions. Here, although the accuracy and precision of predictions were quite high within vegetation types, when parameters developed for one vegetation type were used to predict CO2 flux for the whole data set, the accuracy of the predictions declined slightly, as indicated by the greater deviation of the regression slopes from unity and larger RMSE. We can draw two conclusions from this. First, the very high accuracy and precision of predictions within a vegetation type suggests that this approach might be used successfully to improve predictions of large-area patch models of arctic CO2 fluxes, where each patch represents a different vegetation type. The improvements in this case would result primarily from the use of leaf area as a continuous variable within each patch type, as opposed to assuming no variation in LAI within a patch type. Second, the lesser accuracy and precision of predictions when parameters developed for one vegetation type are used to predict NEE in other vegetation types suggests that there are at least some differences in control of NEE among vegetation types that need to be identified in future research. We cannot yet distinguish the relative importance of several possible differences among vegetation types, including (i) variable role of moss photosynthesis, (ii) differences in the NDVI–LAI relationship or (iii) differences in leaf-level photosynthesis among species. Other factors that might be important include soil factors such as temperature, moisture, pH or thaw depth, but accounting for these would require adding new parameters to the model.

The two sensitivity exercises (Tables 6 & 7), coupled with the observation that apparently little additional information is gained from parameterizing the model on a larger data set (Fig. 4), indicate that the model parameterizations for the data subsets are extremely robust. In large part this is due to strong covariance among parameters, as indicated by the similarity in the canopy-level quantum yields for different values of k and E0 (Tables 4 & 5) and by the relatively minor impact of fixing the k parameter on RMSE and r2. The ranges of the parameter values derived in the subsetting exercises were actually larger than the 95% confidence intervals for mean values of those parameters derived from bootstrap sampling of the whole data set; the narrow range of RMSE and r2 obtained when different parameter sets were used to predict NEE is a reflection of both the covariance among parameters and the efficiency of the complete set of model parameters in capturing the controls on NEE.

continuous variation vs. patch-based approaches

The NEE model is a useful tool for predicting CO2 fluxes across heterogeneous Low Arctic landscapes. As with previous similar models (e.g. Vourlitis et al. 2000), the precision of the model's predictions is high, typically accounting for ~80% of the variance in measured NEE. The model's accuracy and lack of bias are also very good, with an RMSE of ~1.5 over a dynamic range of ~23 µmol m−2 s−1 and essentially a 1 : 1 relationship overall between predicted and measured NEE. A significant advantage of the model is that its input variables (PPFD, air temperature, NDVI–LAI) are all easily measured.

Comparison with our previous analysis of the same Imnavait data set illustrates both advantages and disadvantages of this new model. In Williams et al. (2006), we assumed that ER was a simple exponential function of temperature (ER = R0 × eβT) and that GPP was a saturating function of PPFD [GPP = (Pmax × I)/(k + I)]; thus, we did not incorporate changes in leaf area in the earlier model. We used a maximum-likelihood technique (van Wijk & Bouten 2002) to determine the acceptable parameter space for the light response of NEE in each plot, given a known measurement error (RMSE). We then explored which plots had parameter sets in common – an indication of functional similarity. We found that seven distinct parameter sets were required to explain NEE responses to temperature and light among the 23 plots at Imnavait Creek. One conclusion of the analysis was thus that it is not necessary to parameterize NEE differently for every single plot in order to scale up to the landscape level with acceptable accuracy (some lumping of plots is acceptable), but we also concluded that accurate prediction of NEE would require mapping of the landscape based on some minimum number of vegetation classes and the light response of NEE in each class.

The main advantage of using LAI to represent among-plot differences in the new model is that it eliminates the need to classify and then parameterize separately each vegetation class, and it eliminates any errors associated with classification or variation within a vegetation class. Instead, the new model requires only a single, generic set of parameters to predict NEE throughout the Low Arctic. Both Williams et al. (2006) and Street et al. (2007) found that Pmax was correlated with LAI at Imnavait Creek, Toolik Lake and Abisko. However, when Williams et al. (2006) tried to normalize NEE by leaf area, the number of parameter sets required to explain the data increased, probably because of the additional variation introduced as a result of the NDVI–LAI conversion and to their rigorous criteria for acceptance based on maximum likelihood. In the present model we assumed there was no error associated with the NDVI–LAI conversion, because we wanted to test the limits of our ability to extrapolate over large, heterogeneous areas. The consistently high r2 and 1 : 1 slope of the relationship between predicted and measured NEE indicate that, overall, we were successful. On the other hand, using the new model the RMSE of predicted NEE for Imnavait Creek is 1.34 µmol m−2 s−1, compared with a mean RMSE of 0.70 using the generic parameters developed by Williams et al. (2006). This larger RMSE can be viewed as an indicator of the cost in accuracy of scaling CO2 fluxes from the plot level to heterogeneous landscapes using LAI alone to represent the among-plot differences.

large-area and panarctic models

The model we develop here can also be used to aggregate NEE estimates spatially to develop predictions over areas much larger than our 1-m2 plots. Predictions of this kind generally use remotely sensed (satellite or airplane) data with pixel sizes ranging from 100 m2 to 100 km2 (e.g. Oechel et al. 2000; Williams et al. 2001; Vourlitis et al. 2003). Rastetter et al. (1992) present several approaches to aggregation of such data. In all of them, some quantification of the within-aggregate variability of model variables is required. The model we develop here has only three variables: light, temperature and leaf area. Both light and temperature can be considered constant over the pixel resolution of most remotely sensed data. Thus, the only estimate of variability needed to apply one of the Rastetter et al. (1992) aggregation techniques is the variability in leaf area. Thus, an important next step is to find a way to describe the probability distribution for leaf area within the resolution limits of remotely sensed data. Nevertheless, over the range of LAI found in the Low Arctic (generally < 2), the NEE–LAI relationship is nearly linear except at low light levels (< 500 µmol photons m−2 ground s−1), which means that aggregation errors associated with variation in LAI should be small. The maximum potential aggregation error is in the order of a 7% overestimate of NEE at a PPFD of 1000 µmol m−2 s−1, 12% at 500 µmol m−2 s−1 and 30% at 250 µmol m−2 s−1.

Several past scaling efforts have used NDVI to develop large-area estimates of NEE in the 9219-km2 Kuparuk River watershed that includes both Toolik Lake and Imnavait Creek. Williams et al. (2001), for example, concluded that uncertainty in the assignment of LAI at 1-km2 resolution introduced an uncertainty of ± 15% in basin-wide GPP predictions, roughly equal to the basin-wide NEE. In a series of papers, Vourlitis et al. (2000, 2003; Oechel et al. 2000) used NDVI, air temperature and radiation data to scale NEE directly from chamber and eddy-correlation measurements. Although Vourlitis et al. lacked the kind of detailed information on variation within and among sites and vegetation types provided here, the fact that NEE varies linearly with LAI across vegetation types in our data suggests that aggregation errors associated with scaling up from relatively small plots to the area of satellite pixels should be relatively small. The greater problem is error associated with the NDVI–LAI conversion, including error resulting from vegetation-specific NDVI–LAI relationships (Street et al. 2007) and error associated with differences between satellite-based vs. hand-held sensors (McMichael et al. 1999). Overall, however, our results also show clearly that parameters for models of this kind, developed in one site or vegetation type, can be used to extrapolate over much more heterogeneous areas, with different species composition.

model structure and improvements

We tested three forms of the ER model before settling on one of them for use in our sensitivity analyses. We chose ER2 because it gave us usefully low RMSE, high r2 and the most ecologically reasonable parameter values both in predicting ER and in predicting NEE as part of the NEE2 model. The formulation of ER2 suggests that the majority of ER comes from a pool that is both temperature-sensitive and correlated with LAI; this might include both the vegetation and at least the upper layers of litter and soil organic matter, where daily and seasonal temperature fluctuations are large. It is reasonable to expect litter and soil respiration to be related to LAI as an indicator of primary production and thus litter inputs to soil. The ER2 model structure also suggests a significant source of ER that is independent of both LAI and air temperature, probably deeper in the soil where short-term temperature fluctuations are small. Previous studies have shown that at Toolik Lake most of the increase in soil respiration of wet sedge, tussock and heath tundra in response to greenhouse warming and fertilization is correlated with changes in productivity (≈LAI), while older soil organic matter is relatively insensitive to these treatments (Johnson et al. 2000).

We also chose to use a fixed value of the k parameter in our sensitivity analyses using different data subsets. We did this because an initial analysis of sensitivity to k alone (data not shown) indicated that changes in k from 0.3 to 2.0 had only minor impacts on RMSE and r2, and the remaining parameters still gave ecologically reasonable values. The actual value of k is highly uncertain in an environment where the canopies are very low and therefore compressed, where the maximum zenith angle of the sun is ~45°, where the sun is above the horizon 24 h a day, and where much of the time it is cloudy and radiation is diffuse. A final reason for fixing k at 0.5 is that the number of model parameters was reduced to two in the GPP model and five in the NEE models.

The greatest future improvement in model predictions will probably come by accounting for moss cover as part of the total photosynthetic surface area. We did not attempt this in the present study because (i) the NDVI–LAI relationship (eqn 3; van Wijk & Williams 2005; Williams et al. 2006) was developed without consideration of moss cover, i.e. there were no available data in which NDVI, LAI and moss cover were all measured in the same plots; and (ii) we wanted to use a measure of photosynthetic surface area (NDVI) that could be measured quickly and remotely, without the need for harvesting of every plot for which NEE is to be predicted. Mosses are clearly important in all the vegetation types we studied. In a related study, Douma et al. (2007) show that the contribution of mosses to GPP can be 20–70% of total GPP in plots with continuous moss cover beneath the canopy. Differences in abundance of mosses among vegetation types may also account for much of the deviation from unity of the regression slopes when different data subsets are used to parameterize and predict NEE.

A second means of improving model predictions would be to use vegetation- or site-specific NDVI–LAI relationships. Vegetation types may differ in their NDVI–LAI relationships for several reasons, including differences in leaf reflectance, differences in subplot patchiness of different cover types and differences in canopy architecture. For example, the most likely explanation for the outliers in the graphs of predicted vs. measured NEE (Fig. 2) is that most of these points represent plots dominated by Salix glauca, which has silvery-grey leaves. Street et al. (2007) show that using separate regressions to predict LAI for different vegetation types does improve the accuracy of estimates of GPP. Again, we did not use separate regressions in the present study because we wanted to test the limits of our ability to predict NEE using data that could be sensed remotely, without the need for on-the-ground vegetation classification.

Because of a lack of data on within-plot variation in NDVI, Street et al. (2007) were unable to quantify any effects of within-plot patchiness, but did observe that the greatest outliers in their study were a series of plots on a very dry, patchy heath at the STEPPS site, where LAI may have been underestimated because of high reflectance from patches of rock and lichen cover within plots. Steltzer & Welker (2006), however, were able to examine within-plot variation in NDVI by using a digital camera at Thule, Greenland; they show that consideration of within-plot patchiness greatly improves estimation of leaf area in the High Arctic, where vascular plant cover is typically less than 50%. Steltzer & Welker (2006) also showed that between-species differences in canopy architecture, as reflected in extinction coefficients and overlap of leaves viewed from directly above, had an important effect on NDVI–LAI relationships. On the other hand, they concluded that between-species differences in reflectance were unimportant in improving their model of NDVI–LAI relationships.

Many studies have shown that arctic plant species differ significantly in their photosynthetic rates and light responses (e.g. Bigger & Oechel 1982; Oberbauer & Oechel 1989; Chapin & Shaver 1996). Inclusion of species-specific photosynthesis certainly might improve model accuracy and precision, but scaling exercises to date indicate that this will at best result in only modest improvement. For example, Street et al. (2007) show that at the STEPPS site most plots did not differ in GPP per unit leaf area, while differences in canopy LAI alone explained over 75% of the variance in GPP per unit ground area. Variation in GPP per unit leaf area was probably more important early in the growing season, during leaf expansion and growth, but increases in LAI alone accounted for more than half of the increase in GPP per unit ground area from bud break in June to full canopy development in August (Street et al. 2007).

Finally, we could have used NDVI directly instead of LAI to develop the NEE model. The main reason for not doing so is that leaf area is a real, physical entity that is related to GPP by a single, clear mechanism, incorporated into the GPP model. Leaf area is also measurable by other means including direct sampling of small plots, making it possible for the NEE model to be tested and applied without using any spectral reflectance data. A less important concern is that using NDVI instead of LAI would require adding another parameter to the NEE model. Street et al. (2007, figs 4 & 6) provide a comparative analysis of NDVI vs. LAI as predictors of GPP, using data from both Toolik Lake and Abisko; both NDVI and LAI predict GPP equally well (r2 = 0.78–0.81).

Conclusions

The fact that NEE of heterogeneous Low Arctic tundras can be predicted so well knowing only PPFD, air temperature and NDVI–LAI means that NEE and its components, ER and GPP, must be controlled in very similar ways in different vegetation types. This is consistent with studies showing strong convergence in LAI–canopy N relationships (Williams & Rastetter 1999; van Wijk et al. 2005), production–biomass relationships (Shaver et al. 2001) and overall vegetation N use (Shaver & Chapin 1991) among diverse tundras dominated by very different plant functional types. Clearly, the Low Arctic environment is one in which there are strong constraints on the primary production system, limiting the range and diversity of vegetation architecture and resource allocation.

But if the primary production system of Low Arctic vegetation is so tightly constrained by light, temperature and leaf area, how can there be so many different types of Low Arctic vegetation, dominated by so many different kinds of plants? This is a key issue for further research. Among the most likely explanations is that the distribution of plant functional types and vegetation types over the arctic landscape is largely controlled by other factors, such as N or P availability, water excess or deficit, or wind exposure and snow cover. This would mean that despite the measurable differences in species traits such as maximum photosynthesis per unit leaf area, these differences are minor in comparison with the fact that all plant types appear to have to follow essentially the same general ‘rules’ with respect to canopy-level C exchange. The five (or six) parameters of the NEE2 model capture most of the information needed to describe each species’ or vegetation type's ‘solution’ to this problem. The fact that the RMSE and r2 for predicted NEE are so similar despite variation in individual parameters reflects the covariance within parameter sets that is constrained by the limited range of overall solutions.

A second possible explanation is that species and functional type differences in C cycling are more diverse at longer time scales than the very short-term light responses used in the present study. This might mean, for example, that species and vegetation types have different abilities to change key variables such as leaf area over the course of a season or several years in response to a change in environment (e.g. Bret-Harte et al. 2001; Dormann & Woodin 2002; van Wijk et al. 2004). Regardless, our model results suggest that NEE in the Low Arctic is both easier to predict and harder to explain than we expected when we began this study.

Acknowlegements

This work was supported by grants from the US National Science Foundation to the Marine Biological Laboratory, including grants # OPP-0352897, DEB-0423385 and DEB-0444592. We are especially indebted to Catherine Thompson, who led the field crew at Abisko in 2004, and to Brooke Kaye, Beth Bernhardt, Joe Powers, Carrie McCalley, Kerry Dinsmore and Robert Bell. Thanks also to the Abisko Scientific Research Station, Toolik Field Station, and to James Cook, Andy Fox and our collaborators in the UK STEPPS group (NERC sponsor grant NER/A/S/2001/00460).

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