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A Conceptual Model for Heavy Banded Snow. James T. Moore Cooperative Institute for Precipitation Systems Saint Louis University. WFO St. Louis Winter Weather Workshop: 17 November 2003. Processes Important for Producing Heavy Snow

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a conceptual model for heavy banded snow

A Conceptual Model for Heavy Banded Snow

James T. Moore Cooperative Institute for Precipitation Systems

Saint Louis University

WFO St. Louis Winter Weather Workshop: 17 November 2003


Processes Important for Producing Heavy Snow

  • As with warm season weather we need three critical factors:
      • Lift
      • Moisture
      • Instability
  • Winter storms are typically are accompanied by strong dynamics which produce synoptic-scale lift. The limiting factors are usually moisture and lift.
  • So, the forecaster must diagnose/forecast if:
      • Moisture deep enough to produce ice crystals (temperatures < -12°C), can be advected north, and
      • Instability can be generated to enhance the vertical motion over mesoscale areas (possibly linear bands)
physical processes critical to the production of heavy banded snowfall
Physical Processes Critical to the Production of Heavy Banded Snowfall
  • Development of the TROWAL airstream
  • Mid-level frontogenetical circulation
  • Reduction of Equivalent Potential Vorticity
  • Relatively deep-layer moisture to northwest of the extratropical cyclone (ETC)
  • All of these processes are related to the organization and development of the warm, cold and dry conveyor belts – which can only be visualized through system-relative flow analysis on isentropic ( or w) surfaces!

System-Relative Flow on Isentropic Surfaces

  • A key assumption is that the weather system translates horizontally without change in shape or intensity (anticyclone or cyclone changes only slowly over synoptic time scales).
  • We subtract the speed of the system, C, from the ground-relative wind, V. V – C then becomes the system-relative flow on the isentropic surface, i.e., it is the flow relative to the moving system and takes into account the change in the isentropic topography.
  • C is computed by tracking a feature on the isentropic surface, e.g., a vorticity maximum or a short-wave trough axis.
  • Under the steady state assumption: Streamlines of system-relative wind are identical to trajectories!
  • System-relative flow helps to identify conveyor belts, compute isentropic S-R vertical motion, and even S-R moisture transport vectors.

Streamlines on a 500 hPa isobaric surface at a trough moving from the west at the same speed as the wind in the axis of the trough

Streamlines as in (a) but for flow relative to the motion of the trough (from the west)

Bader et al. (1995, Images in Weather Forecasting)

isentropic system relative vertical motion
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 ( )


System-Relative Flow: How can it be used?

  • Carlson (1991, Mid-Latitude Weather Systems) notes:
  • Relative-wind analysis reveals the existence of sharply-defined boundaries, which differentiate air streams of vastly differing moisture contents. Air streams tend to contain relatively narrow ranges of  and w peculiar to the air stream’s origins.
  • Relative-wind isentropic analyses for synoptic-scale weather systems tend to show well-defined air streams, which have been identified by names – warm conveyor belt, cold conveyor belt, and the dry conveyor belt.
  • A conveyor belt consists of an ensemble of air parcels having nearly the same w (or e) value, starting from a common initial location, which travel over synoptic-scale time periods (> 12 h). They can be several hundreds km wide and several km deep.

Dry Conveyor Belt

Danielsen 1964


Some New Thoughts on the Conveyor Belts Associated with Cyclogenesis

Schultz (2001, MWR) challenged the notion of an anticyclonically-ascending cold conveyor belt (CCB) popularized by Carlson (1980, MWR)

He found that, at least in one case, the anticyclonic path of the CCB represented a transition between the warm conveyor belt and cold conveyor belt. The transition zone begins in the lower troposphere where the circulation around the cyclone is closed and widens with height to the point where the cyclone becomes an open wave. Above this point the anticyclonic path becomes the dominant air stream.

From this viewpoint comma heads that are relatively shallow are likely the result of a cyclonically turning CCB….but comma heads with deeper clouds and heavier precipitation rates (perhaps associated with CSI) are the result of “wraparound” moisture from the cyclonic path of the warm conveyor belt (WCB) – this is essentially how the TROWAL (trough of warm air aloft) develops.


Progressive S/W trough; Short time scale (< 12 h) for precipitation

Westward extension of comma head often disconnected from main precip shield

Weak easterly flow in CCB – is enhanced by the eastward motion of the system

Often a non-occluded system with inverted trough north of low


Slow-moving upper-level system; Long-lasting snow event (> 12 h)

Extensive comma head; Strong easterly flow in CCB, north of warm front

Surface system is typically occluded

what is a trowal penner 1955 q j rms
What is a TROWAL?Penner (1955, Q.J. RMS)

Apex of warm sector

Warm Air

Cold air

Cold Air

Market 2002


TROWAL Characteristics

  • The TROugh of Warm air ALoft (TROWAL) is defined as the 3-D sloping intersection of the upper cold frontal portion of the warm occlusion with the warm frontal zone (Martin 1999,MWR).
  • The trowal can be identified by examining mid-level theta-e. The exact location of the trowal is along the ridge of high theta-e values – it is essentially the cyclonic part of the warm conveyor belt that wraps around to the NW sector of the cyclone.
  • By performing a cross-sectional analysis of theta-e, the trowal can be more easily identified as a sloping canyon of high theta-e air (Martin 1999).
  • Martin (1999) showed that the position of the TROWAL had a greater correlation to the cloud and precipitation features associated with an occluded cyclone than the occluded front itself.
trowal structure
Trowal Structure
  • Sloping, tongue of warm air wrapping westward (typically) around the cyclone center
  • Pre-occlusion:
    • Defines apex of warm sector at successively higher levels (Penner 1955)
  • Post-occlusion:
    • Defines “3-D sloping intersection between warm and cold frontal zones” (Martin 1999)

Market 2002


The TROWAL is a line connecting the crests of the thermal wave at successive heights

The TROWAL marks the crest of the warm air aloft.


Conceptual Model of a TROWAL Associated With a Warm-Type Occlusion

Graphic courtesy of COMET

From Martin (1999, MWR)


Conceptual Model of a TROWAL Associated With a Cold-Type Occlusion

Graphic courtesy of COMET

Sumner (2001, M.S. Thesis)


But….the plot thickens (or at least the clouds)

  • Several points need to be emphasized:
  • Only moisture “wraps around”--- not precipitation
  • Precipitation requires a lifting mechanism…in many cases this mechanism is the direct thermal circulation due to mid-level frontogenesis as warm, moist air associated with the WCB moves northwestward meeting with colder air.
  • TROWAL development is a function of the system-relative flow.
  • Well-developed cyclones have easy-to-recognize TROWALS since the ground-relative flow is strong and over a deep layer.
  • Substantially weaker cyclones can develop TROWAL structures if they have relatively moderate east-northeastward motion, resulting in a cyclonically-curved, mid-level, system-relative flow.

Defining the Orientation of Qs and Qn with Respect to 












Qs is the component of Q associated with rotating the thermal gradient.

Qn is the component of Q associated with changing the magnitude of the thermal gradient.

Martin (1999, MWR)


DefiningQs and Interpreting What It Means (cont.)

 +1

 +1

 +2

 +2





vg/x < 0; therefore

Qs < 0; Qs points such that cold air is to its right; this results in an anticyclonic rotation of the thermal gradient vector

vg/x > 0; therefore

Qs > 0; Qs points such that cold air is to its left; this results in a cyclonic rotation of the thermal gradient vector


Trowal Formation

Qs vector convergence in the presence of a thermal gradient

New Position of 

Rotation of thermal gradient implied by direction of Qs vectors

Orientation of baroclinic zone after differential rotation of thermal gradient on either side of Qs convergence zone

Martin (1999, MWR)


Schematic Isentropic Analysis of Moist and Dry Tongues Around an Occluded Cyclone

Arrows denote system-relative flow

Namias (1939, J. Aeronaut. Sci.)


RUC 2 Initialization 650 mb Theta-E Valid 1500 UTC 10 November 1998




Illustration of TROWAL as depicted by Eta forecast

30 h Eta forecast from 12 UTC 11-09-98 run, valid 18 UTC 11-10-98

309 K e surface

two dimensional frontogenesis function petterssen 1956
Two-Dimensional Frontogenesis Function (Petterssen 1956)

Two-Dimensional Frontogenesis can be computed as:

Where:  = potential temperature

Defr = resultant deformation

 = angle between the isentropes and the axis of dilatation

Div = divergence


Frontogenetical Circulation



Carlson (Mid-latitude Weather Systems, 1991)

frontogenesis and weak symmetric stability
Frontogenesis and Weak Symmetric Stability
  • Emanuel (1985, JAS) has shown that in the presence of weak symmetric stability the frontogenetical circulation is changed.
  • The upward branch of the vertical circulation becomes contracts and becomes stronger. The strong updraft is located ahead of the region of maximum geostrophic frontogenetical forcing.
  • The distance between the front and the updraft is typically on the order of 50-200 km
  • On the cold side of the frontogenetical forcing EPV >>0 and the downward motion is broader and weaker than the updraft.

Frontogenetical circulation with moderate symmetric stability



Emmanuel (1985, JAS)

Frontogenetical circulation with WSS on warm side




Sanders and Bosart, 1985: Mesoscale Structure in the Megalopolitan Snowstorm of 11-12 February 1983. J. Atmos. Sci.,42, 1050-1061.


Emanuel’s Conceptual Model of CSI-associated Vertical Circulation

e surfaces will overturn

Emanuel (1983, JAS)

frontogenetical circulation
Frontogenetical Circulation
  • Frontogenetical circulations typically result in one band of precipitation which is parallel to the frontal zone.
  • The strength of this circulation is modulated by the ambient static stability.
  • Grumm and Nicosia (1997, NWD) found in their studies that a weakly stable environment in the presence of frontogenesis lead to one transient band of heavy precipitation.
  • However, they also found that frontogenesis in the presence of greater stability resulted in classic CSI bands of precipitation.

Three-Dimensional Form of EPV Equation: Interpretive Form

McCann (1995, WAF) derived a 3-D form of the EPV equation which is useful for interpretation:

First term on RHS: is always < 0 in a saturated environment; if the gradient of e is large, then this term becomes strongly negative.

Second term on RHS:is a measure of the convective stability; since e / p < 0 in a convectively stable environment, the whole term will be > 0 and offset the first term which is always < 0. However, the effect of this term is minimized in an area where the geostrophic absolute vorticity ( g ) is small (weakly inertially stable) or negative (inertially unstable).

Note: if the atmosphere is convectively unstable then the second term will be < 0; but parcels will accelerate upward without the release of inertial instability.


Three-Dimensional Form of EPV: Computational Form

McCann (1995, WAF) derived a 3-D form of the EPV equation which can be computed from gridded data:

  • Note that in this form EPV is a function of the:
  • Horizontal gradient of e,
  • Vertical shear of the geostrophic wind (a.k.a. the thermal wind),
  • Absolute geostrophic vorticity, and
  • 4) Convective stability
equivalent potential vorticity epv
Equivalent Potential Vorticity (EPV)
  • When EPV < 0 potential symmetric instability (PSI) is present.
  • However, EPV is also < 0 when there is convective instability – you need to see if the lines of e are “folded” , I.e., where e decreases with height to separate areas of CI from areas of CSI. CI will dominate.
  • Schultz and Schumacher (1999 MWR) suggest using es (saturated e instead of regular e) to assess CSI. However, it is perfectly acceptable to use e and check that the relative humidity is greater than 80%.

Nicosia and Grumm Model for EPV Reduction Near Extratropical Cyclones

Graphic courtesy of COMET

Nicosia and Grumm (1999, WAF) proposed a conceptual model in which a zone of EPV reduction in

concert with an area of mid-level frontogenesis will aid in the prediction of mesoscale bands of snow.

nolan moore conceptual model
Nolan-Moore Conceptual Model
  • Many heavy precipitation events display different types of mesoscale instabilities including:
    • Convective Instability (CI; edecreasing with height)
    • Conditional Symmetric Instability (CSI; lines of esare more vertical than lines of constant absolute geostrophic momentum or Mg)
    • Weak Symmetric Stability (WSS; lines of esare nearly parallel to lines of constant absolute geostrophic momentum or Mg)
nolan moore conceptual model1
Nolan-Moore Conceptual Model
  • These mesoscale instabilities tend to develop from north to south in the presence of strong uni-directional wind shear (typically from the SW)
  • CI tends to be in the warmer air to the south of the cyclone while CSI and WSS tend to develop further north in the presence of a cold, stable boundary layer.
  • It is not unusual to see CI move north and become elevated, producing thundersnow.
nolan moore conceptual model2
Nolan-Moore Conceptual Model
  • CSI may be a precursor to elevated CI, as the vertical circulation associated with CSI may overturn esurfaces with time creating convectively unstable zones aloft.
  • We believe that most thundersnow events are associated with elevated convective instability (as opposed to CSI).
  • CSI can generate vertical motions on the order of 1-3 m s-1 while elevated CI can generate vertical motions on the order of 10 m s-1 which are more likely to create charge separation and lightning.

A Conceptual Model: Cross-sectional View of Key Processes

Dry Air


Convectively unstable layer


Shaded area = CSI

case study 13 14 march 1999

Case Study: 13-14 March 1999

Heavy Banded Snowfall in Southern Missouri and Illinois


Surface-500 mb Mean Relative Humidity



Note strong RH gradient in central MO and southern IL

  • System-relative flow is easy to compute and provides an approximation for trajectories for non-developing systems.
  • Heavy snow can be produced by strong cyclones and weak cyclones in the “wrap around” region (comma head) of the cyclone. There does not have to be an occlusion present.
  • The trowal is an important part of this process. It is the warm, moist air aloft associated with the western edge of the warm conveyor belt; its development is a function of the system-relative (S-R) flow. Weak cyclones can have trowals!


  • System-relative streamlines approximate trajectories for non-developing systems.
  • S-R omegas, moisture advection, MTVs, and LCPs/CDs are useful parameters to isolate possible regions of heavy rain/snow fall.
  • Heavy snow tends to be located:
    • To the southeast of the zone of mid-level frontogenesis
    • To the northwest of the zone of mid-level negative EPV
    • Along and to the north of the TROWAL axis
    • To the north-northwest of the intruding dry slot at mid-levels
    • In a region of substantial isentropic lift and high RH

Future Issues to Consider

  • Is the present conceptual model as useful for occluded as for non-occluded systems? For example, is the trowal weaker for non-occluded systems? Is the trowal found at a lower/higher pressure level for a non-occluded system?
  • What are the respective roles of the warm and cold conveyor belts in EPV reduction? For example, the CCB may play a more prominent role in east coast ETCs for reducing EPV than in the central plains (see Nicosia and Grumm 1999, WAF)
  • How do the roles of Qs and Qn change as the trowal and the ETC evolve? Is Qs more important in trowal formation while Qn is more important in heavy banded snow formation?
  • Does the location and strength of the mid-tropospheric frontogenesis vary with the strength of the ETC? With occluded vs. non-occluded systems?
  • Where is the layer of frontogenesis form with respect to the layer of maximum EPV? How does this vary for weak vs. strong ETCs?