The Qinghai-Tibetan Plateau is the highest plateau in the world. Covered mainly by alpine grasslands, the plateau plays an important role in the region's carbon budget. The plateau is characterized by high irradiance, low atmospheric pressure, and low temperature. To examine the carbon dynamics of grassland ecosystems on the plateau, we developed a new model, the carbon dynamics model for alpine grasslands (CDMag). CDMag is composed of a gross photosynthesis (Ac) submodel including photoinhibition simulation, an ecosystem respiration (ER) submodel that considers both autotrophic and heterotrophic respiration, and an intercellular CO2 partial pressure and canopy conductance submodel. The photoinhibition simulation is included to describe the gross production of alpine ecosystems in response to the high-irradiance environment. A multilayered irradiance transfer scheme is adopted to estimate the irradiance on sunlit and shaded leaves within grassy canopies, and a coupled canopy conductance–net photosynthesis function is integrated into the Ac submodel. CDMag was used to simulate the carbon dynamics of the most extensively distributed alpine grassland, a Kobresia meadow ecosystem on the Qinghai-Tibetan Plateau. CDMag reproduces well the diurnal and seasonal variation of net ecosystem exchange (NEE) and nighttime ER based on data obtained from 2001 to 2003 using the eddy-covariance method. The mean measured NEE was about 1.62 μmol m−2 s−1 for the measured periods of the 3 years; the mean of the deviations between measured and simulated NEE was −0.16 to 0.33 μmol m−2 s−1. Owing to photoinhibition, daily gross photosynthesis lost about 5.3–5.6%. The losses were mainly contributed by the 7.5–7.8% reduction in Ac of sunlit leaves of the upper canopy layer. In addition, the light-use efficiency of the alpine meadow had seasonal dynamics, with the highest values in the middle of the growing season. We have generalized CDMag for other alpine grasslands on the entire plateau.
 The Qinghai-Tibetan Plateau, stretching between Eurasia and India, extends about 2700 km from west to east and about 1400 km from south to north, with a total area of more than 2.5 million km2. The plateau is the youngest and highest land area on earth, averaging more than 4000 m above sea level. More than 60% of the total plateau area is covered by various grassland ecosystems, mainly alpine meadows, alpine shrubs, and alpine swamps [Wang et al., 2002]. Alpine meadows, covering about 35% of the plateau area, comprise the representative vegetation and the major grassland on the plateau [Cao et al., 2004]. The extensively distributed grasslands may play an important role in the regional and global carbon budget because of their large stock of soil carbon [Hunt et al., 2002]. Therefore, to evaluate the carbon budget of the region, it is important to quantify the carbon dynamics between the alpine meadows and the atmosphere on the Qinghai-Tibetan Plateau.
 Observations of CO2 and H2O fluxes have been conducted in a Kobresia meadow ecosystem on the Qinghai-Tibetan plateau since 2001 [Gu et al., 2003; Kato et al., 2004]. The results show that seasonal variation in gross photosynthesis production of the meadow corresponds well with changes in the leaf area index and daily photosynthetically active radiation (PAR) [Kato et al., 2004].
 The alpine meadow ecosystems on the plateau experience much higher solar radiation, lower air temperature, and lower CO2 partial pressure than any other ecosystems at similar latitudes. Most of the plateau's alpine ecosystems are not water-stressed in their growing season because of moderate precipitation and low evaporation [Gu et al., 2003]. Photosynthesis of winter wheat on the Qinghai-Tibetan Plateau can be often inhibited by high solar radiation [Yu et al., 2002]. Leaf photosynthesis (Al) for some alpine plants declines under high-irradiance conditions [Yu et al., 2002; Cui et al., 2003]. Net ecosystem exchange (NEE) of CO2 declines in alpine meadow ecosystems under high irradiance on clear days [Gu et al., 2003; Kato et al., 2004]. The decrease of NEE could be attributed to ecosystem respiration (ER) that increases with the increase of temperature.
 NEE decline could also be ascribed to photoinhibition under high-irradiance conditions, which has been documented frequently. For example, high PAR is considered to be the major environmental stress on carbon uptake by alpine plants [Kőrner, 1999]. Excess light can cause persistent decreases in the rate of photosynthesis [Foyer and Noctor, 1999]. The functional consequences of photoinhibition on photosynthesis are a reduction in initial quantum efficiency (ɛ), a decrease in the convexity (θ) of the photosynthesis light-response curve. A prolonged exposure to excessive light can result in a decrease of light-saturated photosynthesis rate (Asat) [Long et al., 1994]. Photoinhibition even occurs at light levels lower than full irradiance if PAR never reaches 1000 μmol m−2 s−1 [Ogren and Sjostrom, 1990]. Even in vegetation under less stressful conditions, exposure to full sunlight can result in a slowly reversible decrease of Fv/Fm (Fm is the maximum fluorescence level of the induction curve, and Fv is the variable fluorescence), as well as in parallel reductions in ɛ. Recovery occurs in late afternoon and is often complete by dusk [Long et al., 1994]. Photoinhibition under low temperature appears to be small during the growing season because leaf temperature increases rapidly and is high under the sunny conditions [Kőrner, 1999]. Hence thermal limitation of photosynthesis in alpine plants is often restricted to low-PPFD situations.
 To understand the dynamics of CO2 uptake in alpine ecosystems, we need a model to describe photosynthetic performance in response to changes in different environmental factors, including air temperature, light irradiance, CO2 partial pressure, and soil moisture. A simple biochemical model, the nonrectangular hyperbola (NRH) model, is well known for its ability to describe leaf photosynthetic responses to environmental factors [Hanson, 1991; Sands, 1995; Liu, 1996; Cannell and Thornley, 1998; Gilmanov et al., 2003]. The NRH model gives an excellent phenomenological description of leaf photosynthesis [Thornley, 1998] using the three parameters ɛ, θ, and Asat.
 Despite its wide application, however, the NRH model does not consider the influence of photoinhibition, especially under high-irradiance inhibited conditions. The convexity factor θ decreases steadily from 0.98 to zero (indicating Michaelis-Menten kinetics) in response to increasing photoinhibition [Leverenz et al., 1990]. Under a midday peak PPFD of 1800 μmol m−2 s−1, there is an approximately 50% decline in ɛ by mid-afternoon, with a recovery to approximately 90% of maximum ɛ by dusk [Ogren, 1988; Long et al., 1994]. A decline in θ coupled with a decrease in ɛ is significant, because it will extend the influence of a decrease in ɛ to higher photon fluxes [Long et al., 1994]. Leverenz et al.  proposed that the heterogeneity in PSII complexes following photoinhibition will lead to decrease in θ coupled with a decrease in ɛ. Decreases in ɛ and θ have been observed to precede a decrease in Asat, but may also occur without a decrease in Asat [Henley et al., 1991; Long et al., 1994; Ball et al., 1997; Hikosaka et al., 2004].
 Photoinhibition initially describes the decline in photosynthetic viability of oxygen evolving photosynthetic organism due to excessive illumination [Adir et al., 2003]. In the present study, we consider the reduction of gross photosynthetic rate under light conditions beyond the saturating light point. By including a component to quantify the effect of photoinhibition on gross photosynthesis, we developed a new carbon dynamics model for alpine grasslands (CDMag). CDMag was then used to estimate carbon uptake and emission by an alpine meadow ecosystem on the Qinghai-Tibetan Plateau. It quantifies the effects of photoinhibition on carbon uptake. In the model, leaf gross photosynthesis (Al) estimated by the NRH method is scaled up to canopy gross photosynthesis (Ac), while the model considers leaves as sunlit or shaded and the canopy as a multilayer system. In simulations, ecosystem respiration (ER) is divided into soil heterotrophic and plant autotrophic respiration.
 Model output was compared with measurements of NEE by an eddy covariance system over a 3-year period. Parameter sensitivity analysis was run to evaluate which processes and parameters should be given the most attention in future studies. CDMag has been designed in a generalized form that should be suitable for all alpine grassland ecosystems.
2. CDMag Model
 CDMag includes three submodels: (1) a gross photosynthesis simulation model, (2) an ecosystem respiration simulation submodel, and (3) an intercellular CO2 partial pressure and canopy conductance simulation submodel.
2.1. Gross Photosynthesis Submodel
 In general, models describing leaf photosynthesis can be either empirical or mechanistic. Models such as Jarvis's model and the NRH are empirical, which can describe well leaf photosynthesis in responses to environmental factors. The example for mechanistic models is the biochemical model developed by Farquhar et al. . In the Farquhar model, Al is calculated in terms of three potentially limiting assimilation rates,
where Jc represents the gross photosynthetic rate limited by the photosynthetic enzyme Rubisco, Je represents the gross photosynthetic rate limited by the amount of available light, and Js represents the gross photosynthetic rate limited by the capacity to transport photosynthetic products for C3 plants, but is the CO2-limited capacity for C4 plants [Collatz et al., 1991]. The biochemical photosynthesis model integrating mass transfer, stomatal regulation, biochemical reactions and energy balance have been reported [Collatz et al., 1991; Leuning,1995; Yu and Wang, 1998; Yu et al., 2001]. However, this type of models is often difficult in application, as the solution of the models needs complex iterations reflecting interactions among physiological and physical processes [Yu et al., 2002]. We therefore decided to use the NRH to construct a concise and suitable Al model, which describes photosynthesis process in response to changes of environmental factor [Thornley, 1976, 1998]. The response of Al to leaf surface PAR is expressed with the NRH. Replacing PAR, leaf absorbed PAR (APAR) is applied to the NRH to estimate Al [Boote and Loomis, 1991],
Asat is the light saturated gross photosynthesis (μmol CO2 m−2 s−1), ɛ is the initial quantum efficiency (μmol CO2 μmol−1 photon absorbed), and θ is an empirical curvature factor. The ɛ varies with temperature and intercellular CO2 partial pressure (Pi), which is the result of intercellular CO2 concentration in mole fraction (Ci) multiplied by atmospheric pressure (Pa).
 We use the chlorophyll content of a leaf (n0) to calculate PAR absorption (α) and APAR (Table 1). The ɛ and Asat are solved multiplicatively (Appendix A), and ɛ declines under photoinhibition conditions. The curvature factor, θ, declines in parallel with ɛ [Henley et al., 1991; Long et al., 1994; Ball et al., 1997; Hikosaka et al., 2004]. Theoretical analysis shows that a 50% reduction in ɛ results in a 5.4% reduction in Al under 1000 μmol m−2 s−1 PAR conditions (baseline: ɛ0 = 0.08, θ0 = 0.9), whereas under the same PAR conditions, a 50% reduction in ɛ and θ can result in a 23.5% reduction in Al (Figure 1a). A similar situation can be found if we examine other ɛ0 and θ0 baselines (Figures 1b–1d).
Table 1. List of Main Parameters Used for the Qinghai-Tibetan Plateau in the Carbon Dynamics Model of Alpine Grasslands (CDMag)
 The canopy gross photosynthesis rate (Ac; μmol CO2 m−2 s−1) is obtained by weighting the leaf photosynthesis rates of sunlit and shaded leaves (respectively, Al,slt and Al,shade) by their fractions within the canopy (respectively, fslt and fshade) at leaf area depth, L, and then by integrating over the entire depth of the canopy [Choudhury, 2000, 2001a].
where LAI is leaf area index.
 To calculate Al,slt and Al,shade, incident PAR on sunlit and shaded leaves must be solved. We adopted a canopy radiation transfer scheme to estimate diffuse PAR and direct PAR on sunlit and shaded leaves [Choudhury, 2000, 2001a, 2001b] (Appendix B). The canopy was divided into three layers: upper, middle, and bottom. Gross photosynthesis rates in sunlit and in shaded leaves were calculated for each layer, and gross photosynthesis rates in each layer were summed to acquire the canopy gross photosynthesis rate (Ac).
2.2. Ecosystem Respiration Submodel
 Plant autotrophic respiration (Ra), including maintenance respiration (Rc) and growth respiration (Rg), is a function of air temperature (Ta),
Ac is canopy gross photosynthesis rate; Q10 is the air temperature response coefficient (Table 1); YG is the growth conversion efficiency, which is given as 0.74 [Amther, 1989]; I0(1/2KΔTa) is the modified Bessel function [Choudhury, 2001b]; ΔTa is diurnal temperature range; and K is a logarithm function of Q10(K = ln[Q10]/10). YG change is small, with a global value of 0.72 to estimate net carbon accumulation over continental scales [Ruimy et al., 1996].
 Soil temperature is a primary factor in heterotrophic respiration. Thus, we introduce the Q10 approach to estimate Rh:
where Q′10,h is the soil temperature response coefficient (Table 1) and Ts is the soil temperature 2 cm beneath the ground.
2.3. Intercellular CO2 Partial Pressure and Canopy Conductance Submodel
where a is a constant, hs and Cs are the relative humidity and CO2 partial pressure at the leaf surface, respectively of air over leaf surface, and g0 is a parameter. Instead of using hs, Leuning  uses vapor pressure deficit from stomatal pore to leaf surface (VPDs) to estimate gs,
where Γ is CO2 compensation point and VPD0 is a coefficient. Comparing the Leuning's model with the Ball's model shows that the term Cs in the Leuning's model is replaced by (Cs − Γ), and relative humidity, hs, is replaced by a vapor pressure deficit term (1/(1 + VPDs/VPD0)). Whether stomata respond to relative humidity or absolute vapor pressure is still in debate. When the difference between leaf temperature and air temperature is insignificant compared to diurnal change of those temperatures, VPDs is close to the VPD in air [Yu et al., 2002]. On the basis of the Leuning's model, canopy conductance (gc) can be estimated as
where An is canopy net photosynthesis rate (An = Ac − Rc); Pa is atmospheric pressure; a′, b′, and VPD0 are coefficients (Table 1).
 To solve Ac on the basis of the NRH model (equations (2) and (4), details in Appendix A), intercellular CO2 partial pressure (Ci) first needs to be estimated. Ci is a function of An. We consider the equation (11) and other following three equations and apply an iterative method to solve An (Figure 2),
where Ci is CO2 partial pressure inside the leaves; gb is leaf boundary conductance; and Ra is autotrophic respiration rate.
3. Experimental Data
3.1. Site Description
 We evaluated CDMag by using the observations of CO2 flux and environmental factors from an alpine meadow ecosystem (37°29′N–37°45′N, 101°12′E–101°23′E; 3250 m a.s.l.). The observation site is located in a large valley oriented northwest-southeast and surrounded by the Qilian Mountains on the Qinghai-Tibetan Plateau. Climate in the area is characterized by low temperatures, high irradiance, low atmospheric pressure, and relatively high precipitation. Other details of local climate are described elsewhere [Gu et al., 2003; Kato et al., 2004]. The soil is a clay loam with an average thickness of 0.65 m, and it is rich in organic carbon (80–100 g kg−1 at depths of 0–20 cm) [Cao et al., 2004]. Dominant species in the ecosystem are three perennial sedges, Kobresia humilis, Kobresia pygmaea, and Kobresia tibetica (Cyperaceae), and one dwarf shrub species, Potentilla fruticosa (Rosaceae), forming a canopy with erectophile foliage angle distribution. The plants start to grow in May and reach their maximum aboveground biomass and LAI in July and August, when air temperature and precipitation are also greatest; the grasses then dry up and the shrubs go dormant in October.
 The CO2 flux (NEE) has been measured by an eddy covariance system at the site since 9 August 2001. The system was set in a Kobresia meadow with a fetch of at least 250 m in all directions. Wind speed and sonic virtual temperature were measured at 2.2 m aboveground with a sonic anemometer (CSAT-3, Campbell Scientific, Inc., Logan, Utah). Carbon dioxide and water vapor concentrations were also measured at the same height with an open-path infrared gas analyzer (CS-7500, Campbell Scientific, Inc.). Other ancillary measurements including micrometeorological, soil moisture, and rainfall were simultaneously conducted at the same site. Fifteen-minute averages of all data were logged by an analog multiplexer (AM416) and a digital micrologger (CR23X, Campbell Scientific, Inc.) [Gu et al., 2003].
 Several methods, including spike removal, coordinate rotation, and Webb-Pearman-Leuning correction, were used to calibrate the flux calculated from the raw data. On the basis of temperature and humidity density fluctuations, we used the Webb-Pearman-Leuning algorithm to correct fluxes of CO2 and water vapor [Webb et al., 1980]. Nighttime missing data were filled by using an exponential relationship between NEE (i.e., ecosystem respiration) from periods of high turbulence (friction velocity > 0.2 m s−1) and soil temperature at a depth of 0.05 m [Kato et al., 2004]. Daytime missing data were extrapolated from a 7-day moving window [Falge et al., 2001].
4.1. Diurnal and Seasonal Dynamics of NEE
 The diurnal variation of simulated NEE agreed well with the measured NEE during a period of 17 days in 2002 (Figure 3). Both peak and nadir values obtained from CDMag were highly consistent with the measured values. The averaged diurnal pattern for three growing seasons from 2001 to 2003 showed good agreement between the CDMag simulations and the observations (Figure 4). The agreements between the model results and the observations improved when photoinhibition was included in CDMag. NEE evidently declined at noon and in the early afternoon, as compared with runs that did not consider photoinhibition. By including the photoinhibition component, the root mean square error (RMSE) and mean of deviations (MD) decreased (Table 2). The mean measured NEE was 1.28, 1.39, and 2.19 μmol m−2 s−1 in 2001, 2002, and 2003, respectively. The mean peak NEE values with the simulation considering photoinhibition appeared at about 1100 local time (LT) instead of at noon, when PAR was at its maximum. In 2001 and 2003, mean simulated NEE in the morning was slightly lower than mean measured NEE. The mean maximum ER occurred at around 1400 LT. From 1100 to 1400 LT, the mean simulated ER increased to about 1.1, 1.8, and 1.2 μmol m−2 s−1 in 2001, 2002, and 2003, respectively, which greatly contributed to the decline of NEE in the early afternoon. Mean nighttime ER (i.e., nighttime NEE) was about 2 μmol m−2 s−1, which is about one-fifth of the maximum average of daytime NEE values. For other alpine ecosystems, similar rates of nighttime ER (1.5–2.0 μmol m−2 s−1) were observed in their peak growth season, about one sixth to one fifth of peak daytime NEE [Kőrner, 1999].
Table 2. Comparison of Measured Net CO2 Exchange (NEE) and Simulated NEE in Three Seasons, 2001–2003a
RMSD, μmol m−2 s−1
MD, μmol m−2 s−1
RMSD, root mean squared deviation; MD, mean of the deviations; sample number in 2001 is 5768; in 2002 is 11,514; and in 2003 is 11,209. Simulation 1: considering photoinhibition due to high irradiance; simulation 2: not considering photoinhibition due to high irradiance.
 Seasonal dynamics obtained from CDMag also showed good agreement with the observed data (Figures 5a and 5b). The deviation of daily net ecosystem production (NEP) between the simulations and observations ranged between −0.2 and +0.6 mol CO2 m−2 d−1. Both the measured and simulated daytime NEP increased with phenological development, reaching a maximum in August (DOY210–240) and then declining. Both simulated and measured nighttime NEP (i.e., ER) showed no significant changes during the growing season (Figure 5a).
 We examined the model for bias and discrepancy from the observations (Figures 6 and 7). In 2001, CDMag overestimated daytime NEP, nighttime NEP, and daily NEP, but the discrepancy was relatively small in 2002 and 2003. There was only a small discrepancy (–0.015 mol m−2 d−1) for the daily NEP in 2003 (Table 3). It seemed that CDMag agreed better with observed NEP values in 2002 and 2003 than in 2001.
Table 3. Mean Growing Season Discrepancy (CDMag Flux Minus Measured Flux) Between Measured and Simulated Net Ecosystem Production (NEP) in 2001–2003a
NEP in mol m−2 period−1. Period: 0800–2000 LT for daytime NEP; 2000–0800 LT for nighttime NEP. Negative values, ecosystem flux upward; positive values, ecosystem flux downward.
4.2. Photoinhibition in the Canopies
Ac declined when photoinhibition was considered in CDMag (Figure 8). Inhibited Ac occurred from about 0900 to 1800 LT on the two cloud-free days examined. The maximum decline of Ac occurred in the early afternoon instead of at noon, owing to light acclimation (see equation (A9) in Appendix A). The decrease of daily carbon gain due to photoinhibition varied greatly (Figure 9), which could be influenced by weather conditions because Ac declined very little on cloudy days. Maximum daily carbon loss (>0.1 mol m−2 s−1) occurred in late July (about DOY200). The simulation showed that 5.3–5.6% of total gross photosynthesis during the growing season was lost in the 3 years (Table 4) owing to photoinhibition. Further analysis revealed that the highest photoinhibitory reduction occurred in sunlit leaves of the upper canopy layer (Table 4). About 7.5–7.8% of daily gross primary production (GPP) was estimated to be lost because of simulated photoinhibition in the sunlit leaves of the upper canopy layer, whereas leaves in the lower canopy layers showed less photoinhibitory reduction (≤5.0%) in GPP.
Table 4. CDMag Simulated Reduction (%) in Seasonal Gross Photosynthetic Carbon Gain (GPP) in Different Canopy Layers of the Alpine Meadow Due to Photoinhibition
4.3. Light-Use Efficiency
 Light-use efficiency (LUE) is the number of CO2 molecules fixed per day by the canopy per absorbed PAR. It can be expressed as
where t is time (in hours) from 0 to 24.
 LUE exhibited marked seasonal change with phenological development of the canopy, and the maximum LUE was a little higher than 0.05 mol CO2 (mol APAR)−1(Figure 10). LUE evidently declined after DOY260 in the 3 years and was close to zero on DOY280. The average LUE values were 0.016, 0.025, and 0.027 for the growing seasons in 2001, 2002, 2003, respectively. Wofsy et al.  observed LUE near 0.02 mol CO2 (mol APAR)−1 during the active growing season of a mixed forest in England. A midseason value of 0.01 mol CO2 (mol APAR)−1 was observed in a serpentine grassland [Valentini et al., 1995]. For an Arizona grassland, LUE was about 0.027 mol CO2 (mol APAR)−1 if LUE based on dry matter production were doubled. LUE values at our experimental site are comparable to estimates in tropical and temperate grasslands and higher than estimates in Mediterranean and subtropical dry forest [Ruimy et al., 1994]. The values are also comparable to those estimated from crops such as wheat, maize, sorghum, and rice [Choudhury, 2000, 2001b].
4.4. Sensitivity Analyses
 While adjusting CDMag parameters, we ran a series of sensitivity simulations for nine main parameters (Table 5). Except for the weighted light-dose hours (hw), which was adjusted by ±1 hour, all the tested parameters were adjusted by ±10% of their baselines. The changes of 10% for these parameters resulted in a change in GPP of less than 10%. In contrast, changes of more than 10% in NEP resulted from a 10% change in parameters, including θ0, V0, Q″10, and ɛ0.
Table 5. Sensitivity of Carbon Balance Variables (%) to Input Parameters, as Represented by the CDMag Under Given Parameter Conditions Shown in Table 1a
Analysis for 2002; Agslit, gross carbon gain in sunlit leaves; Agshade, gross carbon gain in shaded leaves; An, net carbon gain of canopy; NEP, net ecosystem production; Rauto, autotrophic respiration; Rhetero, heterotrophic respiration; ER, ecosystem respiration. Baseline values are in units of mol m−2 period−1 (period: DOY165–DOY280).
 Changes in θ0, V0, and ɛ0 caused more than 10% changes in Agslit, Agshade, An, with higher θ0, V0, and ɛ0 resulting in higher GPP. Changes in these three parameters not only influenced carbon gain variables but also caused evident changes (>3.8%) in Rauto.
 Higher Q″10 caused reduced carbon gains and autotrophic respiration. An increase or decrease of 10% in Q″10 resulted in a −16% decline or +18% increase in NEP, respectively. However, autotrophic respiration is not sensitive to the temperature response coefficient, Q10. A change of 10% in Q′10 resulted in a change of 2.2% in heterotrophic respiration and a change of 5.2% in RE. Parameters for photoinhibition (equation (A9) in Appendix A), including k and hw, had a small influence on the carbon balance variable, NEP. Ten-percent changes in k and hw resulted in less than 2% changes in NEP. Leaf inclination index, χ (see Appendix B) had little influence on carbon dynamics variables.
5. Discussion and Conclusions
 CDMag is a one-dimensional dynamics model scaled up from leaf to canopy on the basis of NRH. The model considers the response of NRH parameters to air temperature, CO2 partial pressure and soil moisture. Photoinhibition in CDMag is considered by light acclimation of ɛ and θ to a 3-hour weighted light dose. Furthermore, to construct a physiological correlation between stomatal conductance and leaf photosynthesis, CDMag applies a coupled An − gc model to solve Ci.
 Instantaneous carbon fluxes with CDMag considering photoinhibition were consistent with observations from the eddy covariance measurements. CDMag simulated seasonal variation of NEP with errors from −0.015 to 0.05 mol m−2 d−1. The largest error was in 2001, with smaller errors in 2002 and 2003, possibly because the dataset was much smaller in 2001 than in the other 2 years. Thus these results suggest that CDMag may be more reliable for simulating NEP over a longer period.
 To evaluate the performance of CDMag at the seasonal scale, time series discrepancies between measured and simulated NEP values were analyzed. There appeared no evident overestimation or underestimation by the model in 2002. NEP in 2001 and 2003 was overestimated by the model in midseason, and NEP in 2003 was underestimated in early and late in the growing season (Figure 7). One important reason for this discrepancy is that LAI was erroneously estimated in 2003. We used the same LAI in 2003 as that in 2002 because no data were available for 2003. Considering that LAI is mainly controlled by air temperature and based on actual temperature measurements from 2003, LAI in 2003 was probably underestimated at the beginning and end of the growing seasoning and overestimated in midseason. NEP simulation with the CDMag is apparently superior to that with a similar carbon dynamics model, PCARS for peatlands [Frolking et al., 2002; Lafleur et al., 2003]. In summary, CDMag performs well in simulating both NEE and accumulated NEP during the growing season in an alpine meadow habitat.
 Carbon losses due to photoinhibition occurred mainly in midday and peaked in the early afternoon. Daily carbon losses due to photoinhibition showed no significant seasonal change. During the growing seasons, our simulation calculated a reduction of 5.3–5.6% carbon gain in the meadow canopy due to photoinhibition, which is slightly lower than the reduction of 6.1% carbon gain for Quercus coccifera [Werner et al., 2001]. In simulations, photoinhibition resulted in a greater photosynthetic reduction in the upper layer, where a larger proportion of leaf area receives direct sunlight (Table 3). The reduction due to photoinhibition in the upper layer in the current study is similar to that reported for Q. coccifera [Werner et al., 2001]. For a willow canopy, potential carbon loss due to photoinhibition can reach 10% of carbon gain in the leaves of a peripheral shoot [Ogren and Sjostrom, 1990]. One may expect much higher carbon loss from photoinhibition in alpine plants, because radiation is much higher than for plants growing at low altitudes. However, the photosynthetic reduction by photoinhibition estimated in our simulation was of a magnitude similar to those reported for lowland plants. Leaves in the Kobresia meadow grow at a steep inclination, however, which may help the alpine plants to avoid high light intensities. It is clear from the current simulation that neglecting photoinhibition in carbon gain estimates can result in significant overestimation of CO2 uptake [Werner et al., 2001].
 Previous studies have suggested that integrated and weighted light dose over the prior 6 hours best predicts photoinhibition [Ogren and Sjostrom, 1990; Werner et al., 2001], whereas our preliminary study showed that weighted light dose over 2–3 hours is best linearly correlated to maximum quantum yield of photosynthesis II (Fv/Fm; unpublished data). Under photoinhibition, alpine meadows recover more quickly than plants growing on lowland plains, because alpine plants have a strong ability to adapt to high irradiance [Kőrner, 1999]. The time period of the weighted light dose not only relates to the sensitivity of a particular species to photoinhibition but depends on additional environmental stresses (e.g., high temperature and water stress) [Werner et al., 2001].
 When considering NEE decline at midday, we should consider not only carbon loss due to photoinhibition but also that due to ER. ER greatly contributes to carbon loss, especially in the early afternoon, when ER is at its maximum. From 1100 to 1400 LT, mean ER increased by more than 1.0 μmol m−2 s−1 in the three growing seasons, causing an accelerated decline of NEE (Figure 4). Unlike autotrophic respiration, heterotrophic soil respiration accounted for most of the carbon loss in ER (Table 5).
 Soil respiration is also one of the most important variables in carbon dynamics on the Qinghai-Tibetan Plateau. The soil of the alpine meadows is rich in organic carbon (80–100 g kg−1 at depths of 0–20 cm), which provides plentiful carbon release to the atmosphere. CDMag simulates soil heterotrophic respiration with a high Q′10, as determined by previous measurements in the same meadow [Cao et al., 2004]. The Q′10 value in the alpine meadow is evidently higher than in other temperate grassland ecosystems [Novick et al., 2004], suggesting that temperature is much more influential on soil CO2 release in alpine meadows than in other temperate grassland ecosystems.
 Simulation with CDMag showed that the LUE is high at midseason in alpine meadows. During the alpine growing season, soil water content and temperature are favorable for carbon gain. Owing to photoinhibition, the light saturated point is probably reduced, as shown by the fact that maximum carbon gain occurred before noon, but photoinhibition limited only 5.3–5.6% of the overall potential carbon gain (Table 4). In addition, the high leaf inclination angles in alpine meadows cause relatively small diurnal changes in light interception, as compared with that on horizontal leaf surfaces.
 Compared with other integrated carbon models, e.g. SIB-2 [Sellers et al., 1996], CDMag includes a relatively small number of parameters. We performed sensitivity analysis for all major parameters used in the model. Changes of less than 10% in carbon gains or ER were caused by 10% changes in the parameters, whereas a greater than 10% change in NEP resulted from a 10% change in V0, Q″10, θ0, and ɛ0. V0 and Q″10 determine Vm. V0 is a physiological property of the leaf (or chloroplast) and is proportional to the Rubisco pool size [Sellers et al., 1996]. Selection of the appropriate V0 and Q″10 values to use for Vm is the major problem in parameterizing CDMag [Collatz et al., 1991]. In light of preliminary and published experiments on the Vm conducted on the Qinghai-Tibetan Plateau [Cui et al., 2003], we used corrected parameters for Vm in CDMag. The θ0 and ɛ0 are two main parameters in the NRH. Under non-limiting environmental conditions, ɛ0 for C3 plants has a value of 0.081 [Ehleringer, 1978], and a “typical” θ0 value of 0.90 has been estimated [Thornley, 1998]. It is difficult to estimate θ0, especially for leaves grown in strong light, and estimates vary [Leverenz, 1987; Ogren and Evans, 1993], causing some uncertainty in estimating Al with the NRH. NEP has the lowest value among the carbon-gain variables (Table 5); thus small absolute changes in NEP represent a high percentage of change.
 CDMag is the first carbon model devised for alpine ecosystems on the Qinghai-Tibetan Plateau. In a general model, it can be difficult to cope with many of the extreme situations in alpine ecosystems, such as high radiation and large diurnal changes in temperature. Because alpine ecosystems cover a large proportion of the world's terrestrial area, it is necessary to develop an appropriate model in order to examine carbon dynamics for those ecosystems. By focusing on the Kobresia meadow on the Qinghai-Tibetan Plateau, our current model can also be applied to any alpine ecosystem.
 In addition to alpine meadows, alpine shrub and alpine swamps are also important grassland ecosystems on the Qinghai-Tibetan plateau. To further evaluate the model's performance with regard to alpine shrub and alpine swamps, we plan to make carbon flux measurements for these two ecosystems as well. In addition, further studies are expected to improve the function of CDMag by extrapolating the model's results to the whole plateau.
 Light-saturated photosynthesis rate (Asat) is influenced mainly by the factors of air temperature (Ta), intercellular CO2 partial pressure (Ci), and soil water content (Sw), as follows:
where Vm is maximum catalytic capacity of Rubisco per unit leaf area (μmol m−2 s−1); Vm0 is Vm at 25°C air temperature; Tamin, Taopt, and Tamax are minimum, optimum, and maximum Ta for photosynthesis, respectively (Table 1); Q″10 is the temperature response coefficient of the maximum catalytic capacity of Rubisco (Table 1); Ci is intercellular CO2 partial pressure; Γ is the CO2 compensation point; Sw is the relative soil water availability (Sw = (Wa − Wwilt)/(Wfield − Wwilt), where Wa is actual soil moisture in 0–30 cm depth, Wfield and Wwilt are field capacity and wilt point at the same depth, respectively; Table 1); and Co is a parameter reflecting the Michaelis constant for Rubisco reaction and is taken as a constant 3.0 (Pa).
 Quantum efficiency (ɛ) of C3 plants strongly depends on temperature and CO2 partial pressure [Ehleringer, 1978], as well as habitat irradiance [Long et al., 1994],
where ɛ0 is the maximum ɛ under noninhibitory conditions (Table 1); P1 and P2 are parameters for determining ɛ decline with temperature and are given here as 12.0 and 0.75, respectively; PARw is the moving weighted light dose at leaf surface (3 hours); and k is the decline coefficient (Table 1, Figure A1), which is determined by the declining trend of θ and ɛ with PARw.
 The curvature factor, θ, is also dependent on the irradiance condition
where θ0 is the maximum θ without photoinhibition (Table 1). We assumed that the same light dose caused identical relative changes in θ and ɛ [Werner et al., 2001].
 To estimate sunlit and shaded leaf photosynthesis, irradiance within the canopy was separated into direct and diffuse PAR. Sunlit leaves receive both direct and diffuse PAR, whereas shaded leaves receive only diffuse PAR (I). By assuming that the plant canopy is a purely absorptive medium and there is single scattering within the canopy (i.e., photons are absorbed after one scattering), Choudhury  provided a simple solution to diffuse PAR(L, μ) propagating in the direction μ (cosine of zenith angle) at the LAI equivalent of depth L,
where G and G0 are the projection of unit foliage along the radiance I and the direction of incident direct PAR, respectively; ω is the single scattering albedo of a leaf; S0 is the direct PAR on a perpendicular surface at the top of the canopy; μ0 is cosine of the solar zenith angle of incident direct PAR; and Sd is diffuse PAR irradiance on top of the canopy. The total PAR incident on the canopy is equal to (S0μ0 + Sd).
 The diffuse irradiance on a horizontal surface at depth L (Fdif[L]) is obtained by integrating I(L, μ) over the angle as
Adaptive Lobatto quadrature was used to solve equation (B2) for diffuse irradiance at depth L. Similarly, integration of equation (B2) gives Fl,shade(L), and Fl,sun(L) is given by
where G0S0 is the direct PAR on the leaf surface.
G and G0 can be solved with an empirical leaf distribution function [Ross, 1975],
where g1 and g2 are functions of the leaf inclination index (χ; −0.3 ≤ χ ≤ 0.6),
For a uniform (or hemispheric) canopy leaf inclination index, χ = 0; for a horizontal canopy, χ > 0; for a perpendicular canopy, χ < 0. With a perpendicular canopy, the alpine meadow in our experimental is given a minimum χ value, −0.3 (Table 1).
G0 is solved from μ0 as follows:
Assuming that leaves in the canopy are randomly distributed, the fraction of sunlit leaves fslt(L) and the fraction of shaded leaves fshade(L) at a depth L are estimated by
 This study was supported by the Global Environmental Research Program of the Ministry of the Environment, Japan (grant S1) and by Japan Society for the Promotion of Science (grant 13575035). It was also supported by a Visit Professor Research Program of Institute of Geographic Sciences and Natural Resources Research (grant SZW35500). We are grateful to Song Gu and Tomomichi Kato for collecting CO2 flux and ancillary data for the CDMag. We are also thankful to Qiang Yu for his suggestion on the modeling work. We are very grateful to two anonymous reviewers and the editors for providing some valuable suggestions.