evaluating the self-initialization procedure for large

Evaluating the self-initialization procedure for large-scaleecosystem 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 self-

initialization 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 atmo-

sphere is an important research topic. Therefore, several

studies use ecosystem models to assess potential im-

pacts 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

YTnþ1¼ fðYTn

;Tnþ1; a; sÞ; ð1Þ

where YTnþ1 is the set of pool sizes at time Tn 1 1, YTn the

set of pool sizes one recursion step earlier, jTnþ1the set

of model drivers forcing the changes from YTnto YTnþ1

,

a the model parameter set encapsulating specific prop-

erties 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 eco-

system at a time Tn 1 1 depends on its state at time Tn,

and so forth:

YTnþ1 YTn

YTn�1 . . . YT1

YT0ð2Þ

Accordingly, any YTndepends on the values of state

at time T0 (i.e. the initial conditions).

For individual plots the starting values of state vari-

ables may be available from measurements, for large-

scale 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 equationsCorrespondence: Stephan Pietsch, tel. 1 43 1 47654 4249,

fax 1 43-1-47654-4242, e-mail: [email protected]

Global Change Biology (2006) 12, 1658–1669, doi: 10.1111/j.1365-2486.2006.01211.x

r 2006 The Authors1658 Journal compilation r 2006 Blackwell Publishing Ltd

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 eco-

system 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 ecosys-

tem 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 resem-

ble 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 eco-

systems (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 self-

initialization process as it is used in large-scale ecosys-

tem models.

The purpose of this paper is to test this hypothesis by

comparing the results of the self-initialization proce-

dure 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

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 eco-

system 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 hydro-

logy (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 transpira-

tion; soil evaporation, outflow, water potential and

water content; leaf area index (LAI); stomatal conduc-

tance and assimilation of sun-lit and shaded canopy

fractions; growth, maintenance and heterotrophic re-

spiration; 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 gov-

erned by the balance between NPP and heterotrophic

respiration (Rh). Rh is regulated by decomposition ac-

tivity, 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 vege-

tation 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 m�2) 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

E VA L U AT I N G S E L F - I N I T I A L I Z AT I O N 1659

r 2006 The AuthorsJournal compilation r 2006 Blackwell Publishing Ltd, Global Change Biology, 12, 1658–1669

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 resem-

bling 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 m�2 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 151050E and 471460N at an elevation between

950 and 1300 m a.s.l. Parent rock is limestone and dolo-

mite, 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 charter-

house 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

2001 the preserve area Rothwald was declared a wild-

erness 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 topo-

graphy of the surrounding terrain making timber

extraction commercially unprofitable (Splechtna &

Gratzer, 2005).

Field data

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 mea-

sured for volume, with decay class determined accord-

ing 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, Monchengladbach,

Germany.). Table 1 gives the range of site, stand and

soil characteristics for the 18 plots.

Climate data

Daily minimum and maximum temperature, precipita-

tion, 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 cover-

ing 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 m�2 yr�1,

Holland et al., 1999). After a steady state for soil carbon

was reached another 237 years were simulated to ac-

count for the increase in CO2-concentration between the

years 1765 and 2002 (IPCC WGI, 1996). Nitrogen de-

position was annually increased from preindustrial to

present day level (Table 1), according to the relative

Soil

carb

on c

onte

nt

Steady state

Averaging windows

c

c

c c

∆c

∆c

Simulation years

Fig. 1 Scheme of the soil carbon accumulation during self-

initialization. The cn’s represent the averaging windows and

Dcn,n 1 1 the difference between two successive averaging win-

dows. When the difference is below a certain threshold, e.g.

0.5 g C m�2 self-initialization is terminated.

1660 S . A . P I E T S C H & H . H A S E N A U E R


annual increment in CO2-concentration. Daily weather

records from 1960 to 2002 were used repeatedly for self-

initialization 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 develop-

ment stages and their relative abundances at the land-

scape level. Based on this assumption we compared

model results with observations on soil, necromass and

stem carbon content assuming an annual mortality rate

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 indivi-

duals 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 necro-

mass 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 J-

shape 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 sug-

gest the development of a new dynamic mortality

model.

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) 151050–151060E

Latitude (1,0) 471460–471470N

Elevation (m) 1017–1216

Slope (1) 0–30

Aspect E, SE, S, NW

Sand% 23 � 8

Silt% 33 � 4

Clay% 44 � 10

Effective soil depth (m) 0.39 � 0.10

Maximum temperature ( 1C) 12.5 � 9.0

Minimum temperature ( 1C) 3.0 � 7.1

Annual precipitation (mm) 1575 � 233

Vapour pressure deficit (Pa) 543 � 408

Short wave radiation (W m�2 s�1) 231 � 120

Annual nitrogen deposition (g m�2) 1.60

Volume (m3 ha�1) 559 � 280

Mean tree height (m) 25.7 � 8.3

Mean diameter at breast height (mm) 446 � 166

SDI 984 � 329

Soil C (t ha�1) 83 � 31

Necromass C (t ha�1) 96 � 21

Stem C (t ha�1) 138 � 69

Sum C (t ha�1) 316 � 83



The dynamic mortality model

For developing a new dynamic mortality model we

assume the U-shaped mortality development from ju-

venile 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

ðx� cxÞ2

a2þðy� cyÞ2

b2¼ 1; 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

and y the mortality rate. Solving this quadratic equation

for y gives

y ¼ cy �b

a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 � x2 þ 2xcx � c2

x

q: ð4Þ

The semiaxis a, b and the centre coordinates cx, cy of

the ellipse can be expressed as

a ¼ cx ¼L

2; ð5Þ

b ¼ mortmax �mortmin

2; ð6Þ

cy ¼ bþmortmin ¼mortmax þmortmin

2ð7Þ

with L the length of the low or high mortality phases (cf.

Fig. 3), mortmax and mortmin the maximum and mini-

mum mortality rates. Substitution of Eqns (5)–(7) into

Eqn (4) gives

y ¼ mortmax þmortmin

2

�mortmax �mortmin

L

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLx� x2p

: ð8Þ

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. Subtrac-

tion gives the trajectory of the low mortality phase

(Fig. 3a) and addition the trajectory of the high mortal-

ity phase (Fig. 3b).

In the model implementation1 we added new entries

to the model parameter set giving maximum and mini-

mum mortality rate and the length of the low and high

Soil

Necro

mas

s

Stems

Sum

C c

onte

nt (

t ha

–1)

C c

onte

nt (

t ha

–1)

C c

onte

nt (

t ha

–1)

0

200

400

800

1 000 ObservedPredicted: 6.0% mortality

0

200

400

800

1000

Soil Necro

mas

s

Stems

Sum

0

200

400

800

1000

1200

ObservedPredicted: 3.0% mortality

ObservedPredicted: 0.5% mortality

(c)

(b)

(a)

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).

Maximummortality

Minimum mortality

Low mortality phaseL

Ann

ual m

orta

lity

rate

High mortality phase

a

b C (cx /cy)

C (cx /cy)

y y

a

b

x

(b)(a)

L

Simulation years

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.

1Code and implementation available upon request (stephan.

[email protected])



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 representa-

tive 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)), be-

cause 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). Mini-

mum 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 car-

bon content. For these two plots we chose a Monte-

Carlo 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

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 beha-

viour 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) percen-

tiles. 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 combina-

tions. At low mortality settings highly overestimated

carbon contents and predicted model breakdown oc-

curred 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 obser-

vations 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 combi-

nations, three characteristics of the distribution of the

stem carbon predictions (median, 0.1 and 0.9 percen-

tiles) 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 signifi-

cant differences between predictions and observations

(two-sided t-test with a5 0.05, df 5 556; t 5 1.75, 0.23,



Soil C Necromass C

Median predicted0.1, 0.9 perc. pred.Median observed0.1, 0.9 perc. obs.

0

200

400

600

800

1000

0.51.0

1.52.0 2468

1012

14

Sum C – 0.9 percentiles

0

100

200

300

400

500

600

700

0.51.0

1.52.0

2.5

2 4 6 810

1214

Stem C

0

200

400

600

800

1000

0.51.0

1.52.0 2468

1012

14

Sum C – medians

0

200

400

600

800

1000

0.51.0

1.52.0 2468

1012

14

Sum C – 0.1 percentiles

Predictionobservation

Prediction observation

Prediction observation

(a)

(c)

(e)

(d)

(f)

(b)

Instable region

50

100

150

200

250

300

350

0.51.0

1.52.0

2.5

2 4 6 810

1214

Minimum mortality (%)Maximum mortality (%)

Soil

C (

t ha

–1)

Stem

C (

t ha

–1)

Stem

C (

t ha

–1)

Stem

C (

t ha

–1)

Stem

C (

t ha

–1)

0

50

100

150

200

250

300

350

0.51.0

1.52.0

2.5

2 4 6 810

1214

Minimum mortality (%)Maximum mortality (%)

Maximum mortality (%)


Minimum mortality (%)






Nec

rom

ass

C (

t ha

–1)

0

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.



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 pro-

nounced 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 large-

scale ecosystem models do not correspond to landscape

level dynamic equilibria represented by virgin forests.

With commonly used mortality settings (0.5% of

0.5

1.0

1.5

2.0

2.52 4 6 8 10 12 14

Min

imum

mor

talit

y (%

)

0.5

1.0

1.5

2.0

2.5

Min

imum

mor

talit

y (%

)

0.5

1.0

1.5

2.0

2.5

Min

imum

mor

talit

y (%

)

0.5

1.0

1.5

2.0

2.5

Min

imum

mor

talit

y (%

)


2 4 6 8 10 12 14Maximum mortality (%)



Stem C – mediansAbsolute error (% of observed)

Stem C – 0.1 percentiles

Absolute error (% of observed)

Stem C – 0.9 percentiles


Stem C – intersection


< 33%

< 333%< 267% < 200%< 133% < 67%

< 100% < 167% < 233% < 300% < 367% < 433%

< 400%

(c) (d)

(a) (b)

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).



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 car-

bon pools are kept at steady state (Fig. 8a) resulting in a

NEP of zero (Fig. 8c), a phenomenon frequently re-

ported 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 & Hase-

nauer, 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

0.5

1.0

1.5

2.0

2.52 4 6 8 10 12 14

Min

imum

mor

talit

y (%

)

0.5

1.0

1.5

2.0

2.5

Min

imum

mor

talit

y (%

)

0.5

1.0

1.5

2.0

2.5

Min

imum

mor

talit

y (%

)

0.5

1.0

1.5

2.0

2.5

Min

imum

mor

talit

y (%

)

Soil C – intersectionAbsolute error (% of observed)

Necromass C – intersectionAbsolute error (% of observed)

Sum C – intersectionAbsolute error (% of observed)

Intersection of intersectionsAbsolute error (% of observed)

< 33%

< 333 %< 267 %< 200 %< 133 %< 67 %

< 100 % < 167 % < 233 % < 300 % < 367 % < 433 %

< 400 %

Maximum mortality (%)2 4 6 8 10 12 14




(a) (b)

(c) (d)

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.

Soil

Necro

mas

s

Stems

Sum

C c

onte

nt (

t ha

–1)

0

200

400

800

1000

1200

ObservedPredicted: 0.9–6.0%

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 predic-

tions and observations.



where small perturbations may lead to ecosystem

breakdown (cf. Fig. 4e).

Frequent disturbances maintain ecosystem produc-

tivity 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 rou-

tines (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 fre-

quent 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 re-

sembled by the steady state of the mosaic cycle at the

landscape level.

This should be addressed in self-initialization rou-

tines 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 inter-

pretation 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 large-

scale applications a set of grid cells with the same

vegetation type may be simulated using the Monte-

Carlo 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

Simulation years50 100 150 200 250 300

Rh,

NPP

,N

EP (t

C h

a–1 y

r–1)

(t C

ha–1

yr–1

)

–10.0

–7.5

–5.0

–2.5

0.0

2.5

5.0

7.5

10.0

Simulation years50 100 150 200 250 300

Leac

hing

,Vol

atile

loss

(kg

N h

a–1 y

r–1)

0.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Simulation years

50 100 150 200 250 300

Ann

ual m

orta

lity

rate

(%)

1.0

2.0

3.0

4.0

5.0

6.0

Simulation years

50 100 150 200 250 300

Soil

,Nec

rom

ass,

Stem

,Sum

100

200

300

400

500

600

(d)

(b)(a)

(c)

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.



initial conditions and ensures unbiased and consistent

starting values for large-scale applications.

Acknowledgements

This work was supported by a Grant from the University ofNatural Resources and Applied Life Sciences, the AustrianMinistry of Science and Education and the Austrian Ministryof Forest, Agriculture and Environment. Helpful review com-ments were provided by Bruce Michie and four anonymousreviewers.

References

Bachelet D, Lenihan J, Daly C et al. (2001) MC1: a dynamic

vegetation model for estimating the distribution of vegetation and

associated ecosystem fluxes of carbon, nutrients, and water. General

Technical Report PNW-GTR-508, USDA Forest Service, Pacific

Northwest Station, 95 pp.

Bachelet D, Neilson RP, Lenihan JM et al. (2004) Regional

differences in the carbon source-sink potential of natural

vegetation in the US. Environmental Management, 33 (Suppl. 1),

S23–S43.

Bond-Lamberty B, Gower ST, Ahl DE et al. (2005) Reimplementa-

tion of the BIOME-BGC model to simulate successional

change. Tree Physiology, 25, 413–424.

Clements FE (1916) Plant Succession: An Analysis of the Develop-

ment of Vegetation. Carnegie Institute, Washington, DC, Publ.

No. 242, 512 pp.

Churkina G, Tenhunen J, Thornton PE et al. (2003) Analyzing the

carbon sequestration potential of four European coniferous

forests using a biogeochemistry model. Ecosystems, 6, 168–184.

Ciais P, Reichstein M, Viovy N et al. (2005) Europe-wide reduc-

tion in primary productivity caused by the heat and drought

in 2003. Nature, 437, 529–533.

Foley JA, Prentice IC, Ramankutty N et al. (1996) An integrated

biosphere model of land surface processes, terrestrial carbon

balance and vegetation dynamics. Global Biogeochemical Cycles,

10, 603–628.

Harcomb PA (1987) Tree life tables: simple birth, growth and

death data encapsulate life histories and ecological roles.

Bioscience, 37, 557–568.

Hasenauer H, Merganicova K, Petritsch R et al. (2003) Validating

daily climate interpolations over complex terrain in Austria.

Agriculture and Forest Meteorology, 119, 87–107.

Heinselman ML (1973) Fire in the virgin forests of the boundary

waters canoe area, Minnesota. Quaternary Research, 3, 329–382.

Holland EA, Dentener FJ, Braswell BH et al. (1999) Contemporary

and pre-industrial global nitrogen budgets. Biogeochemistry, 46,

7–43.

IPCC WGI (1996) Technical summary. In: Climate Change 1995 –

the Science of Climate Change: Contribution of the Working Group I

to the Second Assessment Report of the Intergovernmental Panel on

Climate Change (eds Houghton JT, Meira Filho LG, Callander

BA, Harris N, Kattenberg A, Maskell K), pp. 9–50. Cambridge

University Press, Cambridge, UK.

Krinner G, Viovy N, de Noblet-Ducoudre N et al. (2005) A

dynamic global vegetation model for studies of the coupled

atmosphere–biosphere system. Global Biogeochemical Cycles, 19,

GB1015.

Law BE, Thornton PE, Irvine J et al. (2001) Carbon storage and

fluxes in ponderosa pine forests at different developmental

stages. Global Change Biology, 7, 755–777.

Lorimer CG, Dahir SE, Nordheim EV (2001) Tree mortality rates

and longevity in mature and old growth hemlock hardwood

forests. Journal of Ecology, 89, 960–971.

Luterbacher J, Dietrich D, Xoplaki E et al. (2004) European

seasonal and annual temperature variability, trends and

extremes since 1500. Science, 303, 1499–1503.

Maser C, Anderson RG, Cromack K Jr et al. (1979) Dead and

down woody material. In: Wildlife Habitats in Managed Forests:

The Blue Mountains of Oregon and Washington (ed Thomas JW),

pp. 78–95. USDA Forest Service Agric, Handbook.

Merganicova K, Pietsch SA, Hasenauer H (2005) Modeling the

impacts of different harvesting regimes on the growth of

Norway spruce stands. Forest Ecology and Management, 207,

37–57.

Monserud RA, Sterba H (2001) Modeling individual tree mor-

tality for Austrian tree species. Forest Ecology and Management,

113, 109–123.

Peterken GF (1996) Natural Woodland: Ecology and Conservation

in Northern Temperate Regions. Cambridge University Press,

Cambridge, UK.

Petritsch R (2002) Anwendung und Validierung des Klimainterpola-

tionsmodells DAYMET in Osterreich. Diploma thesis, University

of Natural Resources and Applied Life Sciences Vienna, 95 pp.

Picket STA, White PS (1985) Natural disturbance and patch

dynamics: an introduction. In: The Ecology of Natural Distur-

bance and Patch Dynamics (eds Pickett STA, White PS), pp. 3–13.

Academic Press, Orlando, FL, US.

Pietsch SA, Hasenauer H (2002) Using mechanistic modeling

within forest ecosystem restoration. Forest Ecology and

Management, 159, 111–131.

Pietsch SA, Hasenauer H (2005) Using ergodic theory to assess

the performance of ecosystem models. Tree Physiology, 25,

825–837.

Pietsch SA, Hasenauer H, Kucera J et al. (2003) Modeling the

effects of hydrological changes on the carbon and nitrogen

balance of oak in floodplains. Tree Physiology, 23, 735–746.

Pietsch SA, Hasenauer H, Thornton PE (2005) BGC-model para-

meter sets for central European forest stands. Forest Ecology

and Management, 211, 264–295.

Reinecke LM (1933) Perfecting a stand density index for even-

aged forests. Journal of Agricultural Research, 46, 627–638.

Remmert H (1991) The Mosaic Cycle Concept of Ecosystems.

Ecological Studies 85. Springer Verlag, Berlin, Germany.

Sitch S, Smith B, Prentice IC et al. (2003) Evaluation of ecosystem

dynamics, plant geography and terrestrial carbon cycling in

the LPJ dynamic vegetation model. Global Change Biology, 9,

161–185.

Spies T (1997) Forest stand structure, composition, and function.

In: Creating a Forestry for the 21st Century: The Science of

Ecosystem Management (eds Kohm K, Franklin JF), pp. 11–30.

Island Press, Washington DC, US.

Splechtna BE, Gratzer G (2005) Natural disturbances in central

European forests: approaches and preliminary results from



Rothwald, Austria. Forest Snow and Landscape Research, 79,

57–67.

Thornton PE (1998) Description of a numerical simulation model

for predicting the dynamics of energy, water, carbon and nitrogen

in a terrestrial ecosystem. PhD thesis. University of Montana,

Missoula, 280 pp.

Thornton PE, Law BE, Gholz HL et al. (2002) Modeling and

measuring the effects of disturbance history and climate on

carbon and water budgets in evergreen needleleaf forests.

Agricultural and Forest Meteorology, 113, 185–222.

White PS (1979) Pattern, process and natural disturbance in

vegetation. Botanical Review, 45, 229–299.

White MA, Thornton PE, Running SW et al. (2000) Para-

meterization and sensitivity analysis of the BIOME-BGC

terrestrial ecosystem model: Net primary production controls.

Earth Interactions Paper 4–003, http://EarthInteractions.

org

Woodward FI, Smith TM, Emanuel WR (1995) A global land

primary production and phytogeography model. Global

Biogeochemical Cycles, 9, 471–490.



evaluating the self-initialization procedure for large

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