OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Light Transmission Solar heating supplies short-wave radiation to ocean surface; Energy (light) penetrates the water column to different depths as a function of its wavelength and the clarity of the water

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Light Transmission I = I o e -kz (k = attenuation coefficient) Attenuation with depth (clear water) 1% light level

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Light Transmission I = I o e -kz (k = attenuation coefficient) Scattering is proportional to 1/ 4 (clear ocean looks blue) Absorption is highest for red compared with blue light Spreading is not a factor (source is evenly distributed over water surface)

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Light Transmission Blue:1% light level ~170m Red:1% light level ~7m (clear ocean case)

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Light Transmission Optical instruments; e.g., PHILLS); Optical instruments; e.g., Portable Hyperspectral Imager for Low-Light Spectroscopy (PHILLS); ~500 spectral bands ~1nm wide Built around CCD cameras 640 pixels across

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Light Transmission PHILLS images offshore New Jersey, 2001 Every pixel in this image includes a full spectrum of information

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Light Transmission Vegetated Land Coastal Water

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Hydrostatic Balance Hydrostatic Equation is a simplification of the vertical component of the equations of motion (momentum equations) Assume, instead that there is no motion in the vertical direction; Balance of forces is between weight of the water and the pressure that builds with depth Force balance at the bottom of this box Many “boxes” stacked up in the water column: Generalizing:

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Hydrostatic Balance What if we want to use the hydrostatic equation to compute pressure? Appropriate to static (not moving) water columns but is also a good approximation to moving situations Integrate (sum up) equation: Expand, where P(atm) = P(0) = Atmos Press: Pressure is equal to the weight of overlying water only if  = constant Related topics: 1)Static Stability of a water column 2)Geostrophic Method for computing (horizontal) currents

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Static Stability The notion of static stability assess whether the vertical distribution of density is stable relative to the downward force of gravity; i.e., is there light water over heavy water, which is stable, or the opposite, which is unstable? Related to compres- sibility (sound speed); often neglected Stability parameter, E E > 0, stable E < 0, unstable E = 0, neutral z 

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Static Stability The notion of static stability assess whether the vertical distribution of density is stable relative to the downward force of gravity; i.e., is there light water over heavy water, which is stable, or the opposite, which is unstable? Related to compres- sibility (sound speed); often neglected Buoyancy Frequency, N Used to characterize internal wave oscillations “Brunt-Väisälä” Frequency; “Natural Frequency”

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Static Stability The Buoyancy Period is P = 2  /N Typical values: min in seasonal thermocline 6 hr in deep ocean Buoyancy Frequency, N Used to characterize internal wave oscillations “Brunt-Väisälä” Frequency; “Natural Frequency” The notion of static stability assess whether the vertical distribution of density is stable relative to the downward force of gravity; i.e., is there light water over heavy water, which is stable, or the opposite, which is unstable?

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Static Stability Enhanced mixing is produced by double diffusion Effect is due to the difference between rate of diffusion of salt versus heat Heat:  = 1.4 x cm 2 sec -1 Salt:  = 1.1 x cm 2 sec -1 e.g.,:

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Static Stability Enhanced mixing is produced by double diffusion Effect is due to the difference between rate of diffusion of salt versus heat Heat:  = 1.4 x cm 2 sec -1 Salt:  = 1.1 x cm 2 sec -1 e.g.,:

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Enhanced mixing is produced by double diffusion Likelihood of double diffusion is measured by the density ratio, R: R must be positive for double diffusion (dT/dz and dS/dz same sign) Static Stability

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Rotation Effects “Even for those with considerable sophistication in physical concepts, one’s first introduction to the consequences of the Coriolis force often produces something analogous to intellectual trauma.” John A. Knauss

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Rotation Effects Gaspard-Gustave de Coriolis ( ) Sir Isaac Newton ( ) (only for non- accelerating reference frames) F = ma

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Rotation Effects

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Rotation Effects Coriolis Acceleration accounts for the fact that the rotating Earth coordinate system is not an inertial reference system Coriolis terms Centripetal Accel    is a vector parallel to the axis of rotation whose magnitude is equal to 1 cycle/day

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics F = ma Equations of Motions Based on momentum balance (Newton’s 2nd Law): Vector form (written as F/m = a): AccelerationCoriolisPress Gravity Friction Gradient Coriolis expanded: f = 2  sin  = Coriolis Parameter

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics F = ma Equations of Motions Based on momentum balance (Newton’s 2nd Law): Vector form (written as F/m = a): AccelerationCoriolisPress Gravity Friction Gradient x-equation y-equation z-equation (hydrostatic) neglect neglect neglect

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Geostrophy x-equation y-equation CoriolisPress Gradient The (numerically) largest terms in the horizontal momentum equations for large-scale oceans currents are the Coriolis acceleration effect and horiz. pressure gradients Currents that follow this dynamical balance of forces (accelerations) are called Geostrophic, which means “earth turning” Note: these currents represent a steady state balance

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Initial movement is driven toward high pressure (or downhill) but Coriolis effect acts to turn track to the right (in the N.H.) and the final, steady state or equilibrium result is parallel to lines of constant pressure (around the hill) Rule: with your left hand in the direction of low pressure, the wind/current will hit you in the back (in the N.H.) Geostrophy

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics F c : Coriolis; F g : Pressure Gradient (related to gravity) F c : Coriolis; F g : Pressure Gradient (related to gravity)Rule: with your left hand in the direction of low pressure, the wind/current will hit you in the back (in the N.H.) Geostrophy

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Geostrophy

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Geostrophy The Dynamic Method (or Geostrophic Method) for computing ocean currents depends on density observations to estimate pressure gradients and, finally, currents 2 or more  profiles p u,v It is not possible to directly measure pressure because depth cannot be determined with enough accuracy Recall the hydrostatic equation: Quantity gdz is related to amount of work to move a unit of mass a unit distance in the vertical direction; we define the geopotential, , by: d  = gdz = –  dp Dynamic Height, D =  /10, is numerical equiv to height in m  Hydrostatic Eqn = d 

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Geostrophy Hydrostatic eqn Integrate wrt depth Let,  =  o +  Solve for press at depth, z < 0 Small“Barotropic” (depth“Baroclinic” (depth) atmos.independent)dependent) pressure Note:  o >>  We usually can’t obtain the barotropic portion so we: 1) Measure sea surface using satellite altimetry 2) Map velocity at one depth directly (current meters, floats) 3) Assume a level of no motion at some depth

OC3230-Paduan images Copyright © McGraw Hill Chap 9: Dynamics Geostrophy Sea Surface SlopeInternal (barotropic)(baroclinic) Use p(z) solution in geostophic equations Typically assume a level of no motion and compute the required surface slope (or dynamic height)