Isentropic Analysis Techniques: Basic Concepts

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Isentropic Analysis
James T. Moore Cooperative Institute for
Precipitation Systems Saint Louis
University COMET COMAP Course
May-June 2002
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Now entering a no pressure zone!
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Thetaburgers Served hot and juicy at the
Isentropic Café! Boomerang Grille Norman, OK
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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

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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 ? lt ?d, q increases with height
• neutral ? ? d, q is constant with height
• unstable ? gt ? d, q decreases with height
• So, isentropic surfaces are closer together in
  the vertical in stable air and further apart in
  less stable air.

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Visualizing Static Stability Vertical Gradients
of ?
Vertical changes of potential temperature related
to lapse rates U unstable N neutral S
stable VS very stable
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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

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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.

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Advection of Moisture on an Isentropic Surface
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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)
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Relative Humidity 305K surface 12 UTC
3-17-87 RHgt80 green
Pressure analysis 305K surface 12 UTC 3-17-87
Benjamin et al.
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Relative Humidity at 500 hPa RH gt 70 green
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Isentropes near Frontal Zones
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Surface Map for 00 UTC 30 December 1990
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Surface Map for 12 UTC 30 December 1990
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Sounding for Paducah, KY 30 December 1990 12 UTC
898 hPa 14.0 C 962 hPa -1.3C
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Cross Section Taken Normal to Arctic Frontal
Zone12 UTC 30 December 1990
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Three-Dimensional Isentropic Topography
cold
warm
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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.

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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.

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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.

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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
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Isentropic Mean Meridional Cross Section
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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.

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Neutral-Superadiabatic Lapse Rates
SAsuperadiabatic and Nneutral
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Vertical Resolution is a Function of Static
Stability
LS less stable (weak static stability) and VS
very stable (strong static stability)
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Surface Map for 00 UTC 27 November 2001
DTX
DDC
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Sample Cross section for 00 UTC 27 November 2001
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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.
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304 K Isentropic Surface for 12 UTC 2 May 2002
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304 K Isentropic Surface for 00 UTC 3 May 2002
Note loss of data in SE U.S. and in Texas304 K
surface went underground
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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!

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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

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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.

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Using an Isentropic Cross Section to Choose a ?
Surface Isentropic Cross Section for 00 UTC
05 Dec 1999
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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 lt 20
  hPa represents saturation. Values lt 100 hPa
  indicated near saturation. Condensation
  difference on an isentropic surface is equivalent
  to dew point depression on a constant pressure
  surface.

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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

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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
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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
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Horizontal Mass Flux
Vertical Mass Flux
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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 gt 0 indicates
regions where deep moisture is advecting into a
region and/or the static stability is decreasing.
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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.
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Local pressure tendency term computed over 12, 6
and 3 hours by Homan and Uccellini, 1987 (WAF,
vol. 2, 206-228)
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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)
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Understanding System-Relative Motion
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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 ( )
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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

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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.
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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
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Computing Isentropic Omegas

• Essentially there are three approaches to
  computing isentropic omegas
• Ground-Relative Method
• Okay for slow-moving systems (?P/ ?t term is
  small)
• Assumes that the advection term dominates (not
  always a good assumption)
• System-Relative Method
• Good for situations in which the system is not
  deepening or filling rapidly
• Also useful when the time step between map times
  is large (e.g., greater than 3 hours)
• S-R velocity vectors are useful in computing S-R
  MTVs
• Brute-Force Computational Method ( ?P/ ?t V ?
  ?P )
• Best for situations in which the system is
  rapidly deepening or filling
• Good approximation when data are available at 3
  h or less interval, allowing for good estimation
  of local time tendency of pressure

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Which Term is Important?

• We chose four cases two cases were
  non-developing systems with weak or little
  cyclogenesis, and two were developing, dynamic
  systems with moderate cyclogenesis.
• We ran simulations of these cases using the MASS
  model (version 5.10.1) model results were
  viewed using GEMPAK.
• Our focus was on those regions on lower to
  mid-tropospheric ? levels where the relative
  humidity was gt99 and for which the model had
  generated precipitation gt 0.5 mm during the
  preceding hour.

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Which Term is Important? (cont.)

• We computed isentropic omegas using all three
  terms noted earlier
• for the local pressure tendency term a simple 2 h
  time centered difference was used
• the pressure advection was computed using a
  centered finite difference
• the diabatic term was computed by first computing
  the diabatic heating/cooling on the isentropic
  surface and then multiplying by the static
  stability centered on the isentropic surface in
  question.
• System-relative vertical motion was also
  computed, using a system speed, C, estimated
  subjectively using the trough motion on the
  isentropic surface previous to the map time.

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Computing Diabatic Heating/Cooling in Isentropic
Coordinates

• Approach developed by Keyser and Johnson (1982,
  MWR)
• Derived from the continuity equation in
  isentropic coordinates
• Vertically integrate the stability flux from the
  level of interest (?)
• to an isentropic surface near the tropopause
  (?t) the difference
• between the pressure tendencies at the same
  two levels
• Note Diabatic heating is modulated by the
  static stability

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Four Precipitation Cases used for Study

• 21 UTC 16 January 1994
• non-developing system associated with long-wave
  trough well to west
• weakly-defined surface system associated with a
  weak-moderate cold front with inverted trough,
  produced banded heavy snow over Kentucky with
  amounts exceeding 60 cm
• 15 UTC 10 April 1997
• non-developing system associated with a weak
  ridge over MO
• light snow (10 cm) fell in a band across central
  MO ahead of a weak west-east oriented stationary
  front in southern MO
• 00 UTC 6 April 1999
• strong S/W trough associated with moderate
  cyclogenesis in central Plains
• strong baroclinic system with 996 hPa low in KS
  movement to NE strong mid-level jet streak
• 21 UTC 15 April 1999
• strong S/W trough and moderate cyclogenesis in
  Ohio Valley
• extensive precipitation shield, 994 hPa low with
  occlusion movement to NE, strong mid-level jet
  streak

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Table 1 Statistical Analysis for 21 UTC 16
January 1994
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Table 2 Statistical Analysis for 15 UTC 10 April
1997
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Table 3 Statistical Analysis for 00 UTC 6 April
1999
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Table 4 Statistical Analysis for 21 UTC 15 April
1999
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Conclusions

• Local pressure tendency and diabatic term do NOT
  generally offset one another
• The advection term alone accounts from 30-60 of
  the total omega and agrees in sign
• The sum of the local pressure tendency
  advection term account from 50-90 of the total
  omega (i.e., this product is a better
  approximation to omega than just using the
  advection term alone
• System-relative omega approximation can exceed
  the sum of the local pressure tendency
  advection term, other times it was about gt 80 of
  their sum. It is also from 50-70 of the total
  omega.
• It you have the data it is worthwhile computing
  the local pressure tendency term using a small
  time difference, otherwise it is best to use the
  system-relative omega method.

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Case Study 26-27 November 2001 Early Season
Snowstorm in the Upper Midwest
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Courtesy of MKE, WI
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Lifting condensation pressure and condensation
difference on the 296 K surface
Moist
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700 hPa ?e for 12 UTC 26 November 2001
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Ground-relative streamlines and isobars on the
296 K surface
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Ground-relative omegas on the 296 K surface
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System-relative streamlines and isobars on the
296 K surface
C 5.5 m s-1 at 314.5
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System-relative omegas on the 296 K surface
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Ground-relative moisture transport vectors
on the 296 K surface
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System-relative moisture transport vectors
on the 296 K surface