# The Gibbs SeaWater (GSW)
Oceanographic Toolbox of TEOS-10

## Contents

- documentaion set
- Practical Salinty (SP), PSS-78
- Absolute Salinity (SA), Preformed Salinity (Sstar) and Conservative Temperature (CT)
- Absolute Salinity - Conservative Temperature plotting function
- other conversions between temperatures, salinities, entropy, pressure and height
- density and enthalpy, based on the 48-term expression for density
- water column properties, based on the 48-term expression for density
- neutral and non-linear properties, based on the 48-term expression for density
- geostrophic streamfunctions, based on the 48-term expression for density
- geostrophic velocity
- derivatives of enthalpy, entropy, CT and pt
- freezing temperatures
- isobaric melting enthalpy and isobaric evaporation enthalpy
- Planet Earth properties
- steric height
- TEOS-10 constants
- density and enthalpy in terms of CT, based on the exact Gibbs function
- basic thermodynamic properties in terms of in-situ temperature, based on the exact Gibbs function
- Library functions of the GSW toolbox (internal functions; not intended to be called by users)
- Licences and third party software

### documentation set

     gsw_front_page                             front page to the GSW Oceanographic Toolbox
     gsw_check_functions                        checks that all the GSW functions work correctly
     gsw_demo                                   demonstrates many GSW functions and features

### Practical Salinity (SP), PSS-78

     gsw_SP_from_C                              Practical Salinity from conductivity, C (inc. for SP < 2)
     gsw_C_from_SP                              conductivity, C, from Practical Salinity (inc. for SP < 2)
     gsw_SP_from_R                              Practical Salinity from conductivity ratio, R (inc. for SP < 2)
     gsw_R_from_SP                              conductivity ratio, R, from Practical Salinity (inc. for SP < 2)
     gsw_SP_salinometer                         Practical Salinity from a laboratory salinometer (inc. for SP < 2)
     gsw_SP_from_SK                             Practical Salinity from Knudsen Salinity

### Absolute Salinity (SA), Preformed Salinity (Sstar) and Conservative Temperature (CT)

     gsw_SA_from_SP                             Absolute Salinity from Practical Salinity
     gsw_Sstar_from_SP                          Preformed Salinity from Practical Salinity
     gsw_CT_from_t                              Conservative Temperature from in-situ temperature

### Absolute Salinity - Conservative Temperature plotting function

     gsw_SA_CT_plot                             function to plot Absolute Salinity - Conservative Temperature
                                                  profiles on the SA-CT diagram, including the freezing line
                                                  and selected potential density contours

### other conversions between temperatures, salinities, pressure and height

     gsw_deltaSA_from_SP                        Absolute Salinity Anomaly from Practical Salinity
     gsw_SA_Sstar_from_SP                       Absolute Salinity & Preformed Salinity from Practical Salinity
     gsw_SR_from_SP                             Reference Salinity from Practical Salinity
     gsw_SP_from_SR                             Practical Salinity from Reference Salinity
     gsw_SP_from_SA                             Practical Salinity from Absolute Salinity
     gsw_Sstar_from_SA                          Preformed Salinity from Absolute Salinity
     gsw_SA_from_Sstar                          Absolute Salinity from Preformed Salinity
     gsw_SP_from_Sstar                          Practical Salinity from Preformed Salinity
     gsw_pt_from_CT                             potential temperature from Conservative Temperature
     gsw_t_from_CT                              in-situ temperature from Conservative Temperature
     gsw_CT_from_pt                             Conservative Temperature from potential temperature
     gsw_pot_enthalpy_from_pt                   potential enthalpy from potential temperature
     gsw_pt0_from_t                             potential temperature with a reference pressure of zero dbar
     gsw_pt_from_t                              potential temperature
     gsw_t90_from_t48                           ITS-90 temperature from IPTS-48 temperature
     gsw_t90_from_t68                           ITS-90 temperature from IPTS-68 temperature
     gsw_z_from_p                               height from pressure
     gsw_p_from_z                               pressure from height
     gsw_depth_from_z                           depth from height
     gsw_z_from_depth                           height from depth
     gsw_Abs_Pressure_from_p                    Absolute Pressure,P, from pressure, p
     gsw_p_from_Abs_Pressure                    pressure, p, from Absolute Pressure, P
     gsw_entropy_from_CT                        entropy from Conservative Temperature
     gsw_CT_from_entropy                        Conservative Temperature from entropy
     gsw_entropy_from_pt                        entropy from potential temperature
     gsw_pt_from_entropy                        potential temperature from entropy
     gsw_molality_from_SA                       molality of seawater
     gsw_ionic_strength_from_SA                 ionic strength of seawater

### density and enthalpy, based on the 48-term expression for density

The functions in this group ending in "_CT" may also be called without "_CT".

     gsw_rho_CT                                 in-situ density from CT, and potential density
     gsw_alpha_CT                               thermal expansion coefficient with respect to CT
     gsw_beta_CT                                saline contraction coefficient at constant CT
     gsw_rho_alpha_beta_CT                      in-situ density, thermal expansion & saline contraction coefficients
     gsw_specvol_CT                             specific volume
     gsw_specvol_anom_CT                        specific volume anomaly
     gsw_sigma0_CT                              sigma0 from CT with reference pressure of 0 dbar
     gsw_sigma1_CT                              sigma1 from CT with reference pressure of 1000 dbar
     gsw_sigma2_CT                              sigma2 from CT with reference pressure of 2000 dbar
     gsw_sigma3_CT                              sigma3 from CT with reference pressure of 3000 dbar
     gsw_sigma4_CT                              sigma4 from CT with reference pressure of 4000 dbar
     gsw_sound_speed_CT                         sound speed (approximate, with r.m.s. error of 0.067 m/s)
     gsw_internal_energy_CT                     internal energy
     gsw_enthalpy_CT                            enthalpy
     gsw_enthalpy_diff_CT                       difference of enthalpy between two pressures
     gsw_dynamic_enthalpy_CT                    dynamic enthalpy
     gsw_SA_from_rho_CT                         Absolute Salinity from density & CT
     gsw_CT_from_rho                            Conservative Temperature from density
     gsw_CT_maxdensity                          Conservative Temperature of maximum density of seawater

### water column properties, based on the 48-term expression for density

     gsw_Nsquared                               buoyancy (Brunt-Vaisala) frequency squared (N^2)
     gsw_Turner_Rsubrho                         Turner angle & Rsubrho
     gsw_IPV_vs_fNsquared_ratio                 ratio of the vertical gradient of potential density
                                                 (with reference pressure, p_ref), to the vertical gradient
                                                 of locally-referenced potential density

### neutral and non-linear properties, based on the 48-term expression for density

     gsw_cabbeling                              cabbeling coefficient
     gsw_thermobaric                            thermobaric coefficient
     gsw_isopycnal_slope_ratio                  ratio of the slopes of isopycnals on the SA-CT diagram
                                                  for p & p_ref
     gsw_isopycnal_vs_ntp_CT_ratio              ratio of the gradient of Conservative Temperature
                                                  in a potential density surface to that in the neutral
                                                  tangent plane
     gsw_ntp_pt_vs_CT_ratio                     ratio of gradients of potential temperature &
                                                  Conservative Temperature in a neutral tangent plane
                                                  (i.e. in a locally-referenced potential density surface)

### geostrophic streamfunctions, based on the 48-term expression for density

     gsw_geo_strf_dyn_height                    dynamic height anomaly
     gsw_geo_strf_dyn_height_pc                 dynamic height anomaly for piecewise constant profiles
     gsw_geo_strf_isopycnal                     approximate isopycnal geostrophic streamfunction
     gsw_geof_str_isopycnal_pc                  approximate isopycnal geostrophic streamfunction for
                                                  piecewise constant profiles
     gsw_geo_strf_Montgomery                    Montgomery geostrophic streamfunction
     gsw_geo_strf_Cunningham                    Cunningham geostrophic streamfunction

### geostrophic velocity

     gsw_geostrophic_velocity                   geostrophic velocity

### derivatives of enthalpy, entropy, CT and pt

     gsw_CT_first_derivatives                   first derivatives of Conservative Temperature
     gsw_CT_second_derivatives                  second derivatives of Conservative Temperature
     gsw_enthalpy_first_derivatives             first derivatives of enthalpy
     gsw_enthalpy_second_derivatives            second derivatives of enthalpy
     gsw_entropy_first_derivatives              first derivatives of entropy
     gsw_entropy_second_derivatives             second derivatives of entropy
     gsw_pt_first_derivatives                   first derivatives of potential temperature
     gsw_pt_second_derivatives                  second derivatives of potential temperature

### freezing temperatures

     gsw_CT_freezing                            Conservative Temperature freezing temperature of seawater
     gsw_t_freezing                             in-situ freezing temperature of seawater
     gsw_brineSA_CT                             Absolute Salinity of seawater at the freezing point (for given CT)
     gsw_brineSA_t                              Absolute Salinity of seawater at the freezing point (for given t)

### isobaric melting enthalpy and isobaric evaporation enthalpy

     gsw_latentheat_melting                     latent heat of melting of ice into seawater (isobaric melting enthalpy)
     gsw_latentheat_evap_CT                     latent heat of evaporation of water from seawater (isobaric
                                                  evaporation enthalpy) with CT as input temperature
     gsw_latentheat_evap_t                      latent heat of evaporation of water from seawater (isobaric
                                                  evaporation enthalpy) with in-situ temperature, t, as input

### Planet Earth properties

     gsw_f                                      Coriolis parameter
     gsw_grav                                   gravitational acceleration
     gsw_distance                               spherical earth distance between points in the ocean

### steric height

     gsw_steric_height                          dynamic height anomaly divided by 9.7963 m s^-2

### TEOS-10 constants

     gsw_T0                                     Celcius zero point; 273.15 K
     gsw_P0                                     one standard atmosphere; 101 325 Pa
     gsw_SS0                                    Standard Ocean Reference Salinity; 35.165 04 g/kg
     gsw_uPS                                    unit conversion factor for salinities; (35.165 04/35) g/kg
     gsw_cp0                                    the "specific heat" for use with CT; 3991.867 957 119 63 (J/kg)/K
     gsw_C3515                                  conductivity of SSW at SP=35, t_68=15, p=0; 42.9140 mS/cm
     gsw_SonCl                                  ratio of SP to Chlorinity; 1.80655 (g/kg)^-1
     gsw_valence_factor                         valence factor of sea salt; 1.2452898
     gsw_atomic_weight                          mole-weighted atomic weight of sea salt; 31.4038218... g/mol

### density and enthalpy in terms of CT, based on the exact Gibbs function

     gsw_rho_CT_exact                           in-situ density from CT, and potential density from CT
     gsw_alpha_CT_exact                         thermal expansion coefficient with respect to CT
     gsw_beta_CT_exact                          saline contraction coefficientat constant CT
     gsw_rho_alpha_beta_CT_exact                in-situ density, thermal expansion & saline contraction coefficient from CT
     gsw_specvol_CT_exact                       specific volume from CT
     gsw_specvol_anom_CT_exact                  specific volume anomaly from CT
     gsw_sigma0_CT_exact                        sigma0 from CT with reference pressure of 0 dbar
     gsw_sigma1_CT_exact                        sigma1 from CT with reference pressure of 1000 dbar
     gsw_sigma2_CT_exact                        sigma2 from CT with reference pressure of 2000 dbar
     gsw_sigma3_CT_exact                        sigma3 from CT with reference pressure of 3000 dbar
     gsw_sigma4_CT_exact                        sigma4 from CT with reference pressure of 4000 dbar
     gsw_sound_speed_CT_exact                   sound speed
     gsw_internal_energy_CT_exact               internal energy
     gsw_enthalpy_CT_exact                      enthalpy from CT
     gsw_enthalpy_diff_CT_exact                 difference of enthalpy from CT between two pressures
     gsw_dynamic_enthalpy_CT_exact              dynamic enthalpy from CT
     gsw_SA_from_rho_CT_exact                   Absolute Salinity from Density & CT
     gsw_CT_from_rho_exact                      Conservative Temperature from density
     gsw_CT_maxdensity_exact                    Conservative Temperature of maximum density of seawater

### basic thermodynamic properties in terms of in-situ t, based on the exact Gibbs function

     gsw_rho_t_exact                            in-situ density
     gsw_pot_rho_t_exact                        potential density
     gsw_sigma0_pt0_exact                       sigma0 from pt0 with reference pressure of 0 dbar
     gsw_alpha_wrt_CT_t_exact                   thermal expansion coefficient with respect to Conservative Temperature.
     gsw_alpha_wrt_pt_t_exact                   thermal expansion coefficient with respect to potential temperature
     gsw_alpha_wrt_t_exact                      thermal expansion coefficient with respect to in-situ temperature
     gsw_beta_const_CT_t_exact                  saline contraction coefficient at constant Conservative Temperature.
     gsw_beta_const_pt_t_exact                  saline contraction coefficient at constant potential temperature
     gsw_beta_const_t_exact                     saline contraction coefficient at constant in-situ temperature
     gsw_specvol_t_exact                        specific volume
     gsw_specvol_anom_t_exact                   specific volume anomaly
     gsw_sound_speed_t_exact                    sound speed
     gsw_kappa_t_exact                          isentropic compressibility
     gsw_kappa_const_t_exact                    isothermal compressibility
     gsw_internal_energy_t_exact                internal energy
     gsw_enthalpy_t_exact                       enthalpy
     gsw_dynamic_enthalpy_t_exact               dynamic enthalpy
     gsw_SA_from_rho_t_exact                    Absolute Salinity from density
     gsw_t_from_rho_exact                       in-situ temperature from density
     gsw_t_maxdensity_exact                     in-situ temperature of maximum density of seawater
     gsw_entropy_t_exact                        entropy
     gsw_cp_t_exact                             isobaric heat capacity
     gsw_isochoric_heat_cap_t_exact             isochoric heat capacity
     gsw_chem_potential_relative_t_exact        relative chemical potential
     gsw_chem_potential_water_t_exact           chemical potential of water in seawater
     gsw_chem_potential_salt_t_exact            chemical potential of salt in seawater
     gsw_Helmholtz_energy_t_exact               Helmholtz energy
     gsw_adiabatic_lapse_rate_t_exact           adiabatic lapse rate
     gsw_osmotic_coefficient_t_exact            osmotic coefficient of seawater
     gsw_osmotic_pressure_t_exact               osmotic pressure of seawater

### Library functions of the GSW toolbox (internal functions; not intended to be called by users)

     The GSW functions above call the following library functions.

     gsw_gibbs                                  the TEOS-10 Gibbs function and its derivatives
     gsw_SAAR                                   Absolute Salinity Anomaly Ratio (excluding the Baltic Sea)
     gsw_Fdelta                                 ratio of Absolute to Preformed Salinity, minus 1
     gsw_deltaSA_atlas                          Absolute Salinity Anomaly atlas value (excluding the Baltic Sea)
     gsw_SA_from_SP_Baltic                      Calculates Absolute Salinity in the Baltic Sea
     gsw_SP_from_SA_Baltic                      Calculates Practical Salinity in the Baltic Sea
     gsw_infunnel                               "oceanographic funnel" check for the 48-term equation
     gsw_entropy_part                           entropy minus the terms that are a function of only SA
     gsw_entropy_part_zerop                     entropy_part evaluated at 0 dbar
     gsw_interp_ref_cast                        linearly interpolates the reference cast
     gsw_interp_SA_CT                           linearly interpolates (SA,CT,p) to the desired p
     gsw_gibbs_pt0_pt0                          gibbs(0,2,0,SA,t,0)
     gsw_specvol_SSO_0_p                        specvol_CT(35.16504,0,p)
     gsw_enthalpy_SSO_0_p                       enthalpy_CT(35.16504,0,p)
     gsw_Hill_ratio_at_SP2                      Hill ratio at a Practical Salinity of 2

     The GSW data set.
     gsw_data_v3_0                              contains
                                                (1) the global data set of Absolute Salinity Anomaly Ratio,
                                                (2) the global data set of Absolute Salinity Anomaly Ref.,
                                                (3) a reference cast (for the isopycnal streamfunction),
                                                (4) two reference casts that are used by gsw_demo
                                                (5) three vertical profiles of (SP, t, p) at known long & lat, plus
                                                   the outputs of all the GSW functions for these 3 profiles, and
                                                   the required accuracy of all these outputs.

### Licences and 3rd party software

     gsw_licence                                creative commons licence for the GSW Oceanographic Toolbox
     cprintf                                    prints colour text to the screen (third part software)
     cprintf_licence                            licence for cprintf software