2Potential Vorticity and Its Application in Operations Philip N. Schumacher11 December 2007This talk is based on work done with Dr. Martin Baxter of Central Michigan University and Josh Boustead of WFO OAX.
3Overview What 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.
4What is potential vorticity Potential vorticity – conserved for frictionless and adiabatic flow.(from Holton 1979)A property of a stably stratified fluid – the atmosphere and oceans.
5PV in the atmosphere PV has characteristics within the atmosphere. Troposphere – PV ~1 PVUStratosphere – PV ~10 PVUTropopause – PV gradient separating the troposphere and stratosphereInternal PV anomalies – Values can reach stratospheric levels.More on these later.
6Defining 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.
7Tropopause undulations Downward 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 surfacehigh static stability (~ 10 K per 50 hPa)high IPV (> 2 PVU)Otherwise known as short-wave troughs.
8From Hirschberg and Fritsch (1991, MWR) WAAW200 hPa heights and temperaturesCross section of temperature advection 10-1 K h-1)SIPVless stable300 hPa static stability (10-3 K hPa-1)250 hPa IPV (PVU units)From Hirschberg and Fritsch (1991, MWR)
9Finding tropopause undulations Try looking at individual pressure surfaces.But which gradients are important and at what level?300 mb350 mb450 mb400 mb
10Let’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!1234
11Hirschberg and Fritsch (1991, MWR) Note ascent ahead of the undulation, subsidence behind. So positive PV advection is forcing for large-scale ascent.Hirschberg and Fritsch (1991, MWR)
12So 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
13Let’s compare 0900 – 2300 UTC 28 Feb 2007 300-500 mb Q-vectors 700 mb Fgen1.5 PV sfc pressure700 mb Fgen500 mb vorticity700 mbFgenMosaic base reflectivity
14ReviewQ-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.
15Other 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
16One other advantageThe “influence” of a wave on lower level circulations is related to:Rossby depth – h ~ fL/Nf - CoriolisL – 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.
17Let’s go back to our tropopause map If stability is constant, then waves 1 and 2 will have the biggest influence because they extend lower in the atmosphere.1432
18Comparing a tropopause map to a constant pressure map 1800 UTC 17 January 1996Tropopause map mb isotachsPotential temperature (yellow), wind, and potential temperature advection (shaded)Wind speed (shaded), height (white)
19Distribution 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.
20PV around 400 mb From Martin 1998 PV anomaly attached to polar vortex. Isolated southern stream PV anomaly.
21309 K Equivalent Temperature Surface From Martin 1998
22Snowfall totals from 19-20 January 1995. Heavy snow north of pressure ridge.Snowfall totals from January 2001.Heavy snow south of pressure ridge.
23Standard maps - 0000 UTC 20 Jan 1996 from Martin Sfc mbNotice the strong gradient along both the cold front and warm front up to 500 mb.700 mb mb
24850 mb and 700 mb 1200 UTC 29 January 2001850 mb mb
26Cross-section of frontogenesis Both cross-sections run from west to east.Frontogenesis (lower left) Frontogenesis (yellow lines), PV (shaded)
27Conceptual Model of Physical Processes within the Trowal from Moore et al. (2005)Frontogenetical circulationFrontogenetical zoneIsobars on an isentropic surfaceeFor cases where PV anomaly is attached to the polar vortex.System-relative flow
28Conceptual model for frontal circulation within a TROWAL associated with an isolated PV anomaly Mid-level frontogenesis
29Example from 1900 UTC 27 Nov 2005 – 1800 UTC 28 Nov 2005 Shaded – Pressure on the 1.5 PVU surfaceRed solid lines – Pressure on the 1.5 PVU surface.Dashed black lines – Pressure on the 310 K theta-E surface0.5 reflectivity
30Induced flow by PV anomalies PV 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
31Non-conservation of PV dθ/dt > 0PV is produced below areas where diabatic heating is maximized. PV is destroyed above areas where diabatic heating is minimizeddθ/dt >> 0dθ/dt > 0PV decreasedPV increased
32Effect 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.
33PV inversions Given 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)
34SO 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!
35Result of a piecewise inversion From Baxter (2006)
36Influence of PV anomalies on the low level jet/warm conveyor belt 950 mb QGPV anomalyQGPV (shaded) and induced geostrophic wind.From Lackmann (2002)950 mb height and wind anomaly from interior QGPV.Full PV and geostrophic wind.
37Impact of LHR and PV generation along cold frontal precip bands A strip of PV will be produced in the lower tropAn associated cyclonic circulation will result, enhancing the cyclonic shear across the frontal zone and contributing substantially to the strength of the cold frontal LLJThis strengthening of the LLJ can result in enhanced downstream moisture transportMartin (2006), after Lackmann (2002)
38Some results of a Partners Project with WFO OAX and Dr Some results of a Partners Project with WFO OAX and Dr. Martin Baxter from Central Michigan UniversityWhat 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
39Three Cases Were Selected We’ll look at two cases involving diabatically generated PV anomalies that were E-W oriented along and north of warm frontal boundariesJan (OAX)Feb (OAX/FSD)48 hour simulations were performed using the WRF-ARWHorizontal Domains: km, two-way nestingVertical Resolution: 50 levels, model top of 100 mbInitial 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
40Case #1 Jan 4-5, 2005 Winter Storm Long 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.
41Event Total Precipitation COOP DataWRF-48 hr Total
47NARR-WRF Difference 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
48Induced 700 hPa Height and Wind Perturbation Inversion from 400 to 200 hPa
49Induced 700 hPa Height and Wind Perturbation Inversion from 900 to 450 hPa NARRWRF
50PV Anomalies (700 mb) – 18 Z 5th NARR WRF “Assumed” flow based on position of PV anomaliesNotice the PV in MO/IL associated with the convection in the NARR
51Summary Jan 3-5 Winter Storm The influence of the upper-level PV anomalies on the low-mid level fields was similar in the NARR & WRFEvaluation of the low-mid level PV anomalies helps us to understand forecast errors and how they can be modifiedThe 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 .
52February 13-14, 2004 Winter Storm Heavy snow and freezing rain fell in the mid-Missouri River Valley into southern IowaHeavy rainfall occurred the mid-Mississippi Valley into the lower Ohio ValleyStrong polar jet along the U.S.- Canadian border remained stationary over 24 hNorthern Plains was in the right entrance of the upper level jetSouthern 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.
53Event TotalsCOOPWRF6 hr accum precip ending 18 Z 14thNARRWRF
54Observed vs. Simulated Reflectivity 18Z 14th F024 WRFLevel III Composite
55NARR-WRF PV and Wind Differences 1800 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
56700 mb temperature difference and 700 to 600 mb EPV difference 700mb Temp differenceNARR-WRFWarm colors = NARR warmerCool colors = NARR cooler700 to 600 mb EPV DifferenceNARR-WRFWarm colors = NARR less stableCool colors = NARR more stable1200 UTC 14 Feb1800 UTC 14 Feb
57700 mb height and wind fields induced by cyclonic PV from 900 to 450 mb WRFNARR
58700 mb height and wind fields induced by cyclonic PV from 900 to 450 mb FGENFGENNARRWRFPosition of FGEN appears to be a function of cyclonic wind shift line largely determined by the location of diabatically produced low-mid level PVThere were no differences between NARR and WRF when the flow at 700 mb induced by the 200 to 400 mb PV anomalies was examined
59PV Anomalies (700 mb) – 18 Z 14th NARR WRF “Assumed” flow based on position of PV anomaliesDifferent placement of PV on NE/SD border; Much stronger PV in WRF further SE, with different orientation
60Feb ConclusionsThe 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 PVThis 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.
61How 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?
62Forecasting ToolsUse 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 pressureSlide from Mike Brennan (NWS-HPC)
63What 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.
64ConclusionsUse 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.
65ConclusionDistribution 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.