Detailed description of our objective trough/jet identification technique.

Commonly used methods of African Easterly Wave (AEW) identification have limitations that may, on occasion, give a less than ideal representation of the synoptic weather systems over tropical North Africa. For example, using the point at which the African Easterly Jet (AEJ)-level meridional wind is equal to zero (perhaps the most often used method) cannot be used reliable in regions where there is a 'background' meridional flow. Using relative vorticity at the same level often leads to confusions between the multiple scales of which an AEW is composed. Some studies have used bandpass filtered winds that give a clear indication of the synoptic scale weather systems, but these methods cannot be employed reliably in a real time situation. As a solution, we suggest that AEW trough axes should be defined based on AEJ-level streamfunction (y), as using y in the tropics is somewhat analogous to using geopotential height in the mid-latitudes. Streamfunction has the distinct advantage that the elimination of the divergent flow reduces noise associated with individual mesoscale convective systems (MCSs) and offers a smoother field that presents less technical difficulties for the computation of objective AEW trough axes. Due to the fact that most numerical models and reanalysis products include this level, we define the AEW trough axes on the basis of y at 700hPa .

For orientation, an example of the 700hPa streamfunction field over tropical North Africa during September 2004, as computed from a global model, is shown in Fig.1 below. Recalling that the zonal (u_y) and meridional (v_y) components of the streamfunction wind () are given by:

(1) and (2),

reveals that streamfunction winds in the tropics are essentially the counterpart of geostrophic winds in the extratropics. Shown by the large red 'A', figure 1 clearly shows a large-scale anticyclone between 20 and 40^oN (marking the upper portion of the Saharan heat low circulation (see e.g. Thorncroft and Blackburn, 1999)). On the equatorward flank of this mid-level anticyclone (between 10 and 20^oN) an intense, zonally orientated streamfunction gradient can be observed (shown by the large red 'B'), denoting the location of the AEJ. The signature of an AEW is a wavelike perturbation to this intense gradient that moves westwards with time, the position of a trough axis marked by a poleward displacement (examples indicated by red letter 'T's) and a ridge marked by an equatorward displacement (examples indicated by res letter 'R's) of the streamfunction contours. Three troughs can be easily seen in Fig.1, near 5^oW, 15^oE and 30^oE.

FIGURE 1 - Example Streamfunction Field (scaled by 10^-6)

The streamfunction wind components (i.e. the non-divergent wind components) for the example period shown in Fig.1 (with a slightly zoomed area) are plotted in Fig.2(a). Note the analogy of streamfunction in the tropics to geopotential height in the mid-latitudes.

FIGURE 2a - Non-divergent wind components (vectors) on the

Streamfunction field shown in figure 1.

Using the non-divergent wind components, we then compute ‘streamfunction vorticity’ () defined as:

(3).

where is a standard gradient operator and the computed streamfunction vorticity is implicitly a vertical component. A map of this quantity for the example period is displayed in Fig.2(b), superimposed on the streamfunction field below. Note that from the streamfunction vorticity the position of a trough or ridge can be simply defined to be where:

(4)

i.e. the point where the advection of the streamfunction vorticity by the streamfunction wind is equal to zero. This concurs with synoptic reasoning – wherein positive vorticity advection lies ahead of a trough axis and negative vorticity advection behind.

FIGURE 2b - 'Streamfunction vorticity' computed from non-divergent wind

components plotted on top of streamfunction. Only positive values are

shown for clarity. Vorticity values scaled by 10⁵.

However, the definition of trough and ridge lines based solely on the advection streamfunction vorticity of is only mathematically correct for idealized 2-dimensional waves (i.e. where v_y is a function of only one horizontal direction). Those that occur over tropical North Africa are not of this type, as Fig.1 clearly shows. This is because a large contribution to the total streamfunction vorticity comes from horizontal shear across the AEJ. The advection of streamfunction vorticity due to the westwards propagation of AEWs is obscured by the advection of streamfunction vorticity associated with relatively small fluctuations in the position or nature of the AEJ. A simple solution is achieved by partitioning the streamfunction vorticity into shear vorticity and curvature vorticity components:

(5).

Plots of these two components for the example period are shown in Fig.2(c) below.

FIGURE 2c - Streamfunction shear (contoured) and curvature

(shaded) vorticity computed from non-divergent wind

components plotted on top of streamfunction. Again,

only positive values are shown for clarity. Vorticity values

are scaled by 10⁵.

Now, the AEW trough and ridge axes are then re-defined to be where:

(6).

This diagnostic is plotted on the example streamfunction field in Fig.2(d) below:

FIGURE 2d - Advection of curvature vorticity equal zero contour on

top of the original streamfunction field.

In order to differentiate between AEW troughs and ridges, these lines are only plotted in regions where curvature vorticity exceeds some threshold (in the case of troughs) or is below some other threshold (in the case of ridges). This has been applied in Fig.2(e), overlaying a mask that obscures region in which the streamfunction curvature vorticity is below 0.5x10^-5s^-1 (the same threshold used for our plots), resulting in only trough lines being displayed.

FIGURE 2e - Advection of curvature vorticity equal zero contour

in regions where curvature vorticity exceeds 0.25x10⁵ s^-1.

However, because there will be instances where curvature reaches a local minimum, yet is still positive (or conversely reaches a local maximum, yet is still negative) a further masking diagnostic is required, to remove spurious lines that are not removed by the streamfunction curvature vorticity mask:

(7),

where K is positive for plotting troughs and negative for plotting ridges. For our plots we simply use a value of K=0. This final mask is applied, along with a mask that removes trough lines in regions where u_y is greater than –8ms^-1 (since we are looking only for eastwards moving disturbances), in Fig.2(f) below.

It can also be noted that lines along which streamfunction shear vorticity () equals zero denotes the cores of streamfunction wind speed maxima or minima. This is used by also noting that wind speed maximum can be removed by applying the following graphical mask:

(8),

where is the unit vector perpendicular to the Earth’s surface. The AEJ axis has been plotted as a dashed line in Fig.2(d-f) for completeness.

FIGURE 2f - FINAL PRODUCT....Advection of curvature vorticity equal

zero contour in regions where curvature vorticity exceeds 0.25x10⁵ s^-1,

where the zonal component of the non-divergent wind is less than zero

and where eq(7) is greater than zero. All plotted on top of the original

streamfunction field from figure 1.

A page that shows these 'background' diagnostics for the current analysis time can be found here.

BACK TO PLOTS MAIN