isentropic analysis techniques: basic concepts james t. moore cooperative institute for...
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Isentropic Analysis Techniques: Basic Concepts
James T. Moore
Cooperative Institute for Precipitation Systems
Saint Louis University
Dept. of Earth & Atmospheric Sciences
COMET-RFC/HPC Hydrometeorology Course
27November – 4 December 2001
Mean Theta!
Now entering a no pressurezone!
Thetaburgers
Served hot and juicy at the Isentropic Café!
Boomerang Grille
Norman, OK
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
Theta as a Vertical Coordinate• = T (1000/P) , where = Rd / Cp
• Entropy = = Cp ln + const
• If = const then = const, so constant entropy sfc = isentropic sfc
• Three types of stability, since / z = ( /T) [d - ]
– stable: < d, increases with height
– neutral: = d, is constant with height
– unstable: > d, decreases with height
• So, isentropic surfaces are closer together in the vertical in stable air and further apart in less stable air.
Vertical changes of potential temperature related to lapse rates:
U = unstable
N = neutral
S = stable
VS = very stable
Visualizing Static Stability – Vertical Gradients of
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 = T (1000/P)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 = = Cp T + gZ
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.
Advection of Moisture on an Isentropic Surface
Advection of Moisture on an Isentropic Surface
Moist air from low levels on the left (south) is transported upward and tothe 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 fromBluestein, vol. I, 1992, p. 23)
RelativeHumidity305K surface12 UTC 3-17-87RH>80% = green
Pressure analysis305K surface12 UTC 3-17-87
Benjamin et al.
RelativeHumidityat 500 mbRH > 70%=green
Isentropes near Frontal Zones
Sounding for Paducah, KY 30 December 1990 12 UTC
898 mb+14.0 C
962 mb-1.3C
Cross Section Taken Normal to Arctic Frontal Zone:12 UTC 30 December 1990
Three-Dimensional Isentropic Topography
Three-Dimensional Isentropic Topography Associated with an Occlusion
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.
Thermal Wind Relationship in Isentropic Coordinates
V C
f
Pk P
p
[ ]( )
1
1 0 0 0
Usually only the wind component normal to the planeof the cross section is plotted; positive (negative) valuesindicate wind components into (out of) the plane of thecross section.With north to the left and south to the right, when isentropesslope down, the thermal wind is into the paper, I.e, the wind component into the cross-sectional plane increases with heightWhen isentropes slope up, the thermal wind is negative, I.e.,the wind component out of the cross-sectional plane increaseswith height.
Thermal Wind Relationship in Isentropic Coordinates
*Isentropic surfaces have a steep slope in regions of strongbaroclinicity. Flat isentropes indicate barotropic conditionsand little/no change of the wind with height.
*Frontal zones are characterized by sloping isentropicsurfaces which are vertically compacted (indicating strongstatic stability).
*In the stratosphere the static stability increases by about one order of magnitude.
Isentropic Mean Meridional Cross Section
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.
Neutral-Superadiabatic Lapse Rates
Vertical Resolution is a Function of Static Stability
Radiational Heating/Cooling Disrupts the Continuity of Isentropic Surfaces
Namias, 1940: An Introduction to the Study of Air Mass and Isentropic Analysis, AMS, Boston, MA.
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 mb) 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!
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) :
– Season Low-Level Isentropic Surface
– Winter 290-295 K
– Spring 295-300 K
– Summer 310-315 K
– Fall 300-305 K
Choosing the “Right” Isentropic Surface(s)
• Compute surface or 1000 mb potential temperature values. Choose an isentropic surface that is at least 4-8 K higher than the highest value in the area of interest and upstream. You don’t want an isentropic surface that will be affected drastically by radiational heating or cooling in the PBL during the next 12-24 hours.
• BEST METHOD: Compute a cross section of isentropes and isohumes 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 mb above the surface. A rule of thumb is to choose an isentropic surface that is located at ~700-750 mb above your area.
Using an Isentropic Cross Section to Choose a Surface: Isentropic Cross Section for 00 UTC 05 Dec 1999
Isentropic Moisture Parameters
• Condensation Pressure: 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: 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 mb represents saturation. Values < 100 mb indicated near saturation. Condensation difference on an isentropic surface is equivalent to dew point depression on a constant pressure surface.
Isentropic Moisture Parameters
• Condensation Ratio: The ratio of the condensation pressure to the actual pressure for a point on an isentropic surface. Values range from 0-1. Condensation ratio on an isentropic surface is equivalent to relative humidity on a constant pressure surface.
• 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.
Lifted Condensation Pressure and Condensation Difference on the 294 K Isentropic Surface for
00 UTC 5 December 1999
t
PV
P PV
dd t
P P dd t
( ) ( ) ( ) ( ) ( )
A B C D
Mass Continuity Equation in Isentropic Coordinates
Term A: Horizontal advection of static stabilityTerm B: Divergence/convergence changes the static stabil-ity; divergence (convergence) increases (decreases) the staticstabilityTerm C: Vertical advection of static stability (via diabaticheating/cooling)Term D: Vertical variation in the diabatic heating/coolingchanges the static stability (e.g., decreasing (increasing) diabatic heating with height decreases (increases) the staticstability
Term A: Horizontal Advection of Static Stability
Increased static stability
Increased static stability
Decreased static stability
Decreased static stability
Term B: Divergence/Convergence Effects
Term C: Vertical Advection of Static Stability
Term D: Vertical Variation of Diabatic Heating/Cooling
Very stable (50 mb/4K)
Less stable (100 mb/4K)
Divergence
Latent Heating
Latent Heating
Evaporative Cooling
V
P PV
PV( ) ( ) ( )
Horizontal Mass Flux
dd t
P P dd t
dd t
P
( ) ( )
Vertical Mass Flux
Moisture Stability Flux
M S F q P V
M S F V q P q P V
[( ) ]
[ ] [ ]
Where q is the average mixing ratio in the layer from to + , P is the distance in mb 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.
d pd t
Pt
V Pdd t
P( )
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.
Computing Vertical Motion
Local pressuretendency termcomputed over 12, 6 and 3 hours by Homan andUccellini, 1987(WAF, vol. 2, 206-228)
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 mb / 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 mb/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 mb (diabatic heating/cooling term):
(d/dt)(P/ ) = (7 K/12 h)(-50 mb/4K) = -2 bars s-1
(ascent)
Understanding System-Relative Motion
Isentropic System-Relative Vertical Motion
d
d t tV
d
d t tC V C
t tC
() ()()
() ()() ( ) ()
() ()()
0
d
d tV C
dp
d tV C P
()( ) ()
( )
Define Lagrangian; no -diabatic heating/cooling
Assume tendency following system is = 0; e.g., no deepening or filling of system with time.
System tendency
Insert pressure, P, as the variable in the ( )
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
( ) V C P
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.
In regions of isentropicupglide, this system-rela-tive motion vector, C, will enhance the uplift (since C is subtracted from the Velocity vector),
Vort Max at to
Vort Max at t1
When is C important to use when compute isentropic omegas?
Kansas Snowstorm: 4-5 December 1999
•Narrow heavy snow band - ~150 km wide
•Snow was displaced from “Parent” cyclone - ~ 300-400 km to the N-NW
•Snowfall amount ranged from 5-10 inches
•Embedded convection was observed within the snow band
•This event proved difficult to forecast
MB-Enhanced IR Satellite Imagery for 00 – 12 UTC 5 December 1999
Visible Satellite imagery for 18 UTC 5 December 1999 with Snowfall Totals in Blue and Surface Temps in Red
Ground-Relative Streamlines and Isobars
294 K Surface 5 December 1999 00 UTC
Ground-Relative Isentropic Vertical Motion
294 K Surface 5 December 1999 00 UTC
System-Relative Streamlines and Isobars
294 K Surface 5 December 1999 00 UTC
C = 257.8° at 10.9 m s-1
System-Relative Isentropic Vertical Motion
294 K Surface 5 December 1999 00 UTC
Ground-Relative Moisture Transport Vectors
294 K Surface 5 December 1999 00 UTC
System-Relative Moisture Transport Vectors
294 K Surface 5 December 1999 00 UTC
RUC-II Initialization 650 mb e valid 00 UTC 5 Dec 1999
RUC-II Initialization Cross section of e valid 00 UTC 5 Dec 1999: Lubbock, TX to Columbia, MO