Site Description
The field site is an alpine pasture near Furka Pass (46° 34′ 36″ N, 8° 25′ 17″ E) in the Swiss central Alps at an elevation of about 2440 m a.s.l. on a southeast facing slope with an inclination of about 10–15°. Average annual precipitation and annual mean temperature at a close by location (Gütsch, 17 km NE, 2283 m a.s.l.) were around 1450 mm and 0.4°C during the period 1981–2010. For the actual site, year-round meteorological data are only available since July 2012 and the mean precipitation during July–August from 2012 to 2016 was 270 mm, the mean air temperature during the same period was 8.3°C. Snow melt usually occurs in June and the growing season lasts about 2.5–3.5 months, with occasional snow events possible year round (Inauen and others 2012). The wind system is bimodal with westerly winds dominating during the night, and both, westerly and easterly winds, occurring during the day. The vegetation west of the EC tower consists of a Nardus community dominated by Nardus stricta and Carex curvula with some wetter patches of Eriophorum scheuchzeri and of Deschampsia cespitosa tussocks, whereas to the east the vegetation is sparser and typical snowbed vegetation dominated by Alchemilla pentaphyllea, Salix herbacea, Soldanella pusilla, Gnaphalium supinum, and Sibbaldia procumbens predominates. The soil was classified as partly podzolized alpine brown earth on siliceous bedrock (Inauen and others 2013).
CO2 Flux Measurements
NEE was measured using the EC method (Aubinet and others 2000, 2012; Baldocchi 2014). Measurements took place from June 21, 2013–October 8, 2014, covering two snow-free periods. The three orthogonal wind components and sonic temperature were measured using a 3-D sonic anemometer (CSAT3, Campbell Scientific, Logan, UT, USA). CO2 and H2O dry mole fractions were measured using an enclosed path infrared gas analyzer (IRGA) (LI-7200, LI-COR Inc., Lincoln, NE, USA) with an intake tube of 0.5 m length. The instruments were mounted at 3.5 m above ground, and data were sampled at 20 Hz on a data logger (CR5000, Campbell Scientific, Logan, UT, USA) and stored on a 2 GB data card. Because of lightning-caused instrument failure, the LI-7200 was temporarily replaced by an open-path gas analyzer (LI-7500, LI-COR Inc., Lincoln, NE, USA) during the period from August 19–October 8, 2013.
Fluxes were calculated according to commonly accepted procedures using the software EddyPro (LI-COR Inc., Lincoln, NE, USA). In brief, CO2 fluxes were derived from the covariance of the vertical wind speed w and the CO2 dry mole fraction c: \( F_{c} = \overline{{w^{\prime }c^{\prime }}} \), where primes denote fluctuations around the mean and the overbar a time average, in our case 30 min. Raw data procedures prior to flux calculation included de-spiking, a double rotation of wind data as well as the detection and compensation of time delays in the CO2 signal. Lag times were estimated for each flux averaging period by maximizing the covariance between the CO2 signal and the vertical wind component within a certain window of plausible time lags.
During winter time the site was not accessible for extended periods of time (because of high risk of avalanches in winter 2013/2014), making raw data storage on the data card impractical. Therefore, 30 min averages of the raw, unprocessed data of all variables as well as their standard deviations and covariances were computed and stored by the data logger from October 8, 2013–July 1, 2014, whereas during summer half-hourly data were logged as well as raw data. Covariances calculated from raw data after the different processing steps were compared to the unprocessed covariances. The post-processing steps increased the covariance between the vertical wind speed and the CO2 dry mole fraction by around 12%, mainly because of the compensation of the time delay of the CO2 signal. Therefore, we multiplied the CO2 fluxes calculated based on half-hourly covariances of unprocessed data (October 8, 2013–July 1, 2014) with a factor of 1.12.
Low-frequency losses due to the finite averaging time were corrected according to Moncrieff and others (2004). Correction for flux spectral losses in the high-frequency range due to the limited response of the instruments, sensor separation, path averaging, and so on, was done using the method by Fratini and others (2012). When no raw data were available, high-frequency losses were corrected according to Massman (2000).
Half-hourly flux data were discarded if the IRGA or sonic anemometer malfunctioned because of technical problems or weather conditions (precipitation, dew, snow). Moreover, time periods with the stationarity test or the deviation of the integral turbulence characteristics (Foken and Wichura 1996) exceeding 100% were excluded from analysis.
NEE was calculated as the sum of the vertical eddy flux and the storage term. The latter was estimated from the CO2 concentrations based on a 1-point profile at the reference height (> 95% of all times less than ± 0.15 μmol m−2 s−1).
Nighttime NEE data were excluded when friction velocity (u
*) was below 0.18 m s−1 to avoid potential underestimation of ecosystem respiration during stable, calm nights when the assumptions underlying the eddy covariance method are not fulfilled. The u
* threshold was estimated based on the Moving Point Test, a method for an objective threshold determination devised by Gu and others (2005).
The random uncertainty was estimated based on the neighboring days approach devised by Hollinger and Richardson (2005) by analyzing the difference of NEE values collected under similar conditions (same time of day, half-hourly photosynthetic photon flux density (PPFD) values within 100 μmol m−2 s−1, air temperature (T
a) within 3°C, soil temperature (T
s) within 2°C, relative humidity (RH) within 20%, and wind speed within 1 m s−1) on two successive days.
For the analysis, net ecosystem exchange was expressed as net ecosystem production (NEP = − NEE), which equals the net gain or loss of C by the ecosystem (Reichle 1975), that is, positive values of NEP represent a net uptake of CO2 by the ecosystem.
Overall, about 60% of the measured flux data were rejected because of quality criteria. This is a rather high rate, although it is quite common that 25–60% of eddy covariance data are omitted (for example, Papale and others 2006; Wohlfahrt and others 2008). To establish seasonal and annual budgets, data gaps were filled using common methodology. Data gaps less than 2 h were filled by linear interpolation. Longer gaps were filled by employing the functional relationship between NEP and soil temperature (T
s, measured at 0.1 m depth) (Arrhenius-type relationship) for nighttime data (PPFD = 0) and between NEP and PPFD (Michaelis–Menten-type relationship, or so-called light response curves) for daytime data (PPFD > 0). For this purpose, the following models were fitted to biweekly blocks of half-hourly data shifted each 5 days:
$$ {\text{NEP}}_{\text{night}} = a*{ \exp }\left( {b*T_{\text{s}} } \right) $$
(1)
$$ {\text{NEP}}_{\text{day}} = \frac{{\alpha *{\text{PPFD}}*{\text{GPP}}_{\text{sat}} }}{{\alpha *{\text{PPFD}} + {\text{GPP}}_{\text{sat}} }} + R_{\text{eco}} $$
(2)
where α (µmol µmol−1) is the quantum yield, GPPsat (µmol m−2 s−1) the asymptotic value of the gross primary production (GPP) at high irradiance (photosynthetic capacity at canopy level), and R
eco (µmol m−2 s−1) the ecosystem respiration, which is the sum of autotrophic (R
a) and heterotrophic (R
h) respiration. Because the vegetation differed in the east and west of the flux tower, α, GPPsat, and Reco and 95% confidence intervals were also estimated for the east (wind direction ≤ 180°) and west (wind direction > 180°) separately (for the analysis only and not used for gap filling).
During the time with a permanent snow cover, no clear relationship between NEP and any environmental driver was found. Larger gaps were therefore filled with the mean value for the specific half-hour estimated from biweekly data blocks [mean diurnal variation; (Falge and others 2001)].
Based on the seasonal time-series of NEP we differentiated two phases: the carbon uptake period (CUP) when the site represented a sink of CO2, defined as the period when the 5-day mean of NEP is positive (Galvagno and others 2013; Wohlfahrt and others 2013), and the period during which the site represented a source of CO2.
Ancillary Measurements
Meteorological conditions, including air temperature (T
a) and relative humidity (RH), global radiation (i.e., diffuse and direct solar radiation; R
g), precipitation (P) and snow height (SH), were monitored by a weather station set up at 2.4 m above ground. In addition, soil temperature (T
s) at 0.1 and 0.25 m below ground and soil moisture (soil water content (SWC) in vol%) at 0.05 and 0.15 m below ground were measured. If not indicated otherwise, T
s at 0.1 m and SWC at 0.05 m were used. Because photosynthetic active radiation was not directly measured, PPFD (µmol m−2 s−1) was approximated as PPFD = 2 * R
g (W m−2) (González and Calbó 2002). The fraction of diffuse radiation was estimated using an empirical relationship between R
g and the clearness index parameterized based on data from a study site in the Eastern Alps (Wohlfahrt and others 2016).
Because the area under the snow height sensor was among the first to become snow free, while the rest of the field site was still covered by snow, snow cover duration was determined from webcam images.
Models
We used a box model based on the Data Assimilation Linked Ecosystem Carbon (DALEC) model (Fox and others 2009; Williams and others 2005) to represent the C cycle of the alpine grassland. The model consists of six C pools that represent the C content of foliage (C
f), roots (C
r), necromass (standing dead biomass) (C
n), litter (C
lit), and soil organic matter (C
som). At our grassland site, many of the dominant species are hemicryptophytes and therefore the model contains a labile C pool (C
lab) that represents the overwintering buds and supports leaf formation in spring. The pools are connected via fluxes as illustrated in Figure 1, where A denotes allocation to a pool, L the litterfall from the respective pool, and D the decomposition of litter. It was assumed [similar to Williams and others (2005)], that
-
autotrophic respiration is a fixed fraction of GPP and that all C fixed during the day is either respired (autotrophic respiration) or allocated to one of the plant tissue pools (C
f, C
r, or C
lab),
-
there is no direct environmental influence on allocation/litterfall and those fluxes are donor-controlled with constant rate parameters,
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soil transformations are temperature-sensitive (see Appendix A) and
-
there is no C loss due to herbivory or leaching.
Preliminary data analysis and model runs indicated that leaf senescence was predominantly driven by photoperiod, as was found in previous studies (Körner 2003). Therefore, in the model a minimum day length threshold, which was estimated during model calibration, controlled leaf senescence in fall.
For a detailed description of the model equations see Appendix A.
The daily C input into the system, i.e., GPP, was calculated as a function of the green plant area index (GAI, area of green plant matter per ground area; directly estimated from C
f) by use of a sun/shade big-leaf model of canopy photosynthesis based largely on de Pury and Farquhar (1997), with modifications according to Goudriaan and Laar (1994), Wang and Leuning (1998) and Smith (1937) (Appendix B).
The model contained 17 unknown parameters, and the starting values of the six C pools were also unknown. Three of the parameters associated with the GPP model were fixed to values taken from the literature (Table 1), the remaining 14 parameters and initial conditions were estimated using DREAM (Vrugt and others 2009) to reconcile model output with measured NEP. For this purpose, two data sets of daily values—NEPday and NEPnight—were generated from the non-gap-filled data; daily values were calculated for days when at least 80 and 50% of the half-hourly NEP measurements during day and night were valid, respectively.
Table 1 Initial conditions and model parameters
DREAM is a multi-chain Markov Chain Monte Carlo (MCMC) algorithm for statistical inference of parameters using Bayesian statistics. A Bayesian calibration estimates the joint probability distribution of all parameters conditional on the available data rather than estimating specific values for each parameter. This so-called posterior distribution is computed from the prior distribution of the parameters and their respective likelihood given the observed data. The prior distribution is determined by the information on the parameters prior to data collection and analysis. The likelihood function provides a measure of how well the model fits the data. For most complex process-based models the posterior distribution cannot be determined analytically and to estimate the likelihood the model needs to be run. This can be realized using a sampling method like MCMC, which generates a random walk through the parameter search space. The basis of this method consists of the following steps: first, based on the starting point, a candidate parameter set is sampled from a proposed distribution. Then the likelihood is estimated and the candidate is either accepted or rejected according to an acceptance probability. If the candidate is accepted, the chain moves to the new location; otherwise, it remains in the current location. Repeating those steps eventually results in a Markov chain representing the target distribution. To explore multi-dimensional parameter spaces rapidly and adequately, multiple chains are run in parallel and achievement of convergence to a limiting distribution is estimated (Gelman and Rubin 1992).
In our case, a uniform prior distribution of the parameters was used with lower/upper bounds (given in Table 1) determined based on information from the literature and initial test runs of the model. To account for non-normality, heteroscedasticity and correlation of model residuals, a common problem in ecological modeling, a generalized likelihood function (Schoups and Vrugt 2010) was applied and the appropriate residual error distribution was determined concurrently with the model parameters. To estimate model uncertainty due to parameter uncertainty, model output was generated with 1000 parameter sets from the posterior distribution and the 97.5 and 2.5% prediction percentiles were calculated. Total predictive uncertainty was estimated by adding the modeled residuals based on the estimated residual error distribution. Collinearity of the model parameters was checked by computing the correlation matrix of the parameter estimates after the chains converged to the target distribution.
To investigate the differences between the two study years, the model was calibrated against NEP data from the individual years, resulting in two sets of model parameters (‘para13’ and ‘para14’). However, the initial condition of the C
lab, C
r, C
lit, and C
som pools was set equal for both years, where the initial magnitude was estimated by calibrating the model against the entire NEP data set of both years. The initial magnitudes of C
f and C
n were set to zero, because simulations commenced before onset of the growing season.
Subsequently, four forward model runs were performed, using the two parameter sets and the environmental conditions of the 2 years in a factorial design (Table 2).
Table 2 Four possible forward model runs using the environmental conditions and the parameter sets of the two individual years in a factorial design
Finally, to analyze the direct effects of growing season weather during 2013 and 2014 on NEP without the complication of seasonally changing C pool sizes, the model was run using each year’s weather conditions and the 2013 parameters, but instead of simulating the dynamics of the C pools, their values were set equal to the C-pool values of the 2013_para13-model output. Thus, the development of the C pools and therefore also GAI was forced to be identical during both years and differences in NEP between the 2 years were only due to differences in environmental conditions (incident radiation and temperature). Simulated values for NEP, GPP, and R
eco were analyzed during a period that was snow free in both years and also covered the peak uptake phase of the 2 years (July 15–August 15).