NOAA Atlas NESDIS 75 doi:10.7289/V5XG9P2W WORLD OCEAN ATLAS 2013 Volume 3: Dissolved Oxygen, Apparent Oxygen Utilization, and Oxygen Saturation Silver Spring, MD September 2013 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Environmental Satellite, Data, and Information Service National Oceanographic Data Center Additional copies of this publication, as well as information about NODC data holdings and services, are available upon request directly from NODC. National Oceanographic Data Center User Services Team NOAA/NESDIS E/OC1 SSMC III, 4th floor 1315 East-West Highway Silver Spring, MD 20910-3282 Telephone: (301) 713-3277 Fax: (301) 713-3302 E-mail: NODC.Services@noaa.gov NODC URL: http://www.nodc.noaa.gov/ For updates on the data, documentation, and additional information about the WOA13 please refer to: http://www.nodc.noaa.gov/OC5/indprod.html This document should be cited as: Garcia, H. E., R. A. Locarnini, T. P. Boyer, J. I. Antonov, A. V. Mishonov, O. K. Baranova, M. M. Zweng, J. R. Reagan, D. R. Johnson, 2013. World Ocean Atlas 2013. Vol. 3: Dissolved Oxygen, Apparent Oxygen Utilization, and Oxygen Saturation. S. Levitus, Ed.; A. Mishonov, Technical Ed. NOAA Atlas NESDIS 75, 27 pp. doi:10.7289/V5XG9P2W This document is available on-line at http://www.nodc.noaa.gov/OC5/indprod.html NOAA Atlas NESDIS 75 doi:10.7289/V5XG9P2W WORLD OCEAN ATLAS 2013 Volume 3: Dissolved Oxygen, Apparent Oxygen Utilization, and Oxygen Saturation Hernan E. Garcia, Timothy P. Boyer, Ricardo A. Locarnini, John I. Antonov, Alexey V. Mishonov, Olga K. Baranova, Melissa M. Zweng, James R. Reagan, Daphne R. Johnson Editor: Sydney Levitus Technical Editor: Alexey Mishonov Ocean Climate Laboratory National Oceanographic Data Center Silver Spring, Maryland September, 2013 U.S. DEPARTMENT OF COMMERCE Penny S. Pritzker, Secretary National Oceanic and Atmospheric Administration Kathryn D. Sullivan, Acting Under Secretary of Commerce for Oceans and Atmosphere National Environmental Satellite, Data, and Information Service Mary E. Kicza, Assistant Administrator To Sydney (Syd) Levitus Syd exemplifies the craft of careful, systematic inquiry of the large-scale distributions and low-frequency variability from seasonal-to-decadal time scales of ocean properties. He was one of the first to recognize the importance and benefits of creating objectively analyzed climatological fields of measured ocean variables including temperature, salinity, oxygen, nutrients, and derived fields such as mixed layer depth. Upon publishing Climatological Atlas of the World Ocean in 1982, he distributed this work without restriction, an act not common at the time. This seminal atlas moved the oceanographic diagnostic research from using hand-drawn maps to using objectively analyzed fields of ocean variables. With his NODC Ocean Climate Laboratory (OCL) colleagues, and unprecedented cooperation from the U.S. and international ocean scientific and data management communities, he created the World Ocean Database (WOD); the world’s largest collection of ocean profile data that are available internationally without restriction. The World Ocean Atlas (WOA) series represents the gridded objective analyses of the WOD and these fields have also been made available without restriction. The WOD and WOA series are used so frequently that they have become known generically as the “Levitus Climatology”. These databases and products enable systematic studies of ocean variability in its climatological context that were not previously possible. His foresight in creating WOD and WOA has been demonstrated by their widespread use over the years. Syd has made major contributions to the scientific and ocean data management communities. He has also increased public understanding of the role of the oceans in climate. He retired in 2013 after 39 years of distinguished civil service. He distilled the notion of the synergy between rigorous data management and science; there are no shortcuts. All of us at the Ocean Climate Laboratory would like to dedicate this atlas to Syd, his legacy, vision, and mentorship. The OCL team members Table of Contents TABLE OF CONTENTS .................................................................................................................................................................................. iii LIST OF FIGURES............................................................................................................................................................................................iv LIST OF TABLES.............................................................................................................................................................................................iv PREFACE .............................................................................................................................................................................................................v ACKNOWLEDGMENTS...............................................................................................................................................................................vi ABSTRACT .............................................................................................................................................................................................................1 1. INTRODUCTION .......................................................................................................................................................................................1 2. DATA AND DATA DISTRIBUTION.........................................................................................................................................................3 2.1. DATA SOURCES .............................................................................................................................................................................3 2.2. DATA QUALITY CONTROL ............................................................................................................................................................4 2.2.1. Duplicate elimination.............................................................................................................................................................4 2.2.2. Range and gradient checks .................................................................................................................................................5 2.2.3. Statistical checks .................................................................................................................................................................5 2.2.4. Subjective flagging of data ...............................................................................................................................................6 2.2.5. Representativeness of the data ...........................................................................................................................................6 3. DATA PROCESSING PROCEDURES.......................................................................................................................................................7 3.1. VERTICAL INTERPOLATION TO STANDARD LEVELS ........................................................................................................7 3.2. METHODS OF ANALYSIS .............................................................................................................................................................8 3.2.1. Overview .............................................................................................................................................................................8 3.2.2. Derivation of Barnes (1964) weight function ..................................................................................................................9 3.2.3. Derivation of Barnes (1964) response function ...........................................................................................................10 3.2.4. Choice of response function ..............................................................................................................................................11 3.2.5. First-guess field determination .....................................................................................................................................12 3.3. CHOICE OF OBJECTIVE ANALYSIS PROCEDURES.............................................................................................................13 3.4. CHOICE OF SPATIAL GRID .....................................................................................................................................................13 4. RESULTS........................................................................................................................................................................................................14 4.1. COMPUTATION OF ANNUAL AND SEASONAL FIELDS ....................................................................................................15 4.2. AVAILABLE OBJECTIVE AND STATISTICAL FIELDS ..........................................................................................................15 4.3. OBTAINING WOA13 FIELDS ON-LINE.................................................................................................................................15 5. SUMMARY..................................................................................................................................................................................................15 6. FUTURE WORK....................................................................................................................................................................................16 7. REFERENCES .......................................................................................................................................................................................16 List of Figures Figure 1. Response function of the WOA13, WOA05, WOA01, WOA98, WOA94, and Levitus (1982) objective analysis schemes.................................................................................................................................26 Figure 2. Scheme used in computing annual, seasonal, and monthly objectively analyzed means for dissolved oxygen, Apparent Oxygen Utilization (AOU), and oxygen saturation ( \( O_2^S \) ) ....................................................27 List of Tables Table 1. Descriptions of climatologies for dissolved oxygen, apparent oxygen utilization, and oxygen saturation in WOA13..................................................................................................................................................21 Table 2. Acceptable distances (m) for defining interior and exterior values used in the reiniger and ross (1968) scheme for interpolating observed level data to standard levels.............................................................................21 Table 3. Response function of the objective analysis scheme as a function of wavelength for WOA13 and earlier analyses..................................................................................................................................................23 Table 4. Basins defined for objective analysis and the shallowest standard depth level for which each basin is defined. ..................................................................................................................................................24 Table 5. Statistical fields calculated as part of WOA13............................................................................................25 Preface The oceanographic analyses described by this atlas series expand on earlier works, e.g., the World Ocean Atlas 2009 (WOA09), World Ocean Atlas 2005 (WOA05), World Ocean Atlas 2001 (WOA01), World Ocean Atlas 1998 (WOA98), World Ocean Atlas 1994 (WOA94) and Climatological Atlas of the World Ocean (Levitus, 1982). Previously published oceanographic objective analyses have proven to be of great utility to the oceanographic, climate research, geophysical, and operational environmental forecasting communities. Such analyses are used as boundary and/or initial conditions in numerical ocean circulation models and atmosphere-ocean models, for verification of numerical simulations of the ocean, as a form of "sea truth" for satellite measurements such as altimetric observations of sea surface height, for computation of nutrient fluxes by Ekman transport, and for planning oceanographic expeditions among others. WOA13 includes analyses on both one-degree and quarter-degree grids. We continue preparing climatological analyses on a one-degree grid. This is because higher resolution analyses are not justified for all the variables we are working with and we wish to produce a set of analyses for which all variables have been analyzed in the same manner. High-resolution analyses as typified by the work of Boyer et al. (2005) will be published separately. We now generate and make available what we term "Extended Vertical Resolution" (EVR) analyses. Analyses are now produced at 102 depth levels between the surface and 5500 m depth in contrast to 33 depth levels that we have produced in the past. This is made possible by the increased amount of high-resolution data available. Ocean data and analyses of such data at higher vertical resolution than previously available are needed to document the variability of the ocean, including improving diagnostics, understanding, and modeling of the physics of the ocean. In the acknowledgment section of this publication we have expressed our view that creation of global ocean profile and plankton databases and analyses are only possible through the cooperation of scientists, data managers, and scientific administrators throughout the international scientific community. I also thank my colleagues and the staff of the Ocean Climate Laboratory of NODC for their dedication to the project leading to publication of this atlas series. Their integrity and thoroughness have made these analyses possible. Sydney Levitus National Oceanographic Data Center Silver Spring, MD June 2013 Acknowledgments This work was made possible by a grant from the NOAA Climate and Global Change Program which enabled the establishment of a research group at the National Oceanographic Data Center. The purpose of this group is to prepare research quality oceanographic databases, as well as to compute objective analyses of, and diagnostic studies based on, these databases. Support is now from base funds and from the NOAA Climate Program Office. The data on which this atlas is based are in World Ocean Database 2013 and are distributed online by NODC/WDC. Many data were acquired as a result of the IOC/IODE Global Oceanographic Data Archaeology and Rescue (GODAR) project, and the IOC/IODE World Ocean Database project (WOD). At NODC/WDC, data archaeology and rescue projects were supported with funding from the NOAA Environmental Science Data and Information Management (ESDIM) Program and the NOAA Climate and Global Change Program which has included support from NASA and DOE. Support for some of the regional IOC/GODAR meetings was provided by the Marine Science and Technology (MAST) program of the European Union. The European Community has also provided support for the Mediterranean Data Archeology and Rescue (MEDAR/MEDATLAS) Project which has resulted in the inclusion of substantial amounts of ocean profile data from the Mediterranean Sea. Additional Black Sea data have been acquired as a result of a NATO sponsored project. We acknowledge the scientists, technicians, and programmers who have collected and processed data, those individuals who have submitted data to national and regional data centers as well as the managers and staff at the various data centers. We thank our colleagues at the NODC. Their efforts have made this and similar works possible. WORLD OCEAN ATLAS 2013 Volume 3: Dissolved Oxygen, Apparent Oxygen Utilization, and Oxygen Saturation ABSTRACT This atlas consists of a description of data analysis procedures and horizontal maps of climatological distribution fields of dissolved oxygen, apparent oxygen utilization (AOU), and dissolved oxygen saturation at selected standard depth levels of the world ocean on a one-degree latitude-longitude grid. The aim of the maps is to illustrate large-scale characteristics of the distribution of dissolved oxygen. The oceanographic data fields used to generate these climatological maps were computed by objective analysis of all scientifically quality-controlled historical dissolved oxygen data in the World Ocean Database 2013. Maps are presented for climatological composite periods (annual, seasonal, monthly, seasonal and monthly difference fields from the annual mean field, and the number of observations) at 102 standard depths. 1. INTRODUCTION The distribution of dissolved oxygen, apparent oxygen utilization, and oxygen saturation in the ocean is affected by both biochemical and physical processes. Biochemical processes include sources and sinks of \( \mathrm{O}_2 \) due to marine production, respiration, and oxidation of organic matter (\( e.g. \), biological pump). Physical processes include sources and sinks of \( \mathrm{O}_2 \) caused by water mass ventilation, air-sea flux exchange, gas solubility (\( e.g. \), thermal pump), and water mixing. The oceanic \( \mathrm{O}_2 \) inventory is sensitive to local to global changes driven by the physical and biological state of the ocean as well as anthropogenic effects acting on different time scales (\( e.g. \), Keeling and Garcia, 2001; Matear and Hirst, 2003; Stramma et al., 2008; Shaffer et al., 2009; Riebesell et al., 2009; Hofmann and Schellnhuber, 2009). This atlas is part of the World Ocean Atlas 2013 (WOA13) series. The WOA13 series includes analysis for dissolved oxygen (this atlas), temperature (Locarnini et al., 2013) salinity (Zweng et al., 2013), and dissolved inorganic nutrients (Garcia et al., 2013). This atlas presents annual, seasonal, and monthly climatologies and related statistical fields for dissolved oxygen (\( \mathrm{O}_2 \)), apparent oxygen utilization (AOU), and oxygen saturation (\( \mathrm{O}_2^S \)). Climatologies in this atlas are defined as mean oceanographic fields at selected standard depth levels based on the objective analysis of historical oceanographic profiles and select surface-only data. An \( \mathrm{O}_2 \) profile is defined as a set of measurements of samples collected at discrete depths taken as an instrument such as a rosette CTD package drops or rises vertically in the water column. This atlas includes an objective analysis of all scientifically quality-controlled historical \( \mathrm{O}_2 \) measurements available in the World Ocean Database 2013 (WOD13; Boyer et al., 2013). We present data analysis procedures and horizontal maps showing annual, seasonal, and monthly climatologies and related statistical fields for \( \mathrm{O}_2 \), Apparent Oxygen Utilization (AOU), and dissolved oxygen saturation (\( \mathrm{O}_2^S \)) at selected standard depth levels between the surface and the ocean bottom to a maximum depth of 5500 m. The complete set of maps, statistical and objectively analyzed data fields, and documentation are all available on-line. All climatologies use all available O_2 data regardless of year of observation. The annual climatology was calculated using all data regardless of the month in which the observation was made. Seasonal climatologies were calculated using only data from the defined season (regardless of year). The seasons are here defined as follows. Winter is defined as the months of January, February, and March. Spring is defined as April, May, and June. Summer is defined as July, August, and September. Fall is defined as October, November, and December. Monthly climatologies were calculated using data only from the given month regardless of the day of the month in which the observation was made. The O_2 data used in this atlas are available from the National Oceanographic Data Center (NODC) and World Data Center (WDC) for Oceanography, Silver Spring, Maryland. Large volumes of oceanographic data have been acquired as a result of the fulfillment of several data management projects including: a) the Intergovernmental Oceanographic Commission (IOC) Global Oceanographic Data Archaeology and Rescue (GODAR) project (Levitus et al., 2005); b) the IOC World Ocean Database project (WOD); c) the IOC Global Temperature Salinity Profile project (GTSPP) (IOC, 1998). The dissolved oxygen data used in the WOA13 have been analyzed in a consistent, objective manner on a one-degree latitude-longitude grid at standard depth levels from the surface to a maximum depth of 5500m. The procedures for “all-data” climatologies are identical to those used in the World Ocean Atlas 2009 (WOA09) series (Locarnini et al., 2010; Antonov et al., 2010; Garcia et al., 2010 a, b), World Ocean Atlas 2005 (WOA05) series (Locarnini et al., 2006; Antonov et al., 2006; Garcia et al., 2006 a, b), World Ocean Atlas 2001 (WOA01) series (Stephens et al., 2002; Boyer et al., 2002; Locarnini et al., 2002; Conkright et al., 2002), and World Ocean Atlas 1998 (WOA98) series (Antonov et al., 1998 a, b, c; Boyer et al., 1998 a, b, c; Conkright et al., 1998 a, b, c; O’Brien et al., 1998 a, b, c). Slightly different procedures were followed in earlier analyses (Levitus, 1982; World Ocean Atlas 1994 series [WOA94, Levitus et al., 1994; Levitus and Boyer, 1994 a, b; Conkright et al., 1994]). Present analysis differs from WOA09 by increasing the number of standard levels used from 33 to 102, increasing the vertical resolution with depth. Objective analyses shown in this atlas are constrained by the nature of the historical O_2 data base (data are non-uniform in space, time, and data quality), characteristics of the objective analysis techniques, and the grid used. These limitations and characteristics are discussed below. Since the publication of WOA09, substantial amounts of additional historical and modern O_2 data have become available. However, even with these additional data, we are still hampered in a number of ways by a lack of oceanographic data. Because of the lack of O_2 data, we are forced to examine the annual cycle by compositing all data regardless of the year of observation. In some geographic areas, quality control is made difficult by the limited number of O_2 data collected in these areas. Data may exist in an area for only one season, thus precluding any representative annual analysis. In some areas there may be a reasonable spatial distribution of data points on which to base an analysis, but there may be only a few (perhaps only one) data values in each one-degree latitude-longitude square. This atlas is divided into sections. We begin by describing the data sources and data distribution (Section 2). Then we describe the general data processing procedures (Section 3), the results (Section 4), summary (Section 5), and future work (Section 6). Global horizontal maps for O₂, AOU, and \( \mathrm{O}_2^S \) at each individual depth levels for each time period are available online. 2. DATA AND DATA DISTRIBUTION Data sources and quality control procedures are briefly described below. For further information on the data sources used in WOA13 refer to the World Ocean Database 2013 (WOD13, Boyer et al., 2013). The quality control procedures used in preparation of these analyses are described by Johnson et al. (2013). 2.1. Data sources Historical oceanographic data used in this atlas were obtained from the NODC/WDC archives and include all data gathered as a result of the GODAR and WOD projects. All of the quality-controlled O₂ (expressed in units of milli-liters per liter, ml l⁻¹) data used in this atlas were typically obtained by means of chemical O₂ analysis of serial (discrete) water column samples. The O₂ values were analyzed following various modifications of the Winkler titration method (Winkler, 1888) using visual, amperometric, or photometric end-detections (e.g., Carpenter, 1965; Culberson and Huang, 1987; Knapp et al., 1990; Culberson et al., 1991; Dickson, 1994). We refer to the discrete water sample dataset in WOD13 as Ocean Station Data (OSD). Typically, each profile in the OSD dataset consists of 1 to up to 36 discrete O₂ observations collected at various depths between the surface and the bottom using Nansen or Niskin bottle water samplers. We note that WOD13 contains O₂ data obtained by electronic sensors mounted on the Conductivity-Temperature-Depth (CTD) rosette frame (i.e., polarographic O₂ electronic sensors). However, in preparation of these climatologies we used O₂ data believed to be obtained by chemical titration methods only. We note that most (>75%) of the O₂ data in the WOD13 OSD dataset were collected on or after 1965 when more or less standard O₂ analysis methods began to be used. AOU (ml l⁻¹) and \( \mathrm{O}_2^S \) (percent, %) are derived (calculated) variables for an O₂ measurement only when in situ temperature and salinity were also measured at the same geographic location, time, and depth (pressure). Section 2.2 describes the calculation of AOU and \( \mathrm{O}_2^S \). To understand the procedures for taking individual oceanographic observations and constructing climatological fields, definition of the terms “standard level data” and “observed level data” are necessary. We refer to the actual measured value of an oceanographic variable in situ (Latin for “in place”) as an “observation”, and to the depth at which such a measurement was made as the “observed level depth”. We refer to such data as “observed level data”. Before the development of oceanographic instrumentation that measure at high frequencies along the vertical profile, oceanographers often attempted to make measurements at selected “standard levels” in the water column. Sverdrup et al. (1942) presented the suggestions of the International Association of Physical Oceanography (IAPSO) as to which depths oceanographic measurements should be made or interpolated to for analysis. Historically the World Ocean Atlas used a modified version of the IAPSO standard depths. However, with the increased global coverage of high depth resolution instrumentation, such as profiling floats, WOA has extended the standard depth levels from 33 to 102. The new standard depth levels include the original depth levels presented up to WOA09, but have tripled the resolution in the upper 100 meters, more than doubled the depth resolution of the upper 1000 meters, and almost three and a half times the resolution for overall depth levels. For many purposes, including preparation of the present climatologies, observed level data are interpolated to standard depth levels if observations did not occur at the desired standard depths (see section 3.1 for details). The levels at which the O_2, AOU, and O_2^S climatologies were calculated are given in Table 1. Table 2 shows the depths of each standard depth level. Section 3.1 discusses the vertical interpolation procedures used in our work. 2.2. Data quality control Performing quality control of the O_2 data is a major task, the difficulty of which is directly related to lack of data and metadata (for some areas) upon which to base statistical checks. Consequently certain empirical criteria were applied (see sections 2.2.1 through 2.2.4), and as part of the last processing step, subjective judgment was used (see sections 2.2.5 and 2.2.6). Individual data, and in some cases entire profiles or all profiles for individual cruises, have been flagged and not used further because these data produced features that were judged to be non-representative or questionable. As part of our work, we have made available WOD13 which contains both observed levels profile data and standard depth level profile data with various quality control flags applied. The flags mark individual measurements or entire profiles which were not used in the next step of the procedure, either interpolation to standard depth levels for observed level data or calculation of statistical means in the case of standard depth level data. Our knowledge of the variability of the world ocean in the instrumental record now includes a greater appreciation and understanding of the ubiquity of eddies, rings, and lenses in some parts of the world ocean as well as interannual and interdecadal variability of water mass properties associated with modal variability of the atmosphere such as the North Atlantic Oscillation, Pacific Decadal Oscillation (PDO), and El Niño Southern Ocean Oscillation (ENSO). Therefore, we have simply flagged data, not eliminating them from the WOD13. Thus, individual investigators can make their own decision regarding the representativeness of the O_2 data. Investigators studying the distribution of features such as eddies will be interested in those data that we may regard as unrepresentative or questionable for the preparation of the analyses shown in this atlas. 2.2.1. Duplicate elimination Because O_2 data are received from many sources, sometimes the same data set is received at NODC/WDC more than once but with slightly different time and/or position and/or data values, and hence are not easily identified as duplicate stations. Therefore, to eliminate the repetitive O_2 data values our databases were checked for the presence of exact and near exact replicates using eight different criteria. The first checks involve identifying stations with exact position/date/time and data values; the next checks involve offsets in position/date/time. Profiles identified as duplicates in the checks with a large offset were individually verified to ensure they were indeed duplicate profiles. All replicate profiles were eliminated at the first step of our processing except one profile. 2.2.2. Range and gradient checks Range checking (i.e., checking whether an O$_2$ value is within preset minimum and maximum values as a function of depth and ocean region) was performed on all O$_2$ values as a first quality control check to flag and withhold from further use the relatively few values that were grossly outside expected oceanic ranges. Range checks were prepared for individual regions of the world ocean. Johnson et al. (2013) and Boyer and Levitus (1994) detail the quality control procedures. Tables showing the O$_2$ ranges selected for each basin and depth can be found in Johnson et al. (2013). A check as to whether excessive vertical gradients occur in the data has been performed for O$_2$ data in WOD13 both in terms of positive and negative gradients. See Johnson et al. (2013) for limits for excessive gradients for O$_2$. 2.2.3. Statistical checks Statistical checks were performed as follows. All data for O$_2$ (irrespective of year), at each standard depth level, were averaged within five-degree latitude-longitude squares to produce a record of the number of observations, mean, and standard deviation in each square. Statistics were computed for the annual, seasonal, and monthly compositing periods. Below 50 m depth, if data were more than three standard deviations from the mean, the data were flagged and withheld from further use in objective analyses. Above 50 m depth, a five-standard-deviation criterion was used in five-degree squares that contained any land area. In selected five-degree squares that are close to land areas, a four-standard-deviation check was used. In all other squares a three-standard-deviation criterion was used for the 0-50 m depth layer. For standard depth levels situated directly above the bottom, a four-standard-deviation criterion was used. The reason for the weaker standard deviation criterion in coastal and near-coastal regions is the exceptionally large range of values in the coastal five-degree square statistics for O$_2$. Frequency distributions of O$_2$ values in some coastal regions are observed to be skewed or bimodal. Thus to avoid flagging possibly good data in environments expected to have large variability, the standard deviation criteria were broadened. The total number of measurements in each profile, as well as the total number of O$_2$ observations exceeding the standard deviation criterion, were recorded. If more than two observations in a profile were found to exceed the standard deviation criterion, then the entire profile was flagged. This check was imposed after tests indicated that surface data from particular casts (which upon inspection appeared to be questionable) were being flagged but deeper data were not. Other situations were found where questionable data from the deeper portion of a cast were flagged, while near-surface data from the same cast were not flagged because of larger natural variability in surface layers. One reason for this was the decrease of the number of observations with depth and the resulting change in sample statistics. The standard-deviation check was applied twice to the O$_2$ data set for each compositing period. In summary, first the five-degree square statistics were computed, and the data flagging procedure described above was used to provide a preliminary data set. Next, new five-degree-square statistics were computed from this preliminary data set and used with the same statistical check to produce a new, “clean” data set. The reason for applying the statistical check twice was to flag (and withhold from further use), in the first round, any grossly erroneous or non-representative data from the data set that would artificially increase the variances. The second check is then relatively more effective in identifying smaller, but questionable or non-representative, \( O_2 \) observations. 2.2.4. Subjective flagging of data The \( O_2 \) data were averaged by one-degree squares for input to the objective analysis program. After initial objective analyses were computed, the input set of one-degree means still contained questionable data contributing to unrealistic distributions, yielding intense bull's-eyes or spatial gradients. Examination of these features indicated that some of them were due to profiles from particular oceanographic cruises. In such cases, data from an entire cruise were flagged and withheld from further use by setting a flag on each profile from the cruise. In other cases, individual profiles or measurements were found to cause these features and were flagged. 2.2.5. Representativeness of the data Another quality control issue is \( O_2 \) data representativeness. The general paucity of data forces the composting of all historical data to produce “climatological” fields. In a given one-degree square, there may be data from a month or season of one particular year, while in the same or a nearby square there may be data from an entirely different year. If there is large interannual variability in a region where scattered sampling in time has occurred, then one can expect the analysis to reflect this. Because the observations are scattered randomly with respect to time, except for a few limited areas, the results cannot, in a strict sense, be considered a true long-term climatological average. We present smoothed analyses of historical means, based (in certain areas) on relatively few observations. We believe, however, that useful information about the oceans can be gained through our procedures and that the large-scale features are representative of the real ocean. We believe that, if a hypothetical global synoptic set of ocean \( O_2 \) data existed and one were to smooth these data to the same degree as we have smoothed the historical means overall, the large-scale features would be similar to our results. Some differences would certainly occur because of interannual-to-decadal-scale variability. Basically, the \( O_2 \) data diminish in number with increasing depth. In the upper ocean, the all-data annual mean distributions are quite reasonable for defining large-scale features, but for the seasonal periods, the data base is inadequate in some regions. With respect to the deep ocean, in some areas the distribution of observations may be adequate for some diagnostic computations but inadequate for other purposes. If an isolated deep basin or some region of the deep ocean has only one observation, then no horizontal gradient computations are meaningful. However, useful information is provided by the observation in the computation of other quantities (e.g., a volumetric mean over a major ocean basin). 2.3 Calculation of AOU and \( O_2^S \) Apparent Oxygen Utilization (AOU, ml l\(^{-1}\)) and oxygen saturation (\( O_2^S \), %) were estimated when quality-controlled *in situ* \( O_2 \) (ml l\(^{-1}\)), temperature (T, °C), and salinity (S) were all measured at the same geographic location, time, and depth (pressure). We note that not all \( O_2 \) observations included simultaneous temperature and salinity measurements (see section 2.2.4). Thus, the total number of observations available for calculating AOU and \( O_2^S \) is slightly smaller in number than the available number of \( O_2 \) observations. AOU represents one estimate of the O₂ utilized due to biochemical processes relative to a preformed value. AOU (ml l⁻¹) was calculated as the difference between the O₂ gas solubility ([O₂*]) and the measured O₂ concentrations and expressed as, \[ \text{AOU} = [\text{O}_2^*] - [\text{O}_2] \] in which: [O₂*] is the O₂ solubility concentration (ml l⁻¹) calculated as a function of in situ temperature and salinity, and one atmosphere of total pressure. The [O₂*] values were calculated using the equation of Garcia and Gordon (1992) based on the [O₂*] values of Benson and Krause (1984); and[O₂] is the measured O₂ concentration (ml l⁻¹). Apparent Oxygen Utilization is an approximate measure of True Oxygen Utilization (TOU). The calculation of AOU assumes that the amount of O₂ used during local biochemical processes can be estimated by the difference in concentration between the observed O₂ and the preformed O₂ values. However, AOU is affected by processes other than biochemical processes such water mixing, departures of [O₂*] from instantaneous full equilibration with the atmosphere, bubble gas injection, skin temperature effects, and other factors (e.g., Broecker and Peng, 1982; Redfield et al., 1963; Garcia and Keeling, 2001; Ito, 2004). We assume that these processes are small in magnitude when compared to the amplitude of the climatological seasonal O₂ signal on basin-scales. The O₂ saturation (O₂^S, %) was estimated as 100% times the ratio of [O₂] to [O₂*], \[ O_2^S = 100\% \left( \frac{[\text{O}_2]}{[\text{O}_2^*]} \right) \] The calculated AOU and O₂^S values were processed following the same quality control methods outlined in section 2. Furthermore, if any of the O₂ (section 2) temperature (Locarnini et al., 2013), or salinity (Zweng et al., 2013) values were flagged during the quality control procedure, then AOU and O₂^S values were flagged also, and not used in the analysis. 3. DATA PROCESSING PROCEDURES 3.1. Vertical interpolation to standard levels Vertical interpolation of observed depth level data to standard depth levels followed procedures in JPOTS Editorial Panel (1991). These procedures are in part based on the work of Reiniger and Ross (1968). Four observed depth level values surrounding the standard depth level value were used, two values from above the standard level and two values from below the standard level. The pair of values furthest from the standard level is termed “exterior” points and the pair of values closest to the standard level are termed “interior” points. Paired parabolas were generated via Lagrangian interpolation. A reference curve was fitted to the four data points and used to define unacceptable interpolations caused by “overshooting” in the interpolation. When there were too few data points above or below the standard level to apply the Reiniger and Ross technique, we used a three-point Lagrangian interpolation. If three points were not available (either two above and one below or vice-versa), we used linear interpolation. In the event that an observation occurred exactly at the depth of a standard level, then a direct substitution was made. Table 4 provides the range of acceptable distances for which observed level data could be used for interpolation to a standard level. In WOA13, the number of standard levels used has increased from 33 to 102, allowing for analysis with greater vertical resolution. The method for interpolating data to standard levels remains the same as in previous analysis. 3.2. Methods of analysis 3.2.1. Overview An objective analysis scheme of the type described by Barnes (1964) was used to produce the fields shown in this atlas. This scheme had its origins in the work of Cressman (1959). In World Ocean Atlas 1994 (WOA94), the Barnes (1973) scheme was used. This required only one “correction” to the first-guess field at each grid point in comparison to the successive correction method of Cressman (1959) and Barnes (1964). This was to minimize computing time used in the processing. Barnes (1994) recommends a return to a multi-pass analysis when computing time is not an issue. Based on our own experience we agree with this assessment. The single pass analysis, used in WOA94, caused an artificial front in the Southeastern Pacific Ocean in a data sparse area (Anne Marie Treguier, personal communication). The analysis scheme used in generating WOA98, WOA01, WOA05, WOA13, and WOA13 analyses uses a three-pass “correction” which does not result in the creation of this artificial front. Inputs to the analysis scheme were one-degree square means of data values at standard levels (for time period and variable being analyzed), and a first-guess value for each square. For instance, one-degree square means for our annual analysis were computed using all available data regardless of date of observation. For July, we used all historical July data regardless of year of observation. Analysis was the same for all standard depth levels. Each one-degree latitude-longitude square value was defined as being representative of its square. The 360x180 gridpoints are located at the intersection of half-degree lines of latitude and longitude. An influence radius was then specified. At those grid points where there was an observed mean value, the difference between the mean and the first-guess field was computed. Next, a correction to the first-guess value at all gridpoints was computed as a distance-weighted mean of all gridpoint difference values that lie within the area around the gridpoint defined by the influence radius. Mathematically, the correction factor derived by Barnes (1964) is given by the expression: \[ C_{i,j} = \frac{\sum_{s=1}^{n} W_s Q_s}{\sum_{s=1}^{n} W_s} \] in which: (i,j) - coordinates of a gridpoint in the east-west and north-south directions respectively; \( C_{ij} \) - the correction factor at gridpoint coordinates (i,j); n - the number of observations that fall within the area around the point i,j defined by the influence radius; \( Q_s \) - the difference between the observed mean and the first-guess at the \( S^{th} \) point in the influence area; \[ W_s = e^{-\frac{Er^2}{R^2}} \quad \text{(for } r \leq R; \ W_s = 0 \text{ for } r > R); \] r - distance of the observation from the gridpoint; R - influence radius; E = 4. The derivation of the weight function, \( W_s \), will be presented in the following section. At each gridpoint we computed an analyzed value \( G_{i,j} \) as the sum of the first-guess, \( F_{i,j} \), and the correction \( C_{i,j} \). The expression for this is \[ G_{i,j} = F_{i,j} + C_{i,j} \] (2) If there were no data points within the area defined by the influence radius, then the correction was zero, the first-guess field was left unchanged, and the analyzed value was simply the first-guess value. This correction procedure was applied at all gridpoints to produce an analyzed field. The resulting field was first smoothed with a median filter (Tukey, 1974; Rabiner et al., 1975) and then smoothed with a five-point smoother of the type described by Shuman (1957) (hereafter referred as five-point Shuman smoother). The choice of first-guess fields is important and we discuss our procedures in section 3.2.5. The analysis scheme is set up so that the influence radius, and the number of five-point smoothing passes can be varied with each iteration. The strategy used is to begin the analysis with a large influence radius and decrease it with each iteration. This technique allows us to analyze progressively smaller scale phenomena with each iteration. The analysis scheme is based on the work of several researchers analyzing meteorological data. Bergthorsson and Doos (1955) computed corrections to a first-guess field using various techniques: one assumed that the difference between a first-guess value and an analyzed value at a gridpoint was the same as the difference between an observation and a first-guess value at a nearby observing station. All the observed differences in an area surrounding the gridpoint were then averaged and added to the gridpoint first-guess value to produce an analyzed value. Cressman (1959) applied a distance-related weight function to each observation used in the correction in order to give more weight to observations that occur closest to the gridpoint. In addition, Cressman introduced the method of performing several iterations of the analysis scheme using the analysis produced in each iteration as the first-guess field for the next iteration. He also suggested starting the analysis with a relatively large influence radius and decreasing it with successive iterations so as to analyze smaller scale phenomena with each pass. Sasaki (1960) introduced a weight function that was specifically related to the density of observations, and Barnes (1964, 1973) extended the work of Sasaki. The weight function of Barnes (1964) has been used here. The objective analysis scheme we used is in common use by the mesoscale meteorological community. Several studies of objective analysis techniques have been made. Achtemeier (1987) examined the “concept of varying influence radii for a successive corrections objective analysis scheme.” Seaman (1983) compared the “objective analysis accuracies of statistical interpolation and successive correction schemes.” Smith and Leslie (1984) performed an “error determination of a successive correction type objective analysis scheme.” Smith et al. (1986) made “a comparison of errors in objectively analyzed fields for uniform and non-uniform station distribution.” 3.2.2. Derivation of Barnes (1964) weight function The principle upon which the Barnes (1964) weight function is derived is that “the two-dimensional distribution of an atmospheric variable can be represented by the summation of an infinite number of independent harmonic waves, that is, by a Fourier integral representation”. If \( f(x,y) \) is the variable, then in polar coordinates \( (r,\theta) \), a smoothed or filtered function \( g(x,y) \) can be defined: \[ g(x, y) = \frac{1}{2\pi} \int_{0}^{2\pi} \int_{0}^{\infty} \eta f(x + r \cos \theta, y + r \sin \theta) \\ \quad d(\frac{r^2}{4K}) d\theta \] (3) in which \( r \) is the radial distance from a gridpoint whose coordinates are \( (x,y) \). The weight function is defined as \[ \eta = e^{-\frac{r^2}{4K}} \] (4) which resembles the Gaussian distribution. The shape of the weight function is determined by the value of \( K \), which relates to the distribution of data. The determination of \( K \) follows. The weight function has the property that \[ \frac{1}{2\pi} \int_{0}^{2\pi} \int_{0}^{\infty} \eta d\left( \frac{r^2}{4K} \right) d\theta = 1 \] (5) This property is desirable because in the continuous case (3) the application of the weight function to the distribution \( f(x,y) \) will not change the mean of the distribution. However, in the discrete case (1), we only sum the contributions to within the distance \( R \). This introduces an error in the evaluation of the filtered function, because the condition given by (5) does not apply. The error can be pre-determined and set to a reasonably small value in the following manner. If one carries out the integration in (5) with respect to \( \theta \), the remaining integral can be rewritten as \[ \int_{0}^{R} \eta d\left( \frac{r^2}{4K} \right) + \int_{R}^{\infty} \eta d\left( \frac{r^2}{4K} \right) = 1 \] (6) Defining the second integral as \( \varepsilon \) yields \[ \int_{0}^{R} e^{-\frac{r^2}{4K}} d\left( \frac{r^2}{4K} \right) = 1 - \varepsilon \] (7) Integrating (7), we obtain \[ \varepsilon = e^{-\frac{R^2}{4K}} \] (7a) Taking the natural logarithm of both sides of (7a) leads to an expression for \( K \), \[ K = R^2 / 4E \] (7b) where \( E \equiv -\ln \varepsilon \) Rewriting (4) using (7b) leads to the form of weight function used in the evaluation of (1). Thus, choice of \( E \) and the specification of \( R \) determine the shape of the weight function. Levitus (1982) chose \( E=4 \) which corresponds to a value of \( \varepsilon \) of approximately 0.02. This choice implies with respect to (7) the representation of more than 98 percent of the influence of any data around the gridpoint in the area defined by the influence radius \( R \). This analysis (WOA13) and previous analyses (WOA94, WOA98, WOA01, WOA05, WOA13) used \( E=4 \). Barnes (1964) proposed using this scheme in an iterative fashion similar to Cressman (1959). Levitus (1982) used a four-iteration scheme with a variable influence radius for each pass. WOA94 used a one-iteration scheme. WOA98, WOA01, WOA05, WOA13, and WOA13 employed a three-iteration scheme with a variable influence radius. 3.2.3. Derivation of Barnes (1964) response function It is desirable to know the response of a data set to the interpolation procedure applied to it. Following Barnes (1964) and reducing to one-dimensional case we let \[ f'(x) = A \sin(c x) \] (8) in which \( \alpha = 2\pi/\lambda \) with \( \lambda \) being the wavelength of a particular Fourier component, and substitute this function into equation (3) along with the expression for \( \eta \) in equation (4). Then \[ g(x) = D[A \sin(\alpha x)] = Df(x) \] (9) in which \( D \) is the response function for one application of the analysis and defined as \[ D = e^{-\left( \frac{\alpha R}{4} \right)^2} = e^{-\left( \frac{\pi R}{2\lambda} \right)^2} \] The phase of each Fourier component is not changed by the interpolation procedure. The results of an analysis pass are used as the first-guess for the next analysis pass in an iterative fashion. The relationship between the filtered function \( g(x) \) and the response function after \( N \) iterations as derived by Barnes (1964) is \[ g_N(x) = f(x) D \sum_{n=1}^N (1-D)^{n-1} \] (10) Equation (10) differs trivially from that given by Barnes. The difference is due to our first-guess field being defined as a zonal average, annual mean, seasonal mean, or monthly mean, whereas Barnes used the first application of the analysis as a first-guess. Barnes (1964) also showed that applying the analysis scheme in an iterative fashion will result in convergence of the analyzed field to the observed data field. However, it is not desirable to approach the observed data too closely, because at least seven or eight gridpoints are needed to represent a Fourier component. The response function given in (10) is useful in two ways: it is informative to know what Fourier components make up the analyses, and the computer programs used in generating the analyses can be checked for correctness by comparison with (10). 3.2.4. Choice of response function The distribution of O$_2$ observations (see appendices) at different depths and for the different averaging periods, are not regular in space or time. At one extreme, regions exist in which every one-degree square contains data and no interpolation needs to be performed. At the other extreme are regions in which few if any data exist. Thus, with variable data spacing the average separation distance between gridpoints containing data is a function of geographical position and averaging period. However, if we computed and used a different average separation distance for each variable at each depth and each averaging period, we would be generating analyses in which the wavelengths of observed phenomena might differ from one depth level to another and from one season to another. In WOA94, a fixed influence radius of 555 kilometers was used to allow uniformity in the analysis of all variables. For the present analyses (as well as for WOA09, WOA98, and WOA01), a three-pass analysis, based on Barnes (1964), with influence radii of 892, 669 and 446 km was used for the 1° analysis. Inspection of (1) shows that the difference between the analyzed field and the first-guess field values at any gridpoint is proportional to the sum of the weighted-differences between the observed mean and first-guess at all gridpoints containing data within the influence area. The reason for using the five-point Shuman smoother and the median smoother is that our data are not evenly distributed in space. As the analysis moves from regions containing data to regions devoid of data, small-scale discontinuities may develop. The five-point Shuman and median smoothers are used to eliminate these discontinuities. The five-point Shuman smoother does not affect the phase of the Fourier components that comprise an analyzed field. The response function for the analyses presented in the WOA13 series is given in Table 4 and in Figure 1. For comparison purposes, the response function used by Levitus (1982), WOA94, and others are also presented. The response function represents the smoothing inherent in the objective analysis described above plus the effects of one application of the five-point Shuman smoother and one application of a five-point median smoother. The effect of varying the amount of smoothing in North Atlantic sea surface temperature (SST) fields has been quantified by Levitus (1982) for a particular case. In a region of strong SST gradient such as the Gulf Stream, the effect of smoothing can easily be responsible for differences between analyses exceeding 1.0°C. To avoid the problem of the influence region extending across land or sills to adjacent basins, the objective analysis routine employs basin “identifiers” to preclude the use of data from adjacent basins. Table 5 lists these basins and the depth at which no exchange of information between basins is allowed during the objective analysis of data, i.e., “depths of mutual exclusion.” Some regions are nearly, but not completely, isolated topographically. Because some of these nearly isolated basins have water mass properties that are different from surrounding basins, we have chosen to treat these as isolated basins as well. Not all such basins have been identified because of the complicated structure of the sea floor. In Table 5, a region marked with an (*) can interact with adjacent basins except for special areas such as the Isthmus of Panama. 3.2.5. First-guess field determination There are gaps in the data coverage and, in some parts of the world ocean, there exist adjacent basins whose water mass properties are individually nearly homogeneous but have distinct basin-to basin differences. Spurious features can be created when an influence area extends over two basins of this nature (basins are listed in Table 5). Our choice of first-guess field attempts to minimize the creation of such features. To provide a first-guess field for the annual analysis at any standard level, we first zonally averaged the observed O_2 data in each one-degree latitude belt by individual ocean basins. The annual analysis was then used as the first-guess for each seasonal analysis and each seasonal analysis was used as a first-guess for the appropriate monthly analysis if computed. We then reanalyzed the O_2 data using the newly produced analyses as first-guess fields described as follows and as shown in Figure 2. A new annual mean was computed as the mean of the twelve monthly analyses for the upper 1500 m, and the mean of the four seasons below 1500 m depth for O_2, AOU, and O_2^S. The new annual mean for each variable was used as the first-guess field for new seasonal analyses. These new seasonal analyses in turn were used to produce new monthly analyses. This procedure produces slightly smoother means. More importantly we recognize that fairly large data-void regions exist, in some cases to such an extent that a seasonal or monthly analysis in these regions might not be realistic or meaningful. Geographic distribution of observations for the all-data annual periods (see appendices) is reasonable for upper layers of the ocean. By using an all-data annual mean, first-guess field regions where data exists for only one season or month will show no contribution to the annual cycle. By contrast, if we used a zonal average for each season or month, then, in those latitudes where gaps exist, the first-guess field would be heavily biased by the few data points that exist. If these were anomalous data in some way, an entire basin-wide belt might be affected. One advantage of producing “global” fields for a particular compositing period (even though some regions are data void) is that such analyses can be modified by investigators for use in modeling studies. For example, England (1992) noted that the temperature distribution produced by Levitus (1982) for the Antarctic is too high (due to a lack of winter data for the Southern Hemisphere) to allow for the formation of Antarctic Intermediate Water in an ocean general circulation model. By increasing the temperature of the “observed” field the model was able to produce this water mass. 3.3. Choice of objective analysis procedures Optimum interpolation (Gandin, 1963) has been used by some investigators to objectively analyze oceanographic data. We recognize the power of this technique but have not used it to produce analyzed fields. As described by Gandin (1963), optimum interpolation is used to analyze synoptic data using statistics based on historical data. In particular, second-order statistics such as correlation functions are used to estimate the distribution of first order parameters such as means. We attempt to map most fields in this atlas based on relatively sparse data sets. By necessity we must composite all data regardless of year of observation, to have enough data to produce a global, hemispheric, or regional analysis for a particular month, season, or even yearly. Because of the paucity of data, we prefer not to use an analysis scheme that is based on second order statistics. In addition, as Gandin has noted, there are two limiting cases associated with optimum interpolation. The first is when a data distribution is dense. In this case, the choice of interpolation scheme makes little difference. The second case is when data are sparse. In this case, an analysis scheme based on second order statistics is of questionable value. For additional information on objective analysis procedures see Thiebaux and Pedder (1987) and Daley (1991). 3.4. Choice of spatial grid The analyses that comprise WOA13 have been computed using the ETOPO2 land-sea topography to define ocean depths at each gridpoint (ETOPO2, 2006). From the ETOPO2 land mask, a quarter-degree land mask was created based on ocean bottom depth and land criteria. If sixteen or more 2-minute square values out of a possible forty-nine in a one-quarter-degree box were defined as land, then the quarter-degree gridbox was defined to be land. If no more than two of the 2-minute squares had the same depth value in a quarter-degree box, then the average value of the 2-minute ocean depths in that box was defined to be the depth of the quarter-degree gridbox. If ten or more 2-minute squares out of the forty-nine had a common bottom depth, then the depth of the quarter-degree box was set to the most common depth value. The same method was used to go from a quarter-degree to a one-degree resolution. In the one-degree resolution case, at least four points out of a possible sixteen (in a one-degree square) had to be land in order for the one-degree square to remain land, and three out of sixteen had to have the same depth for the ocean depth to be set. These criteria yielded a mask that was then modified by: 1. Connecting the Isthmus of Panama; 2. Maintaining an opening in the Straits of Gibraltar and in the English Channel; 3. Connecting the Kamchatka Peninsula and the Baja Peninsula to their respective continents. The one-degree mask was created from the quarter-degree mask instead of directly from ETOPO2 in order to maintain consistency between the quarter-degree and one-degree masks. 4. RESULTS The on-line figures for this atlas include seven types of horizontal maps representing annual, seasonal, and monthly spatial distribution of analyzed data and data statistics as a function of selected standard depth levels for dissolved O_2, AOU, and O_2 saturation over one-degree latitude-longitude grid: a) Objectively analyzed climatology fields. Grid boxes for which there were less than three values available in the objective analysis defined by the influence radius are denoted by a white “+” symbol. b) Statistical mean one-degree fields. Grid boxes for which there were less than three values available in the objective analysis defined by the influence radius are denoted by a white “+” symbol. c) Data distribution fields for the number of observations in each grid box used in the objective analysis binned into 1 to 2, 3-5, 6-10, 11-30, 31-50 and greater than 51 observations. d) Standard deviation fields binned into several ranges depending on the depth level. The maximum value of the standard deviation is shown on the map. e) Standard error of the mean fields binned into several ranges depending on the depth level. f) Difference between observed and analyzed fields binned into several ranges depending on the depth level. g) Difference between seasonal/monthly temperature fields and the annual mean field. h) The number of mean values within the radius of influence for each grid box was also calculated. This is not represented as stand-alone maps, but the results are used on a) and b) maps (see above) to mark the grid boxes with less than three mean values within the radius of influence. These calculations are available as data files. The maps are arranged by composite time periods (annual, seasonal, month) for O_2, AOU, and O_2^S, respectively. Table 5 describes all available O_2, AOU, and O_2^S maps and data fields. We note that the complete set of all climatological maps (in color), objectively analyzed fields, and associated statistical fields at all standard depth levels shown in Table 2, as well as the complete set of data fields and documentation, are available on-line. The complete set of data fields and documentation are available on-line as well. All of the figures use consistent symbols and notations for displaying information. Continents are displayed as light-grey areas. Coastal and open ocean areas shallower than the standard depth level being displayed are shown as solid gray areas. The objectively analyzed fields include the nominal contour interval used. In addition, these maps may include in some cases additional contour lines displayed as dashed black lines. All of the maps were computer drafted using Generic Mapping Tools (Wessel and Smith, 1998). We describe next the computation of annual and seasonal fields (section 4.1) and available objective and statistical fields (section 4.2). 4.1. Computation of annual and seasonal fields After completion of all of our analyses we define a final annual analysis as the average of our twelve monthly mean fields in the upper 1500 m of the ocean. Below 1500 m depth we define an annual analysis as the mean of the four seasonal analyses. Our final seasonal analyses are defined as the average of monthly analyses in the upper 1500 m of the ocean (see Figure 2). 4.2. Available objective and statistical fields Table 5 lists all objective and statistical fields calculated as part of WOA13. Climatologies of oceanographic variables and associated statistics described in this document, as well as global figures of same can be obtained on-line. The sample standard deviation in a gridbox was computed using: \[ s = \sqrt{\frac{\sum_{n=1}^{N} (x_n - \overline{x})^2}{N-1}} \] (11) in which \( x_n \)= the \( n^{th} \) data value in the gridbox, \( \overline{x} \)=mean of all data values in the gridbox, and \( N \)= total number of data values in the gridbox. The standard error of the mean was computed by dividing the standard deviation by the square root of the number of observations in each gridbox. In addition to statistical fields, the land/ocean bottom mask and basin definition mask are available on-line. A user could take the standard depth level data from WOD13 with flags and these masks, and recreate the WOA13 fields following the procedures outlined in this document. Explanations and data formats for the data files are found under documentation on the WOA13 webpage. 4.3. Obtaining WOA13 fields on-line The objective and statistical data fields can be obtained on-line in different digital formats at the WOA13 webpage. The WOA13 fields can be obtained in ASCII format (WOA native and comma separated value [CSV]) and Network Common Data Form (NetCDF) through our WOA13 webpage. For users interested in specific geographic areas, the World Ocean Atlas Select (WOAselect) selection tool can be used to designate a subset geographic area, depth, and oceanographic variable to view, and optionally download, climatological means or related statistics in shapefile format which is compatible with GIS software such as ESRI ArcMap. WOA13 includes a digital collection of "JPEG" images of the objective and statistical fields. In addition, WOA13 can be obtained in Ocean Data View (ODV) format. WOA13 will be available through other on-line locations as well. WOA98, WOA01, WOA05, and WOA09 are presently served through the IRI/LDEO Climate Data Library with access to statistical and objectively analyzed fields in a variety of digital formats. 5. SUMMARY In the preceding sections we have described the results of a project to objectively analyze all historical quality-controlled O$_2$ data in WOD13. We desire to build a set of climatological analyses that are identical in all respects for all variables in the WOA13 series including relatively data sparse variables such as nutrients (Garcia et al., 2010a). This provides investigators with a consistent set of analyses to work with. One advantage of the analysis techniques used in this atlas is that we know the amount of smoothing by objective analyses as given by the response function in Table 3 and Figure 1. We believe this to be an important function for constructing and describing a climatology of any parameter. Particularly when computing anomalies from a standard climatology, it is important that the data field be smoothed to the same extent as the climatology, to prevent generation of spurious anomalies simply through differences in smoothing. A second reason is that purely diagnostic computations require a minimum of seven or eight gridpoints to represent any Fourier component with statistical confidence. Higher order derivatives will require more smoothing. We have attempted to create objectively analyzed fields and data sets that can be used as a “black box.” We emphasize that some quality control procedures used are subjective. For those users who wish to make their own choices, all the data used in our analyses are available both at standard depth levels as well as observed depth levels. The results presented in this atlas show some features that are suspect and may be due to non-representative data that were not flagged by the quality control techniques used. Although we have attempted to eliminate as many of these features as possible by flagging the data which generate these features, some obviously could remain. Some may eventually turn out not to be artifacts but rather to represent real features, not yet capable of being described in a meaningful way due to lack of data. The views, findings, and any errors in this document are those of the authors. 6. FUTURE WORK Our analyses will be updated when justified by additional O$_2$ observations. As more data are received at NODC/WDC, we will also be able to produce improved higher resolution climatologies for O$_2$, AOU, and O$_2^S$. Additional O$_2$ data will likely improve the results. For example, analysis of O$_2$ data collected by the broad-scale global array of temperature/salinity profiling floats (ARGO) and gliders equipped with automated O$_2$ sensors will help provide additional observational constraints on observed interannual to decadal-scale changes in both physical and biochemical O$_2$ processes (e.g., Emerson et al., 2002; Körtzinger et al., 2004; Körtzinger et al., 2005, Garcia et al., 2005a,b; Garcia et al., 1998; Keeling and Garcia, 2002; Bindoff and McDougall, 2002; Deutsch et al., 2005; Stramma et al., 2008; Shaffer et al., 2009; Riebesell et al., 2009; Hofmann and Schellnhuber, 2009). We plan (1) to create climatological fields on a ¼° spatial resolution and (2) provide the O$_2$ and AOU fields in units on a per mass basis (i.e, micro-mole per kilogram). 7. REFERENCES Achtemeier, G. L., 1987. On the concept of varying influence radii for a successive corrections objective analysis. Mon. Wea. Rev., 11, 1761-1771. Antonov, J. I., R. A. 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Oceanographic Variable Depths for Annual Climatology Depths for Seasonal Climatology Depths for Monthly Climatology
O_2, AOU, and O_2^S 0-5500 m (102 levels) 0-1500 m (57 levels) 0-1500 m (57 levels)
Table 2. Acceptable distances (m) for defining interior (A) and exterior (B) values used in the Reiniger-Ross scheme for interpolating observed level data to standard levels.
Standard Level # Standard Depths (m) A B Standard Level # Standard Depths (m) A B
1050200521250200400
25502005313002001000
310502005413502001000
415502005514002001000
520502005614502001000
625502005715002001000
730502005815502001000
835502005916002001000
940502006016502001000
1045502006117002001000
1150502006217502001000
1255502006318002001000
1360502006418502001000
1465502006519002001000
1570502006619502001000
16755020067200010001000
17805020068210010001000
18855020069220010001000
19905020070230010001000
20955020071240010001000
211005020072250010001000
221255020073260010001000
231505020074270010001000
241755020075280010001000
252005020076290010001000
262255020077300010001000
Standard Level # Standard Depths (m) A B Standard Level # Standard Depths (m) A B
2725010020078310010001000
2827510020079320010001000
2930010020080330010001000
3032510020081340010001000
3135010020082350010001000
3237510020083360010001000
3340010020084370010001000
3442510020085380010001000
3545010020086390010001000
3647510020087400010001000
3750010040088410010001000
3855010040089420010001000
3960010040090430010001000
4065010040091440010001000
4170010040092450010001000
4275010040093460010001000
4380010040094470010001000
4485010040095480010001000
4590020040096490010001000
4695020040097500010001000
47100020040098510010001000
48105020040099520010001000
491100200400100530010001000
501150200400101540010001000
511200200400102550010001000
Table 3. Response function of the objective analysis scheme as a function of wavelength for WOA13 and earlier analyses. Response function is normalized to 1.0.
Wavelength* Levitus (1982) WOA94 WOA98, 01, 05, 09, 13
360\( \Delta X \)1.0000.9991.000
180\( \Delta X \)1.0000.9970.999
120\( \Delta X \)1.0000.9940.999
90\( \Delta X \)1.0000.9890.998
72\( \Delta X \)1.0000.9830.997
60\( \Delta X \)1.0000.9760.995
45\( \Delta X \)1.0000.9570.992
40\( \Delta X \)0.9990.9460.990
36\( \Delta X \)0.9990.9340.987
30\( \Delta X \)0.9960.9070.981
24\( \Delta X \)0.9830.8570.969
20\( \Delta X \)0.9550.8010.952
18\( \Delta X \)0.9230.7590.937
15\( \Delta X \)0.8280.6710.898
12\( \Delta X \)0.6260.5320.813
10\( \Delta X \)0.4170.3970.698
9\( \Delta X \)0.2990.3150.611
8\( \Delta X \)0.1860.2260.500
6\( \Delta X \)3.75x10^{-2}0.0590.229
5\( \Delta X \)1.34x10^{-2}0.0190.105
4\( \Delta X \)1.32x10^{-3}2.23x10^{-3}2.75x10^{-2}
3\( \Delta X \)2.51x10^{-3}1.90x10^{-4}5.41x10^{-3}
2\( \Delta X \)5.61x10^{-7}5.30x10^{-7}1.36x10^{-6}
*For \( \Delta X = 111 \) km, the meridional separation at the Equator. Table 4. Basins defined for objective analysis and the shallowest standard depth level for which each basin is defined.
# Basin Standard Depth Level # Basin Standard Depth Level
1Atlantic Ocean1*30North American Basin29
2Pacific Ocean1*31West European Basin29
3Indian Ocean1*32Southeast Indian Basin29
4Mediterranean Sea1*33Coral Sea29
5Baltic Sea134East Indian Basin29
6Black Sea135Central Indian Basin29
7Red Sea136Southwest Atlantic Basin29
8Persian Gulf137Southeast Atlantic Basin29
9Hudson Bay138Southeast Pacific Basin29
10Southern Ocean1*39Guatemala Basin29
11Arctic Ocean140East Caroline Basin30
12Sea of Japan141Marianas Basin30
13Kara Sea842Philippine Sea30
14Sulu Sea1043Arabian Sea30
15Baffin Bay1444Chile Basin30
16East Mediterranean1645Somali Basin30
17West Mediterranean1946Mascarene Basin30
18Sea of Okhotsk1947Crozet Basin30
19Banda Sea2348Guinea Basin30
20Caribbean Sea2349Brazil Basin31
21Andaman Basin2550Argentine Basin31
22North Caribbean2651Tasman Sea30
23Gulf of Mexico2652Atlantic Indian Basin31
24Beaufort Sea2853Caspian Sea1
25South China Sea2854Sulu Sea II14
26Barents Sea2855Venezuela Basin14
27Celebes Sea2556Bay of Bengal1*
28Aleutian Basin2857Java Sea6
29Fiji Basin2958East Indian Atlantic Basin32
*Basins marked with a “*” can interact with adjacent basins in the objective analysis. Table 5. Statistical fields calculated as part of WOA13 ("√" denotes field was calculated and is publicly available).
Statistical field One-degree Field Calculated Five-degree Statistics calculated
Objectively analyzed climatology √
Statistical mean √ √
Number of observations √ √
Seasonal (monthly) climatology minus annual climatology √
Standard deviation from statistical mean √ √
Standard error of the statistical mean √ √
Statistical mean minus objectively analyzed climatology √
Number of mean values within radius of influence √
Figure 1. Response function of the WOA13, WOA05, WOA01, WOA98, WOA94, and Levitus (1982) objective analysis schemes. ![Response function plot showing amplitude (%) vs wavelength (km) for various objective analysis schemes](page_370_312_1012_670.png) Zonal Mean ↓ Annual Mean (OA) ↓ Seasonal Mean (OA) Z ≤ 1500 m Z > 1500 m Monthly Mean (OA) Annual Mean Mean of 3 months Mean of 4 seasons Seasonal Mean Monthly Mean (OA) Mean of 12 months Mean of 4 Seasons Annual Mean Seasonal Mean Annual Mean Legend: First-guess field used to calculate mean field Mean of climatologies Final mean field OA - Objectively analyzed field Z - Depth Figure 2. Scheme used in computing annual, seasonal, and monthly objectively analyzed means for dissolved oxygen, Apparent Oxygen Utilization (AOU), and oxygen saturation (\( O_2^s \)).