--- --- Introduction to Geophysical Fluid Introduction to Geophysical Fluid Dynamics Dynamics

Ch. 6 Fundamentals of Ch. 6 Fundamentals of Atmospheric/Ocean ModelingAtmospheric/Ocean Modeling

Variables and Units

1. Independent Variables

Values are independent of each other

x increases eastwardy increases northwardz increases upwardt time

Later we can use other coordinate systemsp decreases upwardlatitude, longitude

Variables and Units

1. Dependent Variables

Values depend on other variables

wind speedsu > 0 for eastward motionv > 0 for northward motionw > 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 base unitsBase quantity Name Symbollength meter mmass kilogram    kgtime second stemperature       kelvin K

SI prefixes --Factor Name  Symbol1012 tera T109 giga G106 mega M103 kilo k102 hecto h101 deka da  

Factor Name  Symbol 10-1 deci d10-2 centi c10-3 milli m10-6 micro µ10-9 nano n10-12 pico p

So, for Length…

1000 m = 1 km1m = 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 base unitsBase quantity Name Symbollength meter mmass kilogram    kgtime second stemperature       kelvin K

SI prefixes --Factor Name  Symbol1012 tera T109 giga G106 mega M103 kilo k102 hecto h101 deka da  

Factor Name  Symbol 10-1 deci d10-2 centi c10-3 milli m10-6 micro µ10-9 nano n10-12 pico p

SI derived unitsDerived quantity Name Symbolarea square meter m2volume cubic meter m3speed, velocity meter per second m/sacceleration meter per second squared   m/s2mass density kilogram per cubic meter kg/m3specific 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 calculationsTemperatures - 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 Pressure GradientGradient

ForceForce(PGF)(PGF)

Figure 6.7

• 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

Pressure Gradient Force (PGF)Pressure Gradient Force (PGF)

Figure 6.8a

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

Coriolis ForceCoriolis Force

• Due to the rotation of the Earth

• Objects appear to be deflected to the right (following the motion) in the Northern Hemisphere

• Speed is unaffected, only direction

Fig. 6-9, p. 165

The CoriolisThe Coriolis Effect Effect

• -The Coriolis force causes the wind to deflect to the right of its intended path in the Northern Hemisphere and to the left of its intended path in the Southern Hemisphere. It acts at a right angle to the wind.

• - The Coriolis force is largest at the pole and zero at the equator• - The stronger the wind speed, the greater the deflection• - The Coriolis force changes only wind direction, not wind speed. • - We measure motion on the rotating Earth. Thus, we need to be concerned

with the Coriolis force

Geostrophic balanceGeostrophic balance• P diff. => pressure gradient force (PGF) => air parcel moves => Coriolis force• Geostrophy = balance between PGF & Coriolis force .

• 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.

PGF

Coriolis

wind

N. Hem. S. Hem.

wind PGF

Coriolis

• Converging contours of const. pressure (isobars) => faster flow => incr. CF & PGF

Get geostrophic wind patternfrom isobars

Cyclone & AnticycloneCyclone & 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.

Convergence & divergenceConvergence & divergence• Cyclone has convergence near ground but divergence at

upper level.• Anticyclone: divergence near ground, convergence at

upper level.

Upper Atmosphere WindsUpper 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

FrictionFriction• 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

FrictionFriction• Ground

friction slows wind => CF weakens.

• CF+friction balances PGF.

• Surface wind tilted toward low p region.

Pressure Gradient + Coriolis + Friction Forces

SurfaceWind

Figure 6.8c

• 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

Cyclones, Anticyclones, Troughs and Ridges

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

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