NOAA Atlas NESDIS 84

WORLD ATLAS 2018 Volume 4: Dissolved Inorganic Nutrients (phosphate, nitrate and nitrate+nitrite, silicate)

Silver Spring, MD July 2019

U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Environmental Satellite, Data, and Information Service National Centers for Environmental Information

NOAA National Centers for Environmental Information

Additional copies of this publication, as well as information about NCEI data holdings and services, are available upon request directly from NCEI.

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This document should be cited as:

Garcia H.E., K.W. Weathers, C.R. Paver, I. Smolyar, T.P. Boyer, R.A. Locarnini, M.M. Zweng, A.V. Mishonov, O.K. Baranova, D. Seidov, and J.R. Reagan (2019). World Ocean Atlas 2018. Vol. 4: Dissolved Inorganic Nutrients (phosphate, nitrate and nitrate+nitrite, silicate). A. Mishonov Technical Editor, NOAA Atlas NESDIS 84, 35pp.

This document is available on-line at https://www.nodc.noaa.gov/OC5/woa18/pubwoa18.html

ii NOAA Atlas NESDIS 84

WORLD OCEAN ATLAS 2018 Volume 4: Dissolved Inorganic Nutrients (phosphate, nitrate and nitrate+nitrite, silicate)

Hernan E. Garcia, Katharine W. Weathers, Christopher R. Paver, Igor Smolyar, Timothy P. Boyer, Ricardo A. Locarnini, Melissa M. Zweng, Alexey V. Mishonov, Olga K. Baranova, Dan Seidov, James R. Reagan

Technical Editor: Alexey Mishonov

National Centers for Environmental Information (NCEI)

Silver Spring, Maryland July 2019

U.S. DEPARTMENT OF COMMERCE Wilbur L. Ross, Secretary

National Oceanic and Atmospheric Administration Neil Jacobs, Assistant Secretary of Commerce for Environmental Observation and Prediction, Acting Under Secretary of Commerce for and Atmosphere

National Environmental Satellite, Data, and Information Service Stephen Volz, Assistant Administrator

iii 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 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 , , oxygen, nutrients, and derived fields such as 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 ”. 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

iv Table of Contents

Table of Contents ...... 1 List of Figures ...... 2 List of Tables ...... 2 Preface ...... 4 Acknowledgments ...... 5 ABSTRACT ...... 6 1. INTRODUCTION ...... 6 2. DATA AND DATA DISTRIBUTION ...... 8 2.1. DATA SOURCES ...... 8 2.2. DATA QUALITY CONTROL ...... 8 2.2.1. Duplicate elimination ...... 9 2.2.2. Range and gradient checks ...... 9 2.2.3. Statistical checks ...... 9 2.2.4. Subjective flagging of data ...... 10 2.2.5. Representativeness of the data ...... 10 3. DATA PROCESSING PROCEDURES ...... 11 3.1. VERTICAL INTERPOLATION TO STANDARD LEVELS ...... 11 3.2. METHODS OF ANALYSIS ...... 11 3.3. CHOICE OF OBJECTIVE ANALYSIS PROCEDURES ...... 17 3.4. CHOICE OF SPATIAL GRID ...... 17 4. RESULTS ...... 17 4.1. COMPUTATION OF ANNUAL AND SEASONAL FIELDS ...... 18 4.2. AVAILABLE STATISTICAL FIELDS ...... 18 4.3. OBTAINING WOA18 FIELDS ON-LINE...... 19 5. SUMMARY ...... 19 6. FUTURE WORK ...... 20 7. REFERENCES ...... 21

1 List of Figures

Figure 1. Response function of the WOA18, WOA13, WOA05, WOA01, WOA98, WOA94, and Levitus (1982) objective analysis schemes...... 30 Figure 2. Scheme used in computing annual, seasonal, and monthly objectively analyzed means for phosphate, silicate, and nitrate...... 31

List of Tables

Table 1. Descriptions of for each nutrient variable in WOA18...... 25 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...... 25 Table 3. Response function of the objective analysis scheme as a function of wavelength for WOA18 and earlier analyses. Response function is normalized to 1.0...... 27 Table 4. Basins defined for objective analysis and the shallowest standard depth level for which each basin is defined...... 28 Table 5. Statistical fields calculated as part of WOA18 (“√“denotes field was calculated and is publicly available)...... 29 Table 6. Nominal depth average phosphate, nitrate+nitrite, and silicate (µmol/kg) differences (± 1 standard deviation) of the GLODAPv2 minus WOA18 for 1-degree objectively analyzed fields (60°N-60°S)...... 29

List of Acronyms

Acronym Expanded Term APB Autonomous Pinniped Bathythermograph BAMS Bulletin of the American Meteorological Society CSV Comma-Separated Value CTD Conductivity Temperature Depth DBT Drifting Bathythermograph DOC Department of Commerce DOE Department of Energy DRB Drifting Buoy ENSO El Niño-Southern Oscillation ERL Research Laboratory ETOPO2 Earth Topography 2 arc minute EVR Extended Vertical Resolution GIS Geographic Information System GLD Glider GMT Greenwich Mean Time, or Generic Mapping Tools GODAR Global Ocean Data Archaeology and Rescue GTSPP Global Temperature-Salinity Profile Program IAPSO International Association for the Physical Sciences of the Oceans IOC International Oceanographic Commission IODE International Oceanographic Data Exchange IRI International Research Institute for Climate and Society

2 Acronym Expanded Term JAMSTEC Japan Agency for Marine-Earth Science and Technology JPOTS Joint Panel on Oceanographic Tables and Standards LDEO Lamont-Doherty Earth Observatory MAST Marine Science and Technology MBT Mechanical Bathythermograph MEDAR Mediterranean Data Archeology and Rescue MRB Moored Buoy NAO North Atlantic Oscillation NASA National Aeronautics and Space Administration NATO North Atlantic Treaty Organization NCEI National Centers for Environmental Information NESDIS National Environmental Satellite, Data, and Information Service NOAA National Oceanic and Atmospheric Administration NODC National Ocean Data Center OCL Ocean Climate Laboratory ODV Ocean Data View PFL Profiling Float PIRATA Prediction and Research Moored Array in the Tropical Atlantic PSS Practical Salinity Scale RAMA Research Moored Array for African-Asian-Australian Monsoon Analysis and Prediction RDML Rear Admiral SST Surface Temperature SUR Surface TAO/TRITON Tropical Atmosphere Ocean moored buoy array TSK Tsurumi-Seiki Company UNESCO United Nations Educational, Scientific and Cultural Organization UOR Undulating Oceanographic Recorder USA United States of America USN United States Navy WDC World Data Center WOA World Ocean Atlas WOD World Ocean Database XBT Expendable Bathythermograph XCTD Expendable Conductivity Temperature Depth

3 Preface

The World Ocean Atlas 2018 (WOA18) is the latest in a line of oceanographic analyses of subsurface ocean variables at standard depths extending back to the groundbreaking Climatological Atlas of the World Ocean (Levitus, 1982). The WOA has been published semi- regularly since 1994, with versions in 1998, 2001, 2005, 2009, 2013, and now 2018. Previous iterations of the WOA have proven to be of great utility to the oceanographic, climate research, geophysical, and operational environmental forecasting communities. The oceanographic variable 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 , and for planning oceanographic expeditions among others.

WOA18 includes analyses on a one-degree grid for all variables and on a quarter-degree grid for temperature and salinity. Since WOA13, the ocean variable analyses are produces on 102 depth levels from the surface to 5,500 m (previously 33 levels within the same depth limits). Ocean data and analyses of 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.

A pre-release version of WOA18 was made available in September, 2018. The final version of WOA18 was released in July, 2019. In the interim community feedback and our own work has led to changes in the temperature atlas in particular. Animal mounted pinniped temperature profiles have been added as a data source improving coverage in some high latitude areas. A different Expendable Bathythermograph (XBT) correction (Cheng et al., 2014) has been employed. These changes are detailed below. Also, the XBTs were doubly corrected in the pre- release version. The Levitus correction was applied after another correction had been applied (Cheng et al., 2014). This error led to an ocean which was less than 0.1°C cooleer in the pre- release WOA18 as compared to the final WOA18 for the most affected decades (1975-84, 1985- 94, 1995-2004) in the upper 400m with smaller differences below. The 1981-2010 climate normal for temperature is slightly cooler (< 0.05°C) in the final WOA18 than in the pre-release WOA18 due to inadvertent double-weighting of the 2001-2010 decade in the pre-release version.

Ocean Climate Laboratory Team National Centers for Environmental Information Silver Spring, MD July 2019

4 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 (now the National Centers for Environmental Information – NCEI). 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 2018 and are distributed on- line by NCEI. 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). The WOD is a composite of publicly available ocean profile data, both historical and recent. 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 are working on a more substantive and formalized way to acknowledge all those who have collected and contributed to oceanographic measurements, which were used to calculate the fields in the WOA. Until we have such a system in place, we direct the reader’s attention to lists of primary investigators, institutions, and projects, which contributed data (codes can be used to locate data in the World Ocean Database). We also thank our colleagues at the NCEI. Their efforts have made this and similar works possible.

We dedicate this work to Carla Coleman who always contributed with a smile and was taken from us too soon.

5 WORLD OCEAN ATLAS 2018 Volume 4: Dissolved Inorganic Nutrients (phosphate, nitrate and nitrate+nitrite, and silicate)

ABSTRACT

This atlas consists of a description of data analysis procedures and horizontal maps of climatological distribution fields of dissolved inorganic nutrients (phosphate, nitrate and nitrate+nitrite, and silicate) 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 these nutrients. The oceanographic data fields used to generate these climatological maps were computed by objective analysis of all scientifically quality-controlled historical nutrient data in the World Ocean Database 2018. 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. We also provide estimates of the basin- scale uncertainty of the WOA18 nutrient objectively analyzed annual fields.

Climatologies in this atlas are defined as 1. INTRODUCTION mean oceanographic fields at selected The distribution and concentration of standard depth levels based on the objective dissolved inorganic nutrients in the world analysis of historical oceanographic profiles ocean is affected by biochemical (e.g., and select surface-only data. A profile is marine production, respiration, and defined as a set of measurements of samples oxidation or remineralization of labile collected at discrete depths taken as an dissolved and particulate organic matter) and instrument such as a rosette CTD package physical processes (e.g., water mass renewal, drops or rises vertically in the . advection, and mixing). By “nutrients” in This atlas includes an objective analysis of all this atlas, we mean chemically reactive scientifically quality-controlled historical dissolved inorganic nitrate or nitrate and nutrient measurements available in the World nitrite (N+N), ortho-phosphate or phosphate, Ocean Database 2018 (WOD18; Boyer et and ortho-silicic acid or silicate (expressed in al., 2019; Garcia et al., 2019c). We present units of micro-mole per kilogram, µmol kg- data analysis procedures and horizontal maps 1). showing annual, seasonal, and monthly This atlas is part of the World Ocean Atlas climatologies and related statistical fields at 2018 (WOA18) series. The WOA18 series selected standard depth levels between the includes analysis for dissolved inorganic surface and the ocean bottom to a maximum nutrients (this atlas), temperature (Locarnini depth of 5500 m. The complete set of maps, et al., 2019), salinity (Zweng et al., 2019), statistical and objectively analyzed data and dissolved oxygen (Garcia et al., 2019a, fields, and documentation are all available b). This atlas presents annual, seasonal, and on-line. monthly climatologies and related statistical All of the nutrient climatologies use all fields for dissolved inorganic nutrients. available quality control data regardless of

6 year of observation. Most of the data used in World Ocean Atlas 1994 series [WOA94, this atlas were collected after 1960. The Levitus et al., 1994; Levitus and Boyer, 1994 annual climatology was calculated using all a, b; Conkright et al., 1994]). WOA18 uses data regardless of the month in which the 102 standard depth levels. observation was made. Seasonal Objective analyses shown in this atlas are climatologies were calculated using only data constrained by the nature of the historical from the defined (regardless of year). nutrient data base (data are non-uniform in The are here defined as follows. space, time, and data quality), characteristics Winter is defined as the months of January, of the objective analysis techniques, and the February, and March. Spring is defined as grid used. These limitations and April, May, and June. Summer is defined as characteristics are discussed below. July, August, and September. Fall is defined as October, November, and December. Since the publication of WOA13, substantial Monthly climatologies were calculated using amounts of additional historical and modern data only from the given month regardless of nutrient data have become available. the day of the month in which the observation However, even with these additional data, we was made. are still hampered in a number of ways by a lack of oceanographic data and their quality. The dissolved inorganic nutrient data used in The overall precision and uncertainty in the this atlas are available from the National nutrient data have improved over time. Centers for Environmental Information Because of the lack of nutrient data coverage (NCEI) and World Data Service for in time and space, we are forced to examine (WDS-Oceanography). Large the annual cycle by compositing all data volumes of oceanographic data have been regardless of the year of observation. In acquired as a result of the fulfillment of some geographic areas, quality control is several data management projects including: made difficult by the limited number of a) the Intergovernmental Oceanographic nutrient data collected in these areas. Data Commission (IOC) Global may exist in an area for only one season, thus Oceanographic Data Archaeology and precluding any representative annual Rescue (GODAR) project (Levitus et analysis. In some areas there may be a al., 2005); reasonable spatial distribution of quality- controlled data points on which to base an b) the IOC World Ocean Database project analysis, but there may be only a few (WOD); (perhaps only one) data values in each one- c) the IOC Global Temperature Salinity degree latitude-longitude square. Profile project (GTSPP) (IOC, 1998). This atlas is divided into sections. We begin The WOD18 nutrient data used in the by describing the data sources and data WOA18 have been analyzed in a consistent, distribution (Section 2). Then we describe objective manner on a one-degree latitude- the general data processing procedures longitude grid at standard depth levels from (Section 3), the results (Section 4), summary the surface to a maximum depth of 5500m. (Section 5), and future work (Section 6). The procedures for “all-data” climatologies Global horizontal maps for the each of the are identical to those used in the World Ocean nutrients at each individual depth levels for Atlas 2013 (WOA13) series (Garcia et al., each time period are available on-line. 2013 a, b). Slightly different procedures were followed in earlier analyses (Levitus, 1982;

7 2. DATA AND DATA DISTRIBUTION presented the suggestions of the International Data sources and quality control procedures Association of are briefly described below. For further (IAPSO) as to which depths oceanographic information on the data sources used in measurements should be made or WOA18 refer to the World Ocean Database interpolated to for analysis. Historically the 2018 (WOD18, Boyer et al., 2019). The World Ocean Atlas used a modified version quality control procedures used in of the IAPSO standard depths. However, preparation of these analyses are described with the increased global coverage of high by Garcia et al. (2019a). depth resolution instrumentation, such as profiling floats, WOA has extended the 2.1. Data sources standard depth levels from 33 to 102. The new standard depth levels include the Historical oceanographic data used in this original depth levels presented up to atlas were obtained from the NCEI/WDS- WOA09, but have tripled the resolution in the Oceanography archives and include all data upper 100 meters, more than doubled the gathered as a result of the GODAR and WOD depth resolution of the upper 1000 meters, projects. The nutrient data used in this atlas and almost three and a half the were typically obtained by means of analysis resolution for overall depth levels. For many of serial (discrete) samples using manual or purposes, including preparation of the continuous flow analysis photometric present climatologies, observed level data are methods. We refer to the discrete water interpolated to standard depth levels if sample dataset in WOD18 as Ocean Station observations did not occur at the desired Data (OSD). Typically, each profile in the standard depths (see section 3.1 for details). OSD dataset consists of 1 to 36 water samples The levels at which the nutrient climatologies collected at various depths between the were calculated are given in Table 1. Table 2 surface and the ocean bottom using Nansen shows the depths of each standard depth or Niskin samplers. Garcia et al. (2018a, c) level. Section 3.1 discusses the vertical describes the quality control procedures used interpolation procedures used in our work. in preparation of these analyses. To understand the procedures for taking 2.2. Data quality control individual oceanographic observations and Quality control of the nutrient data is a major constructing climatological fields, definition task, the difficulty of which is directly related of the terms “standard level data” and to lack of data and metadata (for some areas) “observed level data” are necessary. We upon which to base statistical checks. refer to the actual measured value of an Consequently we applied certain empirical oceanographic variable in situ (Latin for in criteria (see sections 2.2.1 through 2.2.4), and place) as an “observation”, and to the depth as part of the last processing step, subjective at which such a measurement was made as judgment was used (see sections 2.2.5 and the “observed level depth”. We refer to such 2.2.6). Individual data, and in some cases data as “observed level data”. Before the entire profiles or all profiles for individual development of oceanographic cruises, have been flagged and not used instrumentation that measure at high because these data produced features that frequencies along the vertical profile, were subjectively judged to be oceanographers often attempted to make non-representative or questionable. As part measurements at selected “standard levels” in of our work, we have made available WOD18 the water column. Sverdrup et al. (1942) which contains both observed levels profile

8 data and standard depth level profile data identifying stations with exact with various quality control flags applied. position/date/time and data values; the next The flags mark individual nutrient checks involve offsets in position/date/time. measurements or entire profiles which were Profiles identified as duplicates in the checks not used in the next step of the procedure, with a large offset were individually verified either interpolation to standard depth levels to ensure they were indeed duplicate profiles. for observed level data or calculation of In summary, we eliminated all but one profile statistical means in the case of standard depth from each set of replicate profiles at the first level data. step of our data processing. Our knowledge of the variability of the world 2.2.2. Range and gradient checks ocean based on the instrumental record now includes a greater appreciation and Range checking (i.e., checking whether understanding of the ubiquity of eddies, individual nutrient concentration values are rings, and lenses in some parts of the world within preset minimum and maximum values ocean as well as inter-annual and inter- as a function of depth and ocean region) was decadal variability of water mass properties performed on all data values as a first quality associated with modal variability of the control check to flag and withhold from atmosphere such as the North Atlantic further use the relatively few values that were Oscillation, Pacific Decadal Oscillation, and grossly outside expected oceanic El Niño Southern Ocean Oscillation. concentration ranges. Range checks were Therefore, we have simply added quality prepared for individual oceanic regions. A control flags to the nutrient data, not check as to whether excessive vertical eliminating them from the WOD18. In gradients occur in the data has been addition, some data values include the performed for each nutrient variable in originator’s quality flags (e.g., World Ocean WOD18 both in terms of positive and Circulation Experiment, CLIVAR repeat negative gradients. We flagged and not used ). Thus, individual investigators values that exceeded these gradients. Garcia can make their own decision regarding the et al. (2018 a,c) detail the quality control representativeness of the data. Investigators procedures. studying the distribution of features such as 2.2.3. Statistical checks eddies will be interested in those data that we may regard as unrepresentative for the Statistical checks were performed as follows. preparation of the analyses shown in this All data for each nutrient variable atlas. (irrespective of year), at each standard depth level, were averaged within five-degree 2.2.1. Duplicate elimination latitude-longitude squares to produce a Because data are received from many record of the number of observations, mean, sources, sometimes the same data set is and standard deviation in each square. received at NODC/WDC more than once but Statistics were computed for the annual, with slightly different time and/or position seasonal, and monthly compositing periods. and/or data values, and hence are not easily Below 50 m depth, if data were more than identified as duplicate stations. Therefore, to three standard deviations from the mean, the eliminate the repetitive data values our data were flagged and withheld from further databases were checked for the presence of use in objective analyses. Above 50 m depth, exact and near exact replicates using eight a five-standard-deviation criterion was used different criteria. The first checks involve in five-degree squares that contained any

9 land area. In selected five-degree squares that five-degree-square statistics were computed are close to land areas, a four-standard- from this preliminary data set and used with deviation check was used. In all other squares the same statistical check to produce a new, a three-standard-deviation criterion was used “clean” data set. The reason for applying the for the 0-50 m depth layer. For standard statistical check twice was to flag (and depth levels situated directly above the ocean withhold from further use), in the first round, bottom, a four-standard-deviation criterion any grossly erroneous or non-representative was used. data from the data set that would artificially increase the variances. The second check is The reason for the relatively weaker standard then more effective in identifying smaller, deviation criterion in coastal and near-coastal but non-representative, observations. regions is the exceptionally large variability in the coastal five-degree square statistics for 2.2.4. Subjective flagging of data some variables. Frequency distributions of The nutrient data were averaged by one- some variables in some coastal regions are degree squares for input to the objective observed to be skewed or bimodal. Thus to analysis program. After initial objective avoid flagging possibly good data in highly analyses were computed, the input set of one- variable environments, the standard deviation degree means still contained questionable criteria were broadened. data contributing to unrealistic distributions, For each nutrient variable, the total number yielding intense bull's-eyes or spatial of measurements in each profile, as well as gradients. Examination of these features the total number of nutrient observations indicated that some of them were due to exceeding the standard deviation criterion, profiles from particular oceanographic were recorded. If more than two nutrient cruises. In such cases, data from an entire observations in a profile were found to cruise were flagged and withheld from exceed the standard deviation criterion, then further use by setting a flag on each profile the entire profile was flagged. This check was from the cruise. In other cases, individual imposed after tests indicated that surface data profiles or measurements were found to from particular casts (which upon inspection cause these features and were flagged. appeared to be erroneous) were being flagged but deeper data were not. Other situations 2.2.5. Representativeness of the data were found where erroneous nutrient data Another quality control issue is nutrient data from the deeper portion of a cast were representativeness. The general paucity of flagged, while near-surface data from the data forces the compositing of all historical same cast were not flagged because of larger nutrient data to produce “climatological” natural variability in surface layers. One fields. In a given one-degree square, there reason for this was the decrease of the may be data from a month or season of one number of nutrient observations with depth particular year, while in the same or a nearby and the resulting change in sample statistics. square there may be data from an entirely The standard-deviation check was applied different year. If there is large interannual twice to the data set for each compositing variability in a region where scattered period. sampling in time has occurred, then one can In summary, first the five-degree square expect the analysis to reflect this. Because the statistics were computed, and the data observations are scattered randomly with flagging procedure described above was used respect to time, except for a few limited areas to provide a preliminary data set. Next, new (i.e., time series stations such as Hawaii

10 Ocean Time Series, Bermuda Atlantic Time data to standard depth levels followed Series, CARIACO), the results cannot, in a procedures in JPOTS Editorial Panel (1991). strict sense, be considered a true long-term These procedures are in part based on the climatological average. work of Reiniger and Ross (1968). Four We present smoothed analyses of historical observed depth level values surrounding the means, based (in certain areas) on relatively standard depth level value were used, two few observations. We believe, however, that values from above the standard level and two useful information about the oceans can be values from below the standard level. The gained through our procedures and that the pair of values furthest from the standard level large-scale features are representative of the is termed “exterior” points and the pair of real ocean. We believe that, if a hypothetical values closest to the standard level are termed global synoptic set of ocean data “interior” points. Paired parabolas were (temperature, salinity, dissolved oxygen, generated via Lagrangian interpolation. A nutrients, etc) existed and one were to smooth reference curve was fitted to the four data these data to the same degree as we have points and used to define unacceptable smoothed the historical means overall, the interpolations caused by “overshooting” in large-scale features would be similar to our the interpolation. When there were too few results. Some differences would certainly data points above or below the standard level occur because of interannual-to-decadal- to apply the Reiniger and Ross technique, we scale variability. used a three-point Lagrangian interpolation. If three points were not available (either two The nutrient observations diminish in number above and one below or vice-versa), we used with increasing depth. In the upper ocean, the linear interpolation. In the event that an all-data annual mean distributions are observation occurred exactly at the depth of a reasonable for representing large-scale standard level, then a direct substitution was features, but for the seasonal and monthly made. Table 2 provides the range of periods, the data base is inadequate in some acceptable distances for which observed level regions. With respect to the deep ocean, in data could be used for interpolation to a some areas the distribution of observations standard level. may be adequate for some diagnostic computations but inadequate for other 3.2. Methods of analysis purposes. If an isolated deep basin or some region of the deep ocean has only one 3.2.1. Overview observation, then no horizontal gradient An objective analysis scheme of the type computations are meaningful. However, described by Barnes (1964) was used to useful information is provided by the produce the fields shown in this atlas. This observation in the computation of other scheme had its origins in the work of quantities (e.g., a volumetric mean over a Cressman (1959). In World Ocean Atlas major ocean basin). 1994 (WOA94), the Barnes (1973) scheme was used. This required only one “correction” to the first-guess field at each 3. DATA PROCESSING PROCEDURES grid point in comparison to the successive correction method of Cressman (1959) and 3.1. Vertical interpolation to standard Barnes (1964). This was to minimize levels computing time used in the processing. Vertical interpolation of observed depth level Barnes (1994) recommends a return to a multi-pass analysis when computing time is

11 not an issue. Based on our own experience west and north-south directions we agree with this assessment. The single respectively; pass analysis, used in WOA94, caused an Ci,j - the correction factor at gridpoint artificial front in the Southeastern Pacific coordinates (i,j); Ocean in a data sparse area (Anne Marie Treguier, personal communication). The n - the number of observations that fall analysis scheme used in generating WOA98, within the area around the point i,j WOA01, WOA05, WOA13, and WOA18 defined by the influence radius; analyses uses a three-pass “correction” which Qs - the difference between the observed does not result in the creation of this artificial mean and the first-guess at the Sth point front. in the influence area;

Inputs to the analysis scheme were one- Er 2 − degree square means of data values at 2 W = e R (for r ≤ R; Ws =0 for r > R); standard levels (for time period and variable s being analyzed), and a first-guess value for r - distance of the observation from the each square. For instance, one-degree square gridpoint; means for our annual analysis were computed R - influence radius; using all available data regardless of date of observation. For July, we used all historical E = 4.

July data regardless of year of observation. The derivation of the weight function, Ws, Analysis was the same for all standard depth will be presented in the following section. At levels. Each one-degree latitude-longitude each gridpoint we computed an analyzed square value was defined as being value Gi,j as the sum of the first-guess, Fi,j , representative of its square. The 360x180 and the correction Ci,j. The expression for gridpoints are located at the intersection of this is half-degree lines of latitude and longitude. G = F + C (2) An influence radius was then specified. At i, j i, j i, j those grid points where there was an If there were no data points within the area observed mean value, the difference between defined by the influence radius, then the the mean and the first-guess field was correction was zero, the first-guess field was computed. Next, a correction to the first- left unchanged, and the analyzed value was guess value at all gridpoints was computed as simply the first-guess value. This correction a distance-weighted mean of all gridpoint procedure was applied at all gridpoints to difference values that lie within the area produce an analyzed field. The resulting field around the gridpoint defined by the influence was first smoothed with a median filter radius. Mathematically, the correction factor (Tukey, 1974; Rabiner et al., 1975) and then derived by Barnes (1964) is given by the smoothed with a five-point smoother of the expression: type described by Shuman (1957) (hereafter n referred as five-point Shuman smoother). ∑WsQs The choice of first-guess fields is important = s=1 (1) Ci, j n and we discuss our procedures in section 3.2.5. ∑Ws s=1 The analysis scheme is set up so that the in which: influence radius, and the number of five- (i,j) - coordinates of a gridpoint in the east- point smoothing passes can be varied with

12 each iteration. The strategy used is to begin schemes.” Smith and Leslie (1984) the analysis with a large influence radius and performed an “error determination of a decrease it with each iteration. This technique successive correction type objective analysis allows us to analyze progressively smaller scheme.” Smith et al. (1986) made “a scale phenomena with each iteration. comparison of errors in objectively analyzed fields for uniform and non-uniform station The analysis scheme is based on the work of distribution.” several researchers analyzing meteorological data. Bergthorsson and Doos (1955) 3.2.2. Derivation of Barnes (1964) weight computed corrections to a first-guess field function using various techniques: one assumed that the difference between a first-guess value and The principle upon which the Barnes (1964) an analyzed value at a gridpoint was the same weight function is derived is that “the two- as the difference between an observation and dimensional distribution of an atmospheric a first-guess value at a nearby observing variable can be represented by the summation station. All the observed differences in an of an infinite number of independent area surrounding the gridpoint were then harmonic waves, that is, by a Fourier integral averaged and added to the gridpoint first- representation”. If f(x,y) is the variable, then guess value to produce an analyzed value. in polar coordinates (r,θ), a smoothed or Cressman (1959) applied a distance-related filtered function g(x,y) can be defined: weight function to each observation used in π ∞ 1 2 the correction in order to give more weight to g(x, y) = ∫ ∫ηf (x + r cosθ , y + r sinθ ) observations that occur closest to the 2π 0 0 (3) gridpoint. In addition, Cressman introduced r2 the method of performing several iterations d( )dθ of the analysis scheme using the analysis 4K produced in each iteration as the first-guess in which r is the radial distance from a field for the next iteration. He also suggested gridpoint whose coordinates are (x,y). The starting the analysis with a relatively large weight function is defined as influence radius and decreasing it with r 2 successive iterations so as to analyze smaller − scale phenomena with each pass. η = e 4K (4) Sasaki (1960) introduced a weight function which resembles the Gaussian distribution. that was specifically related to the density of The shape of the weight function is observations, and Barnes (1964, 1973) determined by the value of K, which relates extended the work of Sasaki. The weight to the distribution of data. The determination function of Barnes (1964) has been used here. of K follows. The weight function has the The objective analysis scheme we used is in property that common use by the mesoscale 2π ∞  2  meteorological community. Several studies 1  r  of objective analysis techniques have been ηd dθ =1 (5) 2π ∫ ∫  4K  made. Achtemeier (1987) examined the 0 0   “concept of varying influence radii for a This property is desirable because in the successive corrections objective analysis continuous case (3) the application of the scheme.” Seaman (1983) compared the weight function to the distribution f(x,y) will “objective analysis accuracies of statistical not change the mean of the distribution. interpolation and successive correction

13 However, in the discrete case (1), we only each pass. WOA94 used a one-iteration sum the contributions to within the distance scheme. WOA98, WOA01, WOA05, R. This introduces an error in the evaluation WOA09, WOA13, and WOA18 employed a of the filtered function, because the condition three-iteration scheme with a variable given by (5) does not apply. The error can be influence radius. pre-determined and set to a reasonably small value in the following manner. If one carries 3.2.3. Derivation of Barnes (1964) response out the integration in (5) with respect to θ, the function remaining integral can be rewritten as It is desirable to know the response of a data R ∞ set to the interpolation procedure applied to  r 2   r 2  ηd  + ηd  = 1 (6) it. Following Barnes (1964) and reducing to ∫  4K  ∫  4K  one-dimensional case we let 0   R   f (x) = Asin(αx) (8) Defining the second integral as ε yields

2 in which α = 2π/λ with λ being the R r −  r2  wavelength of a particular Fourier e 4K d  =1− ε (7) ∫  4K  component, and substitute this function into 0   equation (3) along with the expression for η Integrating (7), we obtain in equation (4). Then

2 g(x) = D[Asin(αx)]= Df (x) (9) R − ε = e 4K (7a) in which D is the response function for one application of the analysis and defined as Taking the natural logarithm of both sides of 2 αR   πR 2 (7a) leads to an expression for K, −  −   4   2λ  K = R 2 / 4E (7b) D = e = e where E ≡ -ln ε The phase of each Fourier component is not changed by the interpolation procedure. The Rewriting (4) using (7b) leads to the form of results of an analysis pass are used as the weight function used in the evaluation of (1). first-guess for the next analysis pass in an Thus, choice of E and the specification of R iterative fashion. The relationship between determine the shape of the weight function. the filtered function g(x) and the response Levitus (1982) chose E=4 which corresponds function after N iterations as derived by to a value of ε of approximately 0.02. This Barnes (1964) is choice implies with respect to (7) the N representation of more than 98 percent of the n−1 gN (x) = f (x)D∑(1− D) (10) influence of any data around the gridpoint in n=1 the area defined by the influence radius R. Equation (10) differs trivially from that given This analysis (WOA18) and previous by Barnes. The difference is due to our first- analyses (WOA94, WOA98, WOA01, guess field being defined as a zonal average, WOA05, WOA13) used E=4. annual mean, seasonal mean, or monthly Barnes (1964) proposed using this scheme in mean, whereas Barnes used the first an iterative fashion similar to Cressman application of the analysis as a first-guess. (1959). Levitus (1982) used a four-iteration Barnes (1964) also showed that applying the scheme with a variable influence radius for analysis scheme in an iterative fashion will

14 result in convergence of the analyzed field to gridpoints containing data within the the observed data field. However, it is not influence area. desirable to approach the observed data too The reason for using the five-point Shuman closely, because at least seven or eight smoother and the median smoother is that our gridpoints are needed to represent a Fourier data are not evenly distributed in space. As component. the analysis moves from regions containing The response function given in (10) is useful data to regions devoid of data, small-scale in two ways: it is informative to know what discontinuities may develop. The five-point Fourier components make up the analyses, Shuman and median smoothers are used to and the computer programs used in eliminate these discontinuities. The five- generating the analyses can be checked for point Shuman smoother does not affect the correctness by comparison with (10). phase of the Fourier components that comprise an analyzed field. 3.2.4. Choice of response function The response function for the analyses The distribution of O2 observations (see presented in the WOA18 series is given in appendices) at different depths and for the Table 4 and in Figure 1. For comparison different averaging periods, are not regular in purposes, the response function used by space or time. At one extreme, regions exist Levitus (1982), WOA94, and others are also in which every one-degree square contains presented. The response function represents data and no interpolation needs to be the smoothing inherent in the objective performed. At the other extreme are regions analysis described above plus the effects of in which few if any data exist. Thus, with one application of the five-point Shuman variable data spacing the average separation smoother and one application of a five-point distance between gridpoints containing data median smoother. The effect of varying the is a function of geographical position and amount of smoothing in North Atlantic sea averaging period. However, if we computed surface temperature (SST) fields has been and used a different average separation quantified by Levitus (1982) for a particular distance for each variable at each depth and case. In a region of strong SST gradient such each averaging period, we would be as the , the effect of smoothing generating analyses in which the wavelengths can easily be responsible for differences of observed phenomena might differ from between analyses exceeding 1.0°C. one depth level to another and from one To avoid the problem of the influence region season to another. In WOA94, a fixed extending across land or sills to adjacent influence radius of 555 kilometers was used basins, the objective analysis routine to allow uniformity in the analysis of all employs basin “identifiers” to preclude the variables. For the present analyses (as well as use of data from adjacent basins. Table 5 lists for WOA13, WOA09, WOA98, and these basins and the depth at which no WOA01), a three-pass analysis, based on exchange of information between basins is Barnes (1964), with influence radii of 892, allowed during the objective analysis of data, 669 and 446 km was used for the 1° analysis. i.e., “depths of mutual exclusion.” Some Inspection of (1) shows that the difference regions are nearly, but not completely, between the analyzed field and the first-guess isolated topographically. Because some of field values at any gridpoint is proportional to these nearly isolated basins have water mass the sum of the weighted-differences between properties that are different from surrounding the observed mean and first-guess at all basins, we have chosen to treat these as

15 isolated basins as well. Not all such basins These time-indeterminant monthly mean have been identified because of the objectively analyzed temperature fields were complicated structure of the sea floor. In used as the first-guess fields for each Table 5, a region marked with an (*) can “decadal” monthly climatology. Likewise, interact with adjacent basins except for time-indeterminant seasonal and annual special areas such as the Isthmus of Panama. climatologies were used as first-guess fields for the seasonal and annual decadal 3.2.5. First-guess field determination climatologies. There are gaps in the data coverage and, in We recognize that fairly large data-void some parts of the world ocean, there exist regions exist, in some cases to such an extent adjacent basins whose water mass properties that a seasonal or monthly analysis in these are individually nearly homogeneous but regions is not meaningful. Geographic have distinct basin-to basin differences. distribution of observations for the “all-data” Spurious features can be created when an annual periods (see appendices) is excellent influence area extends over two basins of this for the upper layers of the ocean. By using an nature (basins are listed in Table 6). Our “all-data” annual mean, first-guess field choice of first-guess field attempts to regions where data exist for only one season minimize the creation of such features. To or month will show no contribution to the maximize data coverage and best represent annual cycle. By contrast, if we used a zonal global variability, a set of “time- average for each season or month, then, in indeterminant” climatologies were produced those latitudes where gaps exist, the first- as a first-guess for each set of decadal guess field would be heavily biased by the climatologies. The time-indeterminant few data points that exist. If these were climatologies used the first-guess field anomalous data in some way, an entire basin- procedures developed for earlier versions of wide belt might be affected. WOA: To provide a first-guess field for the One advantage of producing “global” fields “all-data” annual analysis at any standard for a particular compositing period (even level, we first zonally averaged the observed though some regions are data void) is that temperature data in each one-degree latitude such analyses can be modified by belt by individual ocean basins. The annual investigators for use in modeling studies. analysis was then used as the first-guess for each seasonal analysis and each seasonal For the time-indeterminant quarter-degree analysis was used as a first-guess for the first-guess field, the one-degree time- appropriate monthly analysis if computed. indeterminant field was also used. Each of the sixteen quarter-degree boxes enclosed We then reanalyzed the temperature data used the one-degree time-indeterminant using the newly produced analyses as first- value as a first-guess, thereby projecting the guess fields described as follows and as one-degree climatology onto the quarter- shown in Figure 3. A new annual mean was degree grid. In those areas where there was computed as the mean of the twelve monthly no one-degree value due to land or bottom analyses for the upper 1500 m, and the mean mask, the statistical mean for the entire basin of the four seasons below 1500 m depth. This at the given depth was used. This first-guess new annual mean was used as the first-guess field was then used to calculate time- field for new seasonal analyses. These new indeterminant quarter-degree field. The time seasonal analyses in turn were used to indeterminant quarter-degree field was then produce new monthly analyses. This procedure produces slightly smoother means.

16 used for each quarter-degree decadal depth and land criteria. If sixteen or more 2- climatological mean. minute square values out of a possible forty- nine in a one-quarter-degree box were 3.3. Choice of objective analysis defined as land, then the quarter-degree procedures gridbox was defined to be land. If no more Optimum interpolation (Gandin, 1963) has than two of the 2-minute squares had the been used by some investigators to same depth value in a quarter-degree box, objectively analyze oceanographic data. We then the average value of the 2-minute ocean recognize the power of this technique but depths in that box was defined to be the depth have not used it to produce analyzed fields. of the quarter-degree gridbox. If ten or more As described by Gandin (1963), optimum 2-minute squares out of the forty-nine had a interpolation is used to analyze synoptic data common bottom depth, then the depth of the using statistics based on historical data. In quarter-degree box was set to the most particular, second-order statistics such as common depth value. The same method was correlation functions are used to estimate the used to go from a quarter-degree to a one- distribution of first order parameters such as degree resolution. In the one-degree means. We attempt to map most fields in this resolution case, at least four points out of a atlas based on relatively sparse data sets. By possible sixteen (in a one-degree square) had necessity we must composite all data to be land in order for the one-degree square regardless of year of observation, to have to remain land and three out of sixteen had to enough data to produce a global, have the same depth for the ocean depth to be hemispheric, or regional analysis for a set. These criteria yielded a mask that was particular month, season, or even yearly. then modified by: Because of the paucity of data, we prefer not 1. Connecting the Isthmus of Panama; to use an analysis scheme that is based on 2. Maintaining an opening in the Straits second order statistics. In addition, as of Gibraltar and in the English Gandin has noted, there are two limiting Channel; cases associated with optimum interpolation. 3. Connecting the Kamchatka Peninsula The first is when a data distribution is dense. and the Baja Peninsula to their In this case, the choice of interpolation respective continents. scheme makes little difference. The second case is when data are sparse. In this case, an The one-degree mask was created from the analysis scheme based on second order quarter-degree mask instead of directly from statistics is of questionable value. For ETOPO2 in order to maintain consistency additional information on objective analysis between the quarter-degree and one-degree procedures see Thiebaux and Pedder (1987) masks. and Daley (1991). 3.4. Choice of spatial grid The analyses that comprise WOA18 have 4. RESULTS been computed using the ETOPO2 (Earth Topography 2 arc minute) land-sea The on-line figures for this atlas include topography to define ocean depths at each seven types of horizontal maps representing gridpoint (ETOPO2, 2006). From the annual, seasonal, and monthly spatial ETOPO2 land mask, a quarter-degree land distribution of analyzed data and data mask was created based on ocean bottom statistics as a function of selected standard

17 depth levels for dissolved inorganic nutrients climatological maps (in color), objectively over one-degree latitude-longitude grid: analyzed fields, and associated statistical fields at all standard depth levels shown in a) Objectively analyzed climatology fields. Table 2, as well as the complete set of data Grid boxes for which there were less than fields and documentation, are available on- three values available in the objective line. The complete set of data fields and analysis defined by the influence radius documentation are available on-line as well. are denoted by a white “+” symbol. All of the figures use consistent symbols and b) Statistical mean fields. Grid boxes for notations for displaying information. which there were less than three values Continents are displayed as light-grey areas. available in the objective analysis defined Coastal and open ocean areas shallower than by the influence radius are denoted by a the standard depth level being displayed are white “+” symbol. shown as solid gray areas. The objectively c) Data distribution fields for the number of analyzed fields include the nominal contour observations in each grid box used in the interval used. In addition, these maps may objective analysis binned into 1 to 2, 3-5, include in some cases additional contour 6-10, 11-30, 31-50 and greater than 51 lines displayed as dashed black lines. All of observations. the maps were computer drafted using d) Standard deviation fields binned into Generic Mapping Tools (Wessel and Smith, several ranges depending on the depth 1998). level. The maximum value of the We describe next the computation of annual standard deviation is shown on the map. and seasonal fields (section 4.1) and available e) Standard error of the mean fields binned objective and statistical fields (section 4.2). into several ranges depending on the depth level. 4.1. Computation of annual and seasonal fields f) Difference between observed and After completion of all of our analyses we analyzed fields binned into several ranges define a final annual analysis as the average depending on the depth level. of our twelve monthly mean nutrient fields in g) Difference between seasonal/monthly the upper 800 m of the ocean (Figure 2). Our temperature fields and the annual mean final seasonal analysis is defined as the field. average of monthly analyses in the upper 800 h) The number of mean values within the m of the ocean. radius of influence for each grid box was also calculated. This is not represented as 4.2. Available statistical fields stand-alone maps, but the results are used Table 5 lists all objective and statistical fields on a) and b) maps (see above) to mark the calculated as part of WOA18. Climatologies grid boxes with less than three mean of oceanographic variables and associated values within the radius of influence. statistics described in this document, as well These calculations are available as data as global figures of the same can be obtained files. online. The maps are arranged by composite time The sample standard deviation in a grid box periods (annual, seasonal, month). Table 5 was computed using: describes all available maps and data fields. We note that the complete set of all

18 N Climate Data Library with access to 2 ∑(xn − x) statistical and objectively analyzed fields in a s = n=1 (11) variety of digital formats. N −1 To provide an estimate of the uncertainty of th in which xn= the n data value in the grid box, the WOA18 nutrient climatologies, we x =mean of all data values in the grid box, compared the WOA18 and the Global Ocean and N= total number of data values in the grid Data Analysis Project version 2 box. The standard error of the mean was (GLODAPv2, Olsen et al., 2016) gridded computed by dividing the standard deviation fields for phosphate, nitrate, and silicate. by the square root of the number of GLODAPv2 does not have seasonal or observations in each grid box. monthly nutrient gridded fields. The results In addition to statistical fields, the land/ocean suggest that the differences between the two bottom mask and basin definition mask are annual mean climatologies are relatively available on-line. A user could take the small below about 500 m depth at the global standard depth level data from WOD18 with and basin scale (60°N-60°S). The global flags and these masks, and recreate the average difference (± 1 standard deviation) of WOA18 minus GLODAPv2 gridded fields WOA18 fields following the procedures -1 outlined in this document. Explanations and below 500 m depth is -0.02±0.07 µmol kg for phosphate, -0.22±0.95 µmol kg-1 for data formats for the data files are found under -1 documentation on the WOA18 webpage. nitrate, and -0.3±3.8 µmol kg for silicate (Table 6). The average differences are 4.3. Obtaining WOA18 fields on-line generally less than or comparable to the current estimated long-term measurement The objective and statistical data fields can be precision of these nutrients by standard obtained online in different digital formats at colorimetric methods using Continuous Flow the WOA18 webpage. The WOA18 fields Analysis. The data do not show a significant can be obtained in ASCII format (WOA systematic depth offset. Above 500 m depth, native and comma separated value [CSV]) there are significant measurable differences. and Network Common Data Form (NetCDF) This is expected because of larger variability through our WOA18 webpage. For users in the upper ocean. WOA18 is based on a interested in specific geographic areas, the much representative larger spatial and World Ocean Atlas Select (WOAselect) monthly nutrient data coverage than selection tool can be used to designate a GLODAPv2. WOA18 contains all of the data subset geographic area, depth, and used in the creation of GLODAPv2. oceanographic variable to view, and optionally download, climatological means or related statistics in shapefile format which is compatible with GIS software such as 5. SUMMARY ESRI ArcMap. WOA18 includes a digital In the preceding sections we have described collection of "JPEG" images of the objective the results of a project to objectively analyze and statistical fields. In addition, WOA18 all historical nutrient data in WOD18. We can be obtained in Ocean Data View (ODV) desire to build a set of climatological format. WOA18 will be available through analyses that are identical in all respects for other online locations as well. WOA98, all variables in WOA18 including relatively WOA01, WOA05, WOA09, and WOA13 are data sparse variables such as dissolved presently served through the IRI/LDEO inorganic nutrients. This provides

19 investigators with a consistent set of analyses 6. FUTURE WORK to work with. Our analyses will be updated when justified One advantage of the analysis techniques by additional water column nutrient used in this atlas is that we know the amount observations. As more oceanographic of smoothing by objective analyses as given nutrient data are received at NCEI/WDS- by the response function in Table 3 and Oceanography, we will also be able to extend Figure 1. We believe this to be an important the seasonal and monthly nutrient analysis to function for constructing and describing a deeper levels. climatology of any parameter. Particularly when computing anomalies from a standard Additional nutrient collected by automated climatology, it is important that the field be sensors will likely improve the results and smoothed to the same extent as the help provide additional observational climatology, to prevent generation of constraints on observed inter-annual to spurious anomalies simply through decadal-scale biochemical variability. For differences in smoothing. A second reason is example, recent advances in chemical that purely diagnostic computations require a sensors in Biogeochemical profiling minimum of seven or eight grid points to floats enable measurements of nitrate represent any Fourier component. Higher (Johnson et al., 2017a, b). Merging and order derivatives might require more data integrating nutrient data collected by smoothing. classical photometric methods, using We have created objectively analyzed fields continuous flow analysis, with other sensor- and data sets that can be used as a “black based nutrient observing systems will likely box.” We emphasize that some quality improve the results and provide additional control procedures used are subjective. For observational constraints on observed inter- those users who wish to make their own annual to decadal-scale changes. Each of choices, all the data used in our analyses are these different nutrient observing systems available both at standard depth levels as well add much additional data coverage and have as observed depth levels. The results different data uncertainties and calibrations presented in this atlas show some features that must be reconciled before combining that are suspect and may be due to non- into an internally consistent climatology. representative data that were not flagged by We are encouraged by the potential the quality control techniques used. Although acquisition of much additional high-quality we have attempted to eliminate as many of oceanographic observations through recently these features as possible by flagging the data adopted complementary global projects such which generate these features, some as the Global Ocean Observing System obviously could remain. Some may (GOOS) 2030 Strategy and the United eventually turn out not to be artifacts but Nations Decade of Ocean Science for rather to represent real features, not yet Sustainable Development (2021-2030). capable of being described in a meaningful GOOS is sponsored by the Intergovernmental way due to lack of data. The views, findings, Oceanographic Commission of UNESCO, and any errors in this document are those of the World Meteorological Organization the authors. (WMO), the United Nations Environment Programme (UNEP), and the International Science Council (ISC). Expansion of the current global ocean observing system will enable the creation of more robust

20 climatologies that span shorter climatological Barnes, S.L. (1964). A technique for maximizing time-periods of interest (e.g., inter-annual to details in numerical weather map analysis. J. App. Meteor., 3, 396-409. decadal). Barnes, S.L. (1973). Mesoscale objective map analysis Creating WOA18 relies on the unrestricted using weighted time series observations. NOAA and timely open access and use of Technical Memorandum ERL NSSL-62, 60 pp. Barnes, S.L. (1994). Applications of the Barnes oceanographic observations collected Objective Analysis Scheme, Part III: Tuning for worldwide. One country cannot afford the Minimum Error. J. Atmosph. and Oceanic Tech. observational system needed to monitor the 11:1459-1479. entire Earth; and thus, open access and use of Bergthorsson, P. and B. Doos (1955). Numerical observations is essential for formulating Weather map analysis. Tellus, 7, 329-340. Boyer, T.P., S. Levitus, J.I. Antonov, M.E. Conkright, informed science-based societal-relevant T.D. O'Brien, and C. Stephens (1998a). World strategies for sustainable ocean use and Ocean Atlas 1998 Vol. 4: Salinity of the Atlantic respond to environmental challenges. The Ocean. NOAA Atlas NESDIS 30, U.S. Gov. Printing developing research-quality climatologies Office, Washington, D.C., 166 pp. such as WOA nutrients serve as reliable Boyer, T.P., S. Levitus, J.I. Antonov, M.E. Conkright, T.D. O'Brien, and C. Stephens (1998b). World science-based baselines from which to Ocean Atlas 1998 Vol. 5: Salinity of the Pacific estimate low frequency regional to global Ocean. NOAA Atlas NESDIS 31, U.S. Gov. Printing variability. Office, Washington, D.C., 166 pp. Boyer, T.P., S. Levitus, J.I. Antonov, M.E. Conkright, 7. REFERENCES T.D. O'Brien, C. Stephens, and B. Trotsenko, (1998c). World Ocean Atlas 1998 Vol. 6: Salinity Achtemeier, G.L. (1987). On the concept of varying of the Indian Ocean. NOAA Atlas NESDIS 32, U.S. influence radii for a successive corrections Gov. Printing Office, Washington, D.C., 166 pp. objective analysis. Mon. Wea. Rev., 11, 1761-1771. Boyer, T.P., C. Stephens, J.I. Antonov, M.E. Antonov, J.I., S. Levitus, T.P. Boyer, M.E. Conkright, Conkright, R.A. Locarnini, T.D. O'Brien, H.E. T.D. O'Brien, and C. Stephens (1998a). World Garcia (2002). World Ocean Atlas 2001, Vol. 2: Ocean Atlas 1998. Vol. 1: Temperature of the Salinity. S. Levitus, Ed. NOAA Atlas NESDIS 50, Atlantic Ocean. NOAA Atlas NESDIS 27, U.S. Gov. U.S. Gov. Printing Office, Washington D.C., 165 Printing Office, Washington, D.C., 166 pp. pp. Antonov, J.I., S. Levitus, T.P. Boyer, M.E. Conkright, Boyer, T.P, S. Levitus, H.E. Garcia, R.A. Locarnini, T.D. O'Brien, and C. Stephens (1998b). World C. Stephens, and J.I. Antonov (2004). Objective Ocean Atlas 1998. Vol. 2: Temperature of the Analyses of Annual, Seasonal, and Monthly Pacific Ocean. NOAA Atlas NESDIS 28, U.S. Gov. Temperature and Salinity for the World Ocean on a Printing Office, Washington, D.C., 166 pp. ¼ degree Grid, International J. of Climatology, 25, Antonov, J.I., S. Levitus, T.P. Boyer, M.E. Conkright, 931-945. T.D. O'Brien, C. Stephens, and B. Trotsenko Boyer, T.P., J.I. Antonov, H.E. Garcia, D.R. Johnson, (1998c). World Ocean Atlas 1998. Vol. 3: R.A. Locarnini, A.V. Mishonov, M.T. Pitcher, O.K. Temperature of the Indian Ocean. NOAA Atlas Baranova, and I.V. Smolyar (2006). World Ocean NESDIS 29, U.S. Gov. Printing Office, Database 2005. S. Levitus, Ed. NOAA Atlas Washington, D.C., 166 pp. NESDIS 60, U.S. Gov. Printing Office, Antonov, J.I., R.A. Locarnini, T.P. Boyer, A.V. Washington, D.C., 190 pp. Mishonov, and H.E. Garcia (2006). World Ocean Boyer, T.P., J.I. Antonov, O.K. Baranova, H.E. Atlas 2005. Vol. 2: Salinity. S. Levitus, Ed. NOAA Garcia, D.R. Johnson, R.A. Locarnini, A.V. Atlas NESDIS 62, U.S. Gov. Printing Office, Mishonov, T.D. O’Brien, D. Seidov, I.V. Smolyar, Washington, D.C., 182 pp. M.M. Zweng (2009). World Ocean Database 2009. Antonov, J.I., R.A. Locarnini, T.P. Boyer, A.V. S. Levitus, Ed., NOAA Atlas NESDIS 66, U.S. Gov. Mishonov, and H.E. Garcia (2010). World Ocean Printing Office, Wash., D.C., 216 pp., DVDs. Atlas 2009. Vol. 2: Salinity. S. Levitus, Ed. NOAA Boyer, T.P., J.I. Antonov, O.K. Baranova, C. Atlas NESDIS 69, U.S. Gov. Printing Office, Coleman, H.E. Garcia, A. Grodsky, D.R. Johnson, Washington, D.C., 184 pp. T.D. O’Brien, C.R. Paver, R.A. Locarnini, A.V. Mishonov, J.R. Reagan, D. Seidov, I.V. Smolyar, and M.M. Zweng (2013). World Ocean Database

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23 Smith, D.R., M.E. Pumphry, and J.T. Snow (1986). A comparison of errors in objectively analyzed fields for uniform and nonuniform station distribution, J. Atm. Oceanic Tech., 3, 84-97. Stephens, C., J.I. Antonov, T.P. Boyer, M.E. Conkright, R.A. Locarnini, T.D. O'Brien, and H.E. Garcia (2002). World Ocean Atlas 2001. Vol. 1: Temperature. S. Levitus, Ed. NOAA Atlas NESDIS 49, U.S. Gov. Printing Office, Washington, D.C., 167 pp. Sverdrup, H.U., M.W. Johnson, and R.H. Fleming (1942). The Oceans: Their physics, chemistry, and general biology. Prentice Hall, 1060 pp. Thiebaux, H.J. and M.A. Pedder (1987). Spatial Objective Analysis: with applications in atmospheric science. Academic Press, 299 pp. Tukey, J.W. (1974). Nonlinear (nonsuperposable) methods for smoothing data, in “Cong. Rec.”, 1974 EASCON, 673 pp. Wessel, P., and W.H.F. Smith (1998). New, improved version of Generic Mapping Tools released, EOS Trans. Amer. Geophys. U., 79, 579. Zweng, M.M., J.R. Reagan, J.I. Antonov, R.A. Locarnini, A.V. Mishonov, T.P. Boyer, H.E. Garcia, O.K. Baranova, D.R. Johnson, D. Seidov, and M.M. Biddle (2013). World Ocean Atlas 2013. Vol. 2: Salinity. S. Levitus, Ed., A. Mishonov, Tech. Ed. NOAA Atlas NESDIS 74, 39 pp. Zweng, M.M., J.R. Reagan, D. Seidov, T.P. Boyer, R.A. Locarnini, H.E. Garcia, A.V. Mishonov, O.K. Baranova, K.W. Weathers, C.R. Paver, and I.V. Smolyar (2019). World Ocean Atlas 2018. Vol. 2: Salinity. A. Mishonov, Tech. Ed. NOAA Atlas NESDIS 82, 50pp.

24 Table 1. Descriptions of climatologies for each nutrient variable in WOA18. The climatologies have been calculated based on bottle data (OSD) from WOD13. The standard depth levels are shown in Table 2. Oceanographic Depths for annual Depths for seasonal Depths for monthly variable climatology climatology climatology Nitrate (N+N), 0-5500 m 0-800 m 0-800 m Phosphate, and (102 levels) (43 levels) (43 levels) Silicate

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 Standard Standard Standard Depths A B Depths A B Level # Level # (m) (m) 1 0 50 200 52 1250 200 400 2 5 50 200 53 1300 200 1000 3 10 50 200 54 1350 200 1000 4 15 50 200 55 1400 200 1000 5 20 50 200 56 1450 200 1000 6 25 50 200 57 1500 200 1000 7 30 50 200 58 1550 200 1000 8 35 50 200 59 1600 200 1000 9 40 50 200 60 1650 200 1000 10 45 50 200 61 1700 200 1000 11 50 50 200 62 1750 200 1000 12 55 50 200 63 1800 200 1000 13 60 50 200 64 1850 200 1000 14 65 50 200 65 1900 200 1000 15 70 50 200 66 1950 200 1000 16 75 50 200 67 2000 1000 1000 17 80 50 200 68 2100 1000 1000 18 85 50 200 69 2200 1000 1000 19 90 50 200 70 2300 1000 1000 20 95 50 200 71 2400 1000 1000 21 100 50 200 72 2500 1000 1000 22 125 50 200 73 2600 1000 1000 23 150 50 200 74 2700 1000 1000 24 175 50 200 75 2800 1000 1000

25 Standard Standard Standard Standard Depths A B Depths A B Level # Level # (m) (m) 25 200 50 200 76 2900 1000 1000 26 225 50 200 77 3000 1000 1000 27 250 100 200 78 3100 1000 1000 28 275 100 200 79 3200 1000 1000 29 300 100 200 80 3300 1000 1000 30 325 100 200 81 3400 1000 1000 31 350 100 200 82 3500 1000 1000 32 375 100 200 83 3600 1000 1000 33 400 100 200 84 3700 1000 1000 34 425 100 200 85 3800 1000 1000 35 450 100 200 86 3900 1000 1000 36 475 100 200 87 4000 1000 1000 37 500 100 400 88 4100 1000 1000 38 550 100 400 89 4200 1000 1000 39 600 100 400 90 4300 1000 1000 40 650 100 400 91 4400 1000 1000 41 700 100 400 92 4500 1000 1000 42 750 100 400 93 4600 1000 1000 43 800 100 400 94 4700 1000 1000 44 850 100 400 95 4800 1000 1000 45 900 200 400 96 4900 1000 1000 46 950 200 400 97 5000 1000 1000 47 1000 200 400 98 5100 1000 1000 48 1050 200 400 99 5200 1000 1000 49 1100 200 400 100 5300 1000 1000 50 1150 200 400 101 5400 1000 1000 51 1200 200 400 102 5500 1000 1000

26 Table 3. Response function of the objective analysis scheme as a function of wavelength for WOA18 and earlier analyses. Response function is normalized to 1.0. WOA98, 01, 05, Wavelength1 Levitus (1982) WOA94 09, 13, 18 360ΔX 1.000 0.999 1.000 180ΔX 1.000 0.997 0.999 120ΔX 1.000 0.994 0.999 90ΔX 1.000 0.989 0.998 72ΔX 1.000 0.983 0.997 60ΔX 1.000 0.976 0.995 45ΔX 1.000 0.957 0.992 40ΔX 0.999 0.946 0.990 36ΔX 0.999 0.934 0.987 30ΔX 0.996 0.907 0.981 24ΔX 0.983 0.857 0.969 20ΔX 0.955 0.801 0.952 18ΔX 0.923 0.759 0.937 15ΔX 0.828 0.671 0.898 12ΔX 0.626 0.532 0.813 10ΔX 0.417 0.397 0.698 9ΔX 0.299 0.315 0.611 8ΔX 0.186 0.226 0.500 6ΔX 3.75x10-2 0.059 0.229 5ΔX 1.34x10-2 0.019 0.105 4ΔX 1.32x10-3 2.23x10-3 2.75x10-2 3ΔX 2.51x10-3 1.90x10-4 5.41x10-3 2ΔX 5.61x10-7 5.30x10-7 1.36x10-6 1For ΔX = 111 km, the meridional separation at the Equator.

27 Table 4. Basins defined for objective analysis and the shallowest standard depth level for which each basin is defined. Standard Standard # Basin1 Depth # Basin1 Depth Level Level 1 Atlantic Ocean 1* 30 North American Basin 29 2 Pacific Ocean 1* 31 West European Basin 29 3 Indian Ocean 1* 32 Southeast Indian Basin 29 4 Mediterranean Sea 1* 33 Coral Sea 29 5 Baltic Sea 1 34 East Indian Basin 29 6 Black Sea 1 35 Central Indian Basin 29 7 Red Sea 1 36 Southwest Atlantic Basin 29 8 Persian Gulf 1 37 Southeast Atlantic Basin 29 9 Hudson Bay 1 38 Southeast Pacific Basin 29 10 Southern Ocean 1* 39 Guatemala Basin 29 11 Arctic Ocean 1 40 East Caroline Basin 30 12 Sea of Japan 1 41 Marianas Basin 30 13 Kara Sea 8 42 Philippine Sea 30 14 Sulu Sea 10 43 Arabian Sea 30 15 Baffin Bay 14 44 Chile Basin 30 16 East Mediterranean 16 45 Somali Basin 30 17 West Mediterranean 19 46 Mascarene Basin 30 18 Sea of Okhotsk 19 47 Crozet Basin 30 19 Banda Sea 23 48 Guinea Basin 30 20 Caribbean Sea 23 49 Brazil Basin 31 21 Andaman Basin 25 50 Argentine Basin 31 22 North Caribbean 26 51 Tasman Sea 30 23 Gulf of Mexico 26 52 Atlantic Indian Basin 31 24 Beaufort Sea 28 53 Caspian Sea 1 25 South China Sea 28 54 Sulu Sea II 14 26 Barents Sea 28 55 Venezuela Basin 14 27 Celebes Sea 25 56 Bay of Bengal 1* 28 Aleutian Basin 28 57 Java Sea 6 29 Fiji Basin 29 58 East Indian Atlantic Basin 32 1Basins marked with a “*” can interact with adjacent basins in the objective analysis.

28 Table 5. Statistical fields calculated as part of WOA18 (“√“denotes field was calculated and is publicly available). Five-degree One-degree Field Statistical field Statisctics Calculated 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 √

Table 6. Nominal depth average phosphate, nitrate+nitrite, and silicate (µmol/kg) differences (± 1 standard deviation) of the GLODAPv2 minus WOA18 for 1-degree objectively analyzed fields (60°N-60°S).

Variable Depth Atlantic Pacific Indian Global range (m) 0-500 0.02±0.11 0.01±0.13 -0.01±0.12 0.01±0.12 Phosphate 500-5500 -0.01±0.05 -0.02±0.07 -0.02±0.08 -0.02±0.07 Nitrate + 0-500 0.0±1.6 -0.2±1.9 -0.3±1.7 0.2±1.8 Nitrite 500-5500 -0.2±0.7 -0.2±1.0 -0.2±1.0 -0.2±1.0 0-500 0.1±3.1 1.0±3.5 0.9±3.0 0.8±3.6 Silicate 500-5500 -0.5±2.7 0.8±4.1 -0.2±3.9 -0.3±3.8

29

100

80

60

40 Amplitude(%)

Levitus (1982) 20 WOA94 (1-degree) WOA:WOA98, 98, WOA01, 01, 05, 09,WOA05, 13, & WOA09,18 (1-degree) WOA13 (1-degree) WOA:WOA13 13 (1/4-degree) & 18 (1/4 degree)

0 0 1000 2000 3000 4000 Wavelength (km)

Figure 1. Response function of the WOA18, WOA13, WOA05, WOA01, WOA98, WOA94, and Levitus (1982) objective analysis schemes.

30 Zonal Mean

Z > 800 m Annual Mean (OA) = Annual Mean Z ≤ 800 m

Seasonal Mean (OA)

Legend: Monthly Mean (OA) First-guess field used to calculate mean field Mean of 12 Mean of climatologies months Final mean field Annual Mean OA - Objectively analyzed field Z - Depth

Seasonal Mean (OA)

Monthly Mean (OA)

Mean of Mean of 12 months 3 months

Annual Mean Seasonal Mean

Figure 2. Scheme used in computing annual, seasonal, and monthly objectively analyzed means for phosphate, silicate, and nitrate.

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