1!Lecture Ch. 7a!• Stability!• CAPE!• Review of Ch.7 Concepts!– “Homework” Ch. 7, Prob. 3 for discussion!• Cloud Classification!• Precipitation Processes!Curry and Webster, Ch. 7, 8!For Monday: Read Ch. 8!Dry/Moist/Saturated!• Dry! (RH=0%)!– In practice, 0%<RH<100% (moist air) can sometimes be approximated as “dry”!• “Moist” (0%<RH<100%)!– Example: saturated air with some dry air entrained into it (7.27)!• Saturated (RH≥100%)!– Some liquid water is present!– Approximate using “equivalent” or “liquid water” potential temperature!Lapse Rate and Stability!• Lapse Rate (Γ): helps to define the stability of the atmosphere.!• Degree of stability has consequences for atmospheric mixing, e.g. dispersion of pollutants.!• Stability:!– Superadiabatic (unstable)! Γenv > Γad!– Subadiabatic (stable)!Γenv < Γad!– Neutral!Γenv = Γad!Why do we need stability?!• Buoyancy tells us *that* air rises!• Lapse rates tell us *how* air rises!• Stability tells us *whether* rise will continue or reverse!Static stability: “if a parcel of air is displaced vertically, does it return to its original level (stable) or does it continue to move away from it (unstable)” € T€ z€ dTdz= 0€ dTdz< 0€ dTdz> 0Suppose! #If atmosphere had P~constant with z, #then we would find T~constant with z!Then T-Z space would give us stability On this side, higher is hotter so it’s stable because hot rises On this side, higher is colder so it’s unstable because cold falls BUT WAIT!#Pressure is NOT constant with z#So T is not constant with z#But what is constant with z?#2!€ θv€ z€ dθvdz= 0€ dθvdz< 0€ dθvdz> 0Unsaturated Stability Criteria!We can do the same thing as before, but we use θv space On this side, higher is hotter so it’s stable because hot rises On this side, higher is colder so it’s unstable because cold falls BUT WAIT!#θv is NOT constant with z#if atmosphere is saturated.#But what is constant with z?#€ θe€ z€ dθedz= 0€ dθedz< 0€ dθedz> 0Saturated Stability Criteria!We can do the same thing as before, but we use θe space On this side, higher is hotter so it’s stable because hot rises On this side, higher is colder so it’s unstable because cold falls unsaturated!saturated!3!CAPE!Chapter 7, Prob. 3!• Use a mean moist adiabatic lapse rate of 5.77K/km (valid for p = 800 hPa, T = 276 K; assume constant); dry adiabat 9.77K/km (from http://157.82.240.165/~naoki/comp/calc/index.html) – a) use Eq. 7.25 with T to get CAPE= 295.35, assume CAPE=KE (upper bound), v=24.3 m/s. – b) use Eq. 7.25 with Tv to get CAPE=331.5, v=25.8 m/s. – c) use Fig. 6.5 to get wv=1.3g/kg,then Eq. 7.22 to get CAPE, ten v=24.6 m/s. • CAPE is an upper bound on the potential energy that can ever be converted into kinetic energy of a rising buoyant parcel. Lifting Condensation Level!• Lifting condensation level varies with initial relative humidity and is a weak function of initial temperature!10.1 Seinfeld and Pandis, Fig. 15.114!Mixing LineClausius-Clapeyron(with exagerated curvature)Parcel 1 (subsaturated)Parcel 2 (subsaturated)N.B. For mixture to be supersaturated, need two parcels very close to saturation at two somewhat different temperatures.!1.00.80.60.40.20.0Relative Humidity20151050Dewpoint Depression (T-Td) T=2C T=24C
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