sensitivity analysis of nitrogen and carbon cycling in marine sediments

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Estuarine, Coastal and Shelf Science 82 (2009) 632–644

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Estuarine, Coastal and Shelf Science

journal homepage: www.elsevier .com/locate/ecss

Sensitivity analysis of nitrogen and carbon cycling in marine sediments

Jan M. Holstein*,1, Kai W. WirtzGKSS Research Center, Geesthacht, Germany

a r t i c l e i n f o

Article history:Received 20 March 2008Accepted 5 February 2009Available online 20 February 2009

Keywords:sensitivityuncertainty analysissedimentdiagenesisbacteriaWadden Sea

* Corresponding author.E-mail addresses: [email protected] (J.M.

(K.W. Wirtz).1 Present address: Institute for Chemistry and Biolog

(ICBM), University of Oldenburg, P.O. Box 2503, 26111

0272-7714/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.ecss.2009.02.008

a b s t r a c t

Biogeochemical cycles in coastal sediments encompass numerous interconnected processes and aresensitive to a high number of external forces. Usually a small subset of these factors is considered whendeveloping state-of-the-art models of marine nutrient cycling. This study therefore aims to assess thedegree of complexity required in the model to represent the dependency of major biogeochemical fluxeson both intrinsic as well as external factors. For this, a sensitivity analysis (SA) of the generic IntegratedSediment Model (ISM) was performed comparing two different model setups: 1) a back barrier tidal flatin the German Wadden Sea and; 2) a deep sea site in the Argentine Basin. Both setups were first cali-brated to fit pore water profiles of SO4

2þ, NH4þ and CH4. We then employed a new type of SA that evaluates

parameter impact rather than targeting variable change.General structural stability of the model is demonstrated by similar sensitivity patterns of both setupsregarding carbon and nitrogen cycling. Mean temperature, organic carbon bio-availability, bacterialadaptation and sediment texture emerge as the most influential parameters of ubiquitous importance. Itappears that in coastal settings, transport and sediment mixing and the composition of suspendedparticles in the bottom water are especially important. The nitrogen cycle displays a high responsivenessto internal feedback mechanisms as well as interdependencies to carbon and metal cycling, which isstatistically reflected by sensitivities to 79% of all parameters. In contrast, the carbon cycle appears to bemainly controlled by organic matter decay. The SA also pointed to unexpected responses of the sedimentsystem, which are analyzed by further scenario calculations. These, for example, reveal a nonlinearresponse of nitrification, denitrification and benthic fluxes of NH4 and NO3 to changing bioturbation andbioirrigation due to the interactions of different metabolic pathways.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Both the natural and commercial wealth of many coastal areasare at risk of being lost to forces such as eutrophication and climatechange. A particular focal point of land–ocean–atmosphere inter-actions at the coastal zone are near-shore sediments, which hostmajor biogeochemical cycles relevant to not only regional ecosys-tems but also the global climate system. Benthic cycles of carbonand nitrogen have the potential to strongly affect the trophic statusof the overlying water as well as the release or destruction ofgreenhouse gases. However, a multitude of processes interactduring the benthic turnover of carbon and nitrogen that underminesimple cause–effect relationships. Hence, system understanding is

Holstein), [email protected]

y of the Marine EnvironmentOldenburg, Germany

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a prerequisite for the careful assessment of changes in coastalelementary cycles.

Models can, in principle, provide a holistic representation ofbenthic biogeochemistry. The endeavor to understand the impactof environmental change to the carbon and nitrogen cycles incoastal sediment demands highly integrated models. High spatio-temporal variability in external forces (Peng and Zeng, 2007),transport processes (such as physical and biological sedimentmixing), bioirrigation, advection (Meile et al., 2001; Arzayus andCanuel, 2005), and a large number of chemical conversions that aremediated by microbial populations (Thullner et al., 2005) areconstitutive elements of many coastal environments. However,most state-of-the-art biogeochemical sediment models fall shortfor they are constructed for environs that range from continentalshelf to deep sea marine sediments (e.g. Tromp et al., 1995; Dhakarand Burdige, 1996; Wang and Van Cappellen, 1996; Soetaert et al.,1996; Wijsman et al., 2002). Many assume steady state. Usually, theprocesses that may be relevant in highly dynamic and heteroge-neous near-shore systems are only partly integrated.

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J.M. Holstein, K.W. Wirtz / Estuarine, Coastal and Shelf Science 82 (2009) 632–644 633

One major constraint for integrating more processes intomodels is the lack of observations that can be used for parame-terization or validation. Poorly identifiable or nonidentifiablemodel parameters are a well known problem of overparameterizedmodels. However, theoretical studies on the impact of internal feedback mechanisms on biogeochemical cycling can still be conductedeven when data are scarce. Constructed to this purpose, the Inte-grated Sediment Model (ISM) is characterized by a high degree ofgenericity and integration (Wirtz, 2003). The ISM generates redoxzoning through microbial competition with emphasis on reactionsrelated to carbon, nitrogen and metal cycling. Its elevated processand spatial resolution is adapted to the high vertical, lateral andtemporal gradients found in chemical inventories of coastalsediments.

The downside of integrating an increasing number of processesinto a model is that the numerous interdependencies, togetherwith the nonlinearity of many of the processes, inhibit an a prioriunderstanding of the model system. This lack of inferable knowl-edge is due to the unknown relevance of particular parameters,such as specific process coefficients, that cannot easily be measuredaccurately and whose level of uncertainty varies depending on theparameter. The model output uncertainty increases as thecomplexity and number of parameters of uncertain impact andvalue increase. Compared to parsimonious models, the predictivepower is expected to be rather low (Turchin, 2003). It is commonsense that offshore environments can be approximated by a clas-sical steady state approach in most instances. This may not beapplicable for many aspects of coastal systems. A forced perma-nency of otherwise transient conditions can become a majorobstacle for model validation if the system is rather sensitive tostarting conditions or field data are sparse.

Our major motivation in using a highly complex model is to putmore emphasis on important indirect processes that are rarelyincluded, such as the microbial control of redox reactions andcompetition between different chemical pathways. The choice forcomplexity comes at the cost of constraint. A systematic analysis ofthe model will reveal which processes are truly connected tocarbon and nitrogen cycling and can delineate which are parame-ters of major impact and which are parameters of minor impact,even though uncertainties remain. This information will facilitatethe determination of an optimized level of complexity for biogeo-chemical models of coastal sediments.

Automated model analysis methods, such as sensitivity analysis(SA), reveal both counter-intuitive model behavior and feedbacksin the model. Discriminating between unexpected and undesiredmodel behavior by subsequent model analysis can be turned intoknowledge of the system. By evaluating the impact of parameterson specific processes, SA is a tool to cope with uncertainty(Klepper et al., 1994). By combining SA and information on

With i¼ 1, ., N, index of chemical species (N¼ 15); j¼ 1, ., M, indexspatial direction; can be x (horizontal) or z (vertical); Ci, concentrationporosity (f) for solutes or (1� f) for solids; v, sedimentation rate or maith species; bz, bioirrigation coefficient; Rj, rate of jth reaction; si, j, stoi

parameter uncertainty, the crucial parameters for specificprocesses can be systematically identified. More robust modelresults can efficiently be obtained by constraining just the influ-ential parameters of high uncertainty. Alternatively, the respectiveprocesses may be revised.

In this study, key parameters for the biogeochemical cycles ofcarbon and nitrogen in coastal systems are identified by means ofSA applied to the ISM, calibrated for a tidal flat. Parameters that areof specific importance to coastal systems are identified bycomparison of SA results to those for a deep sea setup, withadjusted parameterization. The systematic analyses of the sensi-tivity of specific output variables to variations of single parametersof the ISM provide a look up table for the interdependencies ofmodel dynamics concerning carbon and nitrogen cycling. Thesupposed nonlinear system behavior is assessed by an elaborateSA method using a newly introduced methodology thatacknowledges the large range of uncertainty in many processparameters.

2. Short model description

The ISM (Wirtz, 2003) is a complex sediment model designedto investigate biogeochemical cycles in near-shore sedimentsemploying 55 state variables and 84 parameters. The ISMdescribes transport and reaction of solid and dissolved chemicaland biological species in porous aquatic media according toEq. (1) and was verified in studies of Beck et al. (2008, in press).Spatial discretization is attained using finite boxes. A box volumeis assigned to each node according to simple geometrical calcu-lations and the flux itself is approximated by finite differences.The model is generic in the sense that it captures a large numberof potentially relevant mechanisms, including advection, bio-turbation, bioirrigation, erosion and sedimentation. In contrast tomost other diagenetic models, the ISM resolves organic matter(OM) degradation in greater detail, in particular the OM catabo-lism that is mediated by both heterotrophic and lithotrophicmicrobes as depicted in Fig. 1. Chemical conversions primarilydepend on microbial population dynamics driven by physicalforcing, transport and nutrition. The microbes are subdivided into20 functional groups according to their metabolic redox pathlisted in Table 2. Analogous to the Gibbs free energy of theseconversions, the energy yield of the bacterial catabolism isspecific to the different functional groups and affects thecompetitive position of the microbe. Extending the originalmodel of Wirtz (2003), model boxes may have different poros-ities, chemical species have specific molecular diffusion coeffi-cients and bacteria can switch to dormancy when undersupplied.A more complete description of the ISM is given in Appendix A.

of reactions (M¼ 34); t, r, independent variables: time and space; r,of ith species; C0, I, bottom water concentration of ith species; fp,

croscopic flow velocity; Di, diffusion and bioturbation coefficient ofchiometric coefficient for ith species in jth reaction.

N2CO2 NH+

4 MnII FeII H2S CO2

HM-DOC NO+3 MnIV FeIII SO2+

4

POC LM-DOC CH4

O2fermentating bac.

aerobic

heterotrophs

heterotrophs

lithotrophs

Fig. 1. Sketch of the organic carbon degradation scheme. Positions of functional groups of bacteria therein and the lithotrophic OM oxidant regeneration cascade are roughlyoutlined. The quality class subdivision of POC, high- and low-molecular DOC (HM- and LM-DOC) is not shown.

J.M. Holstein, K.W. Wirtz / Estuarine, Coastal and Shelf Science 82 (2009) 632–644634

3. Sensitivity analysis

A sensitivity analysis (SA) can be used to enhance understandingof a model system by quantifying and visualizing cause-and-effectrelationships. Related to optimization problems often encounteredin traditional model calibration tasks, an SA estimates the contri-bution of parameter uncertainty to model output, thus providinginformation about the relevance of the represented processes forthe overall system dynamics. A SA will yield details on the sensi-tivity of model dynamics to the parameters. In this manner, an SAprovides knowledge essential for a wide range of model applica-tions: planning field studies to assess critical parameters (Klepperet al., 1994), refinement of critical processes, or general modeldevelopment, adaptation and reduction (Snowling and Kramer,2001). SA is related to identifiability analyses which aims to assessif or to what extent parameters are uniquely determined. For smallmodels (in the sense that they have few parameters), the parameteridentifiability problem can be approached by a graphical analysis ofsensitivities in order to analyze parameter interdependencies(Holmberg, 1982; Kelly-Gerreyn et al., 2005). Based on localsensitivity analysis, Brun et al. (2002) developed an formal identi-fiability analyses technique for large models that Andersson et al.(2006) applied on a bioirrigation model in order to assess differentsampling strategies regarding their efficiency to constrain a smallsubset of parameters. It is broadly accepted that sediment biogeo-chemical model studies at least need to assess the sensitivity ofmajor target variables. Soetaert et al. (1996) examined changes tothe carbon mineralized in their large early diagenesis model due toone-at-a-time variation of selected variables. Berg et al. (2003)introduces a sensitivity measure to assess the impact of a one-at-a-time 5% change in selected variables to 2 target variables. Superiorto linear SA are efforts to calculate the local 2nd partial derivatives inorder to factor nonlinearities in Dale et al. (2006).

The initial step of an SA is the definition of target variables. Theselection of variables should align with the research question. Assuch, the set of target variables, which are usually state variables orfunctions thereof, can be very confined, with the goal of testing oneor few specific processes, or broadly diversified, in order to repre-sent major model dynamics.

The standard way of performing an SA is to alternately increaseand decrease a parameter P of interest (standard setting is P0) bythe amount y$P0. The resulting values of the target variable T, Tyþand Ty– are compared with the value at standard parameterizationTR. The sensitivity Sy(T) is then defined as

SyðTÞ ¼ 1=2��TR � Tyþ

TR

��þ 1=2��TR � Ty�

TR

�� (2)

The commonly used index S is a property of a given target variableand critically depends on y. The soundness of the sensitivitymeasure depends on the parity between the natural heterogeneityof the parameter uncertainties and the respective choices of y. Thiscan be avoided by defining the quantity leverage LT ðPÞ of P withregard to T, which is a property of a given parameter and measure

for the magnitude of y corresponding to a predefined sensitivity S*

(here S* ¼ 0:05), i.e. a 5% target variable change

LT ðPÞ ¼ �logjyj; for SyðTÞ � S*; (3)

Assuming continuity of SyðTÞ, LT ðPÞ is estimated by perpetualexecution of the simulation in which the parameter is systemati-cally varied, a procedure referred to as parameter variation. Theparameter variation is controlled by y, which starts at a small valueand is subsequently increased. When SyðTÞ exceeds or equals S*,LT ðPÞ is found. Since L is the negative logarithm of the relativeparameter change, greater leverages stand for higher sensitivity of Twith respect to P. For the application to the ISM, the initial y was setto 0.001 (corresponding to a parameter change of 0.1%) and anupper limit of ymax¼ 1000 was imposed, allowing for an evaluationof target variable sensitivity within 7 magnitudes of parameterrange, i.e. 3 � L � �3. If parameters are only valid on a restrictedscale, e.g. 0> P> 1, insensitivity may already be ascertained fromvalues well below ymax. It should be noted, that due to the iterationscheme, calculating leverages leads to higher numerical effort.

4. Model setups, reference data and variables of interest

The model setup for coastal conditions was calibrated toreproduce the vertical pore water profiles of SO4, NH4 and CH4

and bacterial abundance using an automated Monte-Carlo tech-nique. From preliminary sensitivity studies, a set of parameterswas identified that mainly control organic matter hydrolization,sulfate reduction, methanogenesis and AMO. In subsequentsimulations, these parameters are set to random values withinreasonable limits. The parameter set from which the empiricaldata are reproduced best in terms of integrated square root meanerror was used as tidal flat calibration. We checked whethercalibrated parameter values converge towards unique values. Themodel setup for deep sea conditions is based on the tidal flatcalibration. The differences to the tidal flat setup regardsboundary conditions like bottom water concentrations, tempera-ture, absence of tides, and difference in sediment permeability.According to the valid assumption, that organic matter is lessreactive and that sediment mixing (bioturbation) and pumping(bioirrigation) is less pronounced at the deep sea site, the relatedparameters are adjusted appropriately.

The model setups for coastal and deep sea conditions werecalibrated using vertical pore water profiles of SO4, NH4 and CH4

and bacterial abundance (for the tidal flat setup) data representa-tive of either a typical sandy tidal flat in the back barrier area of theGerman Wadden Sea (53� 43.2700 N, 7� 43.7180 E) (Wilms et al.,2006) or the deep sea site GeoB 6229, located in 3443 m waterdepth at the continental slope to the Argentine Basin in the SouthAtlantic (37� 12.410 S, 52� 39.010 W) (Schulz and cruise participants(1999)), respectively. The agreement between model results anddata shown in Fig. 2 is very good for both sites, though the coex-istence of SO4 and CH4 in the upper part of the tidal flat site could

Table 1Calibrated parameter and boundary values differing between the tidal flat and thedeep sea setup.

Parameter Symbol Setup A(tidal flat)

Setup B(deep sea)

unit

Tidal cycle length s 0.53 N dExposure during low tide g 0.5 0 d/dBioirrigation coefficient b 6.0 0.02 1/dBoturbation coefficient DB 0.2 0.05 cm2/dPorosity f 0.65–0.35 0.9–0.65 cm3/cm3

High quality POC decay rate l0 1.2� 10�2 4.2� 10�3 1/dMedium quality POC decay rate l1 1.0� 10�4 1.2� 10�5 1/dLow quality POC decay rate l2 1.0� 10�5 1.0� 10�6 1/dTemperature amplitude DT 21.6 0.5 �CO2 bottom water concentration BWO2 0.35–0.20a 0.2 mmol/lNH4 bottom water concentration BWNH4 0.01–0.02a 0.03 mmol/lNO3 bottom water concentration BWNO3 0.015–0.0015a 0.03 mmol/lDOC bottom water concentration BWDOC 0.4 0.135 mmol/lPOC bottom water concentration BWPOC 0.1–0.6a 0.001 mmol/l

a changes within a seasonal cycle.

[mmol/l]

0

1

2

3

4

[m

]

SO4 NH4

[mmol/l] [mmol/l]

CH4

0 10 20 30 0 105 0 0.05 0.1 0 0.5 1

[norm. units]

NBA(bacteria)

Tidal flat

0 10 20 30[mmol/l]

0

1

2

3

4

5

6

7

8

[m

]

SO4CH4NH4

Deep sea

a b

Fig. 2. Data and model results for sulfate, ammonium, methane and normalized bacterial abundances (NBA) for two sites. Error bars represent standard deviation from parallelcores. (a) Tidal flat – pore water profiles from Neuharlingersieler Nacken (Wilms et al., 2006). (b) Deep sea – Station GeoB 6229 in the Argentine Basin, 3443 m water depth (Schulzand cruise participants, 1999). Note the different z-axis scales.


not be reproduced. In both setups oxygen penetration turned out tobe low or very low (mm to few cm) and sulfate-methane interfacesare generated, dominated by sulfate reduction at the tidal flat siteand by anaerobic methane oxidation at the deep sea site. The modelcalibration generated two sets of parameter values. The parame-trization differences are summarized in Table 1.

Generally, tidal flat sediments are characterized by a highcontent of labile OM and high activity of bioturbating and bio-irrigating organisms. Daily as well as seasonal variability arepronounced due to tidal forcing and shifts in temperature and inthe concentrations of many chemical species within the bottomwater. In contrast, boundary conditions in the deep sea site remainconstant, except slight annual temperature variations. OM contentof the surface sediment (0.5 cm) is higher than at the tidal flat site,but the material is mostly refractory.

This study aims to achieve a relatively complete assessment offactors controlling the N and C cycling in marine sediments,therefore, nine target variables where selected to represent modeldynamics. In order to manage the total number of target variables,we choose to aggregate the carbon and nitrogen that is processedby each of the specific reaction pathways into Shannon–WienerIndices (e.g. Begon et al., 1990). The Shannon–Wiener Index ofdiversity (SWID) is a measure of how a reactant is distributedamong different reaction pathways. Changes in the indices SWID-OM and SWID-NO3 are calculated from the spatiotemporal meanrates of reactions R-10 through R-15 and R-11, R-17, R-31, R-33 andR-54, respectively (reactions according to Table 2). Shifts in thedominance structure of carbon and nitrogen pathways areindicated by changes in the respective SWID. The SWID iscalculated from the number of different pathways G and theamount of substrate consumed fi by the ith pathway,SWID ¼

PGi¼1 fi=F$lnðfi=FÞ; with F ¼

PGi¼1 fi. The spatiotemporal

mean rates of CO2 and CH4 production actually account the totals ofboth carbon turnover and the gross activity of the heterotrophicfunctional groups. Likewise, spatiotemporal mean rates of nitrifi-cation and denitrification cover the large part of nitrogen turnoverand the gross activity of the nitrogen functional groups. Theaverage benthic fluxes of CH4, NO3 and NH4 serve as further indi-cators for sediment geochemistry. In a final stage of the SA, a moredetailed analysis of how either influential or unconstrained

parameters affect nitrogen dynamics is carried out by a continuousvariation of such model coefficients.

5. Results

5.1. Sensitivity analysis

The SA reveals the ubiquitous relevance of temperature, trans-port and sediment mixing, organic matter composition, andbacterial metabolism for carbon and nitrogen cycles. In contrast,bottom water concentrations and individual reaction specificcoefficients (biotic and abiotic) have marginal impact, as shown inFig. 3. In Fig. 3 the complicated patterns of model sensitivities aresummarized and leverages in each sub-categories are shown asaggregated into a single average value carbon or nitrogen cycle-specific target variables. The structural stability and thereforerobustness of the model dynamics is reflected by the similarity ofthe general sensitivity pattern of the tidal flat and deep sea setups,as seen in Fig. 4. The parameter sub-categories are given on the left.

Temperature is the most influential parameter. Abiotic reac-tions, microbial growth, OM decay and molecular diffusion are

Tidal flat Deep sea

Temperature

Transport & mixing

Organic matter

Global bacterial parameters

Reaction specific energy yield

Bottom water concentrations

Abiotic reaction coeffcients

C-Cyc

le

N-Cyc

le

C-Cyc

le

N-Cyc

le

highly sensitive

−log|v| area654321

210-1-2-3

insensitive

Fig. 3. Condensed view of the sensitivities of the carbon and nitrogen cycles withregard to different parameter subsets for the tidal flat and deep sea setups. Area andshading represent leverage, e.g. leverage 0 is displayed with four times the area ofleverage �3.

Table 2Diagenetic reactions resolved within the model. Organic material is chemicallyrepresented by carbohydrate CH2O.

Hydrolysis of particulate organic matter classes with variable C:N:P:Si ratios

ðCH2OÞcðNH3ÞnðH3PO4ÞpðH4SiO4Þs/cðCH2OÞ þ nðNH3ÞþpðH3PO4Þ þ sðH4SiO4Þ

R-0a

fermentation of high molecular (HM) to low molecular(LM) organic matter

CH2OðHMÞ/CH2OðLMÞ R-1a

Primary redox reactions and adsorptionCH2Oþ O2/CO2 þ H2O R-10a

CH2Oþ 45NO-

3/25N2 þ 1

5CO2 þ 45HCO-

3 þ 35H2O R-11a

CH2Oþ 2MnO2 þ 3CO2/2Mn2þ þ 4HCO�3 R-12a

CH2Oþ 4FeðOHÞ3 þ 7CO2/4Fe2þ þ 8HCO�3 þ 3H2O R-13a

CH2Oþ 12SO2�

4 /12H2Sþ HCO�3 R-14a

CH2O/12CH4 þ 1

2CO2 R-15a

NHþ4 þ 2O2 þ 2HCO�3 /NO�3 þ 2CO2 þ 3H2O R-16a

NHþ4 þ 35NO�3 þ 2

5HCO�3 /85N2 þ 2

5CO2 þ 115 H2O R-17a

NHþ4 þ 32MnO2 þ 3CO2/1

2N2 þ 32Mn2þ þ 1

2H2 þ 3HCO�3 R-18a

NHþ4 4NHþ4;ads R-19

POþ4 4POþ4;ads R-20

Secondary redox reactionsMn2þ þ 1

2O2 þ 2HCO�3 /MnO2 þ 2CO2 þ H2O R-30a

Mn2þ þ 25NO�3 þ 7

5HCO�3 þ 110H2/MnO2 þ 1

5N2 þ 75CO2 þ 3

5H2O R-31a

Fe2þ þ 14O2 þ 2HCO�3 þ 1

2H2O/FeðOHÞ3 þ 2CO2 R-32a

Fe2þ þ 15NO�3 þ 1

5HCOþ3 þ 145 H2O/FeðOHÞ3 þ 1

10N2 þ 15CO2 R-33a

Fe2þ þ 12MnO2 þ HCO�3 þ 2H2/FeðOHÞ3 þ 1

2Mn2þ þ H2O R-34a

H2Sþ 2O2 þ 2HCO�3 /SO2�4 þ 2CO2 þ 2H2O R-35a

H2SþMnO2 þ 2CO2 þ 4H2O/Mn2þ þ H2SO4 þ 2HCO�3 þ 3H2 R-36a

H2Sþ 2FeðOHÞ3 þ 4CO2 þ 2H2O/2Fe2þ þ H2SO4 þ 4HCO�3 þ 6H2 R-37a

CH4 þ 2O2/CO2 þ 2H2O R-38a

CH4 þ SO2�4 /CO2�

3 þ H2Sþ H2O R-39a

Monosulfide precipitation, reoxidation and pyrite formationMn2þ þ 2HCO�3 þ H2S4MnSþ 2CO2 þ 2H2O R-50

Fe2þ þ 2HCO�3 þ H2S4FeSþ 2CO2 þ 2H2O R-51

MnSþ 52O2 þ 2HCO�3 /MnO2 þ SO2�

4 þ H2Oþ 2CO2 R-52

FeSþ 94O2 þ 2HCO�3 þ 1

2H2O/FeðOHÞ3 þ SO2�4 þ 2CO2 R-53

FeSþ 95NO�3 þ 1

5HCO�3 þ 75H2O/FeðOHÞ3 þ SO2�

4 þ 910N2 þ 1

5CO2 R-54

FeSþ 92MnO2 þ 7CO2 þ 5H2O/FeðOHÞ3 þ SO2�

4 þ 92Mn2þ þ 7HCO�3 R-55

FeSþ H2S/FeS2 þ H2 R-56

a Reaction is processed by bacteria.


affected by temperature. In addition, parameters controllingporosity, the decomposition and quality of OM, and the growth andturnover rates of bacteria have universal character and strongleverage. Variation in these parameters generates responses in themajority of the target variables regardless of the setup. The tidal flatsetup does appear to be more sensitive to parameter changesthroughout all categories, with average changes of 0.6 leverageunits. The higher sensitivity of the tidal flat setup is most striking inthe parameter sub-categories for transport and mixing, organicmatter, and global bacterial parameters. External tidal forces, whichare not active in the deep sea setup, also significantly affect alltarget variables. Parameters related to bioturbation and bio-irrigation show medium leverages for the tidal flat setup and lowleverages for the deep sea setup. The transport and mixingparameters are clearly influential on nitrogen cycling outputs, buthave mediocre leverage on carbon cycling. Of all parameters tested,transport and mixing are the least similar in relation to nitrogenand carbon cycling outputs for both tidal flat and deep seaconditions.

Responses to changing bacterial yield constants (reaction specificenergy yields) are more heterogeneous, reflecting the relativeimportance of the reactions in terms of carbon and nitrogen turnover,e.g. the domination of the tidal setup by sulfate reduction versus theimportance of oxic and suboxic reactions in the deep sea setup.

In the tidal setup, a statistical analysis of the leverage classesreveals that insensitivity occurred in about 50% of all cases, asindicated by leverages of -3. However, given a total of 84 parame-ters, the chosen target variables are sensitive to 40 parameters onaverage (leverage above -1). Only 7 parameters have no effect onany of the target variables; these parameters are consistentlyunrelated to C and N cycling and therefore not covered by the targetvariables. Within the set of the leverages above -3, leverage class 0(a parameter change of less than one magnitude is required fora significant system reaction (S*)), forms the largest group,accounting for nearly a third of all cases. The classes -1 and -2(parameters that have milder effects) and class 1 (parameters thathave greater impacts) each constitute about one-fifth of theeffective leverages.

Nitrogen-related target variables display a higher sensitivitycompared to carbon cycle-specific variables. This difference is mostpronounced for transport and mixing parameters, which havenearly no effect for deep sea carbon cycling. The high N-cyclingresponsiveness is reflected by the sensitivities of the five nitrogen-related target variables, which exceed those of the carbon-relatedtarget variables in terms of average sensitivity and number ofinfluential parameters. For example, when counting leverage -1and up, the benthic NO3 flux, SWID-NO3 and nitrification are eachsensitive to changes in more than 40 parameters. In contrast,methanogenesis is sensitive to only a very few, but highly influ-ential, parameters. According to the numbers of influentialparameters, CH4, and especially its production, and the DOC par-titioning are characterized as less interrelated indicators with anintermediate mean effective leverage of a little less than zero. Thestimulating effect of redox environment oscillation created byvariable tidal current and recurrent atmospheric exposure isdocumented by the high leverage of the tidal cycle length. Althoughthe tidal cycle frequency is fixed and completely constrained, redoxoscillation can also occur in the field through bioturbation byrelocating sediment into a different redox environment (Aller,1994). While nitrogen cycling is very sensitive to redox oscillation,the carbon turnover seems unaffected.

Fig. 4. Comparison of sensitivity matrices of setup A (Wadden Sea) and setup B (deep sea). Shading intensity corresponds to the leverage of parameters, i.e. dark shading indicatesthat rather small parameter changes are sufficient to produce a predefined change in the respective target variable. Parameters and target variables that were further investigatedwith scenario analyses are underlined. Parameters denoted as symbols are defined in the Appendix. The parameters have been divided into 7 subsets by relation to the process theyreflect, as shown on the left of the figure.


The carbon cycle responds in a linear way to changing modelcoefficients. Highly influential parameters for CO2 generationcapacity are rare and exclusively relate directly to POC decay. Thelow impact of reaction specific energy yields and bottom waterconcentrations add to the picture of a predominantly electrondonor-limited system.

The general congruence of the leverage patterns of CO2 and theSWID-OM suggests the predominance of a coherent carbondegradation scheme. Thus, shifts in the partitioning of DOCconsumption pathways are not predominantly due to competition.The rare cases in which functional groups of bacteria increase indominance at the expense of other groups usually involve a change

Fig. 4. (continued).


in a parameter that directly relates to the competitiveness of thefunctional group, – the reaction specific energy yield. For example,the methanogenesis yield reflects the potential of methanogens toindirectly compete with sulfate reducers by up and down move-ment of the sulfate–methane interface. Also, a variation in theoxygen reduction yield is, in large part, compensated for bysubsequent pathways (NO3, Mn, etc.). Apart from functional group-specific parameters, global regulatory parameters for bacterialsurvival and proliferation also affect the competitive success ofheterotrophic functional groups e.g. bacterial mortality.

The nitrogen cycle displays an inhomogeneous pattern ofsensitivity to changes in input parameters. Organic matter andcoefficients for bacterial population growth have a relativelyuniform impact, but transport and mixing parameters appearasymmetric in their effect on nitrogen cycling. None of the inputparameters has the same leverage on all nitrogen target variablesand no two parameters have the same leverage pattern. Addition-ally, the leverage pattern of the tidal flat and the deep sea setupdiffer considerably. The variable responses of the nitrogen cycle to

changes of transport and mixing parameters reflect differentfeedbacks of the nitrification/denitrification cascade and partialdecoupling from carbon cycling, even in the monotonous deep seaenvironment. In all, the deep sea nitrogen cycle seems less affectedby changes of global bacterial parameters, especially regardingbacterial uptake, growth, and mortality, which have less leverageon both the N-specific conversion rates and the SWID-NO3. Inopposition to the general trend, bacterial adhesion, dormancy, andtemperature susceptibility of bacteria active in nitrogen metabo-lism mostly gain in relevance in the monotonous and less pros-perous environmental conditions of the deep sea setup.

In summary, when the model is calibrated for a tidal flatsetting, it shows higher sensitivity to changes in the inputparameters than when it is run in the deep sea setup, both withrespect to average sensitivity and the number of parameters withhigh leverage. However, the two setups show a comparablesensitivity pattern. Key parameters are reference temperature,temperature coefficient Q10, microbial growth rate, POC decayrate, and porosity. This emphasizes the universal importance of

0

0.5

1.0

1.5

Bioirrigation rate [1/d]

Av. rate [m

mo

l/m

2 /d

]

0.01 0.1 1 6 10 1 2 3 40

0.5

1.0

1.5

0.2

denitrificationnitrification

Bioturbation rate [cm2 /d]

288 291 294 297 3000

0.5

1.0

1.5

Reference temperature [K]

coldwarm

Fig. 5. Spatiotemporal averaged nitrification and denitrification rates as a function of bioirrigation rate, b, bioturbation coefficient, DB, and reference temperature, TR, for the tidalsetup. The standard parameter values are highlighted. Note that an increase in TR corresponds to a mean temperature decrease of the temperature forcing.


external temperature forcing, bacterial adaptation, and sedimenttexture for diagenesis. The nitrogen cycle appears to be linked toa high number of model processes and all associated targetvariables depend on a notably large number of parameters withmostly medium leverage. The carbon cycle associated targetvariables, on average, have lower responsiveness and lessdependencies. For example, the methane cycle is sensitive only tofew parameters that have high leverages.

5.2. Scenario analyses

Model analysis reveals that essential parts of the tidal flatnitrogen cycle, namely nitrification, denitrification and efflux ofNH4 and NO3, are dependent on bioirrigation and bioturbation ina nonlinear way. Temperature, albeit the most influential param-eter, has a rather unspecific and more linear impact.

The similar dependencies of nitrification and denitrification onbioirrigation are depicted in Fig. 5. A bioirrigation coefficient ofapprox. 1 d�1 marks the turning point where enough oxygen ispumped into the sediment for nitrifers to successfully competewith sulfide oxidizers. Here, the sediment shifts from importing toexporting NO3. This is also expressed by the leveling-off of thebenthic ammonium flux when the bioirrigation coefficient exceeds1 d�1, as illustrated in Fig. 6. Bioturbation has a different effect onnitrification. Below approx. 2 cm2/d, nitrifers benefit from ammo-nium imported from deeper zones where sulfate reducers effi-ciently enhance OM degradation and ammonium release. At higherbioturbation rates, large quantities of surficial OM are transportedto anoxic depths, leading to enhanced sulfide generation andsulfide oxidizers are increasingly outcompeting nitrifers, and thusinhibiting nitrification. At very high bioturbation rates, denitrifi-cation surpasses nitrification, leading to a net NO3 import. Deni-trification decreases with increasing bioturbation due to OM exportfrom suboxic layers. The impact of temperature on nitrification is

−0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.01 0.1 1 6 10Bioirrigation rate [1/d]

Ben

th

ic efflu

x [m

mo

l/m

2 /d

]

1−1

01234567

Bioturbatio

0.2

NH4NO3

Fig. 6. Dependence of mean benthic fluxes of NH4 and NO3 on bioirrigation, b, bioturbaparameter values are highlighted.

lower than on denitrification. Since TR is the reference temperaturefor the rate-modifying temperature function, a raise in TR emulatesa decline in environmental temperature and vice versa, illustratedin Figs. 5 and 6. Nitrifiers are usually oxygen-limited, hence, theydo not benefit from a temperature-related increase of POC decayand subsequent ammonium release. The effect of temperature-regulated metabolic activity on ammonium conversion rates ispartly compensated by increased upward diffusion of reducedchemical species like Mn2þ or H2S at higher temperatures due toenhanced activity of anaerobic or lithotrophic bacteria. Theincreased share of oxygen consumed by the reoxidation of reducedinorganic species exerts competitive stress on nitrifiers and inhibitsa significant rate increase at reference temperatures below 293 K.Consequently, NO3 production remains low at elevated tempera-tures and denitrifiers are outcompeted by sulfate reducers. Thebenthic nitrate flux decreases with lowered reference temperatureaccordingly.

6. Discussion

The leverage table in Fig. 4 provides a holistic view of theinterrelationships within the simulated biogeochemical systems.Generally, sensitivities do not contradict sensible expectations, e.g.the dependence of benthic O2 flux on the O2 bottom waterconcentration. Confirming the results of Andersson et al. (2006),who compared a model setting for shallow conditions with one fordeep sea regarding parameter identifiability, it is found that theinherent model dynamics, expressed by the leverage patterns, issubstantially similar despite the contrasting parameter settingsbetween tidal flat and deep sea. In accordance to other modellingstudies, we identified a few key parameters that, when slightlychanged, lead to drastic variations in the model output. One suchparameter is organic carbon bio-availability, which largely controlsearly diagenetic transformations and is, thus, expected to be of

2 3 4n rate [cm

2 /d]

flux flux

288 291 294 297 300−1

0

1

2

3

4

Reference temperature [K]

coldwarm

tion coefficient, DB, and reference temperature, TR, for the tidal setup. The standard


great importance (Middelburg et al., 1996). The high relevance oftransport, sediment mixing and porosity parameters was alreadyshown by Andersson et al. (2006) and Berg et al. (2001). Berg et al.(2003) also found that organic matter reactivity is one of the mostinfluential parameters. Although temperature is the most influen-tial parameter, it’s normally high level of certainty prevents thattemperature is included in diagenetic model sensitivity studies. It isdemonstrated by high ubiquitous impact of temperature and thescenarios in Section 5.2 that temperature must not be neglected,specifically in highly variable environments where temperatureuncertainty may be quite considerable. Bacterial metabolism israrely included into diagenesis models and therefore sensitivitydata on bacterial parameters are scarce. The high impact of bacte-rial parameters on carbon and nitrogen cycling challenges thecommon approach of including bacterial concerns into reactioncoefficients.

The information compiled in the sensitivity table can be used tocharacterize the biogeochemical mode of the modeled system(such as the SO4 domination of the tidal flat setup or the oxic/suboxic dominance in the deep sea setup) and to isolate influentialprocesses for specific model outputs. In addition, the use of themodel to constrain parameters is limited to parameters with highleverages. Constraints by model calibration of less influentialparameters like most of the reaction specific energy yields or theabiotic reaction coefficients may be tainted with great uncertainty.The SA helps to identify unrealistic parameterizations as well asproblematic or unessential model formulations. For example, thecarrying capacity for bacteria, which should reduce bacterialgrowth at high numbers due to spatial limitations, appears inef-fective in both setups. Further investigation revealed that falseparameterization caused the failed effect. Though efforts to inde-pendently constrain parameters cannot be replaced by SA, param-eters commonly cannot be constrained as desired specifically ifparameters are not physical quantities like the carrying capacity. Inthese cases the SA is helpful to identify the parameter leverages, forinstance, to increase the efficiency of automated fitting or skippingunnecessary processes. It was also revealed by the SA that themodel concept of a minimum starting bacterial population, whichallows bacteria a quick start from resistant dormant bodies, maysignificantly affect mediocre functional groups if the minimumbacterial population parameter is set too high. Specifically, meth-anogenesis may be overestimated since outcompeted metha-nogens are constantly replaced and are able to grow as long as DOCis available. The implementation of minimum bacterial populationwill therefore be critically reviewed to ensure that biogeochemicalcycling is not affected in steady state.

6.1. Inertia of biogeochemical systems

The lower leverages in the deep sea system illustrate the stolidbiochemical cycling in such environment. Less steep gradients,broader redox zones, lower temperatures, less reactive OM, andweak forcing increase the inertia of the system, thus resistingchanges in single intrinsic or external factors. OM half-life, i.e. POCconversion rates, has a self-amplifying effect through enzymaticdecay enhancement: higher bacterial numbers that are supportedby enhanced POC decay in return stimulate the POC decay byenzymatic action. For labile POC, such as in the tidal setup, smallchanges in POC decay, e.g. by seasonal temperature variation, leadto a drastic change in supported population numbers and conver-sion rates. Therefore, in the tidal setup enzymatic decay enhance-ment is one of the most influential parameters.

Due to the very low bioturbation and bioirrigation rates in thedeep sea setup, exchange of matter across the sediment-waterboundary is of much less importance than in the tidal flat setup.

Accordingly, parameters for the bottom water concentrationgenerally have a lower impact in the deep sea setup. This applies tothe composition of particles in the bottom water as well. As theseparticles are thought to be in suspension, they are subject to bio-irrigation transport just like solutes. Thus, the leverages of bottomwater particle composition depend on mixing intensities. Thisindicates that particles have major impact on the sensitivity ofcoastal systems, for they represent an important source of bothlabile OM and metals, as seen in the leverages of POC, MnIV and FeIII

contents.The differences in model output between the tidal flat and the

deep sea setup partly result from the prevalence of differenttransport modes. Since the main transport mechanism in the deepsea setup is diffusion, the porosity- and diffusion enhancement-related parameters gain relevance, whereas in the tidal flat setupsediment mixing- and bioirrigation-related parameters are moreinfluential. When considering the importance of bottom watercomposition, which is characterized by turbulent mixing andshallowness in coastal ecosystems, the relevance of water columnprocesses for coastal sediments becomes evident. Just like manypelagic models partially integrate benthic processes (Baretta et al.,1995; Ebenhoh et al., 1995), a partial integration of water columnprocesses into sediment models appears reasonable in order tofurther assess water column–sediment feedback mechanisms.

The SA reveals a number of unexpected nonconformitiesbetween the setups compared in Fig. 4. Parameters that exhibitdivergent sensitivities to certain target variables include the effectof porosity on carbon cycle-specific variables (especially the SWID-OM, CO2 and CH4 production), the impact of the fractal dimensionof POC on the nitrate flux, the influence of bottom water concen-tration of nitrate, POC and DOC on nitrate flux, the effect of theaerobic ammonium reduction yield on the nitrogen specific vari-ables, the aerobic methane reoxidation yield on methane flux, andthe FeS oxidation rate on NO3 on nitrification. In some cases, theparameters involved are the calibrated parameters from Table 1,such as porosity or bottom water concentrations, or are closelyrelated, such as the fractal dimension of POC relating to POC decayrates. Therefore these divergent sensitivities can be ascribed tomodel nonlinearities. To clarify the remaining discrepancies furtherwork will need to be done to analyze model behavior that is nota priori intelligible in order to discriminate between unexpectedinteractions and model shortcomings.

6.2. Nitrogen cycling and mixing

Variablilty in bioirrigation and bioturbation may cause differentnitrogen dynamics, e.g. shifts from import to export of NO3. Nitri-fication and denitrification are alternatively affected in the same orin the opposite way within certain intervals of bioirrigation andbioturbation intensities, as depicted in Figs. 5 and 6.

In contrast to model formulations, the colonisation density ofirrigating organisms controls the dimension of the transition zonebetween oxic and anoxic environments around burrow structures(Aller, 1994). The suboxic conditions promote denitrification(Gruber and Sarmiento, 1997), but according to Gilbert et al. (2003)the irrigated sediment zone eventually can become fully aeratedwhen the colonisation density becomes very high resulting indecreased denitrification rates. Due to spatial resolution, the modelbioturbation does not account for geometric considerations.Instead, increased bioirrigation simply increases the thickness ofthe suboxic zone. Kristensen and Blackburn (1987), working withpolychaetes in microcosm, report stimulated nitrification, denitri-fication and benthic fluxes through bioturbating organisms, whichis not confirmed for denitrification by model results. However, ifa bioirrigating effect is also assumed for the organisms, increased


denitrification is likely to occur. The effect on biogeochemistry ofspecific colonisation and activity patterns of organisms is rarelyconsidered in models (Meile et al., 2003; Meysman et al., 2005),even though biogenous sediment heterogeneities may haveconsiderable impact on nitrogen cycling (Asmus et al., 1998; Stiefand de Beer, 2006).

The different responses of nitrification and denitrification toparameter changes lead to strong fluctuations of the ratio ofdenitrification to nitrification. Denitrification rates never fall below68% of nitrification and seem to be overestimated compared toliterature data (Henriksen et al., 1981; Hammond et al., 1985; Jen-sen et al., 1990). Since the reaction specific energy yield of bacteriais related to the Gibbs free energy of the respective reaction,denitrifiers in the model derive about as much energy from OMreduction as aerobic heterotrophs, which may not be realistic.Certainly, the model ignores that different organisms can influencenitrogen turnover in specific ways (Svensson and Leonardson,1996), which limits the soundness of model results. Macrobenthicbiota are not explicitly modeled, although excretion of fecal pelletsstimulates ammonium release and nitrification within the pellets(Henriksen et al., 1983). The effect of macroorganisms is incorpo-rated through bioirrigation and bioturbation, but in a static way sothat in the model these effects will not react to habitat changes asproposed by Reise (2002). Likewise, the addition of phytobenthicactivity would add essential habitat characteristics with consider-able effect on benthic nitrogen fluxes. Implications for biogeo-chemical cycles related to carbon fixation, release of oxygen andpolymeric exudates would add a layer of complexity throughsuperposition of day-night and tidal cycles. Food-web effects, suchas top-down control of phytobenthos or bacteria by meio- andmacrobenthic organisms are also lacking in the model (Middelburget al., 2000; An and Joye, 2001). As it stands, the specific activitypatterns of infauna are absolutely important for nitrogen cycling.The physical aspects of bioturbation and bioirrigation, the param-eters of biodiffusion, and the extent of non-local transport arehighly uncertain for most locations. Their impact on nitrogencycling, reflected by the heterogeneous sensitivity pattern of thetransport and mixing parameter subset, suggests that constraints tobioturbation and bioirrigation activity (D’Andrea et al., 2004) aswell as more detailed model formulations (Boudreau, 1994;Meysman et al., 2007) are essential to obtain increasingly realisticmodel results.

6.3. Linking carbon and nitrogen cycles

The carbon cycle has an overall lower sensitivity to changes ininput parameters than the nitrogen cycle; this is not a result of themodel construction. There are about as many heterotrophic redoxreactions (6) as there are nitrogen-related ones (7), denitrificationbeing part of both groups (cmp. Table 2). For nitrogen, a highpotential for internal feedback is created by the four denitrifyingreactions (anaerobic ammonium oxidation and denitrification withMn, Fe and FeS) and depends on nitrification for nitrate supply andcompetition with other secondary redox bacteria for electrondonors. In contrast, the carbon degrading processes generallyinterfere less with each other. The high load of labile OM in the tidalsetup creates a mode of dominate sulfate reduction, where thegenerated H2S effectively scavenges reduced metals, therebyinhibiting the heterotrophic metal oxidizers. Once high H2Sconcentrations build up in surface sediments, even aerobicheterotrophs are decreased through the depletion of oxygen by theH2S oxidation. The dominance and self-amplification of sulfatereducers by suppressing competitors through metabolite restric-tion inhibits major functional shifts. In the deep sea setup, thebiomass of heterotrophic bacteria is mainly distributed among

oxygen and sulfate reducers. Due to scarcity in reduciblesubstances, the remaining heterotrophic functional groups barelysurvive. This is also reflected by the much smaller sensitivitydifference between carbon and nitrogen cycles in the deep seasetup where functional shifts represented by SWID-OM and SWID-NO3 are mainly restricted to changes in POC decay.

Metal cycling is related to both carbon and nitrogen cycling.However, the impact of metal cycling-related parameters generallysuggests predominant nitrogen–metal interrelations, not solelybecause there are 3 metal–nitrogen redox paths and only 2 metal-OM redox paths in the model. The metal–nitrogen redox paths arealso preferentially utilized, especially for the parameter subsets:reaction specific energy yield, bottom water concentrations andabiotic reaction coefficients. Here the SA reveals that the nitrogencycle holds an intermediate position between carbon and metalcycling. Even though the reaction specific energy yield and abioticreaction parameter leverages are mostly low, they may not bedisregarded, since the uncertainty of these parameters is consid-erable. Apart from metal cycling, carbon and nitrogen cycles appearclosely coupled, related to the release of both elements in fixedratios during biomass degradation. Hence, variations in nitrogencycling are usually accompanied by changes in CO2 generation andshifts in heterotrophic pathway partitioning. Exceptions to thecoupling are confined to a few process-specific parameters: e.g. theMnII oxidation yield with NO3.

No interaction of nitrification and aerobic methane oxidationcan be deduced from the SA, although nitrogen limitation ofmethanotrophs as well as inhibition of nitrifers by methanotrophshas been reported by Carini et al. (2003) in coastal sediments. Aninteraction between nitrifers by methanotrophs can be expected,since both compete for oxygen, but the lack of a permanentoxygenated layer in the tidal flat setup makes aerobic methaneoxidation insignificant. A leverage of -2 for the NO3 reduction yieldon the benthic CH4 flux suggests that aerobic methane oxidizers areoutcompeted by denitrifers due to their lower energy yield. Therelatively high leverage of CH4 oxidation with SO4 on benthic CH4

flux confirms that anaerobic methanotrophs metabolize close totheir thermodynamic limit as proposed by Dale et al. (2006).

6.4. Sensitivity in terms of parameter leverages

In contrast to classical sensitivity studies, which map thesensitivity according to a fixed parameter change, y, the use ofleverage specifies the parameter change needed to obtain a signif-icant reaction in the system. It is therefore suited to estimate theactual impact of parameter uncertainty. Predetermination of y

according to an estimative or arbitrary uncertainty of the respectiveparameter is unnecessary. Since leverage indicates the magnitudeof parameter influence, comparison with parameter uncertaintyproduces its actual impact. In other words, an influential but wellknown and invariant parameter may have less importance fora variable than a less influential but unconstrained parameter. Bothleverage and uncertainty add up to the relevance of a parameter formodel soundness. As uncertainty is not a model feature but issubject to a posteriori change, it seems undesirable to use theformer to derive y, as suggested by classical sensitivity analysis.Since leverage is calculated from the relative change in y, gener-ating a specific response level, problems that arise from comparingsensitivities that originate from different values of y can be avoided:the resulting leverage matrix allows the comparison of modelsensitivities that are valid on very different scales. Occurrences ofunrealistic variations, e.g. y¼ 2 for TR or porosity, are still possiblebut are confined to those target variables that are obviouslyinsensitive to this parameter. However, the numerical effort ofcalculating leverage is usually several times higher than that


required for a classical SA, depending on y stepping and howsensitivities are distributed. On the other hand, scanning a range ofparameter values will also return more complete information onhow a specific parameter affects the target variables regardless ofparameter uncertainty. The leverage method can easily beextended to calculate the second derivatives of the model in orderto better assess nonlinear processes.

7. Conclusions

The leverage approach demonstrates its usefulness in assessingmodel sensitivity. The separation of parameter leverage andparameter uncertainty appears advantageous as the sensitivityanalysis is valid for a calibration regardless of research question orstudy site. The model demonstrates robustness in the sense ofstructural stability, as it shows comparable sensitivities regardlessof calibration. While temperature and bacterial parameters areimportant to both analyzed scenarios, the tidal flat setup is char-acterized by specific sensitivities to not only transport and mixingbut also organic matter parameters, especially enzymatic POCdecay enhancement, the OM content of particles, and the yield ofsulfate reducers on DOC. The number of sensitivities found ina steady state setup implicates a rather small potential for ad-hocmodel simplification. In contrast, the deep sea sensitivities aremore detached. Although the deep water setup was overall lesssensitive to changes in the input parameters, parameters such asthe temperature susceptibility of bacterial metabolism, the oxygencontent of the bottom water, and the sediment porosity are on parwith the overall higher sensitivity of the tidal flat setup. Thedifferent effects between the setups and the higher significance ofbioirrigation and bioturbation to the tidal flat demand furtherinvestigations. These should broaden the empirical bases of esti-mates for habitat specific bioirrigation and bioturbation coefficientsrelated to macrobenthic activity and may identify possiblecommonalities between these parameters.

The general high sensitivity of the nitrogen cycle to parameterchanges emphasizes the need for sophisticated models specificallyengaging the nitrogen cycle in order to characterize terms andconditions on which sediments act as sinks or sources for NO3, theinfluence of specific irrigation and mixing habits of macrobenthiccommunities, and the implications for N2O generation. Theextension of leverage to classical sensitivity analyses will add to thearray of tools available for assessing the impact of parameterchange and uncertainty of complex systems. Though numericallymore demanding, it accounts for parameter uncertainty andconsiders not only nonlinear system behavior but also differentparameter scales.

Appendix A. Model principles

A.1. Transport

Transport processes are divided into non-local transport ofsolutes (bioirrigation) and local transport processes of solutes andsolids, i.e. diffusion, bioturbation, advection and sedimentation. Theeffective diffusion coefficient, Di, is a composite of moleculardiffusion and mixing due to bioturbation:

Di ¼Dsw

q2 þ DBz (A1)

The temperature sensitive diffusion coefficient of dissolved chem-ical species Dsw is taken from a comprehensive literature study(Boudreau, 1997) and linearly depends on temperature. Diffusivetransport between two neighboring model boxes is calculated

according to a relaxation scheme using effective box volumes in thevicinity of the respective border. For small box sizes, the solutionconverges to Fick’s second law of diffusion. Bioturbation is scaled bythe depth dependent biodiffusion coefficient DB

z and allows intra-phase mixing only. Bioirrigation is implemented as non-localtransport connecting every sediment box directly to the bottomwater with pelagic matter concentrations C0 hence, for anyconcentration of biochemical species i, the relaxation scheme reads

_Ci ¼ bz$�C0;i � Ci

�(A2)

In order to account for fading mixing in deeper sediment layers, DzB

and bz exponentially decrease with depth and vanish at bio-turbation depth zB and bioirrigation depth zb, respectively. At z¼ 0,Dz

B and bz equal the biodiffusion coefficient DB and bioirrigationcoefficient b. Porosity f and tortuosity q are characteristic for eachbox and, thus, not transported. In order to account for stratification,lateral facies zonation, or inhomogeneous permeabilities, theexponential porosity decreases after Rabouille et al. (1997) and thecalculation of tortuosity from porosity using Boudreau’s law(Boudreau, 1997) may be overridden, allowing predefinition ofporosity and tortuosity for each box. Sedimentation/erosion actslike advection; however, it affects both solids and solutes in thesame way.

A.2. Geochemical reactions

The geochemical module comprises four types of reactions: (i)Hydrolysis of particulate organic matter (represented by POC) todissolved organic matter (DOC) in classes of different quality, (ii)fermentation and oxidation of high molecular weight organiccarbon HM-DOC and oxidation of low molecular organic carbonLM-DOC, (iii) reoxidation of reduced species and (iv) mineralprecipitation. The reactions are summarized in Table 2. The organicmatter degradation module is based on the model presented byBoudreau (1992). Global POC, HM-DOC and LM-DOC pools aresubdivided into three fractions each, defined according to turnovertime and Redfield ratios, reflecting different inherent qualities,origin and degree of decomposition. Since the use of hydrolyticexoenzymes belongs to the disposal of bacterial foraging strategies,POC hydrolysis is enhanced by aerobic bacteria (Vetter et al., 1998;Bidle and Azam, 1999). As only fermentation converts HM-DOC intoLM-DOC, the distribution ratio of POC to the DOC pools may createa fermentation bottleneck for subsequent mineralization processes.

Nitrogen dynamics have an explicit link to the carbon cycle byammonification of the POC classes. Also, denitrifiers compete withother heterotrophs for OM and with metal oxidizing lithotrophs fornitrate. Lastly, two types of anaerobic ammonium oxidizers, nitrateand manganese reducers, compete for ammonium. With interre-lations to carbon as well as metal cycling, seven nitrogen reactionsallow the display of a comprehensive spectrum of nitrogendynamics under oxic, suboxic and anoxic conditions.

NH4 and POþ4 are subject to adsorption, so that they exist inboth solid and aqueous phases at concentrations Cs and Caq,respectively. Adsorption is implemented as first order FreundlichIsotherm, i.e.

Cs

Claq¼ Kad l ¼ 1 (A3)

with Kad being the adsorbtion constant and l the Freundlichexponent.

Monosulfide precipitation (reactions R-23 and R-24 as definedin Table 2) is assumed to be in thermodynamic equilibrium


according to the law of mass action. With Me as a placeholder forthe metals iron or manganese we have�Me�$½H2S� ¼ wðTÞ$Keq (A4)

where Keq is the equilibrium constant for the respective reaction atreference temperature and w(T) a nonlinear temperature term (seeA.4) accounting for the fact that the equilibrium of endothermalreactions (e.g. metalsufide dissolution) is shifted towards theproducts at higher temperatures.

Reoxidation of monosulfides and pyrite formation (reactions R-25–R-29) are rate controlled reactions. The temperature sensitivereaction rate Rn

Rn ¼ rn$wðTÞ$Ln with Ln ¼ a$

�b=blim : if b < blim

1 : else(A5)

depends on the specific rate constant rn and the limitation term Ln.While linear to electron donor concentrations a, the reactionkinetics is shifted from second to first order if the electron accep-tors concentration b exceeds a certain saturation concentration blim.

A.3. Rate limitation by bacterial activity

The major part of the reactions (R-1–R-18; R-30–R-39),fermentation and oxidation of organic carbon and reoxidation, arecontrolled by the catabolic substrate turnover of bacteria. In themodel, each population of bacteria represents a functional groupdefined according to its metabolic pathway. The reaction rates Rn

(n¼ R-1, ., R-18, R-30, ., R39) are linear functions of the activebiomass Xact, n of the respective microbial population. Again, weemploy an electron acceptor-controlled second to first order reac-tion kinetic shift analogous to Eq. (A5),

Rn�Xact;n

�¼ rg$wðTÞ$Ln$Xact;n (A6)

where rg is a global rate constant.In summary, energetically less favorable pathways are not

directly inhibited but can be limited by decreased activities ofoutcompeted microbial populations.

A.4. Activation energy

Activation energy of chemical reactions is implicitly resolved bythe temperature coefficient Q10. It controls the temperaturedependence w of reaction and growth rates, i.e.

wðTÞ ¼ Q1=10ðT�TRÞ10 (A7)

T and TR are ambient and reference temperature in Kelvin. Forsimplicity, all chemical and biological temperature dependenciesuse the same value of Q10.

A.5. Microbial population dynamics

A.5.1. Population growthThe microbial growth module essentially resembles Malthus’

theory of population growth (Malthus, 1798). It also includesdensity regulation, where the reproductive rate depends on thepopulation size and a measure for the carrying capacity Xcap, whichamong others factors, represents spatial limitations. Moreover, onlyactive bacteria with concentration Xact take part in reproductionwhereas dormant bacteria (Xdorm) have their mortality lowered bythe factor d:

_Xn ¼ gXact;n � r�Xact;n þ dXdorm;n

�Xcap

(A8)
with g ¼ yn$s$rg$wðTÞ$Ln$XnþXcap
and r ¼ m$wðTÞ

yn is the reaction specific energy yield which determines how muchenergy the functional group n can convert into biomass from theenergy gain released by catabolic reaction Rn; s denotes an ubiq-uitous growth coefficient and m is the mortality. The temperaturedependent loss term r comprises both respiration and mortality e.g.by grazing. Aside from the metabolic pathway, the functionalgroups solely differ in the specific energy yield of the reactionemployed. In the model we assume all reactions to be catabolic, i.e.there is no assimilation of carbon or any other nutrient by thebacteria, thus bacteria do not represent a pool for chemical species.Therefore, organic carbon is immediately and completely convertedto CO2 upon bacterial use.

A.5.2. Dormancy

Adaptive processes within each functional group are restrictedto behavioral aspects on the level of individual cells such asdormancy and motility. The concept of dormancy as alreadyintroduced by (Wirtz, 2003) was upgraded from extreme valueswitching to continuous behavior. It is a simple analogy to theo-retical considerations made by Boudreau (1999) and refers to thegeneral observation that organisms replicate only when conditionsare beneficial. If not, they concentrate on survival through envi-ronmental stresses. The fraction of active, i.e. non-dormant biomassis expressed by a

Xact ¼ aX where 0 < a < 1 (A9)

Substituting Eq. (A8) with Eq. (A9) gives

_X ¼ brX ¼ ða$½g � rð1� dÞ� � rdÞX (A10)

Changes in a reflect bacterial adaptation to changing environ-mental conditions. Based on the Adaptive Dynamics approach forphenotypic traits proposed by Wirtz (2003), bacteria embark ona strategy of maximizing the growth rate, i.e.

_a :¼ að1� aÞvbr

va(A11)

Adaptive changes will, thus, be rather slow at extreme values ofa and fast at intermediate values and large growth benefits.

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