LOSCAR: Long-term Ocean-atmosphere-Sediment CArbon ......minor bugs and numerical issues have...

Geosci. Model Dev., 5, 149–166, 2012www.geosci-model-dev.net/5/149/2012/doi:10.5194/gmd-5-149-2012© Author(s) 2012. CC Attribution 3.0 License.

GeoscientificModel Development

LOSCAR: Long-term Ocean-atmosphere-Sediment CArbon cycleReservoir Model v2.0.4

R. E. Zeebe

School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 1000 Pope Road, MSB 504,Honolulu, 96822, USA

Correspondence to:R. E. Zeebe ([email protected])

Received: 24 May 2011 – Published in Geosci. Model Dev. Discuss.: 29 June 2011Revised: 12 January 2012 – Accepted: 18 January 2012 – Published: 25 January 2012

Abstract. The LOSCAR model is designed to efficientlycompute the partitioning of carbon between ocean, atmo-sphere, and sediments on time scales ranging from centuriesto millions of years. While a variety of computationally inex-pensive carbon cycle models are already available, many aremissing a critical sediment component, which is indispens-able for long-term integrations. One of LOSCAR’s strengthsis the coupling of ocean-atmosphere routines to a compu-tationally efficient sediment module. This allows, for in-stance, adequate computation of CaCO3 dissolution, calcitecompensation, and long-term carbon cycle fluxes, includ-ing weathering of carbonate and silicate rocks. The oceancomponent includes various biogeochemical tracers such astotal carbon, alkalinity, phosphate, oxygen, and stable car-bon isotopes. LOSCAR’s configuration of ocean geometry isflexible and allows for easy switching between modern andpaleo-versions. We have previously published applicationsof the model tackling future projections of ocean chemistryand weathering,pCO2 sensitivity to carbon cycle perturba-tions throughout the Cenozoic, and carbon/calcium cyclingduring the Paleocene-Eocene Thermal Maximum. The fo-cus of the present contribution is the detailed description ofthe model including numerical architecture, processes andparameterizations, tuning, and examples of input and out-put. Typical CPU integration times of LOSCAR are of orderseconds for several thousand model years on current stan-dard desktop machines. The LOSCAR source code in Ccan be obtained from the author by sending a request [email protected].

1 Introduction

Various carbon cycle models that are computationally inex-pensive have been developed in the past, in particular boxmodels of the ocean’s carbon cycle (e.g.Sarmiento and Tog-gweiler, 1984; Siegenthaler and Wenk, 1984; Walker andKasting, 1992; Toggweiler, 1999; Stephens and Keeling,2000; Kohler et al., 2005; Peacock et al., 2006). How-ever, less studies have coupled a genuine sediment modelto the ocean box model (e.g.Sundquist, 1986; Keir, 1988;Opdyke and Walker, 1992; Sigman et al., 1998; Ridgwell,2001) and also considered long-term carbon cycle fluxesand feedbacks such as carbonate and silicate rock weath-ering (e.g.Munhoven and Francois, 1996; Shaffer et al.,2008). The LOSCAR model (Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir model) closes this gap.In addition, LOSCAR’s configuration of ocean geometry isflexible (cf. Ridgwell, 2001) and allows for easy switchingbetween modern and paleo-versions (see below). Note alsothat LOSCAR’s sediment module includes variable poros-ity (Sect.6.2). LOSCAR is primarily designed to efficientlycompute the partitioning of carbon between ocean, atmo-sphere, and sediments on time scales ranging from centuriesto millions of years. LOSCAR includes various biogeochem-ical tracers such as total dissolved inorganic carbon (TCO2),total alkalinity (TA), phosphate (PO4), oxygen (O2), stablecarbon isotopes (δ13C), and %CaCO3 in sediments. Basedon the predicted tracer distributions, different variables arecomputed including atmospheric CO2, ocean pH, calcite andaragonite saturation state, calcite compensation depth (CCD)and more. LOSCAR also allows for changes in the majorion composition of seawater, including the seawater Mg/Ca

Published by Copernicus Publications on behalf of the European Geosciences Union.

150 R. E. Zeebe: LOSCAR

ratio, which is critical for paleo-applications. The major ionseawater composition affects thermodynamic quantities suchas equilibrium constants and solubility products, which inturn affect the predicted ocean carbonate chemistry and at-mospheric CO2.

We have previously published several applications ofLOSCAR dealing, for instance, with future projections ofocean chemistry and weathering,pCO2 sensitivity to car-bon cycle perturbations throughout the Cenozoic, and car-bon/calcium cycling during the Paleocene-Eocene ThermalMaximum (PETM) (Zeebe et al., 2008; Zachos et al., 2008;Zeebe et al., 2009; Uchikawa and Zeebe, 2008; Stuecker andZeebe, 2010; Uchikawa and Zeebe, 2010; Komar and Zeebe,2011; Zeebe and Ridgwell, 2011; Zeebe, 2012). The subjectof the present contribution is the detailed description of themodel including numerical architecture, processes and pa-rameterizations, tuning, and examples of input and output. Itmay appear that publishing model applications before a de-tailed model description is putting the cart before the horse.One of the reasons for this is that the journals interested inpublishing the model applications have little or no interestin publishing a detailed model description. Journals that pro-vide a forum for technical model descriptions are rare, and sothe recent appearance ofGeoscientific Model Developmenthas encouraged me to provide a coherent model descriptionof LOSCAR that will hopefully be useful for the readershipof the journal, as well as the users of the model. On theother hand, publishing a few model applications before thedetailed model description also has an advantage. LOSCAR,for example, has been extensively tested by now and severalminor bugs and numerical issues have already been fixed (seeSect.7.4).

LOSCAR’s main components include ocean, atmosphere,and marine sediments. The model architecture, main com-ponents, model variables, and process parameterizations willbe described in the following. Finally, two input/output ex-amples will be presented, one dealing with anthropogenicfossil fuel emissions, the other with carbon release duringthe PETM (input files for these examples are included in themodel package).

2 Architecture

The basic numerical architecture of the model is fairly sim-ple. For all model variablesyi , i.e. all tracers in all com-partments (atmosphere, ocean boxes, and sediment boxes), asystem of coupled, first-order ordinary differential equationsis solved:

dyi

dt= F(t,y1,y2,...,yNEQ) , (1)

wheret is time, NEQ is the total number of equations,i =

1,2,...,NEQ, andF ′s are known functions. Note that formost applications, the derivatives (right-hand side of Eq.1)do not explicitly depend on the independent variablet . For

Fig. 1. Schematic representation of the LOSCAR model (Pale-ocene/Eocene configuration). A= Atlantic, I= Indian, P= Pacific,T = Tethys ocean, H= High-latitude surface, L= Low-latitude sur-face, M= interMediate, D= Deep box. Weathering fluxes and gasexchange with the atmosphere (Atm) are indicated by “w” and “g”,respectively. Steps on the faces of ocean boxes indicate sediments(Sed).

given start (initial) conditionsy0 at tstart, the equations arethen integrated forward in time over the interval fromtstart totfinal. Standard numerical procedures (solvers) for this sort ofproblem are available. One thing to keep in mind is that theequations solved in LOSCAR are typically stiff and involvedifferent time scales, which requires a solver for stiff prob-lems with adaptive stepsize control. The solver implementedin the C version of LOSCAR is a fourth-order Rosenbrockmethod with automatic stepsize adjustment (Press et al.,1992).

Once the initial conditionsy0 and derivativesF ’s havebeen supplied, the solution of the problem is usually straight-forward. However, setting upy0 andF requires some work.In the following, the individual model components will bedescribed and expressions will be given for individualF ’sthat enter Eq. (1). The current setup includes two differentmodel versions: a “modern” version and a Paleocene/Eoceneversion (“P/E”-version for short).

3 Ocean

3.1 Geometry

The global ocean is geometrically divided in LOSCAR intoseparate ocean basins representing Atlantic, Indian, and Pa-cific Ocean (plus Tethys in the P/E-version). In turn, eachocean basin is subdivided into surface, intermediate, anddeep ocean (Fig.1). In addition, the model includes a generichigh-latitude box (H-box), representing cold surface waterswithout reference to a specific location (cf.Walker and Kast-ing, 1992; Toggweiler, 1999). As a result, the total number ofocean boxes isNB = 10 in the modern version andNB = 13

Geosci. Model Dev., 5, 149–166, 2012 www.geosci-model-dev.net/5/149/2012/

R. E. Zeebe: LOSCAR 151

Table 1. Model-architecture and ocean geometry parameters.

Parameter Symbol Valuea Unit

# Ocean basins NOC 3 (4) –# Ocean tracers NOCT varies –# Ocean boxes NB 10 (13) –# Atm. tracers NATM 1 or 2b –# Sediment levels NSD 13 –# Equations NEQ NOCT×NB+NATM +NOC×NSD –Total ocean volume Voc 1.29×1018,c m3

Total ocean area Aoc 3.49×1014,c m2

% Area fA 26,18,46,10d %% Area fA (15,14,52,9,10)e,f %Height L-boxg hL 100 mHeight H-boxg hH 250 mHeight M-boxg hM 900 mVolume M-boxesg Vi 0.817, 0.565, 1.445h 1017m3

Volume M-boxesg Vi (0.471, 0.440, 1.633, 0.283)j 1017m3

Volume D-boxesg Vi 2.853, 2.099, 4.739h 1017m3

Volume D-boxesg Vi (1.540, 1.540, 6.547, 0.063)j 1017m3

a Default: modern version, parentheses: P/E-version.b 1: CO2 ; 2: CO2 and13CO2.c Toggweiler(1999). d Atlantic, Indian, Pacific, High-latitude.e (Atlantic, Indian,Pacific, Tethys, High-latitude).f Bice and Marotzke(2002). g L = Low-latitude surface,H = High-latitude surface, M = interMediate, D = Deep.h Atlantic, Indian, Pacific.j

(Atlantic, Indian, Pacific, Tethys).

in the P/E-version. Box areas and volumes are given in Ta-ble 1. The modern ocean geometry in LOSCAR is not un-like the one used byWalker and Kasting(1992). However,Walker and Kasting(1992) combined the warm surface andthermocline waters each into a single reservoir for a total of6 boxes to represent the global modern ocean.

The modern and Paleocene/Eocene ocean bathymetry inLOSCAR is based onMenard and Smith(1966) andBice andMarotzke(2002), respectively. The bathymetry determinesthe surface area and volume of ocean boxes (Table1) and thesurface area-depth level relationship of the sediment boxes(Sect.6).

3.2 Ocean tracer equations

Let yk be a subset ofy (Eq. 1), representing ocean tracervariables including TCO2, TA, PO4, etc. (in this particularorder). Thenk = 1,2, ...,NB for TCO2, k = NB +1,NB +

2,...,2NB for TA, k = 2NB+1,2NB+2,...,3NB for PO4,and so on. If the total number of ocean tracers isNOCT, thenthe total number of equations for all ocean tracers and boxesis NOCT×NB. The differential equation for an ocean traceryk may be written in the general form:

Vk

dyk

dt= Fthm+Fgas+Fbio+Fin +Fsed, (2)

whereVk is the volume of boxk and F ’s are fluxes dueto (thermohaline) circulation and mixing, air-sea gas ex-change (e.g. in case of TCO2), biological uptake and rem-ineralization, riverine/weathering input, and sediment fluxes.The first three flux terms on the right-hand side of Eq. (2)

will be explained in the following subsections; the river-ine/weathering and sediment flux terms will be explained inSects.4 and6.

3.2.1 Circulation, mixing, and air-sea gas exchange

Given a prescribed ocean circulation- and mixing scheme,Fthm is of the form:

Vk

(dyk

dt

)thm

= T∑j

(yj −yk)+∑

l

mlk (yl −yk) (3)

whereT is the volume transport of the conveyor circula-tion andmlk are mixing coefficients between boxesl andk

(Fig. 2, Table2). The box indicesj andl are set by the pre-scribed circulation/mixing scheme (Fig.2). The coefficientsmlk represent bidirectional mixing, hencemlk = mkl .

The air-sea gas exchange term reads:

Vk

(dyk

dt

)gas

= κasAk (pCO2a−PCO2

k) (4)

whereκas is the air-sea gas exchange coefficient for CO2 andAk is the area of surface boxk; pCO2

a andPCO2k is the

atmosphericpCO2 and thepCO2 in equilibrium with dis-solved CO2 in surface boxk, respectively. The indexk runsover all surface boxes for tracers such as TCO2.

To derive the corresponding expression for the13CO2 flux,it is useful to rewriteκas asκas = u β, whereu is the gastransfer velocity andβ the solubility (e.g.Siegenthaler andMunnich, 1981; Wanninkhof, 1985). Hence the air-sea CO2flux per unit area may be written as:

Fgas= u (β ·pCO2a− [CO2]) , (5)

where [CO2] is the concentration of dissolved CO2 in solu-tion. A similar equation holds for13C:

13Fgas=13u (13β ·p13CO2

a− [13CO2]) . (6)

Usingαu =13u/u andαdg =

13β/β, whereαu represents thekinetic fractionation during gas exchange andαdg the equi-librium fractionation between dissolved and gaseous CO2(Mook, 1986; Zhang et al., 1995), it follows:

13Fgas= κasαu (αdg·p13CO2a−Rd β−1 [CO2]) , (7)

whereκas= u β (see above) andRd is the12C/13C ratio ofdissolved CO2. Rd may be calculated taking into accountthe speciation and isotope fractionation among the variouscarbonate species (e.g.Wanninkhof, 1985; Zeebe and Wolf-Gladrow, 2001). Alternatively, a simplified expression forRd may be obtained assuming that the carbon isotope ratioof HCO−

3 (Rb) is approximately equal to that of TCO2 (Rb '

RT). In other words,Rd ' αdb RT, whereαdb is the fractiona-tion between dissolved CO2 and HCO−

3 (Mook, 1986; Zhanget al., 1995). Over the pH range from 7.5 to 8.2 and at 20◦C,this approximation differs from the full calculation by 0.2 to

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Table 2. Physical and biogeochemical parameters (ocean model).

Parameter Symbol Modern P/E-setupa Unit

Conveyor Transport T 20b 25 Svc

Tethys Transport TT – 2 SvUpwelling (D–M)d tA ,tI 0.2,0.2e,f –Mixing (L–M)d mlk 21,17,25g,f 13,13,27g,f SvMixing (H–D)d mlk 4,3,10g,f 5,5,8g,f SvMixing Tethys mlk – 12,1,8h,f SvTemperature (initial) T 0

C 20,10,2,2i 25,16,12,12i ◦CTemp. relax. time τn 20,200,1000j yrSalinity S 34.7 –Gas exch. coeff. CO2 κas 0.06k mol(µatm m2 yr)−1

Biopump-efficiency fepl 0.80f –Remin. fraction (M)d frim 0.78f –Remin. fraction (D)d 1−frim 0.22 –P/C in Corg REDPC 1/130 –N/C in Corg REDNC 15/130 –O2/C (Corg-remin.) REDO2C 165/130 –C-export (H)d Feph 1.8f mol m−2 yr−1

P-export (H)d Fpph Feph× REDPC mol m−2 yr−1

Rain ratiol rrain 6.1 6.7f –CaCO3 water dissol.m νwc 0.31f –

a Same as modern version unless indicated.b Toggweiler(1999). c 1 Sv= 106 m3 s−1. d L = Low-latitude surface, H = High-latitude surface, M = InterMediate, D=Deep.e Fractionupwelled into intermediate Atlantic, Indian (see Fig.2). f Tuned. g Atlantic, Indian, Pacific.h (L−M Tethys, L−D Tethys, I-Tethys−I-Indian). i L, M, D, H-box. j Surface,intermediate, deep.k Broecker and Peng(1998). l Corg : CaCO3. m Fraction of total CaCO3 export dissolved in water column.

0.3 ‰. The simplified expression will thus suffice for mostLOSCAR applications. Noting thatβ−1

· [CO2] = PCO2,the air-sea gas-exchange term for13CO2 can then be writtenas:

Vk

(dyk

dt

)gas

= κasAk αu (αdgk·p13CO2

a−αdb

k RkT ·PCO2

k) . (8)

This expression is readily evaluated in LOSCAR, whichcarriesp13CO2

a, PCO2, and T13CO2 as tracers (note that

RkT = T13CO2

k/TCO2

k). Values for the fractionation factors(α’s) as functions of temperature have been summarized inthe literature (Mook, 1986; Zhang et al., 1995; Zeebe andWolf-Gladrow, 2001). The user can choose between the setsof fractionation factors given byMook (1986) and Zhanget al.(1995). However, the differences between the two setsare minor, except for the fractionation between CO2−

3 andHCO−

3 , which is not used in LOSCAR given the simplifiedexpressions above.

3.2.2 Biological pump

The biological uptake and recycling of tracers is parameter-ized based on phosphate (PO4 for short). For instance, netuptake of PO4 in the low-latitude surface ocean (equivalentto particle export flux from the mixed layer) is calculated as:

Vk

(d[PO4]k

dt

)upt

= F kppl = − fepl mjk [PO4]j , (9)

where the parameterfepl describes the efficiency for PO4 up-take in the low-latitude surface boxes,mjk ×[PO4]j is theflux of PO4 supplied by upwelling/mixing from the underly-ing intermediate boxj into the surface boxk. (Note that inthe model, the conveyor transportT does not directly supplynutrients to the warm surface waters; it does so, however, tothe cold surface waters, see Fig.2). If fepl were to approach1.0 (100 % efficiency), all upwelled PO4 would be convertedto sinking particles and the phosphate concentration of sur-face boxk would be zero. In the model, as well as in reality,fepl is usually less than 1.0 (Table2). The fractionfrim of theexport flux is remineralized in the intermediate box, whereasthe fraction(1−frim) is remineralized in the deep box.

The high-latitude PO4 export flux can be set directly byassigning a value to the flux parameterFpph. If the valuechosen is too large to be supported by the total PO4 influxentering the H-box, simple Michaelis-Menten kinetics pre-vent PO4 from becoming negative. Caution is therefore ad-vised when increasingFpph because the actual high-latitudeexport flux may be less than the value assigned toFpph. Thehigh-latitude export flux is remineralized in the deep boxes.

The fluxes of TCO2 and TA due to biological uptake andrecycling are computed based on PO4 using a given Redfield-



H A

10 L

I P

M

D

1 2 3

4 5 6

7 8 9

MODERN

m9,10

m3,6

T

T

m1,4 m2,5

m7,10 m8,10

tAT tIT (1− tA − tI)T

HA

L

I P

M

D

PALEOCENE/EOCENE (Steady State)

T

T

Teth

TT

Fig. 2. Caption on next page.

32

Fig. 2. Ocean circulation and mixing schemes implemented inLOSCAR for modern setup (top) and Paleocene/Eocene (P/E)steady-state (bottom). A= Atlantic, I= Indian, P= Pacific ocean,H = High-latitude surface, Teth= Tethys. L= Low-latitude sur-face, M= interMediate, D= Deep box.T represents the conveyortransport, while the coefficientsmlk represent bidirectional mixingbetween boxes. The generic H-box represents cold surface waterswithout reference to a specific location. Nevertheless, the modernsetup is motivated by preindustrial circulation patterns with signif-icant deep water formation in the North Atlantic (e.g.Walker andKasting, 1992; Toggweiler, 1999). The P/E steady-state setup is in-spired by observations and modeling studies of Paleocene/Eocenecirculation patterns with significant deep water formation in theSouthern Ocean (e.g.Bice and Marotzke, 2002; Thomas et al.,2003; Lunt et al., 2010). TT (dashed line) represents the Tethyscirculation, which connects to the Indian Ocean (note that theTT-surface and deep branch do not flow through Atlantic boxes, as in-dicated by arcs). Note also that a transient contribution of NorthPacific Deep Water (not shown) was included in our PETM sim-ulations (Zeebe et al., 2009). All ocean boxes (except H-box) inthe modern and P/E-setup are coupled to sediment boxes (schemat-ically indicated only in the bottom panel for the Pacific by the grayshaded area).

and rain ratio (Table2). Note that there is a small contri-bution to alkalinity changes from organic carbon productionand respiration as a result of nitrate uptake and release (e.g.Zeebe and Wolf-Gladrow, 2001). The major contribution to

alkalinity changes in the model is associated with CaCO3fluxes. Of the total CaCO3 export flux, the larger fractionis destined for accumulation or dissolution in sediments, thelatter of which returns total carbon and alkalinity to the ocean(Sect.6). A smaller fraction of the CaCO3 export is assumedto dissolve in the water column (Table2). This assump-tion yields better agreement with observed TA fields and isconsistent with observations and modeling studies indicatingsubstantial water column dissolution above the lysocline (e.g.Archer et al., 1998; Milliman et al., 1999; Feely et al., 2002).In the model, the fraction representing CaCO3 water columndissolution is added to the corresponding deep boxes, henceincreasing TCO2 and TA in these boxes.

The export flux of T13CO2 is determined based on the totalcarbon export flux and a carbon isotope fractionation factorrepresenting the isotope effect associated with the fixation oforganic matter. For example, in the low-latitude surface, theT13CO2 flux is computed as:

13F kepl = α(Corg−T ) Rk

T F kepl (10)

where F kepl is the total carbon export flux from boxk,

RkT = T13CO2

k/TCO2

k, andα(Corg−T ) = 0.9723 representsthe carbon isotope fractionation between organic carbon andTCO2. The fractionation factorα(Corg−T ), or more preciselyits correspondingε-value [ε = (α − 1)103], should not beconfused with the isotopic difference between the carbonsource and fixed carbon, often denoted asεp (e.g. Hayes,1993). While εp requires knowledge about the photosyn-thetic carbon source (e.g. CO2 or HCO−

3 ), ε(Corg−T ) does not.ε(Corg−T ) is a model-specific, tunable parameter representinga globally averaged value for the marine carbon isotope frac-tionation between organic carbon and TCO2. It is tuned soas to reproduce the observedδ13C distribution in the ocean.For the sake of simplicity, no fractionation is associated withthe precipitation and dissolution of CaCO3 in the model.

4 Carbonate and silicate weathering

Weathering of carbonate rocks on the continents takes up at-mospheric CO2 and supplies calcium and bicarbonate ions tothe ocean:

CaCO3+H2O+CO2 Ca2++2 HCO−

3 . (11)

Hence two moles of carbon and one mole of Ca2+ en-ter the ocean for each mole of CaCO3 weathered, raisingocean TCO2 and TA by two units each (Fig.3). If theCaCO3 riverine/weathering influx is denoted byFcc (in unitsof mol CaCO3 yr−1, see Table3), then:

Vk

(d[TCO2]k

dt

)cc

= Vk

(d[TA]k

dt

)cc

= 2 Fcc NOC−1 (12)

wherek = 1,...,NOC runs over all low-latitude surface boxesandNOC is the number of corresponding ocean basins. Note



Table 3. Weathering and sediment model parameters.

Parameter Symbol Valuea Unit

CaCO3 weath. flux (initial) F0cc 12b (16) 1012mol yr−1

CaSiO3 weath. flux (initial) F0si 5c (6) 1012mol yr−1

CO2 degass. flux (initial) F0vc F0

si 1012mol yr−1

CaCO3 weath. exponent ncc 0.4d –CaSiO3 weath. exponent nsi 0.2d –δ13C weath. δ13Cin 1.5 (2.0) ‰δ13C degass. δ13Cvc −4 ‰Height sediment mixed layer hs 0.08 mDensity, solids ρs 2.5×103 kg m−3

non-CaCO3 fluxe Frrf 0.35×10−2 kg m−2 yr−1

Porosity, pure clay φ0 0.85f –Porosity, pure CaCO3 φ1 0.62f –Dissolution rate const. (eff.)g Ksd 20.36×1010 mol m−2 yr−1

Dissolution rate order (eff.)g nsd 2.40 –

a Default: modern version, parentheses: P/E-version.b Morse and Mackenzie(1990). c Walker and Kasting(1992). d Uchikawa and Zeebe(2008). e Rain of refractory, non-CaCO3material to sediments.f SeeZeebe and Zachos(2007). g Effective rate parameters, relating bottom water undersaturation to dissolution rate (Keir, 1982; Sundquist, 1986; Sigmanet al., 1998; Zeebe and Zachos, 2007); nsd is not to be confused with the calcite reaction ordern, relating porewater undersaturation to dissolution rate (typicallyn = 4.5).

that in steady state, subsequent precipitation of CaCO3 in theocean (Reaction11 backwards) releases the same amount ofCO2 back into the atmosphere as was taken up during weath-ering. In other words, the CO2 for carbonate weathering es-sentially originates from the ocean (Fig.3). As a result, al-though the addition of Ca2+ and 2 HCO−

3 increases oceanTCO2 : TA in a 2:2 ratio, on a net basis CaCO3 weatheringincreases ocean TCO2 : TA in a 1:2 ratio because one moleof CO2 returns to the atmosphere. If influx equals burial,carbonate weathering thus represents a zero net balance foratmospheric CO2. The steady-state balance is restored aftera perturbation on a time scale of 5 to 10 kyr and is referred toas “calcite compensation” (Broecker and Peng, 1987; Zeebeand Westbroek, 2003).

Weathering of silicate rocks and simultaneous uptake ofatmospheric CO2 may be described by:

CaSiO3+H2O+2 CO2 Ca2++2HCO−

3 +SiO2 . (13)

If the CaSiO3 riverine/weathering influx is denoted byFsi(in units of mol CaSiO3 yr−1, see Table3), then:

Vk

(d[TCO2]k

dt

)si

= Vk

(d[TA]k

dt

)si

= 2 Fsi NOC−1 . (14)

Note that silicate weathering removes 2 moles of CO2from the atmosphere for each mole of CaSiO3 weathered.Subsequent precipitation and burial of CaCO3 (Reaction11backwards) releases one mole of CO2 back to the atmo-sphere, the other mole is buried in the form of CaCO3 in sed-iments (Fig.3). In steady state, the balance is closed by long-term CO2 input to the atmosphere from volcanic degassing.Putting it the other way, the CO2 released by volcanoes is bal-anced by silicate weathering and subsequent carbonate burial

in the ocean (Fig.3). The net reaction is:

CaSiO3+CO2 CaCO3+SiO2 . (15)

The steady-state balance for silicate weathering is restoredafter a perturbation on a time scale of 105 to 106 yr. Thisprocess also restores the partial pressure of atmospheric CO2in order to maintain a mass balance of long-term carbon cyclefluxes (e.g.Berner et al., 1983; Zeebe and Caldeira, 2008).

The restoring time scale for silicate weathering is muchlonger than for carbonate weathering for two reasons. First,silicate weathering requires whole-ocean TCO2 to adjust,whereas carbonate weathering only requires the ocean’s car-bonate ion concentration to adjust (e.g.Zeebe and West-broek, 2003). On average, the modern TCO2 inventoryis about 20 times larger than mean-ocean [CO2−

3 ] (e.g.Broecker and Peng, 1998). Second, carbonate weatheringfluxes have been estimated to be about 2.5-times larger thansilicate weathering fluxes (Table3; Morse and Mackenzie,1990; Walker and Kasting, 1992). Combined, this gives afactor of about 50, which, multiplied by the calcite com-pensation time scale of 10 kyr, gives 500 kyr, which is aboutright.

4.1 Weathering feedback

The feedback between atmospheric CO2 and weatheringfluxes of carbonates and silicates is parameterized in themodel using the following equations (seeWalker et al., 1981;Berner et al., 1983; Walker and Kasting, 1992):

Fcc = F 0cc

(pCO2/pCO0

2

)ncc (16)

Fsi = F 0si

(pCO2/pCO0

2

)nsi (17)



CaCO3+ CO2+H2O

Ca2++ 2 HCO−3

-

?

(1,0)CO2 (1,0)CO2

Ca2++ 2 HCO−3 CaCO3+ CO2+ H2O

(2,2)

(1,2)

Atmosphere

Ocean

Sediment

(X,Y) = (TCO2,TA)

CaCO3

?

6

Carbonate Weathering

CaSiO3 + 2CO2+H2O

Ca2++ 2HCO−3 + SiO2

-

?

(2,0)CO2 (1,0)CO2

Ca2++ 2 HCO−3 CaCO3+ CO2+ H2O

(2,2)

(1,2)

Atmosphere

Ocean

Sediment

(X,Y) = (TCO2,TA)

CaCO3

?

6

Silicate Weathering

6Fvc

(1,0)

Fig. 3. Schematic illustration of carbonate and silicate weathering fluxes. Numbers in parentheses indicate

steady-state fluxes of TCO2 and TA in mole per mole of CaCO3 or CaSiO3 weathered.

34

Fig. 3. Schematic illustration of carbonate and silicate weather-ing fluxes. Numbers in parentheses indicate steady-state fluxes ofTCO2 and TA in mole per mole of CaCO3 or CaSiO3 weathered.

where the superscript “0” refers to the initial (steady-state)value of the weathering flux andpCO2, respectively. Theparametersncc andnsi control the strength of the weather-ing feedback (Table3). The default values forncc andnsiadopted in LOSCAR were chosen so as to represent conser-vative values, resulting in a weak default weathering feed-back at the lower end of the spectrum (see Fig. 1 inUchikawaand Zeebe, 2008). The user is welcome to change and varythese parameters values (cf.Uchikawa and Zeebe, 2008; Ko-mar and Zeebe, 2011).

As mentioned above, in steady state, the silicate weather-ing flux balances the CO2 degassing flux from volcanism:

F 0si = F 0

vc . (18)

Thus, the long-term steady-statepCO2 of the model is set bypicking a value forpCO0

2, which drives the system towardsequilibrium via the silicate weathering equation (Eq.17).Only when the actual modelpCO2 equalspCO0

2, will thefluxes be balanced (Fsi = F 0

si = F 0vc). The carbon isotope

composition of the volcanic degassing flux is set to−4.0 ‰in the model, while theδ13C of the weathering flux is set to1.5 ‰ and 2.0 ‰ for the modern and P/E-setup, respectively(see Table3).

5 Atmosphere

The model variable tracking the inventory of atmosphericcarbon dioxide, Catm, is related to the partial pressure of CO2in the atmosphere by (analogous for13C):

Catm = pCO2a×q0 (19)

13Catm = p13CO2a×q0 (20)

whereq0= (2.2×1015/12) mol µatm−1 converts from µatm

to mol. Note that for numerical scaling purposes (seeSect.7.4), Catm is normalized to order 1 in the program bymultiplying by (Aoc×100)−1 (arbitrary factor). The differ-ential equations for Catm and 13Catm may be written in thegeneral form:

d Catm

dt= Fgas+Fvc−Fcc−2 Fsi+C′

in (21)

d 13Catm

dt=

13Fgas+13Fvc−

13Fcc−2 13Fsi+13C′

in , (22)

whereF ’s are fluxes due to air-sea gas exchange, volcanicinput and weathering (see Sect.4), and possible carboninput sources. Fluxes of13C due to volcanic degassingand weathering are calculated from13Fj = Rj Fj , whereRj = Rstd(δ

13Cj/1×103+1) andδ13Cj is set to−4.0 ‰ and

1.5 ‰, respectively, for the modern version (see Table3).The air-sea gas exchange terms for the atmosphere read:(d Catm

dt

)gas

=

∑k

κasAk (PCO2k−pCO2

a) (23)

(d 13Catm

dt

)gas

=∑k

κasAk αu(αdbk Rk

T ·PCO2k−αdg

k·p13CO2

a) (24)

whereκas is the air-sea gas exchange coefficient for CO2 andAk is the area of surface boxk; pCO2

a andPCO2k is the

atmosphericpCO2 and thepCO2 in equilibrium with dis-solved CO2 in surface boxk, respectively. For details re-garding the gas-exchange term for13C, see Sect.3.2.1. Thesum runs over all surface boxes. In case of carbon input to



(a) Net accumulation

(b) Erosion

Bottom water

Sediment mixed layer

CaCO3 + H2O Clay + H2O(h1, Φ1) (h2, Φ0)

hs

hs

∆z

rain dissolution

burial

Bottom water

Sediment mixed layer

Sub-surface sediment

hs

(fci, Φi)

Sub-surface sediment(fci, Φi)

∆z

hs

rain dissolution

"mining"

Fig. 4. Schematic representation of the sediment model. The sediment mixed layer (thicknesshs) can be sepa-

rated into pure calcite plus pore water (thicknessh1, porosity φ1) and pure clay plus pore water (thicknessh2,

porosity φ0). (a) Net accumulation equals CaCO3 rain minus dissolution. At the bottom of the sediment mixed

layer, an amount equal to net accumulation is removed via burial (∆z). (b) If dissolution of CaCO3 exceeds the

rain of CaCO3 plus clay, chemical erosion occurs. Previously deposited, underlying sediment is reintroduced

into the top layer and exposed to dissolution (“mining”). Sub-surface sediment properties are based on the

initial steady-state configuration (fci and φi is the initial calcite fraction and porosity, respectively).

35

Fig. 4. Schematic representation of the sediment model. The sed-iment mixed layer (thicknesshs) can be separated into pure cal-cite plus pore water (thicknessh1, porosityφ1) and pure clay pluspore water (thicknessh2, porosityφ0). (a) Net accumulation equalsCaCO3 rain minus dissolution. At the bottom of the sediment mixedlayer, an amount equal to net accumulation is removed via burial(1z). (b) If dissolution of CaCO3 exceeds the rain of CaCO3 plusclay, chemical erosion occurs. Previously deposited, underlyingsediment is reintroduced into the top layer and exposed to disso-lution (“mining”). Sub-surface sediment properties are based onthe initial steady-state configuration (f ci andφi is the initial calcitefraction and porosity, respectively).

the atmosphere from fossil fuel burning or from other carbonsources, for instance, during the PETM, terms of the form:(

d Catm

dt

)Cin

= Cin ×1015/12 (25)

(d 13Catm

dt

)Cin

=13Cin ×1015/12 (26)

are added whereCin is in units of Pg C yr−1 and 13Cin =

Rin Cin, whereRin is the carbon isotope ratio of the carbonsource.

6 Sediments

The sediment model calculates %CaCO3 (dry weight) in theseafloor-bioturbated (mixed) sediment layer of thicknesshsas a function of sediment rain, dissolution, burial, and chem-ical erosion (for more details see Fig.4 andZeebe and Za-chos, 2007). The model is particularly useful for long-termintegrations and has been constructed similar to other modelsof this class (e.g.Keir, 1982; Sundquist, 1986; Sigman et al.,1998). However, the current model also includes variableporosity – a feature critical to simulating strong dissolution

events that lead to sediment erosion, such as expected for thefuture or during the PETM (Zeebe and Zachos, 2007; Zeebeet al., 2008, 2009).

6.1 Chemical erosion

When dissolution of CaCO3 exceeds the rain of CaCO3 plusrefractory material such as clay, the sediment column shrinksand previously deposited, underlying sediment is reintro-duced into the top layer and exposed to dissolution. Thisis referred to as chemical erosion (Fig.4). As a result, signif-icantly more CaCO3 is available for dissolution during ero-sion than originally contained in the top sediment layer. Oncethe top layer is entirely filled with clay, the sediment columnis “sealed” and dissolution ceases. In order to fill the sedi-ment top layer with clay, the sediment volume that was ini-tially filled with CaCO3 + pore water must be replaced byclay + pore water. Thus, if the sediment porosityφ is con-stant, the ratio of total CaCO3 available during erosion to themass contained in the original surface layer is given by:

1+f ci

(1−f ci)(27)

(Broecker and Takahashi, 1977) where f ci and (1− f ci)

are the initial CaCO3 and clay dry weight fraction of thesediment, respectively. However, if porosity varies with%CaCO3 (as observations show, see below), the ratio of totaldissolved to initial CaCO3 is given by:

1+1−φ0

1−φ1

f ci

1−f ci (28)

whereφ0 andφ1 are the porosities of a pure clay and cal-cite layer, respectively. The factor(1−φ0)/(1−φ1) is ofthe order 0.3–0.5 and therefore significant as it reduces theerodible CaCO3 from below the bioturbated layer by 50–70 % compared to the constantφ estimate (Archer, 1996). InLOSCAR, chemical erosion is included based on Eq. (37),see below.

6.2 Variable porosity

In many locations, it has been observed that porosity de-creases with greater CaCO3 fraction f c (e.g.Mayer, 1991;Herbert and Mayer, 1991; deMenocal et al., 1993). That is,sediment with high CaCO3 content has a higher concentra-tion of total solids per unit volume than low carbonate sed-iment. The relationship betweenφ andf c for a sedimentlayer composed of CaCO3, clay, and pore water is given by:

φ =φ0+f c Fφ

1+f c Fφ

(29)

whereFφ = (φ1 −φ0)/(1−φ1). The sediment model usesvariable porosity as given by Eq. (29) and values forφ0 andφ1 as given in Table3. Note that using the non-linear Eq. (29)in the model leads to the correct ratio of initial to erodible



CaCO3 (cf. Eq.28, which was independently derived basedon the geometry of the problem), while a linear relationship,for instance, would not.

6.3 Sediment model equations (single sediment box)

At every time step, calcite and clay rain of solid densityρs isadded to the top sediment layer of thicknesshs (see Table3for values). Dissolution of calcite reduces the calcite contentand net accumulation is hence rain minus dissolution (Fig.4).At the bottom of the sediment mixed layer, an amount equalto net accumulation is removed via burial. If dissolution ofCaCO3 exceeds the rain of CaCO3 plus clay, chemical ero-sion occurs. The sediment model thus has to provide equa-tions to calculate rain, dissolution, burial, and erosion. Atvariable porosity, the top layer can be separated into purecalcite plus pore water at porosityφ1 (volume= Ah1) andpure clay plus pore water at porosityφ0 (volume= Ah2). Forvariable porosity, the model equations can be convenientlywritten in terms of dh1/dt . Conversion to df c/dt merelyrequires multiplication by a factor (see below).

In case rain exceeds dissolution, no erosion needs to beconsidered and we can write for a single sediment box:

dh1

dt= rcs

−rd−wc (30)

wherercs is the calcite rain rate,rd is the calcite dissolutionrate, andwc is the calcite burial rate. All rates refer to volumeof calcite plus pore water per unit area and time (unit m yr−1)at porosityφ1. Total rates of calcite + clay + pore water aredenoted byrs andw. Burial equals rain minus dissolution,i.e. w = rs

− rd, and the condition for no erosion isw > 0.The rain rate of calcite,rcs, depends on the carbon export,the rain ratio, and the fraction of water column dissolution.In the low latitudes, for instance,rcs is given by:

rcs= Fepl rrain

−1 (1−νwc)× k∗ (31)

where Fepl is the low-latitude carbon export (in units ofmol m−2 yr−1), rrain is the rain ratio (Corg : CaCO3), νwc isthe CaCO3 fraction dissolved in the water column (Table2),k∗

= k0/[ρs (1−φ1)] converts from mol m−2 yr−1 to m yr−1,andk0

= (100/103) kg mol−1 converts from mol CaCO3 tokg CaCO3. The rain rate of refractory material,r rs, is cal-culated correspondingly based onFrrf (Table3) and the totalrain rs is given byrs

= rcs+r rs.

The dissolution rate,rd, is calculated as:

rd=Rd

×k∗ , (32)

whereRd is given by the following expression at modernseawater Mg/Ca ratio (Keir, 1982; Sigman et al., 1998):

Rd= (f c)0.5 Ksd ([CO2−

3 ]sat− [CO2−

3 ])nsd (c0)−nsd

if [CO2−

3 ] < [CO2−

3 ]sat (33)

Rd= 0 otherwise, (34)

whereKsd andnsd are “effective” rate parameters (see be-low), [CO2−

3 ]sat and [CO2−

3 ] is the carbonate ion concen-tration at calcite saturation and in the bottom water, re-spectively, andc0

= 1 mol kg−1 so thatRd is in units ofmol m−2 yr−1. It is important to note that the effective rateparametersKsd andnsd relatebottomwater undersaturationto dissolution rate (Keir, 1982; Sundquist, 1986; Sigmanet al., 1998; Zeebe and Zachos, 2007, see Table3 for val-ues). They are not to be confused with reaction parametersrelatingporewaterundersaturation to dissolution rate such asthe calcite reaction ordern (typically n = 4.5).

Finally, an expression is needed for the calcite burial,wc, as a function of total burialw. The thickness of thepure calcite layer within1z(= w 1t) can be expressed asf c 1z (1−φ) but also as 1·1h1 (1−φ1) (calcite fraction=1), which gives:

1h1 = f c 1z1−φ

1−φ1(35)

or expressed per unit time as a rate:

wc= f c w

1−φ

1−φ1. (36)

As a result, all rates have now been expressed by model-predicted quantities and thus by inserting Eqs. (31), (32),and (36) into (30), the change in calcite content per time stepcan be computed. Because we took care of all individualporosities, the relationship betweenφ andf c, Eq. (29), isobeyed automatically.

In case of erosion (w < 0), it can be shown that:

dh1

dt= −(1−f ci) (−w)

1−φi

1−φ0−r rs (37)

wheref ci andφi is the initial calcite fraction and porosity,respectively, andr rs is the clay rain rate (see above). Sub-surface sediment properties are hence based on the initialsteady-state configuration (Fig.4). For model applicationsthat require multiple dissolution cycles with varying con-ditions during accumulation, the model should be restartedwith appropriate initial conditions. The total dissolution ofpure calcite can be derived as:

dhdc

dt= [(−w)+rs

] (1−φ1) . (38)

In other words, all calcite in1z and calcite rain is dissolved.In addition, calcite is being replaced by the clay in1z andby the clay rain (equivalent calcite is also dissolved).

Finally, the sediment model can also be formulated interms off c by simply multiplying by a factor:

df c

dt=

dh1

dtG−1

= (rcs−rd

−wc) G−1 , (39)

where

G =hs

1−φ1

[(1−φ)−f c ∂φ

∂f c

](40)



and

∂φ

∂f c =Fφ (1−φ0)

(1+f c Fφ)2(41)

with Fφ = (φ1−φ0)/(1−φ1).

6.4 Sediment model equations (all sediment boxes)

Let yn be a subset ofy (Eq. 1), representing the CaCO3 dryfraction (f c) in sediment boxes at different depth levels inthe different ocean basins. If the total number of depth levelsis NSD and the total number of ocean basins isNOC (Ta-ble 1), then the total number of equations for all sedimentboxes (total carbon) isNSD×NOC. Based on Eq. (39), thedifferential equation for the CaCO3 dry fraction in sedimentbox j is (analogous equations hold for Ca13CO3):

dyn

dt=

d(f cj )

dt= (rcs

j −rdj −wc

j ) Gj−1 (42)

wherej = 1,2,...,NSD for the first ocean basin (Atlantic),j = NSD+1,NSD+2,...,2NSD for the second ocean basin(Indian), and so on. In case of dissolution, TCO2 and TA arereturned to the ocean, giving rise to the sediment source termin the ocean tracer equation (cf. Eq.2):

Vk

(d[TCO2]k

dt

)sed

=

∑j

Asedj Rd

j (43)

Vk

(d[TA]k

dt

)sed

= 2∑j

Asedj Rd

j (44)

where each sum runs over all sediment boxesj locatedwithin the area and depth range of ocean boxk. The surfacearea of sediment boxj is denoted byAsed

j .

7 Miscellaneous

7.1 Ocean carbonate chemistry

Carbonate chemistry parameters for modern seawater com-position are calculated based on equilibrium constants onthe totalpH scale (Lueker et al., 2000; Zeebe and Wolf-Gladrow, 2001). The C program uses a simplified and fastnumerical routine to compute CO2 parameters from TCO2and TA (Follows et al., 2006). If applied properly, the methodyields accurate results that are essentially identical to thoseobtained with standard routines (Zeebe and Wolf-Gladrow,2001). The method was originally devised to compute mod-ern carbonate chemistry parameters in biogeochemical mod-els where conditions change little between consecutive timesteps (Follows et al., 2006). This is not necessarily alwaysthe case in LOSCAR and can lead to failure in rare cases. Forinstance, if the model is initiated with a very high TA/TCO2ratio, the calculated H+ concentration may become negative.The user is warned in such instances and is advised to change

the initial conditions. Again, such cases are probably rare. Infairness, it should also be noted that non-standard chemistryconditions (which can occur in LOSCAR), are beyond theoriginal intend of the method (Follows et al., 2006). Apartfrom the limitation mentioned above, the method is easy toimplement, sufficiently accurate, and computationally effi-cient.

7.2 Paleocene/Eocene ocean chemistry

Paleocene/Eocene seawater conditions were different frommodern conditions owing to factors such as temperature andmajor ion composition of seawater, including the seawa-ter Mg/Ca ratio (e.g.Tyrrell and Zeebe, 2004). These fac-tors can significantly affect thermodynamic quantities suchas equilibrium constants and solubility products, which inturn have a major impact on the predicted ocean carbon-ate chemistry and atmospheric CO2. The chemistry rou-tines implemented in LOSCAR allow for variations in, for in-stance, temperature, salinity, and the concentrations of Mg2+

and Ca2+ in seawater. For example, due to warmer sur-face and bottom water temperatures in the late Paleocene andEocene, the calcite saturation concentration at a bottom wa-ter temperature of 14–17◦C during the PETM is quite dif-ferent from the modern at 2◦C (see Fig. 3 ofZeebe and Za-chos, 2007). This effect is included in LOSCAR by usingtemperature-dependent equations for the solubility productof carbonate minerals (Mucci, 1983). Pressure correctionsfor solubility products and equilibrium constants are basedon Millero (1995) and references therein; for the latest revi-sions, check:www.soest.hawaii.edu/oceanography/faculty/zeebefiles/CO2Systemin Seawater/csys.html.

Furthermore, the P/E-simulations use[Mg2+] =

30 mmol kg−1 and [Ca2+] = 20 mmol kg−1 rather thanthe modern values of[Mg2+

] = 53 mmol kg−1 and[Ca2+] = 10 mmol kg−1 (Tyrrell and Zeebe, 2004; Zeebeet al., 2009). The effect of seawater Mg2+ and Ca2+ onthe first and second dissociation constant of carbonic acidis estimated using sensitivity coefficients (Ben-Yaakov andGoldhaber, 1973):

sK∗ =1K∗/K∗

1ci/ci

(45)

where1K∗ is the change in the dissociation constantK∗

due to the relative change in concentration,1ci/ci , of com-ponenti. Using1c/c = (c−cm)/cm, where m= modern, itfollows:

1K∗= sK∗ K∗ (c/cm−1) (46)

and finally:

K∗= K∗

m+1K∗

Mg2+ +1K∗

Ca2+ . (47)

Sensitivity parameters for the effect of Mg2+ and Ca2+ onK∗ are (Ben-Yaakov and Goldhaber, 1973):


www.soest.hawaii.edu/oceanography/faculty/zeebe_files/CO2_System_in_Seawater/csys.html

www.soest.hawaii.edu/oceanography/faculty/zeebe_files/CO2_System_in_Seawater/csys.html


sK∗

1= 155×10−3 sK∗

2= 442×10−3 for Mg2+ (48)

sK∗

1= 33.73×10−3 sK∗

2= 38.85×10−3 for Ca2+ . (49)

With these sensitivity parameters, and the modern andpaleo-concentrations of Mg2+ and Ca2+ (see above), the cor-rection to equilibrium constants (Eq.47) can be applied.

Seawater Mg2+ and Ca2+ also affect the calcite solubil-ity product,K∗

sp, and thus the steady-state deep-sea [CO2−

3 ].Following Mucci and Morse(1984), the stoichiometric sol-ubility product drops with decreasing seawater Mg/Ca ratio.In other words, EoceneK∗

sp would have been smaller and,

given roughly constant deep-sea saturation state, [CO2−

3 ]would also have been smaller than modern. The data ofMucci and Morse(1984) may be fitted to an equation of theform:

K∗sp = K∗

sp,m [1−α (xm−x)] (50)

where m= modern,α = 0.0833, andx = Mg/Ca. Usingmodern and P/E-values for[Mg2+

] and [Ca2+] as givenabove, the stoichiometric solubility product of calcite wouldhave been reduced by about 30 %, compared to modern.

Another important consequence of changes in oceanicCa2+, for instance, is its effect on the ocean carbon inven-tory. The long-term carbon inventory and carbonate chem-istry of the ocean-atmosphere system is controlled by atmo-spheric CO2 and the balance between riverine flux and car-bonate burial (Zeebe and Caldeira, 2008). Carbonate burialis tied to the deep-sea carbonate saturation, which is propor-tional to the product of [Ca2+] × [CO2−

3 ]. If oceanic [Ca2+]doubles at constant saturation state, [CO2−

3 ] would drop by50 % (even more if the effect of Mg/Ca onK∗

sp is accounted

for). For example, [CO2−

3 ] prior to the PETM was hencemuch lower than modern if Paleocene/Eocene [Ca2+] was20 mmol kg−1. In the model, this leads to a pre-PETM oceancarbon inventory that is similar to the modern value, despitea higher baseline atmospheric CO2 at the time.

7.3 Temperature sensitivity

The initial temperature of each individual ocean box is setat the start of the run. Throughout the run, temperature canbe held constant, be manipulated based on user input, or becomputed based on a simple expression for the sensitivity oftemperature to changes in atmospheric CO2 as calculated bythe model (cf.Archer, 2005). In order to provide a flexibleand numerically stable option, the C version of the programincludes temperature as an ocean tracer variable. The tem-perature of ocean boxk (TC,k in ◦C) is assumed to respondto a change inpCO2 with a certain time lag and relax to-wards equilibrium temperature. The equilibrium temperatureof boxk is given by:

1.8 2 2.2 2.42.2

2.3

2.4

2.5

TCO2 (mmol/kg)

TA

(m

mol

/kg)

Open symbols: LOSCARClosed symbols: Observ.

0 1 2 3

0

1

2

3

PO4 (µmol/kg)

δ13C

(TC

O2)

(o /oo)

0 1 2 30

0.2

0.4

0.6

PO4 (µmol/kg)

O2 (

mol

/m3 )

Green: Surf Black: IntrmRed: Deep Blue: High

60

70

80

90

100

110

Atlantic Indian Pacific

Dee

p [C

O32−

] (µm

ol/k

g)

Fig. 5. Computed model tracers and observations used for LOSCAR parameter tuning for modern (preindus-

trial) configuration, see text for details.

36

Fig. 5. Computed model tracers and observations used forLOSCAR parameter tuning for modern (preindustrial) configura-tion, see text for details.

TeqC,k = T 0

C,k +s ln(pCO2/pCO0

2

)/ln(2) , (51)

where the superscript “0” refers to the initial (steady-state)temperature andpCO2, respectively, ands is the prescribedtemperature increase per doubling of atmospheric CO2. Theparameters as used here is conceptually similar to what isgenerally referred to as “climate sensitivity”. However, theprecise meaning ofs will have to be defined properly foreach specific application in the context of the time scales andfeedbacks involved (seeZeebe, 2011).

The differential equation for the temperature of ocean boxk then reads:

d(TC,k)

dt=

(T

eqC,k −TC,k

)/τn (52)

whereτn is the relaxation time, which can take on three dif-ferent values depending on whetherk refers to a surface, in-termediate, or deep box (Table2).

7.4 Numerics

As mentioned above, the equations solved in LOSCAR aretypically stiff and require an appropriate solver for the prob-lem. The LOSCAR C-version uses a fourth-order Rosen-brock method with automatic stepsize adjustment (Presset al., 1992). For these kind of solvers, it is critical to scalethe variables properly. Thus, variables have been scaled toorder 1, if necessary, by multiplying by arbitrary factors be-fore passing to the solver. This includes, for instance, atmo-spheric carbon and temperature (see Sects.5 and7.3).

The carbonate dissolution rate,Rd is proportional to thesquare root of the CaCO3 fractionf c (Eq.33). It turned out



Fig. 6. Example of a fossil fuel emission scenario simulated inLOSCAR: total release of 1000 Pg C over 500 yr (seeZeebe et al.,2008). Results shown slightly differ from those inZeebe et al.(2008) because ocean temperature was held constant here for sim-plicity. L = Low-latitude, M= interMediate, D= Deep, H= High-latitude. A= Atlantic, I= Indian, P= Pacific. Note that the stepin the Atlantic calcite compensation depth (CCD, panelh) is due tothe spacing of sediment-box depth levels in the model (adding moresediment boxes would make the curve smoother).

that during strong dissolution,f c occasionally became neg-ative when the CaCO3 fraction approached zero. This issuehas been eliminated (in most cases) by using a linear rela-tionship betweenf c andRd whenf c drops below a certainthreshold valuef c

sml. The threshold value can be changed bythe user and should be increased iff c still becomes negativeduring a run. Another option is to increase the solver accu-racy by reducing the value ofεslv (the default value is usuallynot very accurate).

LOSCAR is quick. Running the fossil fuel scenario over1250 yr (Fig.6) using the LOSCAR C code compiled un-der Linux with gcc 4.4.3, without optimization and default

εslv, takes less than 2 s wall clock time on a current standarddesktop machine with Intel Core2 Duo E8500 @3.16 GHz(no other CPU-demanding processes running). The compu-tational efficiency makes LOSCAR an ideal tool for multi-parameter variations that require a large number of modelruns (e.g.Zeebe et al., 2008, 2009).

8 Tuning

In order for LOSCAR to provide model output that resemblesobservations, several model parameters require tuning. Thisincludes mixing coefficients, biological export fluxes, rem-ineralization fraction (intermediate vs. deep box), rain ratio,and water column dissolution (see Table2). The tuning isbased on comparison between model-predicted variables andmodern observations. For example, parameters were tunedby requiring the ocean tracer variables TCO2 and TA in thevarious model boxes to match GLODAP data, averaged overthe area and depth range of the corresponding boxes (Keyet al., 2004). Note that TCO2 data were corrected for anthro-pogenic carbon by subtracting 45 and 25 µmol kg−1 from thesurface and intermediate values, respectively (see below forδ13C-corrections). The agreement between model and data issatisfactory (see Fig.5). As a result, the global preindustrialTCO2 inventory in LOSCAR is 35 830 Pg C vs. 35 760 Pg Cbased on GLODAP data (Key et al., 2004). Similarly, modelPO4 and oxygen were compared to data summarized in theWorld Ocean Atlas (WOA05, 2005). Again, the agreementbetween model and data is adequate, except perhaps for theoxygen content in intermediate boxes, which appears to beunderestimated by the model. This could be improved. How-ever, it would come at the expense of a larger mismatch in thedeep boxes. This was avoided because for our LOSCAR ap-plications so far, the properties of the deep boxes were moreimportant than those of the intermediate boxes.

Another variable used for parameter tuning is the stablecarbon isotope composition of TCO2 (δ13CTCO2), which wasmatched to the data ofKroopnick (1985). Note that due tothe ocean’s uptake of fossil fuel carbon (which is isotopicallylight, i.e. depleted in13C), the ocean’sδ13CTCO2 is contin-uously dropping (so-called Suess effect). Thus, for prein-dustrial tuning, the earlyδ13C-data sets are more useful thanthe most recent ones, which are increasingly contaminatedwith anthropogenic carbon. Nevertheless,Kroopnick(1985)estimated that surface oceanδ13CTCO2 had already droppedby ∼0.5 ‰ and that the averageδ13CTCO2 of the preindustrialsurface ocean was about 2.5 ‰. This surface value was usedfor model parameter tuning (Fig.5). As a result, the prein-dustrialδ13C of atmospheric CO2 is −6.38 ‰ in LOSCARvs. −6.30 to −6.40 ‰ based on ice core and firn data (e.g.Francey et al., 1999).

Adequate model values for the steady-state carbonate ionconcentration in the deep boxes are important for both theocean and the sediment model component. After parameter



tuning, the preindustrial deep-sea [CO2−

3 ] as predicted byLOSCAR and calculated based on GLODAP data (Key et al.,2004) are in good agreement (Fig.5). The preindustrial in-ventory of CaCO3 in the seafloor-bioturbated sediment layer(in units of carbon) is about 800 Pg C, close to the value ofmore complex models (e.g.Archer et al., 1998).

In summary, after model-data comparison including allvariables shown in Fig.5, the values for the parameters la-beled “tuned” in Table2 were obtained. The preindustrial(steady-state)pCO2 in the model was set to 280 µatm by as-signing this value topCO0

2, which drives the system towardsthe desired steady-statepCO2 via the silicate weatheringequation (Eq.17). Regarding the Paleocene/Eocene modelsetup, several key parameters such as deep-sea [CO2−

3 ] andthe calcite compensation depth (CCD) before and during thePETM have been discussed elsewhere and are not repeatedhere (seeZeebe et al., 2009, Supplementary Information). Inthe default LOSCAR setup, the CCD is taken as the depthat which the CaCO3 sediment content is reduced to 10 wt. %(Ridgwell and Zeebe, 2005). The pre-PETM inventory ofCaCO3 in the seafloor-bioturbated sediment layer (in unitsof carbon) is about 620 Pg C. The initial (steady-state) par-tial pressure of atmospheric CO2 was set to 1000 µatm in ourP/E-simulations. Although this value falls within the (large)range of available proxy estimates, it is somewhat arbitrary.The user is welcome to change the initialpCO2 value in theP/E-setup.

9 Input/output examples

In the following, two input/output examples will be pre-sented, one dealing with anthropogenic fossil fuel emissions,the other with carbon release during the PETM. The inputfiles for these examples are included in the model package.

9.1 Fossil fuel emission scenario

LOSCAR can read in files that supply a time series of fossilfuel emissions in order to project future changes in atmo-spheric CO2, surface ocean pH, calcite and aragonite satu-ration, and other variables (cf.Zeebe et al., 2008, Support-ing Online Material). For example, Fig.6 shows results ob-tained with LOSCAR for a fossil fuel emission scenario witha total carbon release of 1000 Pg C over 500 yr. Note thatthe results differ slightly from those inZeebe et al.(2008)because ocean temperature was held constant here for sim-plicity. The initial conditions from which the scenario wasstarted are the preindustrial steady-state conditions shown inFig. 5. No changes in the biological pump were assumed(PO4 is constant). The temperature of the low- and high-latitude box is 20 and 2◦C, respectively (Table2). This tem-perature difference is mostly responsible for the differencein carbonate ion concentration ([CO2−

3 ]) and saturation state(�) between low- and high-latitude surface boxes. Note that

Fig. 7. Example of a PETM carbon release scenario simulatedin LOSCAR: initial release of 3000 Pg C over a few thousandyears (seeZeebe et al., 2009). L = Low-latitude, M= interMediate,D = Deep, H= High-latitude. A= Atlantic, I= Indian, P= Pacific,T = Tethys. See text for details.

while TCO2 in the surface boxes responds immediately tothe fossil fuel carbon release, there is a delay in TA, whichonly starts rising once sediment dissolution commences andthe calcite compensation depth (CCD) starts shallowing (cf.Ilyina et al., 2009).

9.2 Paleocene-Eocene Thermal Maximum

Using appropriate boundary conditions, LOSCAR can alsobe used to simulate time intervals or events of the past suchas the PETM. During the PETM, a large mass of carbon wasreleased into Earth’s surface reservoirs (e.g.Dickens et al.,1995; Zachos et al., 2005; Dickens, 2011), while surfacetemperatures rose by 5–9◦C within a few thousand years.Figure 7 shows results for a PETM scenario with an ini-tial carbon input of 3000 Pg C over a few thousand years,



which yields close agreement with observations (for moredetails, seeZeebe et al., 2009). Note that the time intervalof the integration now covers 200 kyr (t = 0 refers to theP/E boundary), rather than a few millennia as in the pre-vious example. Changes in boundary conditions comparedto the modern setup include a Paleocene/Eocene bathymetry(Bice and Marotzke, 2002), addition of the Tethys ocean, anddifferent seawater chemistry (see Sect.7.2). Furthermore,the PETM simulations use different initial conditions for e.g.temperature, steady-statepCO0

2, weathering fluxes (Tables2and 3), and different steady-state circulation patterns (seeFig. 2). Note also that a transient contribution of North Pa-cific Deep Water (not shown) during the PETM main phasewas included in our simulations (Bice and Marotzke, 2002;Zeebe et al., 2009). The Southern Ocean source remainsactive during the event but is reduced relative to its pre-event strength (down to 7.5 Sv). The transport associatedwith the North Pacific source is 6.25 Sv. This overall re-duced global overturning circulation during the PETM mainphase is consistent with a sluggish circulation found in afully coupled atmosphere-ocean general circulation modelwith Eocene boundary conditions at high atmospheric CO2concentrations (Lunt et al., 2010).

At steady-statepCO02 of 1000 µatm, but similar carbonate

mineral saturation state as in the modern ocean, the steady-state pH of the Paleocene/Eocene ocean would have beenlower than modern (Fig.7). Because of higher seawater Ca2+

and the effect of Mg/Ca on the solubility product of calcite,the initial carbonate ion concentration in the P/E-simulationsis substantially lower than in the modern ocean (cf. Sect.7.2).As a result, steady-state TCO2 and TA are similar to modernvalues despite higherpCO2 (Fig. 7). Note that the AtlanticCCD shoals dramatically during the event, while there is lit-tle response in the Pacific CCD, consistent with observations(Zachos et al., 2005; Zeebe et al., 2009; Leon-Rodriguez andDickens, 2010). The “overshoot” of the CCD, i.e. the factthat its position is deeper att > 80 kyr than its initial po-sition, is a direct consequence of the weathering feedback(see Sect.4) and is also in agreement with observations (e.g.Kelly et al., 2005). At t > 80 kyr, atmosphericpCO2 is stillelevated over the initialpCO0

2 (Fig. 7), which causes en-hanced weathering of carbonates and silicates. The enhancedweathering raises the ocean’s saturation state and deepens theCCD until a quasi steady-state of riverine flux and burial hasbeen established. The quasi steady-state (t > 80 kyr) must bemaintained at a CCD deeper than the initial depth (becauseof enhanced burial) until atmosphericpCO2 and weatheringfluxes have returned to their initial steady-state values. Thisexplains the “overshoot” of the CCD.

10 Model intercomparison: lifetime of fossil fuel CO2

Several carbon cycle processes as simulated in LOSCAR canbe quantitatively compared to other models by examining the

300

400

500

600

700

Atm

osph

eric

CO

2 (pp

mv)

a 1000 Pg C

Ocean−only+Clim+Clim+Sed+Clim+Sed+Wthr

0 200 400 600 800 1000

500

1000

1500

2000

2500

Time (y)

Atm

osph

eric

CO

2 (pp

mv)

b 5000 Pg C

4000 6000 8000 10000

Fig. 8. LOSCAR simulations of the long tail of the lifetime of fossil fuel CO2 (cf. Archer et al., 2009). (a)

Simulated atmospheric CO2 concentrations in response to a 1000 Pg C pulse, (b) 5000 Pg C pulse. “Ocean-

only” runs include ocean CO2 uptake only (sediments off, weathering feedback off). “+Clim” runs include

an additional temperature feedback of 3◦C per CO2 doubling (see Sect. 7.3). “+Clim+Sed” runs include the

temperature and sediment feedback (weathering fluxes are held constant). “+Clim+Sed+Wthr” runs include the

temperature, sediment, and weathering feedback.

39

Fig. 8. LOSCAR simulations of the long tail of the lifetimeof fossil fuel CO2 (cf. Archer et al., 2009). (a) Simulated at-mospheric CO2 concentrations in response to a 1000 Pg C pulse,(b) 5000 Pg C pulse. “Ocean-only” runs include ocean CO2 up-take only (sediments off, weathering feedback off). “+Clim” runsinclude an additional temperature feedback of 3◦C per CO2 dou-bling (see Sect.7.3). “+Clim+Sed” runs include the tempera-ture and sediment feedback (weathering fluxes are held constant).“+Clim+Sed+Wthr” runs include the temperature, sediment, andweathering feedback.

numerical results. For instance,Archer et al.(2009) con-ducted a model intercomparison focusing on the long tail ofthe lifetime of fossil fuel CO2. The results of that study allowcomparison of carbon cycle dynamics between models, in-cluding processes such as ocean uptake of fossil fuel CO2, re-action of CO2 with deep-sea sediment CaCO3, and the long-term effects of weathering on fossil fuel neutralization. Themodel intercomparison included two experiments in whichpulses of 1000 and 5000 Pg C were added to the models’ at-mospheres and the subsequent model response was followedover 10 000 yr. For each of the pulses, the effects of var-ious feedbacks were tested, including changes in tempera-ture/climate, sediment response, and weathering.

The results of the corresponding model experiments withLOSCAR are shown in Fig.8. Generally, the atmosphericCO2 levels over time as calculated with LOSCAR fall inthe lower to mid range of the atmospheric CO2 levels calcu-lated with the nine models compared byArcher et al.(2009).



LOSCAR’s equilibration time (τ ) for ocean uptake was ob-tained by fitting an exponential,∝ e−t/τ , to the modelpCO2over the first few hundred years for the ocean-only case (nochanges in climate, sediments off, weathering off). Thisyields values forτ of 216 yr and 500 yr for the 1000 and5000 Pg C pulse, respectively. The corresponding averageof all models studied byArcher et al.(2009) is 250 yr and450 yr, respectively. When a temperature feedback of 3◦Cper CO2 doubling is included in LOSCAR (see Sect.7.3),τ for ocean uptake increases to 267 yr and 595 yr for the1000 and 5000 Pg C pulse, respectively. In LOSCAR, the in-creased equilibration time for ocean CO2 uptake is solely dueto higher ocean temperature, which reduces the solubility ofCO2 and leaves a larger fraction of CO2 in the atmosphere.Some of the models analyzed byArcher et al.(2009) showlarger effects of climate change on ocean uptake, presumablydue to additional changes in ocean circulation and mixing.

The next step in the process of fossil fuel neutralization af-ter ocean uptake is reaction of CO2 with carbonate sedimentsin the deep sea, promoting CaCO3 dissolution. In LOSCAR,it takes several millennia for the carbonate content in deep-sea sediments to reach its minimum. In contrast to oceanuptake, however, an exponential is a poor fit to the model’spCO2 decline during the time interval of carbonate dissolu-tion. Nevertheless, in the time window from 1000 to 3000 yr,and exponential fit yields an approximate response time of∼ 4200 yr and∼ 3800 yr for the 1000 and 5000 Pg C pulse,respectively. For comparison, the CaCO3 response time scaleof the models tested byArcher et al.(2009) varies roughlybetween 3000 and 8000 yr. The final step of fossil fuel neu-tralization is enhanced weathering of carbonate and silicaterocks on the continents, which restorespCO2 to its long-term steady-state value (see Sect.4). Note that constant car-bonate and silicate weathering fluxes are also included in theLOSCAR experiments labeled “+Sed” in Fig.8. However,experiments labeled “+Wthr” include a weathering feedbackwith enhanced weathering fluxes at elevatedpCO2. On atime scale of 104 yr, the effect on fossil fuel neutralizationfrom the addition of the weathering feedback is smaller thanthat from the addition of sediments (Fig.8). This is consis-tent with the results ofArcher et al.(2009). However, on timescales> 105 yr, the silicate weathering feedback becomes thedominant effect. Unfortunately, the parameters that deter-mine the strength of the weathering feedback are not wellconstrained, which can lead to significant differences in cal-culated atmospheric CO2 levels on time scales> 105 yr (e.g.Uchikawa and Zeebe, 2008)

In addition to simple carbon input experiments, one mayalso compare the average ocean CO2 uptake between modelsfrom 1990 to 2000 using historical fossil fuel emissions. Theobserved uptake during the 1990s was 2.2± 0.4 Pg C yr−1

(IPCC, 2007). With a few exceptions, the models includedin the intercomparison byArcher et al.(2009) cluster around2.0 Pg C yr−1; LOSCAR’s value is 1.9 Pg C yr−1. The bot-tom line is that in terms of ocean CO2 uptake, a number of

carbon cycle models – including LOSCAR – behave quitesimilar. This is not too surprising, given that ocean CO2uptake is, to a large degree, controlled by seawater carbon-ate chemistry, which is well known. In addition, calibrationof the models is aided by the availability of a tuning target,namely, the observed ocean uptake. The sediment responseamong different models is more difficult to gauge due to sev-eral factors including different sediment model formulations,uncertainties in dissolution rate parameters (e.g.Morse andMackenzie, 1990), and lack of a suitable tuning target basedon observations. Nevertheless, all models tested inArcheret al.(2009) and LOSCAR agree that fossil fuel CO2 neutral-ization via reaction with sedimentary CaCO3 will take sev-eral millennia. Towards the end of the long tail of the CO2lifetime, carbon will be slowly removed from the atmosphereby enhanced silicate weathering. However, it will likely taketens to hundreds of thousands of years untilpCO2 will returnto climatically relevant levels of, say, 400 µatm in the future.

11 Model limitations and future developments

As mentioned above, LOSCAR is designed to compute thepartitioning of carbon between ocean, atmosphere, and sed-iments on time scales ranging from centuries to millionsof years. LOSCAR is not designed to address carbon cy-cle problems on time scales much shorter than centuries.LOSCAR is also not suitable for tackling problems that re-quire fine horizontal and/or vertical resolution. For instance,attempting to model the interannual variability of air-sea CO2exchange in the Weddell Sea with LOSCAR would obvi-ously be silly. On the other hand, LOSCAR does a reason-able job, for example, in calculating the globally averagedocean CO2 uptake over the decade from 1990 to 2000 (seeSect.10). At present, LOSCAR includes one generic high-latitude box and does not explicitly resolve differences, forinstance, between deep water formation sites in the NorthAtlantic and the Southern Ocean. As a result of this andthe current modern ocean configuration in LOSCAR, watermass boundaries, say, between North Atlantic Deep Waterand Antarctic Bottom Water are not being resolved. How-ever, given LOSCAR’s flexible ocean configuration, addi-tional ocean boxes may be included to accommodate suchfeatures. In general, LOSCAR’s components are designed toefficiently compute global carbon cycle dynamics. This phi-losophy also applies to the sediment model, which calculateschanges in %CaCO3 at low computational costs. On the con-trary, if the goal is to model, for example, the detailed effectsof organic carbon and methane oxidation on sediment porewater profiles, a different tool is required (e.g.Zeebe, 2007).

Future versions of LOSCAR may include new featuressuch as additional boxes and tracers such as radiocarbon.Because a meaningful14C model-data comparison gener-ally requires multiple high-latitude surface boxes, radiocar-bon should be included after at least one more high-latitude



surface box has been added. Other future changes may in-clude addition of respiratory-driven carbonate dissolution insediments. Respiratory dissolution could be important, forinstance, for the steady-state position of the lysocline. How-ever, respiratory dissolution is unlikely to have a significanteffect on the evolution of sediment %CaCO3 during mas-sive dissolution events such as those caused by large car-bon inputs from e.g. fossil-fuel burning or during the PETM.Because these events have hitherto been the modeling tar-gets for our LOSCAR applications, respiratory dissolutionhas not been included. Future versions of LOSCAR shouldconsider this feature when processes are modeled for whichrespiratory dissolution is critical. Finally, I emphasize thatLOSCAR’s strength is its simplicity and efficiency, whichwill remain a priority in future developments. For the poten-tial user this could mean that a different model needs to beconsidered altogether, if LOSCAR does not suit the problemat hand.

12 Summary

LOSCAR is a useful tool to tackle carbon cycle problems onvarious time scales as demonstrated in earlier applicationsthat dealt with future projections of ocean chemistry andweathering,pCO2 sensitivity to carbon cycle perturbationsthroughout the Cenozoic, and carbon/calcium cycling dur-ing the PETM (Zeebe et al., 2008; Zachos et al., 2008; Zeebeet al., 2009; Uchikawa and Zeebe, 2008; Stuecker and Zeebe,2010; Uchikawa and Zeebe, 2010; Komar and Zeebe, 2011;Zeebe and Ridgwell, 2011; Zeebe, 2012). The present contri-bution has provided a coherent description of the LOSCARmodel. The description will hopefully be beneficial to thereadership of the journal, as well as users of the model. Ianticipate that future applications will reveal the full spec-trum of problems suitable to be studied with LOSCAR. TheLOSCAR source code in C can be obtained from the authorby sending a request to [email protected].

Acknowledgements.I thank Guy Munhoven and Gary Shaffer(reviewers), and Andy Ridgwell (tachyonic editor) for their com-ments, which have improved the ms. Jim Zachos was instrumentalin sparking my interest in the PETM, which prompted part ofLOSCAR’s model development. C. Chun and M. Zeebe providedinsight into the KATJES algorithm. I also thank Karen Bice forproviding the P/E-bathymetry.

Edited by: A. Ridgwell

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http://dx.doi.org/10.1029/2009GL041436

http://dx.doi.org/10.1029/2008GL035963

http://dx.doi.org/10.1029/2009PA001864

http://www.nodc.noaa.gov/OC5/WOA05/pr_woa05.html

http://www.nodc.noaa.gov/OC5/WOA05/pr_woa05.html

http://dx.doi.org/10.1038/nature06588

http://dx.doi.org/10.1146/annurev-earth-042711-105521

http://dx.doi.org/10.1038/ngeo185

http://dx.doi.org/10.1029/2003GC000538

http://dx.doi.org/10.1029/2006PA001395

http://dx.doi.org/10.1126/science.1159124

http://dx.doi.org/10.1038/ngeo578

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