Pacific DIC Crossovers
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.
Here is a summary Table of crossover results. Click on a point in the figure below to see a graph of the DIC information.
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|
*ΔTCO2 deemed unreliable because of poor fits.
These results are compared with the deltas derived from curve fitting method as shown in the figure below:
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. Here is a summary table of the TCO2 quality assessment results, or see our Adjustments Page for a synopsis of the adjustments we propose for the Pacific dataset.