Simulating Adiabatic Parcel Rise

Presentation by Anna Merrifield, Sarah Shackleton and Jeff Sussman

Buoyancy ForceRelationship of parcel density to atmospheric

densityAt a given pressure, density is determined by

Temperature

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

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

CAPEConvective available potential energy

Amount of potential energy available for parcel rise Important for thunderstorm growth/formation

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

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

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.

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

2. Determining Z(P,T)

Regions of ~Constant Lapse

Rate

Γ = 6.5 K/Km

Γ = .64 K/Km

Γ = 3.6 K/Km

2. Determining Z(P,T)

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

Modeling Saturated Adiabatic Rise

1. Initialize esat(1), Tparcel (1)

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

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

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

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

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

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

Example sounding

CAPE example with entrainment

Image from NWS from Amarillo, TX, July 22,2013

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