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Potential Vorticity and Its Application in Operations Philip N. Schumacher 11 December 2007 This talk is based on work done with Dr. Martin Baxter of Central Michigan University and Josh Boustead of WFO OAX.
Overview • What is potential vorticity and why care. • Tropopause maps and its relationship to synoptic scale forcing • Potential 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 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 atmosphere PV has characteristics within the atmosphere. Troposphere – PV ~1 PVU Stratosphere – 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 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 surface • high static stability (~ 10 K per 50 hPa) • high IPV (> 2 PVU) • Otherwise known as short-wave troughs.
Finding tropopause undulations Try looking at individual pressure surfaces. But which gradients are important and at what level? 450 mb 400 mb 350 mb 300 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 advection • Vorticity advection increasing with height • Convergence of Q-vectors
Let’s compare0900 – 2300 UTC 28 Feb 2007 300-500 mb Q-vectors 700 mb Fgen 1.5 PV sfc pressure 700 mb Fgen 500 mb vorticity 700 mb Fgen Mosaic base reflectivity
Review • Q-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 advantages • Q-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 advantage • The “influence” of a wave on lower level circulations is related to: Rossbydepth – h ~ fL/N f - Coriolis L – horizontal scale of anomaly N – Brunt-Väisäläfrequency (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 If stability is constant, then waves 1 and 2 will have the biggest influence because they extend lower in the atmosphere. 1 4 3 2
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 Martin Sfc 850 mb Notice the strong gradient along both the cold front and warm front up to 500 mb. 700 mb 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 frontogenesis • Both cross-sections run from west to east. Frontogenesis (lower left) Frontogenesis (yellow lines), PV (shaded)
Conceptual Model of Physical Processes within the Trowal from Moore et al. (2005) Frontogenetical circulation Frontogenetical zone Isobars on an isentropic surface e For cases where PV anomaly is attached to the polar vortex. System-relative flow
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 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 influence Larger wave – more influence
Non-conservation of PV dθ/dt > 0 PV 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 PV decreased PV increased
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 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)
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.
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 Martin (2006), after Lackmann (2002)
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 Selected • We’ll look at two cases involving diabatically generated PV anomalies that were E-W oriented along and north of warm frontal boundaries • Jan 4-6 2005 (OAX) • Feb 13-15 2003 (OAX/FSD) • 48 hour simulations were performed using the WRF-ARW • Horizontal Domains: 36-12-4 km, two-way nesting • Vertical Resolution: 50 levels, model top of 100 mb • Initial and Lateral Boundary Conditions: NARR - 32 km, 45 layers, updated every 3 hrs • Lin et al., RRTM, Dudhia, Monin-Obukov, Thermal Diffusion, YSU PBL, Kain-Fritsch (on two outermost domains only) • WRF-ARW simulations were compared with NARR data • Piecewise 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 Storm • Long duration winter storm for the OAX CWA • Initial precipitation on the 4th was in response to strong WAA • The second round of precipitation on the 5th was due to strong dynamical forcing • Little in the way of frontogenesis with this system • Two 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
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
NARR-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
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 Storm • The 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 Storm • Heavy 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 Valley • Strong 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 Valley • Broad 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.