lect_12 - Hydrostatic Balance dp = g dz In the absence of...

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1 Hydrostatic Balance • In the absence of atmospheric motions the gravity force must be exactly balanced by the vertical component of the pressure gradient force. • Because vertical accelerations are very small for large- scale atmospheric motions, this is an excellent approximation for the vertical dependence of pressure in the real atmosphere. g dz dp ρ = = = = z dz g z p dz g dp g dz dp ) ( Pressure at any point is the weight per square meter of the atmospheric column overlying that point. kPa dz g p 325 . 101 ) 0 ( 0 = = For average conditions, This is the mean sea-level pressure.
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g r = Φ We can define a quantity called the geopotential, which is related to gravity. Gravity can be represented as the gradient of the geopotential. , ˆ k g g = r Because If the value of the geopotential is set to zero at mean sea level, the geopotential Φ (z) at height z is the work required to raise a unit mass to height z from mean sea level: g dz d z = Φ Φ = Φ ), ( then = Φ z dz g 0 Units of geopotential are J kg -1 , which are equivalent to m 2 s -2 . dp dp dz g α ρ = = 1 The variation of geopotential with pressure depends on temperature. Integrating in the vertical: ) (ln p d RT dp p RT dp d = = = Φ implies that This is the hypsometric equation, which relates the difference in geopotential to the layer mean temperature. = Since
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This note was uploaded on 10/25/2011 for the course ENVSCI 324 taught by Professor Broccoli during the Spring '11 term at Rutgers.

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lect_12 - Hydrostatic Balance dp = g dz In the absence of...

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