Nutrient data from the global ocean were collected from various sources and separated into categories from 1 to 7 (Table 1). Thirty cruises were assigned to category 1. Twenty-five of the 30 key cruises were carried out by R/V Mirai during 2003–2013. The author used RM/CRM on those cruises as working standards for nutrient measurements at all stations to ensure high quality and comparability among the stations and among the cruises. In the Atlantic Ocean, five cruises were also selected as category 1 because RMs were used on two of the five cruises. Since comparability of nutrient data between JAMSTEC R/V Mirai cruises during the period from 2003 to 2013 and NIOZ cruises conducted in 2005 and 2007 was explicitly confirmed through interlaboratory comparison studies for reference materials of nutrients in seawater conducted in 2006 and 2008 (Aoyama et al., 2008, 2010), these two cruises were also added to category 1 to increase coverage by category 1 cruises in the Atlantic Ocean. Most of the data in category 2 were obtained from the CARINA project dataset. Most of the data in category 3 were obtained from the PACIFICA project dataset for the period 1991–2008. Many data were obtained from the World Ocean Circulation Experiment (WOCE) Global Hydrographic Climatology (WGHC) (Gouretski and Koltermann, 2004) data product. That dataset includes data from many cruises during the period 1925–1996, and those data were assigned to category 4. Category 5 was intentionally blank for future use. Some cruises conducted by the Japan Meteorological Agency (JMA) were not included in the CARINA, PACIFICA, and WGHC datasets. They were therefore included in the dataset for this study and assigned to category 6. Data from about 80 cruises by the JMA and United States institutes that were not included in the above categories were assigned to category 7.

Figures 1–4 show the locations of all the stations where data were collected. In these figures, stations in category 1 are marked in dark blue, stations in category 2 are marked in light blue, and stations in categories 3–7 are marked in red. It is apparent from these figures that the category 1 cruises did not cover the whole ocean, but if category 1 and 2 data are used to create a global dataset, the spatial coverage increases to almost all of the ocean, and the resultant dataset is a high-quality global nutrient dataset.

It is important to do quality control before using this historical dataset because it contains questionable data. In the WOCE dataset and later, there are quality flags (Joyce et al., 1994). Only data associated with quality flag 2 (i.e., data quality is good) were therefore used in this study. In cases where the data did not have quality flags, e.g., for the historical data, a median filter whose criteria for outliers was 3 times the standard deviation was applied to identify questionable data. This median filter procedure was done to datasets after the nutrient data were divided into sets of data which were involved in a region whose size was about a 500km×500km square and whose thickness was 100–300 m in the deep ocean and 10–50 m in the shallow ocean. Questionable data were removed from the dataset before vertical integration, estimation of correction factors, and creation of the global gridded data product.

In general, stations from each cruise within 250 km of 243 points worldwide were selected if there were data from several stations from at least a cruise in category 1 and at least a cruise from category 2. In the Pacific sector of the Southern Ocean, to cover the regions not covered by category 1 and 2 cruises, categories 3–7 were used to construct crossovers. As an example, Fig. 5 shows the locations of the subset of P03 and P14 stations used for a crossover comparison for a crossover at 24.2∘ N and 179∘ E. This crossover is assigned the designation CR081E, and there were two category 1 cruises and two category 3–7 cruises. Figure S1 in the Supplement shows all station locations at the 243 crossovers. Figure 6 shows examples of vertical profiles of nitrate concentrations, phosphate concentrations, nitrate-to-phosphate concentration ratios, and silicate concentrations at crossover CR081. Figure 6 also shows climatological nutrient concentrations in the WGHC dataset and WOA05 dataset for comparison. There were two cruises conducted in 2005 and 2007, which were category 1 cruises, where RMs were used as working standards at all stations by the author. The results from those cruises were in good agreement with data collected within a 250 km radius, and the error bounds (i.e., uncertainties) overlapped completely. In contrast, concentrations from two cruises conducted in 1985 and 1993 were relatively scattered (Fig. 6). To estimate correction factors based on the 30 key cruises, vertical integration between depths of 1000 and 2000 m, 1500 and 2500, and 2000 and 3000 m for nitrate, phosphate, silicate, and oxygen were done at all stations within each of the 243 crossovers. This integration was done based on the Akima interpolation method (Akima, 1970). When the number of profiles of a cruise exceeded 3, the standard deviation of the integrated values was calculated as a metric of the uncertainty of the correction factor. Table 2 shows the valid number of profiles obtained by vertical integration from 1000 to 2000 m depths, from 1500 to 2500 m depths, and from 2000 to 3000 m depths for nitrate, phosphate, silicate, and oxygen concentrations at the P03–P14 crossover stations at 24.2∘ N and 179∘ E. As expected from the vertical profiles at the crossovers, the integrated values in units of micromoles per square meter (µmol m-2) for the two cruises in category 1 (e.g., 49MR0505_2_1 and 49MR0706_1_) agreed to within 2 standard deviations for all four parameters. The standard deviations of two category 2 cruises in 1985 and 1993 were relatively large in general, and there were systematic differences that have already been identified in previous synthesis work. Because there was assurance of comparability of nutrient concentrations among the 30 key cruises, the author set the correction factor for theses cruises to 1.00. Because the measurement uncertainties during these cruises were less than 0.5 % in general, the uncertainty of correction factors was assumed to be 0.00.

To estimate correction factors at all crossovers the author selected to use integrated values by vertical integration from 1500 to 2500 m depths because there was a smaller coefficient of variation (CV), a ratio of the standard deviations of the integrated values to a mean of the integrated value and largest total number of the CV among three integration ranges for nitrate, phosphate and silicate.

The standard deviation of the integrated values for a set of profiles from each cruise within crossovers can be considered as the combined uncertainty of measurement uncertainty at each profile, station–station variability of measurements within a 250 km radius, and natural variability of nutrient concentrations among several stations within a 250 km radius at crossovers. It is expected that when RMs/CRMs are used as working standards to get a calibration curve, the station–station variability of measurements with a 250 km radius becomes very small. When in-house standards were used, station–station variability of measurements within a 250 km radius may contribute meaningfully. Therefore, it is interesting to look at the CV of the four parameters (Table 3). Figure 7 also shows histograms of the CV of the integrated value of the nitrate data in categories 1–7. It is very clear that the mean of the CV of the integrated values was 0.005 for nitrate and phosphate for category 1 cruises and that for silicate it was 0.009. The means of the CV of the integrated values for nitrate, phosphate, and silicate were smaller than those for categories 2–7. The main cause of the smaller mean of the CV of the integrated values for nutrient concentrations measured during the category 1 cruises might be the use of CRMs/RMs. The mean of the CV of the integrated values for nutrient concentrations was similar to the precision of each measurement, roughly 0.2 %–1.0 %. It should be also noted that the silicate measurements were compromised by some difficulties and/or instabilities – unlike the nitrate/phosphate measurements – that were observed in the global IC study discussed in the introduction of this article. On the other hand, the corresponding values for category 1 oxygen measurements were similar to those for category 2–7 cruises because there are no seawater matrix reference materials for dissolved oxygen, and comparability was kept only with potassium iodate solutions.

During the time frame of this study from 2003 to 2013, temporal variation of nutrient concentrations within a 250 km radius at crossovers at 1500–2500 m depth was very small, and it could be assumed to be negligible based on comparison at crossovers between/among category 1 curies, as shown in Fig. S1 especially in the Pacific Ocean. Natural variabilities of nutrients within a 250 km radius at 1500–2500 m depth were similar to or smaller than the combined uncertainty of the uncertainty of measurements and station–station variability of measurements within a 250 km radius based on the data in Table 3 and other crossover points. In other words, deep sea water within a 250 km radius at 1500–2500 m was quite homogeneous horizontally, and the variability of nutrient concentrations observed in category 2 and 4 cruises might be due to the lower comparability of the nutrient measurements made during those cruises. The larger mean of the standard deviations of the integrated values for the four parameters at crossovers for the cruises in categories 2–7 might reflect the relatively larger uncertainty which was the combination of the uncertainty of measurements and within-cruise variability (equal to the variability of measurements among several stations within a 250 km radius).

When we apply the method adopted in this study, we need to consider uncertainties of measurements and within-cruise variability (equal to the variability of measurements among several stations within a 250 km radius) that might cause the correction factors to be uncertain. The uncertainties of the correction factors were estimated in terms of the CV of the integrated values within crossovers as a first step in the estimation of correction factors. Key cruises included two-thirds of the 243 crossover points (Figs. 1–4). To estimate correction factors at the remaining crossover points, correction factor estimations were done progressively. Based on the wider coverage by the cruises in category 2, those cruises were used as secondary key cruises after correction factors, and their uncertainties were applied to the integrated values. Factors for cruises in categories 3–7 were then estimated, with the exception of several crossover stations. Table S1 in the Supplement shows estimated factors and their uncertainties for all cruises.

Comparisons were made between the factors obtained in this study and in GLODAP v2 (Olsen et al., 2016, 2019). Figures 8–11 show the results. For nitrate and phosphate, the correction factors obtained in this study were in good agreement with those obtained by GLODAP v2 when the correction factors deviated relatively far from 1.00. The implication is that both synthesis work and direct comparisons as done by this study can detect differences between cruises and estimate correction factors correctly when the nutrient concentrations obviously differ from values obtained on nearby cruises. For many GLODAP v2 cruises, factors were assigned a value of 1.00, but it is obvious that direct comparisons resulted in factors that were slightly larger or smaller (Figs. 7–9) because synthesis work could not identify differences among cruises if those differences were not large. Direct comparisons, however, could determine correction factors with uncertainties more precisely. In general, the differences of the correction factors obtained by two methods, synthesis like GLODAP v2 and direct comparison as in this study, for nitrate and phosphate were around +0.02 and -0.04, whereas the differences for silicate were relatively large: ±0.06. For oxygen, the differences were much larger: ±0.10.

Based on the factors obtained in this study, a dataset was created at latitude and longitude intervals of 0.5∘ and on 136 isobaric surfaces at intervals of 50 m. The uncertainties of the nutrient concentrations were about 2 % for nitrate and phosphate and 5 % for silicate and oxygen. This uncertainty was equated to twice the standard deviations of the integrated values for the category 2 cruises. The following steps were used to create the global gridded dataset.

Step 1. Profiles of which factor was determined were selected to create the global gridded dataset. Then nutrients and oxygen concentrations were corrected by the factors.

To determine the total amount of nitrate, phosphate, silicate, and oxygen in the ocean, the volume and area corresponding to each grid point were calculated using the ETOPO2 topographic and bathymetric dataset (2 min mesh). The concentrations were multiplied by the volume of the obtained grid point to find the number of moles of nitrate, phosphate, silicate, or oxygen at each grid point, and the results were summed for each sea area. In this way the total amounts of nitrate, phosphate, silicate, and oxygen in the ocean were estimated as well as the associated uncertainties.