12.808: Some Physical Properties of Sea Water or, More than you ever wanted to know about the basic state variables of the ocean

Transcription

1 12.88: Some Physical Proerties of Sea Water or, More than you ever wanted to know about the basic state variables of the ocean Salinity Various salt constituents in 1 m 3 of seawater having (t, S) = (2, 35). Taken from Neumann and Pierson, Princiles of Physical Oceanograhy, 1966, Prentice-Hall. Constituent Mass, kg Running Total, kg NaCl MgCl MgSO CaSO K 2 SO CaCO KBr SrSO H 2 BO Now, based on the equation of state (EOS-198) for seawater, the density of seawater having this (t,s) value should be kg/m 3. So the mass of salts divided by the mass of the water is: (35.956/124.8) = 35.1, which should be 35 but seems a bit off! Salinity used to be based on chlorinity (Cl) since it was found that many of the above salt constituents had a constant ratio with Cl in seawater under a variety of values and locations (based on the Challenger Exedition samles). After later finding out that this was not universally true, a different, more accurate salinity scale was develoed based on the electrical conductance of seawater comared to a standard solution of KCl at 15 o C. A ractical salinity scale was agreed uon in 1978 (PSS1978). Standards based on KCl are available for urchase and are made in batches every year and distributed to the oceanograhic community. See Fofonoff (JGR, 9, , 1985) for a discussion of PSS78 (and EOS198, below). Salinity used to be reorted as arts er thousand or o/oo (or grams er kg of seawater), but now has no formal units under the new salinity scale.

2 Temerature Temerature is measured in an absolute scale (degrees Kelvin, o K) from absolute zero, a temerature of zero molecular motion. Other benchmarks have been icked somewhat arbitrarily based on roerties of various substances, which are readily available and have some rather stable roerties. The temerature scale used on oceanograhy is the Celcius scale (degrees C) such that: T = t , where T is in o K and t is in o C. Temerature scales have changed over the years (in 1948, 1968 and most recently in 199) as various benchmark values have been changed. For the oceanograhic temerature range (-2 to 35 o C), temerature is now based on electrical resistance measurements of a ure latinum wire relative to the resistance at the trile oint of water, which is a temerature value at which solid, liquid and vaor hases are in equilibrium at a standard atmoshere. Other benchmarks and the resistance ratios are given below: Temerature o C Wr Trile oint, mercury Trile oint, water.1 1. Melting oint, Gallium Freezing oint, Indium Wr=R(t9)/R( o K) is the resistance ratio of ure latinum for the t9 temerature scale relative to the trile oint of ure water. For the oceanograhic range, t9 = (Wr-1) (Wr-1) 2 The difference between the old (1968) temerature scale (t68) and the new (t9) is small, basically showing that water now boils at o C not at 1! It can be written as t9=.99976*t68

3 Most formulae for water roerties (e.g. EOS198, PSS1978) were distributed before this temerature change occurred and to be formally correct, they should have their t9 temeratures changed to the t68 scale before using them. In this course, we will usually use the symbol T to reresent t9, unless units are secifically given as o K. Some reresentative rofiles of temerature and salinity vs. deth are given below. The region of raid temerature change with deth due to seasonal heating is called the seasonal thermocline. It lies above a ermanent thermocline, which divides the uer and dee arts of the ocean. Images removed due to coyright concerns.

4 Pressure Pressure is force/unit area acting on a surface. It has several units, with conventional units different in meteorology and oceanograhy. The Standard International (SI) units are based on the MKS (meter-kilogram-second) and is the Pascal. 1 Pascal = 1 newton/m 2, where 1 Newton = 1 kg m / s 2, making 1 Pascal = 1 kg / m s 2. Other units commonly uses are based on the Bar, where 1 Bar = 1 5 Pascal 1 mbar 1-3 bar = 1 2 ascal = 1 hectoascal, 1 dbar = 1-1 bar = 1 4 ascal. Pressure at the bottom of the atmoshere is 1.13 bar or 113 mbar. Meteorologists commonly use millibars as ressure units and oceanograhers use decibars because the additional ressure under a layer of water that is 1 meter high is aroximately 1 dbar. We generally use gauge ressure, or the dearture of ressure from atmosheric values at sea level. Just to make things more comlicated, ressure is often quoted in terms of cm or inches of mercury in a manometer, where a standard atmoshere (113 mbar) will raise a column of mercury a height 76 cm. Pressure measuring instruments can generally be calibrated by adding fixed masses that deress a fluid column a known amount, given that one can indeendently measure or determine the local acceleration of gravity!

5 Short digression on ressure: Consider the diagram at the right: A column of water of density ρ and height h is resting. The column has a cross-sectional area A. The ressure at the to of the column is P t and at the bottom, P b. The Pressure at the bottom can be exressed as the total force er unit area on the bottom surface or ρ h (1) P b = (ρah)g/a + P t = ρgh + P t, where (ρah) is the mass of fluid & g is the acceleration of gravity. For small changes in deth, h = -δz, and P b - P t = δp, the above equation can be written in differential form as: (2) δp/δz = -ρg, where we have inserted the sign convention that z is ositive uward. This is known as the hydrostatic balance & is one of the most imortant relations in the ocean, where for most low frequency changes, it is a reasonable aroximation of the force balance in the vertical. For a column of saltwater with a density of 125 kg/m 3 that is 1 m high with a gravity of 9.81 m/s 2, using (1) we get: δp = (125)(9.81)(1) ~ 1 5 Pa, which is the ressure at the bottom of the atmoshere. Thus, the weight of the entire atmoshere is equivalent to 1 m of seawater! Mercury, which has a secific gravity of 13.6, or a density of 13.6 times that of ure water, would roduce the same ressure at the bottom of a column that is: h = 1 5 Pa / (136 kg/m 3 ) / (9.81 m/s 2 ) =.754 m. sealed With a sea level ressure of 1.1 Bar, this would give.76m. A mercury-filled tube, sealed at one end and evacuated of air on that end, oen to the atmoshere at the other is called a manometer and is one of the easiest ways of routinely and accurately measuring atmosheric ressure. oen.76m

6 Adiabatic Lase Rate & Potential Temerature If a layer of fluid is comletely mixed, then when 2 arcels of fluid from anywhere in the layer are brought together at the same ressure, their roerties are indistinguishable. The arcels must all have constant entroy er unit mass, η. This is exressed thermodynamically as follows: dη = dt d = or T η + η, ( v ) T dt = T = Γ, d C C where T η, T η v T where T is temerature ( o K), v/ T is the change in secific volume (inverse of density) with resect to temerature, C is heat caacity at constant ressure, and Γ is the adiabatic lase rate, or rate at which temerature will change in the vertical in an otherwise vertically mixed layer of fluid. It is often exlained in terms of the comressiblility of air or seawater, but as you can see from the above, it does not directly come from the comressibility ( v/ ), but from the change in volume with temerature. At the surface of the earth in the lower atmoshere and in the dee ocean, the following are aroximate values for Γ: Lower atmoshere: Dee Ocean: -1 o C / 1m increase in height -.1 o C / 1m decrease in deth This is most common to those living near mountains who can move uward to cooler temeratures by ascending the mountain even in a well-mixed lower atmoshere. In the ocean it is most evident in the gradual increase in temerature with increasing deth in the dee ocean. Because of the nonconservative asect of temerature, we often use otential temerature, which is the temerature of a fluid arcel that is moved adiabatically from an initial ressure of i to a reference ressure r. It is exressed as follows: θ t + Γ i d, where Γ is the lase rate and t i is the initial temerature. = r

7 The diagram at the right is taken from Pickard & Emery (who took it from elsewhere) and shows the classic icture of the difference between temerature and otential temerature over a dee trench (Mindanao). On the left, temerature increases with deth and density anomaloy (using in situ temerature) decreases with increasing deth and suggest a tongue of cooler water flowing to the left, over the sill at the right. Potential temerature and otential density anomaly (right anels) correctly show cooler dee water flowing over the sill and into the abyss with stable stratification above. Density Image removed due to coyright concerns. Various different ways are used to describe the density of seawater and its relation to the basic field variables of temerature, salinity and ressure. σ = ρ 1 kg/m 3 = σ(s,t,) v = 1/ ρ = v(s,t,) δ = v(s,t,) - v(35,,) σ θ = σ(s,θ,,r) density anomaly secific volume secific volume anomaly otential density [σ 2 = σ(s,θ,,2)] Usually density is lotted/examined at fixed ressures so that σ θ is much more commonly than σ. The internationally used equation of state of seawater was

8 suggested by Millero and acceted in 198 (EOS8). The density of air at atmosheric ressure is aroximately 1.2 kg/m 3, nearly a thousand times less than seawater. Sound Seed The seed of sound, c, in a fluid is defined as: c -2 = ( ρ / ) η, where the usual notation above alies and the change of density with ressure (related to the inverse of the comressibility) is determined at constant entroy. Values of sound seed (t=15 o C, = sea level) in air (34 m/s) and water (15 m/s) are quite different and c has the roerty that it increases with both t and. In the ocean, because increases with deth and t decreases with deth, one often sees a sound velocity minimum in the water column as sketched below: m/s deth 1m 2m Sound velocity minimum or sound channel: whales use it for long distance communication! In the following figure (taken from Pickard & Emery) an examle of a sound velocity rofile is given for a North Pacific location in which (uer anel) temerature and salinity variations are lotted vs. deth (left), the sound velocity deendence due to temerature and ressure (center) and the resultant sound seed rofile (right) are indicated. In the lower anel(s), near surface and deeer effects of sound seed variation on roagation of rays of sound are shown. Note how, in the lowest lot, sound tends to be channeled in a region defined by the sound velocity minimum. This sound channel enables longdistance communication by whales, and has been exloited by oceanograhers [and the military] for some time.

9 Dynamic Height or Geootential Anomaly Under action of gravity, a geootential Φ, can be defined as the work done er unit mass to move a article a distance dz, where z is the direction of gravity. dφ = g dz, Φ( z) = Φ + z g dz Recalling the hydrostatic balance (from the discussion of ressure), d = ρgdz; Φ( P) = Φ() D( ) P δ d vd = gdz = dφ, thus P α d P δd = Φ() P α d D( ), where D() is dynamic height or geootential anomaly and it contains all of the horizontal and vertical variations of density in the fluid. The term roortional to α is of little dynamic consequence and the term at the ocean surface, Φ, is a deth indeendent art of the geootential or dynamic height that will need to be evaluated based on considerations other than density (or secific volume anomaly). The MKS units for geootential anomaly or dynamic height are m 2 /s 2, but common usage gives values of dynamic height in dynamic meters, which is equivalent to 1 m 2 /s 2. Heat Caacity The amount of heat needed to raise the temerature er unit mass of a substance a temerature T = 1 o K at constant ressure is heat caacity, C. Some tyical values are as follows: Ocean water: C = 4.2 x 1 3 joules/kg/ o K ρc =4.2 x 1 6 joules/m 3 / o K Air C = 1 3 joules/kg/ o K ρc =1.2 x 1 3 joules/ m 3 / o K Granite C =.84 x 1 3 joules/kg/ o K ρc =2.3 x 1 6 joules/m 3 / o K If one multilies the heat caacity times the density of each of the above ρc, one gets the third column, which is a measure of the heat caacity of one m 3 of the substance. Reference: Fofonoff, in The Sea, Vol. 1: Physical Proerties of Seawater.