The study sites
This study focused on a forest site located at Wetzstein Mountain, part of the Thuringian Forest in central-east Germany where measured carbon fluxes and inventory data are available (Wetzstein flux tower, Rebmann et al. 2010). Observed carbon fluxes were derived with the eddy covariance (EC) method, a technique that observes the local carbon flux dynamics of the vegetation and monitors inter-annual changes (Aubinet et al. 1999). The Wetzstein forest is dominated by even-aged Norway spruce (Picea abies) stands on clay loam. In addition, we analyzed another Norway spruce stand at Tharandt, a study site in the Ore Mountains in Germany where EC-data were available (Tharandt Anchor station, Grünwald and Bernhofer 2007). The stand characteristics of both sites are summarized in Table 1.
Table 1 Site characteristics for Wetzstein (Rebmann et al. 2010; Martina Mundt, personal communication) and Tharandt (Grünwald and Bernhofer 2007)
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.
Gross primary production
Photosynthesis is calculated at the leaf level using a light-response function and is then integrated over the entire canopy (Thornley and Johnson 1990). The GPP of an individual tree under optimal climatic conditions (Huth and Ditzer 2000) equals
$$ {\mathrm{GPP}}_{\mathrm{ptree}}\left({I}_{\mathrm{ind}}\left(\mathrm{PPFD}(t)\right)\right)=\frac{p_{\max }}{k} \ln \left\{\frac{\alpha k{I}_{\mathrm{ind}}\left(\mathrm{PPFD}(t)\right)+{p}_{\max}\left[1- m\right]}{\alpha k{I}_{\mathrm{ind}}\left(\mathrm{PPFD}(t)\right){e}^{- kLAI}+{p}_{\max}\left[1- m\right]}\right\}{A}_c\psi $$
(1)
in μmol (CO2)∙m−2∙s−1, where p
max (μmol (CO2)∙m−2∙s−1) is the maximum photosynthetic rate of the tree species (here, spruce), α is the initial slope of the light-response curve (μmol (CO2)∙μmol (photons) –1), k is the light extinction factor, and m is the transmission coefficient of the leaves. I
ind is the fraction of the PPFD at daily time step t that reaches the top of the individual tree. A
c
(m2) is the crown area, and ψ (s) the photosynthetically active period of the time scale. Under non-optimal climatic conditions, GPP
ptree
is limited by the available soil water (SW) and temperature (T) (Bohn et al. 2014):
$$ {\mathrm{GPP}}_{\mathrm{tree}}(t) = {\mathrm{GPP}}_{\mathrm{ptree}}(t)\cdot {\varphi}_{SW}(t)\cdot {\varphi}_T(t), $$
(2)
where φ
SW
is the water reduction factor ([0, 1]), and φ
T
the temperature reduction factor ([0, 1]).
The temperature reduction factor φ
T
is derived from the LPJ-model (Sitch et al. 2003) which includes two ramp functions (Gutiérrez et al. 2012):
$$ {\varphi}_T(t)={\left(1+{e}^{\frac{2 \ln \left(\frac{0.01}{0.99}\right)}{T_{C{ O}_2, l}-{T}_{cold}}\left(0.5\left({T}_{C{ O}_2, l}+{T}_{cold}\right)- T(t)\right)}\right)}^{-1}\cdot \left(1-0.01\ {e}^{\frac{ \ln \left(\frac{0.99}{0.01}\right)}{T_{C{ O}_2, h}-{T}_{hot}}\left( T(t)-{T}_{hot}\right)}\right), $$
(3)
where T (°C) is the daily mean air temperature at time step t. \( {T}_{{\mathrm{CO}}_2, h} \), \( {T}_{{\mathrm{CO}}_2, l} \), T
cold and T
hot (°C) are species-specific parameters representing the higher and lower temperature limits for CO2 assimilation and the monthly mean air temperatures of the warmest and coldest months when production can still occur.
In this study, we also tested a new temperature reduction curve φ
T
*. It is distributed around the optimal temperature for photosynthesis T
opt (°C) and the width T
sig (°C) (June et al. 2004, reduction of the electron transport rate with n = 2) since Eq. 3 could not be properly fitted to the observed data. We suggest fitting this bell-shaped curve because it only relies on two parameters instead of four parameters (Eq. 3):
$$ {\varphi}_T\ast (t)={e}^{-{\left(\frac{T(t)-{T}_{opt}}{T_{sig}}\right)}^n}. $$
(4)
We use a water reduction factor, φ
SW
, as proposed by Granier et al. (1999):
$$ {\varphi}_{S W}(t) = \left\{\begin{array}{cc}\hfill 0\hfill & \hfill : SW(t)< S{W}_{\mathrm{pwp}}\hfill \\ {}\hfill \frac{ S W(t)- S{W}_{\mathrm{pwp}}}{S{W}_{\mathrm{msw}}- S{W}_{\mathrm{pwp}}}\hfill & \hfill :\ S{W}_{\mathrm{pwp}}< S W(t)< S{W}_{\mathrm{msw},}\hfill \\ {}\hfill 1\ \hfill & \hfill : SW(t) > S{W}_{\mathrm{msw}}\hfill \end{array}\ \right. $$
(5)
where SW
pwp is the permanent wilting point, SW
msw = SW
pwp + 0.4(SW
fc − SW
pwp) is the minimum soil water content for maximum photosynthesis, and SW
fc is the field capacity. Available soil water is calculated from the daily precipitation, interception by leaves, above- and below-ground water runoff, and transpiration of trees (Fischer et al. 2014).
Respiration
The respiration of a tree is the sum of its maintenance respiration, R
m
, and its growth respiration, R
g
, a constant fraction of (GPP-R
m
). The maintenance respiration is calculated as follows:
$$ {R}_m(t) = {R}_b(t)\kappa \left( T(t)\right), $$
(6)
where R
b
is a base respiration, a fraction of standing biomass of the tree (Bohn et al. 2014, detailed description in supplementary information A3). κ(T) describes the influence of the daily mean air temperature T on respiration (Prentice et al. 1993):
$$ \kappa \left( T(t)\right)={Q_{10}}^{{}^{\frac{T(t)-{T}_{ref}}{10}}}, $$
(7)
with constants T
ref
and Q
10 (Bohn et al. 2014).
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
The forest model was run with daily time steps for three different parameterizations: literature-based (M1), numerically calibrated (M2) and filter-based (M3) parameterizations (Table 2). The literature-based parameterization (M1) is based on Bohn et al. (2014) for a spruce forest where the parameter values are derived from inventory data and the literature. The soil parameter values were adapted to the clay loam soil type as in Maidment (1993). The calibrated parameterization (M2) is based on parameters derived from a numerical calibration against the NEE, GPP and respiration data (Lehmann and Huth 2015, see Additional file 1 for details). The filter-based parameterization (M3) arose from filtering the EC data (same data as used for calibration of M2) for optimal climatic conditions (see Field data and data filtering) to isolate individual processes. Model functions were directly fitted through filtered data to derive new parameter values and a new temperature reduction curve (Eq. 4).
Table 2 Model parameter values for the literature-based (M1) with references (ref.), calibrated (M2) and filter-based (M3) model version
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.