Isentropic Analysis

Isentropic Analysis: Basic Idea

Limitations of QG Analysis:

Quantitative

results require inverting a Laplacian operator (not easy to do…) •

Qualitative

results require evaluation of vertical derivatives (noisy…) • QG forcing terms could offset each other (Q-vectors help…) • Several restrictive assumptions → small Rossby number (

R o

) → horizontally-uniform static stability (

σ

)

Isentropic Analysis:

  Offers a

practical alternative

for diagnosing

vertical motion

• Results are generally consist with those obtained from QG analysis Can diagnose horizontal and vertical moisture transport  Can visualize vertical motion near fronts • Conceptually simple and insightful Advanced Synoptic M. D. Eastin

Isentropic Analysis: Basic Idea

Underlying Assumption:

→ air parcels flow along potential temperature (

θ

) surfaces → air parcels are “

thermodynamically constrained

” • This constraint is a major advantage over other coordinate systems since there is no dynamical constraint “holding” air parcels along isobaric or geopotential surfaces.

Isentropic Analysis: Constructing Maps

Overview:

• Can use observations or numerical model output • At each location (or for each sounding), find the pressure level that corresponds to the isentropic surface

chosen

for analysis (Example:

θ = 296-K

)   Plotting

pressure values

on an isentropic surface provides “

system topography

” (much like plotting geopotential height on pressure surfaces) Plotting

winds

on an isentropic surface provides “

3-D flow

θ = 296-K Greensboro Sounding H L 705 mb H 296 K

Isentropic Analysis: Interpretation

Parallel Flow:

Any flow oriented

exactly parallel

to the isobars is horizontal motion (analogous to geostrophic flow on isobaric surfaces)

Non-Parallel Flow:

Any

cross-isobar flow

implies the presence of vertical motion    Winds pointing toward lower pressure → ascent Winds pointing toward higher pressure → descent Greater crossing angles → stronger vertical motions

θ = 296-K H θ = 296-K H L L H

H

M. D. Eastin

Isentropic Analysis: Vertical Motion

Three Mechanisms:

• Using the definition of omega (

ω

) and evaluating horizontal derivatives on an isentropic surface, we find three mechanisms which can cause vertical motion:     

p

t

    

V

c

   

p

 

p

    

t

Term A Term B Term C Term A

:

Local pressure tendency

• Accounts for local changes in the pressure surfaces at a fixed location • Often a small contribution to total

ω

• Can be eliminated by assuming steady-state (“frozen wave approximation”)

Term B

:

• Analogous to temperature advection • Evaluated via the cross-isobar wind component (see previous slide

**

) • Often the

dominant term

in total

ω

• Can be evaluated with (or without) removing the system motion (

c

) Advanced Synoptic M. D. Eastin

Isentropic Analysis: Vertical Motion

Three Mechanisms:

• Using the definition of omega (

ω

) and evaluating horizontal derivatives on an isentropic surface, we find three mechanisms which can cause vertical motion:     

p

t

    

V

c

   

p

 

p

    

t

Term A Term B Term C Term C

:

Diabatic forcing

• Heating / cooling due to condensation, evaporation, radiation, etc.

• Can make significant contributions to total

ω

, but often much smaller than Term B • Can also be neglected [more on this later…] Advanced Synoptic M. D. Eastin

Isentropic Analysis: Example Case

QG-Omega Interpretation: 500mb heights and vorticity 500mb heights and SLP Strong PVA Weaker PVA H Strong CAA Moderate WAA L

• Basic QG forcing terms

cancel

over TX and LA → no vertical motion? → Q-vectors… • Basic QG forcing clearly implies ascent across NC and SC Advanced Synoptic M. D. Eastin

Isentropic Analysis: Example Case

QG-Omega Interpretation: 500mb heights and 700mb ω 500mb Q-vectors / Convergence

• Q-vector forcing implies ascent across

both

TX/LA and NC/SC • Analyzed total vertical motion (ω) → Strong ascent over NC/SC → Weak ascent over TX/LA Advanced Synoptic M. D. Eastin

Isentropic Analysis: Example Case

Isentropic Interpretation: …with Mixing Ratio Pressure/ Winds on 296-K surface

• Isentropic forcing (via cross-isobar flow) implies strong ascent across NC / SC / GA / FL and only weak ascent across TX / LA • Accounting for “moisture supply” suggests the SE should experience heavy precipitation and the TX/ LA region should not Advanced Synoptic M. D. Eastin

Isentropic Analysis: Example Case

Isentropic Interpretation: …with Composite Radar Reflectivity Pressure / winds / mixing ratio 296-K surface

• Isentropic forcing (via cross-isobar flow) implies strong ascent across NC / SC / GA / FL • and only weak ascent across TX / LA • Accounting for “moisture supply” suggests the SE should experience heavy precipitation and the TX/ LA region should not Radar confirms the isentropic analysis!!!

Isentropic Analysis: Neglect Diabatic?

Can We Neglect Diabatic Processes?

Unsaturated parcels → conserve potential temperature (θ) → motion (upward) along isentropic (θ) surfaces Saturated parcels → conserve equivalent potential temperature (θ e ) → motion is still upward, but ascent is stronger  Thus, neglecting diabatic processes only results in an

underestimation

but the qualitative results remains the same of isentropic lift Advanced Synoptic M. D. Eastin

 Clear (visual) depiction of air parcel motion and three-dimensional airflow including vertical motion and moisture transport    Conceptual simplicity Adiabatic assumption is valid most of the time → when it’s violated the qualitative answer remains unchanged and

ω is underestimated

QG assumptions of small

R o

and uniform

σ

are

not needed

 Computations must be performed to interpolate pressure, wind, and  moisture data onto isentropic surfaces Isentropic analysis

fails to provide an insightful dynamic interpretation

regarding cause and effect (as QG theory does…)  Occasionally, potential temperature does

not

increase with height (complicating practical application)  User must select the

appropriate isentropic surface

wisely • Relevant surfaces vary with season, latitude, and phenomenon • Surfaces that fall between 850mb and 700mb are used most often • Look at multiple isentropic surfaces!!!

Isentropic Analysis: Websites

Real-time Analyses:

WxCaster College of DuPage: University of Oklahoma http://www.wxcaster.com/isentropic.htm

http://weather.cod.edu/analysis/ http://hoot.metr.ou.edu/upperair/isen/ Advanced Synoptic M. D. Eastin

References

Bluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume I: Principles of Kinematics and Dynamics.

Oxford University Press, New York, 431 pp.

Bluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume II: Observations and Theory of Weather Systems. Oxford University Press, New York, 594 pp.

Byers, H., 1938: On the thermodynamic interpretation of isentropic charts.

Mon. Wea. Rev

.,

66

, 63-68.

Carlson, T. N., 1998:

Mid-latitude Weather Systems

, AMS, 343 pp.

Hoskins, B. J., 1991: Towards a PV-theta view of the general circulation.

Tellus

,

43

, 27-35.

Lackmann, G., 2011:

Mid-latitude Synoptic Meteorology – Dynamics, Analysis and Forecasting

, AMS, 343 pp.

Montgomery, R. B., 1937: A suggested method for representing gradient flow on isentropic surfaces.

Bull. Amer. Meteor. Soc

.,

18

, 210-212.

Moore, J. T., 1993: Isentropic analysis and interpretation: Operational application to synoptic and mesoscale forecast problems. NWS Training Center Manual, 99 pp.