Isentropic Analysis
Advanced Synoptic
M. D. Eastin
Isentropic Analysis
Outline:
• Basic Idea
• Construction of Isentropic Maps
• Interpretation of Vertical Motion
• Example Case
• Can we neglect Diabatic Processes?
• Advantages / Disadvantages
Advanced Synoptic
M. D. Eastin
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 (Ro)
→ 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:
• Adiabatic flow → 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.
Advanced Synoptic
M. D. Eastin
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
296 K
Advanced Synoptic
H
M. D. Eastin
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
θ = 296-K
H
H
L
L
H
Advanced Synoptic
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 
Term A

V  c    p
Term B

p 
 t
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: Pressure advection
• 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 
Term A

V  c    p
Term B

p 
 t
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
Strong
PVA
500mb heights and SLP
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 Q-vectors / Convergence
500mb heights and 700mb ω
• 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:
Pressure/ Winds on 296-K surface
…with Mixing Ratio
• 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:
Pressure / winds / mixing ratio
296-K surface
…with Composite Radar Reflectivity
• 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!!!
Advanced Synoptic
M. D. Eastin
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 (θe)
→ motion is still upward, but ascent is stronger
 Thus, neglecting diabatic processes only results in an underestimation of isentropic lift
but the qualitative results remains the same
Advanced Synoptic
M. D. Eastin
Isentropic: Advantages / Disadvantages
Advantages:
 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 Ro and uniform σ are not needed
Disadvantages:
 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!!!
Advanced Synoptic
M. D. Eastin
Isentropic Analysis: Websites
Real-time Analyses:
WxCaster
http://www.wxcaster.com/isentropic.htm
College of DuPage:
http://weather.cod.edu/analysis/
University of Oklahoma
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.
Advanced Synoptic
M. D. Eastin