Global Change Biology (2006) 12, 1658–1669, doi: 10.1111/j.1365-2486.2006.01211.x
Evaluating the self-initialization procedure for large-scale ecosystem models S T E P H A N A . P I E T S C H and H U B E R T H A S E N A U E R Institute of Forest Growth Research, University of Natural Resources and Applied Life Sciences, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria
Abstract Self-initialization routines generate starting values for large-scale ecosystem model applications which are needed to model transient behaviour. In this paper we evaluate the self-initialization procedure of a large-scale BGC-model for biological realism by comparing model predictions with observations from the central European virgin forest reserve Rothwald, a category I IUCN wilderness area. Results indicate that standard selfinitialization towards a ‘steady state’ produces biased and inconsistent predictions resulting in systematically overestimated C and N pools vs. observations. We investigate the detected inconsistent predictions and use results to improve the self-initialization routine by developing a dynamic mortality model which addresses natural forest dynamics with higher mortality rates during senescence and regeneration vs. lower mortality rates during the period of optimum forest growth between regeneration and senescence. Running self-initialization with this new dynamic mortality model resulted in consistent and unbiased model predictions compared with field observations. Keywords: BGC-models, Fagus sylvatica, mortality, self-initialization, steady state
Received 17 November 2005; revised version received 16 March 2006; accepted 28 March 2006
Introduction The estimation of stocks and fluxes of carbon, water and energy between terrestrial ecosystems and the atmosphere is an important research topic. Therefore, several studies use ecosystem models to assess potential impacts of climate change and changes in land use or management practises. Typical models to be used are ORCHIDEE (Krinner et al., 2005), LPJ (Sitch et al., 2003), MC1 (Bachelet et al., 2001), BIOME-BGC (Thornton, 1998), IBIS (Foley et al., 1996), or SDGVM (Woodward et al., 1995). In such models, state and flux variable changes are modelled explicitly. Although time steps may differ, the general algorithm is classical recursion where the sizes of different pools are changed by fluxes during each simulated time step. The size of any given pool depends on (i) its former state and (ii) the balance between influx and outflux. The general production formula of such models can be written as YTnþ1 ¼ fðYTn ; Tnþ1 ; a; sÞ; Correspondence: Stephan Pietsch, tel. 1 43 1 47654 4249, fax 1 43-1-47654-4242, e-mail:
[email protected]
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ð1Þ
where YTnþ1 is the set of pool sizes at time Tn 1 1, YTn the set of pool sizes one recursion step earlier, jTnþ1 the set of model drivers forcing the changes from YTn to YTnþ1 , a the model parameter set encapsulating specific properties of the modelled ecosystem, s the set of physical site properties, and f the functional algorithm of the model implementation. The modelled state of an ecosystem at a time Tn 1 1 depends on its state at time Tn, and so forth: YTnþ1
Y Tn
YTn1
...
Y T1
Y T0
ð2Þ
Accordingly, any YTn depends on the values of state at time T0 (i.e. the initial conditions). For individual plots the starting values of state variables may be available from measurements, for largescale applications this information is not commonly available. Thus, self-initialization procedures, which generate initial conditions for different combinations of vegetation and climate, were developed to overcome this limitation. During self-initialization, a set of climate records is used repeatedly to run the model until each model output converges towards a steady state. In LPJ (Sitch et al., 2003) and ORCHIDEE (Krinner et al., 2005) the slow equilibration of the soil organic matter pool is shortcut by analytically solving differential equations r 2006 The Authors Journal compilation r 2006 Blackwell Publishing Ltd
E VA L U A T I N G S E L F - I N I T I A L I Z A T I O N relating input of litter to soil carbon pool size. In MC1 (Bachelet et al., 2001) or BIOME-BGC (Thornton et al., 2002) such analytical solutions are impossible because nutrient cycling is explicitly included. The steady state reached at the end of self-initialization is interpreted as the ‘temporally averaged state of an undisturbed ecosystem for a region large enough to encompass all its natural development stages’ (Law et al., 2001). This situation is also described as the ‘dynamic equilibrium in net ecosystem carbon exchange with variable ecosystem age classes’ (Bachelet et al., 2004). Although this interpretation is theoretically reasonable, a practical comparison with observed field data representing such undisturbed ecosystems is still missing. Among real-world ecosystems, virgin forests resemble the best representation of natural conditions. Such forests are traditionally referred to as the climax stage (Clements, 1916) of an ecosystem. The concept of climax (i.e. a stable community condition) has changed since ecologists began to describe climax vegetation as ‘varying continuously across a continuously varying landscape’ (Spies, 1997). Today it is widely accepted that periodic declines of single stands are a normal part of the forest life cycle from regeneration through the juvenile stage and then via maturity and senescence to stand breakdown. On larger scales, a mosaic of different stages shifts over time, but the abundance of all stages remains constant if the area is large enough (Heinselman, 1973). The ‘mosaic cycle’ concept of ecosystems (Remmert, 1991) assumes the maintenance of an overall steady state at the landscape level with local disequilibria due to vegetation dynamics. This concept suggests that data from a virgin forest, covering the full range of successional variability, will represent a mosaic cycle. The mean value for all different stages will then represent the steady state at the landscape level. This steady state should be comparable with the modelled steady state of the selfinitialization process as it is used in large-scale ecosystem models. The purpose of this paper is to test this hypothesis by comparing the results of the self-initialization procedure within the BIOME-BGC model (Thornton, 1998), recently adapted for central European conditions (Pietsch et al., 2005), with field observations from a set of plots located in Rothwald, a virgin forest reserve in Austria. This reserve has a documented absence of logging and forest management for more than 700 years and is one of the last virgin forest areas in the Alps. The specific goals of this study are to: 1. compare results from the model self-initialization with observations on soil, necromass (litter, standing dead and dead and down trees) and stem carbon
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using a set of 18 virgin forest plots covering different successional stages; 2. analyse possible deviations between model results and observations according to key ecosystem processes; 3. enhance the self-initialization within large-scale ecosystem models according to the results of step 2.
Methods
The model For this study BIOME-BGC (Thornton, 1998), including extensions related to species representation and hydrology (Pietsch et al., 2003, 2005), is used. The model simulates, for each day, the cycling of energy, water, carbon and nitrogen within a given ecosystem. Model inputs include meteorological data, such as daily minimum and maximum temperature, incident solar radiation, vapour pressure deficit and precipitation. Aspect, elevation, nitrogen deposition and fixation, and physical soil properties are needed to calculate: daily canopy interception, evaporation and transpiration; soil evaporation, outflow, water potential and water content; leaf area index (LAI); stomatal conductance and assimilation of sun-lit and shaded canopy fractions; growth, maintenance and heterotrophic respiration; gross primary production (GPP) and net primary production (NPP); allocation; litter-fall and decomposition; mineralization, denitrification, leaching and volatile nitrogen losses. In the model, total ecosystem carbon storage is governed by the balance between NPP and heterotrophic respiration (Rh). Rh is regulated by decomposition activity, the seasonal input of vegetation biomass into litter and soil organic matter pools, and the annual mortality rate, which is commonly set to 0.5% of vegetation biomass (see e.g. White et al., 2000). Mortality, thereby, links living biomass with litter and soil organic matter and influences total ecosystem carbon content. Model runs within this study are performed using the species specific parameter set for Common beech (Pietsch et al., 2005).
Model self-initialization The goal of model self-initialization is to achieve a steady state in the temporal averages of all ecosystem pools. The time scale for averaging is 50 years or the number of years with available climate data (e.g. 43 years in our case). A self-initialization simulation is started with a low carbon content in the leaf pool (e.g. 1 g m2) and a certain soil water saturation (e.g. 50% v/v). All other ecosystem pools are set equal to zero. With continuous simulation the different
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Soil carbon content
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c
Steady state
c ∆c
Averaging windows c
∆c
2001 the preserve area Rothwald was declared a wilderness area (IUCN category I). The reasons for the absence of any management activity over the past seven centuries are the remoteness of the area and the topography of the surrounding terrain making timber extraction commercially unprofitable (Splechtna & Gratzer, 2005).
Field data
c Simulation years Fig. 1 Scheme of the soil carbon accumulation during selfinitialization. The cn’s represent the averaging windows and Dcn,n 1 1 the difference between two successive averaging windows. When the difference is below a certain threshold, e.g. 0.5 g C m2 self-initialization is terminated.
ecosystem pools gain mass until their temporal average reaches a steady state. A sketch of this procedure (Fig. 1) indicates that the series of mean soil carbon contents (cn) converges towards a limit. At the same time, the difference Dcn,n 1 1 between two successive mean soil carbon values converges towards zero resembling a steady state. The self-initialization procedure is terminated when the mean soil carbon content (i.e. the last pool to reach a steady state) does not change by more than 0.5 g m2 between two successive simulation periods of 50 years. The time scale to reach this steady state is 3000–60 000 simulation years, depending on ecosystem type as well as site and climate conditions.
Data
Site description Field data came from the central European virgin forest reserve Rothwald, located in the northern limestone alps at 15105 0 E and 47146 0 N at an elevation between 950 and 1300 m a.s.l. Parent rock is limestone and dolomite, soil types range from lithic and rendzic leptosols to chronic cambisols. Mean annual temperature is about 7 1C and mean annual precipitation 1300 mm. Living biomass is comprised of 68% Common beech (Fagus sylvatica L.), and admixture of Norway spruce (Picea abies L./Karst.) and silver fir (Abies alba Mill.). The documented history of the forest reserve starts in 1330, when Albrecht II Habsburg founded the charterhouse Gaming and endowed the area of Rothwald to the contemplative fraternity of the Carthusians. After the charterhouse was abolished in 1782 by Joseph II Habsburg the forest changed owners a couple of times until it became part of the Rothschild estate in 1875. In
The virgin forest reserve Rothwald covers about 250 ha of unmanaged forest with different successional stages from regeneration to optimal and breakdown phases. For our analysis we established 18 permanent field plots across all successional stages to cover the mean average conditions or ‘dynamic equilibrium’ as it is represented by the Rothwald nature reserve. On each 20 20 m2 sample plot the height, diameter at breast height and species were recorded for all standing (dead and alive) trees with height 41.3 m. Lying dead trees were measured for volume, with decay class determined according to Maser et al. (1979). Litter and soil samples were drawn in 9 parallels per plot with a 30 30 cm2 frame (litter) and a soil auger (70 mm diameter, 50 cm depth). Soil samples were additionally subdivided by horizon. Litter and soil samples were deep frozen on site and analysed for carbon content in the lab using an infrared gas analyser (LECO S/C 444, Mo¨nchengladbach, Germany.). Table 1 gives the range of site, stand and soil characteristics for the 18 plots.
Climate data Daily minimum and maximum temperature, precipitation, short wave radiation and vapour pressure deficit data necessary for running the model were interpolated using the point version of DAYMET (Petritsch, 2002) recently validated for Austria (Hasenauer et al., 2003). Climate data for running DAYMET were provided by the Austrian National Weather Center in Vienna and include daily weather data for up to 250 stations covering the years 1960–2002.
Analyses and results For each of the 18 plots self-initialization was run with preindustrial CO2-concentration (280 ppm, IPCC WGI, 1996) and nitrogen deposition (0.0001 kg m2 yr1, Holland et al., 1999). After a steady state for soil carbon was reached another 237 years were simulated to account for the increase in CO2-concentration between the years 1765 and 2002 (IPCC WGI, 1996). Nitrogen deposition was annually increased from preindustrial to present day level (Table 1), according to the relative
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E VA L U A T I N G S E L F - I N I T I A L I Z A T I O N Table 1 Summary statistics (mean and standard deviation) of the 18 plots in the virgin forest. SDI is a measure of stand density which is independent of site index and stand age (Reinecke, 1933) Characteristics
Rothwald (n 5 18)
Longitude (1, 0 ) Latitude (1, 0 ) Elevation (m) Slope (1) Aspect Sand% Silt% Clay% Effective soil depth (m) Maximum temperature ( 1C) Minimum temperature ( 1C) Annual precipitation (mm) Vapour pressure deficit (Pa) Short wave radiation (W m2 s1) Annual nitrogen deposition (g m2) Volume (m3 ha1) Mean tree height (m) Mean diameter at breast height (mm) SDI Soil C (t ha1) Necromass C (t ha1) Stem C (t ha1) Sum C (t ha1)
15105 0 –15106 0 E 47146 0 –47147 0 N 1017–1216 0–30 E, SE, S, NW 23 8 33 4 44 10 0.39 0.10 12.5 9.0 3.0 7.1 1575 233 543 408 231 120 1.60 559 280 25.7 8.3 446 166 984 329 83 31 96 21 138 69 316 83
annual increment in CO2-concentration. Daily weather records from 1960 to 2002 were used repeatedly for selfinitialization with the last 43 year cycle covering the period from 1960 to 2002. The repeated use of climate records was considered to be acceptable since the variation of mean annual temperature among the 18 plots was 1.5 1C, which exceeds the difference in mean annual temperature between the period from 1960 to 2002 and the period from 1500 to 1900, which we estimated as 1 0.75 1C from data presented for Europe by Luterbacher et al. (2004).
Results of the current model The results of the self-initialization procedure may be considered to represent the dynamic equilibrium of a given ecosystem (Law et al., 2001; Sitch et al., 2003; Bachelet et al., 2004; Krinner et al., 2005). Therefore, model outputs should be within the variation range of state variables measured in our sample of virgin forest plots, which is representative for the range of development stages and their relative abundances at the landscape level. Based on this assumption we compared model results with observations on soil, necromass and stem carbon content assuming an annual mortality rate
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of 0.5% of vegetation biomass. The results (Fig. 2a) indicated a discrepancy between predictions and observations, resulting in an overestimation of total carbon stocks by about 400%. These results were achieved with an annual mortality of 0.5% of vegetation biomass, which was used in a number of studies on managed forest stands (Pietsch & Hasenauer, 2002; Thornton et al., 2002; Churkina et al., 2003; Pietsch et al., 2003; Merganicova et al., 2005). In unmanaged forests like Rothwald, a higher mortality rate is to be expected, because over-aged or ill individuals remain in the forest, and – once dead – these individuals fall on and damage or kill surrounding trees. Bond-Lamberty et al. (2005) used a higher annual mortality rate of 1.0% of vegetation biomass to model black spruce stands including stands in the old growth stage. Next, we successively increased annual mortality rate to account for the expected higher mortality rates due to the lack of management. At 3% annual mortality rate (Fig. 2b) predictions on stem carbon were unbiased but modelled necromass (litter, standing dead and dead and down trees) and especially soil carbon remained overestimated by 34% and 98%, respectively, resulting in an overestimation of total carbon stocks. We tried to achieve agreement with data by increasing the rate constants of decomposition turnover to reduce necromass and soil carbon. Increased decomposition, however, resulted in an increase in the proportion of recalcitrant soil carbon from 83% to 96% of total soil carbon and a massive reduction in labile soil carbon. The achieved reduction of total soil carbon was less then 15% and hence insufficient to explain overestimation by the model. With higher mortality rates stem carbon was underestimated but necromass and soil carbon remained overestimated (Fig. 2c). Neither low nor high (Fig. 2) constant mortality rates resulted in unbiased and consistent model results vs. observations. This suggests that the assumed constant mortality rate may be inconsistent or ill defined if we want to mimic the flux of energy, water, carbon and nitrogen in virgin forest ecosystems. Studies on the temporal development of mortality rates in managed forests revealed that mortality rate follows a U- or Jshape vs. stand age (see e.g. Harcomb, 1987; Peterken, 1996; Lorimer et al., 2001; Monserud & Sterba, 2001). Mortality rate obviously decreases from regeneration via juvenescence and reaches a minimum during the optimum phase of stand development. Later, mortality increases again towards the old growth and breakdown stages. These temporal dynamics in mortality rate suggest the development of a new dynamic mortality model.
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(b)
Fig. 3 Trajectory of mortality (bold line) along the lower half (a) and upper half (b) of two individually ellipses (dotted lines). C(cx/cy) are the coordinates of the ellipses centres, a and b the two half axis.
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and y the mortality rate. Solving this quadratic equation for y gives qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b ð4Þ a2 x2 þ 2xcx c2x : y ¼ cy a
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The semiaxis a, b and the centre coordinates cx, cy of the ellipse can be expressed as L ð5Þ a ¼ cx ¼ ; 2
800 400 200
m
b¼
Su
St em s
So il N ec ro m as s
0
Fig. 2 Predicted vs. observed C contents of soil, necromass, stems and their sum assuming 0.5% (a) and 3.0% (b) annual mortality of vegetation biomass. Boxes give the median, the 25% and 75% percentiles, the whiskers the 10th and 90th percentiles of predictions and observations. Note the different scales of (a) and (b).
The dynamic mortality model For developing a new dynamic mortality model we assume the U-shaped mortality development from juvenile to over aged stands. Because the death of old trees creates space for regeneration, the two ends of the ‘U’-shape overlap. Hence, we constructed an elliptic trajectory for mortality, consisting of two half ellipses (Fig. 3a,b), which can be scaled individually. Formally, both ellipses are given by 2
ðx cx Þ2 ðy cy Þ þ ¼ 1; a2 b2
ð3Þ
where cx, cy are the x and y coordinates of the centre of the respective ellipse, a, b the two semiaxis, x is the time
mortmax mortmin ; 2
cy ¼ b þ mortmin ¼
mortmax þ mortmin 2
ð6Þ
ð7Þ
with L the length of the low or high mortality phases (cf. Fig. 3), mortmax and mortmin the maximum and minimum mortality rates. Substitution of Eqns (5)–(7) into Eqn (4) gives mortmax þ mortmin y¼ 2 mortmax mortmin pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi Lx x : ð8Þ L In Eqn (8) the first right-hand term equals the mean annual mortality rate. The second right-hand term governs the changes along the mortality cycle. Subtraction gives the trajectory of the low mortality phase (Fig. 3a) and addition the trajectory of the high mortality phase (Fig. 3b). In the model implementation1 we added new entries to the model parameter set giving maximum and minimum mortality rate and the length of the low and high 1
Code and implementation available upon request (stephan.
[email protected])
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E VA L U A T I N G S E L F - I N I T I A L I Z A T I O N mortality phases. This allows for flexible scaling of high and low mortality phases as they may differ by ecosystem.
Model self-initialization with dynamic mortality The nonlinear long-term variations in mortality are addressed by increasing the averaging window shown in Fig. 1 to the full length of the mortality cycle (cf. Fig. 3). The end point of the self-initialization procedure is then always at the end of a full mortality cycle and reflects a single stage in natural stand development. We performed 30 additional model runs per plot each stopping at an arbitrary point during the mortality cycle to eliminate this effect. The resulting Monte-Carlo set of 540 modelled stand development stages is representative for (i) the variation in modelled C pool sizes along the temporal sequence of annual mortality rates and (ii) the site and climate variation between the 18 plots. All simulation runs were performed identically to the previous runs except that dynamic mortality was used for self-initialization and the period 1765–2002. The time to reach a steady state of temporal averages for our plots was 3000–15 000 simulation years.
Parameterization of the dynamic mortality model For Rothwald we chose 300 years as length for the complete mortality cycle (i.e. the low mortality phase (Fig. 3a) plus the high mortality phase (Fig. 3b)), because from this age class onward the number of trees per hectare decreases (Splechtna & Gratzer, 2005). From this period, we attributed 225 years to the low and 75 years to the high mortality phase. This resulted in a phase of modelled low carbon content in the living biomass (cf. Fig. 8b) which lasts about 40 years or 13% of the total cycle length. This is in agreement to the gap fraction reported for the virgin forest reserve (1991: 12.3%; 1996: 13.8%; Splechtna & Gratzer, 2005). Minimum and maximum mortality rate were parameterized by testing an array of different combinations ranging from 0.5% to 2.5% minimum vs. 0.5% to 15% maximum mortality of vegetation biomass per year. Considering that this gives 4100 combinations to be tested for 540 model runs over thousands of years, we selected the plot with the maximum and minimum simulated carbon content. For these two plots we chose a MonteCarlo set of 30 different stages along the mortality cycle. This gave a set of 60 model self-initialization runs, which we simulated under 160 different mortality combinations, resulting in 9600 simulations and 4100 000 000 years of daily simulation results. From the set of 60 model results we plotted the median, the 0.1 and the 0.9 percentiles for all 160
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mortality combinations in a three-dimensional graph. Figure 4a gives the modelled results for soil carbon and the median, 0.1 and 0.9 percentiles of the observations from all 18 plots. We connected the median values and percentiles with a coloured grid to show model behaviour across the 160 different mortality combinations. The results for necromass and stem carbon are given in Fig. 4b, c, respectively. For simplicity of the figures we do not show the 0.9 (Fig. 4b) and 0.1 (Fig. 4c) percentiles. For total carbon content the 0.1 percentiles, the medians and the 0.9 percentiles are given separately in Fig. 4d–f to illustrate that the regions, where predictions and observations were equal, occurred along different lines of minimum and maximum mortality combinations. At low mortality settings highly overestimated carbon contents and predicted model breakdown occurred within a small range of mortality combinations (Fig. 4e) indicating instable model behaviour, a feature recently discussed by Pietsch & Hasenauer (2005). Next, we calculated areas within the array of 160 mortality combinations, where predictions and observations differ by less than 33% from the observation. In Fig. 5a–c these areas are given in dark blue for the median, the 0.1 and the 0.9 percentiles of stem carbon. All three descriptors of the distribution were fitted to cover the full range of observed variation. When we overlay Fig. 5a–c an intersection of the dark blue areas remains (Fig. 5d). Within this area of mortality combinations, three characteristics of the distribution of the stem carbon predictions (median, 0.1 and 0.9 percentiles) differ by less than 33% from the observations. Figure 6 gives the same results for the intersections of soil (Fig. 6a), necromass (Fig. 6b) and total carbon (Fig. 6c). If we overlay all intersections (Figs 5d, 6a–c), a small intersecting plane around 0.9% minimum and 6.0% maximum mortality remains where predictions and observations deviate by less than 33% according to three descriptors of the distribution (i.e. the median, 0.1 and 0.9 percentiles) for all observed variables (Fig. 6d). The 33% difference was chosen because it resulted in the smallest overall intersecting plane.
Results of the dynamic mortality model With these mortality settings (0.9–6.0%; 225 years low, 75 years high mortality phase) we simulated all 18 plots using the Monte-Carlo approach (i.e. 30 arbitrarily chosen development stages per plot). Results exhibit the improvement in model predictions (Fig. 7) as compared with results with constant mortality (Fig. 2). A statistical evaluation of the model results for soil, necromass, stem and total carbon revealed no significant differences between predictions and observations (two-sided t-test with a 5 0.05, df 5 556; t 5 1.75, 0.23,
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1664 S . A . P I E T S C H & H . H A S E N A U E R Soil C 350
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0.5 2 4 1.0 6 x 8 1.5 i %) 1.5 mu ty ( y( m m 10 12 2.0 2.0 tali alit t r o r o r 14 2.5 tali m mo 2.5 Median predicted ty ( um um %) nim nim 0.1, 0.9 perc. pred. Mi Mi Median observed Stem C Sum C – 0.9 percentiles 0.1, 0.9 perc. obs.
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Fig. 4 (a–c) Three-dimensional representations of the modelled soil (a), necromass (b) and stem carbon (c) showing the 0.1 and 0.9 percentiles (dark red) and the median values (light red). Sixty self-initialization runs were performed with 160 different combinations of minimum and maximum mortality resulting in a total of 9600 self-initialization simulations equivalent to 4100 000 000 simulation years. The 0.1, the 0.9 percentile (dark grey) and the median values (light grey) of the observations are given for comparison. For clarity reasons the 0.9 percentile of predictions and observations were left out in (b) the respective 0.1 percentile in (c). (d–f) Intersections (dashed lines) between the 0.9 percentile (d), the medians (e) and the 0.1 percentile (f) of model predictions and field observations of total ecosystem carbon content. Note that figures (d–f) are rotated clockwise by 901 compared with figures (a–c) to view the instable region (dotted ellipse) occurring at low mortality rates.
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E VA L U A T I N G S E L F - I N I T I A L I Z A T I O N Stem C – 0.1 percentiles Absolute error (% of observed)
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2 < 233% < 200%
4 6 8 10 12 Maximum mortality (%) < 300%
< 267%
< 367% < 333%
14 < 433% < 400%
Fig. 5 (a–c) Projection of the differences between predictions and observations divided into 33% difference classes for the medians (a), the 0.1 percentile (b) and the 0.9 percentile (c) of stem carbon content. (d) Intersection resulting from overlaying (a–c).
0.85 and 1.02 for soil, necromass, stem and total carbon, all o tcrit 5 1.97). We compared the temporal development of modelled pool sizes and modelled fluxes to understand why different model results occur under constant and dynamic mortality. Figure 8 shows an example for a 300-year simulation run at steady state for one of our virgin forest plots using preindustrial CO2 and N-levels. With a constant mortality of 2.38% (i.e. the annual mean of the dynamic mortality cycle) small fluctuations in pool sizes resulted from the annual variation in daily climate input data (Fig. 8a). This variation is also evident in the carbon and nitrogen fluxes (Fig. 8c). NPP is balanced by heterotrophic respiration (Rh) which causes an average net ecosystem production (NEP) of zero. Using the dynamic mortality model the
pool sizes changed during a 300-year mortality cycle (Fig. 8b). These changes were caused by the different trajectories of NPP and Rh (Fig. 8d), whereby pronounced phases of positive and negative NEP and intermittent source/sink shifts are evident. The burst of nutrient release (Fig. 8d) indicates a periodic decline in stand nutrient status resulting in an accumulated nitrogen loss which was 8% higher compared with the simulation with constant 2.38% annual mortality (Fig. 8c).
Discussion Model self-initialization procedures used within largescale ecosystem models do not correspond to landscape level dynamic equilibria represented by virgin forests. With commonly used mortality settings (0.5% of
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1666 S . A . P I E T S C H & H . H A S E N A U E R Necromass C – intersection Absolute error (% of observed)
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Fig. 6 (a–c) Intersections of soil (a), necromass (b) and summed up carbon (c) constructed as depicted in Fig. 5 for stem carbon. (d) Intersection of the intersections given in Figs 5d, 6a–c.
C content (t ha–1)
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m Su
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Fig. 7 Predicted vs. observed C content of soil, necromass, stems and their sums using the dynamic mortality model during self-initialization. Boxes give the median, the 25th and 75th percentiles, the whiskers the 10th and 90th percentiles of predictions and observations.
vegetation biomass per year) ecosystem carbon content was overestimated by 400% and a continuous increase in annual mortality resulted in biased and inconsistent model predictions (Fig. 2). With constant mortality the modelled ecosystem carbon pools are kept at steady state (Fig. 8a) resulting in a NEP of zero (Fig. 8c), a phenomenon frequently reported and discussed in the literature (e.g. Ciais et al., 2005; Krinner et al., 2005). At maximum carbon carrying capacity, as evident with low mortality settings (cf. Figs 4–6), instable model behaviour (cf. Fig. 4e) occurred. This is equivalent to a decrease in model determinism and a reduction in predictive power (Pietsch & Hasenauer, 2005). We consider it unlikely that this stage may be reached by a natural ecosystem and suggest that such phases represent a stage of minimized resilience
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Fig. 8 Comparison of the temporal development of soil, necromass, stem and total modelled carbon for 300 simulation years at steady state with preindustrial CO2 concentration and nitrogen deposition. In (a) the results for a constant annual mortality of 2.38% of vegetation biomass are shown; (b) gives the development using the dynamic mortality routine ranging from 0.9% to 6.0% mortality of vegetation biomass per year, which equals a mean annual mortality of 2.38% (see (a)). In (c) the C-fluxes from heterotrophic respiration (Rh), net primary production (NPP), net ecosystem production (NEP), N-leaching and volatile N losses as simulated with constant 2.38% annual mortality are given for 300 years after the steady state was reached. (d) Depicts the same variables, but using the dynamic 0.9–6.0% annual mortality rate.
where small perturbations may lead to ecosystem breakdown (cf. Fig. 4e). Frequent disturbances maintain ecosystem productivity in natural ecosystem dynamics (White, 1979). The disturbance frequency defines the maximum carbon content a forested landscape may reach (Pickett & White, 1985) and that maximum carbon content is lower as predicted by commonly used self-initialization routines (Fig. 2a). The developed dynamic mortality model (Fig. 3) accounts for the different development stages of a forest including breakdown and recovery phases (Fig. 8b). Under dynamic mortality periodic bursts of nutrient release (Fig. 8d) lowered the average nutrient status and enabled unbiased conditions (Fig. 7). The resulting growth conditions are characterized by frequent reductions in total carbon content (Fig. 8b) and periodic declines in NPP during phases of maximum Rh (Fig. 8d). These regular source sink transitions restrict the ecosystem model to the resilient conditions resembled by the steady state of the mosaic cycle at the landscape level.
This should be addressed in self-initialization routines of large-scale ecosystem models, to avoid biased starting conditions for subsequent transient model runs like simulations of global change. If the modelled initial conditions do not correspond to reality, then the interpretation of model predictions on successive states and fluxes may be difficult, especially when instabilities in model determinism (cf. Fig. 4e) reduce the predictive power of modelled transients (Pietsch & Hasenauer, 2005). We suggest that dynamic mortality routines such as the one presented in this paper should be used for running model self-initializations for forested biomes to include effects resulting from the long term dynamics of regeneration, maturity and break down. For largescale applications a set of grid cells with the same vegetation type may be simulated using the MonteCarlo approach used in this study (i.e. to run the model to different, arbitrarily chosen development stages after steady state was reached). The resulting Monte-Carlo set of development stages represents a mosaic cycle of
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1668 S . A . P I E T S C H & H . H A S E N A U E R initial conditions and ensures unbiased and consistent starting values for large-scale applications.
Acknowledgements This work was supported by a Grant from the University of Natural Resources and Applied Life Sciences, the Austrian Ministry of Science and Education and the Austrian Ministry of Forest, Agriculture and Environment. Helpful review comments were provided by Bruce Michie and four anonymous reviewers.
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