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  • View in gallery

    Idealized cross-sectional representation of diabatic PV redistribution in the presence of latent heating (represented by Q) where the shear is out of the page (after Raymond 1992). The right side of the domain is cooler by the thermal wind relationship. The absolute vorticity vector (large gray arrow) slopes up to the right, and potential vorticity is transported from the upper-right corner of the heated region to the lower-left corner. The thin solid lines are isentropes, and PV+ (PV−) represents the region of diabatic PV generation (destruction).

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    Schematic representation of the major features of a mature extratropical cyclone in the PV framework (adapted from Reed et al. 1992; Lackmann et al. 1997; Martin 1998). The surface cyclone and fronts are indicated by conventional symbols.

  • View in gallery

    Idealized schematic of extratropical cyclogenesis in an adiabatic atmosphere [after Hoskins et al. (1985)], where the thick solid line represents the tropopause and the thin solid lines at the bottom of each panel are surface isentropes. In (a), PV+ indicates the location of upper-tropospheric cyclonic PV anomaly and the dark arrows indicate the flow induced by that anomaly both in the upper troposphere and at the surface. In (b), θ+ represents the warm surface potential temperature anomaly induced by the circulation of PV+, and the gray arrows indicate the circulation associated with θ+ both at the surface and in the upper troposphere.

  • View in gallery

    (a) RUC analysis valid at 0000 UTC 25 Jan 2000 of SLP (solid contours every 2 hPa), 800-hPa wind (barbs, kt), and 900–700-hPa potential vorticity (shaded, PVU). (b) As in (a) but for a 24-h Eta Model forecast. (c) As in (a) but for 800-hPa moisture flux (shaded, g kg−1 m s−1). (d) As in (c) but for a 24-h Eta Model forecast.

  • View in gallery

    (a) The 30-h forecast valid 1800 UTC 17 Feb 2004 from Workstation Eta BMJ run initialized at 1200 UTC 16 Feb 2004 of 900–700-hPa layer potential vorticity (shaded as in legend, PVU), sea level pressure (dashed contours, hPa), and 3-h model forecast of convective precipitation (solid contours, mm). (b) As in (a) but for a 36-h forecast valid 0000 UTC 18 Feb. (c), (d) As in (a), (b) but for a Workstation Eta KF run.

  • View in gallery

    North American Regional Reanalysis (NARR) 900–700-hPa potential vorticity (contours every 0.25 PVU starting at 0.5 PVU) and 2-km radar mosaic reflectivity imagery valid at (a) 0600 and (b) 1200 UTC 14 Jan 2005.

  • View in gallery

    NARR 900–700-hPa potential vorticity (shaded, PVU), 850-hPa winds (barbs, kt), and 850-hPa isotachs (dashed contours every 10 kt starting at 50 kt) valid at (a) 0600 and (b) 1200 UTC 14 Jan 2005.

  • View in gallery

    AWIPS display showing 900–700-hPa potential vorticity (shaded, PVU), total precipitation (blue contours), convective precipitation (red contours), 850-hPa wind (barbs, kt), and sea level pressure (white contours) from a 39-h Eta Model forecast valid 0900 UTC 18 Feb 2004.

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Potential Vorticity (PV) Thinking in Operations: The Utility of Nonconservation

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  • 1 Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina
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Abstract

The use of the potential vorticity (PV) framework by operational forecasters is advocated through case examples that demonstrate its utility for interpreting and evaluating numerical weather prediction (NWP) model output for weather systems characterized by strong latent heat release (LHR). The interpretation of the dynamical influence of LHR is straightforward in the PV framework; LHR can lead to the generation of lower-tropospheric cyclonic PV anomalies. These anomalies can be related to meteorological phenomena including extratropical cyclones and low-level jets (LLJs), which can impact lower-tropospheric moisture transport.

The nonconservation of PV in the presence of LHR results in a modification of the PV distribution that can be identified in NWP model output and evaluated through a comparison with observations and high-frequency gridded analyses. This methodology, along with the application of PV-based interpretation, can help forecasters identify aspects of NWP model solutions that are driven by LHR; such features are often characterized by increased uncertainty due to difficulties in model representation of precipitation amount and latent heating distributions, particularly for convective systems.

Misrepresentation of the intensity and/or distribution of LHR in NWP model forecasts can generate errors that propagate through the model solution with time, potentially degrading the representation of cyclones and LLJs in the model forecast. The PV framework provides human forecasters with a means to evaluate NWP model forecasts in a way that facilitates recognition of when and how value may be added by modifying NWP guidance. This utility is demonstrated in case examples of coastal extratropical cyclogenesis and LLJ enhancement. Information is provided regarding tools developed for applying PV-based techniques in an operational setting.

* Current affiliation: NOAA/NWS/NCEP Hydrometeorological Prediction Center, Camp Springs, Maryland

Corresponding author address: Dr. Michael J. Brennan, NOAA/NWS Hydrometeorological Prediction Center, 5200 Auth Rd., Camp Springs, MD 20746. Email: michael.j.brennan@noaa.gov

Abstract

The use of the potential vorticity (PV) framework by operational forecasters is advocated through case examples that demonstrate its utility for interpreting and evaluating numerical weather prediction (NWP) model output for weather systems characterized by strong latent heat release (LHR). The interpretation of the dynamical influence of LHR is straightforward in the PV framework; LHR can lead to the generation of lower-tropospheric cyclonic PV anomalies. These anomalies can be related to meteorological phenomena including extratropical cyclones and low-level jets (LLJs), which can impact lower-tropospheric moisture transport.

The nonconservation of PV in the presence of LHR results in a modification of the PV distribution that can be identified in NWP model output and evaluated through a comparison with observations and high-frequency gridded analyses. This methodology, along with the application of PV-based interpretation, can help forecasters identify aspects of NWP model solutions that are driven by LHR; such features are often characterized by increased uncertainty due to difficulties in model representation of precipitation amount and latent heating distributions, particularly for convective systems.

Misrepresentation of the intensity and/or distribution of LHR in NWP model forecasts can generate errors that propagate through the model solution with time, potentially degrading the representation of cyclones and LLJs in the model forecast. The PV framework provides human forecasters with a means to evaluate NWP model forecasts in a way that facilitates recognition of when and how value may be added by modifying NWP guidance. This utility is demonstrated in case examples of coastal extratropical cyclogenesis and LLJ enhancement. Information is provided regarding tools developed for applying PV-based techniques in an operational setting.

* Current affiliation: NOAA/NWS/NCEP Hydrometeorological Prediction Center, Camp Springs, Maryland

Corresponding author address: Dr. Michael J. Brennan, NOAA/NWS Hydrometeorological Prediction Center, 5200 Auth Rd., Camp Springs, MD 20746. Email: michael.j.brennan@noaa.gov

1. Introduction

a. Background and motive

Although the concept of potential vorticity (PV) was developed in the 1930s and explored in subsequent years, it was subsequent to the landmark paper of Hoskins et al. (1985) that PV principals became widely applied in atmospheric research. It logically followed that as the use of PV as a research tool increased, “PV thinking” could potentially be utilized by operational forecasters as a compact means of understanding atmospheric dynamics and as a useful tool in the forecast process. For example, plots of potential temperature on the dynamic tropopause [most often defined as a PV isosurface of value between 1 and 2 PVU: 1 potential vorticity unit (PVU) = 10−6 m2 s−1 K kg−1] can be extremely useful because PV surfaces intersect the core of all major upper-level jet streams, even those centered at different altitudes (Morgan and Nielsen-Gammon 1998). However, it is our sense that PV has not gained widespread acceptance within the operational forecasting community in the United States. There are several possible reasons for this, including (i) a lack of emphasis on PV concepts in undergraduate university meteorology curricula, (ii) limited training in PV methodology for operational forecasters, (iii) the time-consuming and technically challenging task of PV inversion, and (iv) the failure to convincingly demonstrate that the use of PV can provide information not obtainable via more traditional means. It is this last issue that we wish to address in this paper.

Previous attempts to introduce PV to operational forecasters in the United States have emphasized upper-tropospheric dynamics, including tropopause folds and stratospheric PV extrusions, as a means of understanding the dynamics of upper-level disturbances. However, traditional quasigeostrophic (QG) concepts and conceptual models of transverse jet circulations are often adequate in providing forecasters with the information needed to diagnose upper-tropospheric dynamics on the forecast floor, meaning that PV thinking offers somewhat limited added value in an operational sense, even if it would be more useful in case-study research, for example.

Here, we advocate the use of a somewhat different set of PV concepts relative to earlier efforts, with an emphasis on PV as a means for identifying the dynamical feedbacks associated with latent heat release and the accompanying PV nonconservation. The goals of this paper are to provide (i) examples of situations where PV diagnosis adds value beyond what traditional forecast methods can readily provide and (ii) specific suggestions for diagnostic PV tools for use in forecasting.

b. Numerical models, PV, and the forecast process

There is no question that numerical weather prediction (NWP) has become entrenched as the most important forecasting tool for today’s operational weather forecaster for time periods beyond a few hours. However, despite verifiable improvements in forecast accuracy that have accompanied the remarkable advance of NWP, several studies (e.g., Mass 2003; Bosart 2003; Doswell 2004) have noted that there is a cost in terms of the time available to forecasters for the diagnosis of a meteorological situation as they sift through an ever-increasing volume of NWP products. To best assess the quality of available model guidance, forecasters need to recognize the differences in the guidance provided by various NWP models and, if possible, understand why these differences exist. This ability is hindered by the fact that a substantial and ongoing investment of time and effort is required for operational forecasters to stay abreast of and understand changes made to the operational models run at the National Centers for Environmental Prediction (NCEP) and elsewhere. Thus, it becomes challenging for forecasters to assess the accuracy of model representation of critical physical processes that may profoundly influence the model solution. Additionally, forecasters must develop the ability to use observational data and high-frequency model analyses to evaluate short-term model forecasts in order to have the confidence necessary to abandon model guidance entirely when, in the words of Bosart (2003), the model forecast is “going off the rails”—not a trivial decision to make in the midst of a potentially high-impact event.

It has been demonstrated that quantitative precipitation forecasting (QPF) is the least accurate parameter in NWP forecasts (e.g., Fritsch and Carbone 2004). Therefore, it follows that the ability of NWP models to accurately represent the magnitude and distribution of latent heat release (LHR), its gradient, and other precipitation-related thermodynamic processes such as melting and freezing presents similar difficulty. Upscale feedbacks resulting from LHR can therefore introduce significant errors to the synoptic-scale forecast (e.g., Dickinson et al. 1997; Zhang et al. 2002; Zhang et al. 2003; Brennan and Lackmann 2005). This is particularly true for convection, and model representation or parameterization of organized convection (e.g., Wang and Seaman 1997; Kain and Fritsch 1998; Mahoney and Lackmann 2006). Since today’s operational NWP models continue to run with a grid spacing that is insufficient to explicitly resolve cumulus convection, the use of cumulus parameterization (CP) schemes remains a necessity in operational NWP, especially for global models. As a result, these schemes must represent the effects of unresolved convection on the model grid by generating “convective” precipitation and redistributing heat and moisture in the model atmosphere.

There are a variety of CP schemes available, with varying adjustment and trigger configurations, that can lead to differences in profiles of heat and moisture tendencies when the CP schemes are active (e.g., Kuo et al. 1996; Baldwin et al. 2002; Kain 2004; Mahoney and Lackmann 2006). Accordingly, there can be significant variability regarding if, when, and where different CP schemes activate and how they redistribute heat and moisture. Therefore, the LHR from different CP schemes can significantly impact the evolution of the PV distribution in the model atmosphere, since latent heating and other diabatic processes lead to PV nonconservation (see section 2a for more details).

Here, we advocate the examination of lower-tropospheric PV in conjunction with several other model output parameters that will serve to (i) alert forecasters to which synoptic or mesoscale features in the model output are strongly influenced by LHR, (ii) provide forecasters with a means of assessing the uncertainty in a particular feature in the model output, (iii) provide forecasters with generalized guidance designed to assist in determining the sign of model biases for specific features, and (iv) provide a conceptual and dynamical framework within which forecasters can ascertain the physical processes responsible for a given feature. Through the use of PV diagnostics, forecasters can obtain an improved recognition of situations in which they are most able to add value to a model forecast.

Section 2 will provide an overview of basic PV concepts and how the PV framework can be applied to extratropical cyclones, moisture transport, and low-level jets (LLJs). Section 3 will present the utility of PV thinking in the operational forecast setting through case examples of moisture transport in an extratropical cyclone, coastal cyclogenesis, and the diabatic enhancement of an LLJ.1 Section 4 will recommend procedures for utilizing PV in the operational environment and section 5 contains concluding remarks.

2. Overview of PV concepts

a. PV principles

Potential vorticity is proportional to the product of the absolute vorticity and the static stability, and is defined after Rossby (1940) and Ertel (1942) as
i1520-0434-23-1-168-e1
where η is the absolute vorticity vector, ρ is the density, and θ is the potential temperature. In the Northern Hemisphere, positive (negative) PV anomalies are associated with cyclonic (anticyclonic) relative vorticity and/or high (low) values of static stability (Hoskins et al. 1985). In other words, PV maxima (minima) in the upper troposphere are generally associated with troughs (ridges), low (high) geopotential heights, and cyclonic (anticyclonic) flow. In addition, Bretherton (1966) showed that surface θ anomalies are mathematically equivalent to PV anomalies, and that cyclonic (anticyclonic) flow is associated with warm (cold) θ anomalies. For a depiction of the balanced flow and geopotential associated with idealized PV anomalies and surface θ maxima and minima, see Thorpe (1986) and Figs. 15 and 16 in Hoskins et al. (1985).

One of the main tenets of the PV framework is that PV is conserved following frictionless, adiabatic flow. It may seem counterintuitive to highlight PV conservation as a foundation of the PV framework when this property does not apply to many of the weather systems in which we hold the greatest interest. However, it is precisely because PV is not conserved in the presence of diabatic processes that evidence of nonconservation can be utilized to unambiguously identify the contribution of specific diabatic processes to the PV field, and then quantify the impact of these processes on the atmosphere via piecewise PV inversion. The feedback on atmospheric dynamics from latent heating can impact cyclone evolution, LLJs, moisture transport, and QPF, all of which can be important in forecasting sensible weather in potentially high-impact events.

Latent heating associated with precipitation impacts the PV distribution by altering the two components of PV, the absolute vorticity and the static stability. Below the level of maximum heating, the static stability often increases2 and the geopotential height is lowered, thus leading to an increase in the absolute vorticity as the flow converges into the area of lowered pressure beneath the heating maximum. The increase of both the static stability and absolute vorticity results in an increase in the PV below the level of maximum heating. The opposite occurs above the level of maximum heating, resulting in a reduction in PV there. Therefore, latent heating associated with precipitation processes generally leads to the generation (destruction) of PV below (above) the level of maximum heating with the PV redistribution occurring along the absolute vorticity vector (Fig. 1), as discussed by Raymond (1992). The rate of PV generation or destruction is determined by the latent heating gradient and the magnitude of the background absolute vorticity (Stoelinga 1996).

It is important to note that processes other than LHR can contribute to the development of cyclonic lower-tropospheric PV anomalies. For example, friction was shown by Stoelinga (1996) to play an important role in the PV budget during a cyclogenesis event, and Aebischer and Schär (1998) discuss the development of PV banners that formed in flow past elevated terrain. Furthermore, radiative processes can lead to the development of strong cyclonic PV anomalies in stable arctic air masses; however, the presence of a pronounced surface cold anomaly (a surrogate anticyclonic PV anomaly) in this instance largely cancels the cyclonic tendency imparted by the interior PV feature.

The second fundamental principle of the PV framework is the invertibility of PV, which allows one to quantify the balanced wind, pressure, and temperature fields associated with a given PV anomaly3 by numerically solving a boundary value problem assuming an independent balance relationship between the wind and mass fields (Davis and Emanuel 1991). The output of the inversion includes the balanced wind and geopotential height fields associated with the specific portion of the PV field that was inverted. While it is not currently practical for operational forecasters to perform PV inversion in real time in the United States,4 previous case studies have quantified the impact of diabatically produced cyclonic PV anomalies on various meteorological phenomena using PV inversion (e.g., Davis and Emanuel 1991; Davis 1992; Davis et al. 1993; Davis et al. 1996; Stoelinga 1996; Martin 1998; Henderson et al. 1999; Huo et al. 1999; Lackmann and Gyakum 1999; Lackmann 2002; Plant et al. 2003; Shapiro and Möller 2003; Ahmadi-Givi et al. 2004; Martin and Otkin 2004; Brennan and Lackmann 2005; Mahoney and Lackmann 2007). The impact of diabatic PV redistribution has also been examined in tropical cyclones and cyclogenesis, through the generation of cyclonic PV anomalies in the lower troposphere due to latent heating (Davis and Bosart 2001; Montgomery et al. 2006; Sippel et al. 2006), the reduction of shear aloft through the modification of PV gradients due to diabatic heating (Davis and Bosart 2003), and through alteration of the structure of the dynamic tropopause in a manner that increases synoptic-scale ascent (Bosart and Lackmann 1995).

An understanding of (i) how LHR alters the PV field and (ii) the relationship between PV anomalies and their associated balanced circulations offers the opportunity for operational forecasters to conceptualize the impact of latent heating on the dynamics of cyclones, LLJs and their impact on moisture transport, and other phenomena. Additionally, this understanding provides a dynamical basis for diagnosing the manner in which NWP model representation of convection or other precipitation systems influences model forecast solutions.

b. Conceptual model of PV and cyclones

In the PV framework, a mature extratropical cyclone can be conceptualized as the interaction of the following features shown in Fig. 2: (i) a tropopause-based cyclonic PV anomaly, (ii) a positive surface θ anomaly, (iii) a diabatically generated cyclonic PV anomaly located in the lower troposphere, and (iv) a diabatically generated upper-tropospheric anticyclonic PV anomaly (e.g., Davis and Emanuel 1991; Reed et al. 1992; Stoelinga 1996). In this framework, cyclogenesis occurs when the cyclonic circulation associated with the upper-tropospheric cyclonic PV anomaly extends to the surface and leads to the formation (through advection) of a surface warm anomaly [Fig. 3, after Hoskins et al. (1985)]. The surface warm anomaly is in turn associated with a cyclonic circulation that may extend to the upper troposphere, and can contribute to the amplification (via negative θ advection on the dynamic tropopause or, alternatively, positive PV advection on upper-level isentropic surfaces) of the cyclonic upper-tropospheric PV anomaly (Fig. 3b).

Diabatic processes, such as those associated with precipitation, lead to the generation of a cyclonic (anticyclonic) PV anomaly in the lower (upper) troposphere as discussed in section 2a. The interactions of these diabatic PV anomalies with the upper-tropospheric cyclonic PV anomaly and cyclonic surface warm anomaly are highly case dependent (e.g., Davis 1992; Stoelinga 1996). In many cases the diabatically generated cyclonic PV anomaly enhances the coupling and mutual interaction between the cyclonic upper-tropospheric PV anomaly and the surface warm anomaly, leading to a stronger feedback process and a more intense cyclone (e.g., Davis 1992; Stoelinga 1996). However, in some other cases the diabatically generated cyclonic PV anomaly has been shown to hinder the interaction of the tropopause and surface anomalies when the rapid downstream propagation of the diabatically generated lower-tropospheric anomaly precludes vertical coupling between the disturbances [i.e., the phase speeds of the tropopause and surface anomalies do not match; Davis (1992)].

The PV framework discussed above is consistent with traditional conceptual models of cyclogenesis such as the Sutcliffe–Petterssen self-development concept (Sutcliffe and Forsdyke 1950; Petterssen 1956). The cyclonic, tropopause-based upper PV anomaly is associated with a trough in the upper-level geopotential height field, and the development of a surface warm anomaly accompanies the formation of a frontal wave during the early stages of cyclogenesis. The role of the diabatic heating is likewise consistent between these frameworks: diabatically generated cyclonic PV anomalies in the lower troposphere are consistent with LHR generating geopotential height falls below the level of maximum heating, which deepens the cyclone, consistent with the findings of Aubert (1957) who showed similar results in an early numerical model. The diabatically generated anticyclonic PV anomaly that forms above the level of maximum latent heating is consistent with the downstream ridge formation that shortens the half-wavelength of the upper-level trough–ridge couplet (see, e.g., Uccellini 1990). Latent heating and the effectively reduced static stability are consistent with both enhanced vertical motion for a given strength of QG forcing for ascent (e.g., Danard 1964) as well as improved vertical coupling and mutual amplification between upper and lower disturbances due to an increased Rossby depth (a parameter that is proportional to the vertical extent of the circulation imparted by the upper- or lower-boundary disturbance).

c. Moisture transport and low-level jets

Diabatically generated cyclonic PV anomalies associated with LHR are typically centered in the lowest 3 km of the troposphere;5 this region is also where atmospheric moisture content is maximized, along with the magnitude of the horizontal moisture flux. Diabatic PV anomalies can be associated with balanced wind fields that make up a large fraction of the total wind; thus, such anomalies can play a significant role in moisture transport and the ultimate distribution of precipitation. Previous research has shown that the balanced flow associated with these diabatic PV anomalies can account for as much as 40% or more of the magnitude of prefrontal LLJs (Lackmann 2002; Mahoney and Lackmann 2007). Diabatically enhanced moisture transport was shown to be important in extratropical cyclones such as the January 2000 U.S. East Coast snowstorm (Brennan and Lackmann 2005). The lower branch of the indirect transverse circulation in the exit region of an upper-level jet streak can also contribute to the enhancement of the LLJ (Uccellini and Johnson 1979). This process in combination with diabatic heating interacted in a synergistic way to enhance the LLJ in the 1979 Presidents’ Day storm (Uccellini et al. 1987; Whitaker et al. 1988).

On a larger scale, cyclonic PV anomalies enhanced by LHR contribute substantially to moisture transport from the tropical Pacific to the Pacific Northwest in “Pineapple Express” events (Lackmann and Gyakum 1999). Additionally, if conditions are favorable for vertical mixing in the planetary boundary layer, such as on the warm side of a lower-tropospheric cyclonic PV anomaly, high-momentum air may mix to the surface, resulting in damaging wind gusts.

3. Case study examples

a. Moisture transport in extratropical cyclones

The East Coast cyclone of 24–25 January 2000 was not well forecasted by operational NWP models, which failed to predict heavy precipitation in a region from the Carolinas northward to Washington, D.C., that received heavy snowfall (e.g., Zhang et al. 2002; Langland et al. 2002; Bosart 2003; Jang et al. 2003; Brennan and Lackmann 2005). Brennan and Lackmann (2005) used piecewise Ertel PV inversion (Davis and Emanuel 1991) to show that a lower-tropospheric PV maximum initially generated by latent heating associated with an area of “incipient precipitation” (IP)6 that formed prior to the rapid cyclogenesis over Alabama and Georgia early on 24 January was critical to moisture transport into the aforementioned region of heavy precipitation. This IP was not forecasted by the operational NCEP models, even in those forecast cycles initialized 6–12 h prior to its formation. The lack of substantial latent heating in the region of observed IP rendered the models unable to generate a lower-tropospheric PV maximum that was critical to the moisture transport into the Carolinas and Virginia during this event (Brennan and Lackmann 2005).

A comparison of the 900–700-hPa layer PV from the Rapid Update Cycle (RUC) model analysis at 0000 UTC 25 January 2000 (Fig. 4a) to the 24-h forecast from the 0000 UTC 24 January 2000 Eta Model run (Fig. 4b) demonstrates that the Eta Model did not forecast the large PV maximum centered along the coast of Georgia and South Carolina seen in the RUC analysis at this time. The cyclonic circulation associated with this PV maximum contributed strongly to onshore flow at the 800-hPa level over the eastern Carolinas, where 30–35 kt of easterly flow generated horizontal moisture flux values of 50–100 g kg−1 m s−1 in this region (Fig. 4c). In contrast, the Eta forecast, which did not include the critical PV maximum along the coast, features winds of 5–10 kt in this region with a variable direction, resulting in a moisture flux of 10–20 g kg−1 m s−1 (Fig. 4d). The PV inversion presented by Brennan and Lackmann (2005) demonstrated that the lower-tropospheric PV maximum was responsible for 20–25 kt of this onshore flow over the eastern Carolinas, a significant enhancement to the moisture flux into the region of heavy precipitation.

It is instructive to overlay lower-tropospheric PV computed from high-frequency gridded analyses, such as those available from the RUC model, with radar imagery, and to compare these fields to model QPF and PV forecasts. Such an approach can allow operational forecasters to evaluate the lower-tropospheric PV forecast in NWP guidance and diagnose potential errors. In this particular case, the development of the PV maximum is closely associated with the area of IP as it moves from Alabama to the Georgia coast from 0600 to 1800 UTC 24 January 2000 (see Brennan and Lackmann 2005, their Fig. 3). In this example, the PV framework allows one to infer that cyclonic flow associated with the lower-diabatic PV maximum would increase the onshore flow in the lower troposphere poleward of its location, and precipitation could be expected to spread farther inland relative to operational model forecasts, which underpredicted the magnitude of the PV maximum associated with the IP.

b. Coastal extratropical cyclogenesis

Potential vorticity provides a compact conceptual tool for diagnosing extratropical coastal cyclogenesis, both in observations and in model forecasts, particularly for cases in which the cyclone dynamics are strongly influenced by LHR. In these instances, the model solution can be strongly dependent on the nature of the physical parameterization schemes. A study by Mahoney and Lackmann (2006) examines a coastal cyclogenesis event that took place on 17 February 2004 in which model predictions of the cyclone exhibited strong sensitivity to the choice of CP scheme in the NCEP Eta Model. This sensitivity affected several critical aspects of model forecasts, including the location and strength of a coastal front, coastal cyclogenesis, and the precipitation distribution.

A primary source of numerical model inconsistency in this case was the genesis of a coastal cyclone and the evolution of a coastal front located along the eastern periphery of a decaying Appalachian cold-air damming event. An examination of the convective precipitation field from operational Eta Model forecasts during the event revealed that the locations of model-predicted coastal cyclones and the coastal front were strongly linked to activity of the Betts–Miller–Janjić (BMJ) CP scheme (e.g., Betts and Miller 1993; Janjić 1994), as there was considerable collocation of the convective precipitation maxima with sea level pressure minima in the operational Eta Model forecast (see Mahoney and Lackmann 2006, their Fig. 7). Because convective precipitation is a parameter often associated with a high degree of uncertainty in many NWP model forecasts (e.g., Molinari 1993; Wang and Seaman 1997; Zhang et al. 2002, 2003), it is useful for human forecasters to be able to recognize situations in which model forecasts are driven by the activity of the CP scheme, and interpret such forecasts with a higher level of uncertainty. We will demonstrate that for the 17 February 2004 case, PV served as a useful tracer to monitor the influence of CP scheme-driven diabatic processes in model forecasts.

To test the sensitivity of the model forecast of this event to CP scheme choice, Mahoney and Lackmann (2006) performed workstation version Eta Model forecasts using both the BMJ CP scheme, and the Kain–Fritsch (KF; e.g., Kain 2004) CP scheme initialized at 12 UTC 16 February 2004. The results of these forecasts confirm that the character of the coastal cyclone was extremely sensitive to convective parameterization, as indicated by the convective precipitation and SLP evolution in Fig. 5. The top (bottom) panels in Fig. 5 show 30- and 36-h forecasts from the BMJ (KF) runs valid at 1800 UTC 17 February and 0000 UTC 18 February 2004. The two forecasts show large differences with respect to the distribution of convective precipitation, sea level pressure, and lower-tropospheric PV. In the BMJ forecast, convective precipitation “bull’s-eyes” and accompanying sea level pressure minima are collocated with model PV maxima in multiple discrete locations. The KF run shows a much more elongated and continuous pattern of convective precipitation and PV, as well as a single surface low pressure system. The accompanying differences in the sea level pressure distribution and surface cyclone location can lead to changes in moisture transport and thermal advection associated with the cyclone, both of which have important operational forecast implications.

The collocation of the convective precipitation bull’s-eyes, sea level pressure minima, and PV maxima in the model forecasts illustrates the utility of PV as an indicator of intense CP scheme activity. These PV maxima can also persist after the convective precipitation has ended, serving as a tracer of the influence of earlier latent heating. Forecasters should be alert to the possibility that CP scheme activity is exerting a strong influence on the forecast when heavy convective precipitation activity is collocated with newly formed lower-tropospheric PV maxima. Additionally, diabatic heating can result in changes in the upper-tropospheric PV structure, due to the destruction of PV aloft above the level of latent heating (e.g., Bosart and Lackmann 1995; Stoelinga 2003). However, it is more difficult to isolate the impact of latent heating on the PV distribution near the tropopause, since other processes (e.g., horizontal advection) can significantly contribute to changes in the PV structure due to the large PV gradients typically found in this region.

c. Low-level jet enhancement

On 13–14 January 2005, a slow-moving cold front moved eastward across the central and eastern United States, producing precipitation totals in excess of 25 mm, as well as widespread damage from high surface winds, hail, and tornados (NCDC 2007). This case featured a strong lower-tropospheric PV maximum that developed along the cold-frontal rainband (Fig. 6). By 1200 UTC 14 January, the PV maximum within the 900–700-hPa layer reached a magnitude of 1.5 PVU in the corridor of heaviest precipitation (Fig. 6b). At the 850-hPa level, an LLJ was evident east of the PV maximum, as a broad wind maximum of 50–60 kt across the mid-Atlantic states at 0600 UTC (Fig. 7a) intensified to more than 80 kt in a narrow band over southern Maine by 1200 UTC (Fig. 7b). Potential vorticity diagnostics were employed for this case in order to clarify and quantify the effects of the precipitation itself on the development and enhancement of the LLJ (Mahoney and Lackmann 2007). A PV budget (e.g., Cammas et al. 1994; Lackmann 2002) demonstrated that latent heating associated with the precipitation along the cold front contributed to the generation of a lower-tropospheric PV maximum over the mid-Atlantic states (see Mahoney and Lackmann 2007, their Fig. 15). In addition, results from quasigeostrophic PV (QGPV) inversion (e.g., Hakim et al. 1996; Lackmann 2002) indicated that more than 40% of the LLJ was due to the presence of the lower-tropospheric PV anomaly (see Mahoney and Lackmann 2007, their Fig. 17). For this case, the diabatic enhancement of the LLJ, as illustrated by the PV budget and QGPV inversion, was also an important factor in anticipating downstream moisture transport and increased precipitation.

By overlaying model analyses of lower-tropospheric PV, winds, and radar imagery, forecasters can identify situations when a lower-tropospheric PV maximum associated with latent heating is enhancing the intensity of an LLJ. By comparing model QPF to short-term observations (gauge values or radar estimates), and examining the PV distribution, forecasters could potentially determine whether model forecasts of the LLJ are over- or underestimated, and make adjustments accordingly. This could be especially important for strong LLJs that provide a highly sheared environment conducive to rotating convection, or severe straight-line winds due to downward mixing of high-momentum air.

4. Operational tools

To promote the use of PV as a means of identifying the impact of latent heating in model forecast output, a “procedure” for the National Weather Service’s Advanced Weather Interactive Processing System (AWIPS) workstations has been developed. The procedure is designed to allow forecasters to examine operational model forecasts of sea level pressure, lower-tropospheric PV and winds, and total and convective precipitation (Fig. 8). This tool will allow users to identify the impact of latent heating on atmospheric dynamics, particularly in the lower troposphere, using the PV framework. In addition, high-frequency analyses of PV, sea level pressure, and winds from the RUC model are also available for comparison to model forecasts in AWIPS. The AWIPS procedures were developed with the assistance of the staff of the Raleigh, North Carolina, NWS office and are available online (http://www.meas.ncsu.edu/nws/www/training). Samples of similar images created with the General Meteorological Package (GEMPAK) and scripts for their generation are also available online (http://tempest.meas.ncsu.edu/pv).

Recent developments at the Met Office have incorporated PV by allowing forecasters to directly alter model-generated PV fields, and then use PV inversion to obtain other fields in a physically consistent way (Carroll and Hewson 2005). For example, by altering the PV distribution of selected features (e.g., an extratropical cyclone) in output from the Met Office model, dynamically consistent adjustments to model forecast variables (e.g., wind and temperature) are made using results from real-time QGPV inversion. This technique provides a means for the human forecaster to adjust NWP model guidance in a quantitative manner using the PV framework, resulting in improved lead times for both short- and medium-range forecasts at the Met Office (Carroll and Hewson 2005). A similar approach for quantifying uncertainty and improving operational forecasts in environments impacted by mesoscale convective vortices (MCVs) through the use of PV-adjusted ensembles was also suggested by Gray (2001).

5. Conclusions

Although there are documented advantages to using tropopause maps and plots of isentropic PV as a means of diagnosing upper-tropospheric dynamics, it can be argued that alternate techniques can provide forecasters with much of the same information. However, here we argue that the use of PV as a means of identifying and diagnosing diabatically produced lower-tropospheric cyclonic PV anomalies represents an additional and more compelling motive for operational forecasters to embrace PV concepts, as fewer alternatives exist that allow forecasters to assess the dynamical impact of often highly uncertain diabatic processes in a model forecast.

The conservation property of PV provides a reliable method for

  • (i) identifying those lower-tropospheric features that are driven strongly by model LHR and
  • (ii) obtaining a ready estimation of the dynamical impact that these features may have on the forecast evolution.

Bearing in mind the uncertainty inherent in model QPF, particularly that due to parameterized convection, the use of PV in this manner provides forecasters with a tool that can be used in conjunction with ensemble forecasts to yield a sense of forecast confidence in given features of a model forecast. For example, suppose a forecaster examines the lower-tropospheric PV distribution for a certain event and finds that the deterministic model forecast of coastal extratropical cyclogenesis is sensitive to convective precipitation. Evaluating the spread associated with the location of the cyclogenesis in a mixed-physics model ensemble with various CP schemes would provide information concerning the magnitude of uncertainty related to the placement of the cyclone, thereby providing an indication of confidence in the deterministic model solution. Also in these situations, additional scrutiny of observational data sources would be more likely to add value to the forecast relative to more benign weather situations.

We advocate plotting of lower-tropospheric PV and winds (appropriate pressure levels will vary slightly with geographic setting) with convective and/or total precipitation to provide an indicator of those PV features associated with model-generated LHR. Additional research, fine-tuning of graphical displays, and training modules would also serve to help this forecasting tool gain deserved acceptance in the operational forecasting community. Additionally, the early success of direct PV editing of gridded model output in the United Kingdom may potentially spur the development of model adjustment tools that allow forecasters in the United States to use the PV methodology to directly alter NWP model output quantitatively, and in a dynamically consistent manner.

Acknowledgments

This research was supported by the National Oceanic and Atmospheric Administration (NOAA) Collaborative Science, Technology, and Applied Research (CSTAR) program through Grant NA03NWS4680007 awarded to North Carolina State University. Thanks to Jonathan Blaes of the NWS Forecast Office in Raleigh, North Carolina, for assistance with developing the AWIPS procedures. Thanks also to David Schultz of NSSL and Pete Banacos of SPC for comments on this topic and to the following for thoughtful comments on a previous version of this manuscript: Lance Bosart of SUNY—Albany; Mike Cammarata of the NWS Forecast Office in Columbia, South Carolina; John Nielsen-Gammon of Texas A&M; Rod Gonski and Kermit Keeter of the NWS Forecast Office in Raleigh; Larry Lee of the NWS Forecast Office in Greer, South Carolina; David Novak of the NWS Eastern Region; Jamie Rhome of the Tropical Prediction Center; and Neil Stuart of the NWS Forecast Office in Wakefield, Virginia. Thanks to two anonymous reviewers who provided comments and suggestions to improve this manuscript. Much of the meteorological data in this study was provided to NCSU through the Unidata program.

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Fig. 1.
Fig. 1.

Idealized cross-sectional representation of diabatic PV redistribution in the presence of latent heating (represented by Q) where the shear is out of the page (after Raymond 1992). The right side of the domain is cooler by the thermal wind relationship. The absolute vorticity vector (large gray arrow) slopes up to the right, and potential vorticity is transported from the upper-right corner of the heated region to the lower-left corner. The thin solid lines are isentropes, and PV+ (PV−) represents the region of diabatic PV generation (destruction).

Citation: Weather and Forecasting 23, 1; 10.1175/2007WAF2006044.1

Fig. 2.
Fig. 2.

Schematic representation of the major features of a mature extratropical cyclone in the PV framework (adapted from Reed et al. 1992; Lackmann et al. 1997; Martin 1998). The surface cyclone and fronts are indicated by conventional symbols.

Citation: Weather and Forecasting 23, 1; 10.1175/2007WAF2006044.1

Fig. 3.
Fig. 3.

Idealized schematic of extratropical cyclogenesis in an adiabatic atmosphere [after Hoskins et al. (1985)], where the thick solid line represents the tropopause and the thin solid lines at the bottom of each panel are surface isentropes. In (a), PV+ indicates the location of upper-tropospheric cyclonic PV anomaly and the dark arrows indicate the flow induced by that anomaly both in the upper troposphere and at the surface. In (b), θ+ represents the warm surface potential temperature anomaly induced by the circulation of PV+, and the gray arrows indicate the circulation associated with θ+ both at the surface and in the upper troposphere.

Citation: Weather and Forecasting 23, 1; 10.1175/2007WAF2006044.1

Fig. 4.
Fig. 4.

(a) RUC analysis valid at 0000 UTC 25 Jan 2000 of SLP (solid contours every 2 hPa), 800-hPa wind (barbs, kt), and 900–700-hPa potential vorticity (shaded, PVU). (b) As in (a) but for a 24-h Eta Model forecast. (c) As in (a) but for 800-hPa moisture flux (shaded, g kg−1 m s−1). (d) As in (c) but for a 24-h Eta Model forecast.

Citation: Weather and Forecasting 23, 1; 10.1175/2007WAF2006044.1

Fig. 5.
Fig. 5.

(a) The 30-h forecast valid 1800 UTC 17 Feb 2004 from Workstation Eta BMJ run initialized at 1200 UTC 16 Feb 2004 of 900–700-hPa layer potential vorticity (shaded as in legend, PVU), sea level pressure (dashed contours, hPa), and 3-h model forecast of convective precipitation (solid contours, mm). (b) As in (a) but for a 36-h forecast valid 0000 UTC 18 Feb. (c), (d) As in (a), (b) but for a Workstation Eta KF run.

Citation: Weather and Forecasting 23, 1; 10.1175/2007WAF2006044.1

Fig. 6.
Fig. 6.

North American Regional Reanalysis (NARR) 900–700-hPa potential vorticity (contours every 0.25 PVU starting at 0.5 PVU) and 2-km radar mosaic reflectivity imagery valid at (a) 0600 and (b) 1200 UTC 14 Jan 2005.

Citation: Weather and Forecasting 23, 1; 10.1175/2007WAF2006044.1

Fig. 7.
Fig. 7.

NARR 900–700-hPa potential vorticity (shaded, PVU), 850-hPa winds (barbs, kt), and 850-hPa isotachs (dashed contours every 10 kt starting at 50 kt) valid at (a) 0600 and (b) 1200 UTC 14 Jan 2005.

Citation: Weather and Forecasting 23, 1; 10.1175/2007WAF2006044.1

Fig. 8.
Fig. 8.

AWIPS display showing 900–700-hPa potential vorticity (shaded, PVU), total precipitation (blue contours), convective precipitation (red contours), 850-hPa wind (barbs, kt), and sea level pressure (white contours) from a 39-h Eta Model forecast valid 0900 UTC 18 Feb 2004.

Citation: Weather and Forecasting 23, 1; 10.1175/2007WAF2006044.1

1

While the cases presented here focus primarily on the eastern United States, other studies such as Lackmann and Gyakum (1999) and Lackmann (2002) have demonstrated the utility of PV diagnosis in moisture transport events in the Pacific Northwest and central United States, respectively.

2

The exception to this would be condensation in a moist-neutral atmosphere, in which case the static stability would remain constant.

3

A PV anomaly is defined as the difference between the instantaneous PV field and a background PV distribution. This background PV distribution is usually defined as a spatial and/or temporal average of the PV field over the domain where the inversion is performed.

4

Operational forecasters are now modifying NWP model output using real-time PV inversion at the Met Office, as described in section 4.

5

At locations near sea level, this would generally correspond to the layer between 950 and 700 hPa, but will vary with the vertical structure of the heating profile. Strictly speaking, it is best to view PV in isentropic layers, as it is not conserved in the isobaric framework. However, experience has shown that the development of isolated, cyclonic PV features in the lower troposphere is invariably attributable to nonconservative processes.

6

Incipient precipitation (IP) was defined by Brennan and Lackmann (2005) as the region of precipitation that formed over Alabama and Georgia early on 24 January 2000 prior to the rapid deepening of the cyclone offshore of the Carolinas on 25 January 2000.

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