The purpose of this analysis was to determine if any significant systematic offset existed between the various legs of the WOCE/NOAA/JGOFS Pacific Ocean TCO₂ measurements. The stations selected for each crossover were those with carbon data which were close to the crossover point. The number of stations selected was somewhat subjective (see map), but was such that sufficient measurements were present for the analysis without getting too far away from the crossover location. In all cases the stations were within approximately 1° of latitude or longitude of the crossover point. Data from deep water (>2000 m) at each of the crossover locations were plotted against the density anomaly referenced to 3000 dB (σ-3) and fit with a second-order polynomial. The difference and standard deviation between the two curves was then calculated from 10 evenly spaced intervals over the density range common to both sets of crossover.

Summary Table of crossover results (opens a new window)

Secondary Checks

A secondary check was performed on crossover with large deltas or large standard deviations from the crossover analysis. A multi-parameter liner least square regression method is used to examine the offsets at selected crossover locations. Data in Cruise 1 are used as a reference to derive a best fit equation:

TCO₂ = a + bSal + cT + dOxy

where a, b, c, and d are constants; Sal is salinity; T is temperature; and Oxy is Oxygen concentration. Once the equation is derived, TCO₂ is calculated fromthe Cruise 2 Sal, T, and Oxy data. The difference between this predicted TCO₂ and the observed TCO₂ at the Cruise 2 stations is defined as ΔTCO₂. Results from the multiple-parameter regression method are listed in Table below:

Crossing no.	Cruise 1 - station	Cruise 2 - station	ΔTCO2 (µmol/kg)	St.dev
23	P13-54,55	P2-48	6.2	8.8
36	P15N-52,54	P2-65	-2.9	3.4
40d	P14S15S-173	P15N-114	-3.3	4.3
40e	P14S15S-172	P15N-116	2.2	1.5
40f	P14S15S-171	P15N-118	-1.3	2.7
40h	P14S15S-170	P15N-120	-1.5	3.2
40j	P14S15S-169	P15N-122	-0.5	3.1
40k	P14S15S-122	EQS92-63	-0.6	1.7
41b	P14S15S-157	EQS92-66	-3.5	3.2
41f	P15N-130,132	P31-54,57,61	-1.2	4.4
44	P14S15S/1-93	P14S15S/2-94	-0.1	2.1
45	P14S15S-33	S4P-755	6.6*	3.4
47	P16N-58,59,66	P17N-78	-10.0	3.4
49	P16N-30,31,32	P2-70	-1.9	1.9
53f	P21-157,160	P31-2,5	3.4*	4.3
54	P16S17S-190	P6-127,129	3.7	1.6
60a	CGC91-12	P17N-28	-7.7	5.3
60b	CGC91-12	P17C-17	-3.5	5.3
60c	P17N-28	P17C-17	11.3	5.5
61	P17C-26	P2-78	2.2	4.6
67	P16A17A-77	P17E19S-128	4.7*	13.6
73	P18-155,159	EQS92-6	-0.6	1.2
77	P18-37	P17E19S-194	2.9*	1.6
80	P19-333	P21-49	-2.2*	2.3

* ΔTCO₂ deemed unreliable because of poor fits.

These results are compared with the deltas derived from curve fitting method as shown in the figure bellow:

The multi-parameter method generally had smaller delta values, suggesting that some of the differences in the crossovers with large deltas could actually be due to real changes in the water mass properties.

Optimizing the crossover Results

Optimum cruise adjustments, based on the crossover results, were evaluated using several approaches. The first approach was a simple least-squares minimization (SLSQ). The optimized cruise adjustments based on an equal weighting of the crossover data are shown in the figures below. The second approach for calculating the adjustments was weighted least-squares (WLSQ); the weighting used the error estimates from the polynomial fits, and focused on making adjustments to minimize offsets at crossover, where they were better determined. The more crossovers used to determine the adjustments, and the smaller the offset uncertainties at those crossovers, the smaller the adjustment uncertainties. The third approach was weighted, damped least-squares (WDLSQ), formally equivalent to a Gauss-Markov model (Wunsch, 1996). The damping used was a prior guess of the variance at crossover, estimated to be a constant 3² µmol/kg for TCO₂ - hopefully, what one might have guessed this RMS value of crossover differences to be before the survey was started. One could also choose to vary the damping on a cruise-by-cruise basis to reflect prior information on the accuracy of individual cruises (e.g. whether or not CRMs were used when determining TCO₂ concentrations, or when the measurements were made, or even who made the measurements); for this study, a constant damping was used. A summary of the proposed adjustments based on the three different models is given below.

In an effort to ensure that sparse sampling combined with either noisy data or variability resulting from water mass variations was not significantly biasing the estimates of the offsets, a second approach to the polynomial fit was examined. In the approach previously described, the data from each cruise were fit with two independent curves. We will call this approach the Del Poly model. For the second approach (termed the Same Shape model) we fitted a second-order polynomial function to data from both Cruise 1 and Cruise 2 in a way that allowed a constant offset for the two cruises but identical slope and curvature terms. The assumption was made that for any given crossover, the differences between the data from the two cruises could be expressed in the Same Shape model as a constant offset for TCO₂ and TALK. The assumption of a constant offset was made partly because an offset was the simplest adjustment; however, with the relatively uniform oceanic values for TCO₂ and TALK, additive or multiplicative adjustments would give similar results. Summary of the proposed adjustments based on the three different models is given in Fig. below. The proposed adjustments from the three different least-squares models were similar to the adjustments from the Del Poly analysis.

 
 

Using the crossover differences estimated from the polynomial fits, the 64 crossovers for TCO₂ had an average and standard deviation of 0.3±4.0 µmol/kg.  The average and of the absolute values of the differences was 2.9±2.6 µmol/kg. Twenty-four TCO₂ crossover with differences from the polynomial fits >3 µmol/kg were further examined using the MLR crossover approach. Unlike the polynomial fit crossover approach, the MLR method does not assume that the waters are identical, only that the relationships between TCO₂ and the other properties do not change, and that the effects of measurement errors in the independent variables can be neglected.  In the South Pacific, most of the crossovers with large differences were from the P14S15S-P15N crossover comparisons near the equatorial region [a series of zonal crossover comparisons between the equator and 12°S along 170°W (crossover 40)].  In general, the use of the crossover MLR analysis resulted in smaller differences, suggesting that the assumption of identical waters may not be valid for this area. The MLR analysis did show, however, that P13 and P17N should be decreased by 6 µmol/kg and 10 µmol/kg respectively, and P16N, CGC91, and S4P should all be increased by 6 µmol/kg.

Both the Del Poly and Same Shape models give very similar differences, but the uncertainties are generally smaller for the Same Shape model. It is difficult to say which approach is more appropriate for these data, since the answer depends somewhat on the nature of the errors. If we assume a priori that the primary difference between the data sets results from a constant offset, then the same shape model is most appropriate. Of the three least squares models examined, the WDLSQ adjustments and errors make use of the most information (error estimates and prior guesses on crossover differences) to determine adjustments and their uncertainties. The results from the WDLSQ show that almost all cruises during the Pacific Ocean CO₂ survey are within ~ 3 µmol/kg for TCO₂.  A few cruises lie outside this cutoff. These results indicate that P9 should be decreased by 3-5 µmol/kg, P17N should be decreased by 5-6 µmol/kg,and P16N should be increased by 3-6 µmol/kg.
 

All of these results must be considered in concert with the other lines of evidence on the quality of the TCO₂ measurements from the various cruises. The TCO₂ data were also examined using a basin-wide MLR approach and using an isopycnal analysis. For a summary table of the TCO₂ quality assessment results click here or see our  Adjustments Page for a synopsis of the adjustments we propose for the Pacific dataset.

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