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Ecological Modelling 222 (2011) 3020– 3032

Contents lists available at ScienceDirect

Ecological Modelling

journa l h o me pa g e: www.elsev ier .com/ locate /eco lmodel

odelling soil carbon development in Swedish coniferous forest soils—Anncertainty analysis of parameters and model estimates using the GLUE method

arina Ortiza,∗, Erik Karltuna, Johan Stendahla, Annemieke I. Gärdenäsa, Göran I. Ågrenb

Department of Soil & Environment, Swedish University of Agricultural Sciences, P.O. Box 7001, SE-75007 Uppsala, SwedenDepartment of Ecology, Swedish University of Agricultural Sciences, P.O. Box 7044, SE-75007 Uppsala, Sweden

r t i c l e i n f o

rticle history:eceived 26 November 2010eceived in revised form 23 May 2011ccepted 24 May 2011

eywords:LUEoil carbononte Carlo

wedish Forest Soil Inventorycots pineorway spruce-modelncertaintiesNFCCCyotoimits of acceptability

a b s t r a c t

Boreal forest soils such as those in Sweden contain a large active carbon stock. Hence, a relatively smallchange in this stock can have a major impact on the Swedish national CO2 balance. Understanding ofthe uncertainties in the estimations of soil carbon pools is critical for accurately assessing changes incarbon stocks in the national reports to UNFCCC and the Kyoto Protocol. Our objective was to analyse theparameter uncertainties of simulated estimates of the soil organic carbon (SOC) development between1994 and 2002 in Swedish coniferous forests with the Q model. Both the sensitivity of model parametersand the uncertainties in simulations were assessed. Data of forests with Norway spruce, Scots pine andLodgepole pine, from the Swedish Forest Soil Inventory (SFSI) were used. Data of 12 Swedish countieswere used to calibrate parameter settings; and data from another 11 counties to validate. The “limitsof acceptability” within GLUE were set at the 95% confidence interval for the annual, mean measuredSOC at county scale. The calibration procedure reduced the parameter uncertainties and reshaped thedistributions of the parameters county-specific. The average measured and simulated SOC amounts variedfrom 60 t C ha−1 in northern to 140 t C ha−1 in the southern Sweden. The calibrated model simulatedthe soil carbon pool within the limits of acceptability for all calibration counties except for one countyduring one year. The efficiency of the calibrated model varied strongly; for five out of 12 counties themodel estimates agreed well with measurements, for two counties agreement was moderate and forfive counties the agreement was poor. The lack of agreement can be explained with the high inter-

annual variability of the down-scaled measured SOC estimates and changes in forest areas over time.We conclude that, although we succeed in reducing the uncertainty in the model estimates, calibratingof a regional scale process-oriented model using a national scale dataset is a sensitive balance betweenintroducing and reducing uncertainties. Parameter distributions showed to be scale sensitive and countyspecific. Further analysis of uncertainties in the methods used for reporting SOC changes to the UNFCCC

omm

and Kyoto protocol is rec

. Introduction

Forest soils in temperate and boreal climates contain large quan-ities of soil organic carbon (SOC) and boreal and temperate forestsave been pointed out as important carbon sinks in the global car-on balance (Raich and Schlesinger, 1992; Goodale et al., 2002).orest soils in Sweden represent a carbon pool of 2200 Tg C with anverage carbon content of 82 t C ha−1 and a total area of 27 M ha thatulfils the FAO definition of forest land (Olsson et al., 2009). Swedeneports changes in dead organic matter (DOM) and SOC with data

rom the repeated Swedish Forest Soil Inventory (SFSI) to the Unitedations Framework Convention on Climate Change (UNFCCC) and

he Kyoto Protocol (UNFCCC, 1992, 1997; SEPA, 2009). As the total

∗ Corresponding author. Tel.: +46 18 67 34 57; fax: +46 18 67 34 70.E-mail address: Carina.Ortiz@slu.se (C. Ortiz).

304-3800/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2011.05.034

ended.© 2011 Elsevier B.V. All rights reserved.

soil carbon pool is approximately two orders of magnitude largerthan Swedish annual emissions, relatively small changes inducedby climatic and/or management changes have the potential to affectthe national greenhouse gas balance. If the expected changes aresmall a large inventory sample size is required to detect significantchanges (Peltoniemi et al., 2004; SEPA, 2009). Vertical and hori-zontal spatial variability in soil horizons, C concentration and bulkdensity give rise to uncertainties in the estimates of SOC stocks andchanges (Ellert et al., 2001; Wilding et al., 2001). There is a needfor assessing uncertainties in the estimations of soil carbon devel-opment in Swedish forest soils in order to determine the level ofcertainty of the reported values and to verify the estimated changesby independent methods.

Process-based modelling offers an alternative way of estimatingthe SOC development in forest soils. However, model simulationsare also associated with uncertainties and it is important that theseuncertainties are communicated so that policy makers are aware

odelling 222 (2011) 3020– 3032 3021

o2smt1baetam1eJteiaomoosaaatwume

1b(optppWietapapar

uccs(oiTms(aod

Fig. 1. Division of Sweden into climatic regions and counties for calibration andvalidation. The lined marked counties were included in the calibration and theremainder in the validation. The division into climatic regions is represented by

by their initial qualities. When litter decomposes, carbon is miner-

C. Ortiz et al. / Ecological M

f the degree of uncertainty of the information (Walker et al.,003). A model assessment should include all three aspects of sen-itivity analysis, calibration, and validation to test whether theodel is suitable for its intended use (Rykiel, 1996) and whether

he results are consistent with observational data (Oreskes et al.,994). Peltoniemi et al. (2007) reviewed six widely applied car-on models and concluded that uncertainty analyses of modelsnd model results are rarely applied in forest soil carbon mod-lling. One calibration and uncertainty estimation methodology ishe Generalized Likelihood Uncertainty Estimation (GLUE) (Bevennd Binley, 1992). It has been tested and successfully applied inany disciplines analysing uncertainty in models (Schulz et al.,

999; Cameron et al., 1999; Martinez-Vilalta et al., 2002; Larsbot al., 2005; Beven, 2006; Mitchell et al., 2009; Pinol et al., 2009;uston et al., 2009). Juston et al. (2010) made a GLUE applica-ion in soil organic carbon modelling of a long-term agriculturalxperiment. GLUE is based on the “equifinality” concept, mean-ng different inputs and parameterizations lead to equally goodnd acceptable performances of a model due to the interactionsf different parameters: this rejects the idea of one “optimum”odel parameterization. The GLUE method describes the model

utput uncertainties relative to measured observations. The coref the GLUE method is that once a likelihood measure (a mea-ure of performance of the model) has been decided, a range ofcceptable models (a specific model structure with specific inputnd parameterization) can be determined. In order to take intoccount uncertainty in observations in the analysis of model uncer-ainty, the “limit of acceptability” approach has been developedithin the GLUE methodology (Beven, 2006). The accepted sim-lations are retained to determine the uncertainty bounds of theodel outputs and the posterior parameter distributions (Smith

t al., 2008).In this study, the process-oriented Q model (Rolff and Ågren,

999) was used, because it has previously been applied in soil car-on modelling of forest ecosystems at a national scale in SwedenÅgren and Hyvönen, 2003; Ågren et al., 2007). A sensitivity analysisf the Q model by Hyvönen et al. (1998) determined an optimumarameter set through varying individual parameters “one-at-a-ime”, a so-called local analysis. However, this approach neglectsossible parameter interactions and might have discarded differentarameter combinations that result in good model performance.e choose to use the GLUE method because it includes uncertainty

n model structure and parameters simultaneously in a transpar-nt way. Moreover, in combination with Monte Carlo simulations,he uncertainty of all parameters can be assessed simultaneously,

so-called global assessment, which guarantees that all possiblearameter interactions and parameter combinations are taken intoccount. One disadvantage of the GLUE method is that it is notossible to generate true confidence limits since the uncertaintynalysis is made on accepted simulations with a subjective crite-ion.

The aim of this study was to assess the effects of parameterncertainties on the estimates of soil carbon stocks in Swedishoniferous forests with data from SFSI and the Q model. Data fromoniferous forest stands either dominated by Scots pine (Pinusylvestris) and Lodgepole pine (Pinus contorta) or by Norway sprucePicea abies) were used. The Q model was calibrated with dataf 12 counties using the GLUE technique. The 95% confidencentervals of the measurements were used as limits of acceptance.he performance of the model was assessed by validating theodel on 11 other counties (Fig. 1). Standard statistical measures

uch as, root mean squared error (RMSE) and model efficiencyME), were used for analysing the model performance for bothccepted calibrated and validated estimates. Finally, the usefulness

f model estimates relative to estimates from measurement wasiscussed.

different colours of the counties. (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of the article.)

2. Materials and methods

2.1. The model

The carbon amounts in Swedish forest soils during the period1994–2002 were estimated with the process-oriented dynamicdecomposition model Q (Rolff and Ågren, 1999; Hyvönen andÅgren, 2001; Ågren et al., 2007). This version of the model calcu-lates decomposition of three different litter fractions with specificdecomposition rates with the litter fractions being characterized

alised and the mineralisation rate decreases when the quality of thelitter fraction decreases. The decomposition rate changes between

3022 C. Ortiz et al. / Ecological Modelling 222 (2011) 3020– 3032

Coarse Roots

Needles

Branches

Stump

Stem

Decomposition & Quality Decrease

Initia

l Qua

lity

Dec

reas

e

Understory Veg.Fine Roots

Yr0 20 40 60 80 100

0 20 40 60 80 100

0 20 40 60 80 100

0.0

0.2

0.4

0.6

0.8

1.0

Time

LitterSoil

Yr

0.0

0.2

0.4

0.6

0.8

1.0

Yr

0.0

0.2

0.4

0.6

0.8

1.0

CO2

.

.

.

descr

tntbif(mabtnm2p(

g

ftid

Fig. 2. A conceptual picture of the version of the Q model used. The curves

1 and t2 (Fig. 2). The initially slower decay of the woody compo-ents is a result of both lower initial quality of the litter fraction andhe time needed for decomposers to access the substrate. Micro-ial invasion rates of coarse woody litter are assumed the same as

n Ågren and Hyvönen (2003). The litter is divided into three dif-erent fractions: (i) needles, fine roots and understorey vegetation,ii) branches and (iii) stumps, coarse roots and stems. New organic

atter is derived from the input of litter during the simulationnd old organic matter represents the accumulated organic matterefore the start of the simulation. The decomposition functions ofhe model describe the fraction of a litter cohort remaining, g(t), inew and old organic matter after t years: the model is described inore detail elsewhere (Hyvönen et al., 1998; Hyvönen and Ågren,

001; Ågren and Hyvönen, 2003; Ågren et al., 2007). The decom-osition function for needle litter and fine roots, g(t), is given in Eq.1) as an example of how the parameters appeared in the model.

(t) = (1 + fCˇ�11u0qˇ0 t)

−(1−e0)/(ˇ�11e0)(1)

C is the carbon concentration in decomposer biomass, q0 is eitherhe initial litter quality in needles (q0n) or the initial litter qual-ty in woody components(q0w). The parameter e0 is microbialecomposer growth efficiency and describes the fraction of car-

ibe the mass remaining of the different litter fractions as functions of time.

bon incorporated into new decomposer biomass per unit of usedcarbon. The rate of decrease in quality is described by �11 and ˇis the shape of decomposer quality response and describes howfast the decomposition rate changes with quality. The decomposergrowth rate (u0 = u00 + u01 × T) is related to the average air temper-ature (T) at the site. For woody litter, Eq. (1) has to be modified toinclude the parameters maxb (year) and maxs (year) to describe thetime required for microorganisms to completely invade branchesand stems. The definition of the parameters is given in Table 1. Themodel parameters can be combined into three lumped parameters:z, ˛n (needles and other finer material) and ˛w (woody material)(Eq. (2)) which are combinations of the decomposer and substrateparameters fC, q0n, q0w, e0, �11, ˇ, and u0. The lumped parameterssimplify the decomposition function to Eq. (2).

g(t) = (1 + ˛nt)−z (2)

where n in ˛n represents the decomposition of needle litter. For the

lumped parameters, z is related to the shape of the decompositioncurves in Fig. 2, and ˛n (needle litter decomposition) and ˛w (woodylitter decomposition) are strongly related to the rate of movementalong the curves.

C. Ortiz et al. / Ecological Modelling 222 (2011) 3020– 3032 3023

Table 1The parameters analysed in the GLUE analysis. PDF is the probability density function used to define the parameter distribution prior and posterior calibration.

Parameter Description Unit Prior Posterior

PDF Range, mean, sd PDF (national mean) Range, mean, peak,sd, no trial, prob.

Singleq0n Initial litter quality in needles – Uniform 0.9–1.3 Triangular 0.9–1.3, –, 0.95, –,

–, –q0w Initial litter quality of wood – Uniform 0.9–1.3 Uniform 0.9–1.3, –, –, –, –, –e0 Microbial decomposer growth efficiency – Uniform 0.2–0.3 Triangular 0.2–0.3, –, 0.29, –,

–, –�11 Rate of decrease in quality – Uniform 0.3–0.4 Triangular 0.3–0.4, –, 0.39, –,

–, –ˇ Shape of decomposer quality response – Uniform 5–9 Triangular 5–9, –, 8.5, –, –, –maxb Time till total invasion of branches year Uniform 1–40 Uniform 1–40, –, –, –, –, –maxs Time till total invasion of stems year Uniform 10–60 Uniform 10–60, –, –, –, –, –u00 Parameter in u0, the basic decomposer rate Uniform 0.04–0.09 Uniform 0.04–0.09, –, –, –, –,

–u01 Parameter in u0, the basic decomposer rate – Uniform 0.01–0.02 Uniform 0.01–0.02, –, –, –, –,

–Lumped˛n Regulates the rate of movement through

qualities in time for needle litterLog normal –, 0.41, 37 Log normal –, 0.38, –, 0.42, –, –

˛w Regulates the rate of movement throughqualities in time for woody litter

Log normal –, 0.41, 0.36 Log normal –, 0.43, –, 0.44, –, –

orma

2

scMdssr(wFr2

oato2plePal

SawSeTuaTsip

z Regulates the shape of decomposition curve N

.2. Model input for driving variables and initial values

Litter input was estimated from national forestry statistics ontanding tree volumes and harvests from 1926 to 2002 in eachounty following the procedure described in Ågren et al. (2007).arklund’s (1988) allometric functions were used to estimate the

ifferent tree components (needles, coarse roots, branches, stumps,tems) from standing stem volumes and harvested volumes. Fortanding biomass each tree component was assigned a turnoverate. Needle and branch turnover rates were corrected for latitudeÅgren et al., 2007; Stendahl et al., 2010). At harvest, the residuesere determined by the above mentioned allometric functions.

ine root litter input was estimated from the correlation of fineoot litter production and needle litter production (Kleja et al.,008).

The bottom layer of the understorey litter consisted dominantlyf bryophytes and lichens, and the field layer of herbs, grasses,nd dwarf shrubs. With data from the SFSI plots understorey lit-er production was estimated from data on the area coverage (%)f the bottom and field layers. A constant cover from 1926 to002 was assumed based on the average during the inventoryeriod 1994–2002. The cover estimates were converted to annual

itter input through biomass models developed by Muukkonent al. (2006) and turnover rates for understorey vegetation fromeltoniemi et al. (2004). For simplicity, the understorey litter wasssumed to have the same quality and decomposition rate as needleitter (Franklin et al., 2003).

The initial SOC stocks in 1926 were estimated assuming thatOC stocks were in steady-state. The period 1926–1993 was useds a spin-off. The initial carbon stock was analytically calculatedith 1926 years litter input. The parameterization used for this

OC estimate was for simplicity fixed and the values for the differ-nt parameters were the same as presented in Ågren et al. (2007).he 1926 stock of carbon in wet soils was estimated by decreasing0 by a factor 0.65 (Anon, 2010). The partitioning between the wetnd dry soils was based on plot moisture classifications from SFSI.

he adjustment of u0 was only necessary for estimating the initialteady state. In the calibration procedure, the parameters reflect-ng the influence of soil moisture were adjusted by the calibrationrocess.

l –, 0.29, 0.32 Binomial –, 1.8, –, –, 1, 0.75

Mean annual temperature is used as a driving variable. Theannual (1961–1990) constant mean air temperature, T, variedbetween counties, with temperatures ranging from −0.3 ◦C in thenorthern counties to 7.38 ◦C in the southern counties (Raab andVedin, 1995; SMHI, 2002).

2.3. Data material for calibration and validation

The data for the calibration and validation were compiled fromthe Swedish Forest Soil Inventory (SFSI) and the Swedish NationalForest Inventory (SNFI) databases. The field data collection of thetwo inventories is integrated, they collect data from the same per-manent plots and they are both designed for the national scale,but data can be reported at county scale. Each year of collecteddata represents an unbiased sample of Swedish forestland at thenational scale. The soil inventory is continuous with 1/10 plots sam-pled each year; thus, a complete inventory takes 10 years. Each plotin the inventories should be considered as one data point in a sam-ple from a specific stratum, i.e. the data from the inventories arealways aggregated before analysis and should not be evaluated onplot level. The inventory includes site descriptions of plot and land-scape properties, basic soil properties, soil type classification, andchemical properties of both organic and mineral soil horizons for asubset of plots.

Sample plots were selected by the criterion that at least 70% ofthe basal area of a plot was either Norway spruce (P. abies) or pine (P.sylvestris and/or P. contorta) on mineral soil. Data collected between1993/1994 and 2002 in all 23 counties in Sweden were used. Oneexception was data for 1993/1994, which were collected in thesouthern counties in 1993 and in the northern counties in 1994:these are reported as data for 1994 hereafter. The soil data werecollected between the beginning of June and the end of Septemberduring the period 1994–2002.

Soil samples were taken from the O horizon (an aerated organichorizon with litter under decomposition), the B horizon (an illuvi-ation horizon in the mineral soil), and in two deeper soil horizons,

one at 45 cm below the ground surface, and the other at 55–65 cmbelow the mineral soil surface. All soil samples were analysed forC (carbon) by dry combustion. For the O horizon, C stocks werecalculated from the determinations of the total amount of mate-

3 odelli

raceatst2

troba

2

(mat(cmdwucc

pfffdtapfpi

fepiw

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024 C. Ortiz et al. / Ecological M

ial in the O horizon and the C concentration of the sample. Themount of C in the mineral soil for each sampled horizon was cal-ulated with C concentration, thickness of the sampled horizon, anmpirical relationship for bulk density (Nilsson and Lundin, 2006),nd stoniness (Stendahl et al., 2009). The total mineral soil C downo 50 cm depth was calculated with the measured amounts in theampled horizons and a combination of linear inter and extrapola-ion for the parts of the profile where no samples were taken (SEPA,009).

The method for estimating the amount of soil carbon is iden-ical to the Swedish method for calculating soil carbon amountseported to UNFCCC. For the entire period, 1994–2002, the numberf sample plots was 2064, of which 45% of the plots were excludedecause they did not meet the tree species criteria or were defineds Histosols.

.4. Calibration, validation and parameter uncertainty analysis

The 23 counties in Sweden were divided into 7 climatic regionsFig. 1, coloured) to regionalise the modelling of national SOC esti-

ates. The climatic regionalisation accounted for the temperaturend the precipitation gradients in Sweden. Twelve of the coun-ies were used in the calibration (shaded) and the remaining 11coloured) were used in the validation of the model (Fig. 1). Thealibration and validation counties were selected so that each cli-atic region was represented in the calibration and validation

atasets. Calibration and validation were done for the period forhich data of the SFSI were available (1994–2002). The model sim-lation started in 1926. The total number of sampling plots perounty varied from 2 to 85. The lower number was found in theounties 10 and 12.

The prior probability density functions (PDFs) of the Q modelarameters for GLUE analysis are presented in Table 1. A fixed valueor the parameter fC (0.5) was used as in Ågren et al. (2007). The PDFsor all the other parameters in the model were based on resultsrom the previous study of Ågren and Bosatta (1996b). Uniformistributions were used as the distributions within the ranges ofhe parameters were unknown. The lumped parameters, z and ˛n

nd ˛w were calculated from the individual parameters from therevious distribution. The model simulations were run separatelyor Norway spruce and Scots pine/Lodgepole pine, with the samearameter ranges for both species, but different litter input and

nitial litter quality.The 95% confidence intervals of the measured soil carbon data

or each individual year were used as “limits of acceptability” inach county. The modelled SOC output for Norway spruce and Scotsine/Lodgepole pine was pooled to be comparable with the soil

nventory data. The simulation results lying within these limitsere considered acceptable simulations according to Eq. (3).

Cmin(x, t) < Csim(�, x,t) < Cmax(x, t),

for all x and t ∈ [1994, 2002] (3)

here Csim is the model simulation with a parameter and modeltructure � for county x and year t for Norway spruce and Scotsine/Lodgepole pine together and Cmin and Cmax are correspondingstimated lower and upper 95% confidence limits around the meanalues (Cmean) of the observations. Thus, the criterion for an accept-

ble simulation was that the Q model should simulate SOC amountsn Norway spruce and Scots pine/Lodgepole pine forest soils withinhe limits of acceptability for all years (t) in each county (x) of thealibration period 1994–2002.

ng 222 (2011) 3020– 3032

Likelihood, L, for each accepted simulation, Csimiwith the spe-

cific parameter set �j was calculated with Eq. (4).

L(Csimi(�j), Cmin(x,t)

, Cmean(x,t) , Cmax(x,t) ) ∝

⎧⎨⎩

Csimi− Cmin

Cmean − Cmin, Csimi

≤ Cmean

Si − Cmax

Cmean − Cmax, Csimi

≥ Cmean

(4)

This likelihood function is proportional to the model residualsand likelihood is estimated by a triangular distribution. Thus, eachaccepted simulation within the limits of acceptability had higherlikelihood the closer it is to the observation (both sides/over andunder estimation): i.e. the closer to one, the values of L are thehigher the likelihood and the better the estimations. The modelresiduals were scaled with the confidence limits of the observa-tions and values close to zero indicated little difference betweenthe model estimate and the mean of the observations. Positive ornegative scaled residual values implied the model simulated withinthe 95% confidence intervals of the observations, but either under-or overestimated the SOC in comparison to the mean of the obser-vations.

The model performance was analysed with the statistical mea-sures root mean squared error (RMSE) and model efficiency (ME)(Janssen and Heuberger, 1995; Smith et al., 1997). The RMSE (Eq.(5)) is the root mean square the total difference between the obser-vations (Oi) and the simulated (St) values at time t as.

RMSE =√∑n

i=1(St − Oi)2

n(5)

ME =∑n

i=1(Oi − O)2 −

∑ni=1(St − Oi)

2

∑ni=1(Oi − O)

2(6)

ME (Eq. (6)) is a measure of how efficiently the estimates repro-duce the observations relative to the mean of the observations. TheME values range from a maximum of one to negative values. A pos-itive value indicates that the model reproduces the mean of theobservations better than the observations. Negative values indicatethat the model results in poorer estimates than of the observations.The Kruskal–Wallice (Hollander and Wolfe, 1973) test was usedto find differences in simulation patterns in northern and south-ern Sweden and in calibrated and validated counties. The test is aone-way variance analysis by ranks and can be used when testingequality of population medians among groups without assuminganything about the groups’ distributions.

3. Results

Approximately 60,000 Monte Carlo simulations were run intotal for all calibration counties and tree species and the number ofsimulations varied between the counties and each species from 500to 5000. Of these Monte Carlo simulations, the number of acceptedsimulations varied from 46 to 221 among the twelve calibrationcounties. At the national scale, the percentage of the accepted simu-lations was 6% of the total number of MC simulations: at the countyscale, the fraction of accepted simulations varied between 1 and22% of the simulations run. The calibration resulted in acceptablesimulations in accordance with the limits of acceptance criteriain all calibrated counties, except in one county (16) for one year(1994): in this case, the criterion was relaxed and a simulation wasaccepted if the estimates were within the limits of acceptability for8 out of 9 years.

3.1. Uncertainty analysis of parameters

The accepted simulated SOC of pine and spruce forests in county15 (county with highest number of accepted simulations) for 2002

C. Ortiz et al. / Ecological Modelling 222 (2011) 3020– 3032 3025

F nitiol t: spr

iptomipsbcudTcapTa(do

3

wtaa

ig. 3. Dotty plots for combinations of the accepted parameters (see Table 1 for defiocation): 199 simulations were accepted in this county. Left: pine (black dots); righ

s illustrated in the dotty plots in Fig. 3 (the other counties dis-layed similar patterns and are not presented here). In county 15,here were 199 accepted simulations, which was equivalent to 13%f the Monte Carlo simulations realised for this county. The asym-etric dotty plots presented the sensitivity of a parameter, such as

n the case of the individual parameters e0, �11 and ˇ. Moreover, thearameters e0 and differed in sensitivity between pine or spruceimulations. For pine stands low SOC stocks could only be describedy high values of e0 and while for spruce stands high SOC stocksould only be described by high values of e0 and ˇ. The individ-al parameter distributions were updated from uniform to variableistributions after calibration for each county (Fig. 4 and Table 1).he distributions that varied mostly where found in the southernounties 19 and 23 for the parameters q0n, q0w, ˇ, tmaxs and z devi-ted most from other counties’ parameter distributions. The meanosterior distributions for all calibrated counties are described inable 1. Posterior distributions of the lumped parameter z werelso updated from a lognormal to a binomial distribution for theTable 1) acceptable simulations indicating that there were twoifferent optima for acceptable simulations (Fig. 3). Regarding ˛,nly the range changed slightly.

.2. Uncertainty analysis of model estimates

The distributions of carbon stocks in the accepted simulations

ere narrower in some counties than in others e.g. county one and

wo in the north of Sweden, with ranges between 5 and 10 t ha−1

nd county eight and 23 in south Sweden, with ranges between 25nd 35 t ha−1 (Fig. 5 results for 2002). The accepted distributions

ns) and simulated SOC in the calibration of the Q-model in county 15 (see Fig. 1 foruce (grey dots).

differed from the observation distribution. The accepted simula-tions were between the lower limit and the mean of the observedvalues in six cases (counties 3, 10, 12, 15, 19 and 22), the rangewas between the mean and the higher limit in three cases (coun-ties 1, 17 and 16); and the entire acceptable range was covered inthree (counties 4, 8, 23) cases. The model estimate distributionsdeviated from the distribution of the observations for some coun-ties: e.g. the distributions in county 7 and 10 are clustered at theends of the acceptable ranges. Some counties had narrow distribu-tions (county 22) whereas others had broad distributions (county4). The distributions of the accepted simulations changed over time,as for three counties presented in Fig. 6, where the scaled resid-uals (SR) and likelihood (L) are displayed for counties 7, 10 and16. The estimated carbon amounts were both higher and lowerthan observations during the calibration time span for all coun-ties. One accepted simulation might obtain a high L in one year,but a low in another. However, the Q model could simulate withinthe acceptability limits of the observed data for all counties andall time steps, except for county 16 in the first time step (1994)when the scaled residuals exceeded one (Fig. 6). In counties 7 and10 most simulations were above and below the observed mean(the zero line in Fig. 6). The distributions of the accepted simu-lations were clustered towards the ends of the acceptable rangesin some counties like 7 and 10 (Fig. 5): this appeared as a shift inthe distribution in the scaled residuals to either above or below

the zero line (Fig. 6). In county 16, the model did not simulatewithin the limits of acceptability, therefore, the scaled residualsexceeded one in 1994. The reason for this was that a low num-ber of observations in comparison to other years (Fig. 7) lead to

3026 C. Ortiz et al. / Ecological Modelling 222 (2011) 3020– 3032

F el for

p in ea

hTtTbfec2

ig. 4. Posterior parameter distributions after the GLUE procedure of the Q-modarameter values. Each distribution represents the posterior parameter distribution

igher observations which resulted in unacceptable simulations.he simulated and measured amounts of SOC in the twelve calibra-ion counties during the calibration period are presented in Fig. 7.he amount of SOC was lower in the northern counties (low num-ers) in Sweden, with approximately 60 t C ha−1 being estimated

or the most northerly county, compared to 140 t ha−1 in the south-rn counties. The range of confidence limits varied among counties:ounty 12 had a range of 100 t C ha−1 and county 1 had a range of0 t C ha−1.

each calibrated county. On the y-axis are the distributions and on the x-axis thech county.

For 2002, the agreement between observations and simulationsof SOC in the validation counties was comparable to the calibra-tion (Fig. 8, except for two counties (counties 11 and 13)) wheresimulations and observations differed in SOC. Both the range of thevalidated simulations and the confidence intervals of the observa-

tions crossed the 1:1 line for six counties out of 10 of the validationcounties. The counties with overestimated SOC store and largeuncertainties were mainly small counties with few observationspoints.

C. Ortiz et al. / Ecological Modelling 222 (2011) 3020– 3032 3027

Fig. 5. The probability density of the accepted simulations (histogram) and the mean of the observations with their 95% confidence intervals (bold lines – the middle line isthe mean and the other two lines are the limits of acceptability) in the calibration for the year 2002. SOC store is on the x-axis, and the frequency of Monte Carlo simulationsis on the y-axis; n is the number of samples in each county.

3028 C. Ortiz et al. / Ecological Modelling 222 (2011) 3020– 3032

F ns fors ent th

coilsvv

ig. 6. The scaled residuals (left) and the likelihood (right) of the accepted simulatiocaled residuals (SR) and the likelihood (L) are on the y-axis. Dashed lines SR repres

After dividing Sweden in north and south at Limes Norrlandi-us (National Encyclopedia, 2011) a Kruskal–Wallis test (p = 0.05)n the RMSE values (Table 2) indicated that errors were not largern the south of Sweden than in the north. At the 5% confidence

evel, the RMSE of calibrated and validated counties was found to beimilar. The calibrated counties represented the mean of the obser-ations better than the validated simulations. For five counties, MEalues of the calibrated simulations were close to one. With the

three of the calibration counties (7, 10 and 16). The years are on the x-axis and thee uncertainty bounds of the observations.

exception of one county, the ME values of the validated simulationswere negative, and in one case very low (county 21).

4. Discussion

The calibration procedure resulted in a model description of SOCmeasurements with five good, two moderate, and five poor MEvalues. There was a high correlation (r = 0.82) between observed

C. Ortiz et al. / Ecological Modelling 222 (2011) 3020– 3032 3029

Fig. 7. Soil carbon development between 1994 and 2002 in the twelve calibration counties. The solid lines represent the 5th and 95th percentiles, and the means of theaccepted simulations. The long dashes represent the means and upper and lower 95% confidence intervals of SFSI measurements. The years simulated are on the x-axis andthe SOC stocks in t C ha−1 are on the y-axis. The bars illustrate the number of samples (y-axis right side) each year (x-axis).

3030 C. Ortiz et al. / Ecological Modelli

Fig. 8. Modelled and simulated SOC in Sweden in 2002. The black dots are the meancarbon stores from the calibration counties and the grey triangles represent the val-idation counties. The errors bars on the SFSI-axis show the 95% confidence intervalsatt

aatotcvfsw

TM(o

nd the error bars on the modelled axis represent the 95th and 5th percentiles ofhe accepted simulations. The inserted figure in the right is the same except withouthe uncertainty bounds.

nd calibrated values but poor correlation between the observednd validated values (Fig. 8). The lack of correlation (r = 0.03) inhe validation was caused by the two counties where the modelverestimated SOC by more than 50% and the two counties wherehe model underestimated the SOC by more than 20%. Except inounty 13, the disagreement between measured and simulatedalues could be explained by the change in forest areas resulting

rom adjustments in administrative borders since 1923. The rea-on for assuming a constant forest area between 1951 and 2000as that the total national forest area changed less than 1% during

able 2odel performance root mean squared error (RMSE) (Tg C) and model efficiency

ME) (–) estimated with the mean of the accepted simulations and the mean of thebservations in each county (both pine and spruce stands included).

County RMSEcalibration

RMSEvalidation

MEcalibration

MEvalidation

1 6.17 – 0.02 –2 – 17.57 – −1.653 19.69 – −1.49 –4 3.61 – 0.99 –5 – 4.49 – −0.306 – 10.90 – −6.537 8.62 – 0.99 –8 7.37 – 0.96 –9 – 18.43 – −3.56

10 20.51 – −0.04 –11 – 75.25 – −0.1312 14.43 – 0.98 –13 – 47.78 – −5.2014 – 20.64 – −0.2215 11.49 – 0.99 –16 20.86 – −0.001 –17 – 37.44 – −4.7518 – 16.26 – 0.1019 12.87 – 0.05 –20 – 10.05 – −1.4421 – 31.67 – −25.4822 29.04 – −0.71 –23 15.41 – −0.44 –

ng 222 (2011) 3020– 3032

this period. However, at county scale, changes have taken place, forexample in county 11, with the overestimate of 50% in the valida-tion, forest area decreased by 35% between 1951 and 2000 (Erikssonand Janz, 1975; Swedish Forest Agency, 2011). Correcting for thischange in forest areas by introducing area development functionswould result in a more precise stock estimate and place county 11nearer the 1:1 line in Fig. 8. Such an adjustment would imply func-tions describing area development for each county to be able toestimate the correct area each year. A change in forest area couldnot explain the overestimation of SOC stocks in county 13 (secondlargest outlier in validation); here the deviation might be relatedto uncertainties in conversions from standing stocks to litter pro-duction or that the model excludes a factor which underestimatesdecomposition like that the soils are in general more shallow, whichcould affect tree growth and decomposition. Removing those out-liers would give a higher correlation of r = 0.53.

The SFSI is designed for national scales. We down scaled it tocounty scale as the Q-model is designed for ecosystem-countyscale. When down scaling the SFSI to county scale, some of the smallcounties had a low number of sample plots that fulfilled the crite-ria (70% pine or spurce forest land) like county 8, 10 and 12. Everyyear, 10% of the plots were sampled. If the plot for adjacent yearsdiffered a lot in stand age and/or soil type, this could have resultedin high inter-annual variation of the observations of small coun-ties, which is hard to capture with a model and therefore resultsin low ME. As the model used an average constant temperature,the impacts of annual variation in climate on decomposition andlitter production were not included and could as well have reducedthe ME values. However, the effect of average constant temperatureshould be small compared to the random variability in observationsin small counties.

The parameter sensitivity and uncertainty results confirmedan earlier sensitivity analysis of the same model (Hyvönen et al.,1998), that e0, �11 and are the most sensitive parameters. Theseparameters control the interaction between the quality of car-bon and the rate of carbon use by microbes (ˇ) and regulate therate of change of quality of soil organic matter (�11) and the effi-ciency of decomposer growth (e0). Acceptable simulations resultedin updated distributions for the individual parameters. These newdistributions are valuable since we can with less parameter uncer-tainty simulate the SOC development at the county scale. The rangeof the lumped parameter z was narrowed, meaning that regionalestimation of SOC stocks could only be described with a more lim-ited combination of parameters. The two optimums identified inthe calibration for the lumped parameter z indicated two possibletypes of systems. The division between the two systems appearswhen z equals one. When z exceeds one, a steady state betweenthe decomposition of organic material and litter input is possi-ble, but when z is below one a steady state is not possible andunder constant litter input, there will be an infinite accumulationof SOC. For a system to attain a steady state, the decomposersneed to decompose litter input at a sufficiently high rate. In themodel this was determined by three factors. First, the efficiencyin carbon use (e0); if the decomposers are efficient, i.e. high e0,less carbon will be lost and SOC will accumulate. Second, the rateconversion to low quality carbon (�11); a high rate of conversionto low quality means SOC rapidly becomes less accessible to thedecomposers and SOC accumulates. Third, the sensitivity of car-bon use to the quality (ˇ); with high sensitivity, carbon qualityand the decomposer access to quality rapidly decrease and SOCaccumulates.

In the dotty plots (Fig. 3), no patterns indicated that the model

had highly interactive parameters. These results agreed with theequifinality theory of Beven (2006), as different parameterizationsrendered equally good simulations. After calibration, the param-eters and e0 were the most sensitive at higher values and had

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etter defined ranges. Parameter distributions similar to the con-itions as for the southern counties 19 and 23, should be chosenarefully, especially for e.g. that has a higher peak value than theest of the calibrated counties. The higher value of means thathe decomposition rate changes fast with quality. Higher values of

result in higher SOC stocks and slower decomposition. In theseounties (19 and 23) the soils are characterized by either high cal-ium carbonate or clay content. Liming has been shown to increaseecomposition of soil organic matter (Persson et al., 1990), proba-ly through increased solubilisation of carbon (Ågren and Bosatta,996a). However, it is not clear if this effect would be the same

n areas with continuously high carbon carbonate contents. On thether hand, increasing clay content increases soil carbons stocksue to the binding of organic material to clay mineral surfacesAllison et al., 1949; Hassink, 1992) and this can be coupled to aigher value in the Q model (Bosatta and Ågren, 1996). Also, the

nitial quality of both needle and woody material is lower in theseounties, resulting in slower decomposition.

The model results were further conditional to the input, mean-ng the model results would be different if other inputs are used orther uncertainties related to the inputs are included (Beven, 2006).he uncertainty related to the total litter input was not quantita-ively assessed in this study, mainly due to lack of information.he litter input was calculated on stem volume data from foresttatistics and SNFI combined with biomass functions and turn-overates at county level, which was the only level forest statistics werevailable for the long periods required in this study. Nevertheless,he litter input estimates warrant a separate investigation, espe-ially how uncertainties in input affect the uncertainties in modelstimates. The litter input to the steady-state initialization step ismportant, as it affects the determination of the level of the SOCtore and the rate of change. In county 15, 70% of the old carbonas already consumed before 1994, resulting in marginal effects on

he decomposition after 1994. As Peltoniemi et al. (2006) pointedut impact of initialization decreases with time. This also justifiedhe use of the parameterization combination with the steady statessumption for the initialization in 1926.

Our modelling study estimated approximately 70 t C ha−1,hich is close to the national average of 83 t C ha−1 from the SFSI.

hese estimates were higher than the earlier estimates for pod-olised Swedish forest soils by Olsson et al. (2009) (85 t ha−1)nd Ågren et al. (2007), 40 t C ha−1 in 2000. The higher carbonmounts modelled in this study could be explained by the intro-uction of a decreased decomposition rate in wet soils and the

nclusion of litter input from the understorey vegetation. Thenderstorey litter production is quantitatively important, espe-ially in the northern parts of Sweden, where it contributes up to0% of the total litter input. In this study, the SFSI data resulted

n comparable stores (60–150 t ha−1) and the modelled estimates50–150 t C ha−1). Liski et al. (2006) estimated the Finnish SOCtocks to be 63 t C ha−1 in 2004, i.e. somewhat lower than thewedish stocks. The biomass production in the south of SwedenLal, 2005; Svensson et al., 2008; Swedish Forest Agency, 2010) isigher than that in northern Sweden and Finland. Liski et al. (2006)id not either take into account the slower decomposition in wetoils.

Mechanisms regulating changes in carbon stocks need to benderstood for estimating the possible effects of land-use on cli-ate change. Both the inventories and soil carbon model estimates

re based on stock estimations. Annual SOC changes are mostlyriven by changes in litter input and short-term decomposition,hile stocks are determined by slow decomposition. A process

ased model like Q-model includes both slow and fast decompo-ition. That is why understanding the different sources of possiblerror and uncertainty in stock estimates is essential, as they willffect the estimations of change. In the IPCC guidelines, both model

ng 222 (2011) 3020– 3032 3031

estimates and national inventories classified as Tier 3 methods,should be reported along with uncertainty estimations from errorpropagation or Monte Carlo simulation (IPCC, 2003). However, theorigin of the uncertainty as well as the way it can be describedand assessed differs between observation and model estimated. Inthis study, differences in the uncertainties and in the inter-annualvariations of the estimates between the methods were identified(Figs. 5 and 7), and it was apparent that reflecting the uncertainty isimportant in the choice of methods. The large inter-annual variabil-ity in the observations of small countries revealed the importance ofscale difference among inventory and model. Model estimates aremore stable over time and could supplement the measurementswhen data at county scale are needed.

The SFSI was designed for the national scale and at the countyscale the uncertainty in soil inventory data is to the major partdetermined by the number of sample plots available. All naturalvariation is included in inventory data. Manzoni and Porporato(2009) argue that the use of models out of their intended scalecan cause biased results. If a model is run on a larger scale thanit is designed for, errors might be introduced due to inaccuratemodel representation and generalizations in parameters and inputdata. On the other hand, data become more uncertain at a smallscale (Häkkinen et al., 2010), which introduces uncertainty in theparameter estimations. We stroke a balance between these twomethods of different scales. Dividing the country in larger areascould reduce the uncertainty in observations, but then the modelwould be further from its intended use. Applying the model at plotlevel is feasible but problematic because the SOC estimates will rep-resent the plot poorly in comparison to the litter input estimates.Still, the model results from a plot level application could be up-scaled and tested against regional or national observations fromthe inventory dataset.

The focus of this study was on parameter and model estimateuncertainty. However, if litter input uncertainty is included, thiswould generate further insight in uncertainty bounds for the modeloutput. In addition, the Q model version used, was driven by aconstant mean temperature in each county. The introduction ofa variable temperature into the model would represent decompo-sition more accurately, and increase the inter-annual variation inthe modelled SOC estimates together with the uncertainty in SOCchanges. This might be important in climate change assessmentstudies. Further modelling comparisons with other SOC models areimportant for evaluating the importance of uncertainties in themodel structures.

5. Conclusions

The main observation from this study was that the parameteruncertainty was decreased due to updated parameter distribu-tions of the Q-model and that the posterior parameter distributionswere county-specific, which has to be considered in future applica-tions. Further, we recommend investigations on how litter inputuncertainties and inter-annual climate variability affect modelestimates.

We conclude that it is problematic and a scientific challengeto calibrate an ecosystem model initially intended for stand levelpredictions to a national scale dataset. In this study the selec-tion of a county level resolution resulted in large uncertainties inthe inventory data. Calibration of process-oriented models usingregional datasets is a trade-off between dataset quality and modelinput specificity. Continued discussion on uncertainties in the

methods used for reporting SOC changes to UNFCCC and theKyoto protocol is necessary for determining when definite con-clusions on whether soils are sources or sinks for CO2 can bedrawn.

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cknowledgements

This study was partly funded by The Swedish Energy Agency. Wehank Professor Keith Beven for useful discussions on the appliedncertainty method, and comments on the manuscript and Suevalon for checking the language.

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