TCO₂ Measurements

The TCO₂ was determined by using two automated dynamic headspace sample SOMMA processors with coulometric detection of the CO₂ extracted from acidified samples. A description of the SOMMA-coulometry system and its calibration can be found in Johnson et al. (1987), Johnson and Wallace (1992), and Johnson et al. (1993). Details concerning the coulometric titration procedure can be found in Huffman (1977) and Johnson et al. (1985). Samples were collected in 300-mL precombusted (450°C for 24 h) glass standard Biological Oxygen Demand (BOD) bottles and analyzed for TCO₂ during the cruise. During the cruise the samples were not poisoned with HgCl₂ as per normal operating procedure (DOE 1994), but they were analyzed within 24 h of collection. Before analysis, samples were kept in darkness in a cold room and subsequently thermally equilibrated for at least 3 h to the analytical temperature. Analyses of duplicate samples separated in time by up to 8 h showed no evidence of any significant biological consumption or production of CO₂ during storage. The CRMs were supplied by Dr. A. Dickson of Scripps Institution of Oceanography (SIO) (DOE 1994) and were also routinely analyzed. CRMs from batches 7 and 11 were available for this work (batch 7: S = 37.120, TCO₂ = 1926.41 ± 0.82 µmol/kg; batch 11: S = 38.5, TCO₂ = 2188.77 µmol/kg). The CRMs were made from filtered sterile salt solutions spiked with Na₂CO₃, and their TCO₂ concentrations were determined by vacuum-extraction/manometry in the laboratory of Dr. C. D. Keeling at SIO.

Seawater introduced from an automated "to deliver" (TD) pipette into a stripping chamber was acidified, and the resultant CO₂ from continuous gas extraction was dried and coulometrically titrated on a model 5011 UIC coulometer. The coulometers were adjusted to give a maximum titration current of 50 mA, and they were run in the counts mode [the number of pulses or counts generated by the coulometer's voltage-to-frequency converter (VFC) during the titration was displayed]. In the coulometer cell, the hydroxyethylcarbamic acid formed from the reaction of CO₂ and ethanolamine was titrated coulometrically (electrolytic generation of OH^- ) with photometric endpoint detection. The product of the time and the current passed through the cell during the titration (charge in Coulombs) is related by Faraday's constant to the number of moles of OH^- generated and thus to the moles of CO₂ that reacted with ethanolamine from the acid.

Each system was controlled with an IBM-compatible personal computer equipped with two RS232 serial ports, a 24-line digital input/output card, and an analog-to-digital card. The latter were manufactured by Real Time Devices (State College, Pa.). These were used to control the coulometer, barometer (BNL system only), solid-state control relays, and temperature sensors, respectively. The temperature sensors (model LM34CH, National Semiconductor, Santa Clara, Calif.), with a voltage output of 10 mV/°F built into the SOMMA, were calibrated against thermistors certified to 0.01°C (PN CSP60BT103M, Thermometrics, Edison, N.J.) using a certified mercury thermometer as a secondary standard. These sensors monitored the temperature of SOMMA components, including the pipette, gas sample loops, and the coulometer cell. The SOMMA software was written in GWBASIC Version 3.20 (Microsoft Corp., Redmond, Wash.), and the instruments were driven from an options menu appearing on the personal computer (PC) monitor. With the coulometers operated in the counts mode, conversions and calculations were made by using the SOMMA software rather than the programs and the constants hardwired into the coulometer circuitry.

The BNL SOMMA-coulometry system was calibrated with pure CO₂ by using hardware that consisted of an 8-port gas sampling valve (GSV) with two sample loops of known volume [determined gravimetrically by the method of Wilke et al. (1993)]. This GCV was connected to a source of pure CO₂ through an isolation valve with the vent side of the GSV plumbed to a barometer. When a gas loop was filled with CO₂, the mass (moles) of CO₂ contained therein was calculated by dividing the loop volume (V) by the molar volume of CO₂ at the ambient temperature and pressure. The molar volume of CO₂ [V(CO₂)] was calculated iteratively from an expression using the instantaneous barometric pressure (P), loop temperature (T), gas constant (R), and the first virial coefficient B(T) for pure CO₂:

V(CO₂) = RT / P[1 + B(T) / V(CO₂)] (1)

The gas calibration factor (CALFAC)--the ratio of the calculated mass to that determined coulometrically--was used to correct the subsequent titrations for small departures from 100% recoveries (DOE 1994). Pressure was measured with a barometer, model 216B-101 Digiquartz Transducer (Paroscientific, Inc., Redmond, Wash.), which is factory-calibrated for pressures between 11.5 and 16.0 psia. The standard operating procedure was to make gas calibrations daily for each newly prepared titration cell (normally, one cell per day and three sequential calibrations per cell).

The "to deliver" volume (V_cal) of the BNL SOMMA sample pipette was determined (calibrated) gravimetrically during the cruise by periodically collecting aliquots of deionized water dispensed from the pipette into preweighed serum bottles. The serum bottles were crimp sealed and returned to shore, where they were reweighed on a model R300S (Sartorius, Güttingen, Germany) balance. The apparent weight (g) of water collected (W_air) was corrected to the mass in vacuo (M_vac) from

M_vac = W_air + W_air (0.0012/d - 0.0012/8.0) (2)

where 0.0012 is the sea level density of air at 1 atm, d is the density of the calibration fluid at the pipette temperature and sample salinity, and 8.0 is the density of the stainless steel weights. V_cal was calculated by using the following equation:

V_cal = M_vac/d (3)

The V_cal of the pipette for the BNL system was 20.6114 ± 0.0024 mL (n = 23) at a mean temperature of 14.67°C (hereafter the calibration temperature t_cal). During the cruise, the mean pipette temperature was 14.95 ± 0.97°C, and the vast majority of samples were analyzed at a measurement temperature (t) that was within 1°C of this calibration temperature. The sample volume (V_t) at the measured pipette temperature was calculated from the expression

V_t = V_cal [1 + a_v (t - t_cal)] (4)

where a_v is the coefficient of volumetric expansion for pyrex-type glass (1 × 10^-5 °C^-1) and t is the temperature of the pipette at the time of a measurement.

The BNL coulometer was periodically electronically calibrated as described in Johnson et al. (1993, 1996) and the DOE Handbook of Methods (1994). Briefly, at least two levels of current (usually 50 and 2 mA) were passed through an independent and very precisely known resistance (R) for a fixed time. The voltage (V) across the resistance was continuously measured and the instantaneous current (I) across the resistance was calculated from Ohm's law and integrated over the calibration time. Then, the number of pulses (counts) accumulated by the VFC during this time was compared to the theoretical number computed from the factory-calibration of the VFC [frequency = 105 pulses (counts) generated/sec at 200 mA] and the measured current. If the VFC was perfectly calibrated at the factory, the electronic calibration procedure would yield a straight line passing through the origin (intercept = 0) with a slope of 1. For the BNL coulometer, the mean electronic calibration slope during the R/V Meteor Cruise 22/5 was 0.999616 ± 0.000056 (n = 12, r.s.d. = 0.006%) with an intercept of -0.000533 µmol/min. From the factory calibration of the VFC and the value of the Faraday (96489 Coulomb/mol), a scaling factor of 4.82445 ± 103 counts/µmol was derived. The theoretical number of micromoles of carbon titrated (M) from samples or the gas loops was

M = [Counts/4824.45 – (Blank × T_t) – (INT_ec × T_i)]/SLOPE_ec (5)

where T_t is the length of the titration in minutes, Blank is the system blank in µmol/min, INT_ec is the intercept from electronic calibration in µmol/min, T_i is the time in minutes during the titration where current flow was continuous, and SLOPE_ec is the slope from electronic calibration. Note that the slope obtained from the electronic calibration procedure applied for the entire length of the titration, but the intercept correction applied only for the period of continuous current flow (usually 3-4 min) because the electronic calibration can be carried out only for periods of continuous current flow. The TCO₂ concentration in µmol/kg was calculated from

TCO₂ = M × CALFAC × [1/(V_t × ρ )] × d_Hg × CF_crm (6)

where p is the density of sea water in g/mL at the measurement temperature and sample salinity calculated from the equation of state given by Millero and Poisson (1981), d_Hg is the correction for sample dilution with bichloride solution (for this cruise d_Hg = 1.0 for the BNL and Kiel analyses because HgCl₂ was not used), and CF_crm is a correction factor based on the daily liquid calibration by CRM analysis (CF_crm = 1.0 for all BNL analyses; no correction based on the CRM data).

The BNL SOMMA-coulometry system was equipped with a conductance cell (Model SBE- 4, Sea-Bird Electronics, Inc., Bellevue, Wash.) for salinity measurement as described by Johnson et al. (1993). The conductance cell was factory calibrated, but SOMMA-measured salinities were continuously compared with the CTD salinities to ensure that the salinities of the analyzed samples matched the assigned salinities. Generally, agreement between CTD and SOMMA salinities was 0.02 or better.

A leak in the gas calibration hardware of the BNL system was discovered on January 12, 1993. It affected the gas calibrations by diluting the CO₂ calibration gas during the gas calibration procedure so that CALFACs determined between December 28, 1992, and January 12, 1993, were in error by approximately +0.1%. These CALFACs caused an error of +2 µmol/kg in the CRM analyses. Repairs were made on January 12, and from this point through January 28, daily CALFACs were determined and used to calculate the values of CRM and TCO₂. The mean CALFAC for the period January 12-28 was 1.004270 ± 0.000818 (n = 12 ). This CALFAC was used to recalculate the values of CRM and TCO₂ for the period from December 28 through January 11.

The IfMK system did not possess a gas calibration system, and gas calibration was not carried out during the cruise. This IfMK system was calibrated at the IfMK in Kiel prior to the cruise with liquid standards (Na₂CO₃ solutions) according to the method of Goyet and Hacker (1992). A mean CALFAC (1.005 ± 0.07%) was obtained in the laboratory from the ratio (true TCO₂ / measured TCO₂). This value was used in Eq. 6 to calculate the CRM and TCO₂ values throughout the cruise. During the calibration and at-sea work, the pipette volume, V_cal (also determined prior to the cruise), used for the IfMK system was 25.2347 mL at 20.02°C (see Eq. 4 ). This TD pipette volume was not redetermined gravimetrically during the cruise. Instead, an additional CF_crm based on the daily (cell-specific) CRM results was used to account for changes in pipette volume and/or system response by multiplying the TCO₂ sample results by the ratio (see Eq. 6):

CF_crm = CRM (certified) / CRM (measured) .

In summary, the IfMK system was calibrated as follows: a daily (cell-specific) CF_crm was applied to the water sample analysis results based on a laboratory-determined constant CALFAC (1.005) and a constant value of V_cal (25.2347mL at 20.02°C). The IfMK coulometer was not electronically calibrated during the cruise, and the theoretical response (Slope = 1, Intercept = 0) was assumed in Eq. 5 for all calculations. Note, however, that the CRM analysis results from the IfMK (Kiel) system (Fig. 3) were calculated with CF_crm = 1 in order that the variability of the CRM analyses and the magnitude of CF_crm could be assessed.

Problems were encountered with the pinch-valve tension of the IfMK System. This valvecontrols the delivery of samples to the stripper. Although it always operated, it affected the analytical results by periodically allowing additional samples to be injected into the stripper. The weak valve tension prevented the complete sealing of the tubing connecting the pipette to the stripper. The resulting errors for the CRM analyses were on the order of 0.1 to 0.5%. The valve tension was adjusted during the cruise, and the effect of these errors on data quality was minimized because poor results for the CRM analyses caused by the malfunctioning pinch valve prompted repair of the system before any samples were run. However, the possibility remained that during the sample analyses periodic pinch valve failures may have occurred, and this prompted extensive quality control-quality assurance (QA-QC) of the data.

The first phase of the QA-QC procedure was an assessment of accuracy using the data from the CRM analyses. These data are summarized in Table 1. For the BNL system, during the period from December 29, 1992, through January 11, 1993, a constant CALFAC (1.004270) was used to calculate CRM TCO₂, whereas between January 12 and 28, 1993, a daily (cell-specific) CALFAC was used to calculate CRM TCO₂. For the IfMK system, a constant CALFAC (1.005) was used for all calculations.

Table 1. Summary of CRM TCO₂ determinations made during R/V Meteor Cruise 22/5

System	No. (n)	Batcha	Mean µmol/kg	St. Dev. µmol/kg	Errorb	Dates	CALFAC	Outliersc
BNL	14	7	1926.7	0.65	+0.27	12/29/1992-01/11/1993	Constant	1
BNL	16	11	2188.7	0.89	-0.11	01/12/1993-01/28/1993	Daily	0
IfMK	18	7	1928.1	1.57	+1.68	12/30/1992-01/12/1993	Constant	3
IfMK	11	11	2191.0	1.88	+2.20	01/13/1993-01/28/1993	Constant	3

^aThe CRM were from Batch 7 and 11 with salinities of 37.12 and 38.50, and TCO₂ of 1926.41 ± 0.82 µmol/kg (n = 13) and 2188.77 ± 0.56 µmol/kg (n= 5), respectively.
^bThe mean difference between measured and certified TCO₂.
^cAn outlier is defined as a CRM analysis with an error > or= 5.0 µmol/kg.

Mean errors in the BNL system were significantly lower than the consistently positive errors observed in the IfMK system. For the BNL system, an outlier was obtained on January 4 (CRM bottle no. 2), but a second CRM (no. 275) run on the same cell gave a satisfactory result, and this cell was subsequently used to run samples. For the IfMK system, outliers were observed on January 7 and 12 (no. 353 and no. 8). In each case, a second CRM analysis (no. 318 and 244) gave satisfactory results, and the system was operated as normal. On January 20 two consecutive CRM analyses (no. 370 and 112) were classified as outliers, but a third CRM (no. 312) analysis gave a satisfactory result and the system was operated. Overall, 5 of 64 CRM analyses from Table 1 (7.8%) were classed as outliers, but 4 of these 5 outliers were obtained on the IfMK system which was further evidence for the slightly better performance of the BNL system. The greater number of outliers on the IfMK system could possibly be the result of malfunctioning of the IfMK pinch valve as described earlier. In general, the CRM results on the BNL system were identical to the manometric reference analyses at SIO. The BNL system response remained constant over the duration of the cruise (Fig. 3) whether an average CALFAC (12/28/1992-01/11/1993) or a cell-specific CALFAC (01/12/1993-01/28/1993) was used to calculate CRM TCO₂. These results confirm a similar finding obtained when mean CALFACs were used to calculate the TCO₂ data of the R/V Meteor Cruise 18/1 (WOCE Leg A1E) (Johnson et al. 1996).

The second phase of the QA-QC procedure was an assessment of sample precision on each system (instrument-specific precision). The system precision data are given in Table 2. For these data, "within-sample" precision is the average absolute difference between two replicates analyzed from the same sample bottle, "between-sample" precision is the average absolute difference between duplicate sample bottles taken from the same Niskin bottle, and "between-Niskin" precision is the average absolute difference of analyses of samples taken from two Niskin bottles that were closed at the same depth. The IfMK group assessed instrument-specific precision by periodically running two replicates from the same bottle ("within-sample"), whereas precision on the BNL system was assessed by running one replicate from each of two sample bottles filled from the same Niskin bottle ("between-sample"). The pooled standard deviation (S_p²) is the square root of the pooled variance from the "between-samples" replicates (n = 2) according to Youden (1951):

(7)

where K is the number of samples analyzed and are the degrees of freedom for the calculation.

Table 2. Summary of sample precision for TCO₂ analyses made during R/V Meteor Cruise 22/5

System	Mean precision and St. Dev. (µmol/kg)a			Sp2 (K, n, d.f.)
	Within-sample (n)	Between-sample (n)	Between-Niskin (n)
BNL	0	1.04 ± 1.11 (53)	1.26 ± 1.41 (12)	1.07 (53, 106, 53)
IfMK	1.16 ± 1.62 (46)	0.98 ± 0.36 (6)	1.53 ± 2.04 (5)	0.73 (6, 12, 6)
Combined		1.03 ± 1.06 (59)	1.34 ± 1.55 (17)	1.04 (59, 118, 59)

^aMean precision is , where n is the number of comparisons between duplicates analyses, x1 and x2.

Table 2 shows that there was no significant difference between the precision estimated using the three different methods; however, the standard deviation of the between-sample estimates was the lowest of the three methods. The same pattern was found for the TCO₂ data of the R/V Meteor Cruise 18/1 (WOCE Section A1E) when within-sample and between-sample precision were compared (see Johnson et al. 1996), and these data were also consistent with results for other WOCE Sections (Johnson et al. 1995; Johnson et al. 1996). For the instrument-specific S_p², K is the number of between-sample samples analyzed on the same instrument, n is the total number of replicates analyzed from K samples, and n - K is the degrees of freedom (d.f.).

The third phase of the QA-QC procedure was to assess the performance of the systems by comparing results from aliquots of the same sample analyzed on each system. The precedent was set by the R/V Meteor Cruise 18/1 TCO₂ data set when two SOMMAs were also run in parallel to generate the data set (Johnson et al. 1996). For the R/V Meteor 18/1 data, a method-specific S_p², assuming homogeneous variance, was calculated from aliquots of the same sample analyzed on each system. The same calculation was made for the applicable R/V Meteor Cruise 22/5 samples, and the method-specific precision (S_p²) for this cruise calculated from 31 such samples (K = 31, n = 2, d.f. = 31) was ±1.92 µmol/kg. This is a more conservative estimate of overall cruise-wide precision than the instrument-specific precision shown in Table 2. For any measurement, irrespective of the instrument it was made on, the precision was ±1.92 µmol/kg. This includes all sources of error-random as well as any uncorrected systematic errors (bias).

Figure 4 is a histogram that shows the frequency distribution of the differences between aliquots of 31 samples that were measured on both systems. The mean and standard deviation of the mean difference was 0.81 ± 2.46 µmol/kg (BNL - IfMK TCO₂ results) with most of the differences falling within the ±1.0 µmol/kg range (Fig. 4). The IfMK calibration procedure therefore appears to have been successful in eliminating any overall system bias seen for the IfMK CRM analyses given in Table 1. For the CRM, the BNL system (gas calibrated) gave more accurate results than the IfMK system (not gas calibrated), and no corrections have been made to any of the sample data analyzed on the BNL system based on the CRM results. In summary, the mean difference between aliquots of the same sample analyzed on both systems was < 1.0 µmol/kg, and the method-specific pooled variance (S_p² = ±1.92 µmol/kg) calculated from Youden (1951) is a credible estimate of precision and accuracy for the R/V Meteor Cruise 22/5 data set generated by two systems run in parallel but calibrated differently.

The fourth step in the QA-QC procedure, the at-sea to onshore comparison, involved analyzing replicates of the same sample in real time at sea and later, after storage, on shore. This procedure was carried out on 14 samples collected at 7 stations. The onshore analyses were made by vacuum extraction/manometry in the laboratory of Dr. C. D. Keeling at SIO. The results of the comparison are given in Table 3 (Guenther et al., personal communication, 1998).

Table 3. Comparison of at-sea analyses of TCO₂ by coulometry and the onshore analyses of TCO₂ by manometry on aliquots of the same sample

Date (1993)	Station (no.)	Niskin no.	Depth (m)	At-sea (µmol/kg)	Onshore (µmol/kg)	Storagea (mo)	Difference (µmol/kg)	CRM diffb
BNL analyses
1/13	48	318	10.2	2045.68	2047.49	11	-1.81	0.18
1/13	48	308	3002	2188.44	2189.98	10	-1.54	0.18
1/15	54	323	10.7	2044.96	2047.51	5	-2.55	-0.76
1/15	54	301	2808	2200.83	2202.68	5	-1.85	-0.76
1/19	68	323	10.4	2064.83	2068.02	10	-3.19	-0.14
1/19	68	307	3003	2200.10	2203.27	10	-3.17	-0.14
1/21	76	208	12.4	2057.86	2060.61	4	-2.75	-1.12
1/21	76	306	3003	2203.31	2207.06	4	-3.75	-1.12
1/24	85	213	11.8	2041.48	2047.61	3	-6.13	-0.68
1/24	85	312	3002	2200.73	2207.66	4	-6.93	-0.68
1/27	93	213	12	2029.99	2033.69	3	-3.70	-0.39
1/27	93	305	3004	2200.52	2205.61	3	-5.09	-0.39
Mean (n = 12)						6	-3.54	-0.11
St. Dev.						±3	±1.71	±0.69
IfMK analyses
1/17	62	208	12	2046.45	2054.22	4	-7.77	2.04
1/17	62	307	3004	2190.57	2202.12	5	-11.55	2.04
Mean (n = 2)						4	-9.55
St. Dev.						±1	±2.67

^aStorage refers to the elapsed time (in months) between sample collection and onshore analysis by manometry.
^bThe SIO difference between the determined and certified CRM TCO₂ for the specific coulometer cell used to titrate the at-sea replicate sample.

On the BNL system the initial comparisons (Jan. 13-15, n = 4, mean error -1.93 µmol/kg) were consistent with the precision and accuracy (±1.92 µmol/kg) of the method, but larger differences were observed after January 15. The mean difference for the cruise was -3.54 µmol/kg [for the R/V Meteor Cruise 18/1, the corresponding results were -2.13 µmol/kg (n = 7) with a method-specific precision and accuracy of ±1.65 µmol/kg]. Overall, the ship-to- shore difference is clearly not depth dependent. The poorest results were the very negative differences for samples collected on January 17 at station 62 and run on the IfMK system. There were other reasons to suspect the accuracy of the shipboard analyses from station 62 made on the IfMK system, so these samples have been averaged separately in Table 3. Note that only 3 of the remaining 12 differences were within the analytical precision of the shipboard method and these occurred early on in the cruise; 6 of the 12 were essentially within 2 standard deviations (±3.84 µmol/kg), but 3 differed by more than 2 standard deviations. All of the differences were negative. The CRM differences were not nearly as large as the ship-to-shore sample differences. The length of time the samples were stored prior to analysis onshore was also not correlated with the at-sea vs onshore differences. The reason for the difference between shipboard and shore-based analyses remains to be determined.

The data given in Tables 2 and 3 suggested that further QA-QC analysis of the data was justified. As described above, the two SOMMA systems used during R/V Meteor Cruise 22/5 employed different calibration strategies, and the number of replicate samples analyzed on both instruments was insufficient to assess bias on a station-by-station basis. As an additional cross- check on the intercomparability of TCO₂ concentrations measured using the two analytical systems, the correlation of the TCO₂ was compared with other measured oceanographic parameters. Brewer et al. (1995) and Wallace (1995) have previously noted that strong multivariate relationships exist between TCO₂ and other hydrographic parameters (e.g., temperature, salinity, oxygen, and nutrients). These relationships are remarkably robust over basin-scales and have been used to examine the temporal buildup of CO₂ in the oceans (Wallace 1995; Wallace et al. 1996; Holfort et al. 1998) and to interpolate sparse data (Brewer et al. 1995).

Multiple linear regressions were initially performed for TCO₂ data collected from three geographical sections of the R/V Meteor Cruise 22/5. Earlier work had suggested that regression fits varied slightly from one ocean basin to another. The section was therefore broken down into three groups of stations: those occupied in zone 1 defined as being west of 13° W (west of the Mid-Atlantic Ridge; southern Brazil Basin); stations occupied in zone 2, defined as being between 13° W and 3° E (between the Mid-Atlantic and Walvis Ridges; Southern Angola Basin); and stations occupied in zone 3, defined as being east of 3° E (east of the Walvis Ridge; Northern Cape Basin). For each group of stations, all samples collected from below 200 m for which TCO₂ had been measured (on either system) were extracted, and a stepwise multiple linear regression was performed with TCO₂ as the dependent variable and the wide range of other measured hydrographic parameters as independent variables. The regression models determined that only potential temperature, salinity, apparent oxygen utilization (AOU), and silicate were significant predictors [this is the same group of parameters as found previously by Wallace (1995) for the WOCE Section A9 along 19° S]. In addition, a single regression was performed for all of the data collected below 200 m from the entire section. The regression parameters for these four different geographical groupings of stations (the defined zones 1, 2, and 3 and the entire section) are presented in Table 4. For each of these four geographical groupings, two sets of regression coefficients are presented: one was derived from a regression that employed the measured silicate concentration as an independent variable and one for a regression that did not use silicate as a predictor.

This initial exercise was not particularly satisfactory, as illustrated by the regression coefficients that varied significantly from one geographical zone to another and depended on whether silicate was employed as a predictor (Table 4). For example, the AOU coefficient varied from 0.33 to 0.63 when silicate was employed as an independent variable, and it reached as high as 0.86 when silicate was not used as a predictor. The salinity coefficient was even more variable, ranging from -21 to +24. In general, the potential temperature, AOU, and salinity coefficients were stable across the geographical groupings when silicate was not used in the regression: the inclusion of silicate caused the other coefficients to vary significantly. Use of silicate as a predictor could also shift the coefficients for the other parameters outside of their "oceanographically reasonable" ranges. For example, the AOU coefficient, if interpreted to reflect the respiratory quotient for organic material, should be 0.68 (Takahashi et al. 1985), 0.69 (Anderson and Sarmiento 1994), or 0.77 (Redfield et al. 1963). Clearly the AOU coefficient derived from regression no. 2A falls well outside this accepted range. Likewise, even the sign of the salinity coefficient is variable. "Oceanographic reasoning" suggests that there should be a positive partial correlation between TCO₂ and salinity because of the strong positive correlation between carbonate alkalinity and salinity in the ocean (the countervailing tendency of CO₂ gas solubility to decrease with increasing salinity is a relatively minor effect). The use of silicate did significantly reduce the overall standard error of the predictions (Table 4) and eliminated or markedly reduced certain systematic patterns in the distribution of the residuals with depth (results not shown).

Table 4. Summary of initial multiple regression results with (A) and without (B) silicate as an independent variable.

Regression no.	Longitude range	Intercept	Pot. temp. coeff.	Salinity coeff.	AOU coeff.	Sio4 coeff	Standard error
0A	All section	1987.32	-4.296	4.045	0.62	0.482	4.37
0B	All section	1370.40	-6.254	22.038	0.827		6.88
1A	Zone 1	1975.58	-4.259	4.37	0.633	0.462	4.77
1B	Zone 1	1395.65	-5.957	21.178	0.864		7.12
2A	Zone 2	2858.72	-2.531	21.163	0.327	1.126	4.44
2B	Zone 2	1316.58	-6.623	23.822	0.754		4.42
3A	Zone 3	2201.00	-3.949	-2.246	0.621	0.538	2.65
3B	Zone 3	1540.28	-7.049	17.431	0.764		7.76

In order to examine further the influence of silicate, the residuals evaluated from regressions based upon only potential temperature, salinity, and AOU against silicate were plotted. This plot (not shown) showed that for silicate concentrations between 0 and ~40 µmol/kg, the residuals averaged zero and there was no discernible trend; however, for silicate concentrations greater than ~40 µmol/kg, there was a very clear positive correlation of the residuals with silicate. On the basis of this it was decided to define a new parameter, the "silicate index" (I_Si), as

I_Si = ([SiO₄] > 40) × ([SiO₄] - 40)

This index is equal to zero for SiO₄ concentrations less than 40 µmol/kg, and it is equal to [SiO₄] - 40 when silicate is greater than or equal to 40 µmol/kg.

The results of regressions using the silicate index, potential temperature, salinity, and AOU as independent variables, are presented in Table 5. It can be seen that use of the silicate index, rather than the silicate concentration, makes the regression coefficients for the other parameters much more consistent from one geographical zone to another (see Table 4). Given the overall consistency of fit, it is right to use a single regression equation to predict the TCO₂ over the entire section (Regression no. 0, Table 5).

The distribution of residuals arising from this single section-wide regression equation are presented separately for the three defined geographical zones in Figure 5. Separate symbols are employed for the residuals derived from measurements made on the BNL and IfMK SOMMA systems. In general, there was little or no systematic structure apparent in the residual distribution (except perhaps at the very low TCO₂ concentrations that are found close to the surface where seasonal effects may be significant), and the regression fits the data from all three zones reasonably well.

Table 5. Summary of multiple regression results when the Silicate Index (I_Si) was used as a predictor

Regression no.	Longitude range	Intercept	Pot. temp. coeff.	Salinity coeff.	AOU coeff.	ISi coeff	Standard error
0	All section	1706.33	-5.747	12.474	0.722	0.434	4.59
1	Zone 1	1704.61	-5.565	12.443	0.746	0.422	4.98
2	Zone 2	1863.67	-6.075	8.217	0.618	0.77	4.17
3	Zone 3	1964.15	-5.867	5.135	0.688	0.464	2.99

In order to assess the intercomparability of TCO₂ measurements made on the two SOMMA systems on a station-by-station basis, the mean residuals (calculated for each station) have been plotted (Fig. 6) on the basis of the section-wide fit. This plot permits an assessment of the overall consistency of the measured TCO₂ with the other measured hydrographic parameters over the entire cruise. The plot demonstrates the following:

1. There is some slight spatial structure to the station-mean residuals, with the mean residual in zone 2 (12.9° W < longitude < 3° E) being ~1-2 µmol/kg higher than for the rest of the section. No corresponding trend in the CRM analyses on the BNL system was seen (Fig. 3), and it was therefore hypothesized that this slight variation is "real" and is associated with different origins for water masses in this zone.
2. In general, there is no consistent difference between the station-mean residuals on the basis of measurements made with the BNL and IfMK SOMMA systems. The overall consistency of the two sets of measurements appears to be better than ±2 µmol/kg, which is consistent with the accuracy and precision bounds (±1.9) for the overall data set. This confirms that the cruise-wide calibration of the TCO₂ data analyzed with the two instruments was nearly identical.
3. Three stations (625, 46, and 62) appear to be outliers from the overall pattern. These stations have a mean residual that is significantly different from the overall mean of the station-mean residuals analyzed with the BNL SOMMA. All of these three stations were measured by means of the IfMK SOMMA. While the possibility could not be ruled out that these deviations arise from errors in the measurement of the independent variables used in the regressions (e.g., the oxygen or silicate analyses or from "real" oceanographic variability), it was hypothesized that they were the result of calibration error of the TCO₂ analysis at these stations.

Given the approach used to calibrate the IfMK SOMMA, such deviations could arise from a single incorrect analysis of a CRM which would cause the correction factor (CF_crm in Eq. 6) for an entire station to shift based on an incorrect analysis. The BNL SOMMA analyses were less prone to such errors because the primary calibration was based on analyses of pure CO₂ (gas calibration) with the CRM analyses being used as an independent cross-check on this primary calibration. With this approach, any calibration errors that may lead to systematic errors for an entire station are more likely to be identified and corrected.

The residual intercomparison confirms that the overall quality of the combined BNL and IfMK data set is very high. However, three anomalous stations were identified. The TCO₂ results at station 62 appear to be low by 5-7 µmol/kg. This station was also sampled for onshore manometric analyses, and the results in Table 3 confirm that, whereas other stations had a mean (ship-shore) difference of -3.54 µmol/kg (±1.71 µmol/kg), the shipboard analyses from station 62 were 8-12 µmol/kg lower than the shore-based results. Therefore it was concluded from these two independent lines of evidence that the station 62 results are too low, and they have been flagged as incorrect in the original data file. On the basis of the residual analysis, the TCO₂ results at station 46 may also be high by ~2-4 µmol/kg ,and TCO₂ results from station 625 may be high by as much as 14 µmol/kg. However, there is no independent way to assess the data from these stations, and the anomalous residual could be "real" as a result of error in the predictor variables. Therefore, the TCO₂ data from these stations have been flagged as "questionable." Only these three stations have been flagged; the data collected at the remaining 51 stations that were sampled for TCO₂ appear to be internally consistent.