Quasi-geostrophic diagnosis of baroclinic waves (II)
1 Distinction between stable and unstable waves
With the reasoning given in Part I we can attempt to understand the different behaviour of
baroclinic waves simulated by a model. To some extent this is already possible by means of a
comparison between surface and upper-air forecast maps.
The example in Fig.1 shows a frontal zone over the north-western Atlantic at which three
waves develop during the forecast time of 72 hours. The behaviour of these waves is forecast
quite differently. The first wave experiences a quick intensification into a cyclone which
becomes quasi-stationary east of Iceland. The second wave moves without significant changes
from Newfoundland to the area west of the British Isles and then undergoes a dissolution. The
third wave deepens somewhat while travelling from Newfoundland north-eastwards but then
the development comes to an end although the warm sector of it is still relatively wide open.
The position of the fronts in the surface maps has been fixed with the aid of the field of
equivalent potential temperature at 850 hPa.
When comparing it with the 500 hPa-forecasts, we can see why the model has produced a
different life cycle of the three waves. The crest of the first frontal wave lies immediately
ahead of an upper trough with short wave-length and therefore shows the behaviour of the
growing wave mode. The intensification ends after 36 hours when the axis has been erected.
The second wave is also connected with an upper trough but with much smaller amplitude and
hardly visible in some forecast fields of geopotential 500 hPa. It has an upright position just
above the surface low or trough, resp., so that the system remains stable while travelling
eastwards. But after 36 hours the speed of the upper trough becomes faster and it overtakes
the surface wave which quickly dies out under the rear of the trough. Ahead of the southeastward swinging trough the occlusion of the first wave experiences some new
intensification.
The third wave forms in the 24 hours-forecast ahead of a significant upper trough so that its
further deepening is immediately understandable. However, the development must end after
36 hours since a secondary upper trough has then reached the position of the surface low,
whereas the main trough remains south-west of it. At the end of the forecast run the surface
low and the connected secondary trough lie at the outer flank of a broad ridge of the 500 hPacurrent.
That is, of course a very rough explanation of the simulated wave behaviour using only the
fields of surface pressure and 500 hPa-geopotential. Normally, at least the distribution of
advection and vertical motion should be considered, as demonstrated by the following
examples.
Fig.1a: Analysis and forecasts of surface pressure and fronts
Fig.1b: Analysis and forecasts of 500 hPa- geopotential and surface pressure (dashed)
2 A developing frontal wave
The analyses of Fig.2 show a case in which an initial frontal wave has just formed over the
North Atlantic. The question which immediately arises is whether this wave will develop into
a cyclonic storm or will whether it remains stable and will quickly move along the front
without deepening.
Comparing with the 500 hPa-analyses (a,b), we find the frontal wave and the surface trough in
which it is embedded ahead of a cold upper trough with a significant maximum of positive
vorticity in it. The trough has approached the surface front from its rear so that the
constellation corresponds to the scheme by Petterssen as described in Part I. The area of
strong PVA aloft (e) is still behind the surface front and works partly above the lower CA (f),
but it has already encroached on the crest of the wave where the CA cannot compensate for
the effect of the PVA. In combination with the WA ahead of the front we should therefore
expect a strong forcing of ascent over the wave connected with convergence and production
of cyclonic vorticity in lower levels. The vertical motions simulated by the model and shown
in Fig.2 (g) do indeed contain a large area of ascent at 700 hPa around the wave. An effect of
the ascent is a broadening and deepening of the frontal cloud shown in the satellite image (d).
In the image another typical feature of such a development is visible, namely a separate cloud
mass west of the frontal cloud band. It directly reflects the ascent of colder air ahead of the
upper trough and indicates with its displacement the movement of the upper trough relative to
the surface systems. The ascending motion in this area is also well simulated by the model.
In accordance with this reasoning the wave did indeed develop while travelling northeastwards. In Fig.3(a) we find a low south-west of Ireland 12 hours later, which deepened
further since the upper vorticity maximum still had a position to the rear of it. Surprisingly,
the fine-mesh model used did not simulate this development or did so only to a very limited
extent (3b). A forecaster producing surface forecast charts would therefore have had a good
chance of improving the model forecast by following the diagnostic considerations given
above.
Fig.2: Analyses from 29-03-1993, 12 UTC. (a) Isohypses (thick solid) and isotherms at
500hPa, (b) relative vorticity and winds at 500 hPa, (c) surface fronts, isobars (thick) and
isotherms of equivalent potential temperature at 850 hPa, (d) IR-satellite image
Fig.2 (cont.): (e) absolute vorticity advection at 500 hPa, (f) thickness advection
500/1000 hPa, (g) model omega at 700 hPa
Fig.3: (a) Surface analysis from 30-03-1993, 00 UTC, (b) 12 hourly forecast of the model
3 Diagnosis of a strong cyclogenesis
The following example should demonstrate how quasi-geostrophic diagnosis should be
applied in order to understand model forecasts which might be surprising or even incredible at
first sight.
The surface analysis of the case in Fig.4(a) shows a frontal wave about to develop at a frontal
zone over the North Atlantic which extends from a large low south-east of Newfoundland up
to the British Isles. In the 24 hour-forecast (b) we find the wave as a flat depression south-east
of Iceland with a well-defined cold front extending south-westwards. But afterwards the low
should stop its movement and remain quasi-stationary while deepening rapidly. The
intensification is most strongly simulated at the cold front swinging south-eastwards so that
the low-pressure centre in the 36 hour forecast (c) has a position even further south of that in
the 24 hour prognosis. This surprising surface forecast can only be understood using the
methods of diagnosis described in Part I and outlined below.
The comparison with the upper-air current (here 300 hPa) given in Fig. 5-8 shows that, in
accordance with the Petterssen scheme, development is simulated under the fore part of a
marked trough and upper low swinging south-eastwards from Greenland and approaching the
surface system. At the beginning we find two areas of PVA within the trough. The frontal
wave lies under the eastern region and therefore can be intensified while travelling eastwards
following the WA at work there. The CA, however, is relatively weak behind the surface
wave and is more concentrated in the west, leading to an intensification of the upper trough
there. The vertical motion simulated by the model show ascent over the surface wave and to
the east of it and descent over the western coast of Greenland and are in agreement with the
reasoning given above.
After 24 hours (Fig.6) the first deepening phase has finished, since the eastern PVA area has
moved forward relative to the surface low and now lies over its eastern flank. Most significant
is the large area of strong CA still far behind the surface low, but just below the upper trough
indicating its further intensification and extension towards the south. The intense PVA ahead
of the upper trough works over the eastern part of the area of CA but obviously dominates the
omega forcing, and the forecast of 500 hPa vertical motion contains an area with ascent which
covers the cold front trough and its rear at the surface. That means we have to expect a new
cyclonic development in this region of low pressure.
That diagnosis is confirmed by the 36 hour forecast in Fig.7, showing the new low-pressure
centre west of Scotland. A strong further deepening is indicated by the PVA aloft now at work
directly above the surface low. With WA ahead and intense CA behind the new low, the
situation corresponds very well with the model of a growing baroclinic wave. However, since
the ascending motion is concentrated above the new centre and not ahead of it we should
expect only slow movement. This is confirmed by the 48 hour forecast (Fig.8) which shows
the cyclonic storm slightly displaced in a north-easterly direction.
Also the forecast for this date still shows PVA in 300 hPa above the surface low and therefore
a tendency for a further deepening. A typical feature now is that the area with WA and CA
begin to rotate cyclonically around the centre, with this movement strongly influencing the
distribution of vertical motions and the behaviour of the synoptic systems in the lower and
upper troposphere. Since the surface low tends to follow the WA and the movement of the
upper vorticity maximum is influenced by the CA, we can often observe that both features
also rotate cyclonically before the axis becomes upright.
Fig.4: (a) Surface analysis from 07-07-1993, 00 UTC and forecasts for (b) 24, (c) 36 and
(d) 48 hours with fronts and isobars.
Fig.5: Analysis from 07-07-1993, 00 UTC. (a) Isohypses 300 hPa, (b) vorticity advection
300 hPa, (c) model omega 500 hPa, (d) thickness advection 500/1000 hPa
Fig.6: As in Fig. 5, but for the 24-hour forecast
Fig.7: As in Fig.5, but for the 36-hour forecast
Fig.8: As in Fig.5, but for the 48-hour forecast
4 An upper trough and release of potential instability
In this case the behaviour of a trough is decribed which was confined to upper levels only.
According to Fig.9, it is a cold trough lying above a ground layer with a slack pressure
gradient and a quasi-stationary air mass border south of the trough. The analyses for 500 and
300 hPa (a) show significant vorticity maxima inside the trough. Whereas the thickness
advection is very weak around the trough, there is strong vertically increasing PVA and NVA
at its flanks and therefore a strong forcing of ascent ahead and forcing of descent behind of
the trough (b).
The ascending motion ahead of the trough is reflected by a well developed cloud comma – an
feature often observed in such upper systems (e). There is mainly medium and high cloud and
not much precipitation at the beginning.
But some thunderstorms are also observed at the south-eastern flank of the trough where the
conditions are potentially unstable with regard to convection. This is indicated by the
distribution of the so-called KO-index (f). It is defined as
KO = ½ ( Θ e500 + Θ e700 ) – ½ ( Θ e850 + Θ e950 )
and reflects approximately the vertical gradient of the equivalent potential temperature Θ e. A
vertical decrease of Θ e, i.e. negative values of KO, points to potential instability of the
temperature/moisture distribution. This is one of the prerequisites of stronger convective
turnovers. However, in many cases a trigger effect is necessary to release this instability. That
is a lifting of the air which is potentially unstable.
According to the vorticity advection, a movement of the trough in an easterly direction is to
be expected. Compared with the distribution of the KO-index, we see that during that
movement the ascent ahead of the trough would cover more and more unstable air masses.
That means that we also have to expect and forecast an increase of the convection, especially
in the southern part of the region with ascent.
That was indeed the case during the day in question. A line of thunderstorms had crossed
eastern France and southern Germany by noon causing heavy precipitation in part and gusty
winds. In addition a flat surface low developed at the air-mass border over southern Germany
as the trough was approaching (c).
Fig.9(a): Analyses from 20-06-93, 00 UTC. Top: Geopotential and relative vorticity at
300 hPa (left) and 500 hPa (right). Bottom: Surface pressure and Θe at 850 hPa (left)
and geopotential and temperature at 500 hPa (right)
Fig.9(b): Top: Vorticity advection at 300 hPa (left) and thickness advection 500/1000 hPa
(right). Bottom: Vorticity advection (left) and omega forcing (right) at 500 hPa
Fig.5(c): As Fig.5 (a), but for 20-06-1993, 12 UTC
Fig.5(d): As Fig.5 (b), but for 20-06-1993, 12 UTC
Fig.5(e): Geopotential and vorticity at 500 hPa and high cloud
Fig.5(f): Distribution of the KO-index for 20-06-1993, 00 UTC (left) and 12 UTC
Reference:
Kurz, M. (1994): The role of diagnostic tools in modern weather forecasting. Met Apps 1,
45-67