--- Introduction to Geophysical Fluid Dynamics Ch. 7 Fundamentals of Atmospheric/Ocean Modeling --- Introduction to Geophysical Fluid Dynamics

Variables and Units Independent Variables Values are independent of each other x increases eastward y increases northward z increases upward t time Later we can use other coordinate systems p decreases upward latitude, longitude

Variables and Units Dependent Variables Values depend on other variables wind speeds u > 0 for eastward motion v > 0 for northward motion w > 0 for upward motion Temperature T = T(x,y,z,t) Pressure p = p(x,y,z,t) Density  = (x,y,z,t)

Part II - The International Unit System (SI) SI prefixes -- Factor Name  Symbol 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deka da   Factor Name  Symbol 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p  SI base units Base quantity Name Symbol length meter m mass kilogram    kg time second s temperature       kelvin K So, for Length… 1000 m = 1 km 1m = 1000 mm And so forth. Much simpler!

As of 2005, only three countries hang on to the messy Imperial Units, Myanmar, Liberia, and the United States.

Part II - The International Unit System (SI) SI prefixes -- Factor Name  Symbol 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deka da   Factor Name  Symbol 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p  SI base units Base quantity Name Symbol length meter m mass kilogram    kg time second s temperature       kelvin K SI derived units Derived quantity Name Symbol area square meter m2 volume cubic meter m3 speed, velocity meter per second m/s acceleration meter per second squared   m/s2 mass density kilogram per cubic meter kg/m3 specific volume cubic meter per kilogram m3/kg

In meteorology/ocean, we almost always use SI units, journals require it. Force - Newtons (kg m/s) Pressure - We still use millibars (mb) 1 mb = 100 Pa = 1 hPa (PASCALS N/m2) (hpa: hecto-pascal) Pressure = force / unit area; Must use correct (SI) units in calculations Temperatures - Always use Kelvin in calculations T(K) = T( C ) +273

Dimensions and Units All physical quantities can be expressed in terms of basic dimensions Mass M (Kg) Length L (m) Time T (s) Temperature K (K) Velocity = Distance / Time, so it has dimensions L/T, or m/s Acceleration = Velocity / Time, so it has dimensions L/T2, or m/s2 Force = Mass x Acceleration, so it has dimensions M LT-2, or Kg m/s2 Pressure, density

Pressure Gradient Force (PGF) pressure gradient: high pressure  low pressure pressure differences exits due to unequal heating of Earth’s surface spacing between isobars indicates intensity of gradient flow is perpendicular to isobars Figure 6.7

Pressure Gradient Force (PGF) Figure 6.8a

Coriolis effect seen on a rotating platform, as 1 person throws a ball to another person.

Coriolis Effect Shell fired in N. Hem. deflects right. In S. Hem., it deflects left. Coriolis (1835): deflection due to Earth’s rotation Consider object moving northward in N. Hem.: As Earth rotates, speed of surface is greatest at Equator and 0 at Poles. WWI, battle of Falkland Islands in S. Hem. British warships had guns which only correct for the N. Hem. Coriolis effect. [KKC Fig.4-12]

Obj. A has greater eastward speed than B. => When A is moved northward, it ends up at X, ahead of B´. => Appears to be a ‘force’ deflecting the obj. to the right (Coriolis force) Obj. moves southward (in N.Hem.) ends up further west => Coriolis deflection to right. Consider obj. moving eastward: It moves faster than Earth in circular orbit => incr. ‘centrifugal force’ => obj. pushed away from Earth’s spin axis.

Obj. moving westward is deflected poleward => deflection to right (N.Hem.) Mathematically E-W and N-S movements can be treated in same way => obj. moving in any horiz. direction deflects to the right in N. Hem., and to the left in S. Hem. Coriolis effect 0 at Equator, & max. at Poles. Strength of Coriolis force proportional to speed of obj.

The Coriolis Effect objects in the atmosphere are influenced by the Earth’s rotation Rotation of Earth is counter-clockwise results in an ‘apparent’ deflection (relative to surface) deflection to the right Northern Hemisphere (left, S. Hemisphere) Greatest at the poles, 0 at the equator Increases with speed of moving object CE changes direction not speed

Geostrophic balance P diff. => pressure gradient force (PGF) => air parcel moves => Coriolis force Geostrophy = balance between PGF & Coriolis force . [Tarbuk & Lutgens 2003, Fig.17.5]

S. Hem. wind PGF Coriolis PGF Coriolis wind N. Hem. Approx. geostrophic balance for large scale flow away from Eq. Q: Why no geostrophic balance at Equator? A: No Coriolis force at Eq. In N. Hem., geostrophic wind blow to the right of PGF (points from high to low P) In S. Hem., geostrophic wind to left of PGF. S. Hem. wind PGF Coriolis PGF Coriolis wind N. Hem.

Converging contours of const Converging contours of const. pressure (isobars) => faster flow => incr. CF & PGF Get geostrophic wind pattern from isobars

Cyclone & Anticyclone Large low pressure cells are cyclones, (high pressure cells anticyclones) Air driven towards the centre of a cyclone by PGF gets deflected by Coriolis to spiral around the centre. Spencer Fig.12.5

Difference between PGF & Coriolis (CF) is the centripetal force needed to keep parcel in orbit. [Ahrens, 2003, Fig.9.26, 9.27]

Convergence & divergence Cyclone has convergence near ground but divergence at upper level. Anticyclone: divergence near ground, convergence at upper level. [Ahrens 2003, Fig.9.33]

Pressure Gradient Force + Coriolis Force Geostrophic Wind

Upper Atmosphere Winds upper air moving from areas of higher to areas of lower pressure undergo Coriolis deflection air will eventually flow parallel to height contours as the pressure gradient force balances with the Coriolis force this geostrophic flow (wind) may only occur in the free atmosphere (no friction) stable flow with constant speed and direction

Supergeostrophic flow Subgeostrophic flow

Geostrophic flow too simplistic  PGF is rarely uniform, height contours curve and vary in distance wind still flows parallel to contours HOWEVER continuously changing direction (and experiencing acceleration) for parallel flow to occur pressure imbalance must exist between the PGF and CE  Gradient Flow Two specific types of gradient flow: Supergeostrophic: High pressure systems, CE > PGF (to enable wind to turn), air accelerates Subgeostrophic: Low pressure systems, PGF > CE, air decelerates supergeostrophic and subgeostrophic conditions lead to airflow parallel to curved height contours

Friction factor at Earth’s surface  slows wind varies with surface texture, wind speed, time of day/year and atmospheric conditions Important for air within ~1.5 km of the surface, the planetary boundary layer Because friction reduces wind speed it also reduces Coriolis deflection Friction above 1.5 km is negligible Above 1.5 km = the free atmosphere

Friction Ground friction slows wind => CF weakens. CF+friction balances PGF. Surface wind tilted toward low p region. [Ahrens 2003, Fig.9.29]

Pressure Gradient + Coriolis + Friction Forces Surface Wind Figure 6.8c

Cyclones, Anticyclones, Troughs and Ridges 4 broad pressure areas in Northern hemisphere High pressure areas (anticyclones)  clockwise airflow in the Northern Hemisphere (opposite flow direction in S. Hemisphere) Characterized by descending air which warms creating clear skies Low pressure areas (cyclones)  counterclockwise airflow in N. Hemisphere (opposite flow in S. Hemisphere) Air converges toward low pressure centers, cyclones are characterized by ascending air which cools to form clouds and possibly precipitation In the upper atmosphere, ridges correspond to surface anticyclones while troughs correspond to surface cyclones

Surface and upper atmosphere air flow around high pressure systems (anticyclones)

Surface and upper atmosphere air flow around low pressure systems (cyclones)