Salinity

Salinity is the total amount of dissolved material in grams in one kilogram of sea water (Ideal, hard to measure)

On average, there is around 35 gram salt in a kilogram of sea water, 35g/kg, written as S=35‰ or S=35ppt, read as “thirty-five parts per thousand” (non-dimensional)

Globally, S can go from near 0 (coast) to about 40 ppt (Red Sea), BUT 90% is between 34-35 ppt

Salinity is an aggregate variable. The most abundant ions in sea water:

chlorine Cl- 55.0% sodium Na+ 30.6% sulphate SO4

++ 7.7%magnesium Mg++ 3.7% potassium K+ 1.1%

Basic properties of salt in sea water1). The ratio of the more abundant components remain almost

constant. (ocean is very well mixed globally over geological time~millions of years, much longer than the time for water to circulate through the oceans~thousands of years) (Major exceptions are found in coastal and enclosed regions, due to land drainage and biological processes)

2). There are significant differences in total concentration of the dissolved salts from place to place and at different depths. (Processes, such as local evaporation and precipitation, as well as oceanic circulation, continually concentrate and dilute salt in sea water in specific localities)

3). The presence of salts influences most physical properties of sea water (density, compressibility, freezing point).

4). The conductivity of the sea water is partly determined by the amount of salt it contains.

Early Definition (1902)

Total amount of solid materials in grams dissolved in one kilogram of sea water when all the carbonate has been converted to oxide, the bromine and iodine replaced by chlorine and all organic matter completely oxidized

Given by a commission of the International Council for the Exploration of the Sea

Salinity based on chlorinitySalinity can be determined through the amount of chloride ion (plus the

chlorine equivalent of the bromine and iodine), called as chlorinity, which is measured using titration with silver nitrate (Knudsen et al., 1902)

The relationship between salinity and chlorinity is based on laboratory measurements of sea water samples collected from different regions of the world ocean and was given in 1969 by UNESCO as

SA (‰) = 1.80655 Chlorinity (‰)

SA is called as “Absolute Salinity”, unit: ppt

chlorinity Cl is defined as "the mass of silver required to precipitate completely the halogens in 0.328 523 4kg of the sea-water sample."

Practical salinity Scale of 1978• The practical salinity, symbol S, of a sample of sea water, is defined

in terms of the ratio K15 of the electrical conductivity of a sea water sample of 15°C and the pressure of one standard atmosphere, to that of a potassium chloride (KCl) solution, in which the mass fraction of KCl is 0.0324356g, at the same temperature and pressure. The K15 value equal to one corresponds to a practical salinity equal to 35.

• The corresponding formula is: S = 0.0080 - 0.1692 K1/2 + 25.3853 K + 14.0941 K3/2 - 7.0261 K2 + 2.7081 K5/2 +….

• Note that in this definition, S is a ratio and is non-dimensional, but

salinity of 35‰ corresponds to a value of 35 in the practical salinity.

• S is sometimes given the unit “psu” (practical salinity unit) in literature (probably unnecessarily)

Salinity measurement

Total resolved material is hard to measure routinely in sea-water (e.g., evaporation of sea-water sample to dryness)

In practice, some properties of sea water are used to estimate salinity.

Method #1: Salinity is determined by measurements of a substitution quantity since it is contributed by its components in a fixed ratio.

Method #2: Salinity is inferred from measurements of sea water’s electrical conductivity.

Salinity measurement

Knudsen (Titration) method (precision ±0.02, prior to 1960) • time consuming and not convenient on board ship• not accurate enough to identify deep ocean water mass

Electrical conductivity method (precision ±0.003~±0.001) • Conductivity depends on the number of dissolved ions

per volume (i.e. salinity) and the mobility of the ions (ie temperature and pressure). Its units are mS/cm (milli-Siemens per centimeter).

• Conductivity increases by the same amount with S~0.01, T~ 0.01°C, and z~ 20 m.

• The conductivity-density relation is closer than density-chlorinity

• The density and conductivity is determined by the total weight of the dissolved substance

A conductivity cell. Current flows through the seawater between platinum electrodes in a cylinder of borosilicate glass 191mm long with an inside diameter between the electrodes of 4mm. The electric field lines (solid lines) are confined to the interior of the cell in this design making the measured conductivity (and instrument calibration) independent of objects near the cell. From Sea-Bird Electronics.

Conductivity is measured by placing platinum electrodes in seawater and measuring the current that flows when there is a known voltage between the electrodes. The current depends on conductivity, voltage, and volume of sea water in the path between electrodes. If the elecrodes are in a tube of non-conducting glass, the volume of water is accurately known, and the current is independent of other objects near the conductivity cell. The best measurements of salinity from conductivity give salinity with an accuracy of ±0.005.

Potential temperature and temperature, (b) conductivity, and (c) salinity in the northern North Pacific.

Note that conductivity is a function of temperature and pressure also, which should be compensated in the salinity measurements

Standard deviation of salinity measurements at depths below 1500 m in the South Atlantic from 1920 to 1993. Each point is the average of data collected for the decade centered on the point. The value for 1995 is an estimate of the accuracy of recent measurements. From Table 1 of Gouretski and Jancke (1995).

Gouretski and Jancke (1995) estimated accuracy of salinity measurements as a function of time. Using high quality measurements from 16,000 hydrographic stations in the south Atlantic from 1912 to 1991, they estimated accuracy by plotting salinity as a function of temperature using all data collected below 1500m in twelve regions for each decade from 1920 to 1990.

conductivity-temperature-depth probe

In situ CTD precision: S~±0.005 (0.001)T ±0.005K (0.001K) z~±0.15% z

The vertical resolution is highT measured by thermistorS measured by conductivity cellP measured by quartz crystal

CTD sensors should be calibrated (with bottle samples before 1990s)

Subsurface driftersModern subsurface floats remain at depth for a period of time, come to the surface briefly to transmit their data to a satellite and return to their allocated depth. These floats can therefore be programmed for any depth and can also obtain temperature and salinity (CTD) data during their ascent. The most comprehensive array of such floats, known as Argo, began in the year 2000. Argo floats measure the temperature and salinity of the upper 2000 m of the ocean. This will allow continuous monitoring of the climate state of the ocean, with all data being relayed and made publicly available within hours after collection.

When the Argo programme is fully operational it will have 3,000 floats in the world ocean at any one time.The accuracy of the data from the floats is 0.005oC for temperature, 5 decibars for pressure, and 0.01 for salinity (Riser et al., 2008)

Summary of Measurement Accuracy

Variable Range Best Accuracy 

Temperature 42°C ±0.001°CSalinity ±0.02 by titration

±0.005 by conductivityPressure 10,000 dbar ± 0.65 dbarDensity ± 0.005 kg/m3

Equation of State ± 0.009 kg/m3

Quality Controlled in situ ocean temperature and salinity profiles database:

As of 2008:~one million XBT profiles~700,000 CTD profiles~60,000 Argo profiles~1,100,000 Nansen bottle data

Density (, kg/m3)• Determine the depth a water mass settles in equilibrium.• Determine the large scale circulation. changes in the ocean is small.

1020-1070 kg/m3 (depth 0~10,000m)• increases with p (the greatest effect)

ignoring p effect: ~1020.0-1030.0 kg/m3 1027.7-1027.9 kg/m3 for 50% of ocean

• increases with S. decreases with T most of the time.

• is usually not directly measured but determined from T, S, and p

Density anomaly

Since the first two digits of never change, a new quantity is defined as

s,t,p = – 1000 kg/m3

called as “in-situ density anomaly”. (1000 kg/m3 is for freshwater at 4oC)

Atmospheric-pressure density anomaly (Sigma-tee)

t = s,t,0= s,t,0 – 1000 kg/m

(note: s and t are in situ at the depth of measurement)

Equation of StateThe dependence of density (or ) on temperature T, salinity S and

pressure p is the Equation of State of Sea Water.

=(T, S, p) is determined by laboratory experiments.

International Equation of State (1980) is the most widely used density formula now.

• This equation uses T in °C, S from the Practical Salinity Scale and p in dbar (1 dbar = 104 Pascal = 104 N m-2) and gives in kg m3.

• Range: -2oC≤ T ≤ 40oC, 0 ≤ S ≤ 40, 0 ≤ p ≤ 105 kPa (depth, 0 to 10,000 m)

• Accuracy: 5 x 10-6 (relative to pure water, ±0.005)• Polynomial expressions of (S, t, 0) (15 terms) and K(S, t, p) (27

terms) get accuracy of 9 x 10-6.

),,(1

)0,,(),,(

ptSKp

tSptS

−=

Bulk modulus K=1/, is compressibility.

1== KC , C speed of the sound in sea water.

Simple formula:(1)

kpSSbtta +−+−=− )()( 000 accuracy: ±0.5 kg/m3

where 0=1027 kg/m3, T0=10oC, S0=35 psu,

a=-0.15 kg/m3oC, b=0.78kg/m3, k=4.5x10-3 /dbar

TSPTTpTSppC )35)(,(),()()( −−−+= γα2048.0053.583.999 ppC −+=

p0085.0808.0 −=

))0683.01(068.0351.01(0708.0 Tpp −++=α))064.01(012.0059.01(003.0 Tpp −−−=γ

For 30≤S≤40, -2≤T≤30, p≤ 6 km, good to 0.16 kg/m3

For 0 ≤S≤40, good to 0.3 kg/m3

(2)

where

Coefficient of thermal expansion:

SpT,1⎟⎠⎞⎜⎝⎛∂∂−=−αCompressibility:

STp,1⎟⎟⎠⎞⎜⎜⎝⎛∂∂=−γCoefficient for sali necontraction:

TpS,1⎟⎠⎞⎜⎝⎛∂∂=−

Thermobaricity

Relation between (T,S) and t

The temperature of density maximum is the red line and the freezing point is the light blue line

t as a function of T and S• The relation is more nonlinear with respect to T • t change is more uniform with S• t is more sensitive to S than T near freezing point • max meets the freezing point at S =24.7

S < 24.7: after passing max surface water becomes lighter and eventually freezes over if cooled further. The deep basins are filled with water of maximum density

S > 24.7: Convection always reaches the entire water body. Cooling is slowed down because a large amount of heat is stored in the water body

Mixing in the Ocean: Cabelling

Specific volume and anomaly

Specific volume: α=1/ (unit m3/kg)

Specific volume anomaly:

= αs, t, p – α35, 0, p (usually positive) = s + t + s,t + s,p + t,p + s,t,p

• In practice, s,t,p is always small (ignored) s, p and t, p are smaller than the first three terms

(5 to 15 x 10-8 m3/kg per 1000 m)Thermosteric anomaly:

S,T = s + t + s, t (50-100 x 10-8 m3/kg or 50-100 centiliter per ton, cL/t)

Converting formula for S,T and t :

Since α(35,0,0)=0.97266x10-3 m3/kg,

TStts

ts ,)0,0,35(1000

1

)0,,(

1)0,,( +=

+== α

α

3, 1097266.0

1000

1000 −×⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=

tTS , m3/kg

1.280105.0 , +−= TSt

For 23 ≤ t ≤ 28,

,26751.95, +−= tTS accurate to 1 in cL/ton

For most part of the ocean, 25.5 ≤t≤28.5. Correspondingly, 250 cL/ton ≥ S,T ≥ -50 cL/ton

, accurate to 0.1