In general, the tropical wind field provides more information about synoptic conditions than
the pressure or geopotential height field. According to Helmholtz’s theorem, the wind
velocity can be separated into two components:
⃗ =𝑉
⃗ 𝑟𝑜𝑡 + 𝑉
⃗ 𝑑𝑖𝑣
𝑉
(1)
⃗ 𝑟𝑜𝑡 , has all of the vorticity and no divergence and 𝑉
⃗ 𝑑𝑖𝑣 has all of the
The rotational wind, 𝑉
divergence and no vorticity. Vorticity, a measure of the local rotation of the flow, is
calculated as the cross product of the vector wind. Vorticity, a measure of the local rotation of
the flow, is calculated as the cross product of the vector wind and has units of inverse seconds
(s-1). Divergence measures the spreading out of the flow (also with units of s-1). Figure 9.7
illustrates the differences between the rotational and divergent components of the wind
velocity. The two components can be further broken down into variables that are useful for
tropical weather analysis, the stream function,𝜓 , and velocity potential, χ :
⃗ × ∇𝜓
⃗ 𝑟𝑜𝑡 = 𝑘
Rotational wind, 𝑉
(2)
⃗ 𝑑𝑖𝑣 = ∇𝜒
Divergent wind, 𝑉
(3)
Rotational winds are parallel to the stream function contours and their speeds are proportional
to the stream function gradient. Divergent winds flow out low velocity potential and their
speed is proportional to the gradient of velocity potential (Fig. 9.7b,c). Velocity potential and
stream function are defined at the equator which makes them useful for model initialization in
the tropics.
Because the velocity potential is proportional to divergence, it can be used to track regions of
upper-level divergence where convection is enhanced (Fig. 9.8). Divergence from deep
convection drives tropical circulations.
Fig. 9.7. Illustration
showing the relationship
among the rotational wind,
divergent wind, and the
velocity potential at 300
hPa for January (sample
data from the NCAR
Community Climate
Model, CCM2).
Anomalies or deviations from the mean velocity potential are much more useful than actual
values for distinguishing the regions of deep convection or suppression. Figure 9.8 illustrates
the correspondence between 200 hPa velocity potential anomalies and deep convection
identified by enhanced satellite IR imagery. In this example, the ITCZ can be identified as the
broken band of convection extending from Central Africa west to the central Pacific. A broad
area of deep convection is apparent over the Western Pacific.
Fig. 9.8. Daily 200 hPa velocity potential anomalies (base period 1971-2000) and enhanced
satellite IR (color shading). Velocity potential anomalies are proportional to divergence with
green (brown) contours corresponding to regions in which convection tends to be enhanced
(suppressed).
The Climate Prediction Center at NOAA produces daily maps of velocity potential anomalies at
200hPa for the globe. The velocity potential is a scalar field that describes the divergent irrotational
part of the horizontal velocity field. This part of the wind vector is given by the gradient of the velocity
potential. The divergence of the velocity field is given by the Laplacian (i.e. curvature) of the velocity
potential. Generally, the centers of regions of positive potential (i.e. negative Laplacian) have
converging winds at 200hPa and subsidence beneath. Regions of negative potential have diverging
winds and rising air motion beneath. This relationship is evident on the NOAA charts as they also
show the outgoing IR radiation, expressed as a brightness temperature. In regions of deep convection
(i.e. cold IR temperature) the velocity potential is negative, consistent with upper level air diverging
away from the updrafts. An example of this relationship is shown in the figure below. On 21 October,
2010, positive potential and subsidence are seen over the eastern Pacific and western Atlantic.
In DOMEX, the level of convective activity and the strength of the tradewind inversion may be
controlled by the mid-troposphere subsidence. Klotzbach (2010) shows that large scale subsidence
can suppress hurricanes in the tropical Atlantic. Thus the 200hPa velocity potential may be a useful
predictive tool for DOMEX. Positive anomalies suggest subsidence, weak convection and less
precipitation. Animations of the velocity potential are found HERE. Note the general west-to-east drift of
the anomalies associated with the Madden-Julian Oscillation (MJO).
The eastward drift of the velocity potential anomalies is well seen in the NOAA time-longitude (i.e.
Hovmoller) diagrams. Shown below is the diagram for the latitude range 10 to 20N which includes
Dominica (15N). Note that about every month, a high velocity potential anomaly reaches the longitude
of Dominica (61W) from the west. Typically such suppressed periods last for about ten days. During
the five week field phase of DOMEX, one or two of these suppressed periods might occur. The current
Hovmoller diagram is found HERE (item 16).