Isentropic Analysis

1. Isentropic Analysis James T. Moore Cooperative Institute for Precipitation Systems Saint Louis University COMET COMAP Course May-June 2002

2. Now entering a no pressure zone!

3. Thetaburgers Served hot and juicy at the Isentropic Café! Boomerang Grille Norman, OK

4. Utility of Isentropic Analysis • Diagnose and visualize vertical motion - through advection of pressure and system relative flow • Depict 3-Dimensional advection of moisture • Compute moisture stability flux - dynamic destabilization and moistening of environment • Diagnose isentropic potential vorticity • Diagnose dry static stability (plan or cross-section view) and upper-level frontal zones • Diagnose conditional symmetric instability • Help depict 2-D frontogenetical and transverse jet streak circulations on cross sections

5. Theta as a Vertical Coordinate • q= T (1000/P)k, where k= Rd / Cp • Entropy =  = Cp lnq + const • If  = const then q = const, so constant entropy sfc = isentropic sfc • Three types of stability, since dq/ dz = (q/T) [d - ] • stable:  < d, q increases with height • neutral:  = d, q is constant with height • unstable:  > d, q decreases with height • So, isentropic surfaces are closer together in the vertical in stable air and further apart in less stable air.

6. Visualizing Static Stability – Vertical Gradients of  Vertical changes of potential temperature related to lapse rates: U = unstable N = neutral S = stable VS = very stable

7. Theta as a Vertical Coordinate • Isentropes slope DOWN toward warm air, UP toward cold air – this is opposite to the slope of pressure surfaces: since q= T (1000/P)k, as P increases (decreases), T increases (decreases) to keep  constant (as on a skew-T diagram). • Isentropes slope much greater than pressure surfaces given the same thermal gradient; as much as one order of magnitude more! • On an isentropic surface an isotherm = an isobar = an isopycnic (const density); (remember: P = RdT) • On an isentropic surface we analyze the Montgomery streamfunction to depict geostrophic flow, where: M = y = Cp T + gZ ;

8. Isentropic Analysis: Advantages • For synoptic scale motions, in the absence of diabatic processes, isentropic surfaces are material surfaces, i.e., parcels are thermodynamical bound to the surface • Horizontal flow along an isentropic surface contains the adiabatic component of vertical motion often neglected in a Z or P reference system • Moisture transport on an isentropic surface is three-dimensional - patterns are more spatially and temporally coherent than on pressure surfaces • Isentropic surfaces tend to run parallel to frontal zones making the variation of basic quantities (u,v, T, q) more gradual along them.

10. Advection of Moisture on an Isentropic Surface

11. Advection of Moisture on an Isentropic Surface Moist air from low levels on the left (south) is transported upward and to the right (north) along the isentropic surface. However, in pressure coordinates water vapor appears on the constant pressure surface labeled p in the absence of advection along the pressure surface --it appears to come from nowhere as it emerges from another pressure surface. (adapted from Bluestein, vol. I, 1992, p. 23)

12. Relative Humidity 305K surface 12 UTC 3-17-87 RH>80% = green Pressure analysis 305K surface 12 UTC 3-17-87 Benjamin et al.

13. Relative Humidity at 500 hPa RH > 70% =green

14. Isentropes near Frontal Zones

15. Surface Map for 00 UTC 30 December 1990

16. Surface Map for 12 UTC 30 December 1990

17. Sounding for Paducah, KY 30 December 1990 12 UTC 898 hPa +14.0 C 962 hPa -1.3C

18. Cross Section Taken Normal to Arctic Frontal Zone:12 UTC 30 December 1990

19. Three-Dimensional Isentropic Topography cold warm

20. Isentropic Analysis: Advantages • Atmospheric variables tend to be better correlated along an isentropic surface upstream/downstream, than on a constant pressure surface, especially in advective flow • The vertical spacing between isentropic surfaces is a measure of the dry static stability. Convergence (divergence) between two isentropic surfaces decreases (increases) the static stability in the layer. • The slope of an isentropic surface (or pressure gradient along it) is directly related to the thermal wind. • Parcel trajectories can easily be computed on an isentropic surface. Lagrangian (parcel) vertical motion fields are better correlated to satellite imagery than Eulerian (instantaneous) vertical motion fields.

21. Thermal Wind Relationship in Isentropic Coordinates • Usually only the wind component normal to the plane of the cross section is plotted; positive (negative) values indicate wind components into (out of) the plane of the cross section. • With north to the left and south to the right: • when isentropes slope down, the thermal wind is into the paper, i.e, the wind component into the cross-sectional plane increases with height • when isentropes slope up, the thermal wind is negative, i.e., the wind component out of the cross-sectional plane increases with height.

22. Thermal Wind Relationship in Isentropic Coordinates • Isentropic surfaces have a steep slope in regions of strong • baroclinicity. Flat isentropes indicate barotropic conditions • and little/no change of the wind with height. • Frontal zones are characterized by sloping isentropic surfaces which are vertically compacted (indicating strong static stability). • In the stratosphere the static stability increases by about one order of magnitude.

23. Cross section of  and normal wind components; dashed (solid) yellow = out of (into) the cross-sectional plane. 24 h Eta forecast valid 00 UTC 29 November 2001

24. Isentropic Mean Meridional Cross Section

25. Isentropic Analysis: Disadvantages • In areas of neutral or superadiabatic lapse rates isentropic surfaces are ill-define, i.e., they are multi-valued with respect to pressure; • In areas of near-neutral lapse rates there is poor vertical resolution of atmospheric features. In stable frontal zones, however there is excellent vertical resolution. • Diabatic processes significantly disrupt the continuity of isentropic surfaces. Major diabatic processes include: latent heating/evaporative cooling, solar heating, and infrared cooling. • Isentropic surfaces tend to intersect the ground at steep angles (e.g., SW U.S.) require careful analysis there.

26. Neutral-Superadiabatic Lapse Rates SA=superadiabatic and N=neutral

27. Vertical Resolution is a Function of Static Stability LS = less stable (weak static stability) and VS = very stable (strong static stability)

28. Surface Map for 00 UTC 27 November 2001 DTX DDC

29. Sample Cross section for 00 UTC 27 November 2001

30. Radiational Heating/Cooling Disrupts the Continuity of Isentropic Surfaces As time increases solar heating causes the 300 K isentropic surface to become “redefined” at higher pressures Namias, 1940: An Introduction to the Study of Air Mass and Isentropic Analysis, AMS, Boston, MA.

31. 304 K Isentropic Surface for 12 UTC 2 May 2002

32. 304 K Isentropic Surface for 00 UTC 3 May 2002 Note loss of data in SE U.S. and in Texas…304 K surface went underground

33. Isentropic Analysis: Disadvantages • The “proper” isentropic surface to analyze on a given day varies with season, latitude, and time of day. There are no fixed level to analyze (e.g., 500 hPa) as with constant pressure analysis. • If we practice “meteorological analysis” the above disadvantage turns into an advantage since we must think through what we are looking for and why!

34. Choosing the “Right” Isentropic Surface(s) • The “best” isentropic surface to diagnose low-level moisture and vertical motion varies with latitude, season, and the synoptic situation. There are various approaches to choosing the “best” surface(s): • Use the ranges suggested by Namias (1940) : • SeasonLow-Level Isentropic Surface • Winter 290-295 K • Spring 295-300 K • Summer 310-315 K • Fall 300-305 K

35. Choosing the “Right” Isentropic Surface(s) BEST METHOD: • Compute a cross section of isentropes and isohumes ( mixing ratios) normal to a jet streak or baroclinic zone in the area of interest. • Choose the low-level isentropic surface that is in the moist layer, displays the greatest slope, and stays 50-100 hPa above the surface. • A rule of thumb is to choose an isentropic surface that is located at ~700-750 hPa above your area.

36. Using an Isentropic Cross Section to Choose a  Surface: Isentropic Cross Section for 00 UTC 05 Dec 1999

37. Isentropic Moisture Parameters • Lifting Condensation Pressure (LCP): The pressure to which a parcel of air must be raised dry-adiabatically in order to reach condensation. Represents moisture differences better than mixing ratio at low values of mixing ratio. Condensation pressure on an isentropic surface is equivalent to dew point on a constant pressure surface. • Condensation Difference (CD):The difference between the actual pressure and the condensation pressure for a point on a isentropic surface. The smaller the condensation difference, the closer the point is to saturation. Due to smoothing and round off errors, a difference < 20 hPa represents saturation. Values < 100 hPa indicated near saturation. Condensation difference on an isentropic surface is equivalent to dew point depression on a constant pressure surface.

38. Isentropic Moisture Parameters Moisture Transport Vectors (MTV): • Defined as the product of the horizontal velocity vector, V, and the mixing ratio, q. Units are gm-m/kg-s ; values typically range from 50-250, depending upon the level and the season. • Typically, stable precipitation due to isentropic upglide falls downstream from the maximum of the moisture transport vector magnitude in the northern gradient region. The moisture transport vectors and isopleths of the magnitude of the moisture transport vectors are usually displayed. • Note that the negative divergence of the MTVs is equal to the horizontal moisture convergence, since

39. Mass Continuity Equation in Isentropic Coordinates A B C D Term A: Horizontal advection of static stability Term B: Divergence/convergence changes the static stabil- ity; divergence (convergence) increases (decreases) the static stability Term C: Vertical advection of static stability (via diabatic heating/cooling) Term D: Vertical variation in the diabatic heating/cooling changes the static stability (e.g., decreasing (increasing) diabatic heating with height decreases (increases) the static stability

40. Term A: Horizontal Advection of Static Stability Very stable (50 hPa/4K) Decreased static stability Less stable (100 hPa/4K) Term B: Divergence/Convergence Effects Increased static stability Divergence Term C: Vertical Advection of Static Stability Increased static stability Latent Heating Term D: Vertical Variation of Diabatic Heating/Cooling Decreased static stability Evaporative Cooling Latent Heating

41. Horizontal Mass Flux Vertical Mass Flux

42. Moisture Stability Flux Where q is the average mixing ratio in the layer from to q + Dq, DP is the distance in hPa between two isentropic surfaces (a measure of the static stability), and V is the wind. The first term on the RHS is the advection of the product of moisture and static stability; the second term on the RHS is the convergence acting upon the moisture/static stability. MSF > 0 indicates regions where deep moisture is advecting into a region and/or the static stability is decreasing.

43. Computing Vertical Motion A B C Term A: local pressure change on the isentropic surface Term B: advection of pressure on the isentropic surface Term C: diabatic heating/cooling term (modulated by the dry static stability. Typically, at the synoptic scale it is assumed that terms A and C are nearly equal in magnitude and opposite in sign.

44. Local pressure tendency term computed over 12, 6 and 3 hours by Homan and Uccellini, 1987 (WAF, vol. 2, 206-228)

45. Example of Computing Vertical Motion 1. Assume isentropic surface descends as it is warmed by latent heating (local pressure tendency term): P/ t = 650 – 550 hPa / 12 h = +2.3 bars s-1 (descent) 2. Assume 50 knot wind is blowing normal to the isobars from high to low pressure (advection term): V   P = (25 m s-1) x (50 hPa/300 km) x cos 180 V   P = -4.2 bars s-1 (ascent) 3. Assume 7 K diabatic heating in 12 h in a layer where  increases 4 K over 50 hPa (diabatic heating/cooling term): (d/dt)(P/ ) = (7 K/12 h)(-50 hPa/4K) = -2 bars s-1 (ascent)

46. Understanding System-Relative Motion

47. Isentropic System-Relative Vertical Motion Define Lagrangian; no - diabatic heating/cooling System tendency Assume tendency following system is = 0; e.g., no deepening or filling of system with time. Insert pressure, P, as the variable in the ( )

48. System-Relative Isentropic Vertical Motion • Defined as: • ~ (V – C)   P Where  = system-relative vertical motion in bars sec-1 V= wind velocity on the isentropic surface C = system velocity, and • P = pressure gradient on the isentropic surface C is computed by tracking the associated vorticity maximum on the isentropic surface over the last 6 or 12 hours (one possible method); another method would be to track the motion of a short-wave trough on the isentropic surface

49. System-Relative Isentropic Vertical Motion Including C, the speed of the system, is important when: * the system is moving quickly and/or * a significant component of the system motion is across the isobars on an isentropic surface, e.g., if the system motion is from SW-NE and the isobars are oriented N-S with lower pressure to the west, subtracting C from V is equivalent to “adding” a NE wind, thereby increasing the isentropic upslope.

50. When is C important to use when compute isentropic omegas? Vort Max at t1 In regions of isentropic upglide, this system-rela- tive motion vector, C, will enhance the uplift (since C is subtracted from the Velocity vector), Vort Max at to