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Modeling (Subject) / Jose Jacob (Lesson)

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• ocean models combination of what Observations and physics - predict oceans state anytime anywhere
• Water and air same physical properties of two thin layered fluids on rotating sphere with solar heating as main energy source differences in main factors: salinity (no heat transfer)/density for ocean and humidity  (heat transfer-evaporation...) for atmopshere
• Basic and advanced predictions basic: salinity, density, pressure advanced: current, sea surface elevation, waves
• basic physical laws conservation of mass (continuity equation-transport of quantity) conservation of energy (waves,heat budget...) Newtons 1, 2, 3 law of motion Conservatin of angular momentum (conservation of vorticity) Newtons law of graviation
• coordinates systems a)spherical (long west (-), east (+), lat (north, south),Elevation (origin center of earth) b)cartesian: ENU (East x, North y, Up z)
• Primitive equation = 3basic principles 1) second law of newton F=ma and F is sum of friction, graity, horizontal pressure, coriolis force, attraction sun/moon Navier Stokes = rewritten Newtons law including all these forces
• Conservation of mass and energy scenario in model a) and b) which variables affected Model outcome either a) no net gain or net loss b) if changes then there is imbalance in the system e.g. glacier ice melting affects salinity, water mass, heat expressed by continuity equation
• equation of state density is non linear equation of temperature, salinity and  pressure »pressure gradient force can lead to sloping or horizontal density differences
• Scaling non dimensional number the size of a term might lead the neglecting it in a certain equation to simplify the equation, as it might not be too important. Eliminate free parameters example is the reynolds number (molecular friction) <1000 laminar flow if > 10^6 then turbulent
• Grids Horizontal grids - regular girds - rectangles with same spacing though might vary due to earth spehrical shape but change in resolution only possible for whole area  =plaid grid irregular grid: triangular and can change resolution e.g. higher resolution on coast and lower resolution offshore vertical grids: 4 different types (z grid, sigma gird, density grid, hybrid) z grid: cannot change resolution near boundaries only all! sigma: can handle lateral boundaries and bathymetry eg. more resolution near coast density: good in deep stratified oceans- fail in shallow well mixed areas hybrid: combine
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• Parameterization how why cannot simulate process within the gird cell » accoutn for these effects by a) emulation: numerically estimation of the effects b) simulation: model process itself »»cumulative effects of these small scale effects can lead to big change anyhow bc either cmoputer to slow or process not understood well enough
• boundary conditions type of start a) cold start: need spin up time for general processes such as currents to start and spin up into final conditions. using climatology and weather models for meteorological conitions and temp/salinity b)warm start: circulation already developed »using results of previous model run and ocean adjusts to new condictions (problem: take over errors of previous models and accmulate)
• Assimilation and Hindcast in cold start warm start input of observations a)cold start: input of observations when weather input and model set in motion b)warm start: run model 3 dys earlier and rerun after with observations =hindcast example: observation input from global model into regional model
• Dynamic forcings on the ocean occure where and which forcings exactly affect the surface wind stress solar radiation salt exchange mass exchange tidal forcing latent heat fluxes
• bathymetry and seafloor roughness control what? a nd how affect friction force and global values influence major currents friction force leads to removing of tidal/current energy through heat and mixing global value for seafloor roughness is 1
• Source of errors in models - cumulative effect of truncation and rounding -simplyfying -weather prediciton incorrect (eg wind, precipitation, evaporation..) -prarameterization -input of observation: (mistakes in instrument, wring temporal sampling sparseness of data)
• Tides in relation to which law and force Newtons law of gravity: attraction b/w 2 objects depends on size and distance centrifugal resulting from rotation of earth »»in combination result in tides (attraction moon/sun and earth, and rotation of earth) centrifugal force everywhere the same but gravitational force depends on position
• Tractive force tides and counter force tractive force is horizontal component of gravitational force with only the firction of the bottom as acting counter force = genertes tides
• tide generating force equation tide generating force is related to mass and distance of bodies / b/w bodies
• relation sun and moon and earth »strength of tides sun is a lot bigger than the moon but also more far away : has approx. 46 % of generating tide force of the moon thus when sun and moon are in conjunction (new moon): spring tide when opposing (full moon): same when moon and sun quadrature : neap tide
• lunar day lunar month tropical and equatorial tides lunar day= 24h and 50 min! thus diurnal tide: every 12h 25min (time to rotate around the earth) lunar months: 27.2 days on tropics= moon at maximum inclination (28degrees) =highest dirunal inequality on equator: tilting at 0degrees so lowest/no dirunal inequality »inclination responsible for 20% of variation in tides
• Tidal harmonics and most common = tide composed of partial tides each defined by unique position of earth/moon/sun »identified over 400 different harmonics ! most common: principal lunar (T=12 h 42), Pincipal solar (12h), ...
• type of tides and range flood = rising sea level ebb = lower sea level high tide = highest point (here slackwater) low tide = lowest point (here slackwater) microtidal below 2m mesotidal between 2 and 4 m macrotidal over 4 m
• amphidromic system in constraint basin coriolis force reacting on tides tides give rise to amphidromic system here the tide circulates around amphidromic point (no change in sea level) anti clockwise. =considered a  kelvin wave Tidal range increase exponentially outwrds amphdromic point! in long and narow basin have a stangind wave on a node (back and forth movement) bc coriolis force has low effect
• tidal currents = horizontal aspect of currents! move in elliptical path which becomes smaller owards the bottom (friction force) » feature same periodicity like vertical movement »depent on basin geometry and constraint by continental mass » in open basin: partical approches coast and becomes parallel to coast »in semienclosed: alternating in acceleration and velocity!
• tidal current on the coast and in estuaries intensify towards coast since shallow depth increases velocity (mathematical) »great influence on circulation »in estuaries 10x faster than other currents (when partially mixed)
• tidal bore when tidal current hits entrance of enclosed river mouth = development of tidal boer (wie eine wulst auf dem wasser)
• Secular changes eustatic changes long term trends in sea leel change b) variation of sea level throughout areas of the world
• what causes sea level variation (long term and short term) long term: glacier melting, thermal expansion. coastal subsidence, tectonic action short term: wind force, waves , tides, change in atmospheric pressure
• types of waves introduction material waves: travel through a medium like seimic waves surface waves: travel between 2 mediums (eg air/water) or same fluid with different densities (internal waves) waves caused by periodic disturbing forces eg tides and winds other
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• progression of a wave a) longitudinal: fore and backwords direction of energy transmission b) transverse : up and downward movement : perpendicular to energy transmission c) orbitall : orbital path : transmission of energey b/w 2 fluids of different densities d) Rayleigh: also orbital but only through solids
• Resoring forces of waves when L < 1.7 cm its surface tension = capillary waves when bigger its gravity = gravity waves
• Energy spectrum in waves most energy transmitted through waves on surface by wind waves! tsunami eg less bc happens so rare. Tides are concentrated in 12/24h intervall
• difference wind sea and sweel wind sea: random waves with small amplitude, low period, high steepness, and are locally generated = high variable due to changes in wind swell: long period, low steepness, large amplitude wave group, generated kms away. less variable and have a regular shape
• fetch area of ocean surface over which wind blows without an obstacle »influenced by wind velocity, period and effect on wave height
• white capping in deep ocean energy dissipation only through waves breaking called white capping »state of ocean closely related to wind »gas exhcange air/water - give rise die aersosoles and airborne droplets
• movement of particles in gravity waves gravitational waves dont transport mass but energy : offshore: small amplitude orbital motion which decreases exponentially towards bottom and become more elliptical if water gets shallower d<L/2
• classification of waters by depth deep: d>L/2 intermediate: L/20<d<L/2 shallow: d< L/20
• stokes drift crest moves faster than trough and results in forward propagation of particle  (need large amplitude)
• assumption of linear theory of ocean surface waves a small compared to L and d viscosity and surface tension neglibible coriolis force and vorticity negilgible flat and orizontal bottom 2 dimensional flow sinusoidal wave form
• linear theory of ocean surface waves - wave freuquency and dispersion relation looking at graphs! 2 approximatins: (dispersion relation of wave frequency to wave number) deep water when d>> L then tanh(kg) = 1 shallow water when d<<L then tanh(kd) = kd sooo»» when d> L/4 dann substitute 1 in euqation (deep water)             when d <L/11dann subsitute kd (shallow)
• linear theory of ocean sruface waves wave lengths when d >L/2 dann deep: kann tanhh weglassen in equation of L= when d<L/20 shallow: kann tanh weglassen general cases: complicated - need computer to solve L
• dispersive and non dispersive waves deep water wave phase speed are dispersive waves since they are dependent on L or f shallow water wave phase speed are only dependent on the depth thus they are non dispersivee
• wave interference constructive destructive mixed = superposition of 2 wave trains (similar a and L interact) and result is single wave train with wave areas and flat areas (amplifying and cancelling each other)
• phase velocity individual and group in deept and shallow water indeep water group travels half speed of individual in shallow water its the same energy transmission: same is with the travelling of distance: deep water the single wave moves twice as much as the group as front wav transmit to surface before and to wave after thus disappear and create new wave at the back
• swell faster waves leave area of wave formation earlier = cause smooth undulation (rising and falling of waves) in water = swell
• types of wave energy kinetic: orbital motion potential: displacement vertical of particle of average position
• density of energy inn the wave the energy in a wave is exponentially related to its height thus a wave double the wave height carries 4x as much energy
• shoaling wave becomes more steep when reacing to shore and become instable (H increase, L decrease and steepness inrease and c decrease)
• wave behavior at coast (difrraction...)  refraction:waves approaching shore with inclination - truh decrease in c at one side (closer to shore) the other side moves faster and the crests becomes parallel to shore diffraction: distribution of energy to crest with less energy -non uniform spatial distribution of wave height  reflection: suddeen change of direction of energy due to ostacle

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