1. Systematic errors in medium-range forecasts of tropopause structure
Suzanne Gray, Caroline Dunning, John Methven, Giacomo Masato, Jeffrey Chagnon.
University of Reading
September 2013

2. Climatology of PV (in PVU) and q in NH winter (Hoskins, 1990)
Potential vorticity
tropopause
Potential vorticity is conserved following fluid parcels for adiabatic frictionless flow.
This makes it a good tracer for upper-tropospheric air over several days.
330K
270K
Define tropopause in terms of PV
A summary of the climatological PV and theta distribution below 100mb in the NH winter. PV in PVU, theta every 30K
Climatology of PV (in PVU) and q in NH winter (Hoskins, 1990)

3. ECMWF analyses of PV on 315K isentrope.
Potential vorticity
Rossby Waves
(or planetary waves): PV conserving motion that owes its existence to the isentropic gradient of PV.
Define Rossby waves
A summary of the climatological PV and theta distribution below 100mb in the NH winter. PV in PVU
ECMWF analyses of PV on 315K isentrope.

4. Forecast errors in upper-level PV
PV on 320 K isentrope (analysis and 96h forecast): 1200 UTC 16 Jan 2002 (Davies and Didone 2013)
Are there errors?
Rossby wave amplitude at the extratropical tropopause inadequately developed in ECMWF operational forecasts: DJF so 10 years ago (Dirren et al. 2003).

5. Mechanisms of Rossby-wave growth
Initial time
Later time
What might cause these errors?
FIG. 12. Schematic of various mechanisms for generating and/or enhancing a wave disturbance on a jet stream. From
top to bottomthe rows relate to the influence of horizontal deformation, baroclinic growth, a stratosphericPVanomaly,
realignment and unshielding of a PV perturbation pattern, and a tropospheric PV anomaly. For each row the left panel
refers to an initial time and the right panel displays the outcome of the mechanism’s influence at a subsequent time. In
each panel the bold black line signifies the location and configuration of the jet stream (i.e., the 2-PVU isoline on an
isentropic surface). (a) The arrowed dashed line refers to the deformation field; (c),(e) the black domains denote the PV
anomalies; (b) the ‘‘1’’ and ‘‘2’’ symbols refer to cyclonic and anticyclonic circulation centers, respectively, associated
at upper levels with PV perturbations and near the surface with thermal (u) perturbations; and the long- and shortdashed
line denote a u isoline and the relative phasing of the perturbations, respectively. (d) In these vertical sections the ‘+’ and ‘-’ refer to positive and negative PV anomalies respectively.
(Davies and
Didone 2013)

6. Mechanisms of Rossby-wave growth
Band of anomalously low PV on the equatorward side of the tropopause
What might cause these errors? – link to DIAMET project
FIG. 12. Schematic of various mechanisms for generating and/or enhancing a wave disturbance on a jet stream. From
top to bottomthe rows relate to the influence of horizontal deformation, baroclinic growth, a stratosphericPVanomaly,
realignment and unshielding of a PV perturbation pattern, and a tropospheric PV anomaly. For each row the left panel
refers to an initial time and the right panel displays the outcome of the mechanism’s influence at a subsequent time. In
each panel the bold black line signifies the location and configuration of the jet stream (i.e., the 2-PVU isoline on an
isentropic surface). (a) The arrowed dashed line refers to the deformation field; (c),(e) the black domains denote the PV
anomalies; (b) the ‘‘1’’ and ‘‘2’’ symbols refer to cyclonic and anticyclonic circulation centers, respectively, associated
at upper levels with PV perturbations and near the surface with thermal (u) perturbations; and the long- and shortdashed
line denote a u isoline and the relative phasing of the perturbations, respectively. (d) In these vertical sections the ‘+’ and ‘-’ refer to positive and negative PV anomalies respectively.
Deflects tropopause equatorward
(Davies and
Didone 2013)

7. Mechanisms of Rossby-wave growth
longitude
Figure 10. A schematic representation of the net diabatic PV (shaded) relative to large-amplitude waves on the tropopause (solid line). Positive diabatic
PV associated with longwave cooling is greatest in the troughs T1, T2, T3, enhancing the PV anomalies associated with equatorward advection of
stratospheric air. The negative diabatic PV enhances the ridges R1, R2 and R3. The net diabatic effect is greater amplitude in the Rossby wave along the
tropopause.
Schematic illustration of the diabatic PV dipole relative to the tropopause in Rossby wave – based on extratropical cyclone case study
(Chagnon et al. 2012)

8. Extratropical cyclone influence on Rossby wave growth
Intersecting WCB2 air parcels on 305K surface
Intersecting WCB1 air parcels on 315K surface
So where does the anomalously low PV come from? Outflow from WCBs
Jeff Chagnon presented this work in the dynamical meteorology session on tues.
Martínez-Alvarado et al (submitted)

9. Forecast errors in upper-level PV
analysis
Control run
Reduced LH
Long lead time forecast
TIGGE forecasts for Nov 2009 case study (MSc thesis, Sideri 2013 supervised by Chagnon and Martínez-Alvarado)

10. AIM
Quantification of the systematic error in tropopause structure in medium-range weather forecasts.

11. Data
Data extracted from the TIGGE (THORPEX Interactive Grand Global Ensemble) archive*.
Daily (12 UTC) northern hemisphere fields of PV on the 320K isentrope used from the control runs
Three operational centres: ECMWF, the Met Office, and NCEP
Six winter seasons (December, January and February from 2006/7 (2008/9 for NCEP) to 2011/12).
*The TIGGE archive consists of global model ensemble forecast data from ten NWP centres, starting from October 2006: see

12. Example forecast errors
Two types:
Amplitude error
Location error
PV on 320K isentrope

13. Categorisation Define using
PV value (greater or less that the assumed tropopause value: 2.24PVU assumed here).
Equivalent latitude (north or south) where the equivalent latitude is the limiting latitude if the area, A, in which the PV on an isentope < tropopause PV is reshaped into a pole-centred circle.

14. Average RMS forecast – analysis difference.
Hemispheric errors
Average RMS forecast – analysis difference.

15. Hemispheric errors
Average RMS forecast – analysis difference scaled by mean analysis PV for forecast centre.

16. Ridge PV gradient forecast

17. Ridge area forecast 2.55x107 km2
2006/7
2007/8
2008/9
2009/10
2010/11
2011/12
Reduced forecast resolution after day 10

18. Ridge PV forecast

19. Conclusions
Upper-level PV forecast errors in operational global models saturate after about 9 days.
Met Office and ECMWF forecasts show a decrease in ridge area with forecast leadtime and increase in mean ridge PV out to 5 days.
NCEP results vary strongly with year but also show an increase in mean ridge PV with forecast lead time.
The forecast biases in PV in analysed ridges are consistent with a reduction in
the Rossby wave amplitude and
PV gradient across the tropopause
Mechanism causing error growth is not proven here but ……
…errors are consistent with a systematic failure of forecasts in the representation of the outflow of air with a negative anomalies of PV from diabatic processes in warm conveyor belts into ridges.

20. Example forecast errors
PV on 320K isentrope

21. Ridge area forecast:
tropopause PV = 3.35 PVU

22. Ridge PV forecast
tropopause PV = 3.35 PVU

23. Sources and sinks where H is the heating rate Instantaneous heating
Steady heating
Figure 1. Schematic diagram depicting the orientation of the PV dipole arising from heating applied against (a) a barotropic environment having
a background vertical (planetary) vorticity, and (b) a baroclinic environment containing vertical wind shear (directed into the page). Positive
(negative) PV anomaly is indicated by light (dark) shading.
PV dipole arising from heating applied in a barotropic environment

24. PV effect on cyclones: direct effect
Figure 2. Schematic diagram to illustrate the impact of latent-heat release on the low-level circulation of the
Fronts and Atlantic Storm-Track EXperiment Intensive Observing Period 18. (a) Shows the situation at early
times, before latent-heat release occurs. The upper line illustrates a tropopause fold, with associated positive
potential vorticity (PV) anomaly. A low-level, cyclonic circulation is induced. (b) Illustrates the dominant effects
of latent heating within the mature system. A positive low-level anomaly is formed which intensi. es the lowlevel
circulation. A local sink of PV is located above, which weakens the upper-level feature. A surface thermal
anomaly remains weak throughout. (After Ahmadi-Givi et al )
Tropopause erosion and/or upper-level divergence.
Associated with ‘type C’ cyclogenesis (Plant et al., 2003).

25. PV effect on cyclones: indirect effect
Jet enhancement leading to modified Rossby wave propagation