The intended purpose of the **real-time analyses and forecasts of the quasi-geostrophic (QG) diagnostic equations** web page is to provide an interactive tool that can be used to enhance classroom education and/or weather discussions by providing visualizations of QG equations.

The calculations and visualizations are produced using NCAR Command Language version 6.6.2 on computer resources at the NOAA National Severe Storms Laboratory (NSSL). While every attempt is made to keep the images up-to-date, it is possible that there will be interruptions to the image generation services as system updates occur.

In **sections 1-5 **below, all fields are computed using 6-hourly pressure-level data from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) deterministic forecasts available in GRIB2 format at 1×1 degree latitude-longitude grid spacing. The raw NCEP-GFS forecasts are smoothed using a 9-point local smoother run 40 times to produce cleaner results for the QG diagnostics. A detailed description of the fields displayed on each set of images is provided in the Users’ Guides and as captions on the animations themselves. Each animation provided at the links below includes a 10-day analysis archive and the most recent forecast out to 192 hours. Images older than 10 days are not archived. **Current status of QG diagnostics:** .

In **section 6**, potential vorticity maps are generated using GFS analyses and forecasts available at 0.25×0.25 degree latitude-longitude grid spacing. These data are not smoothed, unless noted in the captions, and are provided for comparison with the smoothed QG diagnostics. **Current status of PV maps:** .

**1. Sutcliffe Development Theory: (click here for Users’ guide)**

- 1000 hPa Z, ζ
_{g}, and 1000–500 hPa ΔZ: NorAmer**||**NH**||**SH - 1000 hPa Z, 1000–500 hPa ΔZ, and ζ
_{T}: NorAmer**||**NH**||**SH - 1000 hPa Z, 1000–500 hPa ΔZ, and total RHS: NorAmer
**||**NH**||**SH - 1000 hPa Z, 1000–500 hPa ΔZ, and steering term (A): NorAmer
**||**NH**||**SH - 1000 hPa Z, 1000–500 hPa ΔZ, and amplification term (B): NorAmer
**||**NH**||**SH - 1000 hPa Z, 1000–500 hPa ΔZ, and Beta term (C): NorAmer
**||**NH**||**SH

**2. Petterssen Development Equation: (click here for Users’ guide)**

- 500 hPa Z and η
_{g}: NorAmer**||**NH**||**SH - 700 hPa Z, T, and ω: NorAmer
**||**NH**||**SH - 1000 hPa Z, 1000–500 hPa ΔZ, and total RHS: NorAmer
**||**NH**||**SH - 1000 hPa Z, 500 hPa Z, and amplification term (A): NorAmer
**||**NH**||**SH - 1000 hPa Z, 1000–500 hPa ΔZ, and steering term (B): NorAmer
**||**NH**||**SH - 1000 hPa Z, 1000–500 hPa ω, and adiabatic term (C): NorAmer
**||**NH**||**SH

**3. Height Tendency Equation: (click here for Users’ guide)**

Traditional Form:

- 500 hPa Z,
**v**and η_{g}_{g}: NorAmer**||**NH**||**SH - 300 hPa Z, T,
**v**, and –_{g}**v**·_{g}**∇**T: NorAmer**||**NH**||**SH - 700 hPa Z, T,
**v**, and –_{g}**v**·_{g}**∇**T: NorAmer**||**NH**||**SH - 500 hPa Z and total RHS: NorAmer
**||**NH**||**SH - 500 hPa Z and propagation term (A): NorAmer
**||**NH**||**SH - 500 hPa Z and amplification term (B): NorAmer
**||**NH**||**SH

QGPV Form:

**4. Omega Equation: (click here for Users’ guide)**

Traditional Form:

- 700 hPa Z and total RHS: NorAmer
**||**NH**||**SH_{ } - 700 hPa Z and -(f
_{0}/σ)[∂(-**v**·_{g}**∇**η_{g})/∂p] term (A): NorAmer**||**NH**||**SH - 700 hPa Z, T, and -(R/σp)[∇
^{2}(-**v**·_{g}**∇**T)] term (B): NorAmer**||**NH**||**SH

Trenberth Form:

- 700 hPa Z, ζ
_{g}, and 900–500 hPa ΔZ: NorAmer**||**NH**||**SH - 700 hPa Z, 900–500 hPa ΔZ, and total RHS: NorAmer
**||**NH**||**SH - 700 hPa Z, 900–500 hPa ΔZ, and (f
_{0}/σ)[2(∂**v**/∂p)·_{g}**∇**ζ_{g}] term (A): NorAmer**||**NH**||**SH - 700 hPa Z, 900–500 hPa ΔZ, and (f
_{0}/σ)[(∂**v**/∂p)·_{g}**∇**f] term (B): NorAmer**||**NH**||**SH - 700 hPa Z, 900–500 hPa ΔZ, and -2D
^{2}(∂θ_{D}/∂p) term (C): NorAmer**||**NH**||**SH

Q- and F-vector Form:

- 700 hPa Z, T,
**Q**, and total RHS: NorAmer**||**NH**||**SH - 700 hPa Z, T, and
**Q**/**Q**/_{n}**Q**intercomparison: NorAmer_{s}**||**NH**||**SH - 700 hPa ψ, T,
**F**, and total RHS: NorAmer**||**NH**||**SH - 700 hPa ψ, T, and
**F**/**F**/_{n}**F**intercomparison: NorAmer_{s}**||**NH**||**SH

**5. QG Energetics: [Lackmann (2011), p. 57–65]**

- 500 hPa Z and Z′: NorAmer
**||**NH**||**SH_{ } - 500 hPa Z and
**v**: NorAmer_{g}′**||**NH**||**SH - 500 hPa Z′,
**v**Φ′, and -∇·(_{a}′**v**Φ′): NorAmer_{a}′**||**NH**||**SH

**6. Potential Vorticity Maps:**

- PW, SLP, 1000–500 hPa ΔZ, and DT |
**v**|: NorAmer**||**NH**||**SH_{ } - DT θ,
**v**, and 925–850 hPa ζ: NorAmer**||**NH**||**SH - DT P, 850 hPa–DT
**Δv**, and 925–850 hPa ζ: NorAmer**||**NH**||**SH - 300–200 hPa and 850–700 hPa PV and
**v**: NorAmer**||**NH**||**SH - 300–200 hPa PV &
**v**, 250 hPa |_{ir}**v**| & RH, & 600–400 hPa ω: NorAmer**||**NH**||**SH

**7. References:**

Bluestein, H. B., 1992: *Principles of Kinematics and Dynamics*. Vol. I. *Synoptic-Dynamic Meteorology in Midlatitudes*. Oxford University Press, 431 pp.

Carlson, T. N., 1998: *Mid-Latitude Weather Systems.* Amer. Meteor. Soc., 507 pp.

Davies-Jones, R., 1991: The frontogenetical forcing of secondary circulations. Part I: The duality and generalization of the Q vector. *J. Atmos. Sci.,* **48,** 497-509.

Hakim, G. J., L. F. Bosart, and D. Keyser, 1995: The Ohio Valley wave-merger cyclogenesis event of 25-26 January 1978. Part I: Multiscale case study. *Mon. Wea. Rev.,* **123,** 2663-2692.

Hoskins, B. J., I. Draghici, and H. C. Davies, 1978: A new look at the omega equation. *Quart. J. Roy. Meteor. Soc.,* **104,** 31-38.

Keyser, D., M. J. Reeder, and R. J. Reed, 1988: A generalization of Petterssen’s frontogenesis function and its relation to the forcing for vertical motion. *Mon. Wea. Rev.,* **116,** 762-780.

Keyser, D., B. D. Schmidt, and D. G. Duffy, 1992: Quasigeostrophic vertical motions diagnosed from along- and cross-isentrope components of the Q vector. *Mon. Wea. Rev.,* **120,** 731-741.

Lackmann, G., 2011: *Midlatitude Synoptic Meteorology: Dynamics, Analysis, and Forecasting.* Amer. Meteor. Soc., 345 pp.

Martin, J. E., 1999a: Quasigeostrophic forcing of ascent in the occluded sector of cyclones and the Trowal airstream. *Mon. Wea. Rev.,* **127,** 70-88.

Martin, J. E., 1999b: The separate roles of geostrophic vorticity and deformation in the midlatitude occlusion process. *Mon. Wea. Rev.,* **127,** 2404-2418.

Martin, J. E., 2006: *Mid-Latitude Atmospheric Dynamics: A First Course*. John Wiley & Sons Ltd., 324 pp.

Petterssen, S., 1956: *Motion and Motion Systems.* Vol. I. *Weather Analysis and Forecasting.* McGraw-Hill, 428 pp.

Sutcliffe, R. C., 1947: A contribution to the problem of development. *Quart. J. Roy. Meteor. Soc.,* **73,** 370-383.

Sutcliffe, R. C., and A. G. Forsdyke, 1950: The theory and use of upper air thickness patterns in forecasting. *Quart. J. Roy. Meteor. Soc.,* **76,** 189-217.

Trenberth, K. E., 1978: On the interpretation of the diagnostic quasi-geostrophic omega equation. *Mon. Wea. Rev.,* **106,** 131-137.