Determination of in-situ Dissolved Inorganic Carbon and Alkalinity in Marine Sedimentary Interstitial Water

Porewater inorganic carbon concentration and total alkalinity from deeply buried marine sediment reflect biological activity, mineral diagenesis, sedimentary processes and past bottom ocean water composition. Reliable interpretation of these data is often complicated and/or limited due to (i) major physical environment changes taking place during sediment core retrieval, and (ii) the resulting precipitation of calcium carbonate (CaCO3) in the course of sample collection, processing and storage. Here we describe a robust method for quantifying the in-situ porewater carbonate system chemistry in deepsea sediment cores. The method relies on the over-determination of the dissolved carbonate system by measuring three of its parameters, and explicitly assumes CaCO3 saturation in the sediment and equilibrium conditions in-situ. The principles of the method are presented. We experimentally test the proposed approach using concentration profiles of dissolved carbonate system components collected from the Integrated Ocean Drilling Program (IODP) Site U1368 in the Southern Pacific. Our results show that this method can be used to accurately reproduce the in-situ aqueous carbonate system chemistry if dissolved inorganic carbon, total alkalinity and calcium concentration are measured simultaneously. The method is well suited for use over a broad range of porewater chemistry and applicable for sediment over ca. 50% of the seafloor.


INTRODUCTION
Throughout the past 50 years of scientific ocean drilling, profiles of many dissolved chemicals derived from extraction and analysis of sedimentary interstitial water on deepsea drilling expeditions have significantly contributed to major advances in climatic and oceanographic sciences (Gieskis, 1975). The marine carbonate system was and remains an extensively studied subject that will bring new insights into a wide range of oceanographic disciplines. Two new areas that the study of dissolved inorganic carbon (DIC) and total alkalinity (TA), two major parameters of the carbonate system, can contribute to are (i) secular changes in the carbonate system of ocean bottom waters, and (ii) subseafloor microbial activity. The marine carbonate system is a crucial component in controlling the pH of the world's oceans and reflects the variable distribution of CO 2 between the ocean and the atmosphere (Sigman and Boyle, 2000;Elderfield, 2002;Yu et al., 2010). DIC and TA reconstructions in deep subseafloor sediment have the potential to supply fundamental information for our understanding of the ocean's role in the global carbon cycle and climate. Particularly interesting in this respect is the reconstruction of past preformed carbonate ([CO 3 2-] PF ) of the ocean's interior. Preformed nutrients represent that fraction of unutilized nutrients in surface waters that gets transported into the interior ocean (Ito and Follows, 2005). Because of the generally inverse relationship between preformed carbonate ([CO 3 2-] PF ) and the surface seawater CO 2 content, reconstruction of past preformed carbonate through the Last Glacial Maximum (LGM) [24 to 18 thousand years ago] can help to constrain the CO 2 equilibration history of the ocean and the atmosphere and hence provide clues to the causes of atmospheric CO 2 concentration variations on these time scales. Stephens and Keeling (2000) suggested that low glacial atmospheric CO 2 levels resulted from reduced air-sea gas exchange due to increased sea-ice cover at high southern latitudes. If true, glacial [CO 3 2-] PF should be lower compared to modern equivalents. In contrast, assuming that atmosphere and surface oceans could equilibrate during glacial periods, we expect higher preformed CO 3 2concentrations. Highly important in this matter is the precision and accuracy of the measurements involved in the reconstruction of preformed nutrients. Assuming equilibrium between surface oceans and atmosphere, Yu and colleagues (2010) calculated that the change in [CO 3 2-] PF during the LGM should be on the order of 60 µmol kg -1 higher compared to modern equivalents (i.e. ca. 250 µmol kg -1 ) (Yu et al., 2010;Williams and Follows, 2011). Therefore, in the endeavor of reconstructing past [CO 3 2-] PF using pore fluid chemistry, precise measurements of carbonate-related chemicals are necessary because the expected changes in [CO 3 2-] PF are subtle and thus prone to lie within the analytical uncertainty margin of the reconstructed preformed nutrients.
Also, DIC (CO 2 + HCO 3 -+ CO 3 2-) is a major metabolic product of microbial respiration, and quantification of its abundance in deepsea sediment is essential to understand the metabolic activities and biogeochemistry of the marine sedimentary biosphere (D'Hondt et al., 2002;D'Hondt et al., 2004;D'Hondt et al., 2009).
Shipboard measured values of TA and DIC of the interstitial water using standard techniques often do not match actual in-situ abundances (Sayles and Manheim, 1975;Berner, 1980 (Paull et al., 1996). This change in pore fluid composition is attributed to drastic modification of the physical environment during core retrieval and storage. Decompression and warming of the sediment during core recovery, followed by core handling on deck and storage, induces precipitation of carbonate due to pressure and temperature dependent solubility of carbonate minerals (Paull et al., 1996). Therefore, shipboard measured DIC and TA are commonly lower than in-situ values. In general, the longer it takes for interstitial water samples to be extracted and analyzed post-core recovery, the more offset from in-situ values are the measurements. The sample-handling-and-processing routine on scientific drilling vessels frequently results in samples being stored for hours (sometimes days) prior to analysis, leaving ample time for carbonate precipitation. Consequently, for accurate use of carbonate-related interstitial water chemistry data, it is critical to develop a method for correcting the measured abundances to in-situ values.
Here, we present a rigorous technique to quantify the in-situ dissolved inorganic carbon system chemistry in subseafloor marine sediment. This technique does not require significant additional drilling and processing time. We provide experimental validation of the proposed approach using sedimentary pore fluid concentration profiles of DIC, TA, calcium, and other dissolved species collected during Integrated Ocean Drilling Program (IODP) Expedition 329 to the South Pacific Gyre.

Conceptual framework
The central concept upon which this method is built is that by measuring three parameters of the carbonate system (i.e. DIC, TA and Ca 2+ ) in the porewater we mathematically over-determine that system which allow us to solve for the amount carbonate precipitation taking place during the sample recovery process, and thus determine the complete set of in-situ carbonate system parameters (Park, 1969 Rearranging and combining Eq. (8), Eq. (9) and Eq. (7) we formulate a 2 nd order polynomial of the form A(X CaCO3 ) 2 + B(X CaCO3 ) + C = 0 with following coefficients:

Thermodynamic considerations
We take the aqueous chemistry of carbon dioxide, silica, boron, phosphate, and sulfate into consideration to characterize the complete carbon system in a sample of porewater at a particular temperature and pressure (Dickson, 2007). We calculate equilibrium and solubility constants for the acid dissociation reactions in the porewater at in-situ salinity, temperature and pressure to account for the change in physical environment during core retrieval. Expressions of equilibrium constants as a function of salinity and temperature, derived from the Total Hydrogen ion Scale by Millero et al. (2006) and Dickson et al. (2007), are used in this study. The effect of pressure on the equilibrium constants is taken into account Zeebe and Wolf-Gladrow, 2001). The detail of the calculation steps for the determination of in-situ equilibrium constant is given in the Appendix.

Conceptual reliability test
To validate the method computationally and conceptually, we applied the approach to modern water column chemistry. Concentration profiles for DIC, TA, silica, and phosphate, together with salinity and temperature data, extracted from the Hydrographic Atlas of the World Ocean Circulation Experiment, WOCE, are used (Talley, 2007). If the algorithm works properly and has correctly calculated the thermodynamic constants, then we should calculate X CaCO3 to be zero mol kg -1 at the carbonate saturation horizon (above this depth X CaCO3 will be negative and below it positive).
For sites located near the center of the South Pacific Gyre, the algorithm correctly positioned the level of the calcite saturation horizon at a water depth of ca. 3000 m (Peterson, 1966;Williams and Follows, 2011). At that level, the variable X CaCO3 reaches a value of zero mol kg -1 . Water at depths above and below that level are increasingly calcite-supersaturated and calcite-undersaturated, respectively. This result agrees with the proposed conceptual framework. Samples below the calcite saturation horizon are undersaturated with respect to calcite, resulting in a positive X CaCO3 value.
Therefore to restore equilibrium, an a priori assumption of the approach, calcite precipitation has to take place. The inverse is true for water samples located above the calcite saturation horizon.

Interstitial water collection and analytical methods
The method was tested using published data of pore fluid concentration profiles from IODP Expedition 329 to the South Pacific Gyre (Expedition 329 scientists , 2011). The data we used was collected at IODP Site U1368, located near the Interstitial water of the Site U1368 sediment was extracted by squeezing ca.
10-cm long whole-core rounds using Manheim squeezers (Manheim, 1966). For the purpose of this study, two core handling-and-storage procedures were adopted. In one method we did not try to minimize storage and handling time of whole-round samples before interstitial water extraction. We refer to this as the 'conventional process'. In contrast, we designed the second method to minimize the time between core retrieval and interstitial water extraction. The goal was to minimize the lapse of time during which carbonate precipitation might occur. We refer to this as the 'rapid process'.
Time records of the consecutive steps of sample storage and handling for each whole-core round sample were documented. Sample handling and laboratory storage time for the conventional processed samples varied from a couple of hours to as long as seven hours. The rapid process samples were stored for less than 2 hours before extraction (Figure 2A; Expedition 329 scientists, 2011). For both procedures, sedimentary core samples that couldn't be processed by the biogeochemistry laboratory right away were stored in a 4°C refrigerator until they could be squeezed and analyzed. Characteristic prevailing temperature, pressure and salinity laboratory conditions were 20°C, 1 Atm and 34.7 ppt, respectively.
Interstitial waters from 33 whole-round samples from Site U1368, Hole C, were collected and analyzed by the shipboard scientific party. The samples were obtained at a spatial resolution of approximately one sample every 50 cm. Eleven of the whole-round samples taken for interstitial water chemistry were rapid process  2011). A detailed description of the shipboard pore fluid geochemical campaign, including details of the method is found in the Proceedings of IODP, Volume 329 (2011).
We used the measured in-situ bottom water temperature and thermal gradient of Site U1368 (i.e. 1.6 °C and 113 °C km -1 , respectively) to calculate in-situ temperature. We assumed the in-situ pressure to be hydrostatic and it was calculated from the water and sediment depth, considering average ocean water density.
Downhole salinity was inferred based on measured interstitial water chloride ( Table   3-4). Equilibrium and solubility constants for the acid dissociation reactions in the porewater are calculated for in-situ temperature and salinity and are corrected for insitu pressure conditions ( Table 5-8).

Figure 2 (B through D) illustrates the shipboard measured [DIC], [TA] and
[Ca 2+ ] data for the studied site (conventionally and rapidly processed samples). Total alkalinity and dissolved inorganic carbon in the interstitial water exhibit similar behavior with depth, starting at 2.682 and 2.553 mmol kg -1 , respectively, and gradually decreasing with depth to a value of ca. 2.427 and 2.373 mmol kg -1 , respectively, at the bottom of the sequence. The general downhole pattern of the DIC and TA profile for the conventional samples at Site U1368 clearly deviates from the smooth profile generated by diffusive transport you would expect for sediment of that age and characterized by equilibrium conditions in-situ. The presence of multiple and irregular offsets in the carbonate chemistry profiles for conventional samples emphasize the significant impact of alteration on the measured chemistry and thus the need to correct these biased measurements for accurate use of this data. In contrast, the DIC and TA profile resulting from the rapid sampling process more closely leans toward a smooth diffusive downhole profile.
We assessed the impact of storage time by comparing catwalk versus conventional porewater chemistry data throughout the analyzed sequence. TA and DIC abundances of core samples that were handled with the conventional process were consistently lower compared to the rapidly processed samples (i.e. 0.172 mmol kg -1 and 0.126 mmol kg -1 lower concentration, respectively, as averaged over the entire sequence). These differences reflect more important carbonate precipitation in sediment before interstitial water squeezing in the case of conventionally handled samples.
Alteration of interstitial water chemistry was not uniformly distributed throughout the cored sequence.
[DIC] is strongly altered in the interval between 8 and 11 meter below seafloor (mbsf), where [DIC] from rapidly processed samples is ca.

Method validation strategy
Calcium carbonate is present throughout the core and is between 61.3 and 87.4 wt% (Figure 3). Also, calcareous microfossils, including planktonic foraminiferal assemblages, have been observed throughout the sequence (Shipboard Scientific Party ,   2011). The lack of Mg variation between rapidly and conventionally processed samples implies that dolomite formation isn't significant during core recovery and interstitial water extraction (given the precision of the measurement

Experimental assessment results
Based on the in-situ temperature and pressure and dissolved chemical concentration data measured shipboard for Site U1368, we calculate the in-situ abundances of the measured components (i.e. DIC, TA, and Ca 2+ , Figure 4, Table 10 & 12) together with the complete set of associated species involved in the carbonate system and in-situ pH that weren't measured shipboard (i.e., CO 3 2-, H + , OH -, HCO 3 -, H 2 CO 3 , B(OH) 4 -, HPO 4 2-, etc.). Averaged X CaCO3 values for conventionally and rapidly processed samples are on the order of 0.109 mmol kg -1 and 0.060 mmol kg -1 , respectively ( To place the obtained results by this newly developed method into a concrete evaluation context we performed a full error analysis of the reconstructed in-situ chemistry parameters. This was done in two distinct steps: (i) characterization of the analytical precision associated with the reconstructed parameters of the carbonate system, followed by (ii) a statistical assessment of the precision with which we can reconstruct the in-situ carbonate chemistry.
The analytical error on the measured DIC, TA and Ca 2+ was propagated on the calculated X CaCO3 by taking the sum of the squares of the analytical error on each measurement: Where f represents a function to quantify X CaCO3 based on the three measured parameters (i.e. X CaCO3 = f [TA, DIC, Ca]) and σ , the precision of the considered measurement: σ TA (%) = 0.78% of the measured value σ DIC (%) = 0.59% of the measured value σ Ca (%) = 0.60% of the measured value We solve equation (14) numerically: We further propagate the analytical uncertainties (i.e. associated with the measured parameters and the calculated X CaCO3 ) on the reconstructed in-situ DIC, TA and Ca 2+ :  (18) The error propagation analysis resulted in analytical uncertainty estimates (1σ) on the order of 2.195E-2 mmol kg -1 , 1.811E-2 mmol kg -1 , 6.239E-2 mmol kg -1 , and 6.551E-2 mmol kg -1 for calculated X CaCO3 and in-situ DIC, TA, and Ca 2+ abundances, respectively (Figure 4, Table 11 & 13).
The precision with which we can reconstruct in-situ parameters of the carbonate system using the proposed method was quantified based on pooled standard deviations calculations for so called 'duplicate runs'. In this study we consider (1) Where S p is the pooled standard deviation, x i1 and x i2 duplicate measurement (with i = DIC, TA, or calcium) and k the number of series of measurement.
Performing the calculation for Site U1368, eleven (i.e. coinciding with the number of rapid process samples) measurement series were delineated. For this end, each rapid process sample (i.e. x i1 in Eq. 19) was bracketed by its surrounding conventionally measured samples (i.e. conventional interstitial water sample taken above and below the rapid process one). The average of the two conventional sample values that bracket each rapid process sample was used as x i2 .
Applying this approach we obtained a pooled standard deviation of 8.427E-2 mmol kg -1 , 7.952E-2 mmol kg -1 and 0.160 mmol kg -1 for the in-situ [DIC], [TA], and [Ca 2+ ] calculations, respectively ( Table 14). The pooled standard deviation between reconstructed in-situ DIC, TA and Ca 2+ for conventionally and rapidly processed samples exceeds the analytical error associated with each of the reconstructed DIC, TA and Ca 2+ , respectively. These results provide quantitative evidence that our approach is reasonable for the quantification of the in-situ interstitial water carbonate chemistry throughout deeply buried sediment given the analytical precision of the available measured parameters.
We ultimately quantify the uncertainty associated with the application of the proposed approach by subtracting the pooled standard deviation estimate of a species by the propagated analytical uncertainty associated with the reconstructed in-situ concentration of that species. This uncertainty estimate is thus purely methodological and separate from the source of uncertainty due to the analytical precision limitations of the available measurements. The methodological uncertainty amounts 6.617E-02 mmol kg -1 , 1.713E-02 mmol kg -1 , and 9.509E-02 mmol kg -1 for the reconstruction of DIC, TA, and Ca 2+ respectively. These uncertainties encompass possible gas exchange during the core retrieval process, impact of processes affecting alteration intensity unaccounted in this method, etc. We argue that by increasing the number of samples analyzed we could improve these statistics by averaging out the remaining offsets found in the reconstructed carbonate chemistry (e.g. between 6-11 mbsf for reconstructed [TA]).

APPLICATION OF THE APPROACH
The method that we describe is applicable for measurements that span a broad range of interstitial water chemistries and environments.  (Schulz, 2000), we argue that this method is widely applicable.
An indirect application of the approach involves the detection of minor traces of calcium carbonate. Detection of low concentrations of CaCO 3 is often challenging with routinely used instruments. Downhole calcium saturation being a critical requirement for the successful application of the approach, we suggest that this method could be used to effectively evaluate the carbonate content of sediment cores.
For carbonate under-saturated sediment, application of the approach will result in the development of many method related artifacts downhole (i.e. profile obviously deviating from a smooth trend) as the basic requirement for the correct development of the iteration won't be fulfilled. In contrary, for carbonate-saturated columns like Site U1368, application of the method will result in an improvement of the measured downhole chemistry porfiles by smoothening out possible offsets in the measured carbonate chemistry.

COMMENTS AND RECOMMENDATIONS ON THE METHOD
Our method calculates in-situ carbonate system porewater chemistry in deeply buried marine sediment. For this end it assumes a priori calcium carbonate saturation in the sediment and equilibrium in-situ. The method successfully deals with any relative size of [DIC] and [TA] input values and incorporates physical environment information that affect the carbonate-related porewater chemistry upon core retrieval.
Although our approach has the potential to effectively quantify the complete in-situ dissolved carbon system of deeply buried marine sediment, it has limitations.
The first limitation is the assumption that the calcite is the dominant carbonate phase.
In the case of a different carbonate phase or the co-occurrence of multiple phases throughout the sediment, the iteration algorithm would have to be adapted to incorporate this more complex carbonate speciation. A second limitation is that roughly half of the seafloor is not characterized by carbonate-bearing sediment.
Alteration effects in carbonate-free sediment are unclear and further experiments are required to explore the influence of these effects. Finally, our approach assumes a priori equilibrium conditions in-situ. This is generally true but close scrutiny should be applied to this assumption in high sedimentation environments, and other subseafloor environments characterized by not fully equilibrated systems.

CONCLUSION
Our approach successfully quantifies the in-situ dissolved carbonate system chemistry of subseafloor sediment based on measured concentrations of dissolved carbonate system constituents that have been altered by core recovery and handling.
The method accounts for variations in temperature, chemical gradients, and physical context during the core retrieval and sample handling process. We illustrate the use of our method by applying it to IODP Site U1368. The results quantitatively demonstrate that chemical alteration associated with the core retrieval and handling processes can be significant, especially in low sedimentation rate environments like the South Pacific Gyre. For correct use of this data the method described here should therefore be implemented when the necessary interstitial water chemistry data is available and the two requirements for the application of the method are fulfilled.
Our example of Site U1368 illustrates that this approach is also an effective tool for inferring concentration profiles of dissolved carbonate-related chemicals that have not been measured on the ship.
Where ! , ! and ! represent the total concentration of boric acid, phosphate and silicic acid, respectively.
We solve for x and the remaining chemical species of interest using a combination of mass balance, equilibrium reactions between species in solution and thermodynamics relationships. Following equations describing these relationships form the core upon which the iteration method is based: Mass balance of dissolved inorganic carbon species: Expression of total alkalinity as defined by Dickson (2007) α = γ + minor species (33) Reorganizing Eq. (31): (37) Eliminate ! in Eq. (36) and Eq. (14) and set them equal to each other: Eq. (11) through Eq. (38) form a determined system that can be solved for x.
Reorganizing Eq. (38) results in a 2 nd order polynomial of the form Ax(x²)+Bx(x)+Cx =0 with following coefficients: This polynomial can be solved for x: To avoid enormous polynomials we develop an iteration procedure that neglects the minor species in the first iteration round. In the second iteration step, minor species determined in this first iteration will be incorporated in the equation set.
The following iterations will subsequently refine the calculated species concentrations until a stable solution is attained.

First iteration:
(1) An initial estimate of the in-situ hydrogen concentration is obtained by inputting a ballpark estimate of the in-situ pH: H ! ! = 10 !!" .
(4) Adding the minor species concentrations up results in a first estimate of the minor species term (i.e. minor species ! ). In the case of Site U1368 (see manuscript) we assume [NH 3 ], [HF -] and [HS] to be negligible and therefore not solved for.

Second and subsequent iterations:
(6) From the left hand side of Eq. (38) and from ! we can refine our hydrogen concentration estimate: (9) Solve for ! (Eq. (30)) including the refined estimates of the minor species.
(10) Repeat steps 6 to 9 until there is convergence. We regard the obtained solution as stable as the difference in between former and subsequent iterations is not greater than 0.000001. Such stable solution was obtained in less than 15 iterations in the example discussed in the paper.
We validate the result of the iteration algorithm by checking that mass balance  (2011) of IODP Leg 329. Physical property data include bottom water temperature (°C) and the sediment thermal gradient (°C/km).

Laboratory conditions:
We assume room temperature (~20°C), standard atmospheric pressure (~ 1 Atm) and a salinity value of 34.7 psu as characteristic laboratory conditions.
Secondly, apparent equilibrium constants were adapted to account for in-situ pressures using the general formulation derived by :