Evaluating CaCO 3-cycle modules in coupled global biogeochemical ocean models

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Introduction
According to Sabine et al. (2004), the ocean has taken up about 43 % of the anthropogenic CO 2 emissions into the atmosphere since preindustrial times.The partitioning of CO 2 between atmosphere and the ocean is controlled by the buffer capacity of the CO 2 -system in the surface ocean together with the meridional overturning.The buffer capacity of the CO 2 -system varies with temperature and the distribution of total inorganic carbon and alkalinity (e.g.Omta et al., 2010Omta et al., , 2011)).Biogeochemical processes, namely the organic tissue pump and the CaCO 3 counter pump, strongly affect the ocean's internal cycling and distribution of carbon and alkalinity, which in turn influences the surface ocean buffer capacity and hence the ocean's ability to take up anthropogenic CO 2 .Also, the invasion of CO 2 into the ocean leads to ocean acidification, which is suspected to modify life conditions in the surface ocean potentially changing fluxes of carbon and alkalinity within the ocean.Potential feedbacks are likely to exist on the ocean's future capacity to take up anthropogenic CO 2 .To better understand and quantify possible global implications of CO 2 -induced changes in ocean chemistry, numerical models of marine biogeochemistry and circulation are promising tools.Databased model evaluation is an important step in the development of prognostic models suitable for studying the complex interactions of ocean acidification, global warming, ocean biogeochemistry, and their net effect on global ocean carbon uptake and storage.
Considerable effort has been devoted to the evaluation of models of the organic tissue pump, i.e. the production, transformations, and fluxes of organic matter in the ocean.The distributions of nutrients (e.g.phosphate), oxygen, as well as derived properties like AOU, the apparent oxygen utilization (Pytkowicz, 1971), provide suitable constraints on organic matter fluxes in the ocean (Najjar et al., 2007;Schneider et al., Figures Back Close Full 2008; Kriest et al., 2010;Duteil et al., 2013).These tracers are suitable because the effects of ocean biology on them has a large signal-to-background ratio, i.e. the biotic effect is large compared with other effects.For example, the ratio of phosphate remineralised in the interior of the ocean to total observed phosphate ranges between 20 and 45 % in high latitudes and oxygen minimum zones, respectively.With AOU the signal-to-background ratio is even better.Were it not for uncertainties in the oxygen saturation assumption required in its computation (Duteil et al., 2013) the effect of biota on AOU would be almost 100 %.The skill of state-of-the-art models to represent the organic tissue pump may hence be well judged from their ability to reproduce the global distribution of AOU (Najjar et al., 2007) or the recently suggested Evaluated Oxygen Utilization (EOU, Duteil et al., 2013).
In contrast, evaluating models of the marine CaCO 3 cycle is more difficult.In this study we look for adequate tracers that are suited to evaluate the marine CaCO 3 cycle in biogeochemical models.Total alkalinity (TA) has frequently been used for this purpose.However, patterns of TA are not from the production and dissolution of CaCO 3 alone.In Sect. 2 we show that surface ocean patterns of TA are dominated by evaporation and precipitation.Using observations as well as model results we discuss these and other limitations of TA for model evaluation.In Sect. 3 we introduce an approach which has been proposed to explicitly account for non-CaCO 3 effects on TA, the TA Introduction

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TA distribution and CaCO 3 transformations
Production and dissolution of CaCO 3 affect the concentrations of calcium, total dissolved inorganic carbon (TCO 2 ), and total alkalinity (TA).However, it is only TA and TCO 2 for which the total number of observations and their distribution (GLODAP, Key et al., 2004) can support model evaluation on a global scale.The sensitivity of TCO 2 to production and dissolution of CaCO 3 is very low since TCO 2 is predominately modified by decay of organic matter and influenced by the invasion of anthropogenic CO 2 .
In 99 % of the ocean interior, organic matter decay has a larger effect on TCO 2 than CaCO 3 dissolution (Fig. 1a).On the contrary, the effect of CaCO 3 dissolution on TA exceeds that of organic matter remineralisation in about 60 % of the ocean volume (Fig. 1b) making TA more appropriate to evaluate CaCO 3 models.Therefore TA is often used as a data constraint in global CaCO 3 modelling (e.g.Gehlen et al., 2007;Ilyina et al., 2009;Ridgwell et al., 2007).
A major concern, however, in using TA concentrations for data-based model evaluation is the fact that it has a large background.In the deep North Pacific Ocean, where the largest time-integrated imprint of CaCO 3 dissolution is observed (about 120 mmol TA m −3 , Feely et al., 2002), it is equivalent to 5 % of the observed TA only.Everywhere else the contribution of CaCO 3 dissolution on TA is even lower.On a global average, the ratio of the CaCO 3 -dissolution imprint to TA-background is about 0.02.The global mean ratio of the alkalinity effect stemming from organic matter remineralisation to TA background is only 0.005.Contributions from N 2 -fixation, denitrification, sulfate reduction, and shelf alkalinity fluxes are even smaller or of local importance only.Due to the dominance of the TA background, TA behaves to a large extent like a conservative tracer, very much like salinity.In fact about 71 % of the variation of surface-ocean alkalinity of the GLODAP data composite is explained by salinity variation (Fig. 2).This is easily understood since alkalinity represents the charge balance of the major constituents of sea salt.Like salinity, surface ocean alkalinity is largely determined by evaporation and precipitation (e.g.Friis et al., 2003).In the ocean interior Introduction

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Full its distribution is largely explained by advection and mixing of "preformed alkalinity" (Fig. 3a and b).In analogy to the concept of preformed nutrients or preformed oxygen (Redfield et al., 1963;Duteil et al., 2012Duteil et al., , 2013) ) preformed alkalinity (in the following denoted TA 0 ) refers to the alkalinity which a water mass had when last in contact with the atmosphere before being subducted (Chen and Millero, 1979).In the ocean interior TA 0 is a strictly conservative tracer, whereas TA is variable due to transformations of CaCO 3 and organic matter.Although these principles apply both to models and the real ocean, there is the difficulty that in the real ocean TA 0 cannot be separated from TA by measurements.In a model, the distribution of TA 0 can be studied by designing an explicit tracer of TA 0 (see Sect. 4 for details).Along a section at 30 • W in the Atlantic (Fig. 4), the range of modelled TA 0 values is equivalent to 97 % of the range of modelled TA, along a section at 150 • W in the Pacific (not shown) the respective value is 69 % in our model (see Sect. 4 for a description of the model).Given that physical processes can never be represented perfectly in coupled biogeochemical circulation models (e.g.Doney et al., 2004), it is not recommendable to use the distribution of bulk TA as a descriptor of CaCO 3 transformations in a data-model comparison.Small deficiencies in the representation of TA 0 , e.g.due to errors in the surface salinity balance, or errors in ocean circulation and mixing can have profound effect on TA distribution in the ocean interior.Apparently, good (Fig. 5a) or bad (Fig. 5c and d) fits of model and observed TA (Fig. 5b) may hence betray our judgement of the respective CaCO 3 modules.
Recognizing these shortcomings of using TA patterns to estimate CaCO 3 cycling, different approaches have been proposed to overcome them.For example, Howard et al. (2006), suggested a tracer Alk * = Alk − Alk mean /S mean • S, with Alk mean and S mean being the oceanwide means of alkalinity and salinity, respectively.Variation of this Alk * tracer in the deep ocean is supposed to be driven by CaCO 3 dissolution (increase in alkalinity) and the remineralisation of organic matter (decrease in alkalinity) only (Howard et al., 2006).(For the purpose of not confusing Howard's Alk CaCO 3 production (and/or organic matter remineralisation) in the North Atlantic and of CaCO 3 dissolution in waters originating from the Southern Ocean.Applying Howard's approach to our model tracer TA 0 , we compute the anomaly TA 0 − TA 0 ave /S ave • S. As the TA 0 tracer behaves conservatively, its anomaly should not reflect any effects of either CaCO 3 dissolution or organic matter remineralisation.Ideally, the salinitynormalised TA 0 -anomaly should be constant everywhere.This is, however, not the case for the actual pattern in our model simulation (Fig. 6b).This pattern is very similar to the pattern of the Howard et al. (2006) tracer.The similarity between the simulated spurious patterns in Fig. 6b and those in Fig. 6a resembles the spurious behaviour of observed salinity-normalized TA in surface waters shown by Friis et al., 2003.Another property suggested to obtain a tracer of CaCO 3 transformations, which excludes any effects of salinity and organic tissue production or remineralisation, is Potential Alkalinity (PALK = (TA + NO 3 )/S • 35, e.g.Sarmiento et al., 2002).Here, the salinity normalisation is to correct for the effects of the freshwater balance and the nitrate term is to compensate for the alkalinity effects of organic matter dynamics.Yet again, modelled patterns of both PALK and PALK 0 (= TA 0 + PO 4 0 • 16)/S • 35) in the Atlantic (Fig. 6c, d) trace characteristic water masses observed in the Atlantic Ocean, like North Atlantic Deep Water, Antarctic Intermediate Water and Antarctic Bottom Water.Also, PALK 0 should display a uniform distribution if salinity normalization were an effective means of cancelling out salinity effects since none of the ingredients of PALK 0 are subject to biogeochemical modifications.
In the real ocean, simple salinity normalization like in the TA H06 or PALK metrics cannot remove water mass effects due to non-zero alkalinity freshwater sources (Robbins, 2001;Friis et al., 2003), which are highly variable on a global scale.In the Atlantic, for example, riverine zero-salinity alkalinity ranges from about 250 (Amazon) to 2500 ocean's interior of our model simulation.Here, two additional problems of the PALKconcept become obvious: the biogenic modifications of TA in the surface ocean and the recirculation of TA, in particular in the Southern Ocean.CaCO 3 production in the surface ocean changes TA and consequently affects TA 0 .The PALK concept does not correct for this effect and hence the imprint of surface CaCO 3 production travels with PALK and PALK 0 through the interior of the ocean where, being subject to mixing, it complicates the interpretation of PALK with respect to CaCO 3 dissolution.Concerning the PALK (and TA H06 ) patterns in the South Atlantic, however, the recirculation of TA is likely to be most important.The Southern Ocean is the major site of deep water returning to the surface (Marshall and Speer, 2002).Water which has accumulated the imprint of CaCO 3 dissolution in the North Pacific returns to the surface in the Southern Ocean.Subsequently, most of this water is re-injected into the interior of the ocean either as Antarctic Intermediate Water or Antarctic Bottom Water.Similarly, the imprint of oxygen utilization in the ocean's interior wells up in the Southern Ocean, indicated by significant oxygen undersaturation there (Ito et al., 2004).Gas exchange with the atmosphere, however, is able to reset oxygen to values corresponding to surface temperature and salinity nearly completely.But for TA no equivalent restoring process to reset it to values consistent with actual surface salinity exists.The PALK pattern observed in the South Atlantic must hence be interpreted as a recirculation of the imprint of CaCO 3 dissolution which took place as far away as the North Pacific.We conclude that neither TA data nor derivatives like TA H06 or PALK are well suited for the data-based evaluation of ocean CaCO 3 -cycle models.
In the next section we describe TA * , a property suggested earlier as a measure of the time-integrated effect of CaCO 3 dissolution in the ocean (Feely et al., 2002;Sabine et al., 2002;Chung et al., 2003).The advantage of the TA * approach is that it treats the issue of preformed alkalinity explicitly.We study the applicability of this method for the data-based evaluation of CaCO 3 cycle model components.Introduction

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Full The TA * approach (Feely et al., 2002;Sabine et al., 2002;Chung et al., 2003) has been used to quantify the time-integrated imprint of CaCO 3 dissolution.Precursors of this method have been vital for the determination of anthropogenic CO 2 in the ocean since the early paper of Chen and Millero (1979).The underlying concept (Eq. 1) of the TA * approach is that the observed alkalinity (TA) in the interior of the ocean is composed of a preformed component, TA 0 , a term due to the remineralisation of organic matter, TA r , and a term due to CaCO 3 dissolution, usually coined TA * .(Unlike in other publications, and for the sake of direct comparison of computed TA * and the TA * -tracer introduced below, all terms are reported in units of mmol TA m −3 ).
Remineralisation of organic matter, through the regeneration of nitrate, phosphate, and sulphate, decrement TA while the dissolution of CaCO 3 increments it (Wolf-Gladrow et al., 2007).The alkalinity effect of organic matter decomposition can be parameterized as a function of AOU, i. Preformed alkalinity denotes the alkalinity, which a water parcel had during its last contact with the atmosphere (Chen and Millero, 1979).Since all water masses in the interior of the ocean are mixtures of various end-members, the preformed alkalinity is also a mixture of different end-member alkalinity concentrations.For a given location Introduction

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Full in the ocean interior, neither the preformed alkalinity end-member concentrations nor their mixing ratios are known.Preformed alkalinity, TA 0 , must therefore be diagnosed.This is usually done by an empirical approach which comprises two steps (e.g.Feely et al., 2002;Matsumoto and Gruber, 2007).First, a multi-linear regression of alkalinity with salinity, temperature and PO (or NO) is derived from near-surface data (Eq.2).
PO (or NO) are considered conservative tracers within the ocean (Broecker, 1974) and defined as PO = O 2 + r −O 2 :PO 4  , 1994).Second, the coefficients derived from surface data are subsequently applied to salinity, potential temperature and PO (or NO) data from the interior of the ocean to compute TA 0 everywhere (Eq.3): We will here use salinity, temperature and PO from the upper 100 m to derive the regression coefficients of Eq. ( 2).Salinity normalization of alkalinity has been applied sometimes with the TA * approach, but it is omitted here following Friis et al. (2003) and the results presented in Sect. 2. Given these estimates of TA 0 and TA r and observations or model tracer data of TA, TA * can be computed after rearranging Eq. (1).

Modelling approach
Though variants of the TA * method have been in use for decades there has, to our For the physical model we use the transport matrix method (TMM) described in detail by Khatiwala et al. (2005) and Khatiwala (2007).In this approach, passive tracer transport is represented by a matrix operation involving the tracer field and a transport matrix, which has been extracted from the MIT general circulation model, a primitive equation ocean model (Marshall et al., 1997).Seasonally cycling (monthly) coarse resolution matrices were derived from a 2.8 • × 2.8 • global configuration of this model with 15 layers in the vertical, forced with monthly mean climatological fluxes of momentum, heat, and freshwater, and subject to a weak restoring of surface temperature and salinity to observations.The same transport matrices were employed by Kriest et al. (2012) in their data-based assessment of biogeochemical models.
The model of the organic tissue pump used with the TMM is the NPZD-O 2 -DOP model of Schmittner et al. (2005) as modified by Kriest et al. (2010Kriest et al. ( , 2012)).The primary model currency is phosphorus (phosphate, DOP, phytoplankton, zooplankton, detritus) with oxygen as an additional model tracer.The molar O 2 : P ratio is fixed at 170 (Anderson and Sarmiento, 1994).Sinking and remineralisation of detritus are parameterized by a combination of a constant remineralisation rate and particle sinking speeds increasing with depth, together reflecting a power law function of the flux profile (Martin et al., 1987) with an exponent of 1.075 (Kriest et al., 2010).The latter value has been found to yield global oxygen and phosphate distributions in good agreement with observations (Kriest et al., 2012).
In order to represent oceanic alkalinity in a pragmatic way we implement the tracer TA and couple the production and remineralisation of organic matter with fixed ratios to the uptake and release of phosphate in the NPZD-O 2 -DOP model.We use a TA : P ratio of 21.8.CaCO 3 is produced with a temperature-dependent inorganic carbon: organic carbon ratio bound to the rate of detritus production in the model.The global CaCO 3 export production of our model is 0.9 Gt C yr −1 , similar to other models and observational estimates (Berelson et al., 2007).In our model, CaCO 3 export and dissolution are instantaneous and follow an exponential decay function with a decay length scale

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Full of 2000 m.We present preindustrial Holocene steady-state results from a model run over 6000 yr of model integration.

Idealized tracers
We implement a number of idealised tracers.The tracer of preformed alkalinity, TA 0 , is restored to model TA everywhere at the surface and at every time step.In the interior of the model ocean this tracer has no sinks or sources, but is transported and mixed conservatively according to our model's physics.The TA * -tracer is set to zero at the surface.In the interior of the model ocean this tracer collects the effect of CaCO 3 dissolution whenever it occurs.Similarly, a TA r tracer is set to zero at the surface and collects the alkalinity effect of organic matter remineralisation in the ocean interior.All idealised tracers are transported and mixed according to model physics.That is, in the model we perfectly know TA 0 , TA * , and TA r at any point and time.The model is run for 6000 yr until at basically each grid point of the model the sum of the idealised tracers equals the model's TA, i.e.Eq. ( 1) is fulfilled.In order to test the TA * concept we shall compare the model tracers TA 0 and TA * (in the following denoted TA 0 true and TA * true ) with these two properties as diagnosed from the model TA, PO 4 , T, S, O 2 , and AOU, according to Eqs. ( 1)-(3).In the following the diagnosed properties are denoted TA 0 diag and TA * diag , respectively.

TA 0 algorithms
The initial step in the TA * approach is to derive a multi-linear relationship between alkalinity and temperature, salinity and PO in the surface ocean (see Eq. 2).Where TA * has been computed from observations, such algorithms have been either based on global data sets (e.g.Matsumoto and Gruber, 2005) or basin-wide subsets (Feely et al., 2002;Sabine et al., 2002;Chung et al., 2003), depending on the scope of the respective studies.Here, we shall test whether a more regional algorithm will provide an improved estimate of TA 0 and eventually TA * for data from our model experiment.

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Full Another limitation of TA 0 algorithms derived from observations may be a seasonal bias in high latitude observations of alkalinity (and many other surface-ocean properties).Water masses present in the deep ocean usually form in high-latitude outcrop regions at the end of winter, a season when ship-based field studies are difficult.Ship-based data from the winter season in high latitudes are therefore scarce (e.g.Koeve, 2006) and sampling is biased toward spring, summer and autumn.This seasonal bias may pose a problem since the data used to derive a multi-linear regression with surface alkalinity, namely sea surface temperature and surface ocean PO do not behave conservatively over the seasonal cycle.Temperatures are higher in summer than in winter and, because of temperature-induced outgassing of oxygen, PO is lower in summer.It may therefore be speculated that TA 0 -algorithms derived from seasonally biased surface data do not predict interior ocean TA 0 reliably.We test this by deriving algorithms based on sampling the surface ocean of our model either seasonally unbiased, summer biased or winter biased.The expectation is that winter-biased TA 0 -algorithms should provide the best predictions of TA * .

TA * evaluation
In the following we compare the model's true TA * (TA * true being the TA * tracer) with TA * diag estimated from the model output (according to Eq. 1-3).Using TA * true as a reference we compute volume weighted root mean square errors of TA * diag aggregated on global and basin scales and for different depth levels, i.e. (Eq.4) We apply this approach to different sets of diagnosed TA * which are distinguished by the different seasonally biased estimates of TA 0 (see previous section).In order to Introduction

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Full isolate the error related to the computation of TA 0 we here ignore any error related to the estimation of TA r from diagnosing AOU and use the explicit model tracer of TA r when computing TA * , i.e.TA * diag = TA − TA 0 diag + TA r true .Using a single global algorithm (Table 1, #1) derived from seasonally unbiased sampling of surface ocean data for the computation of preformed alkalinity, we can reproduce the TA * true distribution relatively well: The global average volume weighted RMS error of TA * in the interior of the ocean (below 100 m) is 5.8 mmol m −3 (Table 2, #1) and the global mean profiles of TA * diag and TA * true show very similar vertical patterns with TA * diag being usually somewhat smaller than TA * true (Fig. 7a).The performance of the global algorithm varies with ocean basin, with RMS errors as low as 2.8 mmol m −3 and as high as 10.4 mmol m −3 in the Pacific and Atlantic Oceans, respectively (Table 2).
Using TA 0 algorithms derived from regional data reduces the RMS error slightly in the Atlantic and Indian Oceans, while increasing it in the Pacific Ocean.The surface alkalinity RMS error (column 1 in Table 2) has little predictive power for the RMS error of TA * in the interior of the ocean.Basin-averaged vertical profiles (Fig. 7b-d Ocean during summer (Table 2).However, using only surface Atlantic Ocean data to derive the TA 0 algorithm does not solve the problem of high TA * RMS errors there.It is worth noting that despite the large RMS errors, diagnosed TA 0 still resembles the overall regional patterns of true TA 0 in the interior of the Atlantic Ocean (Fig. 9).We speculate that this is caused by the complex mixture of waters subducted in the north and south with their different end-member properties.Neither the global nor the basinscale TA 0 algorithm can predict TA 0 in the interior of the Atlantic Ocean well enough to enable reasonable TA * estimates.This is also reflected by particularly large RMS errors of the TA 0 estimate in the North Atlantic Deep Water (NADW) (Fig. 9d), where the TA 0 algorithm overestimates TA 0 by 10-14 mmol m −3 (Fig. 9c).
In Fig. 10 zonal averages of TA * true in the Pacific and Atlantic Oceans are compared with the difference of diagnosed and true TA * (Fig. 10).In intermediate waters of the Atlantic, but also in the North Atlantic Deep Water, uncertainties of TA * are of similar magnitude as TA * .It is only in Antarctic Bottom Water that uncertainties are small enough to detect TA * in the Atlantic.In the Pacific the picture is quite different.TA * is detectable almost everywhere except in surface and mode waters of the upper hundreds of meters.As a note of caution it is stressed again that TA * is a time-integrated property subject to advection and mixing.The occurrence of a large TA * values does not indicate the rate of CaCO 3 dissolution to be particularly large there.This characteristic of TA * is shared with many other cumulative properties, notably AOU, which represents the timeintegrated measure of remineralisation of organic matter, not its actual, local rate.The observation of TA * in shallow waters oversaturated with respect to the dominant minerals of CaCO 3 , calcite and aragonite, respectively, has sometimes been erroneously interpreted as indicating shallow CaCO 3 dissolution (see Friis et al., 2006Friis et al., , 2007 for a discussion).Here we show that, in addition, TA * in these waters usually cannot be determined accurately due to uncertainties in the TA 0 estimate.Introduction

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Full  Antonov et al., 2009).As for the models, we use output prepared for the OCMIP5 control runs.Specifically, we use the first available annual time slice of either the CTL or HIST runs, representing the end of the respective model spin up.We use output of the IFM/UVIC2-8 (Oschlies et al., 2008; http://ocmip5.ipsl.fr/models_description/ifm_uvic2-8.html),MPI-M-ESM (Ilyina et al., 2013; http://ocmip5.ipsl.fr/models_description/mpi-m_cosmos.html)and IPSL/IPSL-CM4 (Aumont and Bopp, 2006; http://ocmip5.ipsl.fr/models_description/ipsl_ipsl-cm4.html)models.It is beyond the scope of this paper to provide a full evaluation or model intercomparison of the three models.Instead we focus on a comparison of global mean profiles of TA, TA 0 , TA r and TA * from the three models and the observations with the only objective to illustrate the advantage of explicitly accounting for preformed alkalinity in a data-based model evaluation.
The global mean profile of alkalinity in the observations is characterized by an absolute minimum at the surface, a shallow maximum at about 100 to 200 m, a subsurface minimum at about 500 m, and a broad maximum between 3000 m and the bottom (Fig. 11a).The three models reproduce this structure to different degrees.The UVIC2-8 tracks the overall vertical gradient well while not reproducing the small-scale subsurface structures.The MPI-ESM tracks the vertical structure well, albeit with a slightly too small overall vertical gradient, but has a clear negative offset of about 80 mmol m

Conclusions
In this study we tested the applicability of the TA * approach (Feely et al., 2002) in order to quantify the time-integrated and advected signal of CaCO 3 dissolution in models and observations by means of an ocean carbon cycle model augmented with idealized tracers of CaCO 3 dissolution.The method of computing TA * according to the scheme described in Sect. 3 is found to reproduce tracer-based TA * in our model experiment robustly in most of the global ocean.It is mainly in the Atlantic Ocean, but also in the upper 500 to 1000 m of the Pacific and Indian Oceans, respectively, where computed TA * has elevated uncertainty, which make it unsuited to derive cumulative CaCO 3 dissolution in these waters.Since most of this uncertainty arises from the uncertainty of the TA 0 estimate, alternative approaches to derive isopycnal-specific preformed alkalinity, e.g. from methods of isopycnal analysis (e.g.Körtzinger et al., 2001), in combination with techniques to estimate water mass fractions in the ocean interior (e.g.Karstensen and Tomczak, 1998;Khatiwala et al., 2012) may be worth testing for regional applications.
As demonstrated from observations and model experiments, TA includes a large (and generally dominant) fraction of preformed alkalinity, closely associated with the salinity field and hence the physics of the ocean.Approaches in which alkalinity is normalized to salinity, like PALK or TA H06 are, however, shown to produce artificial patterns in the interior of the ocean often unrelated to local biogeochemical processes.These In the TA * approach the conservative component of alkalinity is treated explicitly and separated from the biogeochemical effect, a procedure which turned out to be successful in much of the ocean in our method-evaluation model experiment.Applying the TA * approach to model output from three state-of-the-art ocean carbon-cycle models we demonstrated the advantage of explicitly taking preformed alkalinity into account when comparing a range of CaCO 3 cycle models with observations.The comparison of this though limited number of models with observations points to larger uncertainties in CaCO 3 -modules of coupled carbon cycle models compared with the representation of the organic tissue pump in these models.
Finally, we propose to use the TA * approach for the data-based evaluation of models of the oceanic CaCO 3 -cycle.Similar to a proposal made for the organic tissue pump by Najjar et al. (2007), we suggest to implement idealized tracers of either TA 0 or TA * in ocean biogeochemical models in order to ease model intercomparison, but also to decide whether the results from this model study are applicable to a wider range of ocean models.Introduction

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Full  Full  Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | * tracer with other tracers we use in our study, we rewrite Alk * as TA H06 = TA − TA ave /S ave • S.) The emerging pattern of this tracer along a transect in the Atlantic (Fig. 6a) suggests a dominance of Discussion Paper | Discussion Paper | Discussion Paper |

(
Mississippi) mmol m −3 (e.g.Cai et al., 2010).Freshwater alkalinity depends on geochemical conditions of the respective drainage basins.In models alkalinity zero-salinity endmembers depend on model specific alkalinity ocean-boundary conditions.However, neither of these effects can explain the distribution of PALK and PALK 0 in the Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3 TA * approach e. TA r = r Alk:NO 3 • r NO 3 :−O 2 • AOU.Values for r NO 3 :−O 2 and r Alk:NO 3 are usually derived from observations, e.g.r NO 3 :−O 2 = 1/10.625,r Alk:NO 3 = 1.26 (Andersonand Sarmiento, 1994;Kanamori and Ikegami, 1982), and are generally prescribed in biogeochemical models.Considering maximum values of AOU observed in the ocean (about 350 mmol O 2 m −3 ), the largest TA r is about 40 mmol TA m −3 .The global average TA r (using AOU from World Ocean Atlas) is 18.1 mmol m −3 .Considering that AOU overestimates true oxygen utilization by 20-25 %(Ito et al., 2004;Duteil et al., 2013), TA r computed from AOU is probably also overestimated by this percentage.
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | knowledge, not been any explicit evaluation of this method.Here, we apply a prognostic global ocean carbon-cycle model for this purpose.The model consists of an offline representation of ocean physics providing transport and mixing within the ocean, a NPZD-type model to represent the organic tissue pump, and a CaCO 3 -cycle module.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | improves the TA * computation in some cases, like in the Indian Ocean or in the Pacific Discussion Paper | Discussion Paper | Discussion Paper |6 Application of the TA * approach to GLODAP and three OCMIP5 models Finally, we apply the TA * approach to an observation-based data product and to the output from three different models available at the Ocean Carbon Cycle Model Intercomparison Project data server (http://ocmip5.ipsl.fr;accessed April 2012).As for the observations, we combine the GLODAP gridded dataset of TA(Key et al., 2004) with T , S, PO 4 and O 2 from the annual climatology of the World Ocean Atlas 2009 (e.g. due to a rescaling of the global oceanic carbon content in order to compensate for losses to the sediment during the spinup.The IPSL-CM4 shows too high an alkalinity in the upper 1000 m and too low a TA in the deep ocean by up to 40 mmol m −3 each.Subdividing TA into its components (TA 0 , TA * , and TA r ) indicates that much of the Discussion Paper | Discussion Paper | Discussion Paper | TA derivatives do not fully remove the salinity association of patterns.In addition TA derivatives can be biased by the imprint of remote biogeochemical processes.For example, Southern Ocean upwelling and re-injection of water with an imprint from CaCO 3 dissolution in the North Pacific can give the false impression of CaCO 3 dissolution taking place in the South Atlantic.We conclude that data-model comparisons based on TA or salinity-normalised alkalinity alone cannot evaluate the CaCO 3 model independently of any possible deficiencies in the physical model.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Schmittner, A., Oschlies, A., Giraud, X., Eby, M., and Simmons, H. L.: A global model of the marine ecosystem for long-term simulations: sensitivity to ocean mixing, buoyancy forcing, particle sinking, and dissolved organic matter cycling, Global Biogeochem.Cy., 19, GB3004, doi:10.1029/2004GB002283,2005.Schneider, B., Bopp, L., and Gehlen, M.: Assessing the sensitivity of modeled air-sea CO 2 exchange to the remineralization depth of particulate organic and inorganic carbon, Global Biogeochem.Cy., 22, GB3021, doi:10.1029/2007GB003100,2008.Wolf-Gladrow, D. A., Zeebe, R. E., Klaas, C., Körtzinger, A., and Dickson, A. G.: Total alkalinity: the explicit conservative expression and its application to biogeochemical processes, Mar.Chem.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .Fig. 2 .Fig. 4 .Fig. 9 .
Fig. 1.Ratio of the imprint of the organic tissue pump and the CaCO 3 pump on TCO 2 (a) and TA (b) at 2000 m water depth.∆DICtissue and ∆TA tissue are computed from estimates of the apparent oxygen utilization (AOU) and the mean molar oxygen : carbon ratio of 1.4 and the mean molar oxygen : alkalinity ratio of 0.119 (= 1/170 • 16 • 1.26), respectively.AOU is estimated using oxygen, potential temperature and salinity data from the World Ocean Atlas (gridded data, analysed annual means).∆TA CaCO 3 is computed using the TA * method described • PO 4 , and NO = O 2 + r −O 2 :NO 3 • NO 3 , assuming that r −O 2 :PO 4 and r −O 2 :NO 3 are constant in the interior of the ocean (r −O 2 :PO 4 = 170; r −O 2 :NO 3 = 10.625;Anderson and Sarmiento

Table 2 .
Volume weighted root mean square (RMS) errors of global and regional TA 0 and TA * estimates.Errors given in column "Surface" refer to the ability of the respective algorithm to reproduce the surface (upper 100 m) alkalinity of the model.Under TA 0 RMS errors of subsurface preformed TA as compared with TA 0 from the explicit tracer are given.Under TA from the explicit tracer are given.Global algorithms are also evaluated concerning their skill on regional scales.
* RMS errors of computed TA * compared with TA *

Table 3 .
Volume weighted RMS errors for TA 0 and TA * estimates based on seasonally unbiased TA 0 algorithm (all months) and winter and summer biased algorithms respectively.Column "surface" refers to the skill of the respective algorithm to reproduce the surface (upper 100 m) alkalinity of the model.Column TA 0 gives RMS errors of subsurface preformed TA as compared with TA 0 from the explicit tracer.Column TA * gives the RMS of computed TA * compared with TA * from the explicit tracer.Global algorithms are also evaluated concerning their skills on regional scales.