#### Transcript Isentropic Analysis

# 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 (

**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:**

•

*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 H 296 K**

Advanced Synoptic 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 H θ = 296-K 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*

*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**

:

*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*

*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!!!

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 (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

### 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

**R o**

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 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.

Advanced Synoptic M. D. Eastin