SIO 210 Problem Set 1
October 3, 2016
Due October 17, 2016 (2 weeks)
If you work together on these, please make sure that you understand the concepts and use
your group discussion to help with the understanding.
10 points total, 2 points each.
1. (a)Explainbrieflytheusefulnessofthenon-dimensionalparameter‘aspect
ratio’.TheaspectratioistheratiooftheheightHtothelengthscaleL.Ittellsus
ifafluidmotionwillhavesimilarorverydifferentverticalandhorizontalscales.
Iftheyaresimilar(H/L~1),thenverticalvelocitiesandhorizontalvelocities
mightbethesameorderofmagnitude.Iftheaspectratioissmall(H/L<<1),
thenverticalvelocitieswouldbeverysmallcomparedwithhorizontal.
Forthefollowing,estimatetheRossbynumber
TheRossbynumberis1/(fT),whereTisthetimescale.Estimate1/f~1day.
UsingthescalesfromtheIntroductorylecture:
(b)TsunamiT=minutestohours.Ro=1day/(minutes,hours)>>1
(c)DiurnaltideT=24hours.Ro=1day/1day=O(1)
(d)GlobaloverturningcirculationT=100sto1000syears.Ro=1day/(100syears)
<<1
(e)BubblesT=0.01sec.Ro=1day/(0.01sec)>>1
12pointstotal,4pointseach
2.UsetheMindanaoTrenchtemperatureandpotentialtemperaturegraphical
comparisonfromclass(propertiesofseawatersecondlecture)andthetextbook:
(a)Estimatefromthegraphthetemperatureandpotentialtemperatureat5000m
depth,andthedifferencebetweenthem.
T~1.5°C.q~1.0°C.(T-q)~0.5C.
(b)Usethisestimatedvalueofpotentialtemperatureandcalculatetheheatcontent
ifthisvalueiscorrectforalayerthatis1000mthickandoveraregionthatis
10,000kmx5,000km.Fordensity,lookatothergraphsorverticalsectionsonline
andestimatethedensity.Useaspecificheatofcp=3850J/kg°C.Expressyour
answerinJoules.
Thiswasreallynotquitetherightquestion.Itshouldhavebeenspecifiedintermsof
achangeintemperature.
Q=rcp(q+273.16)(V)=1040kg/m3(3850
J/kg°C)(274.16)(1000m)(10x103x103m)(5x103x103m)=5.48x1026J
(c)Calculatethedifferencebetweenyourheatcontentandaheatcontentthat
wouldbecalculatedfromthetemperature.ExpressyouranswerinJoules.
Samecalculationbutjust0.5°Cinsteadof274.16.Q=1.00x1024J.
Aside:thereisaunit,theZetaJoule.1ZJ=1021J.
OceanheatcontentchangesarebeingexpressedinZJs.Thetotalchangeindeep
oceanheatcontentsince1955isabout80ZJ,forcomparisonwiththenumberthat
isbeingcalculatedhere.
12 points total, 4 points each part.
3.
Use your web browser and look at an online SST anomaly animation produced by
NOAA, using satellite data.
Site: http://www.ospo.noaa.gov/Products/ocean/sst/anomaly/2015.html
(a)
Explain what an anomaly is. How was it calculated for this animation? (Look for
the information on the website: you are most welcome to critique what you find if it’s
inadequate.)
Anomalyisthedifferencebetweentheactualobservationandthemean,however
themeanisdefined.What’simportantindescriptionofmethodistoclearlydefine
howthemeanwasconstructed.
(b)
Describe the overall structure of the field that you find. (You do not need to learn
all about the climate phenomenon – we will do this later. Please just describe what you
see.)
Any nice general description of this field and what one sees through having an animation
will likely be a good answer.
(c)
Pick one local feature and describe how it evolves with time.
Any nice general description of this field and what one sees through having an animation
will likely be a good answer.
18 points total, 2 points each for the calculation, 5 points each for plots
4. A computer file that is a time series of water temperature at the end of the Scripps
pier is now linked on the course website.
http://www-pord.ucsd.edu/~ltalley/sio210/class_assignments/Shore-Stations_20152016.zip
SIO pier data are found on several sites. Data set provided here is in csv (ascii)
format, easy to use with excel and other programs. I retrieved it from:
http://www.sccoos.org/data/manualshorestations/?study=SIO%20Pier%20Shore%20
Station
Another way in to the SIO pier data sets is here, with lots of plots available, but data
not easily accessed:
http://sccoos.ucsd.edu/data/piers/
Use this file and compute the
a. mean
b. variance
c. standard deviation
d. standard error
Use whatever plotting capability you have (matlab, R, python, etc), plot the time series
and then plot its anomaly relative to the record mean (i.e. the mean value over the entire
record).
20 points total, 4 points each
5. (a)Ontheattachedverticalsection,fromthePacificOceanat160°E,findatleast
onelocationthathasastronghalocline.Whatisahalocline?
Ahaloclineisdepthrangethroughwhichsalinitychangesveryrapidlyinthe
vertical.Itisusuallyassociatedwithfreshwaterabovesaltywater,henceincrease
stabilityofthewatercolumn
Inthefigure,thereisahalocinebetween100and150minthenorth.
Thereisanotherhalocline,muchstronger,inthetropics,about4°Nto15°N,with
weakerhaloclinealsoextendingtothesouthernendofthesectionatabout4°S.The
4°N-15°NhaloclineisduetotheITCZexcessprecipitationinthewarmpoolregion.
(b)Goonlinetofindthissection(inhttp://woceatlas.ucsd.edu-followlinksuntil
youfindit.)
Findthepotentialdensitysection.Identifythepycnoclinethatgoeswiththis(these)
haloclines.
I’veattachedthefigure,fromhttp://whpatlas.ucsd.edu/whp_atlas/pacific/p13/sections/printatlas/P13_SIGMA_final.jpg
Northernhalocline:shallowpycnoclinethatmatchesthehaloclinedepth
Equatorialhalocline:thestronghaloclineiswithinthe<22.0kg/m3layer,which
apparentlydoesn’thaveenoughcontourintervalstodelineatethehalocline’s
contributiontodensity.
(d) Findthepotentialtemperaturesection.Describetheverticalpotential
temperaturestructurethatgoeswiththehalocline(s).
I’veattachedthepotentialtemperaturesection.
http://whpatlas.ucsd.edu/whp_atlas/pacific/p13/sections/printatlas/P13_THETA_final.jpg
Inthenorthernhalocline,thereisatemperatureminimum.ATminimumcanbe
sustainedonlyifitswaterisrelativelyfresh.TheTminimumandhaloclinecoincide,
soherethehaloclineisaccompaniedbyandstabilizesthecoldwater,whichisa
remnantofwintercoolingthatisverticallystablebecausethesurfacewaterisso
fresh.
Inthetropicalhalocline,thesurfacewaterisverywarm,withnohintofa
temperatureminimum.Herethereisactuallyuniformtemperaturethroughthe
halocline,aso-called‘barrierlayer’,althoughthatisbeyondthescopeofthis
question.
(e) Backonthesalinitysectionabove:identifytheSubtropicalUnderwaterand
explainwhatcreatedit.
TheSTUWisthesubsurfacesalinitymaximumbetweenabout10°Nand17°N.Itis
createdthroughsubductionfromthesurfacesalinitymaximumwater.
(ThereisalsoanSTUWatthesouthernboundaryofthesection,whichissubducted
fromtheSouthPacific’ssurfacesalinitymaximum,whichisclosertotheequator
thantheNorthPacific’smaximum,astheatmosphericforcing‘equator’isinthe
ITCZwhichisnorthoftheequator.)
ToseethesurfacesourcesoftheseSTUWs,lookatthemapsofsalinityonthesame
websiteinhttp://whpatlas.ucsd.edu/whp_atlas/pacific/maps/salnty/propmaps.htm
(f) Locatethelowsalinityintermediatewateronthissection(it’scalledNorth
PacificIntermediateWater).Explainwhythereisasalinityminimum.
TheNPIWsalinityminimumliesbetween4°Nand42°Nalthoughitismoststrongly
developednorthofabout15°N.Itssourceisfreshersurfacewatersinthesubpolar
NorthPacific.Wedonotneedmoredetailherethanthis.
4 points total, 1 point for answer, 3 points for mechanism explanation
6. In the vertical profile of density shown in the figure, the arrow points to the
(a) Thermostad
(b) Mode water
(c) Abyssal ocean
(d) Pycnocline
(circle one).
(Identified as pycnocline because density changes rapidly with depth. There is also a
seasonal pycnocline very close to the surface, but we know that d is the righ answer
because this feature is not a thermostad, mode water, or the abyssal ocean.)
(e) explain why this feature exists.
At any given location in the ocean, the water we see at different depths comes from
different sea surface locations. Pycnocline water comes from subduction of sea surface
waters in the subtropics and higher latitudes and subsequent advection to the location of
our measurement. The density range reflects the densities that outcrop at the sea surface.
The intensity of the pycnocline, how rapidly its density varies with depth, is more subtle.
It involves the amount of water that is subducted in each isopycnal outcrop at the sea
surface, and also involves vertical velocity and mixing that can intensify the vertical
gradient of density.
24 points total, 4 points each.
7. Two volumes of water with different properties are mixed together. The potential
temperature and salinity of volume A are 17°C and 36 psu. The potential temperature
and salinity of volume B are 4°C and whatever salinity is required for the potential
density of A and B to be the same.
a. Estimate the salinity for Volume B from the graph.
Plotting as attached: salinity is about 33 psu for the 4°C water.
Could double check this if one already had a subroutine to computer density.
b. If Volumes A and B are the same, what are the potential temperature and salinity of
the mixture?
Mixing must be on a straight line between two points in T,S. I did not mention of
emphasize this in class. This could be a point to raise in tutorial.
Mixing is proportional: T = (4 + 17)/2 = 10.5°C; S = (33+36)/2 = 34.5 psu.
c. If both volumes cover the same horizontal surface area, but Volume A is 500 m thick
and Volume B is 2000 m thick, what are the potential temperature and salinity of
mixture?
Now need to weight the mixing by the volume, just use thickness:
T = (2000*4 + 500*17)/2500 = 6.6°C; S = (2000*33+500*36)/2500 = 33.6 psu
d. Using the plot, what is the potential density for mixture (b)?
Mixing along straight line: density is about 26.5 kg/m3
e. Compare this with the potential density mixture (a) would have if the equation of state
were linear.
Mixing would retain original density of about 26.2 kg/m3
f. On the figure, sketch the potential density contours that you would have if referencing
to 4000 dbar rather than 0 dbar.
Sketch in flattened and rotated isopycnal curves.
A"
Mix"
equal"
B"