5.2.1. Parameterization of Soil Respiration
 The original formulation of soil respiration in SiB3 [Baker et al., 2003] was a slightly modified version of the submodel described by Denning et al.  which was based on the approach of Raich et al.  used in the Terrestrial Ecosystems Model (TEM). In this formulation the relative intensity of soil respiration (R*) is calculated from the soil moisture fraction and soil temperature (in kelvin) for each soil layer at each time step, as follows:
In equations (9)–(11) the influence of soil moisture on decomposition is defined by f(M), which has a minimum value of 0.2. The percentage of pore space occupied by water in each soil layer is w, and zm defines the skewness of the curve relating relative respiration to soil moisture [see Raich et al., 1991, Figure A5]. The parameter wsat determines the value of f(M) when the soil pore space is saturated with water. Soil respiration is greatest when the soil moisture is wopt but less in drier or moister conditions.
 The original version of SiB3 assumes that carbon storage of terrestrial ecosystems is in a steady state on an annual basis, i.e., that the annual sum of respiration loss is equal to the annual sum of canopy net carbon assimilation, and the net annual flux of CO2 is zero. This assumption is implemented by calculating individual monthly scaling factors of relative soil respiration (i.e., the ratio of monthly R* values to annual sum of R*) which are then applied to the canopy net assimilation. The approach has been successfully used in a variety of ecosystems [Baker et al., 2003, 2008; Hanan et al., 2005; Stöckli and Vidale, 2005] and even in a global assessment of CO2 exchange between land surfaces and atmosphere [Randall et al., 1996]. However, Denning et al.  pointed out that the constraint of imposing an annual balance in carbon fluxes results in a loss of generality and is unsuitable to the assessment of sources and sinks of CO2 for periods longer than 1 year.
 In the controlled environment B2-TRF imposing an annual carbon balance is unrealistic, not least because perturbation experiments can be performed for periods longer than 1 year. Consequently, the original soil respiration formulation used in SiB3 is arguably not appropriate. A modified approach was therefore developed in which the total soil respiration Rs is calculated as the sum of layer-by-layer contributions R*(i) defined by applying equation (9) to each layer, weighted by the root fraction root f(i) in the i layers, and then normalized to the observed long-term carbon balance of B2-TRF using a reference soil respiration rate (〈R0〉), i.e.,
This approach is similar to the original formulation of soil respiration proposed by Raich et al.  which also contained a scaling factor to be determined by model calibration on a vegetation-specific basis. However, the net flux is now envisioned as being a multilayer weighted sum assuming a link between decomposition rates and the presence of roots in the soil, with a common scaling factor then applied for all layers. In TEM [Raich et al., 1991], monthly average rates were calculated, but in SiB3 they are calculated at each time step (i.e., hourly in this study.)
 The plausibility of this modified version of the SiB3 submodel soil respiration after calibration against B2-TRF data was investigated relative to alternative calibrated submodels of soil respiration. These alternatives included assuming a fixed respiration rate and submodels that had been applied in earlier versions of SiB (Norman et al.  described by Colello et al. ) or developed for tropical rain forest ecosystems [Sotta et al., 2004; Chambers et al., 2004; da Rocha et al., 1996; Malhi et al., 1998] (see Table 1). In each case submodel calibration was made against observed nighttime average values of NEE when photosynthesis does not occur, and assuming soil respiration to be the dominant component to CO2 flux as supported by Chambers et al. , Malhi et al. , and Meir et al. . Other studies in the Amazon, however, report soil respiration to be only about 30%–40% of the total ecosystem respiration [Hutyra et al., 2008; Saleska et al., 2003], and that may introduce some uncertainty in our calibration approach. Each of the eight different soil respiration parameterizations contains parameters that were calibrated against nighttime NEE by generating 1000 parameter sets using the Latin Hypercube Random Sampling method and then selecting the best set of parameters from among these using a multiobjective approach [Gupta et al., 1998]. Selection was made to minimize two objective functions simultaneously, i.e., the mean absolute error (MAE) and (1 – ρ), where ρ is the Pearson correlation coefficient. The first objective function is a measure of closeness to the observed nighttime NEE, while the second is a measure of the timing of changes in soil respiration rates within the time series. The parameter set selected is here referred to as the compromise solution, this being the solution that tries to the minimize MAE and (1 – ρ) as much as possible by minimizing the normalized (i.e., ranging from 0 to 1, where 0 is the minimum observed objective value and 1 is the maximum) average of the two objectives. Typically, “mean-square” quantities (e.g., root-mean-square error, RMSE) are used when calibrating energy, water, and carbon fluxes with these models [Gupta et al., 1999; Liu et al., 2004, 2005; Rosolem et al., 2005]. MAE and RMSE are measures of dispersion of the model residual around zero and cannot therefore reasonably be considered as unrelated. The choice of MAE was made based on how we would like to weight small and large errors (i.e., deviations from measurements) in our simulation. We have decided to use MAE because we assume NEE values are reasonably good regardless of whether it is daytime or nighttime (an assumption not often met in natural ecosystems). Nighttime differences tend to be smaller (flux is more steady at night), but we would like to weight these differences equally relative to daytime errors (when NEE follows closely the diurnal cycle; see section 5.2.2).
 Figure 2 shows that the majority of soil respiration submodels tested represent the observed B2-TRF nighttime soil respiration rates very poorly even after they had been calibrated. Note that after calibration the Malhi et al.  and Sotta et al.  submodels give a near-constant soil respiration rate, which also translates into a near-constant ecosystem respiration rate (i.e., soil plus canopy respirations) in Figure 2. Although we adopted a multiobjective approach when selecting SiB3 soil respiration submodels, ultimately our selection is subjective and based on results shown in Figure 2. For example, although the correlation coefficient (ρ) measures the strength of a linear relationship between simulated and observed values, this does not necessarily reflect a 1:1 relationship in Figure 2. Thus, had our selection been solely based on the two objective functions with no subjective analysis, we would have selected the model of Chambers et al. , but this does not represent the observed variation in nighttime NEE successfully (i.e., being as close as possible to the 1:1 line). On the basis of Figure 2, only three models gave acceptable agreement with measurements: the SiB3 original formulation (Figure 2a), the model of Norman et al.  (Figure 2c), and the revised SiB3 formulation given as equation (12) (Figure 2g). Although the performance from none of these three was outstanding, these three submodels were selected for further consideration in the study of the thermal tolerance of B2-TRF plant species described next.
Figure 2. Comparison between nighttime averages of simulated and observed NEE inside B2-TRF (μmol m−2 s−1) for each soil respiration submodel tested in SiB3. The mean absolute error (MAE) and correlation coefficient (ρ) are also shown. The 1:1 line is shown as a black line.
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5.2.2. Thermal Tolerance
 In SiB3, Sellers et al. [1992, 1996a] calculated photosynthetic rates based on the model of Farquhar et al.  following the approach proposed by Collatz et al.  scaled to canopy levels. Photosynthesis is calculated as the minimum of three potential limiting factors, namely the efficiency of the photosynthetic enzyme system (ribulose 1,5-bisphosphate carboxylase/oxygenase, rubisco), the amount of photosynthetically active radiation captured by the leaf chlorophyll, and the capacity of the leaf to export or utilize the products of photosynthesis. Dark respiration rates are also scaled to the leaf carboxylase content (rubisco). The effect of temperature is included in each limiting factor, e.g., the Michaelis-Menten constants for CO2 and O2 in the case of the catalytic capacity of rubisco. For a detailed description of the temperature stress functions used in SiB, see the work by Sellers et al. [1996a, Appendix C].
 A previous study [Rosolem et al., 2005] using observed surface flux data taken in the Amazon basin showed that simulated surface fluxes were not sensitive to the parameter values in temperature stress functions used in the SiB model and that the default values given by Sellers et al. [1996b] for evergreen broadleaf forests were therefore acceptable. More recently, Baker et al.  showed good agreement between simulated and observed NEE values at a Tapajós National Forest site (KM83) using a slightly modified version of SiB3. However, none of their modifications relate to the parameterization of temperature stress, suggesting that the parameterization currently used in SiB3 is appropriate for Amazon rain forest sites. Further analyses of SiB3 parameters at Amazon sites are being made under the Large-Scale Biosphere-Atmosphere Experiment in Amazonia Data-Model Intercomparison Project (LBA-DMIP) (R. Rosolem et al., manuscript in preparation, 2010). As previously discussed, temperatures inside B2-TRF differ substantially from those in the Amazon. The annual mean temperature inside B2-TRF is on average about 1.9°C warmer than those observed above the forest at the Manaus, Tapajós, and Reserva Jarú LBA eddy covariance tower forest sites in the Amazon and, on average, also has a larger diurnal amplitude (12.2°C) in air temperature than those observed above the canopy at these Amazon forest sites (4.6°C) [de Gonçalves et al., 2010]. When compared to climatological data from weather stations near these Amazon sites [Rosolem et al., 2008], the mean annual temperature inside B2-TRF is less warm, i.e., about +0.7°C.
 The lack of sensitivity of SiB3 to temperature stress parameters in simulating forests in the Amazon, as reported by Rosolem et al. , presumably means that current conditions in natural tropical forest do not activate an internal mode in SiB3 which allows these parameters to play a major role. However, it seems that the large diurnal amplitude and higher air temperatures inside B2-TRF trigger sensitivity to these parameters, and it is therefore of interest to investigate the model's temperature stress sensitivity under these conditions. The parameters directly related to temperature stress functions in SiB3 were therefore calibrated against data from B2-TRF using a calibration procedure similar to that used to evaluate soil respiration parameterizations (see above), but with MAE and (1 − ρ) now calculated for hourly measurements of NEE measured during daylight hours when the photosynthesis is the dominant component of CO2 exchange and likely to be most influenced by temperature stress.
 In fact, when the three submodels of soil respiration retained after the analysis described in section 5.2.1 were used to calculate hourly daytime NEE, there were few discernible differences in their performances relative to hourly daytime observations; see Figures 3a–3c. However, the cumulative NEE for hours when observations are available is much better simulated when the revised SiB3 formulation given as equation (12) is used to describe soil respiration rather than either the original SiB3 formulation or the submodel of Norman et al.  (see Figure 3d). This is also reflected in the calculated mean bias for each submodel. The original SiB3 formulation and the submodel of Norman et al.  have mean biases of −0.35 and 0.48 μmol m−2 s−1, respectively, while the revised SiB3 formulation has a mean bias of just −0.07 μmol m−2 s−1. The revised SiB3 submodel is therefore preferred and at this stage was adopted and used during the calibration of temperature stress related parameters in SiB3 although, in practice, this submodel selection had little influence on the calibrated values of temperature stress parameters since these are mainly determined by the ability of SiB3 to simulate daytime photosynthesis.
Figure 3. Comparison between simulated and observed hourly NEE (μmol m−2 s−1) for (a) the original soil respiration model in SiB3, (b) the soil respiration model of Norman et al. , and (c) and the alternative soil respiration model in SiB3 introduced in this paper (see equation (12)). In each case the mean absolute error (MAE) and correlation coefficient (ρ) are also shown. Daytime data are shown in green; nighttime data are shown in red. (d) Cumulative NEE (g m−2) calculated by summing available observations, or summing only those simulated values that correspond to available observations. The blue line is for the original soil respiration model in SiB3, and the red line is for the model of Norman et al. . Simulation results with the alternative of the original approach introduced in this paper are shown as a green line and the observed NEE is shown as a black line. All the results shown are for each model after calibration of soil respiration submodel parameters using observed nighttime NEE and after calibration of temperature stress parameters using hourly observed daytime NEE. Note that cumulative NEE shown in Figure 3d does not correspond to seasonal or interannual variations in NEE because the results shown are constrained to periods when observational data were available. The 1:1 line is shown as a black line in Figures 3a–3c.
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 In SiB3 the maximum catalytic capacity of rubisco (Vm) is calculated by
where Vmax is defined by
and Vmax0 is defined as the Vmax for top of canopy leaves; Qt is calculated as
where Topt is a prescribed coefficient in the model (see Table 2). In SiB3 the temperature stress function, ft(Tcanopy), is calculated as follows:
and the leaf respiration rate (Rd) is calculated as a fraction (fd) of Vm:
Table 2. Description of the Parameters Associated With Temperature Stress Functions in SiB3 and Their Default and Calibrated Values
|Parameter||Description||Units||Default Value [Sellers et al., 1996a, 1996b]||Calibrated Value [This Study]|
|Vmax0||Maximum rubisco capacity at canopy top||μmol m−2 s−1||100||61|
|fd||Respiration fraction of Vm||–||0.015||0.017|
|s1||Temperature inhibition parameter for C3 Vm||K−1||0.3||1.7|
|s2||Half-inhibition temperature for C3 Vm||K||313||319|
|s5||Temperature inhibition parameter for C3 Rd||K−1||1.3||0.3|
|s6||Half-inhibition temperature for C3 Rd||K||328||339|
|Topt||Temperature coefficient used to calculate Q10||K||298||296|
 The soil water stress function (fW) is calculated on the basis of the formulation proposed by Baker et al. . All temperature variables are calculated in kelvin.
 The parameter nomenclature used by Sellers et al. [1996a, 1996b] was adopted in this study and is used in Table 2 to summarize the calibration results for the seven parameters that determine temperature inhibition functions in SiB3. The calibrated value of the maximum rubisco capacity at canopy top (Vmax0) is 61 μmol m−2 s−1 in B2-TRF, much lower than the default value. For comparison, da Rocha et al.  calibrated SiB2 using Amazon data and found Vmax0 = 81 μmol m−2 s−1 while Rosolem et al.  report values in the range 83–101 μmol m−2 s−1 in a similar calibration using data from the LBA Tapajós KM83 site in eastern Amazonia. Upper leaf values of Vmax reported by Meir et al.  for the Manaus site in the Amazon were in the range 35–50 μmol m−2 s−1, and using slightly different temperature sensitivity functions to describe the Vmax of an Amazonian rain forest site, Lloyd et al.  estimated a leaf level (as opposed to canopy top) value of 68 μmol m–2 s–1 at 25°C. In fact, Lin et al.  successfully used this last value when analyzing plant response to CO2 enrichment inside B2-TRF and, in unpublished data, also report similar estimates of Vmax from gas exchange measurements on upper leaves of two canopy trees in B2-TRF, which suggests that Vmax0 may have a similar value.
 The low value of Vmax0 found by calibration in this study may be associated with nitrogen available in leaves: the leaf nitrogen profile observed in B2-TRF [Lin et al., 1998] is similar to the profile reported by Lloyd et al. . However, the reduced radiation levels that result from artificial space frame shading inside B2-TRF may also be significant. According to Bonan , plant species growing in a shaded environment achieve no photosynthetic gain by investing in energetically expensive rubisco and so have low values of Vmax, while low leaf nitrogen content is directly related to low photosynthetic capacity in low radiation environments [Meir et al., 2002; Carswell et al., 2000].
 Curvature of the exponential temperature stress functions are described by the several s terms in equation (16), and these are presented in Table 2; s1 and s2 specify the temperature stress function that affects Vm for the photosynthetic process in C3 plants (hereinafter referred to as C3 Vm), whereas s5 and s6 specify the function associated with Vm when calculating dark respiration (Rd) (hereinafter referred to as Rd Vm). Small (large) values of s1 and s5 correspond to a more gradual (abrupt) change in the curvature of these functions, while s2 and s6 define the half-inhibition points associated with high temperature. The temperature stress functions for C3 Vm calculated using parameters before and after calibration are shown in Figure 4a. There is a marked difference in the change from default to calibrated values for parameters associated with function curvature (s1 and s5), but the half-inhibition temperatures for both the C3 Vm and Rd Vm temperature functions (s2 and s6) are higher, by 6 and 11 K, respectively, suggesting that plants inside B2-TRF have a higher thermal tolerance than that given with default parameter values. The fraction of Vm that characterizes canopy respiration, fd, and the temperature parameter (Topt) associated with Qt in the model are little changed by calibration, as are canopy respiration rates, which are around ∼1 μmol m−2 s−1 at 25°C and in excellent agreement with estimated rates from Lloyd et al. . The range of air temperature typical of both B2-TRF and the Amazon tropical rain forest are also shown in Figure 4a. These ranges are the observed minimum and maximum temperatures recorded in B2-TRF (Tmin = 20.4°C and Tmax = 46.9°C) and in the Amazon (i.e., Tmin = 17.2 ± 3.7°C and Tmax = 33.6 ± 1.4°C), respectively, with the values for the Amazon being the mean values of minimum and maximum temperatures for the Manaus K34, Tapajós K67 and K83, and Reserva Jarú LBA rain forest sites [de Gonçalves et al., 2010].
Figure 4. (a) Relationships of Vm temperature stress factor (applied to photosynthesis in C3 plants), (b) maximum catalytic capacity of rubisco, (c) net assimilation, and (d) soil respiration modeled by SiB3 during daytime hours versus modeled canopy temperature using default parameters (black circles) and calibrated parameters (red crosses). (e) Difference between the modeled NEE given by SiB3 and the observed value during daytime hours as a function of modeled canopy temperature before (black circles) and after (red crosses) calibration, respectively. The ranges of air temperature (ΔTair, in °C) typical of B2-TRF (solid red line) and natural Amazon rain forest (solid black line) are shown in Figure 4a. Units are in μmol m−2 s−1, except for fT(Tcanopy) in Figure 4a, which is unitless.
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 The effect of canopy temperature on the model parameter Vm before and after calibration is shown in Figure 4b. There is a marked difference between the two curves. Vm is systematically lower after calibration compared to the default value for the range where air temperatures commonly observed both in the Amazon and inside B2-TRF coincide with each other (i.e., 22°C ≤ ΔTair ≤ 34°C). Over this range, the mean value of Vm calculated prior to calibration is 136 ± 19 μmol m−2 s−1 but it is 104 ± 20 μmol m−2 s−1 after parameters are calibrated. With the default parameter values, Vm reaches a maximum value at about 36°C and then declines, a result that is consistent with the idea that tropical rain forest plant species are near a high-temperature threshold. However, after calibration, Vm increases substantially up to around 43°C and then sharply declines to near zero before 50°C, which suggests that this high-temperature threshold appears to occur at a much higher temperature not yet observed in natural tropical rain forests. Within the range of air temperatures observed inside B2-TRF but not in the Amazon (i.e., 34°C ≤ ΔTair ≤ 47°C), the mean value of Vm calculated after calibration is 174 ± 38 μmol m−2 s−1 compared with the mean value calculated with the default parameter of 156 ± 26 μmol m−2 s−1. The mean Vm calculated over the entire range of air temperature observed inside B2-TRF (i.e., 22°C ≤ ΔTair ≤ 47°C) is 125 ± 41 μmol m−2 s−1 after calibration, representing the higher end of the Vm range reported by Wullschleger  for tropical forest species.
 Net assimilation calculated as photosynthesis minus canopy respiration is shown in Figure 4c. The overall effect of using calibrated (as opposed to default) parameters is to reduce the modeled net assimilation rate but then to maintain this rate to higher temperatures. However, note that SiB3 simulates leaf but not stem respiration, and stems will experience a different temperature regime from soil, and net assimilation and stomatal conductance are strongly related [Collatz et al., 1991; Wong et al., 1985a, 1985b, 1985c]. Soil respiration, which is about an order of magnitude less than net assimilation, is little altered by the calibration of temperature stress parameters (Figure 4d). Figure 4e shows a comparison between observed and modeled NEE for default and calibrated temperature stress parameters. There is substantial variability in Figure 4e associated with the effect of other controls on NEE, but the generally improved description given with the calibration of temperature stress parameters is still apparent. NEE measurements were available for approximately 63% of the time, but unfortunately no measurements were available in the summers of 2000 and 2002 (the two hottest years compared to 2001); hence the range of canopy temperatures presented in Figure 4e is slightly smaller relative to those shown in Figures 4a–4d.
 As discussed by Arain et al. , radiation has a strong seasonal signal inside B2 because of its midlatitude location, and Figure 5 shows the average observed and model-calculated diurnal cycle of NEE (prior to and after calibration of temperature stress parameters) in the winter (Figure 5, left) and summer (Figure 5, right), with the winter months being centered on December and the summer months centered on June. Overall, the simulated results after calibration (red lines) show remarkable agreement with observations (black lines), especially when the percentage of observations available in a month is high (percentage availability is given in Figure 5). In winter (see Figure 5, left) SiB3 simulations prior to calibration calculate unrealistically higher assimilation (more negative NEE) during daylight hours compared with both observations and simulated values after calibration. Nighttime fluxes confirm the improvement obtained when the new soil respiration parameterization is used and also exhibit good agreement relative to observations. We suspect the quality of the observations made in December 2001 when the nighttime and to a lesser extent daytime fluxes agree less well, but given a lack of evidence for discarding these data, we retained them in the calibration and comparison.
Figure 5. Average diurnal variation of NEE (μmol m−2 s−1) inside B2-TRF simulated prior to (blue lines) and after calibration (red lines) of the temperature stress parameters in SiB3 compared to observations (black circles), calculated for (left) winter (i.e., November–December–January) and (right) summer (May–June–July). Error bars and shading correspond to one standard deviation calculated for observations and simulations, respectively.
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 In the morning during summer (see Figure 5, right) the results are similar to those found in winter, but there is observed and correctly simulated reduction in assimilation in the afternoon (i.e., NEE is less negative). This is consistent with a limitation on rubisco activity starting around midday, as reported by Lloyd et al. . There is also an abrupt fall in simulated assimilation, that is, an abrupt increase in NEE during morning to afternoon transition in the summer months caused by the substantial increase in temperatures, and this is more pronounced in the two hottest summers (2000 and 2002). Unfortunately, summertime observations were only available for 2001 to confirm this modeled behavior, but the agreement in the summer of 2001 suggests that the simulated fluxes are arguably realistic in this respect. Again, nighttime NEE fluxes are simulated well by SiB3 during the summer, confirming the improvement obtained with the revised parameterization soil respiration.
 The time variation of the soil water stress factor in SiB3 indicated that the vegetation inside B2-TRF was never under significant water stress during the period of this simulation (not shown) and B2-TRF released approximately 4850 kg of C ha−1 during this 3 year period (2000–2002), which on a per unit area basis is comparable to values reported for sites in the eastern Amazon [Saleska et al., 2003].