-
asul, Cra
ent,
Keywords:Sediment diagenesis model
neses i
study summarised and categorised the variables,
parameterisations and applications of 83 models
Models have been applied to a range of environments, however,
there was no corresponding difference
the sequatic
processes than the entire overlying water column (Boudreau,
sophisticated models that parameterise and combine
transportprocesses and reaction pathways, in order to explore the
systemresponses of complex aquatic environments (see, for
example,
developed to examine specically a range of systems and
processes,rndt et al., 2013),aters (Pe~na et al.,2004;
Jrgensen,
and Zheng, 2012),. In recent years,the development
sport models (see,, 2008) and devel-ce and suitability
(Bennett et al., 2013). With this context, it is therefore
timely toanalyse the development and performance of a large body
ofliterature that has emerged on sediment reactive transport
models.
The basis of numerical sediment diagenesis models was laid outby
Berner (1980) and further developed by authors such as VanCappellen
et al. (1993), Van Cappellen and Wang (1995), andBoudreau (1997,
2000); readers wishing to understand the theoryof diagenesis models
should begin with these publications. Thefundamentals were taken
into early numerical models by authors
* Thematic Issue on Novel Approaches to Challenges in Aquatic
EcosystemModelling.* Corresponding author.
Contents lists availab
Environmental Mod
journal homepage: www.els
Environmental Modelling & Software 61 (2014) 297e325E-mail
address: [email protected] (D.W. Paraska).2000) and
it is a hotspot for biogeochemical function. An explo-ration of the
physical, chemical and biological dynamics in thisnear-surface
sediment, termed early diagenesis, gives us a betterunderstanding
of the natural processes that shape elementalpathways, and allows
us to assess the effects of human activity,which include the
disruption of nutrient, oxygen and carbon cy-cles associated with
eutrophication and contamination of aquaticecosystems.
Sediment models are part of the greater group of
increasingly
including marine organic matter degradation (Acarbon cycles
(Mackenzie et al., 2004), hypoxic w2010), aquatic ecology
(Arhonditsis and Brett,2010; Mooij et al., 2010), groundwater
(Huntand heavy metal transport (Boudreau, 1999)increasing attention
has been given to analysingof the features and applications of
reactive tranfor example, Jakeman et al., 2006; Robson et al.oping
standards for assessing their performanecology. The upper layer of
the sediment can have more chemical (Luff and Moll, 2004). Reactive
transport models have also beenMeta-analysisAquatic systems
1. Introduction
Chemical interactions betweencolumn are a key component of
ahttp://dx.doi.org/10.1016/j.envsoft.2014.05.0111364-8152/ 2014
Elsevier Ltd. All rights reserved.include: aligning conceptual
models of organic matter transformations with measurable
parameters;gathering accurate data for model input and validation,
including datasets that capture a range of time-scales; coupling
sediment models with ecological and spatially-resolved hydrodynamic
models; andmaking the models more accessible for water quality and
biogeochemical modelling studies by devel-oping a consistent
notation through community modelling initiatives.
2014 Elsevier Ltd. All rights reserved.
diment and the waterbiogeochemistry and
Steefel et al., 2005; Soetaert and Herman, 2008, for general
works).The models of this eld are able to estimate chemical
concentra-tions and reaction rates at a temporal and vertical
resolution that isdifcult to reproduce with in situ or laboratory
experimentationAccepted 6 May 2014Available online 7 August 2014in
approach or complexity. The major challenges and opportunities for
the development of the models16 April 2014 published since 1996.
The choice of variables and processes used was found to be largely
arbitrary.Sediment diagenesis models: Review ofopportunities*
Daniel W. Paraska a, *, Matthew R. Hipsey a, b, S. Ura Aquatic
Ecodynamics, School of Earth & Environment, University of
Western Australiab The Oceans Institute, University of Western
Australia, Crawley, WA 6009, Australiac National Centre for
Groundwater Research and Training, School of Earth and Environm
a r t i c l e i n f o
Article history:Received 8 July 2013Received in revised form
a b s t r a c t
A range of sediment diagehowever, the diversity makpproaches,
challenges and
a Salmon c
wley, WA 6009, Australia
University of Western Australia, Crawley, WA 6009, Australia
is modelling approaches have been developed over the last two
decades,t difcult to identify the best approach for a particular
aquatic system. This
le at ScienceDirect
elling & Software
evier .com/locate/envsoft
-
such as Rabouille and Gaillard (1991a, b), Tromp et al.
(1995),Furrer and Wehrli (1996), Dhakar and Burdige (1996) and
Parkand Jaffe (1996). Of the models that were developed in
thisperiod, the studies by Boudreau (1996), Van Cappellen and
Wang(1996) and Soetaert et al. (1996a) have emerged as the basis
formost of the numerical models developed by other authors
sincethen (these three are cited 155, 294 and 201 times,
respectively,in ISI Web of Knowledge, as of December 2013). The
studies thatdeveloped from these three papers share some common
processdescriptions and general conceptual bases (Fig. 1),
however,many variations in the implementation and the
increasingcomplexity of the biogeochemical processes in subsequent
ap-plications have made it difcult to absorb the
terminology,compare the models and identify the best approaches for
a givenapplication that an aquatic ecosystem modeller entering
theeld may be interested in. Further, while many of the
originalmodels were intended for the coastal or open ocean,
theyhave since been applied widely across the spectrum of
aquaticenvironments, including from oligotrophic to eutrophic
inlandand coastal waters. The connection between models
purpose,structure and performance (as has been done recently for
moregeneral models of P dynamics by Robson, 2014)
remainsunexplored.
It is the aim of this article to conduct a review
andmeta-analysisof sediment diagenesis model publications that have
emerged sincethe theoretical texts and the key 1996 model
applications. By doingso we aimed a) to identify commonality
between the studies anddene a practical classication of commonly
used approaches, b) to
2. Analysis approach and scope
We gathered 83 sediment diagenesis modelling studies from
thepeer reviewed literature in the period between 1996 and
2013,which are listed after themain reference list at the end of
the paper.We considered vertically multi-layered, rather than one-
or two-layer models, process-based rather than empirical models and
nu-merical rather than analytical models. The focus of this
analysis isnot on the software codes themselves, which have been
examinedby Meysman et al. (2003a), nor the numerical solution
methods.
This analysis is primarily focussed on the multi-G models
thatwere developed from the Gmodel of Berner (1980).
Continuous-Gmodels have also been developed, in which the
properties of thecomplex mixture are considered to be a function of
depth, which inturn has reected organic matter age (originally by
Middelburg,1989 then Boudreau and Ruddick, 1991, followed up
recently byauthors such as Wallmann et al., 2008; Arndt et al.,
2009; Vahataloet al., 2010; Rodriguez-Murillo et al., 2011; Gelda
et al., 2013). Theadvantages of these empirical models are that
they can be adjustedto t depth proles closely, they require few
input parameters andthey recognise the importance of the changing
reactivity of organicmatter over time, which is a factor that many
other models do nottake into account (Van Cappellen et al., 1993).
However, thecontinuous-G model studies generally neglect the
reactions of theoxidants and other secondary and mineral reactions
that areimportant in determining other environmental geochemical
pro-cesses, such as the uxes of nutrients, oxygen and
contaminants,and so this analysis is solely focused on multi-G
models. Rather
D.W. Paraska et al. / Environmental Modelling & Software 61
(2014) 297e325298compare the model studies in the context of the
questions theyaddress and study environments, c) based on the above
analysis, toidentify challenges for the development and improvement
ofsediment diagenesis models and opportunities for advancingmodel
accuracy and performance, and d) ultimately to assist andencourage
the uptake and application of these models by the widerecological
modelling community.Fig. 1. Schematic of the main physical and
chemical processes that cause chemical concenttherefore are
included in most sediment diagenesis models. The chemicals and
reaction prothan organic matter reactivity being assigned as
proportional todepth or age, multi-G models have a few distinct
pools each withdifferent reactivity. The origins of most of the
recent multi-Gmodels can be traced back to one of three sources
that had devel-oped Berner's model, based on either the CANDI model
(Boudreau,1996), the STEADYSED model (Van Cappellen and Wang,
1996), orthe OMEXDIA model (Soetaert et al., 1996a). As will be
explained inration and ux change in the sediment and across the
sedimentewater interface, andcesses included in different studies
vary widely and are shown in the following tables.
-
the following sections, these three sources differed originally
withrespect to the choice of organic matter oxidants and rate
lawparameterisation (Table 1), but subsequent studies have
introducednumerous other changes.
We believe that this meta-analysis should help readers
toidentify more easily how specic model applications comparewith
the range of model features published to date. As will beshown
below, any classication that was useful for the features ofthe
models was less useful for the applications of the models, andso in
order to analyse these 83 diverse studies more easily, westarted
the classication of their features according to the threemajor
approaches. Although there is no underlying philosophicaldifference
between these approaches, the features of many of themodels are
explained as a result of the historical development ofeach model
from another previously-published models. Thisstudy summarises the
model features, which include the con-ceptualisation of organic
matter pools with respect to their reac-tivity, the choice of
organic matter oxidants, the selection ofthe organic matter rate
laws and parameters, and the range ofsecondary redox reactions,
mineral reactions, and physical andbiophysical transport processes.
For the analysis of model appli-cations, the study describes how
these fundamental model com-ponents have been used in different
environments and identiesapplications of the models where the
effects of anthropogenicactivity have been the specic motivation.
The study then assesseswhere the models have been applied with
steady or dynamic
simulations, including where seasonal timescales of change
havebeen examined, and where the coupling of sediment models
tospatially resolved water column models has occurred. Finally,
thefeatures and applications are brought together to assess
thechallenges identied from the previous sections, and
potentialopportunities to help improve model rigour and use by the
widerscientic community are suggested.
3. Model components
Here a concise summary of the common features of
numericalsediment diagenesis models is given, to provide context
for theclassications used in the meta-analysis. The models have
theirorigin in the general diagenetic equation, dened by Berner
(1980)as the sum of chemical reactions and physical processes e
advec-tion, diffusion and biological mixing:
v1frCsvt|{z}
Solid particle
concentration
change in time
DBv21frCs
vx2|{z}biodiffusion
v1furCsvx|{z}
advection
sedimentation
1frX
Rs|{z}reaction
(1)
Table 1The three major approaches to the parameterisation of
organic matter oxidation. Terms are explained in Section 3.
ROM total organic matteroxidation rate
Oxidation rate due to ith oxidant ROxi Oxidation term FTEAi
Inhibition term FIniFIn1 1
Approach 1i from reactions (3) to (8)ROM
P6i1 ROxi
ROxi kOMFOMFTEAi FIni for i 1e5,FTEAi
OxiKOxiOxi
; FTEA6 1* for i 2 to 6,FIni
Yi1j1
KOxj
Oxj KOxj
!**
Approach 2
i from reactions (3)e(8)
for i 1 to 5ROxi kOMFOMFTEAi FIniand
for i 1 to 58>>>< 0 when Oxi1 > LOxi1w
for i 2 to 5
FIni Yi1
1 Oxj!
Oxi
OxiOxi
O
ferenforionrametexe, 19ijsm004,h et al., 2009, Couture et al.,
2010, Massoudieh et al., 2010, Reed et al., 2011a, b,inh Anh et
al., 2012, Tsandev et al., 2012, Dale et al., 2013, Katsev and
en 1., 20et al
Her, So
akar
D.W. Paraska et al. / Environmental Modelling & Software 61
(2014) 297e325 299ROM P6
i1 ROxi ROx6 kOMFOM P5
i1 ROxi FTEAi >>>:1
OxiLOxi
FTEA6 1Approach 3
i from reactions(3), (4) and (9)
ROM P3
i1 ROxi
ROxi kOMFOMFOxi FIni for i 1, 2, F
for i 3;K
Approach 1
* Boudreau (1996) and Boudreau et al. (1998) use a difApproach 1
papers report the same Monod expression** Three Approach 1 studies
use a simple on-off inhibit*** Classication based on organic matter
oxidation pa**** Also include a term for bacterial reaction, FBact.
SeeBoudreau, 1996*, Park and Jaffe, 1996**, Smith and JaffMorse,
2000, Haeckel et al., 2001, Konig et al., 2001, WWallmann, 2003,
Luff and Moll, 2004, Eldridge et al., 2Eldridge and Morse, 2008,
Devallois et al., 2008, DittricBektursunova and L'heureux, 2011,
Dale et al., 2011, TrDittrich 2013, McCulloch et al., 2013
Approach 2 Van Cappellen and Wang 1996, Wang and van
CappellFossing et al., 2004, Aguilera et al., 2005, Thullner et
alJourabchi et al., 2008, Sochaczewski et al., 2008, KasihBessinger
et al., 2012, Smits and Van Beek, 2013
Approach 3 Soetaert et al., 1996a, b, 1998, Middelburg et al.,
1996,Sohma et al., 2004, Berg et al., 2007, Dedieu et al.,
2007Pastor et al., 2011
Others Rabouille and Gaillard, 1991a**, Tromp et al., 1995,
Dh
Berg et al., 1998, Rabouille et al., 2001, Archer et al.,
2002,996, Rysgaard and Berg 1996, Van Den Berg et al., 2000, Berg
et al., 2003,05****, Jourabchi et al., 2005, Canavan et al., 2006,
2007a**,b***,., 2008, 2009, Dale et al., 2009, Brigolin et al.,
2009, 2011,
man et al., 2001, Sohma et al., 2001, Epping et al., 2002, Talin
et al., 2003,hma et al., 2008, Soetaert and Middelburg 2009,
Hochard et al., 2010,
and Burdige 1996, Furrer and Wehrli 1996, Hensen et al.,
1997,when Oxi1 < LOxi1 and Oxi > LOxi
hen Oxi1 < LOxi1 and Oxi < LOxi
j1 LOxj
Oxi
KOxiOxi
8>>>>>>>:
O2
KO2O2
NO3KNO3NO3
KNO3O2O2KNO3O2
!
KAnoxNO3NO3KAnoxNO3
KAnoxO2
O2KAnoxO2
9>>>>=>>>>;
xi
1
for i 2, 3
FIni Yi1j1
KInj
Oxj KOxj
!
Yi1j1
1 Oxj
Oxj KInj
!
t expression for Mn and Fe reduction to that shown in Table 1
but subsequenteach oxidation pathway.term.terisation, yet could be
argued to belong to another approach. See text in 3.1.3.t in
3.1.3.98**, Boudreau et al., 1998*, Park et al., 1999, Luff et al.,
2000, Eldridge andan et al., 2002***, Meysman et al., 2003a, b,
Regnier et al., 2003, Luff andBenoit et al., 2006, Katsev et al.,
2006a, b, 2007, Morse and Eldridge 2007,Sengor et al., 2007, Dale
et al., 2008, Muegler et al., 2012
-
A common approach for organic matter oxidation in multi-G
odean inherent property of organic matter (Middelburg,
1989;Boudreau and Ruddick, 1991). Nevertheless, the multi-Gbe
approximated as a function of two distinct carbon pools(Berner,
1980; Westrich and Berner, 1984). This was criticised inearly years
on the basis that the assignment of rates to fractions inmulti-G
models is a result of the laboratory processes, rather
thanvfCdvt|{z}
Dissolved
concentration
change in time
DBv2fCdvx2
fDSv2Cdvx2|{z}
biodiffusion and
molecular diffusion
vfyCdvx|{z}
advection
flow
aCd0 Cd|{z}irrigation
fX
Rd|{z}reaction
(2)
where Rs is a generic reaction term identier that applies to
thesolid substance reactions and Rd to dissolved substance
reactions, Cis a species concentration, r is sediment density, t is
time, DB is thebiodiffusion coefcient,DS is themolecular diffusion
coefcient, x isdepth, f is porosity, u is the rate of burial, y is
the velocity of owrelative to the sediment surface, a is an
irrigation constant and Cd0is the concentration of a dissolved
substance at the sedimente-water interface (Berner, 1980; Van
Cappellen and Wang, 1996).While the models chosen in this analysis
all include equationssimilar to one (1) and (2), there are specic
differences in thechemical reactions and transport processes that
serve as the focusof our comparison below. There are also
differences in the nu-merical discretisation, but in general, the
models are solved by asemi-implicit (CrankeNicholson) scheme with
an iterative solutionperformed at each step to resolve the
non-linearities in the set ofcoupled reaction equations (see for
example, Van Cappellen andWang, 1996; Berg et al., 1998).
3.1. Primary redox reactions of organic matter
The primary redox reactions describe the microbial oxidationof
organic matter, which is one of the major processes drivingchemical
changes in the sediment (Gaillard and Rabouille, 1992;Middelburg et
al., 1997). The rate of oxidation directly de-termines the fate of
many important constituents, such as nutri-ents and oxygen, and
indirectly affects the rate of many otherprocesses, such as the
secondary oxidation of by-products. Themodelling of organic matter
mineralisation can be traced back toBerner's (1964) G model, where
the reaction rate was dened asproportional to the organic matter
concentration, rather than theoxidant concentration, thereby
assuming that organic matteravailability was the primary control on
the mineralisation rate. Inthe current sediment diagenesis models,
this formulation has beenretained, and below we explore the
inclusion of additional factorssuch as the number and reactivity of
the organic matter pools, thechoice of oxidants, the different ways
to parameterise rate laws,and the choice of the values for rate
constants and otherparameters.
3.1.1. Organic matter types and pools
3.1.1.1. Particulate organic matter. A major challenge in
modellingorganic matter oxidation has always been conceptualisation
andsimplication of the reactions of thousands of different
organicmolecules. The multi-G model divides organic matter
intoseveral classes, based on reactivity, which are mineralised to
CO2at different rates. The basis of the multi-G assumption came
fromlaboratory experiments that showed organic matter decay
could
D.W. Paraska et al. / Environmental M300approach has continued
to be used because of its conceptualand mathematical simplicity
(Boudreau and Ruddick, 1991;OM 2xMnO2 3x y 2zCO2 x y 2zH2O/2xMn2 4x
y 2zHCO3 yNH4 zHPO24
(5)
OM 4xFeOH3 7x y 2zCO2 x 2zH2O/4xFe2
8x y 2zHCO3 yNH4 zHPO24 3x y 2zH2Omodels is through the sequence
of reactions (3)e(8), based ongeneral observations from authors
such as Froelich et al. (1979) andEmerson et al. (1980):
OM xO2 y 2zHCO3/x y 2zCO2 yNH4 zHPO24 x 2y 2zH2O (3)
OM 0:8xNO3/0:2x y 2zCO2 0:4xN2 0:8x y2zHCO3 yNH4 zHPO24 0:6x y
2zH2O H3PO4 177:2H2O
(4)Thullner et al., 2007). Of the 83 modelling studies in this
anal-ysis, 22 use only one pool; 31 use two, 22 use three and two
usefour. For 3G models, in general, there is a highly reactive
frac-tion, a moderately reactive fraction and an unreactive
fraction(Table 2). However, the variety in number of pools, rate
constants,and indeed even terminology in Table 2 shows that there
islimited consistency, and assignment of G type is not based on
anyinherent property of organic matter.
3.1.1.2. Dissolved organic matter (DOM). While different solid
phaseorganic matter fractions of varying reactivity are routinely
consid-ered in sediment models, organic matter in the dissolved
phase isincluded in only eight models, which have been published in
thir-teen papers (Table 2). Within these, a range of techniques are
used:Approach 1 models input DOM to the sediment surface as a
uxfrom the water column; Approach 2 models have DOM form as
aproduct of the breakdown of particulate organic matter
(POM).Approach 3 papers specify the individual DOM sources, such
asphytoplankton, zooplankton and benthic algae; the DOM is
con-ceptualised as one or two pools that are mineralised through
thesame processes as POM and transported through diffusion.
DOMadsorption to solid particles has been used in three of the
studies(Sohma et al., 2004, 2008; Massoudieh et al., 2010).
3.1.1.3. Microbial biomass. Most models do not consider
variationin microbial biomass as a control on organic matter decay,
howeversediment bacteria are included in some models as a
dynamicallyvarying organic matter pool. This has been either as
total bacteria(Talin et al., 2003), groups that oxidise organic
matter through eachof the six pathways (Thullner et al., 2005), or
assuming a steady-state biomass (Dale et al., 2008a, based on Dale
et al., 2006,which explicitly models acetogenic, sulphate-reducing
and fer-menting bacteria, and methane-oxidising and
methanogenicarchaea reactions, but without transport
processes).
3.1.2. Choice of reaction pathways
lling & Software 61 (2014) 297e325(6)
-
Table 2Different organic matter pools, uxes, rate constants, and
stoichiometry.
Reference Fractions Flux to sediment surface
Approach 1 POMpools
DOM Pool names % Of ux, Datasource
POM uxmmol cm2 y1
kOMy1
C:N or C:N:P
Boudreau, 1996 2 e e a 18.5 12.2 105
200:21:1 for deepsea, rise, slope/shelf106:16:1Coastal
Park and Jaffe, 1996 1 Total e b 100 By O2 1NO3 0.5Mn(IV)
0.01Fe(III) 0.005SO42 0.1Meth 0.01
106:16:1
Boudreau et al., 1998 2 Highly reactiveWeakly reactive
3%, 74%, 50%97%, 26%, 50%
r No ux: xed bottomwater concentrationof OM as a fractionof
solids
Various 1, 35 105, 1 103,2 103
106:22 for one site106:25 for two sites
Smith and Jaffe, 1998 1 Total e b 100 By O2 1NO3 0.04Mn(IV)
0.01Fe(III) 0.005SO42 0.17Meth 0.05
Not given
Park and Jaffe, 1999 1 Total e b 2555(Sensitivity analysis:36.5,
365, 730, 1825,3650)
By O2 10.95NO3 1.825Fe(III) 0.0365SO42 14.6Meth 0.146
106:16:1, 106:32:1,106:52:1
Luff et al., 2000 3 Extremely labileModerately
labileRefractory
6e82%15e90%1e6%
e 70, 75, 55, 160, 25, 20, 10, 168, 1.2, 2, 0.7
30, 15 Extremely0.6, 0.35, 0.34, 0.2Moderately5 104, 3 104,2.2
104 Refractory
106:16:1 for allfractions
Eldridge and Morse, 2000 2 1 LabileRefractoryDOM
5.8e73%26e94%
e 51.1e678.9248.2e901.6
6.5e15.5 Labile0.06e0.3 Refractory0.25e6 DOM
105:12, 6, 9:0.2,105:4, 6, 8:0.1105:3:0.1
Haeckel et al., 2001 2 LabileRefractory
97%3%
e 12, 9, 6.50.4, 0.15
1 102, 8 103 Labile1 106, 5 106 Refr.
106:16:1 for allfractions
Konig et al., 2001 3 Very labileLabileRefractory
85%15%0.30%
e 4070.15
1, 0 Very labile8 103, 0 :Labile1 106 Refractory
106:16:1 for allfractions
Wijsman et al., 2002 3 Fast-decayingSlow-decayingRefractory
29%, alsodependent onwater depth
e Maximum 6351 27.5 Fast1.1 Slow
106:16 fast106:11 slow
Meysman et al., 2003b 3 Fast degradableMedium degradableSlowly
degradable
18%16%66%
e 6760250
2 Fast0.056 Medium1.1 104 Slow
106:16:1.5 fast106:16:1.5 med265:24.5:1 slow
Luff and Wallmann, 2003 2 LabileRefractory
68%32%
e 5526
0.2 Labile3 104 Refractory
Not given
Luff and Moll, 2004 3 LabileModeratelydegradableRefractory
40%55%5%
e 60827
30 Labile0.2 Moderate5 104 Refractory
106:16:1for all
Eldridge et al., 2004 2 LabileRefractory
e 25 Labile0.12 Refractory
105:5:0.6105:4:0.6
(continued on next page)
D.W
.Paraskaet
al./Environm
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&Softw
are61
(2014)297
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301
-
Table 2 (continued )
Reference Fractions Flux to sediment surface
Benoit et al., 2006 2 ReactiveautochthonousmarineLess
reactiveallochthonousterrestrial
Changing alongstream fromeld data
a 100e200, 50e1100e500, 0e60
10 Reactive0.4 sedimentation^0.6Less
C:N 106:16C:N 106:8.83
Katsev et al., 2006a 1 e 100% b 1.25e5 0.9 C:P 200:1Katsev et
al., 2006b 1 Reactive
(Refractory)99.6%(0.4%)
b 2.33 1021.0 104
0.1 Reactive4 105 Refractory
Not given
Katsev et al., 2007 2 ReactiveRefractory
30%70%
e 100230
1.8 Reactive0.02 Refractory
67:3.3:1250:12.5:1
Morse and Eldridge, 2007 2 1 LabileNon-labileDissolved
68%, 83%, 80%32%, 17%, 20%
e Sensitivity:791, 1034, 365365, 213, 91
20 Labile0.8 Non-labile35 Dissolved
105:25:0.158105:25:0.10105:25:0.10
Eldridge and Morse, 2008 2 2
ReactiveRelativelynon-reactiveDOMDOMI
d Taken from Morseand Eldridge, 2007
20 Reactive0.080 Relatively non-35 DOM
105:25:0.158105:25:0.10105:25:0.10
Devallois et al., 2008 1 e e b Not given 2 108 July, 2
109November
106:16:1
Dittrich et al., 2009 3 Fast degradableSlow
degradableNon-degradable
30%20%50%
d 0.210.140.35
For degradable only: byO2 9.2NO3 7.3MnO2 0.04FeOOH 1.8 104SO42
0.04Meth 5.8 103
93:13:1 fast93:13:1 slow357:15:1 non
Couture et al., 2010 1 e e b Not given 400 e(0.183depth) Not
givenMassoudieh et al., 2010 1 Easily mineralisable e b Not given
25 C:N 106:815Reed et al., 2011a 2 Reactive
Refractory91.5%8.5%
g 2.70.25
0.07 Reactive0 Refractory
106:30:1 reactive106:7.6:1 refractory
Reed et al., 2011b 3 Highly reactiveLess
reactiveNon-reactive
50%16%34%
a Maximum 438 24 4 Highly-1.4 0.7 Less-
106:16:1290:29:1
Bektursunova andL'heureux, 2011
1 e e b Not given e Not given
Dale et al., 2011 3 G1G2G3
100%Fixedconcentration
e/g 329, 767 0.05 G11.5 103 G24.2 104 G3
C:N 106:9.5106:8106:27
Trinh Anh et al., 2012 2 DegradableRefractory
48, 57, 6352, 43, 37
a 8517, 12167, 203709125, 9125, 12167
By O2 36.5NO329.2Fe30.011SO420.29Meth 0.146
27.5:3:1 degradable60:2:1 refractory
Tsandev et al., 2012 3 Very labileModerately
labileRefractory
90% d 7.5, 15 0.15 Very0.0015 ModeratelyRetardation by SO42
and Meth 7 104
200:21:1
Dale et al., 2013 4 G0G1G2G3
89%11%Fixedconcentration
e/g 5.84 G00.05G11.5 103 G 24.2 104 G3
C:N 106/9.5106/9.5106/8106/27
Katsev and Dittrich, 2013 3 ReactiveWeakly
reactiveRefractory
401446
e 11440130
2 Refractory0.05 Weak0 Refractory
50:7:1
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McCulloch et al., 2013 2 DegradableRefractory
48%52%
e 1.61.7
By O2 8.8NO3 763MnO2 1.6 103FeOOH 1.2 104SO42 3.6 102
106:16:1
Approach 2 POMpools
DOM Pool names % of ux Datasource
POM uxmmol cm2 y1
kOM y1 C:N or C:N:P
Van Cappellen andWang, 1996
Rate assigned tomeasured depthprole
Wang and VanCappellen, 1996
Rate assigned tomeasured depthprole
Rysgaard and Berg, 1996 1 e e b Not given Rate by O20.0035 nmol
cm3 s1
Rate by NO3
0.00058 nmol cm3 s1
106:16:1
Van Den Berg et al., 2000 1 Total OM from cores e b Not given
150, 600,950 mmol cm3 y1
at sediment-waterinterface
20:1.6:1
Berg et al., 2003 3 Fast decomposingSlow decomposingNot
decaying
25%75%
a 292e1200 Calculated by depthfrom core data
Trials of 106:14,106:10.3, 106:16for all fractions
Fossing et al., 2004 3 Degraded fastDegraded slowlyNot
degraded
42%50%8%
g 44553085
303 Fast0.378 Slow0
80:8:1 for allfractions
Aguilera et al., 2005 2 LabileRefractory
c 32 total 30 Labile0.3 Refractory
Not given
Jourabchi et al., 2005 1 e e b 80 0.01 200:21:1Thullner et al.,
2005 1 1 Labile
DOMe b 660, 650, 635 0.95 106:12:1
Canavan et al., 2006 3 Most reactiveLess
reactiveNon-reactive
42%21%37%
e 630315546
1 Most0.01 Less0
112:20:1 mostreactive200:20:1 lessreactive
Canavan et al., 2007b 3 Highly reactiveLess
reactiveRefractory
42%, 33%21%, 25%37%, 43%
e 630, 420315546
25 Highly0.01Less0
106:19106:11106:5
Kasih et al., 2008 3 2 Fast degradable POMSlow degradable
POMNon-degradable POMFast degradable DOMSlow degradable DOM
40%40%20%
g a 31.5 Fast0.00315 Slow0
70:8.75:1 forall fractions
Sochaczewski et al., 2008 2 Fast reactingSlow reacting
Not given c Not given 302 Fast0.378 Slow
Not given
Jourabchi et al., 2008 2 Highly degradableRefractory
50e100%(13 values)
e 4.3e29 (13 values) 1.16e10 (13 values) 106:16:1200:21:1
Kasih et al., 2009 3 2 Fast degradableSlow
degradableNon-degradableFast degradableSlow degradable
40%40%20%43%57%
a 328328164
78.8 Fast0.00378 Slow0 Non
70:8.75:1 forall fractions
Dale et al., 2009 3 Fast reacting
labileIntermediatereactivitySlowly reactingrefractive
53%34%12%
e 700450160
2 Fast0.03 Intermediate1.4 104 Slowly
106:11
(continued on next page)
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Table 2 (continued )
Reference Fractions Flux to sediment surface
Brigolin et al., 2009 3 RefractoryLabileSalmon farmorganic
deposit
67%33%
d 9030
0.10.01
80:8:180:8:170:8:1
Brigolin et al., 2011 2 RefractoryLabile
0.40.6
a 160240
0.001 Refractory1.0 Labile
106:16:1106:16:1
Bessinger et al., 2012 1 1 e b SOM ux not givenDOC 1e10 mg/L
0.002 POM0.001 DOM
Not given
Smits and Van Beek, 2013 4 1 FastModerately slowSlowVery
slowRefractory
f Calculateddynamically
Approach 3 POMpools
DOM Pool names % of ux Datasource
POM uxmmol cm2 y1
kOM y1 C:N or C:N:P
Soetaert et al., 1996a 3 Most degradableLeast
degradableRefractory
74%26%
e 207, 48, 1873, 17, 6
26 Most0.26 Least0 Refractory
C:N 106:16C:N 106:14
gSoetaert et al., 1996b 2 Most reactive
Least reactive50%50%
d 32.532.5
2 Most0.02 Least
C:N 6.6C:N 7.5
Middelburg et al., 1996 2 FastSlow
Not given c Sensitivity analysis0.00365 to 365
C:N 6.6, 8C:N 10, 20
Soetaert et al., 1998 2 Highly reactiveLess
degradableRefractory
70e80%0.32%
a Total 64 28.5 Highly0.03 Less
Not given
Sohma et al., 2001 2 1 Fast labileSlow labileDissolved
f 0.438 Fast8.76 103 Slow8.76 103 DOM
106:15106:15106:9.6
Herman et al., 2001 2 Fast degradingSlowly degrading
Calibrated with Monte Carlosensitivity analyses
different
Epping et al., 2002 2 DegradableRefractory
60e85% d ~11.4e189.8 0.066e7.91 Degrad.0.0002e0.319 Refr.
C:N 106:16to 106:7
Talin et al., 2003 1 e e b BW conc, no ux 14.6 Not givenSohma et
al., 2004 3 2 Fast labile
Slow labileRefractoryLabileRefractory
f 4.38 Fast0.0438 Slow0.000876 Refr.8.76DOM Lab0 DOM Ref
Not given
Berg et al., 2007 2 Fast decomposingSlowly decomposing
50%50%
d Total 230 63 Fast9.5 102 Slow
Not given
Dedieu et al., 2007 2 LabileMore refractory
80, 85, 90%20, 15, 10%
e 350.4e3153.687.6e788.4
21.9, 36.5 Labile0.365 More
C:N 6.6:1C:N 10:1
Sohma et al., 2008 3 2 Fast labileSlow labileRefractoryFast
labileRefractory
90%7.5%2.5%
c From the model 4.4 Fast4.4 101 Slow4.4 103 Refr8.8 DOM fast0
DOM Refr.
27.6:6.2:147.6:7.5:1500:37:125:6:1500:37:1
Soetaert andMiddelburg, 2009
2 Rapidly decayingSlowly decaying
50%50%
d or a Input by pelagicmodel
26 Rapid0.26 Slow
C:N 106:16C:N 106:14
Hochard et al., 2010 3 Labile, fast decayingStable, slow
decayingEPS (labile, particulate)
38%62%
d 12612050
27.4 Labile1.1 Stable
106:16 fast106:7 slowCH2O
Pastor et al., 2011 2 Fast degradedSlow degraded
50e94% e 1.96 103 to 95.47 11, 33 Fast0.21 to 0.36 Slow
106:15 fast106:7.4 slow
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Others POMpools
DOM Poolnames
% of ux Datasource
POM uxmmol cm2 y1
kOM y1 C:N or C:N:P
Rabouille andGaillard, 1991a
1 Reactive(Inert)
100% of POC ux(0.1% of dry solids)
b 25.2, 17.3, 9.5 By O2 0.047By NO3 0.0158By Mn 1.58 1080
106:16:1
Tromp et al., 1995 2 LabileRefractory
90%10%
g/a Many sites Function ofsedimentation rate0
106:16:1
Dhakar and Burdige, 1996 1 e e b 4.2e8.5 By O2 1.3 103, 2.3
103,6.8 103NO3 6 104, 1.2 103Mn 5.2 104, 1.3 103Fe 6.5 104, 1
103
106:16:1
Furrer and Wehrli, 1996 1 e e b 620.5 Various 106:16:1Hensen et
al., 1997 1 e e b Assumed excess Depth dependent C:N
106:16Rabouille et al., 2001 2 Labile
Intermediate reactivity79%, 54%21%, 46%
e 34, 14 1.6, 1.60.012, 0.008
C:N 9.3:1
Archer et al., 2002 2 LabileRefractory
50%50%
e 0e905 Proportional to sedimentdepth
Not given
Sengor et al., 2007 1 Acetate e g 7000 M 0.16 Not givenDale et
al., 2008 3 Labile
IntermediateRefractorySpecic DOM molecules
95%, 25%0%, 6%5%, 9%
e 450, 1000, 2325, 270
0.22, 0.12e, 0.00350, 0(Not kOM, rather hydrolysisrate)
Not given
Dale et al., 2008 2 LabileRefractorySpecic DOM molecules
90%10%
e Not given
Muegler et al., 2012 1 1 OMpptOMred
e b 8 104 M By O2 272, Anoxic 9.86 Not given
The assignment of the organic matter reactivity fractions is
given by methods a to g.(a) Assigned according to eld data:
Boudreau, 1996 fromMurray and Kuivila, 1990. Berg et al., 2003 e
FromWestrich and Berner 1984, Otsuki and Hanya, 1972, Rysgaard et
al., 1998; Fossing et al., 2004 e Fast: from literaturevalues; Not
degraded: function of sedimentation rate and bottom concentration;
Benoit et al., 2006e relative uxes actually estimated in this
source; Kasih et al., 2008e Total ux hasmonthly data; For the
reactive particulate,cites Fossing et al., 2004 and Berg, 2003; For
the dissolved, tuned in this study; Reed et al., 2011be
FromWestrich and Berner 1984; Brigolin et al., 2011e Tentative,
from Giordani et al., 2002; Trinh Anh et al., 2012 from TrinhAnh et
al., 2006.(b) 1G.(c) Not given.(d) Proportions assigned at the
outset: Soetaert et al., 1998 e Based on Soetaert et al., 1996a;
Berg et al., 2007 e From Soetaert et al., 1996b; Eldridge andMorse,
2008 e Taken fromMorse and Eldridge, 2007; Kasih et al., 2009
eBased on Kasih, 2008.(e) Tuned to t a chemical depth prole or ux
data from the site of the study.(f) Flux input from a coupled
model.(g) Assigned by a function: Tromp et al., 1995 e From Ingall
and Vancappellen, 1990 e a general rule for sediment carbon, not a
site ux; Reed et al., 2011a e estimated based on primary production
data from the site. Sengor etal., 2007 e concentration set to be
higher than values measured at the study site, and always to be in
excess.
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OM 0:5xSO24 y 2zCO2 y 2zH2O/0:5xH2S x y 2zHCO3 yNH4 zHPO24
(7)
OM y 2zH2O/0:5xCH4 0:5x y 2zCO2 y 2zHCO3 yNH4 zHPO24 (8)
where x, y and z represent the user-dened C:N:P ratios (Table
2)and OM is organic matter. The reaction stoichiometry shown hereis
from Canavan et al. (2006), with most studies adoptingdifferent
stoichiometric relationships. Many studies (28) use allsix
pathways, however, depending on reasons specic to indi-vidual
applications, any of the pathways may be left out (Table 3).A
subset of the models combines the pathways in reactions
Table 3Organic matter oxidation pathways used in sediment
diagenesis models.
D.W. Paraska et al. / Environmental Modelling & Software 61
(2014) 297e325306
-
te expat, witpprr sim
ode(5)e(8) together to produce oxygen demand units (ODU),
whichare a combination of reduced-species products of the
anoxic
Fig. 2. The reaction rates of each oxidation pathway compared
between the three raamount of organic matter, with no further
inputs, was simulated to decay via six redoxApproach 2 (Van
Cappellen and Wang, 1996) and Approach 3 (Soetaert et al.,
1996a)pathways to occur simultaneously, albeit at low rates for
inhibited pathways, whereas Athe overall rate of mineralisation in
Approach 3 as all three pathways are able to occu
D.W. Paraska et al. / Environmental Moxidation of organic
matter:
OM TEA!RAnox 106ODU 106CO2 12NO3 HPO24 106H2O (9)
where TEA is a terminal electron acceptor. The models
thatcombine the anoxic processes fall into the rate law
formulationcategory that we dene as Approach 3, described below.
The samereactions are generally applied to all organic matter
pools, althoughdifferent rate constants are applied for different
pools and some-times for different oxidants (see Table 2 and text
below).
3.1.3. Rate law formulationMost models inspected in this
analysis employ one of three
main approaches to organic matter oxidation rate laws;
togetherthese three approaches have made up the bulk of
depth-resolvednumerical process-based models since 1996 (Table 1).
In Ap-proaches 1 and 2 the total organic matter reaction rate (ROM)
is thesum of some combination of the oxidation pathways (3) to (8).
InApproach 3, the total ROM is the sum of pathways (3), (4) and
(9),where equation (9) combines Mn(IV), Fe(III) and SO42 reduction.
Acommon feature of all three approaches is that the oxidation
rateexpression ROx is a product of up to seven terms: an organic
matterreaction rate constant kOM; a factor for dependence on the
organicmatter concentration, FOM; a temperature dependence FTem; a
mi-crobial biomass factor, FBio; a term FTEA for limitation; an
inhibitionterm FIn; and a thermodynamic factor, FT (Arndt et al.,
2013):
ROxi kOMFOMFTemFBioFTEAi FIni FT (10)The FTem is rarely
employed, but in a handful of cases a Q10
relationship between 2 and 4 is used (see Fossing et al., 2004
for aclear explanation of how temperature affects reaction rates
andEldridge and Morse, 2008 or Reed et al., 2011b for a specic
ex-
pressions approaches in representative marine and freshwater
conditions. An initialhways using rate constants from the original
sources for Approach 1 (Boudreau, 1996),hout simulation of
secondary or transport processes. Approach 1 equations allow
alloach 2 equations create a more distinct inhibition sequence.
There is a brief increase inultaneously at close to their maximum
rate.
lling & Software 61 (2014) 297e325 307amination of the
effect of temperature). The limitation term ac-counts for the ROx
dependence on the oxidant concentration whenthe oxidant
concentration is low. The FTEA term in Approach 1 is aMonod
expression (Table 1), which uses Monod half-saturationconstants
(KOx), and which is chosen because it best reects labo-ratory data
of bacterially-controlled oxidation reactions (Boudreauand
Westrich, 1984; Gaillard and Rabouille, 1992). The FTEA ofApproach
3 uses Monod functions, modied to include inhibitionterms. In
Approach 2 the FTEA is either 0, 1 or the ratio of the
con-centration of the ith oxidant (Oxi) to a specied limiting
concen-tration (LOxi). We use the notation KOx and LOx to emphasise
that adistinction should be made between the Monod half constants
inApproaches 1 and 3 and the limiting concentrations used
inApproach 2; the difference in conceptual representation is not
al-ways clear in Approach 2 papers that use the notation KOx.
The redox zonation commonly observed in the sediment
isimplemented in the models through inclusion of the
inhibitionfactor, FIn. This term limits ROx for a pathway that
yields less energywhile higher-energy pathways continue to be
active. MostApproach 1 and 2 papers set KOx and KIn or LOx and LIn
to have thesame value, whereas Approach 3 papers generally specify
sepa-rate KOx and KIn values, as does the Approach 1 study by
Coutureet al. (2010). The inhibition term FIn in Approaches 1 and 3
is aMonod function, while in Approach 2 it is the modied Monodterm,
which employs Blackman kinetics (Boudreau, 1997). Theorganic matter
oxidation rate expressions of the three approacheshave been
compared by conducting simple experiments usingcommon boundary
conditions and constants, and it has beenfound that while the
overall rate of organic matter consumption islargely the same, the
rates of oxidant consumption can bedifferent as a result of the
rate expressions alone (Paraska et al.2011) (Fig. 2).
-
Table 4Secondary redox reactions implemented in sediment
diagenesis models.
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odeD.W. Paraska et al. / Environmental MThe FOM term is usually
a rst order dependence on organicmatter concentration, however
Dhakar and Burdige (1996), Smithand Jaffe (1998), Regnier et al.
(2003) and Thullner et al. (2005)(scenario three) have included a
Monod limitation term:
OMOM KOM
(11)
where KOM is a half-saturation constant inducing limitation of
theorganic matter breakdown rate.
The models described above that include bacteria as an
organicmatter pool also include a term for the effect of bacteria
FBio, whencalculating ROx. The very rare inclusion of bacteria in
sedimentdiagenesis models is adapted from approaches used in
ground-water models, such as the model of Schafer et al. (1998a,
b). Thisapproach has been used in surface water sediment models by
Talinlling & Software 61 (2014) 297e325 309et al. (2003), who
compared their model to Approach 3, and byThullner et al. (2005)
who compared theirs to Approach 2. In bothcases, the authors found
that including bacteria makes a largerdifference under dynamic
conditions than at steady state (seebelow for discussion of steady
and dynamic conditions). Theexclusion of bacteria from most
diagenesis models is based on theassumption that when the microbial
populations are at steadystate, ROM should not be limited by the
biomass (Van Cappellenet al., 1993).
Many of the early authors have referred to the work of
Froelichet al. (1979), who showed not only an organic matter
oxidationsequence, but also explained the sequence in terms of the
freeenergy made available in each reaction. However, the most
modelsdistribute the rates via the inhibition terms. The
consideration offree energy as a controlling factor in the
oxidation process (FT) hasmostly not been considered in sediment
models, except for where
-
Table 5pH and mineral reactions in sediment diagenesis
models.
D.W. Paraska et al. / Environmental Modelling & Software 61
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odeit has re-emerged in the work of Dale et al. (2008), who have
builtonwork by authors such as Jin and Bethke (2002, 2003, 2005).
Notehowever, that the Dale et al. (2008) model did not include many
ofthe primary and secondary reactions that have been included in
themajority of papers from the last two decades, thus we are yet to
seea full diagenesis model that uses free energy as a controlling
factorin its rate calculations. FT is usually expressed as in
equation (12),where DG is the energy released upon reaction of an
organicmolecule, DGATP the energy required to synthesise ATP, m and
cstoichiometric coefcients, R is the gas constant and T
temperature(Jin and Bethke, 2007; LaRowe and Van Cappellen, 2011;
LaRoweet al., 2012).D.W. Paraska et al. / Environmental MFT 1
expDGmDGATP
cRT
(12)
The difculty in using an FT term lies in reconciling the
veryspecic reaction energetics of individual molecules with
theimprecise basis of kOM values used in multi-G models.
3.1.4. Choice of parameter valuesAs can be seen from the range
of conceptualisations and
parameterisations discussed 2 above, the maximum rate
ofdegradation, kOM (Fig. 3, Table 2), could represent a rate
constantfor a wide range of different reactions, so a direct
comparison ofkOM from different modelling studies remains difcult.
Mostmodels have separate kOM values for each G fraction and
assumethis is the same for all oxidation pathways. Some account for
anincreased oxic mineralisation rate with an acceleration factor
forthe faster rate of aerobic mineralisation (25 for Canavan et
al.,2006; Brigolin et al., 2009; Couture et al., 2010; 10 for
Daleet al., 2011; Bessinger et al., 2011), while Reed et al.
(2011a, b)attenuate SO42 reduction and methanogenesis rates by1.57
103, based on eld data from Moodley et al. (2005) andTsandev et al.
(2012) by 7 104. Nine studies have separateoxidation rate constant
values (kOM) for each oxidant (Table 2),however, in the majority of
studies, kOM represents an average ofall of the oxidation pathways
and is assigned a constant value.Sourcing locally relevant
parameters has been a challenge formany studies, and only in a few
cases has direct measurement ofkOM been possible (for example,
Boudreau, 1996; Sohma et al.,2008; Reed et al. 2011a). Most
applications therefore rely on liter-ature values and/or
calibration. Van Cappellen and Wang (1996)obtained their oxidation
rate from sediment incubation experi-ments by Caneld et al. (1993),
situated at the same study site astheir modelling study. Couture et
al. (2010) measured organicmatter breakdown with depth in a
sediment column and used theexperimental value for kOM in their
diagenesis model. However,most studies calibrate kOM to t
concentration depth proles or usean assumed value from the
literature, where those that are taken
lling & Software 61 (2014) 297e325 311from previous papers
have often been determined by calibration toanother dataset, rather
than originating from an experimentaldetermination. Many of these
can be traced back to Van CappellenandWang (1995), where several
parameter values are tted to coreproles. Most papers have
calibrated their depth proles against4e7 measured variables, except
Approach 3 papers, where fewvariables are simulated; a few Approach
1 and 2 studies calibrate upto 16 variables (Berg et al., 2003;
Fossing et al., 2004; Dittrich et al.,2009). Other kOM estimates
are based on denitrication laboratoryexperiments (for example,
Billen, 1978; Esteves et al., 1986; Murrayet al., 1989) and sulfate
reduction experiments (Boudreau andWestrich, 1984). While some
publications have consideredparameter sensitivity and
identiability, detailed investigationsadopting contemporary model
performance metrics (see, forexample, Bennett et al., 2013) remain
limited.
Some studies (e.g., Brigolin et al., 2009, 2011) use the kOM
valuedirectly from, or use the method of, Tromp et al. (1995). With
thismethod, kOM is determined using a statistical relationship
betweenu (burial) and 22 measured organic matter degradation rates
fromsites in the Pacic Ocean. Caneld (1994) and Middelburg et
al.(1997) present similar methods for determining the oxidationrate
from u in the sea and Li et al. (2012) in lakes, and Burdige et
al.(1999) developed a relationship between the organic
matteroxidation rate and the DOM ux. The other important
parameterswithin the rate laws are the Monod half saturation
constants (KOxand KIn) in Approaches 1 and 3, and the limiting
concentrations (LOxand LIn) in Approach 2, as described above.
While these parameters
-
SCO2, SH2S and SBOH. In the advancement approach, the progressof
all acidebase speciation reactions towards equilibrium is used
Some models include the ageing of iron and manganese
odeminerals from the more-reactive amorphous form to the
less-reactive crystalline form (Table 5). The notation for more
reac-tive (MnO2A, Fe(OH)3A) and less reactive (MnO2B, Fe(OH)3B)
isconsistent across all Approach 2 papers, while one Approach
1paper uses the notation a and b (Reed et al., 2011b). The
crys-talline phases do not react with organic matter, but they do
reactwith
PH2S, and MnO2B oxidises Fe2. The inclusion and treat-
ment of pH and mineral transformations has no relation to theto
calculate pH. The latter approach also allows transport of
in-dividual species rather than lumped parameters, and
thereforeallows implementation of species-specic diffusion
coefcients.The advantages of these approaches are primarily
compared as abalance between computation time and accuracy.
Computationtime is minimised by reacting or transporting lumped
species,whereas accuracy is maximised by reacting or transporting
manyindividual species (Luff et al., 2001). Meysman et al. (2003b)
addan acidebase equilibrium of the solid phase to the
alkalinityconservation model. Most papers that calculate pH use the
alka-linity conservation approach. Jourabchi et al. (2005) and
Devalloiset al. (2008) focus specically on calculating pH proles
indiagenesis models.have a slightly different use in the respective
approaches, inspec-tion of the literature shows that values have
been used inter-changeably between Approach 1 and 2 papers. For
example, sevenApproach 1 papers source constants from the Approach
2 papersVan Cappellen and Wang (1996). However, Approach 3
constantsare consistently sourced from the original Approach 3
paper(Soetaert et al., 1996a).
3.2. Other chemical processes
3.2.1. Secondary redox reactionsThe subsequent reactions of
chemical species produced by the
primary redox reactions (3)e(8) are referred to as secondary
redoxreactions, and are usually given bimolecular rate laws that
are rstorder with respect to the oxidant and reductant. Secondary
re-actions in Approaches 1 and 2 include the oxidation of
reducedspecies by oxygen and other reoxidation pathways, though
theseare not always included and are quite variable depending on
theapplication (Table 4). Approach 3 models treat these more
simplyand include only the oxidation of ODU and NH4 by oxygen, in
mostcases.
3.2.2. pH Control and mineral solubilityMany Approach 1 and 2
papers include ability for a calculated or
xed pH, but pH is not simulated in 26 papers, and it is not
includedin the Approach 3 papers (Table 5). When pH is considered,
it isoften calculated as a result of the reaction and transport of
speciessuch as H2CO3, H2S, H3PO4, NH4 and B(OH)3. The fast,
reversibleequilibrium reactions are in some cases calculated
separately fromthe slower, kinetic organic matter oxidation
reactions. Luff et al.(2001) discuss advantages and disadvantages
of three methodsfor calculating pH in marine systems, comparing the
charge bal-ance approach in CANDI (Boudreau, 1996) and the
alkalinityconservation (or proton condition in Meysman et al.,
2003a, b)approach in STEADYSED (Van Cappellen and Wang, 1996) with
anequilibrium advancement approach (Luff et al., 2001). With
thecharge balance approach, H concentration is calculated from
thesum of all charged species, whereas in the alkalinity
conservationapproach, H is calculated from total alkalinity, which
is the sum of
D.W. Paraska et al. / Environmental M312treatment of primary or
secondary redox reactions, and theminerals are typically chosen in
any study are based on theenvironmental context and
application.
3.2.3. Nutrients and adsorptionNumerous studies include
nutrients (Table 6). Most generate
NO3 via oxidation of NH4 (nitrication; Table 4), and only
Dhakarand Burdige (1996) include oxidation of NH4 by NO2,
(anammox)despite this being a potentially important denitrication
pathway(Lam and Kuypers, 2011). Some studies include the adsorption
ofammonium to iron minerals, which makes it unavailable to
livingorganisms (Table 6). Sohma et al. (2001, 2004, 2008) have a
detailedtransport of organic PO43 through water column
microorganisms.Several studies include acid/base reactions that
change the speci-ation of H3PO4, while others allow PO43 to be
adsorbed to partic-ulate metal phases (Table 6).
3.3. Physical and biophysical transport processes
3.3.1. Benthic faunaMost studies account for bioturbation by
including constant
mixing down to a certain depth, with a decreasing amount
belowthat. This decrease is calculated by a function applied to the
bio-diffusivity (or bioturbation) term DB (see equations (1) and
(2)).Many studies use depth-dependent exponential decay and t
thefunction to the data according to their study site, while
manyCANDI modellers use a function dependent on burial rate u.
Therelationship between DB and u is generally explained on the
basisthat a higher ux of organic matter will sustain a higher
density ofbenthic macrofauna, as was tested statistically by Tromp
et al.(1995) against 37 eld studies. Haeckel et al. (2001) required
arange of bioturbation coefcients, based on radionuclide data
oftheir study site. Due to the limits of the sediment diagenesis
model,they applied a higher bioturbation rate with a lower organic
matterux, though this does not reect the general understanding
thathigher organic matter depositionwould support more
bioturbation(Haeckel et al., 2001). Berg et al. (2003) and Fossing
et al. (2004)suggest that DB should be assigned differently to
solids and sol-utes, as bioturbation affects solutes much more than
solids, and sothe coefcient could be around 10 times larger.
However, few otherauthors (Kasih et al., 2008, 2009) have
implemented separate DBvalues for solids and solutes.
The onset of hypoxic conditions can reduce or stop the
activityof benthic animals, especially larger ones, and the return
of oxicconditions, which causes the return or growth of animals,
requiressite-specic information, as regions with a history of low
O2 mayhave benthic organisms that have adapted to the conditions
(Diazand Rosenberg, 2008). Soetaert and Middelburg (2009)
usedifferent DB values for oxic and anoxic bottom water
conditions.Fossing et al. (2004) account for bioactivity with an
index (A) be-tween 0 and 1 for the rate of bioturbation as
DADt
KmA Kn1 A (13)
where Km is a potential rate of animal mortality, Kn a potential
rateof growth, and the value of A is dependent on the amount of
oxygenin the system. In periodically hypoxic waterways (Sohma et
al.,2004, 2008), this is accounted for by making the
bioturbation(D
0B) and bioirrigation (DI) coefcient dependent on the biomass
of
deposit (DFB) and suspension (SFB) feeders, e.g.,:
D DFB SFB $D (14)
lling & Software 61 (2014) 297e325i DFB SFB HFi i max
-
odeTable 6Inclusion of nitrogen and phosphorus as nutrients in
diagenesis models.
D.W. Paraska et al. / Environmental Mwhere i refers to either
bioturbation or bioirrigation, HFi is a halfsaturation coefcient
and Di max is the maximal coefcient of eitherbioturbation or
bioirrigation. The concentrations of DFB and SFB areproportional to
the dissolved oxygen concentration. Depending onthe growth rates,
such formulations show the rate of recovery ofbenthic fauna biomass
after reoxygenation, and a possible delay inthat recovery. In
environments where eld studies show that irri-gation is a minor
transport process, especially anoxic waterswithout macrofauna, the
irrigation function is simply not used(Soetaert et al., 1998; Luff
et al., 2000; Dale et al., 2009; Reed et al.,2011a). Detailed 3D
transport models of irrigating worms havebeen developed (Meysman et
al., 2006a, b, 2007) but are yet to beroutinely integrated with
reactive transport models (see Meilelling & Software 61 (2014)
297e325 313et al., 2003 and Sochaczewski et al., 2008 for recent
studies inthis area).
3.3.2. Resuspension of sediment particlesAn early coupled
benthic-pelagic model by Wainright and
Hopkinson (1997) examined the effect of resuspension on
aerobicoxidation of organic matter and denitrication in the
sediment andwater column, however, this study was limited to a
subset ofchemical reactions. There has not been the same adoption
orexpansion of this approach over the last two decades as there
waswith the diagenesis models, except for a recent study
byMassoudieh et al. (2010) who demonstrate a full
vertically-resolveddiagenesis model that also includes
resuspension.
-
Table 7Application of diagenesis models to different
environments with either steady or non-steady solutions.
D.W. Paraska et al. / Environmental Modelling & Software 61
(2014) 297e325314
-
D.W. Paraska et al. / Environmental Modelling & Software 61
(2014) 297e325 315
-
provides a useful starting point from which to consider
theirtimescales, their coupling to the water column, and
chemicaluxes in more detail.
4.1. Application environment
Here the studies are classied according to the nature of
theenvironment in which the study was set: deep ocean,
coastal,estuarine, riverine or lacustrine. Of the 83 studies
inspected,coastal environments have received the highest number
(35) ofapplications of sediment models, followed by the deep sea
(17)(Table 7). One reason for the high number of coastal studies is
thatlarge datasets have been collected at a few key sites, such as
YoungSound and the Skagerrak. After 1996 when many new modelswere
introduced, most deep ocean studies were published be-tween 1998
and 2002; most coastal studies were published from
D.W. Paraska et al. / Environmental Modelling & Software 61
(2014) 297e3253164. Applications
Next we highlight some of the practical issues involved in
Fig. 3. Plot of the range and median of kOM values, the maximum
organic matterreaction rate coefcient. 2G-1 and 3G-1 are the most
reactive fractions of 2- and 3-Gmodels, and 2G-2 and 3G-2 are the
second-most reactive fractions of 2- and 3-Gmodels.applying a
sediment diagenesis model that are not easily graspedby reading the
theoretical resources (Table 7 provides an overviewof application
approach). In general terms, early publicationsfocused on
development of a new model code or simulated depthproles and
surface uxes of the main chemicals involved in theearly diagenesis
process, with focus on examining the t of modelresults to eld data,
and establishing the sediment models as t forpurpose. Later
publications have tended to target application ofthe models to a
more specic research questions, by conductingbroad sensitivity
analyses and examining system behaviour(Archer et al., 2002; Katsev
et al., 2006a; Dittrich et al., 2009),while others have been more
management oriented. An overviewof the application of the models in
different environments
0 1 2 3 4 5
61995199619971998199920002001200220032004200520062007200820092010201120122013
Fig. 4. Number of publications each year per environment. 1996
stands out as the key yeapublished between 1998 and 2002, and most
coastal studies from 1996.2002 onwards (Fig. 4). Marine studies
(coastal and deep ocean)have been used to test the abilities of the
models to reproduceeld measurements of depth proles and the
associated chemicalreactions, with a focus on understanding
biogeochemical cyclesrather than focussing on a specic applied
problem.
In contrast, the 13 studies based in estuaries are much
moretargeted at management-related questions, especially in terms
ofrepresenting more complex hydrodynamics, spatial heterogene-ity
and ecology, by coupling the sediment models to physicalmodels of
the overlying water body and to ecological models (seebelow). Other
differences to the marine studies are that most ofthe estuarine
studies were published from 2004, 5 of the 13include DOM, and a one
study (Bessinger et al.) included heavymetals.
Up to the late 1990s, the geochemistry and ecology of
marinesediments had generally been studied more than freshwater
sedi-ments (Boudreau, 1999); this is also true for the sediment
diagen-esis modelling studies inspected here, where only 15 studies
arebased in freshwater lakes and 4 in freshwater rivers. The
moststriking contrasts between the freshwater lake studies and
themarine studies are that 5 studies were motivated to model the
uxof heavy metals, and no lake studies to date include
dynamiccoupling to an ecological model or a spatially-resolved
water col-umn model.
4.2. Steady state and dynamic simulations
Many diagenesis model papers refer to the concept of a
steadystate, a term that applies to both the solution of the
differentialequations and to the assumption about the condition of
the
7 8 9 10 11 12
Deep seaCoastalEstuaryRiverLaker for publishing diagenesis model
studies. After 1996, most deep ocean studies were
-
processes, but the solid substances are not. In some
diagenesis
kinetic reactions (Smith and Jaffe, 1998; Luff et al., 2000).
Once the
odesteady state has been calculated, a few models cease their
simu-lation (for example, STEADYSED in Van Cappellen and Wang,
1996;Wang and Van Cappellen, 1996; Van den Berg et al., 2000)
whereasmost use the steady state as an initial condition for
time-dependentmodel papers, the difference between the observed and
calculatedconcentrations is explained as a result of the inability
of a steadystate model to capture dynamic changes in that
environment,especially in the uppermost layers of the sediment
(Boudreau et al.,1998; Haeckel et al. 2001; Wijsman et al., 2002;
Canavan et al.,2006).
In theory, conditions in the deep ocean are more likely
toresemble steady state than lake or coastal marine sediments,
whereseasonal or episodic effects should be stronger and
thereforeexternal conditions uctuate on early diagenetic
timescales(Rabouille and Gaillard, 1991a; Gallon et al., 2004).
However,Table 7 shows that in practice, simulations of deep-sea
systems areequally likely to have been run at steady state or
dynamically, whilesomewhat counter-intuitively more applications to
freshwaterlakes have been assumed to be at steady state rather than
dynamic.Seasonal changes are also considered more often in marine
studies(5/17 in deep sea and 7/33 in coastal) than in estuarine
(2/13) andfreshwater lakes (2/15).
4.2.2. Steady state as a numerical techniqueThere are two main
numerical methods by which steady state is
reached. The most common method is to set the temporal
deriva-tive to zero in the governing equations, then iterate the
differentialequations until convergence, where the concentration
change be-tween iterations is less than an error tolerance (106 in
VanCappellen and Wang, 1996, and 103 in Benoit et al., 2006, or
aresidual of 1014 in Rabouille and Gaillard, 1991a). Meysman et
al.(2003b) refer to this as the steady-state calculation. The
alterna-tivemethod is to solve the dynamic equations overmany time
stepsuntil the concentration changes stabilise, known as an
asymptoticrun (Meysman et al., 2003b). With constant boundary
conditions,the main practical difference between the methods is
that theasymptotic run is more computationally demanding. Some
modelscan be run with a combination of both methods, with steady
statecalculations for some kinetic reactions, such as organic
matteroxidation, and a time-dependent solution for adsorption and
othersedimentary environment. Steady state is where the
concentrationsdo not change in time; the total inows and production
are inbalance with the outows and consumption of all species.
4.2.1. Steady state as a description of the environmentSteady
state can be a valid approximation when the changes at
the interface occur over a much longer timescale, such as a
shift inclimate, or shorter timescale, such as bioirrigation, than
the time ofresponse of thewhole system to aperturbation
(VanCappellen et al.,1993). Deciding whether the system is at
steady state depends onwhich sediment constituents are examined and
the reference timescale. Generally, pore water responds to
environmental changesfaster than the solid phase. Pore water
solutes are transportedthrough the reactive part of the sediment
over a fewmonths and sodo not reach steady state on a seasonal time
scale, but can beconsidered at steady state on a decadal time scale
(Pe~na et al., 2010).On the other hand, solids take decades or
centuries to travel throughthe reactive sediment zone and so are at
steady state on a seasonaltime scale but not a decadal time scale
(Pe~na et al., 2010). Soetaertet al. (1996b) found that dissolved
substances are at steady statewith respect to the instantaneous
uxes of carbon mineralisation
D.W. Paraska et al. / Environmental Mcalculations with changing
boundary conditions.The models with time-dependent calculations
(Table 7) andchanging boundary conditions also adopt a range of
approaches.Those that use the iterative steady state calculation
can go througha series of successive steady states over time, which
is the approachof Soetaert et al. (1996a), later taken up by
authors such as Archeret al. (2002) andWijsman et al. (2002). The
BRNSmodel, which waspartly developed from STEADYSED, has the
capacity to use a similarapproach (Regnier et al., 2003; Aguilera
et al., 2005; Thullner et al.,2005) or the asymptotic run (Canavan
et al., 2006; Dale et al., 2009;Brigolin et al., 2009, 2011). Those
that use the asymptotic methodspin up to a newasymptote over
time.Within these, either a singleperturbation may be introduced
(Wijsman et al., 2002; Talin et al.,2003; Katsev et al., 2006a), a
stationary average of uctuations canbe set as the boundary (Fossing
et al., 2004) or a uctuating quasi-steady boundary condition can be
run, such as a pattern of seasonalchange (Luff and Moll, 2004;
Kasih et al., 2008). The advantage ofusing the asymptotic method is
that the time taken to respond tothe perturbation or the regular
uctuation can be examined.
There is no pattern in the application of these techniques
ac-cording to the groups used in the classication. Rather, in
general,these models have developed to allow any combination of
steady-state calculations, asymptotic runs, constant boundary
conditions,perturbations or quasi-steady uctuations. While the
options inearly studies were limited by the code of the model, most
recentmodels provide the option of steady or time-varying
conditions andthe choice can be made as to how the model is best
applied to thestudy site.
4.3. Organic matter ux from the water column
The input of organic matter to the sedimentewater interface
isone of the most important chemical inputs driving changes in
thesediment (Tromp et al., 1995). Across the papers, there is a
sur-prisingly large range of total organic matter inputs, which
aremostly arrived at by calibrating the model against sediment
depthprole data, usually total organic carbon or O2 depth
proles.However, in a handful of cases, the studies have used
sedimenttraps and SCO2 uxes (Berg et al., 2003; Fossing et al.,
2004; Benoitet al., 2006; Katsev et al. 2006a; Kasih et al., 2008,
2009) whileothers predict the input with data and estimates based
on primaryproduction (Reed et al., 2011b) or full water column
models(Eldridge andMorse, 2000; Sohma et al., 2001, 2004; Eldridge
et al.,2004; Morse and Eldridge, 2007; Brigolin et al., 2009;
Pastor et al.,2011). Each environment shows a straightforward
relationshipwithPOM uxes, which are generally smallest in the deep
sea, as thedeep sea nutrient inputs are lower and more of the
organic matteris oxidised in the water column before it reaches the
sedimentsurface. The lowest total POM uxes, around 1 mmol cm2 y1,
arefound in deep sea sites andmost of the highest uxes, around
1000,are found in the coastal sea. The quantities of these uxes
arebroadly consistent with the estimates of Van Cappellen and
Wang(1995) for uxes in each environment, suggested in the early
daysof these models. For freshwater eutrophic lakes, however, there
isno typical amount of lake sediment organic matter input.
In multi-G models, one of the more difcult parameters to sethas
been the percentage of labile and refractory carbon, for whichthere
is no simple experimental or theoretical guide. Of the fty-ve 2, 3
and 4 G models presented here, in 24 cases the diagenesismodel has
been used to estimate the proportions of the fractions inthe ux to
the sediments by back calculating from depth proles orsurface uxes
(see Table 2). In eight cases the proportion is simplyassumed (ve
of these are Approach 3) and in ve cases theamounts are estimated
based on an empirical relationship to otherfactors such as
sedimentation rate or primary productivity. Only
lling & Software 61 (2014) 297e325 317Benoit et al. (2006)
estimate the uxes and proportions by using
-
odeuxes from a compilation of water column measurements at
thesite itself. Those studies with lower amounts of labile
organicmatter (where the most reactive fraction is less than 50% of
theux) are mostly in near shore marine waters, coastal lagoons
andone freshwater lake, which might reect a higher
allochthonousinput from the catchment. However, many other coastal
andfreshwater lake studies have much higher proportions of
highlyreactive organic matter, so no typical labile-refractory
ratio can bedistilled from the analysis in relation to
environmentalcharacteristics.
4.4. Coupling to water column models
Most sediment models are one-dimensional with depth, whereone
sediment column is used to represent an entire study site, or
anidealisation of various representative sampling locations. Most
ofthese have a simple water column boundary condition at the
sed-imentewater interface, or a diffusive boundary layer.
Conversely, inbiogeochemical water column models, the
sedimentewater inter-face has usually been represented as a simple
ux, resolved in one(Oguz et al., 2000; Shen et al., 2008; Lopes et
al., 2010), two (Bruceet al., 2011) or three dimensions (see for
example, Kiirikki et al.,2006; Xu and Hood, 2006; Kremp et al.,
2007).
A fewsedimentdiagenesismodelling studies couple the
sedimenttowater columnhydrodynamic and ecologymodels; rather than
justa bottomwater boundaryat the sedimentewater interface,
thewatercolumn is resolved with depth in one (Soetaert et al.,
2001; EldridgeandMorse, 2008; Soetaert andMiddelburg, 2009), two
(Benoit et al.,2006; Brigolin et al., 2011) and three dimensions
(Sohma et al., 2001,2004, 2008; Luff and Moll, 2004; Smits and Van
Beek, 2013). Luffand Moll (2004) undertook a thorough
three-dimensional sed-imentewater modelling study where a spatially
resolved model ofthe North Sea was used. The advantage of using a
coupled model isthat both models are buffered by the dynamic
feedback of the other,providing realistic forcing to the sediment.
The studies by Sohmaet al. (2001, 2004, 2008) are dynamic
three-dimensional modelsbased in estuaries, which examine the
effects of oxic/anoxic uctu-ations in the water column on the
sediment. While these estuarystudies have lower spatial resolution
than in Luff and Moll (2004),they includemore complex
ecologicalmodels and consider planktonand seagrass as sources of
POM, DOM, nutrients and O2.
4.5. Applications to assess the effects of human activity
Beyond simply understanding the chemical processes in
thesediment, some studies have been applied to assess the effects
ofhuman activity onwaterways (Table 7). The models have been usedas
predictive tools to assess management options: Canavan et al.(2006)
predict the effect of opening up a freshwater coastal lagoonto the
sea; Brigolin et al. (2009) use themodel to predict theeffects
ofash farm in a fjord;Koniget al. (2001) predict theeffects of deep
seamining on sea oor geochemistry; and Eldridge et al. (2004)
predictthe effects of dredging and harmful algal blooms. They have
also beused to examine the past drivers of water quality
deterioration:Dittrich et al. (2009) examine the change of state in
Lake Zug fromoligotrophic to eutrophic; Kasih et al. (2008, 2009)
examine thedeterioration of the former pearl shery in Ago Bay; and
Katsev andDittrich (2013) examine phosphorus uxes over decadal
timescales.
Many of the studies have included nutrients (Table 6), which
isessential for model studies examining eutrophication,
however,models have rarely been used as a tool for examining
contaminantux. There are many sediment reactive transport models
that werenot within the scope of this analysis, which calculate
heavy metaltransport in the sediment (for example, Gallon et al.,
2004;
D.W. Paraska et al. / Environmental M318Carbonaro et al., 2005,
see also the review by Boudreau, 1999)but few use the full
diagenesis model to relate contaminants to thefate and transport of
other sediment components.
5. Challenges and opportunities
5.1. Conceptualisation and measurement of organic
matteroxidation
5.1.1. Reconnecting models to conceptual understandingSediment
modellers have developed some elegant simplica-
tions of what they knew to be highly complex reaction
processes,in order to reproduce commonly-observed sediment
characteris-tics. It is shown above that the focus in the early
period ofdevelopment was on establishing the organic matter
oxidationprocess and its effects on redox zonation, whereas
recentmodelling studies have focussed on applying the same or
similarmodels to more specic chemical and ecological questions,
aprogression that solidied the multi-G method as the
standardpractice for diagenesis modelling. Despite the limits to
the multi-G conceptual model, which were apparent in the earliest
years ofits development, it was widely adopted because of its
simplicity.The general process of organic matter oxidation used in
mostmodels now involves one to three POM phases of different
reac-tivity oxidising to CO2 through some of the reactions (3)e(8).
Theoverall challenge seen when reviewing the sediment literature
isthat these model structures have become increasingly
separatedfrom laboratory and eld studies, which have in parallel
led to thedevelopment of more rened conceptual models and
classica-tion approaches for characterising organic matter groups
andbreakdown rates.
One of the manifestations of the separation of the
multi-Gmodelling studies from experimentally based studies is
theassignment of the proportions of labile and refractory
organicmatter, which in many cases is either adjusted to t eld data
orsimply assumed, irrespective of the model approach or the
envi-ronments in which the studies were based. The few studies
thatinclude eld or laboratory data highlight the difculties
inmeasuring these fractions, since measurable equivalents of
eachfraction do not exist. One example of these differences is that
lab-oratory studies have shown that aquatic organic matter
generallybreaks down faster than terrestrial organic matter in the
case ofmarine (Burdige, 2005), estuarine (Dai et al., 2009) and
freshwater(Bastviken et al., 2004; Sobek et al., 2009) organic
matter, yet this israrely explicitly considered in the model
parameterisations.Another major difference between the numerical
models and thelaboratory and eld studies is that only 13 of the 83
numericalmodelling papers include a DOMpool. This is despite the
signicantbody of data that has been collected on sediment DOM (see,
forexample, Hansell and Carlson, 2002; Schmidt et al., 2009) and
thefact that DOM accumulated with sediment depth is one of
thelargest pools of organic carbon globally (Hedges and Keil,
1995;Burdige, 2007). Understanding labile DOM mechanistically
isimportant for understanding the reactive intermediates in
thebreakdown of POM to CO2, and although refractory POM and DOMmay
play a smaller part in the reaction processes, they both makeup the
total organic matter prole and their local transport pro-cesses are
quite different.
A further gap between the current modelling approaches andthe
eld and laboratory data is the relatively common use in themodels
of one value of kOM for all oxidants. This is despite
severallaboratory studies that have reported signicantly different
ratesthrough each of the six pathways (Westrich and Berner,
1984;Caneld et al., 1993; Arnosti and Holmer, 2003). There are
alsomany studies that have compared the different rates of
organic
lling & Software 61 (2014) 297e325matter breakdown under
oxic and anoxic conditions (Kristensen
-
odeet al., 1995; Dai et al., 2009; Abril et al., 2010). The
oxidation rate canalso change upon reoxidation after a period under
anoxic bottomwater, and the rate can also depend on the duration of
the previousanoxic period or priming (Aller et al., 2008; Abril et
al., 2010). Theincreased oxidation rate upon reoxidation may be due
to thepresence of chemical species such as H2O2, present only in
oxicconditions, which are small enough to diffuse through large
mo-lecular clusters (Bastviken et al., 2003). It is also known that
organicmatter is preserved over the long term only under
persistentlyanoxic conditions (Henrichs, 1995; Hedges and Keil,
1995; Burdige,2007); the preservation of organic matter may also
occur throughthe processes of geopolymerisation (Hedges and Keil,
1995), sul-disation (only included in the diagenesis models of Dale
et al.,2009 and Couture et al., 2010), interaction with iron
(Lalondeet al., 2012) and adsorption of DOM. Berner (1995) foresaw
DOMadsorption as a major potential addition to the multi-G model,
yetto date it has only been used in two models (Sohma et al.,
2004,2008; Massoudieh, 2010).
Van Cappellen et al. (1993) identied one of the obstacles tothe
determination of precise rate constants as the lack of a set
ofinhibition constants (KIn and LIn). The lack of data available
forinhibition constants is partly a result of inhibition being
animprecise theoretical concept used to explain redox zonation.
Theorganic matter oxidation rate laws assume inhibition of all
sub-sequent pathways when the oxidant concentration is above itsKOx
or LOx. However, eld studies have shown that the pathwayscan often
overlap, such as Fe3 reduction and SO42 reduction,denitrication and
annamox, methanogenesis in the presence ofSO42, and SO42 reduction
in the presence of O2 (Postma andJakobsen, 1996; Jakobsen and
Postma, 1999; Caneld andThamdrup, 2009). Van Cappellen and Wang
(1996) observe thatthe separation between processes is clearer in
environments withlower net organic matter oxidation. We showed
above that manyof the early models were designed for deep sea sites
with a loworganic matter input, therefore the increasingly common
ten-dency to apply the models to highly productive environmentsmay
require further development of the conceptual model of theredox
sequence. One possible clue to understanding the redoxzonation may
come from the recent discovery of centimetre-longliving micro
cables of bacteria that transport electrons betweenthe aerobic and
sulphate-reducing zones (Pfeffer et al., 2012),which is also an
exciting opportunity for diagenesis models toexplore.
Experimental biogeochemists have developed conceptualmodels of
carbon pools and transformations that may serve as aguide for
ongoing model development efforts. Models have beendesigned based
on aspects such as molecular weight (forexample, Burdige and
Gardner, 1998), partial equilibrium withhydrolysis, fermentation
and respiration steps (Alperin et al.,1994; Lovley and Chapelle,
1995), and organic matter origin(Findlay and Sinsabaugh, 1999;
Zonneveld et al., 2010). Bio-geochemists have also collected
datasets of specic identiablemolecules in sediment organic matter
and the calculated freeenergies of reaction (see for example, Amend
and Shock, 2001;LaRowe and Van Cappellen, 2011; LaRowe et al.,
2012), howeverthis data may be difcult to incorporate without
making theconceptual model too reductive or the numerical model
overlyparameterised. Designing a diagenesis model with DOM,
adetailed organic matter breakdown sequence, bacterial biomassand
thermodynamic factors, as well as the secondary reactionsand
transport processes already in the main stream of models, isan
exciting opportunity for future model development. Indeed,numerical
models may be very useful tools for probing the manyinteractions
that laboratory studies have identied through
D.W. Paraska et al. / Environmental Mtesting the relative
performance of model structures of differentcomplexity,
acknowledging that the sacrice of the multi-Gsimplicity could
compensated with the gain of more renedpredictions of process
rates.
5.1.2. Challenges of using experimentally-derived values
forparameters
The need for a new conceptual model of organic matter oxida-tion
is clearer whenwe consider the lack of
experimentally-derivedparameter values, shown in the section on the
choice of parametervalues. Moving away from some of the theoretical
simplications ofthe multi-G model may make it easier to use
laboratory or eldmeasurements as input or validation data for
sediment diagenesismodels.
Many authors have identied the sheer lack of data availablefor
determining the rate constants in biogeochemical modelsgenerally
(Middelburg et al., 1997; Mooij et al., 2010; Pe~na et al.,2010).
Boudreau (1999) writes that kinetic laws in sedimentmodels are
largely educated guesses, because of the difculty inobtaining data
without disturbing the natural sedimentary envi-ronment. The
inherent difculty in measuring kOM in particular,the main rate
constant for organic matter oxidation, comes fromthe spectrum of
reaction rates that can span ten orders ofmagnitude, from minutes
to 106 years under deep sea sediments.Any experiment to measure the
rate will miss materials withbreakdown rates much shorter or longer
than the observationtime span (Hedges and Keil, 1995). We have
shown that there hasgenerally been a wide range of parameter
values, most of whichhave been calibrated, which creates the risk
that a set of theseconstants calibrated to one dataset might not be
readily transfer-able to other study sites or models.
The transfer of the parameter values through the
literaturewarrants further consideration since the range of
environmentsand questions that the models are being applied to is
widening eyet the values are still often taken from the original
papers. Further,an Approach 1 or 2 study with its parameters tuned
to a datasettypically has depth proles of only around 7 variables,
which is stilltrue for papers published in recent years. Thus,
although the scopeof the models has broadened, the collection of
data for constrainingparameters or validating model processes has
hardly increasedsince 1996.
Another risk is that the parameter set could be wrong,
yetgenerate a good t to eld data e known as the problem of
equi-nality (Luo, 2009). However, Van Cappellen and Wang
(1996)argued that because diagenesis models have so many
highlycoupled reactions, the range that the values could be
calibratedwithin is in fact quite small. An error in one constant
could possiblybe hidden by an error in another constant through the
non-linearfeedbacks that shape the system, but it is unlikely that
it could behidden through all of themany reactions. Therefore these
guessesin diagenesis models are not necessarily unrealistic. Some
diagen-esis modelling studies have conducted identiability
analyses,which seek to show the sensitivity of model outputs to
sets ofparameters, within which only some of the parameters are
tted(Dittrich et al., 2009; McCulloch et al., 2013). Nevertheless,
nomatter what the conceptual models of future sediment
diagenesismodels will be, future endeavours to collect more specic
and ac-curate determinations of process rates in situ will help us
under-stand the range of uncertainty in our model simulations.
It must be emphasised that the sediment is a difcult
environ-ment to collect data from and it is not a small task to
collect aperfect eld dataset for a modelling study. Nevertheless,
in situanalytical instruments have improved since the creation of
thesediagenesis models in the 1990s, which may give us an
opportunityto overcome the inherent difculty in measuring sediment
data
lling & Software 61 (2014) 297e325 319(see reviews by
Viollier et al., 2003; Moore et al., 2009). Sediment
-
odebiogeochemical measurements have been conducted with
benthiclanders (see for example, Maerki et al., 2009; Sommer et
al., 2010;Zhang et al., 2010), benthic chambers (see for example
Chapmanand Van den Berg, 2005; Sommer et al., 2008; Ferron et al.,
2008)and diffusive gradients in thin lms and diffusional
equilibration inthin lms (see for example Jezequel et al., 2007;
Monbet et al.,2008; Robertson et al., 2009). In combination with
more rigorousperformance assessment using a wider range of metrics
(e.g.,Bennett et al., 2013), modellers should ultimately be better
able tojustify whether a model is t for purpose.
5.2. Opportunities to improve understanding of physical
andbiological processes
5.2.1. Capturing the multiple scales of change affecting
thesedimentewater interface
Another general challenge for sediment modellers is copingwith
the different spatial scales, from the length of a study site
tosediment pores, and the different scales of perturbation,
fromseasonal oscillations to intense, one-off events. We showed
abovethat there are only a few examples of depth-resolved
sedimentmodels that are resolved horizontally, as part of a greater
modellingsystem. At the large scale, most of these studies are
based inestuarine and coastal environments, while freshwater lakes
areunder-represented. The general lack of spatially-resolved
modelshas occurred despite the benets that could be gained from
higherresolution, such as the inclusion of specic physical and
ecologicalfeatures of a study site or the ability to capture
benthic-pelagicfeedbacks.
A deterrent to building spatially resolved models may be thelack
of data at the appropriate spatial scale to calibrate the modelto,
which could become less of a problem with the increasing
so-phistication of eld instruments, as described above.
Anotherdeterrent from adopting these models may be the perception
thatspatial resolution requires signicant computation time.
Forexample, a comparative study by Soetaert et al. (2000)
concludedthat the best balance between model accuracy and
computationalefciency for coupled water column models was struck
when thesediment component was a simple ux term rather than a
one-dimensional multi-layered sediment model. In the 13 years
sincethat study, the computational efciency has increased
substantially.Aside from only relying on the increasing processing
power ofcomputers, the problem of long computation time can be
mini-mised by separating the time step of the water column, which
hasfaster transport, from the time step of the sediment. The
sedimentcan also be divided into zones with a 2D resolution lower
than thewater column resolution (as is done in Sohma et al., 2008
andBrigolin et al., 2011). Berg et al. (2007) have also addressed
thegeneral problem of computation time in diagenesis models
withoptions for faster numerical solution.
5.2.2. Using small-scale spatial resolution and reduced modelsAt
a small scale, ne spatial resolution allows models to capture
variations such as localised deposition and the effects of
bio-turbation. We have found a few examples of models where
thesedetailed processes have been included, such as that
inSochaczewski et al. (2008) andMuegler et al. (2012), which, like
thelarge scale spatial models, are computationally
demanding.Meysman et al. (2006b) compare 1D, 2D and a 3D
bioirrigationtransport models, without any chemical reactions, and
concludethat their 2D model gives the best balance between accuracy
andsimplicity. The opportunity lies in creating reduced models
(Rattoet al., 2012) with these ne-scale spatially-resolved models
todetermine simple parameterisations that could then be used in
D.W. Paraska et al. / Environmental M320more
computationally-demanding diagenetic model applications.5.2.3.
Including resuspension of sedimentResuspension is well understood
in physical models but rarely
used in biogeochemical models (Massoudieh et al., 2010). It is
lessimportant in a calm water body such as the deep ocean,
wheremany of the early sediment diagenesis modelling studies have
beenbased, but as we have shown above, more studies are attempting
tomodel shallower, higher-e