1. Advanced SynopticM. D. Eastin Isentropic Analysis

2. Advanced SynopticM. D. Eastin Isentropic Analysis Outline: Basic Idea Construction of Isentropic Maps Interpretation of Vertical Motion Example Case Can we neglect Diabatic Processes? Advantages / Disadvantages

3. Advanced SynopticM. D. Eastin 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 consistent with those obtained from QG analysis  Can diagnose horizontal and vertical moisture transport  Can visualize vertical motion near fronts Conceptually simple and insightful Isentropic Analysis: Basic Idea

4. Advanced SynopticM. D. Eastin 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. Isentropic Analysis: Basic Idea

5. Advanced SynopticM. D. Eastin 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” Isentropic Analysis: Constructing Maps L H H Greensboro Sounding 296 K 705 mb θ = 296-K

6. Advanced SynopticM. D. Eastin 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 Isentropic Analysis: Interpretation L H H θ = 296-K L H H

7. Advanced SynopticM. D. Eastin 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: 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) Isentropic Analysis: Vertical Motion Term A Term B Term C

8. Advanced SynopticM. D. Eastin 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: 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…] Isentropic Analysis: Vertical Motion Term A Term B Term C

9. Advanced SynopticM. D. Eastin QG-Omega Interpretation: Basic QG forcing terms cancel over TX and LA → no vertical motion? → Q-vectors… Basic QG forcing clearly implies ascent across NC and SC Isentropic Analysis: Example Case 500mb heights and vorticity500mb heights and SLP Strong PVA Weaker PVA Strong CAA Moderate WAA L H

10. Advanced SynopticM. D. Eastin QG-Omega Interpretation: 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 Isentropic Analysis: Example Case 500mb Q-vectors / Convergence 500mb heights and 700mb ω

11. Isentropic Interpretation: 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 SynopticM. D. Eastin Isentropic Analysis: Example Case Pressure/ Winds on 296-K surface…with Mixing Ratio

12. Isentropic Interpretation: 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 SynopticM. D. Eastin Isentropic Analysis: Example Case Pressure / winds / mixing ratio 296-K surface …with Composite Radar Reflectivity

13. 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 of isentropic lift but the qualitative results remains the same Advanced SynopticM. D. Eastin Isentropic Analysis: Neglect Diabatic?

14. 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 SynopticM. D. Eastin Isentropic: Advantages / Disadvantages

15. Real-time Analyses: WxCasterhttp://www.wxcaster.com/isentropic.htmhttp://www.wxcaster.com/isentropic.htm College of DuPage: http://weather.cod.edu/analysis/http://weather.cod.edu/analysis/ University of Oklahomahttp://hoot.metr.ou.edu/upperair/isen/http://hoot.metr.ou.edu/upperair/isen/ Advanced SynopticM. D. Eastin Isentropic Analysis: Websites

16. Advanced SynopticM. 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.