10. The Adiabatic Approximation 1.The Adiabatic Theorem 2.Berry’s Phase.
Simulating Adiabatic Parcel Rise
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Transcript of Simulating Adiabatic Parcel Rise
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Simulating Adiabatic Parcel Rise
Presentation by Anna Merrifield, Sarah Shackleton and Jeff Sussman
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Buoyancy ForceRelationship of parcel density to atmospheric
densityAt a given pressure, density is determined by
Temperature
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Buoyancy ForceIf the parcel is less dense (warmer) than the
atmosphere it will rise adiabatically and coolT’ > Tenv
If parcel is more dense (cooler) than the environment it will sink adiabatically and warmT’ < Tenv
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Real World Examples of Parcel RiseCloud formation
If the environment is stable, clouds that form will be shallow (stratus clouds)
In an unstable environment, vertical motion occurs, cumulus and cumulonimbus form
Thunderstorms/TornadoesWith enough parcel rise, thunderstorms can form
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CAPEConvective available potential energy
Amount of potential energy available for parcel rise Important for thunderstorm growth/formation
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Parcel Method1. The parcel does not mix with the surrounding
environment2. The parcel does not disturb its environment3. The pressure of the parcel adjusts
instantaneously to its environment4. The parcel moves isentropically
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The Model1. Obtain the data from Figure 7.2 using DataThief2. Determine Z(P,T) 3. Model Parcel Temperature assuming:
1. Dry adiabatic rise to LCL2. Saturated adiabatic rise to LNB3. “Moist” adiabatic rise above the LNB
4. Model Parcel Temperature assuming:1. Dry adiabatic rise to LCL2. Saturated adiabatic rise while entraining dry air to LNB3. “Moist” adiabatic rise above the LNB
5. Sensitivity analysis: find lapse rates that reproduce the model
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1. Obtaining the DataThe plot lines were redrawn in
color to allow for effective tracing. Markers indicate the
axes and the beginning, color, and end of the line we want to
trace.
After the line is traced, the program picks points on the line and the data can be output and
read into Matlab.
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1. Problems with DataThiefSolution: Rather than throwing out points (they aren’t “bad”, we
determined Z using a linear least-squares fit to 3 regions of constant lapse rate
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2. Determining Z(P,T)
Regions of ~Constant Lapse
Rate
Γ = 6.5 K/Km
Γ = .64 K/Km
Γ = 3.6 K/Km
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2. Determining Z(P,T)
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Dry & Saturated Adiabatic Lapse RatesDry lapse rate: assumptions – ideal gas,
atmosphere is in hydrostatic equilibrium, no water vapor
Saturated lapse rate: assumptions – no loss of
water through precipitation, only liquid and vapor phases, system at chemical equilibrium, and heat capacities of liquid and water vapor are negligible, parcel has reached 100% relative humidity
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Modeling Saturated Adiabatic Rise
1. Initialize esat(1), Tparcel (1)
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3. Model Parcel Temperature (No Entrainment)
Γ to LCL
9.8 K/Km
Γ at LCL 5 K/Km
Γ at LNB 7.5 K/Km
Γ above LNB
3 K/Km
LCL
LNB
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The Second ModelEntrainment: The mixing of the rising air parcel
with the surrounding environmentEntrainment rate: 1/m dm/dzAssumptions: entrainment of dry air, constant
entrainment rate, isotropic entrainment
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4. Model Parcel Temperature (Entrainment)
λ(1/m)
Γm at LCL
(K/Km)
Γm at LNB
(K/Km
)
5*10-10
5.0 7.5
5*10-5 5.4 7.4
1*10-4 5.7 7.2
5*10-4 8.6 4.8
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DiscussionLack of CAPE in all modelsLimitations of the simplified model
Parcel movement adiabatic and reversible (no precipitation)
Entrainment of dry airSounding given as lnP versus T, not given with
altitude which then needed to be derived using assumption of constant lapse rate atmosphere in three regions
DataThief does not give monotonically increasing data points
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5. Reproduction of Figure 7.2
Γ to LCL
9.8 K/Km
Γ at LCL 2 K/Km
Γ at LNB 6.5 K/Km
Γ above LNB
3 K/Km
LCL
LNB
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Summary of Lapse RatesEnvironment
NoEntrainment
λ = 5*10^-10 1/m
λ = 5*10^-5 1/m
λ = 1*10^-4 1/m
λ = 5*10^-4 1/m
Best
Reproduction
Approximate Parc
elΓ to LCL
6.5 9.8 9.8 9.8 9.8 9.8 9.8 10.9
Γ at LCL 6.5 5.0 5.0 5.4 5.7 8.6 2.0 3.1
Γ at LNB 0.64 7.5 7.5 7.4 7.2 4.8 6.5 6.1
Γ above LNB
0.64 3.0 3.0 3.0 3.0 3.0 3.0 3.1
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Example sounding
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CAPE example with entrainment
Image from NWS from Amarillo, TX, July 22,2013
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Conclusions and Further WorkFailure to reproduce plot using simplified
governing assumptions of adiabatic parcel riseFurther work using soundings from a database
http://weather.uwyo.edu/upperair/sounding.html