Synoptic monthly gridded global and regional four‐dimensional World Ocean Database and Global Temperature and Salinity Profile Programme (T, S, u, v) fields with the optimal spectral decomposition and P‐vector methods

Synoptic monthly gridded (SMG) world ocean temperature (T) and salinity (S) fields with (1° × 1°) horizontal resolution and 28 standard vertical levels from the ocean surface to 3000 m deep have been established from the observational (T, S) profiles from the NOAA National Centers for Environmental Information (NCEI) World Ocean Database (WOD) from January 1945 to December 2014 and the Global Temperature and Salinity Profile Programme (GTSPP) from January 1990 to December 2009 using the optimal spectral decomposition (OSD) method. The world ocean abstract geostrophic currents (u, v) are calculated from the 4D SMG‐WOD and SMG‐GTSPP (T, S) data using the P‐vector inverse method. The SMG‐WOD (T, S, u, v) and SMG‐GTSPP (T, S, u, v) fields with a higher horizontal resolution (0.25° × 0.25°) have also been produced for the Mediterranean Sea, the Japan/East Sea, and the Gulf of Mexico.


Introduction
Ocean observational temperature (T) and salinity (S) profiles after quality control are available in the NOAA/ National Centers for Environmental Information (NCEI) for public use: World Ocean Database (WOD; Boyer et al., 2013) and the Global Temperature and Salinity Profile Programme (GTSPP; Sun et al., 2009). Both datasets are not evenly distributed in time and space. The NOAA/NCEI WOD was established more than five decades ago and has been serving the world oceanographic community ever since. There are 12 808 409 (T, S) stations in WOD13 dataset. Interested readers can find detailed information about WOD from the NOAA Atlas NESDIS 72 (Boyer et al., 2013) or from the website: https://www.nodc.noaa.gov/OC5/WOD/ pr_wod.html. However, the GTSPP data are relatively new (Sun et al., 2009). There are total 6 662 209 (4 273 991) GTSPP temperature (salinity) stations with yearly profile number <80 000 from 1990 to 1999, increasing exponentially to 1.7 million in 2009 from 1999 as the Argo floats into practice (Figure 1). The GTSPP stations are over the global oceans, as shown in Figure 2a for temperature and in Figure 2b for salinity.
The absolute geostrophic currents (u, v) can be determined from (T, S) profiles using the inverse methods (e.g. Stommel and Schott, 1977;Wunsch, 1978;Chu, 1995Chu, , 2006. To enhance their utility to the oceanographic and climate research, as well as operational environmental forecasting communities, establishment of objectively analysed synoptic monthly gridded (SMG) four-dimensional (T, S, u, v) datasets on regular spatial grid points and time step (1 month) is an urgent need in various aspects such as use as boundary and/or initial conditions in numerical ocean circulation models, verification of numerical simulations of the ocean, as a form of 'sea truth' for satellite measurements such as altimetry observations of sea surface height among others (Boyer et al., 2013). The optimal spectral decomposition (OSD) method is used to establish 4D objectively analysed global SMG (T, S) datasets with monthly increment, 1°9 1°( 0.25°9 0.25°for the Mediterranean Sea, the Japan/ East Sea, and the Gulf of Mexico) horizontal resolution, and 28 standard NCEI vertical levels from the ocean surface to 3000 m deep (Table 1). With such a vertical resolution, that is, 10 m in upper 50 m depth, 25 m between 50 m and 150 m, etc., it cannot well represent global ocean mixed layer and the thermocline variability. The authors are working on the derived WODisothermal (isohaline, isopycnal) layer temperature (salinity, density) and depth as well as thermocline (halocline, pycnocline) strength. The P-vector inverse method is used to establish 4D objectively analysed SMG absolute geostrophic current (u, v) datasets.

OSD method
The OSD method (Chu et al., 2003a(Chu et al., ,b, 2004(Chu et al., , 2016, used to produce SMG-(T, S) datasets, can be outlined as follows. Let r = (x, y) be the horizontal coordinates and z the vertical coordinate. The horizontal position vector (r) is represented by r n (n = 1, 2, . . ., N) at grid points and by r (m) (m = 1, 2, . . ., M) at observational locations. Here, N is the total number of the grid points, and M is the total number of observational points. Gridded temperature and salinity can be ordered by grid point and by variable, forming a single vector c = (T, S) of length NP with N the total number of grid points and P the number of variables. For example, the background field (c b ) is on the grid points and represented as where the superscript 'T' means transpose. The observation (c o ) is on the observational points and represented by Usually, the data analysis and assimilation is to blend c b (at the grid points r n ) with observational data (c o ) (at observational points r (m) ) into the assimilated (or analysis) field (c a ) at the grid points r n , to represent the (unknown) 'truth' c t with an analysis error (e a ) and an observational error (e o ) Here, H = [h mn ] is the M 9 N linear observation operator matrix; d is the innovation (also called the observational increment) at the observational points r (m) ; W = [w nm ], is the N 9 M weight matrix interpolating the innovation d into the grid points r n (Figure 3). The background and observational error covariance matrices should be given as a priori in order to determine the weight matrix W, such as in the optimal interpolation (OI), Kalman filter, and variational method (3DVar, 4DVar, . . .).
On the other hand, the OSD has been developed without using the weight matrix (Chu et al., 2003a,b). Existence of a lateral boundary (Г) for an ocean domain (Ω) provides a great opportunity to use a spectral method in ocean data analysis and assimilation through decomposing the variable anomaly at the grid points [c(r n ) À c b (r n )] into the spectral form , where {/ k } are basis functions; K is the mode truncation, which is determined using the steep-descending method . The eigenvectors of the Laplace operator with the same lateral boundary condition of (c À c b ) can be used as the basis functions {/ k }. The K 9 N basis function matrix Φ is calculated by Figure 4 shows the first three basis functions for the Atlantic Ocean, Indian Ocean, and Pacific Oceans. The first basis-function / 1 ðx n Þ for all the three oceans shows a near-zonal structure. The second basis function / 2 ðx n Þ shows a near-meridional structure for the Indian Ocean and Pacific Ocean and for the lower latitudes (30°N-30°S) of the Atlantic Ocean. The third basis-function / 3 ðx n Þ shows the east-west slanted dipole pattern with opposite signs in northeastern and southwestern regions in the Indian Ocean and Pacific  Ocean, and near-meridional structure in the North Atlantic and near-zonal structure in the South Atlantic. The higher order basis functions have more complicated variability structures. In producing the SMG-WOD and SMG-GTSPP (T, S) data, around 30 basis functions are used. The OSD data assimilation equation is given by (Chu et al., 2016) where F is an N 9 N diagonal observational contribution matrix In computing SMG-WOD and SMG-GTSPP (T, S) data, the World Ocean Atlas 2013 (WOA13) monthly mean fields were used as the background c b . The analysis error (i.e. analysis c a vs 'truth' c t ) at the grid points is given by e a ðr n Þ c a ðr n Þ À c t ðr n Þ ¼ c a ðr n Þ À c b ðr n Þ ½ Àc o ðr n Þ À c b ðr n Þ ½ þc o ðr n Þ À c t ðr n Þ ½ ¼ s K ðr n Þ À Dðr n Þ þ e o ðr n Þ Here, Equations (4) and (8) are used. The analysis error is decomposed into two parts e a ðr n Þ ¼ e K ðr n Þ þ e o ðr n Þ ð 10Þ with the truncation error given by e K ðr n Þ ¼ s K ðr n Þ À Dðr n Þ ð 11aÞ and the observational error given by The analysis error variance over the whole domain is given by is the truncation error, e 2 o is the observational error variance, and the Cauchy-Schwarz inequality is used. The mode truncation is optimally determined from the relative analysis error reduction exceeding the threshold c th , After the mode truncation K OPT is determined, the spectral coefficients (a k , k = 1, 2, . . ., K OPT ) in Equation (4) can be calculated, and so as the truncation error variance E 2 K OPT . Advantages of the OSD versus other data assimilation methods such as the OI, Kalman filter, and variational method (3DVar, 4DVar, . . .) are no background error covariance matrix needed, capable of filtering out noises since the basis functions are the eigenvectors of the Laplace operator, and continuity of the temperature and salinity at the boundary connecting the regional and global products.
The third advantage is due to the same boundary condition used to obtain the basis functions from the regional sea side and the open ocean side, which guarantees the continuity of the basis functions and in turn the (T, S) fields at the open boundary. Total numbers of temperature and salinity observations increase dramatically after 2000 because of Argo project (see Figures 1 and 2), which indicated that the quality of SMG-WOD and SMG-GTSPP synoptic monthly gridded dataset in that time span is better than those before 2000s.
The OSD method has been proven an effective ocean data analysis method (Chu et al., 2016). With it, several new ocean phenomena have been identified from observational data such as a bimodal structure of chlorophyll-a with winter/spring (February-March) and fall (September-October) blooms in the Black Sea (Chu et al., 2005a), fall-winter recurrence of current reversal from westward to eastward on the Texas-Louisiana continental shelf from the current meter, near-surface drifting buoy (Chu et al., 2005b), propagation of long Rossby waves at mid-depths (around 1000 m) in the tropical North Atlantic from the Argo float data (Chu et al., 2007), and temporal and spatial variability of global upper ocean heat content (Chu, 2011).

P-vector method
The P-vector inverse method was first proposed by Chu (1995) and described in detail in a book by Chu (2006). It can also be found from the authors' previous paper  published in the Geoscience Data Journal (see the website: http://online library.wiley.com/doi/10.1002/gdj3.31/full).

Quality control of WOD/GTSPP profile data
Quality control (QC) has been conducted on the WOD and GTSPP temperature and salinity profiles. The general procedures include position and time checks from platforms track looking, min/max range checks, spike checks (excessive gradients and inversions), stability checks, standard deviation outlier checks, and duplication checks either by having received the data more than once, or same profile with different resolutions. QC flags values carried with the observations represent particular QC tests failed, not a verdict on the overall quality of the data (Sun, 2013;Boyer, 2014). As mentioned by Boyer (2014), 'All QC (automatic and manual) for the WOD are performed with a specific purpose in mindthe calculation of the World Ocean Atlas (WOA) climatological mean fields and ocean heat/salt content calculations. The tests deliberately flag data which may be good observations, but do not represent a long-term mean or (for heat/salt calculations) a short-term large scale pattern'. However, the QC for GTSPP does not have such a constraint. The WOA climatology is taken as a measure for the statistical tests (Sun, 2013).
In addition to the general QC procedures, the WOD standard depth level data for the expendable bathythermograph (XBT) and mechanical bathythermograph (MBT) have bias correction through depth adjustment since 2009. Such an adjustment is to diminish the documented time-dependent temperature biases as described by Levitus et al. (2009), which is in addition to the correction of depths to the fall rate for all XBT data. The observed level data do not have any adjustment since only the standard level depth XBT and MBT data are contributed to construct the WOA climatological data. Interested readers are referred to the NCEI website https://www.nodc. noaa.gov/OC5/XBT_BIAS/xbt_bias.html for detailed information.
The GTSPP Argo salinity data have salinity drift. This is 'because 90% of the Argo floats have electrode-type conductivity cell (see Sea-Bird online at http://www. seabird.com/), the "prolonged and unattended" presence in the ocean make them susceptible to foulingbiofilm formation inside the cell, which alters the conductivity and thereby the salinity measurements (Thadathil et al., 2012)'. As mentioned in the Argo data management (Wong et al., 2013), statistical comparison methods that are used to determine conductivity sensor drift (e.g. Wong et al., 2003;Owens and Wong, 2009) are suitable for correction of positive salinity drift; for example, pressure error of À20 dbar will cause a positive salinity error of approximately 0.01 PSS-78. There are no cycles that have salinity drift adjustment (ΔS > 0.001 PSS-78 in bottom data to distinguish from thermal lag adjustment at shallower levels); no cycles following ones that have salinity drift adjustment (ΔS > 0.001 PSS-78 in bottom data); and no cycles in the 6 months prior to salinity drift adjustment (ΔS > 0.001 PSS-78 in bottom data). Sun and Chu (2013) shows the capability of the OSD method in the QC of the GTSPP/Argo data. Take May 2000 GTSPP and Argo (T, S) profile data as an example (Figure 5a). In the track of CTD measurements, a fake spike of À24°C is added from the surface to the bottom of the temperature profile at the middle marked by a green spot (Figure 5a). The sea surface temperature filed is unrealistic with a strong closed fake cold data point (Figure 5b). After using the OSD method the fake data have been eliminated (Figure 5c).

SMG data
Both SMG-WOD and SMG-GTSPP datasets are in the Network Common Data Form (netCDF) (see the website: http://www.unidata.ucar.edu/software/netcdf/), which is an interface for array-oriented data access, a library for implementation of interface, and a machineindependent format for representing data. The netCDF software was developed at the Unidata (http://www. unidata.ucar.edu) Program Center in Boulder, Colorado. Each element is stored at a disc address which is a linear function of the array indices (subscripts) by which it is identified. Hence, these indices need not be stored separately (as in a relational database). This provides a fast and compact storage method. The external types supported by the netCDF interface are listed in Table 2. These types are chosen to provide a reasonably wide range of trade-offs between data precision and number of bits required for each value. The external data types are independent from whatever internal data types are supported by a particular machine and language combination. These types of extracted data are called 'external', because they correspond to the portable external representation for netCDF data.

Four-dimensional data
The SMG-WOD global (1°9 1°) and regional (Gulf of Mexico, Japan/East Sea, and Mediterranean Sea, 0.25°9 0.25°), and SMG-GTSPP (1°9 1°) datasets are four-dimensional with 28 vertical levels (Table 1)  for SMG-GTSPP, the time sequence in years, and t l = 1, 2, . . ., 12, the monthly sequence within a year. The fourdimensional data (T, S, u, v) can be represented by Ψ(r n , z j ,t s ) with r n the horizontal grid points, z j (j = 1, 2, . . ., 28) the vertical levels. Since mesoscale eddies have typical horizontal scales of <100 km and timescales on the order of a month, the SMG-WOD and SMG-GTSPP do not have any mesoscale signal such as the footprint of the mesoscale eddy. To resolve mesoscale eddy, finer resolution in space and time is needed.

Climatological monthly mean
Wðr n ; z j s m ; t l Þ ð15Þ and total-time mean Wðr n ; z j Þ ¼ 1 12 X 12 l¼1 Wðr n ; z j ; t l Þ ð 16Þ are calculated. Subtraction of Wðr n ; z j Þ from Wðr n ; z j ; t l Þ, dWðr n ; z j ; t l Þ ¼ Wðr n ; z j ; t l Þ À Wðr n ; z j Þ ð17Þ represents the mean seasonal variability. Subtraction of Wðr n ; z j ; t l Þ from Ψ(r n , z j s m , t l ), DWðr n ; z j s m ; t l Þ ¼ Wðr n ; z j s m ; t l Þ À Wðr n ; z j ; t l Þ ð18Þ is the monthly anomaly (relative to the climatological monthly mean) and represents the interannual to interdecadal variability. The characteristics of the SMG-WOD global datasets are presented for illustration. Since the WOA13 monthly (T, S) data were used as the background field (c b ), the total mean and seasonal variability of the SMG-WOD (T, S) are the same as the WOA13 (T, S). In the following sub-sections, the temperature, salinity, and geostrophic currents are presented at 50 and 500 m depths. It is noted that in China adjacent Figure 6. Total mean temperature ( T ) (upper panels) and seasonal anomalies (T ) (lower quad-panels) at 50 m (left panels) and 500 m (right panels) depths calculated from the SMG-WOD dataset within the lower two panels for the seasonal anomalies: (a) January to March, (b) April to June, (c) July to September, and (d) October to December. seas such as the East China Sea, the water depth is shallower than 500 m or 50 m. The SMG-WOD (T, S, u, v) data are blank in these regional seas.

Total mean and seasonal variability
At 50 m depth, the total-time mean  of temperature ( T ) shows the following features: (1) colder than 8°C north of 40°N and south of 40°S, (2) warm areas associated with the subtropical gyres such as a strong warm core (>26°C) from the South Atlantic with a triangular shape of the Brazilian-Argentine Coast (0°to 30°S) to the Gulf Stream region, extending eastward and reaching the northwest African Coast, a warm core located in the western Pacific including the Kuroshio and its extension regions, western equatorial/South Pacific, as well as the Indian Figure 7. SMG-WOD January temperature anomaly (relative to climatological January mean) (°C) at 50 m depth in selected years : 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2014. Ocean north of 20°S. The mean seasonal variability of temperature (dT) shows the following features: (1) range of seasonal variability from À3°C to +3°C, (2) warm seasonal anomalies occurring in the Northern Hemisphere in summer (July to September) and fall (October to December) and in the Southern Hemisphere in winter (January to March) and Spring (April to June), (3) cold seasonal anomalies occur in the Northern Hemisphere in winter (January to March) and Spring (April to June) and in the Southern Hemisphere in summer (July to September) and fall (October to December) (Figure 6a). At 500 m depth, the total-time mean  of temperature ( T ) shows the following features: (1) noticeable warm cores in the western part of middle latitudes (Northern and Southern Hemispheres) Figure 8. SMG-WOD July temperature anomaly (relative to climatological July mean) (°C) at 50 m depth in selected years: 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2014. in the three oceans such as the Gulf Stream region in the North Atlantic, Kuroshio region in the North Pacific, and Arabian Sea in the Northern Indian Ocean, and (2) warm areas are associated with the subtropical gyres in the Atlantic and Pacific Oceans. The mean seasonal variability in temperature (dT) shows the following features: (1) the range of seasonal variability from À1°C to +1°C, (2) dominating eddy-like structure throughout the year, and (3) no evident differential Northern/Southern Hemispheric seasonal variability (Figure 6b). It is noted that 'eddy' is referred to large eddy from here on.

Interannual to interdecadal variability
Interannual and interdecadal variability are identified from monthly temperature anomaly DT at 50 m depth in January (Figure 7) and July (Figure 8) from 1960 to 2004 with five year increment. The Pacific Ocean in Figure 9. SMG-WOD January temperature anomaly (relative to climatological January mean) (°C) at 500 m depth in selected years : 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2014. January is characterized by alternating zonal-varying pattern and multi-eddy structure such as, a zonalvarying pattern in 1960 with two warm anomalies (near 1.5°C) occurring in the western North Pacific and eastern Pacific and a cold anomaly (around À1°C) appearing in the western South Pacific, a multi-eddylike structure from 1965 to 1980, a zonal-varying pattern in 1985 with a weak anomaly sandwiched by two evident cold anomalies (À2.0°C) occurring in the western North Pacific and eastern Pacific, a zonal-varying pattern in 1990, 1995 with weak cold anomaly (À0.5°C) in the western North Pacific and evident warm anomaly (1°C) in the eastern Pacific, a reverse zonal-varying pattern in 2000 with warm anomaly (1°C) in the western North Pacific and cold anomaly (<À1.5°C) in the eastern Pacific, evident warm Figure 10. SMG-WOD July temperature anomaly (relative to climatological July mean) (°C) at 500 m depth in selected years: 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2014. anomaly in tropical Pacific in 2005, 2010, and a multieddy-like structure in 2014. Different from January, the Pacific Ocean in July (Figure 8) is characterized by a multi-eddy-like structure in most years except in 1975, when weak anomaly (À0.5°C to 0.5°C) dominates the whole Pacific Ocean. The Atlantic Ocean is characterized by alternating meridional-varying pattern and multi-eddy structure at 50 m depth in January ( Figure 7) and July (Figure 8). In January, meridionalvarying pattern in 1960 with strong cold anomaly (À2.5°C) occurring in the South Atlantic and weak warm anomaly (<0.5°C) appearing in the North Atlantic, a multi-eddy-like structure in 1965, 1970, 1975, a meridional-varying pattern in 1980 with warm anomaly (1.5°C) occurring in the South Atlantic and weak cold anomaly (À0.5°C) in the North Atlantic, a multi-eddylike structure in 1985, 1990, 1995, 2000, 2010, and weak anomaly in 2005, 2014 (Figure 7). The Atlantic Ocean is characterized by a multi-eddy-like structure in most years (Figure 8). The Indian Ocean is characterized by a multi-eddy structure at 50 m depth in January ( Figure 7) and July (Figure 8).
Reduced interannual to interdecadal variability is also noted at 500 m depth from five-yearly January DT(r n , 500 m, s m , Jan) ( Figure 9) and July DT (r n , 500 m, s m , Jul) ( Figure 10) from 1960 to 2004. The world oceans are characterized by alternating low variability (À1°C to 1°C) pattern and multi-eddy structure with variability larger than (À2°C to 2°C). The Pacific Ocean has a low variability pattern in 1960,1965,1985,1995,2000,2005,2014 in January ( Figure 9) and in most years except in 1970 in July ( Figure 10) and a multi-eddy-like structure in rest of years. The Atlantic Ocean has a multi-eddy structure in 1970, 1980, 1985, 1990 in January (Figure 9) and in 1970(Figure 9) and in , 1975(Figure 9) and in , 1985(Figure 9) and in , 1990(Figure 9) and in , 1995(Figure 9) and in , 2000 in July ( Figure 10) and a low variability pattern in rest of years. The Indian Ocean has a low variability pattern in 1965, 1975, 1980, 2010in January (Figure 9) and in 1965, 1980, 1985, 1990 in July ( Figure 10) and a multi-eddy structure in rest of years.

Total mean and seasonal variability
At 50 m depth, the total-time mean  salinity ( S) shows following features: (1) strong salty ( S > 37.0 psu) areas are associated with the North and South Atlantic subtropical gyres; (2) less salty (37.0 > S > 35.0 psu) areas are associated with the North and South pacific subtropical gyres, Arabian Sea, and Southern Indian subtropical gyre, and (3) least salty ( S < 33.0 psu) region is associated with the North Pacific subarctic gyre. The mean seasonal variability of salinity (dS) at 50 m depth shows the following features: (1) the range of seasonal variability from À0.5 to 0.5 psu, (2) no hemispherical asymmetry in the Atlantic and Pacific Oceans, and (3) larger dS in the Indian Ocean than in the Atlantic and Pacific Oceans (Figure 11a). At 500 m depth, Figure 11. Total mean salinity ( S) (upper panels) and seasonal anomalies (S) (lower quad-panels) at 50 m (left panels), and 500 m (right panels) depths calculated from the SMG-WOD dataset within the lower two panels for the seasonal anomalies: (a) January to March, (b) April to June, (c) July to September, and (d) October to December. the total-time mean ( S) shows following features: (1) strong salty ( S > 36.0 psu) areas associated with the North Atlantic subtropical gyre, (2) least salty ( S < 34.0 psu) region associated with the North Pacific subarctic gyre, and (3) less salty (36.0 > S > 34.0 psu) areas are rest of the world oceans. The mean seasonal variability of salinity (dS) shows very minor seasonal variability from À0.1 to 0.1 psu all over the world oceans (Figure 10b).

Interannual to interdecadal variability
Evident interannual to interdecadal variability from 1960 to 2004 is noted at 50 m depth from five-yearly January DS(r n , 50 m, s m , Jan) (À3.0 to 3.0 psu) (Figure 12) and July DS(r n , 50 m, s m , Jul) (À2.0 to 1.5 psu) (Figure 13). The Pacific Ocean is characterized by alternating zonal-varying pattern (1990,1995,2000) and low-variability pattern (À0.5 to 0.5 psu) in rest of years in January, and by a multi-eddy structure Figure 12. SMG-WOD January salinity anomaly (relative to climatological January mean) (psu) at 50 m depth in selected years: 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2014. (1975, 1990) and low-variability pattern in rest of years in January, and by a multi-eddy structure in 2000, and low-variability pattern in rest of years in July. The Atlantic Ocean is characterized by a multieddy structure in 1965,1970,1980,1990,2000 and low-variability pattern in rest of years in July. The Indian has low variability pattern in 1965,1970,1980,1995,2000,2005, and a multi-eddy structure in rest of years in January and by a multi-eddy structure in 1965,1975, and low-variability pattern in rest of years in July.

Absolute geostrophic velocity
The equatorial region (À8°S-8°N) is excluded for the absolute geostrophic velocity data since the geostrophic balance is not valid there. Description of interannual to interdecadal variability of the absolute Figure 14. SMG-WOD January salinity anomaly (relative to climatological January mean) (psu) at 500 m depth in selected years : 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2014. geostrophic velocity (u, v) from the datasets is beyond the scope of this paper. Only the total time mean and seasonal variability is presented. At 50 m depth, the total-time mean  absolute geostrophic velocity ð u; vÞ with a maximum speed near 0.4 m/s shows the existence of subtropical gyres with major currents: the North Equatorial Current (NEC) flowing westward from the west coast of Africa to the Brazilian cost (North Atlantic), from the west coast of Baja California to west of Philippines and turning the direction to join the Kuroshio in the North Pacific and the Gulf Stream in the North Atlantic; the North Equatorial Counter Current (NECC) moving eastward south of the NEC (evident in the North Atlantic and North Pacific); the South Equatorial Current flowing westward from the eastern South Atlantic to the Brazilian coast, from Figure 15. SMG-WOD July salinity anomaly (relative to climatological July mean) (psu) at 500 m depth in selected years : 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2014. the west coast of Africa to western South Pacific, and from northwest coast of Australia to east coast of Africa; eastward flowing South Atlantic Current, South Indian Current, South Pacific Current, and Antarctic Circumpolar Current. The mean seasonal variability (du, dv) is almost an order of magnitude smaller than the total-time mean with a maximum of around 0.06 m/s (Figure 16).
At 500 m depth, the total-time mean  absolute geostrophic velocity ð u; vÞ with a maximum speed near 0.2 m/s shows the existence of weaker subtropical gyres with evident Gulf Stream, Kuroshio, and Antarctic Circumpolar Current. The mean seasonal variability (du, dv) is an order of magnitude smaller than the total-time mean with a maximum of around 0.02 m/s ( Figure 17).

Data download
The data can be downloaded directly from the NCEI websites (see Datasets section). Please contact NCEI Customer Service if you need further assistance (http://www.nodc.noaa.gov/about/contact.html).
To read the data, the free Netcdf package needs to be downloaded from the website: https://www.image.uca r.edu/GSP/Software/Netcdf/. The MATLAB (version 2008b and later) provides access to more than 30 functions in the netCDF interface. This interface provides an application program interface that you can use to enable reading data from and writing data to netCDF files (known as datasets in netCDF terminology). The MATLAB code is listed as follows to read the SMG-GTSPP data in netCDF as an illustration. v Þ (upper panel) and seasonal anomalies (ũ;ṽ ) (lower quad-panels) at 500 m depths calculated from the SMG-WOD dataset within the lower panels for the seasonal anomalies: (a) January to March, (b) April to June, (c) July to September, and (d) October to December.