Although the rest of the world, and all scientists in the U.S. use the Celsius (previously called centigrade) scale to express ocean temperature, the equivalent values in degrees Fahrenheit are included in parentheses here since the U.S. Navy still commonly uses the Fahrenheit scale. The conversion from °Celsius (C) to °Fahrenheit (F) and vice-versa is given below.

Salinity

The concentration of dissolved salts in ocean water is called the salinity. While the total dissolved salts varies from place to place in the ocean due to evaporation, precipitation, river inflow, and mixing, the ratio among the various major dissolved salts remains essentially constant.

Note: Salinity used to be expressed in terms of parts per thousand (ppt) or by weight (). Currently, salinity is usually denoted by S and is a dimensionless quantity.

The currently used definition of salinity was adopted when techniques to determine salinity from measurements of conductivity, temperature and pressure were developed. The UNESCO Practical Salinity Scale of 1978, PSS78, defines salinity in terms of a conductivity ratio, so is dimensionless. Therefore practical salinity is correctly written without units, although often you will see the numeric value followed by “psu” which stands for “practical salinity unit”.

Salinity may increase or decrease in depth. Open ocean salinities are generally in the range between 32 and 37, but may be much lower near freshwater sources or at the surface, and may be as high as 42 in the Red Sea.

Pressure

Pressure, abbreviated p, is often used instead of depth to express the vertical coordinate in the ocean. Pressure is a function of depth, density, and gravitational acceleration.

Although the total pressure at a point in the ocean would be due both to the weight of the seawater above it and the atmospheric pressure, unless otherwise specified, the pressure at a point in the ocean is taken to be just that due to the seawater, not the seawater plus atmosphere. Therefore the sea pressure at the surface is 0 dbar. The pressure in dbar and the depth in meters are approximately equal, so the pressure in the ocean at 1 m depth is approximately 1 dbar, and that at 1000 m approximately 1000 dbar etc.

Density

The density, , of seawater is function of temperature, salinity, and pressure. It increases with increasing salinity and pressure, and decreases with increasing temperature. The density is expressed in units of kg/m³, or sometimes g/cm³. Oceanographers use a number of different ways to express the density of seawater, so you may see the terms density anomaly, potential density, (pronounced sigma-theta), specific volume, specific volume anomaly or others. The most commonly used of these are defined below.

Sigma, is a short-hand for seawater density, where 1000 kg/m3 has been subtracted. So for = 1024.32 kg/m3, = 24.32 kg/m3. While all the versions of have units of kg/m3, it is often reported without units, which is a throwback to when the definitions included a ratio of the seawater density to the density of freshwater, thus rendering the variable dimensionless.

Sigma-t, is density of seawater calculated with in situ salinity and temperature, but pressure equal to zero, rather than the in situ pressure and 1000 kg/m3 is subtracted.

Sigma-theta, is the density calculated with in situ salinity, potential temperature, and pressure = 0, minus 1000 kg/m3. If a pressure reference level other than the surface is used, it will be indicated by using the reference level as the subscript for . When comparing the density of water samples from different depths, it is preferable to use .

Specific volume, , is the inverse of density; . It has dimensions of volume/mass, units of m3/kg, cm3/g, or centiliters per metric ton (cliter/ton) are usually used, where 1 cliter/ton=10-5 cm3/g.

Specific volume (steric) anomaly, , is the difference between the in situ specific volume and the specific volume of seawater at the same pressure with S = 35 and T = 0°C. The specific volume anomaly analogy to is called the thermosteric anomaly.

Dynamic Height

Dynamic height, D, is the integral of the specific volume over pressure. It is expressed in units called dynamic meters, which actually has dimensions of work per unit mass, or m²s^-2. With this choice of units, the difference in dynamic height between points 1 m apart in the vertical is approximately 1 dynamic meter.

Sea Surface Height

Sea surface height, usually abbreviated SSH and often denoted by the symbol , is a measure of the difference between the actual sea surface height at any given time and place, and that which it would have if the ocean were at rest. It refers to changes in the sea surface height, or thickness of the water column from the seabed to the free surface, over horizontal spatial scales of many meters and time scales of many minutes. The SSH will be affected by tides, stratification, winds, and currents. Satellite altimeters measure the round-trip travel time of a radar pulse to estimate SSH.

SSH = O - (R + A) - G, where O is the satellite orbital height above the reference ellipsoid; R is the range, or height, of the satellite above the sea surface; A is a correction to R due to atmospheric influences; and G is the geoid height. The geoid height is the distance between the reference ellipsoid and sea surface if the sea surface were at rest and there were no currents.

Special care must be taken when using satellite SSH measurements near coastlines. An altimeter's ground footprint, or the area over which the SSH anomaly is computed is approximately 7 km. Any footprint that includes both land and sea is contaminated, so all data within about 10 km of the coast cannot be used. Problems due to land contamination extending further out to sea occur when a satellite's track crosses from land to sea (but not the other way around). Several footprints may be affected, so SSH data within 50 km of the coast may be suspect. Also, tidal effects are removed in SSH anomaly products that are used for location of mesoscale features, so the quality of the tide model for the shelf areas of interest may affect this product.

Ocean currents are expressed as velocity vectors (often denoted by ), either by giving a speed and direction or by giving two perpendicular components, for example east-west (u) and north-south (v) or along-shore and cross-shore flow.

Other components, such as tangential and perpendicular to a boundary, may also be used so be sure you understand how the velocity is being represented. Speed is commonly expressed in units of cm/s, m/s, or knots. A knot is a nautical mile per hour. 1 kt = 51.44 cm/s. Current directions are generally expressed as the direction towards which the current is flowing, as opposed to winds, which are named by the direction they are coming from. So an easterly current is flowing towards the east, whereas an easterly wind is blowing from the east. To avoid confusion, it is recommended that current directions be expressed unambiguously with the suffix "ward" attached, for example an eastward current flows toward the east and a poleward flows toward the north pole in the northern hemisphere or towards the south pole in the southern hemisphere.

Two different types of velocity fields are used in oceanography, Eulerian and Lagrangian. The first refers to the velocity as it would be measured over time at a number of fixed points in space. Streamlines are lines which at any given time are tangent to the Eulerian velocity. Current meters on a mooring measure the Eulerian velocity for example (see left panel of figure below). The Lagrangian velocity describes the paths that water parcels would follow over time. A perfect water-following drifter (right panel of figure below) would measure the Lagrangian velocity.

Schematic of a moored current array anchored on the ocean bottom. A buoy relays the data to a satellite.	Lagrangian drifter being deployed.

The difference between an Eulerian and a Lagrangian representation is demonstrated by the following figure:

In this figure, the red arrows represent the flow at time t_o at fixed positions A, B, C, and D. The blue arrows represent the flow at a later time t₁ at the same locations. The squiggly line represents a Lagrangian trajectory during the time period from t_o to t₁.