Horizontal Pressure GradientsSlide 2Horizontal Pressure ForcePressure GradientsSlide 5GeostrophySlide 7Geostrophic RelationshipEstimating tanqSatellite AltimetrySlide 11Slide 12Modeling TidesThe GeoidSlide 15GroundtracksPowerPoint PresentationValidationMapped SSHSlide 20Calculating CurrentsSlide 22Slide 23Slide 24Our Simple CaseBarotropic ConditionsSlide 27Isobars & IsopycnalsSlide 29Baroclinic ConditionsBaroclinic vs. BarotropicSlide 32Slide 33Baroclinic FlowSlide 35Slide 36Example as a f(z)Slide 38Slide 39Slide 40Slide 41Slide 42Geostrophy as a f(z)Level of No MotionExample of an Eddy in Southern OceanSo Ocean ExampleSlide 47Slide 48Dynamic HeightSurface Currents from HydrographySlide 51Slide 52Slide 53Surface Currents from AltimetrySlide 55Slide 56Slide 57Slide 58Slide 59Horizontal Pressure Gradients•Pressure changes provide the push that drive ocean currents •Balance between pressure & Coriolis forces gives us geostrophic currents•Need to know how to diagnose pressure force•Key is the hydrostatic pressureHorizontal Pressure Gradients•Two stations separated a distance x in a homogeneous water column ( = constant)•The sea level at Sta. B is higher than at Sta. A by a small distance z•Hydrostatic relationship holds•Note, z/x is very small (typically ~ 1:106)Horizontal Pressure ForcePressure Gradients@ Sta A seafloor ph(A) =  g z@ Sta B seafloor ph(B) =  g (z + z)p = ph(B) - ph(A) =  g (z + z) -  g z p =  g z HPF p/x =  g z/x =  g tan or HPF per unit mass = g tan[m s-2]Horizontal Pressure ForceGeostrophy•What balance HPF?•Coriolis!!!!Geostrophy•Geostrophy describes balance between horizontal pressure & Coriolis forces•Relationship is used to diagnose currents•Holds for most large scale motions in seaGeostrophic Relationship•Balance: Coriolis force = 2 sin u = f u HPF = g tan•Geostrophic relationship:u = (g/f) tan •Know f (= 2 sin) & tan, calculate uf = Coriolis parameter (= 2 sin)Estimating tan•Need to slope of sea surface to get at surface currents•New technology - satellite altimeters - can do this with high accuracy•Altimeter estimates of sea level can be used to get at z/x (or tan) & ugeo•Later, we’ll talk about traditional methodSatellite AltimetrySatellite AltimetrySatellite Altimetry•Satellite measures distance between it and ocean surface •Knowing where it is, sea surface height WRT a reference ellipsoid is determined•SSHelli made up three important partsSSHelli = SSHcirc + SSHtides + Geoid•We want SSHcircModeling Tides•Tides are now well modeled in deep water SSHtide = f(time,location,tidal component)•Diurnal lunar O1 tideThe Geoid•The geoid is the surface of constant gravitational acceleration•Varies in ocean by 100’s m due to differences in rock & ocean depth•Biggest uncertainty in determining SSHcircThe GeoidGroundtracks•10 day repeat orbit•Alongtrack 1 kmresolution•Cross-track 300 kmresolutionValidation•Two sites– Corsica– Harvest•RMS ~ 2.5 cmMapped SSH•SSH is optimally interpolated•Cross-shelf SSH SSH ~20 cm over ~500 km•tan = z/x~ 0.2 / 5x105 or~ 4 x 10-7Geostrophic Relationship•Balance: Coriolis force = fu HPF = g tan•Geostrophic relationship:u = (g/f) tan •Know f (= 2 sin) & tan, calculate uCalculating Currents•Know tan = 4x10-7•Need f (= 2 sin)–  = ~37oN – f = 2 (7.29x10-5 s-1) sin(37o) = 8.8x10-5 s-1•u = (g/f) tan = (9.8 m s-2 / 8.8x10-5 s-1) (4x10-7) = 0.045 m/s = 4.5 cm/s !!Mapped SSH•u = 4.5 cm/s•Direction is along’s in SSH•The California CurrentGeostrophy•Geostrophy describes balance between horizontal pressure & Coriolis forces•Geostrophic relationship can be used to diagnose currents - u = (g/f) tan•Showed how satellite altimeters can be used to estimate surface currents•Need to do the old-fashion way nextGeostrophy•Geostrophy describes balance between horizontal pressure & Coriolis forces•Geostrophic relationship can be used to diagnose currents - u = (g/f) tan•Showed how satellite altimeters can be used to estimate surface currents•What if density changes??Our Simple CaseHere,  tan & u are = constant WRT depthBarotropic Conditions•A current where u  f(z) is referred to as a barotropic current •Holds for  = constant or when isobars & isopycnals coincide•Thought to contribute some, but not much, large scale kinetic energyBarotropic ConditionsIsobars & Isopycnals•Isobars are surfaces of constant pressure•Isopycnals are surfaces of constant density•Hydrostatic pressure is the weight (m*g) of the water above it per unit area•Isobars have the same mass above themIsobars & Isopycnals•Remember the hydrostatic relationship ph =  g D•If isopycnals & isobars coincide then D, the dynamic height, will be the same•If isopycnals & isobars diverge, values of D will vary (baroclinic conditions)Baroclinic ConditionsBaroclinic vs. Barotropic•Barotropic conditions – Isobar depths are parallel to sea surface – tan = constant WRT depth– By necessity, changes will be small•Baroclinic conditions – Isobars & isopycnals can diverge– Density can vary enabling u = f(z)Baroclinic vs. BarotropicBaroclinic vs. BarotropicBaroclinic Flow•Density differences drive HPF’s -> u(z)•Hydrostatics says ph =  g D•Changes in the mean  above an isobaric surface will drive changes in D (=z)•Changes in D (over distance x) gives tan to predict currents•Density can be used to map currents following the Geostrophic MethodBaroclinic Flow•Flow is along isopycnal surfaces not across•“Light on the right”•u(z) decreases with depthGeostrophic Relationship•Balance: Coriolis force = fu HPF = g tan•Will hold for each depth•Geostrophic relationship:u(z) = (g/f) (tan(z))Example as a f(z)A  B Goal: 1 or z1Example as a f(z)• Define pref - “level of no motion” = po• Know p1@A = p1@B -> A g hA = B g hB• z = hB - hA = = hB - B hB / A = hB ( 1 - B / A )Example as a f(z) u = (g/f) ( z/x) = (g/f) hB ( 1 - B / A ) / L If A > B (1 - B/A) (& u) > 0 If A < B (1 - B/A) (& u) < 0Density ’s drive uExample as a f(z)•Two stations 50 km apart along 45oN•A(500/1000 db) =