--- Introduction to Geophysical Fluid Dynamics Ch. 6 Fundamentals of Atmospheric/Ocean Modeling

Variables and Units 1.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 1.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 base units Base quantityNameSymbol length meterm mass kilogram kg time seconds temperature kelvinK SI prefixes -- FactorName Symbol teraT 10 9 gigaG 10 6 megaM 10 3 kilok 10 2 hectoh 10 1 dekada Factor Name Symbol decid centic millim microµ nanon picop 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 base units Base quantityNameSymbol length meterm mass kilogram kg time seconds temperature kelvinK SI prefixes -- FactorName Symbol teraT 10 9 gigaG 10 6 megaM 10 3 kilok 10 2 hectoh 10 1 dekada Factor Name Symbol decid centic millim microµ nanon picop SI derived units Derived quantityName Symbol area square meterm 2 volume cubic meterm 3 speed, velocitymeter per secondm/s accelerationmeter per second squared m/s 2 mass densitykilogram per cubic meterkg/m 3 specific volumecubic meter per kilogramm 3 /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/m 2 ) (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 MassM (Kg) LengthL (m) TimeT (s) TemperatureK (K) Velocity = Distance / Time, so it has dimensions L/T, or m/s Acceleration = Velocity / Time, so it has dimensions L/T 2, or m/s 2 Force = Mass x Acceleration, so it has dimensions M LT -2, or Kg m/s 2 Pressure, density

Pressure Gradient Force (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) Figure 6.8a

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

Coriolis Force Coriolis 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 Coriolis 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 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 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.

Convergence & divergence Cyclone has convergence near ground but divergence at upper level. Anticyclone: divergence near ground, convergence at upper level.

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.

Pressure Gradient + Coriolis + Friction Forces Surface Wind 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)