Estimating the carbon fluxes of forests with an individual-based forest model

The study sites

The forest model FORMIND

FORMIND (Köhler and Huth 2004; Fischer et al. 2016) is an individual-based forest gap model in which growth is calculated for each tree individually. The approach uses patches to describe the vertical and horizontal forest structures. The main processes of the model include establishment, growth, mortality and competition. Important driving factors are daily means of incoming light (photosynthetic photon flux density, PPFD), temperature and precipitation (based on a model verison for temperate forests as in Bohn et al. 2014). In this study, the model was applied to an even-aged spruce forest (1 ha). Establishment and mortality were deactivated for the short simulation time of 6 years. A full model description can be found in Fischer et al. (2016) and at www.formind.org.

The model runs with daily variable observed climate inputs of PPFD, day length, temperature and precipitation measured onsite. PPFD and day length serve as the driving forces for forest productivity. The sum of the GPP over all trees thus equals the GPP of the ecosystem. The ecosystem respiration is the sum of the respiration of all trees plus that of the soil and deadwood. The NEE is calculated as the difference between the ecosystem GPP and the ecosystem respiration (Fischer et al. 2014). A positive NEE corresponds to increasing carbon stocks.

Field data and data filtering

We compared the simulation results of the forest model with the EC data of the Wetzstein site (Table 1). For the Wetzstein site, the EC data were pre-processed as described in Rebmann et al. (2010). The net ecosystem exchange (NEE) was gap filled since the data are compared at daily time scales and partitioned into GPP and respiration. We use an algorithm that extrapolates day-time ecosystem respiration from night-time respiration considering temperature sensitivities (Reichstein et al. 2005).

We filtered the EC data to identify days that are affected by specific limitations. Optimal temperature or soil water conditions were defined for days when the daily mean GPP was maximal (98th percentile for the years 2003 to 2008). We assumed that on those days the GPP is not affected by any limitation. The filtered range of the optimal temperature (daily daytime mean) conditions was identified at 7.3 °C < T < 18.0 °C, and the threshold for non-limiting soil water conditions at SW > 16.0%. Optimal light conditions were defined for days when values rise above the monthly 80th percentile. We define night-time as time periods when PPFD < 20 μmol (CO₂)∙m⁻²∙s⁻¹. When we use normalized GPP values in our analyses, we normalize GPP values yearly by its annual 98th percentile.

The model setup

All model setups were initialized according to the inventory data for Wetzstein and Tharandt (Table 1). Trees were spread equally over the 25 patches of the 1 ha model area (at Wetzstein, 410 stems∙ha⁻¹ with a mean stem diameter of 0.33 m). The deadwood pool was filled with 4.14 tC∙ha⁻¹ (Wetzstein inventory, personal communication from Martina Mund, University of Goettingen). The fast-decomposing soil stock was initialized with 2.0 tC∙ha⁻¹, and the slow-decomposing soil stock with 1.5 tC∙ha⁻¹ (means in the climax stage of long-term simulations). The simulation period at the Wetzstein site was from 2003 to 2008 and at Tharandt from 1999 to 2004. All model simulations were deterministic since none of the model setups included recruitment or stochastic mortality.

Simulation of daily carbon fluxes at Wetzstein forest

The measured and modeled (parameterization M1) GPP and respiration at Wetzstein forest for the dry year 2003 are shown in Fig. 1. The forest model performed well for daily GPP. It reproduced the seasonal cycle, and the daily fluctuations showed similar magnitudes to those observed. Differences were observed during times of low soil water availability, very low and high temperatures and bright days. In late summer (July-September), the simulated respiration diverges from the observational data. In general, simulated respiration shows stronger fluctuations than the observed respiration.

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Simulation of carbon fluxes at Wetzstein forest for three different parameterizations

We compared the simulations of all three model versions with the observed fluxes at Wetzstein at the daily time scale (Table 3, Fig. 2). The correlation is best for the numerically calibrated parameterization (M2), closely followed by the filter-based parameterization (M3). Simulated respiration correlates with the observed values with an R ² of 0.44–0.54; NEE with an R ² of 0.63–0.66. Simulated and observed GPP values match best with an R ² of 0.73–0.82. High GPP values above 30 tC∙ha⁻¹∙a⁻¹ can only be reached with the filter-based parameterization (M3, Fig. 2).

Table 3

R ² and root mean square error (RMSE, in tC∙ha⁻¹∙a⁻¹) at the calibration and validation sites

	Wetzstein (calibration site)		Tharandt (validation site)
	R 2	RMSE	R 2	RMSE
GPP
Lit.-based (M1)	0.73	7.91	0.59	10.47
Calibrated (M2)	0.82	5.39	0.61	8.83
Filter-based (M3)	0.80	5.72	0.61	9.57
Respiration
Lit.-based (M1)	0.44	6.31	0.58	5.14
Calibrated (M2)	0.54	4.64	0.62	4.92
Filter-based (M3)	0.53	4.73	0.62	5.12
NEE
Lit.-based (M1)	0.63	6.25	0.30	7.90
Calibrated (M2)	0.66	5.43	0.38	6.87
Filter-based (M3)	0.65	5.42	0.38	7.62

Simulated fluxes are compared to observed values at the daily time scale (scale of the simulation output)

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In a second step, we calculated annual GPP, NEE and respiration for the Wetzstein forest (Fig. 3a). The simulated annual NEE values fit the observed annual values best for the calibrated parameterization (M2, deviation from observed data by 3.5% for average values throughout the simulation years). The simulated annual GPP fits quite well and only diverges from the observed data by 0.8% for the calibrated (M2) and 2.6% for the filter-based (M3) version; simulated respiration by 0.3% (M2) and 0.9% (M3). The literature-based model version clearly underestimates all ecosystem fluxes.

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Simulation of carbon fluxes at another spruce forest

We applied the forest model to another spruce forest (Tharandt) for the years 1999–2004 (Fig. 3b). The model parameters were the same as at Wetzstein. Only the climate input and the initialization of the forest model (forest state based on inventory data) were adapted to the site.

Both, the filter-based (M3) and calibrated (M2) model version, performed well for the daily GPP (R ² = 0.61 (M2), R ² = 0.61 (M3), RMSE = 8.83 tC∙ha⁻¹∙a⁻¹ (M2) and RMSE = 9.57 tC∙ha⁻¹∙a⁻¹ (M3), Table 3). The simulated respiration was even better than at Wetzstein, at the daily scale (R ² = 0.62); the NEE performed worse at Tharandt than at Wetzstein (R ² = 0.38).

The annual simulated GPP is best for the calibrated (M2) and filter-based (M3) parameterizations (2 and 7% deviations). In April 2001, the tree density was reduced by 30% (at Tharandt and in the forest model), which is reflected in the lower GPP values after 2001. In the dry year 2003, the simulated annual GPP is 0.47 tC∙ha⁻¹ lower than in the previous year for the calibrated model version (M2) and 1.37 tC∙ha⁻¹ lower for the filter-based (M3). The observed GPP in 2003 is 1.87 tC∙ha⁻¹ lower than in 2002. The annual carbon budget (NEE in Fig. 3bmatches the observed budget well (M2: mean deviation of 20% from observations; M3: deviation of 16%). Note that NEE is the balance between GPP and respiration and the bias is consequently more sensitive. Respiration is partly overestimated for the model versions M2 and M3 (deviations of 14% and 19%).

Limiting factors for productivity

As an example, we analyze here the GPP limitation due to temperature (Fig. 4). Daily GPP values were normalized and filtered for optimal soil water conditions and sunny days to distinguish them from days with other limitations. Filtered, normalized data thus represent the reduction factor due to temperature.

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On colder days, the literature-based model (dashed line) shows a reduction in GPP which seemed stronger than the observed. For example, at the freezing point, the observed GPP was reduced to 20% of its optimum, whereas the model reduced the GPP to nearly 0. For higher temperatures, the observed data show a reduction of photosynthesis starting at 20 °C, whereas the literature-based parameterization barely showed a reduction in photosynthesis until 30 °C was reached. For the calibrated model version, the reduction curve showed a steep slope at 0 °C, attained its highest values between 3 °C and 20 °C and reached zero at 30 °C. The solid black line shows the best fit of the bell-shaped curve (Eq. 4) through filtered EC-data.

We further analyzed the relationships between the PPFD and productivity, temperature and respiration, as well as the soil water and productivity (see Additional file 1 and Table 1 for the derived filter-based parameter values).

Simulating carbon fluxes at daily and yearly time scales

We analyzed the overall model performance for three parameterizations at the daily scale (Table 3, Fig. 2) and the annual scale (Fig. 3). At the Wetzstein site, the forest model performed best for the numerical calibration. This performance is not surprising since the calibration method aims for the least error (Lehmann and Huth 2015). In any case, it is satisfying that we found a parameter combination that reproduces the observations with such good performance at the daily and annual time scales. This shows that the simplifications assumed in this forest model are sufficient to reproduce the complex interactions of climate and ecosystem fluxes even with the literature-based model version (M1). By comparison, LPJ-Guess simulated daily GPP with a similar performance (RMSE of 6.50–8.94 tC∙ha⁻¹∙a⁻¹ and R ² of 0.62–0.72) for a pine stand in the Netherlands in a similar study (the range results from different model setups, Vermeulen et al. 2015).

Simulated respiration shows a stronger bias than GPP. The deviation from the observed data can be explained in several ways. On the one hand, respiration is strongly coupled to GPP in the forest model. Consequently, strong GPP fluctuations induce strong fluctuations in respiration which is also seen at Tharandt. On the other hand, observed respiration shows a rather smooth curve (Fig. 1b), which is a consequence of the flux-partitioning method that derives respiration from the measured NEE (Reichstein et al. 2005). Respiration data thus arise from a modeling approach. The forest model additionally uses a simplified soil module (as in SEIB-DGVM, Sato et al. 2007). Some of the rhizosphere processes are neglected, such as the release of organic compounds by roots (Nguyen 2009). Rhizomicrobial respiration might have effects on short-term CO₂ efflux but should have no effect on the long-term carbon stock in the soil (Kuzyakov 2006). Also, note that different forest histories, such as different forest management at Wetzstein and Tharandt, might thus lead to different soil pools and respiration rates. The fact that the soil carbon pool of the forest model was initialized with a soil pool in a steady state might lead to an overestimation of ecosystem respiration at Tharandt.

The simulation results of Tharandt after the dry year 2003 show that the filter-based version (M3) reproduced the drought and heat event of 2003 better than the calibrated version (M2). Hence, parameter values of individual processes of the filter-based version (M3) might be more appropriate than the calibrated ones (M2) although the overall performance of M2 is better than the performance of M3 (Table 3). This might indicate that the numerical calibration compensates individual processes of extreme events to achieve an overall best performance throughout all simulation years while the filter-based version aims for the best parameterization of individual processes.

The overall performance of all parameterizations let us conclude that carbon fluxes of forest ecosystems can also be modeled with individual-based models. The characteristic of simulating each individual tree has the advantage to investigate in plant-population dynamics, forest structure and their interaction with carbon dynamics in future studies.

Analyzing limiting factors for productivity with the help of EC data

To test whether the parameter values (M1, M2) correctly describe the limiting factors of photosynthesis and respiration in the forest model, we filtered the EC data. The filtering singled out time steps that are mainly influenced by a single constraint such as temperature or water stress. This approach resulted in an additional parameterization of the forest model for which the functional relations between the variable climate and model processes were directly fitted through the filtered data (M3). As an example, we here discuss the relationship between temperature and productivity. The other relationships are discussed in detail in the Additional file 1.

The relationship between the measured GPP and temperature (Fig. 4) showed that the literature-based parameterization, which was validated for long-term simulations (Bohn et al. 2014), underestimated GPP for low and overestimated it for high temperatures. The function was taken from the LPJ model (Sitch et al. 2003). In LPJ, the function was applied as a “bulk” temperature-response function for different plant functional types in temperate forests to reproduce the current vegetation distribution (Stephan Sitch, personal communication). In FORMIND, this function seems to be sufficient to estimate the current mean carbon budgets from long-term simulations (Bohn et al. 2014), but the model version is not able to display inter-annual changes correctly. A similar study that tested the temperature-response curve in LPJ-Guess in a pine stand concluded that the curve needs to be shifted to lower temperatures (Vermeulen et al. 2015). This finding also agrees with the fact that trees can photosynthesize down to a temperature of about −5 °C (root zone temperature), while growth seems to stop at approximately 0 °C (Körner and Paulsen 2004). The numerical calibration experiment also shows that shifting the curve towards lower temperatures results in a better fit to the observed data. The EC data indicate photosynthetic activity down to about −10 °C. This is plausible considering that the air temperature is generally lower than temperature in the root zone during winter. In addition, the trees at the Wetzstein site are adapted to low temperatures and cold winter conditions due to the elevation. Note, that positive ecosystem GPP does not necessarily implicate tree growth since respiration compensates for GPP at low temperatures and low PPFD in the forest model.

GPP was not limited due to high temperatures with the literature-based parameterization (M1). High temperatures might go along with a vapor pressure deficit limitation (Körner 1994; Lasslop et al. 2010), which is not considered in our model approach. This assumption is supported by the results of the numerical calibration (the limiting factor is 0 at 31.6 °C). This reduction in temperature might compensate for the missing vapor pressure deficit limitation.

Since the original reduction curve did not fit the filtered data, we introduced a new functional relationship for the temperature reduction factor (Eq. 4, methods). The new curve originates from a normal distribution that describes the temperature dependence of the photosynthetic electron transport rate (June et al. 2004). A completely normal distribution (n = 2) led to a very small plateau in the temperature reduction function, which means a small range of optimal temperature conditions. n = 4 led to a much wider range of optimal conditions. An advantage of the introduced function is that it uses only two instead of four parameters. We therefore suggest using the less complex bell-shaped curve for future studies.

The fact that the original temperature curve could not be fitted through filtered data properly supports the assumption that a pure calibration against ecosystem fluxes does not necessarily result in optimal parameter values of the individual model processes. We can conclude that eddy covariance data and the filtering-approach can give important insights into the correct parameterization of model processes (the limiting factors).

Sources of uncertainty

This study comes with a variety of uncertainties from various sources that must be considered. The first source of uncertainty comes from the EC data. NEE is measured at a half-hourly scale. However, it comes with data gaps that are filled to compare the observed data with the simulated data at a daily time scale. The gap-filled NEE is based on a modeling procedure (Reichstein et al. 2005). At the Tharandt site, for example, the uncertainty of the gap filling methods is up to 10% (Grünwald and Bernhofer 2007). In addition, GPP and respiration are not directly measured, but are partitioned from the NEE, which is based on another modeling procedure (Reichstein et al. 2005). When we analyzed the drought event of 2003 at Tharandt, we found that GPP was 1.87 tC∙ha⁻¹ less than in the previous year. A multi-site study on the event in 2003 reported a reduction of 2.08 tC∙ha⁻¹ at Tharandt (Ciais et al. 2005). These deviations demonstrate the uncertainties implied by gap filling and the partitioning of EC data, especially at the annual time scale.

The second potential source of uncertainties comes from the filtering method and the concept of limiting factors. The forest model, and thus also the filtering method, consider only temperature and water as limiting factors. The vapor pressure deficit and its influence on productivity (as in BIOME-BGC, Kimball et al. 1997; 3PG, Landsberg and Waring 1997), for example, is not considered. However, we still assume that the filtered data are reasonable for singling out different constraints in forest productivity.