Definition
Any wind field on a surface (here horizontal) can be split into two components, one corresponding to a divergent field VD feeding the vertical speeds, and the other rotational VR, according to the formula :
- The divergent wind field VD derives from a velocity potential VP analogous to a relief map whose slope is proportional to the divergent wind.
- The rotational wind field VR derives from a streamfunction SF. The non-divergent but rotational wind flows along the streamlines.
The velocity potential VP and the streamfunction SF are interesting parameters because they are spatial integrals (on the horizontal in this case) of the wind which “naturally” filter out the small-scale structures to highlight the large-scale structures. are interesting parameters because they are spatial integrals (on the horizontal in this case) of the wind which “naturally” filter out the small-scale structures to highlight the large-scale structures. They also enable to make a separation between the convergent/divergent small-scale circulation associated with convection and the large-scale balanced flow partly fed by convective heat sources through the adjustment process explained in the diagram below.
The adjustment process
Very fine-scale convective heat sources generate gravity waves (GW) which propagate rapidly (typically ~ 50 ms-1 for the deepest and fastest) from the convective source towards the environment, thus evacuating the energy. At the same time, the action of the Earth’s rotation (Coriolis term f) tends to balance the pressure variations induced by convective heating. After a characteristic time of 1/f, the heating is redistributed by the GWs over a horizontal distance called the Rossby radius λ = NH/f, where N (Brunt Vaïsala frequency) is the stability of the atmosphere and H its thickness. The induced expansion of the atmosphere generates negative and positive pressure disturbances at the bottom and top of the convective layer respectively. The circulation reaches geostrophic equilibrium after a characteristic time ~ 1/f (about 9 h at 12.5°N) with cyclonic circulation at the bottom of the layer and anticyclonic circulation at the top (a). On scales smaller than the Rossby radius, the convection-induced circulation takes on different dynamic characteristics: convergent below the convective heating layer and divergent above. This circulation feeds the upward movements of the convective zone.
anticyclonic circulations at the scale of the Rossby radius λ. Source: Fig. 3.6 of the Handbook.
Due to the predominantly dry conditions over West Africa, cloud bases are high, which favours strong evaporation of precipitation before it reaches the surface and cooling below the “hot convective towers” (b). The resulting contraction of the air in the lower layers, combined with the expansion above, generates a pressure triplet (H-L-H) in the lower, middle and upper layers respectively. On scales larger than the Rossby radius, geostrophic equilibrium results in anticyclonic circulation in the lower and upper layers, and cyclonic circulation at mid-level, i.e. in the JEA layer. On a finer scale, maximum convergence occurs at mid-level (typically 700-500 hPa), which feeds convective lift above and mean subsidence below. Over West Africa, the low-level flow tends to be divergent and anticyclonic beneath the convective zones. This is one of the important characteristics of semi-arid continental regions such as the Sahel in West Africa.
Advantages of this decomposition
1. Velocity Potential (VP)
According to the previous diagram, it is judicious to examine the velocity potential (VP) and its anomaly above the convective areas at 200 hPa where divergence is at its maximum, as shown in Fig. opposite during a wet period over West Africa.
- The VP is negative (divergent in green) over Africa, in contrast to the climatology, reflecting very strong convective activity, confirmed by a very negative VP* anomaly.
- The strong activity of the Indian and Asian monsoons corresponds to a vast green zone of VP, slightly higher than climatology since VP* is also green.
- The decomposition of the equatorial waves on the VP* map shows that this active period corresponds to the passage of the active phases of the MJO (black isolines), a Kelvin wave (blue) crossing a Rossby (red) and MRGs (green) reinforcing the easterly waves.
Use of the VP field
Outre les cartes de VP (cf. exemple ci-dessus), ce paramètre permet:
- the detection of equatorial waves,
- and the Hovmöllers plot (longitude-time) with the contributions of the different waves to highlight their propagation.
- Although the 200 hPa level is the most commonly used, it may be interesting to examine the VP at the 700 hPa level where convergence is at its maximum over Africa, in accordance with the conceptual scheme of the “adjustment” (b) explained above.
- Negative VP anomalies at 200 hPa correspond to the active phase of waves reinforced by convective activity. These active phases are maintained over time by their own dynamics, and in turn they force convection, which is more intermittent (diurnal cycle, among others). There is therefore a two-way interaction between waves and convection.
2. Streamfunction
The figure opposite shows the SP current function at 200 hPa for the same situation as that used above for the VP.
- The active zones of the West African, Indian and Asian monsoons, marked by strong divergences, also correspond to anticyclonic circulations (in brown) in line with the adjustment process. This is the case for both the total SF field and its SP* anomaly, showing the intensity of this wet period, particularly over West Africa.
- This map also highlights the Rossby waves at mid-latitudes, with SF oscillations and a succession of cyclonic and anticyclonic nuclei for the SF* anomaly.
Use of the SF field
Outre les cartes de SF (cf. exemple ci-dessus), ce paramètre permet :
- The detection of the Rossby waves,
- the Hovmöllers plot (longitude-time) to highlight their propagation. However, their exploitation is more difficult because their route is sensitive to the choice of latitude band.
- The 700 hPa level can potentially help to detect AEWs, equatorial Rossby waves and the Sahelian mode.