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Absolute Geostrophic Velocity Inverted From World Ocean Atlas
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  Absolute geostrophic velocity inverted from World Ocean Atlas2013 (WOAV13) with the P-vector method Peter C. Chu* and C. W. Fan Naval Ocean Analysis and Prediction (NOAP) Laboratory, Department of Oceanography, Naval Postgraduate School, Monterey,California, 93943  * Correspondence  Peter C. Chu, Naval Postgraduate School, Monterey, CA 93943. E-mail: pcchu@nps.edu  The research presented in this paper was funded by the Of 󿬁 ce of Naval Research. The World Ocean Atlas-2013 (WOAV13) dataset comprises 3D global gridded climatological  󿬁 elds of absolute geos-trophic velocity inverted from WOA13 temperature and salinity   󿬁 elds using the P-vector method. It provides a climato-logical velocity   󿬁 eld that is dynamically compatible to the WOA13 ( T  ,  S  )  󿬁 elds. The WOAV13 has the same spatialresolution and temporal variation (annual, monthly, seasonal) as WOA13 ( T  ,  S  )  󿬁 elds, but does not cover the equatorialzone (5 ° S  –  5 ° N) due to the geostrophic balance being the theoretical basis for the P-vector inverse method. Dataset  Identi 󿬁 er: http://gov.noaa.nodc:0121576Creator: NOAP Lab, Department of Oceanography, Naval Postgraduate School, Monterey, CA Title: World Ocean Geostrophic Velocity Inverted from World Ocean Atlas 2013 with the P-Vector MethodPublisher: National Oceanographic Data Center, USA Publication year: 2014Resource type: NOAA/NCEI Version: http://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.nodc:0121576 Geosci. Data J.  2  : 78   –  82 (2015), doi:  10.1002/gdj3.31Received: 20 July 2015, revised: 3 November 2015, accepted: 3 December 2015 Key words: World ocean geostrophic velocity, WOA13, WOAV13, P-vector method, climatology  Introduction World Ocean Atlas 2013 (WOA13), published by theNOAA National Centers for Environmental Information(NCEI) (US), contains annual, seasonal, and monthly means of temperature ( T  ), salinity ( S  ), dissolved oxy-gen, apparent oxygen utilization, percent oxygen satu-ration, phosphate, silicate, and nitrate for the WorldOceans with horizontal resolution of 1 °  9  1 °  at stan-dard 102 depth levels from the surface to the sea  󿬂 oor(5500 m depth) (Boyer  et al. , 2005; Locarnini  et al. ,2013; Zweng  et al. , 2013). It also includes associatedstatistical  󿬁 elds of observed oceanographic pro 󿬁 le datainterpolated to standard depth levels on 5 ° , 1 ° , and0.25 °  grids (http://www.nodc.noaa.gov/OC5/woa13/).However, an important variable, ocean currentvelocity vector ( u ,  v  ), is not included in the WOA13dataset. This is primary due to the lack of velocity observations, which are dif  󿬁 cult and costly to make.Physical oceanographers usually have a relatively fre-quent ( T  ,  S  ). For example, the NOAA NCEI WOD-2013contains nearly 13 million temperature pro 󿬁 les andalmost 6 million salinity measurements, but does notcontain any ocean current velocity data.Inclusion of ocean current velocity data into theWOA13 becomes important for climatic and oceano-graphic studies (Chu and Lan, 2003). Absolute geos-trophic velocity, representing the large-scale oceancirculation, is calculated from the WOA13 ( T  ,  S  ) datausing the P-vector inverse method (Chu, 1995; Chu2006) with the same spatial and temporal resolutionsas the ( T  ,  S  ) data. This velocity dataset is called theWOAV13 (i.e. WOA13-Velocity). 1. Data production method The P-vector inverse method was  󿬁 rst proposed by Chu (1995) and described in detail in a book by Chu ª  2016 The Authors.  Geoscience Data Journal   published by Royal Meteorological Society and John Wiley & Sons Ltd.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution andreproduction in any medium, provided the srcinal work is properly cited.  (2006). It can be outlined as follows. Let (  x  ,  y  ,  z  ) bethe coordinates with  x  -axis in the zonal direction (east-ward positive),  y  -axis in the latitudinal direction(northward positive), and  z  -axis in the vertical (up-ward positive); and  V   the velocity vector with ( u ,  v  , w  ) the components in the three coordinate axes. Thelarge-scale motions in the ocean interior are geos-trophic and hydrostatic balanced, continuous, anddensity ( q ) conserved,  V  r q  ¼  0 :  ð 1 Þ These conditions lead to the conservation of thepotential vorticity ( q  =  f  @  q  / @   z  ),  V  r q  ¼  0 ;  ð 2 Þ where  f   is the Coriolis parameter. Therefore, thestreamline must be along the intersection of the twosurfaces of ( q ,  q ) (Figure 1), and thus the velocity vector  V   should satisfy the following form,  V   ¼  c ð  x  ;  y  ;  z  Þ P ; P  ¼ r q r q jr q r q j ;  ð 3 Þ where  P  is calculated from hydrographic data;  c  is thespeed parameter with  c j j  the speed. A two-step method was proposed by Chu (1995)(i.e. the P-vector inverse method): (a) determinationof the unit vector  P , and (b) determination of the sca-lar  c  from the thermal wind relation, c ð k  Þ P  ð k  Þ  x    c ð m Þ P  ð m Þ  x   ¼  D u km ;  ð 4 Þ c ð k  Þ P  ð k  Þ  y    c ð m Þ P  ð m Þ  y   ¼  D v  km ;  ð 5 Þ where D u km    gf  q 0 Z   z  k   z  m @  q @   y dz  0 ;  ð 6 Þ D v  km     gf  q 0 Z   z  k   z  m @  q @   x dz  0 ;  ð 7 Þ are geostrophic shear at depth  z  k   relative to  z  m . If thedeterminant of the two linear algebraic equations (4)and (5) is nonzero (Figure 2),sin ð D a km Þ ¼  P  ð k  Þ  x   amp ; P  ð m Þ  x  P  ð k  Þ  y   amp ; P  ð m Þ  y   6¼  0 ;  ð 8 Þ That is, the P -vector spiral exists (Chu, 2000), the speedparameter  c  at these two levels  c ( k  ) and  c ( m ) can bedetermined after solving the linear algebraic equations(4)and(5),andinturnthehorizontalvelocity.This method was evaluated (Chu  et al. , 1998) andapplied to calculate the absolute velocity from hydro-graphic data for the South China Sea (Chu and Li,2000), Japan Sea (Chu  et al. , 2001a), and NorthwestPaci 󿬁 c (Chu  et al. , 2002, 2003). In conjunction withthe wind forcing, the P-vector method is also used tocalculate the global volume transport (Chu and Fan,2007). To reduce error, a variational P-vector methodwas developed (Chu  et al. , 2001b). 2. Data The WOAV13 dataset is in the Network Common DataForm (netCDF) (see the website: http:// Figure 1.  Intersection of surfaces of and  q   (from Chu 1995,Marine Technology Society Journal). Figure 2.  Illustration of P-spiral (left panel) and turningangle (right panel) between two levels. WOAV13: world ocean absolute geostrophic velocity 79 ª  2016 The Authors. Geoscience Data Journal   published by Royal Meteorological Society and John Wiley & Sons Ltd.  Geoscience Data Journal   2 : 78 – 82 (2015)  www.unidata.ucar.edu/software/netcdf/), which is aninterface for array-oriented data access, a library forimplementation of interface, and a machine-indepen-dent format for representing data. The netCDF soft-ware was developed at the Unidata (http://www.unidata.ucar.edu) Program Center in Boulder,Colorado. Each element is stored at a disk addresswhich is a linear function of the array indices (sub-scripts) by which it is identi 󿬁 ed. Hence, these indicesneed not be stored separately (as in a relational data-base). This provides a fast and compact storagemethod. The external types supported by the netCDFinterface are listed in Table 1. These types are chosento provide a reasonably wide range of trade-offsbetween data precision and number of bits requiredfor each value. The external data types are indepen-dent from whatever internal data types are supportedby a particular machine and language combination.These types of extracted data are called  ‘ external ’  ,because they correspond to the portable external rep-resentation for netCDF data. Figure 3 shows the glo-bal annual mean, January, and July volume transportstream function (unit: Sv, 1 Sv   =  10 6 m 3 sec  1 ) withthe absolute geostrophic velocity for the extra-equa-torial region (north of 8 ° N and south of 8 ° S) calculatedby the P-vector method (Chu and Fan, 2007) as exam-ples. The combined WOA13 and WOAV13 provide glo-bal 3D annual and monthly ( T  ,  S  ,  u ,  v  ) data. 3. Data Download The data can be downloaded directly from the NCEIwebsite: http://www.nodc.noaa.gov/cgi-bin/OAS/prd/accession/download/121576. Please contact NCEICustomer Service if you need further assistance(http://www.nodc.noaa.gov/about/contact.html). Toread the data, the free ncdf package needs to bedownloaded from the website: https://www.im-age.ucar.edu/GSP/Software/Netcdf/. The MATLAB(version 2008b and later) provides access to morethan 30 functions in the netCDF interface. This inter-face provides an application program interface (API)that you can use to enable reading data from andwriting data to netCDF  󿬁 les (known as  datasets  innetCDF terminology). The MATLAB code is listed asfollows to read the WOAV13 data in netCDF.% open netcdf datancid=netcdf.open(  ‘ WOA13pv.nc ’  , ’  nowrite ’  );% get the year-month-season datayms_id=netcdf.inqVarID(ncid, ’  year-month-sea-son ’  );yms=netcdf.getVar(ncid,yms_id) ’  ;% get the logitude datalon_id=netcdf.inqVarID(ncid, ’  lon ’  );lon=netcdf.getVar(ncid,lon_id);% get the lattitude datalat_id=netcdf.inqVarID(ncid, ’  lat ’  );lat=netcdf.getVar(ncid,lat_id);% get the vertical coordinate zz_id=netcdf.inqVarID(ncid, ’  z ’  );z=netcdf.getVar(ncid,z_id);% get the zonal and meridional relative geos-trophic velocities from the bottomug_id=netcdf.inqVarID(ncid, ’  ug ’  );vg_id=netcdf.inqVarID(ncid, ’  vg ’  );% get the unitsunits=netcdf.getAtt(ncid,ug_id, ’  units ’  );% get all dataug=netcdf.getVar(ncid,ug_id);vg=netcdf.getVar(ncid,vg_id);% get part of the data% example: annual at depth level k ug=netcdf.getVar(ncid,ug_id,[0,0,k-1,0],[179,360,1,1vg=netcdf.getVar(ncid,vg_id,[0,0,k-1,0],[179,360,1,1ug(ug>1e30)=NaN; vg(vg>1e30)=NaN; % setthe garbage data to NaN.% Example: month (m) at depth level k ug=netcdf.getVar(ncid,ug_id,[0,0,k-1,m],[179,360,1,1vg=netcdf.getVar(ncid,vg_id,[0,0,k-1,m],[179,360,1,1ug(ug>1e30)=NaN; vg(vg>1e30)=NaN; % setthe garbage data to NaN.% example: winter at depth level k ug=netcdf.getVar(ncid,ug_id,[0,0,k-1,13],[179,360,1,1vg=netcdf.getVar(ncid,vg_id,[0,0,k-1,13],[179,360,1,1ug(ug>1e30)=NaN; vg(vg>1e30)=NaN; % setthe garbage data to NaN.% get zonal and meridional absolute geostrophicvelocitiesu_id=netcdf.inqVarID(ncid, ’  u ’  );v_id=netcdf.inqVarID(ncid, ’  v  ’  );\ % get the unitsunits=netcdf.getAtt(ncid,u_id, ’  units ’  );% get all datau=netcdf.getVar(ncid,u_id);v=netcdf.getVar(ncid,v_id); Table 1.  Extracted data type and characteristics. Data type Characteristics char 8-bit characters intended forrepresenting textbyte 8-bit signed or unsigned integersshort 16-bit signed integersint 32-bit signed integersFloat/real 32-bit IEEE  󿬂 oating-pointdouble 64-bit IEEE  󿬂 oating-point 80 P. C. Chu and C. W. Fan ª  2016 The Authors. Geoscience Data Journal   published by Royal Meteorological Society and John Wiley & Sons Ltd. Geoscience Data Journal   2 : 78 – 82 (2015)  u(u>1e30)=NaN; v(v>1e30)=NaN; % set thegarbage data to NaN.% get part of the data% example: Annual at depth level k u=netcdf.getVar(ncid,u_id,[0,0,k-1,0],[179,360,1,1v=netcdf.getVar(ncid,v_id,[0,0,k-1,0],[179,360,1,1u(u>1e30)=NaN; v(v>1e30)=NaN; % set thegarbage data to NaN.% example: Month m at depth level k u=netcdf.getVar(ncid,u_id,[0,0,k-1,m],[179,360,1,1v=netcdf.getVar(ncid,v_id,[0,0,k-1,m],[179,360,1,1u(u>1e30)=NaN; v(v>1e30)=NaN; % set thegarbage data to NaN.% example: Autumn at depth level k u=netcdf.getVar(ncid,ug_id,[0,0,k-1,16],[179,360,1,1v=netcdf.getVar(ncid,vg_id,[0,0,k-1,16],[179,360,1,1u(u>1e30)=NaN; v(v>1e30)=NaN; % set thegarbage data to NaN.% close the data  󿬁 lenetcdf.close(ncid); (a)(b)(c) Figure 3.  Inverted global volume transport stream function (unit: Sv): (a) annual mean, (b) January, and (c) July (from Chu andFan 2007, Journal of Marine Systems). WOAV13: world ocean absolute geostrophic velocity 81 ª  2016 The Authors. Geoscience Data Journal   published by Royal Meteorological Society and John Wiley & Sons Ltd.  Geoscience Data Journal   2 : 78 – 82 (2015)
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