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Potential Vorticity and Its Application in Operations

Philip N. Schumacher11 December 2007

This talk is based on work done with Dr. Martin Baxter of Central Michigan University and Josh Boustead of WFO OAX.

OverviewWhat is potential vorticity and why care.Tropopause maps and its relationship to

synoptic scale forcingPotential vorticity distribution and TROWALs.Internal potential vorticity anomalies.PV and its impact on the warm conveyor belt.The future - using PV to analyze model

differences.

What is potential vorticity IPV g

f

P

Potential vorticity – conserved for frictionless and adiabatic flow.(from Holton 1979)

A property of a stably stratified fluid – the atmosphere and oceans.

PV in the atmospherePV has characteristics within the atmosphere.

Troposphere – PV ~1 PVUStratosphere – PV ~10 PVU

Tropopause – PV gradient separating the troposphere and stratosphere

Internal PV anomalies – Values can reach stratospheric levels.More on these later.

Defining the tropopause

WMO definitition – lapse rate of -2˚C/km.

Dynamic tropopause (Morgan and Nielsen-Gammon 1998). The level where the PV exceeds some critical value.

Usually between 1 and 2 PVU.

The pressure of the dynamic tropopause is generally defined as the last time PV exceeds the critical value (moving up in the atmosphere).

Removes internal anomalies.

Tropopause undulationsDownward extension of the tropopause due to descent at

and above the tropopause.• Macroscale features covering over 1000 km horizontally.

• Characterized by:

• a warm pool on an upper-level (e.g., 200 hPa) pressure surface

• high static stability (~ 10 K per 50 hPa)

• high IPV (> 2 PVU)

• Otherwise known as short-wave troughs.

Finding tropopause undulationsTry looking at individual pressure surfaces.

But which gradients are important and at what level?

450 mb400 mb350 mb300 mb

Let’s take another look!If we trace the 1.5 PVU line, we find that different waves are available at different levels.

What if we plot pressure on a PV surface (1.5 PVU)?

Then multiple short-waves are visible on one map!

1

2

3

4

So what is the advantage?All of these can be associated with synoptic-

scale forcing for ascent:Positive PV advectionVorticity advection increasing with heightConvergence of Q-vectors

Let’s compare0900 – 2300 UTC 28 Feb 2007

300-500 mb Q-vectors

700 mb Fgen

500 mb vorticity

700 mbFgen

1.5 PV sfc pressure

700 mb Fgen

Mosaic base reflectivity

ReviewQ-vectors did not isolated the second wave

moving into central Nebraska.500 mb vorticity grid is more “noisy” to

examine.Can be difficult to discern subtle features. This

is a big advantage in summer.

Other advantagesQ-vectors have be smoothed and on low-

resolution grids.Even smoothed fields on grids < 50 km

resolution are too noisy.

RUC 80 km RUC 40 km

One other advantageThe “influence” of a wave on lower level

circulations is related to: Rossby depth – h ~ fL/N

f - Coriolis L – horizontal scale of anomalyN – Brunt-Väisälä frequency (stability)N = (g/)(/z)

For a given wave the less stable the atmosphere, the deeper into the atmosphere it influences the winds and ageostrophic circulation.

Stability is why “weaker” waves in summer have a big influence on vertical motion.

Let’s go back to our tropopause map

1

2

3

4

If stability is constant, then waves 1 and 2 will have the biggest influence because they extend lower in the atmosphere.

Comparing a tropopause map to a constant pressure map

1800 UTC 17 January 1996

Tropopause map 300 mb isotachs

Potential temperature (yellow), wind, and potential temperature advection (shaded)

Wind speed (shaded), height (white)

Distribution of PV and how it influences precipitation with TROWALS

How PV is organized near the tropopause can also influence where precipitation falls.

TROWALs are areas with low stability and ample moisture.

Determining where precipitation is favored within a TROWAL is critical to warning decisions and QPF/snowfall forecasts.

PV around 400 mb

From Martin 1998

PV anomaly attached to polar vortex. Isolated southern stream PV anomaly.

309 K Equivalent Temperature Surface

From Martin 1998

Snowfall totals from 19-20 January 1995.Heavy snow north of pressure ridge.

Snowfall totals from 28-29 January 2001.Heavy snow south of pressure ridge.

Standard maps - 0000 UTC 20 Jan 1996from MartinSfc 850 mb

700 mb 500 mb

Notice the strong gradient along both the cold front and warm front up to 500 mb.

850 mb and 700 mb 1200 UTC 29 January 2001

850 mb 700 mb

300 mb and 500 mb - 1200 UTC 29 January 2001

500 mb 300 mb

Cross-section of frontogenesisBoth cross-sections run from west to east.

Frontogenesis (lower left) Frontogenesis (yellow lines), PV (shaded)

Frontogenetical zone

System-relative flow

e

Isobars on an isentropic surface

Frontogenetical circulation

Conceptual Model of Physical Processes within the Trowal

from Moore et al. (2005)

For cases where PV anomaly is attached to the polar vortex.

Conceptual model for frontal circulation within a TROWAL associated with an isolated PV anomaly

Mid-level frontogenesis

Example from 1900 UTC 27 Nov 2005 – 1800 UTC 28 Nov 2005

Shaded – Pressure on the 1.5 PVU surface

Red solid lines – Pressure on the 1.5 PVU surface.

Dashed black lines – Pressure on the 310 K theta-E surface

0.5 reflectivity

Induced flow by PV anomaliesPV anomalies can induce flow away from where they are located.

The strength of the flow is determined by the size of the anomaly (wave) and the vertical stability.

Less stable – more influenceLarger wave – more influence

Non-conservation of PVPV is produced below areas where diabatic heating is maximized.

PV is destroyed above areas where diabatic heating is minimized

dθ/dt > 0

dθ/dt > 0

dθ/dt >> 0

PV increased

PV decreased

Effect of non-conservation

From Martin (2006)

Destruction of PV near the tropopause by latent heat release can increase amplitude of an upper level wave.

Production of PV below the tropopause by latent heat release can induce mid- or low level circulations (i.e. mesocyclone vortices).

Both can influence weather downstream.

PV inversionsGiven PV distribution through the atmosphere you can:

• Determine the balanced wind field at all levels.

•Determine the height field at all levels.

•Recovers only the balanced wind (divergence is ignored).

From Baxter (2006)

SO WHAT???Piecewise PV inversions (where the power is):

Isolate anomalies or layers.

Can determine the influence of individual anomalies throughout the atmosphere.

Can create new conceptual models – and more!

Result of a piecewise inversion

From Baxter (2006)

Influence of PV anomalies on the low level jet/warm conveyor belt

950 mb QGPV anomaly

QGPV (shaded) and induced geostrophic wind.

From Lackmann (2002)

950 mb height and wind anomaly from interior QGPV.

Full PV and geostrophic wind.

Martin (2006), after Lackmann (2002)

Impact of LHR and PV generation along cold frontal precip bands

•A strip of PV will be produced in the lower trop

•An associated cyclonic circulation will result, enhancing the cyclonic shear across the frontal zone and contributing substantially to the strength of the cold frontal LLJ

•This strengthening of the LLJ can result in enhanced downstream moisture transport

Some results of a Partners Project with WFO OAX and Dr. Martin Baxter from Central Michigan University

What role does convection play in the physical processes that create banded snowfall?Does warm-sector convection aid or inhibit the

development of banded snowfall?How can convection influence the balance of processes that

create banded snowfall?Is convection always the dominant source of model forecast

errors in these situations?Previous work by Brennan and Lackmann (2006), Mahoney

and Lackmann (2007), and Baxter (2006) examine the role of N-S oriented convection, our cases feature E-W oriented convection

Three Cases Were SelectedWe’ll look at two cases involving diabatically

generated PV anomalies that were E-W oriented along and north of warm frontal boundariesJan 4-6 2005 (OAX)Feb 13-15 2003 (OAX/FSD)

48 hour simulations were performed using the WRF-ARWHorizontal Domains: 36-12-4 km, two-way nestingVertical Resolution: 50 levels, model top of 100 mb Initial and Lateral Boundary Conditions: NARR - 32 km, 45

layers, updated every 3 hrsLin et al., RRTM, Dudhia, Monin-Obukov, Thermal Diffusion,

YSU PBL, Kain-Fritsch (on two outermost domains only)WRF-ARW simulations were compared with NARR

dataPiecewise inversion performed on the NARR and

WRF were done in two layers, 400 to 200 mb and 900 to 450 mb every 50 mb for each inversion

Case #1Jan 4-5, 2005 Winter StormLong duration winter storm for the OAX CWAInitial precipitation on the 4th was in response

to strong WAAThe second round of precipitation on the 5th

was due to strong dynamical forcingLittle in the way of frontogenesis with this

systemTwo events added up to large snowfall totals

across eastern Nebraska and western Iowa.We’ll be focusing on the 5 January.

Event Total Precipitation

COOP Data

WRF-48 hr Total

Surface Analysis1800 UTC 5 Jan

Central Plains Radar Mosaic

Valid 1500 UTC 5 Jan

Valid 1800 UTC 5 Jan

3-hr Accumulated PrecipitationValid 1500 UTC 5 Jan

NARR Data WRF-ARW Data

Operational NAM/GFS12-hr Accumulated Precipitation valid 0000 UTC 6 Jan

NAM GFS

PV Comparison

NARR-WRF DifferenceShaded – PV around 700 mb from NARR.

Red lines – NARR – WRF PV difference around 700 mb.

Wind barbs – Narr – WRF wind vector difference at 700 mb

Induced 700 hPa Height and Wind PerturbationInversion from 400 to 200 hPa

Induced 700 hPa Height and Wind PerturbationInversion from 900 to 450 hPa

NARR WRF

PV Anomalies (700 mb) – 18 Z 5th

NARR

WRF

•“Assumed” flow based on position of PV anomalies

•Notice the PV in MO/IL associated with the convection in the NARR

Summary Jan 3-5 Winter StormThe influence of the upper-level PV anomalies on

the low-mid level fields was similar in the NARR & WRF

Evaluation of the low-mid level PV anomalies helps us to understand forecast errors and how they can be modified

The more E-W orientation of the 700 mb PV anomaly in the WRF led to an incorrect focus for precipitation. While the convection in the NARR led to a different PV structure resulting in greater temperature advection in Northern IA and increased westerly flow over MO/AR/OK .

February 13-14, 2004 Winter StormHeavy snow and freezing rain fell in the mid-

Missouri River Valley into southern Iowa Heavy rainfall occurred the mid-Mississippi

Valley into the lower Ohio ValleyStrong polar jet along the U.S.- Canadian border

remained stationary over 24 h Northern Plains was in the right entrance of

the upper level jet Southern stream wave was moving into Texas

and the lower Mississippi ValleyBroad baroclinic zone extended from the lower

Mississippi Valley into the Missouri Valley.A large-scale warm advection and

frontogenesis was observed within this baroclinic zone.

Event Totals

COOP

WRF

6 hr accum precip ending 18 Z 14th

NARR

WRF

Observed vs. Simulated Reflectivity 18Z 14th F024

Level III Composite WRF

NARR-WRF PV and Wind Differences1800 UTC 14 Feb

Shaded – PV around 700 mb from NARR.

Red lines – NARR – WRF PV difference around 700 mb.

Wind barbs – Narr – WRF wind vector difference at 700 mb

700 mb temperature difference and 700 to 600 mb EPV difference

1200 UTC 14 Feb

1800 UTC 14 Feb

700mb Temp difference

NARR-WRF

Warm colors = NARR warmer

Cool colors = NARR cooler

700 to 600 mb EPV Difference

NARR-WRF

Warm colors = NARR less stable

Cool colors = NARR more stable

700 mb height and wind fields induced by cyclonic PV from 900 to 450 mb

NARRWRF

700 mb height and wind fields induced by cyclonic PV from 900 to 450 mb

•Position of FGEN appears to be a function of cyclonic wind shift line largely determined by the location of diabatically produced low-mid level PV

•There were no differences between NARR and WRF when the flow at 700 mb induced by the 200 to 400 mb PV anomalies was examined

NARR

WRF

FGENFGEN

PV Anomalies (700 mb) – 18 Z 14th

NARR

WRF•“Assumed” flow based on position of PV anomalies

•Different placement of PV on NE/SD border; Much stronger PV in WRF further SE, with different orientation

•The area of precipitation responsible for the inaccurate generation of low-mid level PV was stratiform.

•The development of this precipitation and associated PV led to the formation of a positive feedback between precipitation and the cyclonic circulation associated with the PV

•This allowed the mid level frontogenesis band to set up along I-80 later 6-12 h later instead of along the Iowa and Missouri border.

Feb 13-15 2003 Conclusions

How can we apply this?Examine precipitation and 700 mb PV in model.

While convection is most efficient in producing PV, persistent stratiform precipitation can be effective.

Infer induced mid-level wind fields from internal anomaly. Are wind field differences the result of model

precipitation differences? If so, determine where initial precipitation will

develop and which model solution does this favor? What is the impact on the warm conveyor belt and

frontogenesis?

Forecasting Tools

Use PV thinking to adjust model guidance by understanding impact of latent heating on moisture transport, cyclogenesis, low-level jets.

AWIPS Procedure (NWS Raleigh)

QPF (total and/or convective)

Lower-tropospheric PV, wind,

Sea level pressure

Slide from Mike Brennan (NWS-HPC)

What about the future?The effect of internal PV anomalies can be

calculated.WFO FSD and WFO OAX will be testing

GEMPAK software to invert PV on output from the WRF-ARW.Initially will be displayed on web pages but

someday in AWIPS????Can examine how sensitive the forecast is to

location and timing of precipitation.

ConclusionsUse of tropopause maps provide an easy way

to see short-waves at different levels.Depth of wave into troposphere can help

determine its ability to interact with mid-level boundaries.

Can be used with higher resolution grids than Q-vectors can be applied.

ConclusionDistribution of PV near the tropopause can determine where

precipitation is favored within a TROWAL. Favors development of mid-level boundaries.

Diabatically-produced PV can influence strength of warm conveyor belt. Wind-parallel anomalies can increase moisture transport .

While convection is most efficient, stratiform precipitation can produce significant PV anomalies. Location of anomalies can determine where the warm conveyor

belt is located. Can determine where mid-level front becomes established several

hours later.Examining mid-level PV (800 – 500 mb) in models can help

forecasters understand if precipitation development in the model is resulting in differences.