The role of upper level diffluence in the Tropical Easterly Jet in the formation of the recent strongest Atlantic hurricanes

In this paper we report the evidence of the potential role of diffluence in the 200hPa wind field off the coast of West Africa in the formation of a significant number of Category 4 and Category 5 hurricanes in the recent decade. It is shown that on an average of 65% cases of hurricanes at Category 4 and above is preceded by upper level diffluence in the Tropical Easterly Jet (TEJ) by 0–3 days. This TEJ is the outflow from the southern flank of the Tibetan anticyclone from the Asian monsoon region.


Introduction
The Tropical Easterly Jet (TEJ) that originates in the heart of the monsoon (Arabian sea) and makes it way to the eastern Atlantic via all of North Africa (Figure 1) is one of the most well known features of the Asian monsoon circulation in the upper troposphere (Koteswaram 1958, Flohn 1964. The TEJ forms the outflow in the southern flank of the Tibetan anticyclone. Koteswaram (1958) explained that the TEJ was an outcome of the zonally symmetric meridional differential heating between the elevated heat source of the Tibetan plateau and the cooler Indian ocean. However, detailed energetics study of the TEJ following Kanamitsu et al. (1972) and Chen (1980) reveal that the TEJ is maintained by the tropical divergent circulations that includes both the Hadley and Walker circulations.

Datasets
Winds at various vertical levels from ECMWF ReAnalysis (ERA)-Interim (Dee et al. 2011) and the NOAA (National Oceanic & Atmospheric Administration) OISST (Optimum Interpolation Sea Surface Temperature) version 2 daily data (Reynolds et al. 2007) are used here. Temporal resolution of the data is 6-hourly and horizontal resolution is 0.75 • × 0.75 • .

What is diffluence
Diffluence is a kinematic feature of the horizontal motion field. Balance of forces can be better understood if a horizontal coordinate system is chosen which is naturally aligned with the flow, instead of Cartesian or spherical coordinates. Diffluence arises from the translation of the familiar horizontal divergence in Cartesian coordinates (x, y) into natural coordinates (s, n). In natural coordinates, one direction is chosen aligned with the streamline (s), parallel with the flow, and another direction is always normal to its left (n). Figure 3 represents the (x, y) and (s, n) coordinates. Unit vectors (s, n) represent a right-handed curvilinear coordinate system. Horizontal velocity is defined as V = V s. Angle α denotes the angle of the flow with respect to the west-east direction, with positive values indicate counter-clockwise rotation.
Horizontal gradient operator in (s, n) system is defined as Simple calculations lead to the derivation of horizontal divergence in natural coordinate system from Cartesian coordinates: The first term of the natural coordinate system denotes speed divergence or along-flow speed variations and the second term denotes diffluence. Diffluence arises from changes of the flow angle with respect to the normal to the direction n. The computations of these two terms of the natural coordinates were facilitated by the transformation functions provided by Bell & Keyser (1993). The transformation relation for the first term is: where, V is the total wind speed, and u, v are the local west to east and south to north wind components.
The subscripts denote respective derivatives with respect to x and y.
Diffluence (V ∂α ∂n ) can be found out by subtracting the speed divergence in Equation 3 from the x y s n s n α Figure 3: Schematic illustration of natural coordinate system (s, n) used to define diffluence in this study. s is always parallel to the flow and n is orthogonal it. This coordinate system is defined locally. The unit vectors, s(= V/V ) and n(= k × s) are also shown. Angle between the direction of motion (s) and west-east direction (x-axis) is α. (Following Bell & Keyser (1993)) total divergence easily obtained from the Cartesian coordinates system. Therefore, These are easy to use and fields of speed divergence and diffluence can be mapped. The Tropical Easterly Jet (TEJ) at the 200hPa level weakens abruptly as it exits west coast of Africa and shows a speed convergence ( Figure 4). Whereas, the diffluence of the TEJ is positive and larger in magnitude. This implies that the directional divergence exceeds the speed convergence, thus, in general there is a net divergence over the eastern Atlantic Ocean. In subsequent discussions, we shall show more precise values of these two terms in the context of several intense hurricane formation periods.

Results
The July-September average fields during 2017 shown in Figure   The primary aim of this study is to investigate whether this diffluent patterns over the eastern Atlantic play a role in generating some of the strongest hurricanes in recent time. Table 1 lists the category 4 and 5 hurricanes formed over the Atlantic in the most recent 11 years (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017). Most of these hurricanes (13 out of 20) formed between 1 August-15 September. TEJ is strongest during this period and weakens after mid-September. Paloma occurred in November and is excluded from any of the analysis in this study. Tracks of these 20 hurricanes and upper-level wind fields on days before the hurricanes were named were also investigated. Almost all the hurricanes which formed over the eastern Atlantic are associated with a bifurcation of TEJ (not shown). This leads us to investigate the structure of diffluence over that region before the storm formed and intensified.   This raises an important question: As AEW emanate in every 2-6-days, not all AEW turn into major hurricanes. Therefore, what are the important factors that critically modulates the growth of these waves and transform them into intense storms? The analysis presented till now hints towards the fact that the upper level diffluence is strongly associated with the formation of Irma. We also found similar patterns of diffluence for other hurricanes (not shown).
Further investigation on how diffluence plays a major role in formation of Irma is done by calculating upper level diffluence averaged over a horizontal region to the west of the African coast (8 • N-15 • N, 15 • W-45 • W) during the passage of the AEW associated with Irma ( Figure 7). Latitudinally, this box centers the location where AEW typically exits the African land (Pytharoulis & Thorncroft 1999, Thorncroft & Hodges 2001, Kiladis et al. 2006. Figure 7a shows the evolution of SST over the African coast. Although SST in this region remains above 27 • C during boreal summer, it went up to nearly 28.6 • C when Evolution of upper level diffluence is tested for all the 20 hurricanes listed in Table 1. Compositing all the storms based on their naming date could be one way of observing the mean picture. However, this method can actually lead to misinterpretation of diffluence and vorticity association. Primarily, because of the variability of speed in the propagation of diffluence patterns and low-level vorticity. Furthermore, the translation speed varies for different tropical cyclones. Another reason is two hurricanes can occur very close temporally, which would make it difficult to separate out the peaks in diffluence for two different hurricanes and associate them with the development of low level vorticity. Therefore, compositing based on a fixed date (naming date or the date when the vorticity maxima left Africa) can be misleading or might average out the signal.
Therefore, we investigate each storm separately and find out the local peak in upper level diffluence before the local maxima in low level vorticity related to the storm (Table 2). Now, these values are calculated   Table 2 provides the values of temporally local maxima in low level vorticity, upper level diffluence and the time the peak in diffluence leads the vorticity maxima for each storm. It is observed that maxima in diffluence occurs almost 0-5 days prior to the peak in low level vorticity (except for Nicole). This table clearly points to a potential role of the upper level diffluence facilitating the further maturation of the low level vorticity to a major hurricane category.

Summary and Discussions
This work documents the close relationship of the occurrence of diffluence in the TEJ when it is exiting the west African coast preceding the cyclogenesis of the potential Category 4 and Category 5 Atlantic hurricanes. It is shown that of the 21 Category 4 and Category 5 hurricanes in the Atlantic between 2007-2017, 19 of them were preceded by significant diffluence in TEJ exiting the west African coast. 13 of them shows a peak in diffluence 3 days before the hurricane formed. A detailed examination for the case study of hurricane Irma of 2017 indicate that the peak in low level vorticity over eastern Atlantic was preceded by a maximum in diffluence at 200hPa.
We posit that under favorable conditions of warm SST, abundant mid-level moisture, the precursor of upper level diffluence provided sufficient positive forcing for the incipient low level vorticity to mature to Category 5 hurricane in the case of Irma.