# SIO 210 housekeeping Tutorials: Math tutorials (finalize time) (M or W 3-4) Course material tutorials (finalize 2 times) Exam format: in-class, closed.

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SIO 210 housekeeping Tutorials: Math tutorials (finalize time) (M or W 3-4) Course material tutorials (finalize 2 times) Exam format: in-class, closed book but you may bring 1 page of your own notes (both sides, any fontsize OK) Course url: http://www-pord.ucsd.edu/~ltalley/sio210http://www-pord.ucsd.edu/~ltalley/sio210 Email: ltalley@ucsd.edultalley@ucsd.edu Put SIO210 or SIO 210 in the subject line to help me see your email Talley SIO 210 (2013)

SIO 210 Physical properties of seawater (3 lectures) First lecture: 1. Depth and Pressure 2. Temperature 3. Heat 4. Potential temperature Course url: http://www-pord.ucsd.edu/~ltalley/sio210http://www-pord.ucsd.edu/~ltalley/sio210 Talley SIO 210 (2013) Second and third lectures: 1. Salinity 2. Density 3. Freezing point, sea ice 4. Potential and neutral density, Brunt-Vaisala freq. 5. Sound speed 6. Tracers: Oxygen, nutrients, transient tracers

NASA SST animation Talley SIO 210 (2013) http://podaac.jpl.nasa.gov/AnimationsImages/Animations

SIO 210 Properties of Seawater These 2 powerpoint presentations include only the figures, not the blackboard work or notes. Reading for this and the next 2 lectures: DPO Chapter 3.1 to 3.6; Chapter 4.2 to 4.6 Extra: DPO Java Ocean Atlas examples for Chapter 3 Stewart chapter 6, and just look at Gill Appendix 3 Study questions: see website Talley SIO 210 (2013)

Definitions 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. Talley SIO 210 (2013) Mean: average value Median: center of distribution (equal number of values above and below) Mode: most common value

Ocean range: 0-6000 meters (mean 3734 m, median 4093 m, mode 4400 m since file had depths by 100 m intervals) 1. Depth Talley SIO 210 (2013) FIGURE 2.2

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 Newtons 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 1. Pressure Talley SIO 210 (2013)

1. Pressure Units of pressure: dyne/cm 2 and N/m 2 1 Pascal = 1 N/m 2 1 bar = 10 6 dynes/cm 2 = 10 5 N/m 2 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. (Dont use the abbreviation db because dB is used for decibels – sound intensity.) Talley SIO 210 (2013)

1. Relation of pressure to depth (1) Hydrostatic balance From Newtons law, 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/m 3 Talley SIO 210 (2013)

1. Relation of pressure to depth (2) 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/m 3, and g = 9.8 m/s 2, we get p = - g z = (1025 kg/m 3 )(9.8 m/s 2 )(1 m) = 10045 kg/(m s 2 ) = 0.10045 bar = 1.0045 dbar Talley SIO 210 (2013)

1. Pressure vs. depth for actual ocean profile Z DPO Figure 3.2 Talley SIO 210 (2013)

1. Pressure measurements Reading the reversing thermometers Old: pair of mercury reversing thermometers New - quartz transducers that produce digital output DPO Chapter S16 Talley SIO 210 (2013)

1. Pressure measurement accuracy and precision AccuracyPrecision ~5 dbar? 3 dbar0.5 dbar (0.1% of range)(0.01% of range) Talley SIO 210 (2013) Old-fashioned reversing thermometers Quartz pressure sensor on modern instrument

2. Temperature, heat and potential temperature Temperature units: Kelvin and Celsius Kelvin is absolute temperature, with 0 K at the point of zero entropy (no motion of molecules) Celsius 0°C at melting point at standard atmosphere (and no salt, etc) T K = T C + 273.16° Ocean temperature range: freezing point to about 30° or 31°C (Freezing point is < 0°C because of salt content) Talley SIO 210 (2013)

Surface temperature (°C) DPO Figure 4.1: Winter data from Levitus and Boyer (1994) Talley SIO 210 (2013) Note total range and general distribution of temperature

Pacific potential temperature section (potential defined on later slides) Talley SIO 210 (2013) DPO Fig. 4.12a Note total range and general distribution of temperature

2. Temperature 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 Talley SIO 210 (2013)

2. Heat Energy: 1 Joule = 1 kg m 2 / sec 2 Heat is energy, so units are Joules Heat change per unit time: 1 Watt = 1 J/sec Q = total amount of heat dQ/dT = C p where C p is heat capacity q= heat per unit volume = Q/V, units are J/m 3 dq/dT = c p where c p is specific heat = C p /mass For seawater, typical values (with a wide range) are: c p ~3850 J/kg °C and ~ 1025 kg/m 3 Talley SIO 210 (2013)

2. Heat flux Flux of heat from air into ocean or vice versa: Heat/(unit time x unit area) Units are Joules/(sec m 2 ) = (J/sec)/m 2 = W/m 2 Where 1 Watt = 1 W = 1 J/sec Talley SIO 210 (2013)

What sets temperature? Surface heat flux (W/m 2 ) into ocean DPO Figure 5.12 Yellow: heating. Blue: cooling Map shows the annual mean (total for all seasons) Talley SIO 210 (2013)

Heat flux and temperature change: sample calculation Compute the temperature change over 1 month in a volume of fluid that is 1m 2 in surface area and 100 m thick, if the heat flux through the sea surface is 150 W/m 2. (Net heat flux is due to solar radiation and various heat loss terms – later lecture.) i.e. dq/dt = 150 W/m 2 Total heat flux into the column of water is dQ = (dq/dt)*Area*time = (150 W/m 2 )(1 m 2 )(30 days) = 3.8888 x 10 8 J Total heat change of the water column in terms of temperature: dQ = (Volume) c p dT since dq = dQ/volume Thus dT = (3.8888 x 10 8 J)/(100 m 3 x 1025 kg/m 3 x 3850 J/kg°C) = 0.99 °C or ~ 1°C Talley SIO 210 (2013)

2. (cont.) Potential temperature Water (including seawater) is compressible If we compress a volume of water adiabatically (no exchange of heat or salt), then its temperature increases. (adiabatic compression) We are interested in tracking water parcels from the sea surface down into the ocean. We are not interested in the adiabatic compression effect on temperature. We prefer to track something that is conserved following the parcel. Define potential temperature as the temperature a parcel of water has if moved adiabatically (without heat exchanges or mixing) to the sea surface. Use the Greek letter to denote potential temperature. Potential temperature is always lower than measured temperature except at the sea surface (where they are the same by definition) Talley SIO 210 (2013)

Potential temperature expressions The change in temperature with pressure that is due solely to pressure is called the adiabatic lapse rate: Γ(S,T,p) = T/ p (> 0) In the atmosphere, the adiabatic lapse rate is equivalent to 6.5°C per 1000 m altitude. In the ocean, the adiabatic lapse rate is about 0.1°C per 1000 m depth (1000 dbar pressure). Potential temperature is defined as Again: potential temperature is always lower than measured temperature except at the sea surface (where they are the same by definition) (p ref = 0 dbar, p is > 0 dbar) Talley SIO 210 (2013)

Pressure effect on temperature: Mariana Trench (the most extreme example because of its depth) DPO Figure 4.9 X Note the measured temperature has a minimum around 4000 dbar and increases below that. Potential temperature is almost exactly uniform below 5000 m: the water column is adiabatic. (This is because all of the water in this trench spilled into it over a sill that was at about 5000 m depth.) Talley SIO 210 (2013)

Temperature and potential temperature difference in S. Atlantic (25°S) X Note that this water column has a temperature and potential temperature minimum at about 1000 m (must be balanced by a salinity feature). Talley SIO 210 (2013)

Atlantic temperature and potential temperature sections for contrast Temperature Potential temperature Talley SIO 210 (2013)

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