Second (and third) lectures: SIO 210 Physical properties of seawater (2 to 3 lectures) Fall, 2016 L. Talley First lecture: Accuracy and precision; other definitions Depth and Pressure Temperature Salinity and absolute salinity Density Sea ice, freezing point Second (and third) lectures: Heat Potential temperature and conservative temperature Potential density Neutral density Sea surface height Stability, Brunt-Vaisala frequency Sound speed Tracers: Oxygen, nutrients, transient tracers Clicker questions Which temperature scale, Kelvin or Celsius, gives you 0 at point of no thermal energy? Is the freezing point of salty water at 0 C? Why doesn’t hydrothermal vent water at 400C boil? Talley SIO 210 (2016)

SIO 210 Properties of Seawater Reading for this and the next 2 lectures: DPO Chapter 3.1 to 3.6, 3.9, skim 3.7 Study questions: see website Talley SIO 210 (2016)

1. Definitions for measurements Accuracy: reproducibility relative to a chosen standard Precision: repeatability of an observation by a given instrument or observing system A very precise measurement could be wildly inaccurate. Mean: average value Anomaly: difference from the mean value Median: center of distribution (equal number of values above and below) Mode: most common value Talley SIO 210 (2016)

Ocean range: 0-6000 meters (mean 3734 m, median 4093 m, mode 4400 m since file had depths by 100 m intervals) 2. Depth and pressure Edited version of Figure 2.2 FIGURE 2.2 Talley SIO 210 (2016)

2. Depth and pressure FIGURE 2.1 TALLEY Copyright © 2011 Elsevier Inc. All rights reserved Map of the world based on ship soundings and satellite altimeter derived gravity at 30 arc-second resolution. Data from Smith & Sandwell (1997); Becker et al. (2009); and SIO (2008). FIGURE 2.1

Pressure (mostly) results from overlying mass of water (and air); total mass depends on the water density and height Ocean range: 0-6000 dbar (get to this unit below) (note that 1 dbar is equivalent to about 1 m) Pressure is a force per unit area Newton’s law: F = ma where F and a are 3-D vector force and acceleration, and m is mass. Units of force: mass x length / (time)2 cgs: 1 dyne = 1 gm cm / sec 2 mks: 1 Newton = 1 kg m / sec 2 2. Depth and Pressure Talley SIO 210 (2016)

2. Depth and Pressure Units of pressure: dyne/cm2 and N/m2 1 Pascal = 1 N/m2 1 bar = 106 dynes/cm2 = 105 N/m2 approximately the atmospheric pressure at sea level 1 atmosphere = 1000 millibar = 1 bar 1 decibar = 0.1 bar Decibar or “dbar” is the most common pressure unit used in oceanography because it is so close to 1 m, given the density of seawater: approximately the pressure for 1 meter of seawater. (Don’t use the abbreviation “db” because dB is used for decibels – sound intensity.) Talley SIO 210 (2016)

2. Relation of pressure to depth (extra) “Hydrostatic balance” From Newton’s law a = F/m use the force balance in the vertical direction vertical acceleration = (vertical forces)/mass vertical acceleration = vertical pressure gradient force + gravity Pressure gradient (difference) force (“pgf”) is upward due to higher pressure below and lower pressure above pgf = - (pressure/depth) = -(p/z) (since z increases upward and p increases downward) Gravitational force per unit volume is downward = - g where  is the density of seawater,  ~1025 kg/m3 Talley SIO 210 (2016)

2. Relation of pressure to depth (extra) We now assume vertical acceleration is approximately zero, so the vertical pressure gradient (pressure difference force) almost exactly balances the downward gravitational force. This is called “hydrostatic balance”. 0 = vertical pgf + gravitational force 0 = - (p/z) - g We can then solve for the change in pressure for a given change in depth. For: z = 1 meter, density  ~1025 kg/m3, and g = 9.8 m/s2, we get p = -  g z = (1025 kg/m3)(9.8 m/s2)(1 m) = 10045 kg/(m s2) = 0.10045 bar = 1.0045 dbar Talley SIO 210 (2016)

2. Pressure vs. depth for actual ocean profile Z DPO Figure 3.2 Talley SIO 210 (2016)

3. Temperature, heat and potential temperature Temperature is measure of energy at molecular level Temperature units: Kelvin and Celsius TK Kelvin is absolute temperature, with 0 K at the point of zero entropy (no motion of molecules) TC Celsius 0°C at melting point at standard atmosphere (and no salt, etc) TK = TC + 273.16° Ocean temperature range: freezing point to about 30° or 31°C (Freezing point is < 0°C because of salt content) Add note about hydrothermal vents - > 400C http://www.whoi.edu/main/topic/hydrothermal-vents Doesn’t boil because of pressure. Talley SIO 210 (2016)

3. Surface temperature (°C) Note total range and general distribution of temperature DPO Figure 4.1: Winter data from Levitus and Boyer (1994) Talley SIO 210 (2016)

Pacific potential temperature section (“potential” defined on later slides) Note total range and general distribution of temperature DPO Fig. 4.12a Talley SIO 210 (2016)

T = temperature, Q is heat, S is entropy Temperature is defined in statistical mechanics in terms of heat energy T = temperature, Q is heat, S is entropy Heat content is zero at absolute zero temperature (Kelvin scale) dQ = TdS Heat is not 0 at 0°C!!!! Talley SIO 210 (2016)

4. Salinity “Salinity” in the oldest sense is the mass of matter (expressed in grams) dissolved in a kilogram of seawater = Absolute salinity Units are parts per thousand (o/oo) or “psu” (practical salinity units), or unitless (preferred UNESCO standard, since salinity is mass/mass, but this has now changed again, in 2010) The concept of salinity is useful because all of the constituents of sea salt are present in almost equal proportion everywhere in the ocean. This is an empirical “Law of equal proportions” (There are really small variations that are of great interest to marine chemists, and which can have a small effect on seawater density, but we mostly ignore them; note that the new definition of salinity in TEOS-10* takes these small variations into account.) *TEOS-10 is “Thermodynamic Equation of State 2010” Talley SIO 210 (2016)

1. Salinity range and composition Typical ocean salinity is 34 to 36 gm seasalt/kg seawater What is the composition of sea salt? Millero et al. (Deep-Sea Res. I, 2008) Talley SIO 210 (2016)

1. Salinity measurements Oldest: evaporate the seawater and weigh the salts Old: titration method to determine the amount of chlorine, bromie and iodine (prior to 1957) Modern: Use seawater conductivity, which depends mainly on temperature and, much less, on salinity, along with accurate temperature measurement, to compute salinity. Modern conductivity measurements: (1) in the lab relative to a reference standard (2) profiling instrument (which MUST be calibrated to (1)) Talley SIO 210 (2016)

4. “Absolute salinity” (TEOS-10) Absolute salinity = reference salinity + correction for other stuff (stuff = dissolved matter that increases sea water density) SA = SR + δSA Reference salinity SR = 35.16504/35 * Practical salinity = 1.0047*psu Reference salinity has been corrected for new knowledge (since 1978) about sea water stoichiometry as well as new published atomic weights. The correction δSA is for dissolved matter that doesn’t contribute to conductivity variations: silicate, nitrate, alkalinity Millero et al. (2008), IOC, SCOR and IAPSO (2010), McDougall et al. (2010) Talley SIO 210 (2016)

4. Surface salinity Note range of values and general distribution Surface salinity (psu) in winter (January, February, and March north of the equator; July, August, and September south of the equator) based on averaged (climatological) data from Levitus et al. (1994b). Talley SIO 210 (2016) DPO Figure 4.15

4. What sets salinity? Precipitation + runoff minus evaporation (cm/yr) Salinity is set by freshwater inputs and exports since the total amount of salt in the ocean is constant, except on the longest geological timescales NCEP climatology DPO 5.4 Talley SIO 210 (2016)

4. Atlantic salinity section Talley SIO 210 (2016) DPO Figure 4.11b

Return to Atlantic potential temperature: what about this permanent inversion – how can there be cold water (blue) over warm (red) - is it vertically stable? Talley SIO 210 (2016)

1. S. Atlantic (25°S) temperature and salinity X 1. S. Atlantic (25°S) temperature and salinity We now see how the water column can be stable with a temperature minimum, since there is also a large salinity minimum. Talley SIO 210 (2016)

5. Seawater density  Seawater density depends on S, T, and p  = (S, T, p) units are mass/volume (kg/m3) Specific volume (alpha) α= 1/ units are volume/mass (m3/kg) Pure water has a maximum density (at 4°C, atmospheric pressure) of (0,4°C,1bar) = 1000 kg/m3 = 1 g/cm3 Seawater density  ranges from about 1022 kg/m3 at the sea surface to 1050 kg/m3 at bottom of ocean, mainly due to compression Talley SIO 210 (2016)

5. Equation of state (EOS) for seawater Common way to express density is as an anomaly (“sigma”)  (S, T, p) = (S, T, p) - 1000 kg/m3 The EOS is nonlinear This means it contains products of T, S, and p with themselves and with each other (i.e. terms like T2, T3, T4, S2, TS, etc.) Talley SIO 210 (2016)

5. Seawater density From Gill textbook Appendix Seawater density is determined empirically with lab measurements. New references: TEOS-10 and Millero et al. (linked to notes) UNESCO tables (computer code in fortran, matlab, c) (see link to online lecture notes) Rescan this! From Gill textbook Appendix Talley SIO 210 (2016)

5. Equation of state for seawater See course website link for correction to DPO Section 3.5.5 (S, T, p) Changes in  as a function of T,S,p: Thermal expansion coefficient Haline contraction coefficient Adiabatic compressibility Generally positive for seawater Positive Positive Talley SIO 210 (2016)

5. Dependence of density on Temperature, Pressure Add plot with dependence on salinity Talley SIO 210 (2016)

5. Surface density  (winter) Surface density sq (kg m–3) in winter (January, February, and March north of the equator; July, August, and September south of the equator) based on averaged (climatological) data from Levitus and Boyer (1994) and Levitus et al. (1994b). Talley SIO 210 (2016) DPO Figure 4.16

6. Freezing point and sea ice Freezing point temperature decreases with increasing salinity Temperature of maximum density decreases with increasing salinity They cross at ~ 25 psu (brackish water). Most seawater has maximum density at the freezing point Why then does sea ice float? Talley SIO 210 (2016)

6. Sea ice and brine rejection Why then does sea ice float? (because it is actually less dense than the seawater, for several reasons…) Brine rejection: as sea ice forms, it excludes salt from the ice crystal lattice. The salt drips out the bottom, and the sea ice is much fresher (usually ~3-4 psu) than the seawater (around 30-32 psu) The rejected brine mixes into the seawater below. If there is enough of it mixing into a thin enough layer, it can measurably increase the salinity of the seawater, and hence its density This is the principle mechanism for forming the densest waters of the world ocean. Staudigel video under sea ice. Look about 10 minutes in for brinicles. http://www.youtube.com/watch?v=CSlHYlbVh1c Talley SIO 210 (2016)

3.,4.,5.,6.. Where does most of the volume of the ocean fit in temperature/salinity space? First set of slides repeats what was shown in physical properties lectures 75% of ocean is 0-6°C, 34-35 psu 50% is 1.3-3.8°C, 34.6-34.7 psu (=27.6 to 27.7 kg/m3) Mean temperature and salinity are 3.5°C and 34.6 psu DPO Figure 3.1 Talley SIO 210 (2016)

Summary: definitions Accuracy Precision Mean Median Mode Pressure Newton’s Law Hydrostatic balance Dyne Newton Decibar Temperature Kelvin Celsius Heat and heat flux Joule Watt Potential temperature Adiabatic lapse rate Talley SIO 210 (2016)