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# Lec-7.pdf

climate change

climate change

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## Weitere Verwandte Inhalte

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### Lec-7.pdf

1. 1. Tropical Climatology
2. 2. ® ® ® ® ® ® + + Ñ - ´ W - = r F g P U dt U d r 1 2 0 . . = Ñ + Ñ + ¶ ¶ ® ® u u t r r r . Q dt dp dt dT Cp = -a Complete set of model equations when moisture (q = specific humdity) is included There are seven unknowns: U (u, v, w); T, p, (ρ or α) and q; and seven equations 3 Momentum equations for the 3 components (u, v, w) Continuity equation Thermodynamic energy equation RT p = a Equation of state ( ) ) ( . C E Uq t q - + -Ñ = ¶ ¶ r r r Moisture equation E = Evaporation (moisture source) C = Condensation (moisture sink) α = Inverse of density = Specific volume
3. 3. Recall Newton’s second law; Momentum Equations Equation of Motion ® ® ® ® ® ® + + Ñ - ´ W - = r F g P U dt U d r 1 2 Rate of change of velocity following the motion = Sum of forces acting per unit mass. ® ® ´ W - U 2 Coriolis force ® Ñ - P r 1 Pressure gradient force ® ® * ® W + = R g g 2 Gravity force per unit mass = Sum of the gravitational and centrifugal force terms ® r F Frictional force in the fluid
4. 4. Pressure Gradient Force x-component of the PGF per unit mass !! " = ⎯ # \$ %& %' y- and z components of the PGF per unit mass: !" " = ⎯ # \$ %& %( !# " = ⎯ # \$ %& %) ! " = ⎯ # \$ ∇𝑃 It is important to note that: • The pressure gradient points from low to high pressure, but the pressure gradient force points from high to low pressure. • The pressure gradient force is proportional to the gradient of the pressure field, not to the pressure itself.
5. 5. Geostrophic motions ug = - 1 rf ¶p ¶y vg = 1 rf ¶p ¶x with the Coriolis parameter f = 2W sinf. !! "! vg = 1 rf "! k ´ Ñp Component form: Vector form: Ø The geostrophic wind describes the dominant balance between the pressure gradient force and the Coriois force. • Just above the top of the boundary layer the atmosphere is close to geostrophic balance…
6. 6. Physics of Geostrophic Wind
7. 7. Hydrostatic Balance F w v x P a uw a uv dt du x + W - W + ¶ ¶ - = + - f f r f cos 2 sin 2 1 tan F u y P a vw a u dt dv y + W - ¶ ¶ - = + + f r f sin 2 1 tan 2 F u g z P a v u dt dw z + W + - ¶ ¶ - = ÷ ÷ ø ö ç ç è æ + - f r cos 2 1 2 2 Components of Equation of Motion
8. 8. Tropical M. D. Eastin Land / Ocean Forcing: Land • Major elevation features deflect air over (clouds and precipitation) and around (cyclonic / anticyclonic flow) • Differences in elevation create thermal gradients due to surface heating (e.g. Indian Monsoon) Ocean • Oceans are a heat and moisture reservoir that the atmosphere “taps” (ocean has a large heat capacity) • Differential solar heating leads to thermal gradients and ocean currents Land-Ocean • Large heat / moisture gradients often help force atmospheric circulations (nor-easterlies and land-sea breezes)