INTEGRAL VERTICAL ON A LAYER

Benefits of vertical integration

In addition to the advantage of retaining only a single map for the layer under consideration, this so-called barotropic approach has a number of advantages:

Small and unimportant structures present at only a few pressure levels are attenuated, such as eddies near the surface that are not found at 700 hPa.
On the other hand, structures present over a large part of the air column under consideration will be highlighted. This is the case, for example, of a deep eddy (marked between 950 and 600 hPa) with a shallow slope, which will therefore be well organised and powerful, often associated with the breaking of an African easterly wave and in some cases with an extreme precipitation event.
This integral gives quantitative information about the layer as a whole, its energy, or its humidity, or its mass flux… depending on the variable under consideration.

Vertical structure

Before performing a vertical integration, it is important to bear in mind the vertical structure of the monsoon as summarised below by the composite analysis of Poan et al. (2013) during the passage of AEWs over West Africa. The time t0 corresponds to the passage of the wet phase of these waves (maximum humidity). The composite is performed from 5 days before to 5 days after t0, making it possible to document the entire 5-day period of AEWs. The main findings of this vertical-time composite are as follows:

The humidity anomalies (a and c) have a fairly homogeneous vertical structure, justifying a vertical integration over the whole troposphere as done for PW or up to 600 hPa concentrating the maximum of the specific humidity anomalies (a).
The temperature anomalies (b) also have a homogeneous and marked vertical structure below 600 hPa. So it is relevant to average this field over this layer, which helps to explain the surface pressure oscillations (d), in particular the deepening of the thermal low in the dry zone preceding the passage of the trough. In practice, the temperature anomaly at the 850 hPa level is sufficient to characterise the thermal low as seen on this site.

Vertical-time composite of easterly waves for (a) specific humidity (g kg^-1 , colour) and meridional wind anomaly (m s^-1, contours), (b) potential temperature anomaly (K, colour) and vertical velocity anomaly (mm s^-1, contours), (c) relative humidity anomaly (%, colour) and zonal wind anomaly (m s^-1, contours). (d) Temporal evolution of reduced pressure at sea level (hPa). All fields are averaged over the domain [12°-20°N, 2°W-2°E]. Source : Adapted Fig. 9 of Poan et al. 2013].

Meridional wind anomalies (a) can be used to identify troughs and ridges (changes in the meridional direction of the wind), and their slope on the vertical: eastwards below the AEJ associated with meridional baroclinicity and vice versa above. Integrating the meridional wind into the layer below the AEJ will therefore make it possible to identify the characteristics of an African easterly wave (troughs, ridges) averaged over the layer. Because of the vertical inclination of the structure of an AEW, the mean thalweg is located between the surface trough and the trough at 700-600 hPa. There is a lag of about 2° in longitude between the mean trough and the trough at 700-600 hPa.

For which variables?

1. Humidity (mixing ratio)

Integral over the whole atmosphere : This concerns the precipitable water PW, the properties of which are described in detail under Precipitable water parameter.
Integral over the monsoon layer : is used to define an equivalent monsoon layer thickness (MD for Monsoon Depth).

This diagnostic (bottom panel of the figure below) is calculated from PW (top panel) using the formula :
MD = [z_s q (T₈₅₀) + PW] / q_s (T₈₅₀) = z_s RH₈₅₀ + PW / q_s (T₈₅₀)

where z_s is the surface altitude, q_s(T850) the vapor mixing rztio zt saturation at 850 hPa, and RH₈₅₀ the relative humidity at this level.This latter is chosen to avoid the diurnal cycle maximum at the surface. The advantage of this empirical formula is that the MD decreases rapidly over the warm zones as well as in the heat low area.

To go further: To avoid an artificial decrease in MD over the mountains due to the decrease in PW (cf. decrease over the Cameroon, Aïr and Fouta Djalon mountains in the figure above), PW is corrected by adding a virtual part in the layer between sea level and the surface (inside the mountains) by assuming a mean value of q(T₈₅₀) extrapolated to mean sea level (the first term in the MD equation), to compute its contribution to PW.

In Practice: As defined here, the MD is a thermodynamic measurement of the thickness of moist air in the monsoon layer, and represents a smoother field than dynamic measurements of the monsoon thickness based on wind fields. As the MD is a relatively smoothed field, it can help in identifying monsoon penetrations and retreats, as well as the positions of the Monsoon Trough (MT) where the MD is thickest and the Inter-Tropical Front (ITF) where the MD gradient is strongest. The addition of the wind shear vector in the 600-950 hPa layer also provides useful information for forecasting the organisation of convection.

In this example, the MD reaches a maximum thickness of more than 4,000 m in the north of Ghana, Togo and Benin.

(Top) PW field superposed on the 925 hPa wind vector (m s⁻¹) and (bottom) monsoon equivalent depth MD (metres) with the superposition of the wind shear vector (m s⁻¹) in the 600–950 hPa layer for the 15 August 2012 at 00UTC. The heavy isoline in (b) outlines areas with shear above 20 ms⁻¹. Source : Fig. 11.16 of the Handbook.

2. Meridional wind (Mean-Vwind)

Given the strong meridional gradient of humidity (towards the south) and temperature (towards the north – baroclinicity) up to the altitude of the AEJ (700-600 hPa), any movement towards the north in this layer will humidify and cool the atmosphere, and vice versa towards the south. The vertical mean of the meridional mass flow (close to the meridional wind in practice) in the 925-600 hPa layer will therefore be an indicator of the intensity and thickness of the monsoon flow (towards the north) or the Harmattan flow (towards the south), which will feed the oscillations of the Easterly waves. In practice, this is the integral of the meridional wind weighted by the mass. The corresponding products are identified on the MISVA website by the parameter Mean-Vwind.

As these air mass transports associated with the mean meridional wind in this layer are at the origin of the changes in the humidity field, it is important to analyse at the same time the PW fields and their PW* anomalies, which are preceded by 1-2 days by the integrated meridional wind field, as shown in the figure opposite.

The combined use of these 2 diagnostics is very rich and is detailed in the product section under the link Precipitable water map and mean meridian wind 925-600 hPa. However, we would like to make a few comments:

The alternating blue (southerly flow) and red (northerly flow) zones show a powerful train of easterly waves, connected in this case to mid-latitude and equatorial circulations (Fig. b).
These meridional wind oscillations over the 925-600 hPa layer induce strong PW* anomalies (Fig. a) corresponding to the signature of the easterly wave train located 1/4 wavelength east of the integrated meridional wind signature.

Diagnostics complémentaires issus de l’approche en PW de la structure des ondes d’est et de « l’analyse barotrope » pour le 15 août 2012 à 0000 UTC : (a) PW* (en couleur, en mm) et anomalies de vent horizontal à 925 hPa (m s^–1) ; (b) vent méridien moyen dans la couche 925-600 hPa (couleur, en m s^–1) et vecteur vent horizontal moyen dans la couche 925-850 hPa. Source: Figure 11.13a et b du Handbook.

3. Streamlines and vertical vorticity (LowLev-Diag)

Streamlines

The vertical average of the horizontal wind in the 950-600 hPa layer can be used to plot the average flow lines (Fig. opposite in blue). They do not correspond to an actual trajectory, since the layer exhibits vertical wind shears in both speed and direction. However, this barotropic diagnostic (average over the layer) is useful for the forecaster as a complement to the other diagnostics (integrated meridional wind in particular) for :

Draw the axes of the “mean” thalwegs and ridges (solid and dotted red lines respectively).
The intensity maxima of this mean flow (black isoline) correspond to accelerations of the AEJ or to strong monsoon bursts or forcings from mid-latitudes.
Closed cyclonic circulations can be used to detect the genesis of an AEW, or a zone favourable to the convection development.

Streamlines (blue) for the mean flow in the 950–600 hPa layer, with mean horizontal wind intensity (black isolines above 7.5 m s⁻¹) and vorticity (10⁻⁵ s⁻¹ – colour); the locations of the trough and ridge mean axis, as detected by the mean circulation in the 950–600 hPa layer are superposed with solid and dashed red lines respectively. Source : Fig. 11.13c of the Handbook.

Vertical vorticity

Based on the above barotropic analysis, it is possible to calculate a mean vertical vorticity in the 925-600 hPa layer, superimposed in colour on the previous map. The most intense cyclonic eddies (in warm colours) are associated with the breaking of an AEW and intense or even extreme precipitation events. Conversely, the cold colours identify the strongest anticyclonic zones, which are not very favourable to the development of convection.