J8.8�� BETTER
UNDERSTANDING OF QG THEORY THROUGH THE USE OF D3D
Andrew I.
Watson*, Todd P. Lericos, Jeffery D. Fournier,
NOAA/National
Weather Service
Tallahassee,
Florida
and
Edward J.
Szoke
NOAA/Forecast
Systems Laboratory
Boulder,
Colorado
1.�� INTRODUCTION
Quasi-geostrophic
(QG) Theory is one of the most important concepts, put forth in the late 1940s
(Charney 1948), for interpreting the present state of the atmosphere, and
evaluating short-term tendencies of synoptic scale systems.� It is elegant in its simplicity and
usefulness, though in its simplicity also lies drawbacks and problems.� In spite of these drawbacks, QG Theory is
still very useful, especially to the new student of atmospheric processes.
The
Forecast System Laboratory (FSL), in cooperation with the National Weather
Service (NWS), has developed the Display 3-Dimensional workstation (D3D).� D3D allows users to view real-time
meteorological model data in a three-dimensional interactive display.� D3D has evolved from the WFO-Advanced D2D
system, which is currently the operational interactive display software on the
Advanced Weather Interactive Processing System (AWIPS) installed in all NWS
forecast offices (WFOs).
Since
atmospheric processes are inherently three-dimensional, it was natural for FSL
to extend its D2D and WFO-Advanced system to three dimensions.� At the core of D3D capability is the Vis5D
software developed at the University of Wisconsin.
The NWS
has begun establishing D3D test sites at several WFOs in the NWS Southern Region,
including WFO Tallahassee, as well as Regional Centers.� D3D was developed primarily on HP
workstations, but now has been ported to PC/Linux platforms, a convenient and
low-cost workstation.
This paper
will show how D3D can be used in a training environment. The terms in the QG
omega equation, such as temperature advection and vorticity advection, can be
visualized and related to vertical motion (omega).� Other quantities such as potential vorticity will also be examined.
2. � QG THEORY
����� In QG Theory, the primary horizontal
circulation is defined by the geostrophic wind, which remains in hydrostatic
and thermal wind balance.� The secondary
ageostrophic circulation is composed of both a horizontal component (an order
of magnitude weaker than the geostrophic wind) and a vertical component.� Assumptions in QG Theory are: synoptic scale
motions, hydrostatic balance, geostrophic wind, advection by the geostrophic
wind, no friction or terrain, a constant Coriolis parameter, adiabatic motion
(no radiation, latent heat or sensible heat release), the ageostrophic wind is
much less than geostrophic wind, and parcel accelerations are approximated by
geostrophic accelerations.� QG Theory
reduces the governing equations to a set of easily understood equations, which are
applicable to forecasting the weather, and which provide a method for
understanding some of the complexities of the atmosphere.����
3.�� QG
OMEGA EQUATION
����� One form
of the QG Omega equation is:
��������������������������������������������������
(1)
Vertical
motion is forced by vertical variations of geostrophic vorticity advection, and
horizontal variations in geostrophic temperature advection.� In the following sections, we will show how
D3D can be used, in both operational and training environments, to visualize
terms such as temperature advection and vorticity advection in the QG Omega
equation.�
4.�� CASE
STUDY: 4 May 1999
����� To
fully appreciate the advantages of D3D, we focus our attention on 4 May 1999,
the day after the devastating tornado outbreak on the Southern Plains.� A strong jet streak has moved into the
southern Rockies, with the nose of the jet moving through the base of the
trough producing a strong surface low pressure system in the central Great Plains.
����� We
will use D3D to analyze this situation, illustrating how it could be used in a
training situation.� Numerical model
data can be selected using the 3D Volume Browser window (Fig. 1).� Following the selection of the model
desired, various fields can be examined as�
3-dimensional surfaces, cross sections, or plan views.� Three dimensional rendering can be obtained
by selecting isosurface in the 3D Volume Browser.� An isosurface is the 3D contour surface of a
field at a particular value.� It depicts
the volume bounded by that value, allowing one to visually depict the field�s
3D structure at any desired viewing angle.�
Isosurface skin values and presentation colors can easily be
modified.�
Figure 1.� D3D Volume
Browser window showing model source and available fields.
����� Planview
permits viewing of a horizontal section of data.� Cross section allows vertical cross sections of data to be
viewed.� Volume rendering is a
technique for displaying a 3D field as a semi-transparent colored fog.� Surface allows viewing data on the 3D
topography surface, and wind allows viewing of horizontal and vertical
cross sections of wind data in both the 3D volume and at the surface.
����� The
Eta 80-kt jet streak isosurfaces are shown in Figs. 2 and 3 for 1200 UTC 4 May
1999.� Since it is very difficult to get
a perspective of a 3D surface on a 2D sheet of paper, especially using only shades
of gray, a top quarter view (Fig. 2) and a view from the south (Fig. 3) are
provided for comparison.� Since the jet
streak is aloft, some parallax error is introduced.� However, the 80 kt jet streak is a significant volume of air,
moving southeastward into the trough located in the southern Rockies.� To show surface features, sea-level pressure
is plotted at 1-mb increments.� Notice
that the Gulf of Mexico is open, with moderate southerly flow pushing warm
moist air northward into Canada.� An
elongated low pressure system is situated in the Upper Plains, defining the
boundary between warm moist Gulf air and Pacific maritime air spilling across
the Rockies.� The depth of the 80-kt jet
streak is evident in Fig. 3, dipping as low as 500 mb.� The vertical coordinate is pressure, (not
the log of pressure).� The top of the
volume is 100 mb in all displays.
����� According
to QG Theory, both differential horizontal warm air advection and vertical
differential positive vorticity advection contribute to upward vertical
motion.� In equation (1), a LaPlacian
operator acts on the temperature advection term, which complicates the
situation.� However, we can examine the
simple quantities of warm air temperature advection and positive vorticity
advection.
The
associated Eta warm air advection is shown in Fig. 4, while Fig. 5 illustrates
positive vorticity advection.� Warm air
advection is concentrated on the eastern extension of the jet streak, and
extends from Mexico to Canada.�
Vorticity advection (Fig. 5) covers much the same area.
Having
seen the results of the thermal and vorticity advection terms, we look at
upward vertical motion. Figure 6 shows the large region of upward vertical
motion (omega) associated with the deepening surface low and jet streak. Eta
ascent exceeding �4 :bar s-1 covers much of Plains States.
5.�� POTENTIAL
VORTICITY
����� From
the divergent vorticity equation, it can be shown that
���������������������������������������� (2)����
where 0 =
absolute vorticity and,
M2/Mp = static
stability.
����� From
the above equation, the most common form of Isentropic Potential Vorticity
(IPV) is:
����������������������������������������������������������������������������������������������
����������������������������������� ��������������������������������������������
(3)
Since IPV is a conservative
property, parcels that descend from the stratosphere into the less stable
troposphere must increase their absolute vorticity to conserve potential
vorticity.
Figure 7 depicts an IPV anomaly, a stratospheric
intrusion into the troposphere.� The IPV
isosurface of 2 units or greater is shown.�
Potential vorticity advection into the troposphere, can precede the
increase in relative vorticity and cyclogenesis by 12 hours or more.�
6.
� SUMMARY
����� A presentation in a preprint volume cannot
adequately depict this visually powerful tool.�
With the use of a mouse, any perspective can be examined and shifted
fluidly and continuously to another perspective.� The forecaster can look around corners, zoom in, zoom out, loop,
change colors, change parameter settings, and even change the opaqueness of a
field.�����
Only a small portion of the 3D Volume Browser has
been examined in this paper.� Cross
section and plan views can be easily shifted from one level to another.� Other sampling techniques include a sounding
and hodograph viewing mode.� Selecting
the probe mode makes it possible to inspect data values at any location in the
grid.� Finally, wind trajectories can
trace air motions in time through the 3D volume.
The NWS Tallahassee has placed the D3D PC/Linux machine
in a prominent place in the operations area.�
It has been found to be more useful during the winter and transition
months.� It has not become a replacement
for D2D, but is used as a complement to D2D.�
We look forward to integrating D3D into office operations and hope to
see D3D as an option on all of the WFO AWIPS workstations in the very near
future.
7.�� REFERENCES
Charney,
J.G., 1948: On the scale of atmospheric motion. Geofys. Publ., 17,
No 2.
Figure 2.� D3D rendering of the Eta 80-kt jet streak isosurface at 1200 UTC 4 May 1999.� Surface pressure contours at 1-mb increments are also shown.
Figure 3.� Same as Fig. 2, except looking north into the volume.� Topography is shown at bottom of figure.
Figure 4.� Same as
Fig. 2, except with the addition of the Eta 7� C/12 h or greater temperature
advection isosurface (red).
Figure 5.� Same as
Fig. 2, except with the addition of the Eta 4 x 10-9 m s-1
or less vorticity advection isosurface (blue).
Figure 6.� D3D rendering of the Eta ascent exceeding -4 ubar s-1 omega isosurface at 1200 UTC 4 May 1999.
Figure 7.� D3D
rendering of the 2 and greater potential vorticity units (PVU) isosurface for
the 42-hr forecast at 0600 UTC 6 May 1999.