Large-scale patterns of small-scale vorticity interactions foster moist convection during cyclogenesis

TL;DR

This study analyzes how small-scale vorticity interactions organize into large-scale patterns during cyclogenesis in the Bay of Bengal using time-varying spatial-proximity networks derived from 850 hPa relative vorticity. It links emergent large-scale coherence with organized moist convection, showing sustained CAPE/CI coupling within patches of high vorticity connectivity that distinguish developing from non-developing depressions. Through Katz-based communicability, the work identifies how local coherence propagates via large-scale broadcast/receiving modes, a moisture-feedback-driven percolation mechanism that expands coherent regions ahead of cyclone formation. The findings propose a criterion to predict cyclone development and reveal a multiscale, emergent process that connects sub-meso vorticity dynamics to synoptic-scale organization, with implications for improving cyclogenesis prediction.

Abstract

The formation and intensification of a tropical cyclone is a complex phenomenon involving several feedback interactions between momentum and energetics of the storm, and across multiple spatio-temporal scales. Background vorticity interactions in the turbulent atmosphere play a crucial role in the formation of cyclones. How these vorticity interactions lead to convective organization and sustain a disastrous cyclonic vortex amidst a turbulent atmosphere remains elusive. Moreover, what processes distinguish depressions that develop into a cyclone from those that do not? Here, we investigate the role of small-scale vorticity interactions in the background flow in sustaining large-scale organization during the emergence of a cyclone. We construct time-varying complex networks where geographical locations are nodes and connections between nodes represent short-time vorticity correlations. Only those nodes are connected that are in spatial proximity corresponding to sub-meso length scales. Each network is constructed for 29 hours of data; consecutive networks are separated by three hours, thus revealing the evolution of local coherence in vorticity dynamics. We discover that small-scale vorticity interactions manifest as large-scale emergent patterns. Further, we establish that organized moist convection is significantly correlated to regions of locally coherent vorticity dynamics during the intensification of a depression that forms a cyclone; however, such correlations are not sustained during non-developing cases. Using modal analysis of time-evolving network connectivity, we show that these large-scale patterns are essentially large-scale modes of propagation of coherence in small-scale vorticity dynamics. We explain that such propagation is facilitated by moisture feedback at small-scales and self-organized patterns at large-scales.

Figures (11)

• Figure 1: Diagram representing (a) the horizontal and (b) the vertical spatial extents (not to scale) of tropical cyclones as compared to easterly waves, mesoscale convective systems (MCS), and low-level convective vortices associated with lower tropospheric cloud-generated vorticity. Extreme convection zones can form within an MCS. A tropical cyclone is $> 500$ km in diameter and spans from sea surface to troposphere ($\sim 12$ km in height). (c) A schematic flow chart showing the various thermo-fluid feedback interactions that sustain and foster genesis and intensification of tropical cyclones (Appendix). (d) A diagrammatic representation of interdependence between the pattern of organized convection, and thermo-fluid feedback interactions including radiative cooling in regions of dry subsidence, moist air thermodynamics and convergence of rotating moist air. A tropical cyclone is essentially a self-sustained and intensified pattern of organized convection.
• Figure 2: A schematic showing the method for the construction of time-evolving spatial-proximity networks. A network is a set of nodes connected by links; here, geographical locations are nodes and links represent statistical relation between the relative vorticity dynamics at the two nodes. Two consecutive network time frames are indicated on a representative time series plot of relative vorticity ($\omega$). Networks $k$ and $k+1$ are separated by a period of three hours and each network is constructed for a period of $29$ hours. Representative spatial variation of $\omega$ is shown in the left panel. The network is constructed in the entire spatial domain ($-5^\circ$ to $35^\circ$ N and $75^\circ$ to $110^\circ$ E) and the results from the network connectivity are analyzed in a smaller domain ($0^\circ$ to $30^\circ$ N and $80^\circ$ to $105^\circ$ E) indicated by the box drawn with red dashed line. During one network time-frame, the weight of the link between nodes $i$ and $j$ is equal to the maximum value of short-window delayed correlation between the $29$-hour time series of relative vorticity ($\omega$) with a maximum time delay of $5$ hours. A link is established between nodes $i$ and $j$ only if the value of correlation is statistically significant ($>99$ percentile of random surrogate correlations) and both nodes are in a spatial proximity of less than $2^\circ$ in latitude and longitude. Hence, we establish links that represent local vorticity interactions between neighboring locations, and examine if patterns emerge at much larger scales.
• Figure 3: (a-l) Spatial distribution of node strengths $NS$ obtained from the network analysis prior to the formation of tropical cyclone Amphan (2020) during time-frame $k$, overlapped with contour lines representing isolines of relative vorticity ($\omega$) averaged over 29-hour period during the time-frame $k$. The time periods and network frame number ($k$) are mentioned in the title of each subplot (date/month (hrs) format). Strong positive and negative $\omega$ are represented by red and blue lines respectively, while black contours represent regions of weak vorticity. The term 'weak vorticity' should not be confused with negligible vorticity fluctuations; instead the term here refers to the vorticity perturbations that are weak relative to the strength of the much stronger vorticity around the low pressure anomaly. Patches of high node strengths appear to be arranged in a large-scale pattern that evolves with $k$. The trajectory of cyclone Amphan (2020) is represented by black dots beginning from the tropical depression state identified by IMD on 16/05 (00 hrs). Larger red dots along the trajectory represent the location of cyclone Amphan during that time-frame. We can also visualize the large-scale pattern evolving over consecutive network time-frames (i.e., every three hours, see animations in supplementary).
• Figure 4: (a) Temporal variation of the spatial average of vorticity strength ($\langle\omega\rangle$) and node strength ($\langle NS \rangle$) during each network time-frame. (b) Overall spatially averaged intensity ($\langle CAPE\rangle$), and fractional intensity ( $\langle CAPE \rangle _{HNS}/\langle CAPE\rangle$) of convection potential. (c) Overall spatially averaged intensity ($\langle CI\rangle$), and fractional intensity of convection inhibition ( $\langle CI \rangle _{HNS}/\langle CI\rangle$). Subscript $HNS$ represents spatial average over regions of high node strengths where $NS>15$. (d) Variations of the number density of locations, $f_{CAPE,NS}$ where $NS>15$ and $CAPE>900$ J/kg, and $f_{CI,NS}$ where $NS>15$ and $CI>200$ J/kg. Subplots (a-d) are for cyclone Amphan; abscissa demarcates time relative to the critical time $t_{cr}$ at which a depression is identified (indicated by a dashed line at zero). The second dashed line indicates the time when the cyclone intensity began weakening. (e) Spearman rank correlation ($\rho_s$) between $f_{CAPE,NS}$ and $f_{CI,NS}$ for various developing and non-developing cases during time periods, (i) $P_1=[t_{cr}-60, t_{cr}]$ hrs, and (ii) $P_2=[t_{cr}-30, t_{cr}+72]$ hrs.
• Figure 5: Simultaneous evolution of node strengths ($NS$) obtained from vorticity correlation networks, and 29-hour average of convective available potential energy (CAPE, contours) and regions of strong convective inhibition (CI, marked by magenta dots) during the (a-j) formation of an identifiable tropical depression, and (k-p) its intensification to form cyclone Amphan and subsequent dissipation. The 29-hour average of CAPE and CI are taken corresponding to the network time-frame indicated in each subplot (date/month (hrs) format). Also, the spatial contours of CAPE do not vary much during cyclogenesis, evident in subplots (a-l). Initially, regions of strong CI are spread in northern and central BoB (see patches of red dots in (a-d)). Also, CI reduces in central BoB during cyclogenesis (compare (a-d) to (e-l)), and increases in the wake of the cyclone during its intensification (m-p). Some patches of high node strength are associated with high CAPE and some with high CI during each network time-frame. Some patches of coherent vorticity dynamics initially appear near the boundaries between strong and weak CI; for example, see patches in northern and central BoB region in (a-c). Subsequently, we observe that CI weakens in these regions where CI and $NS$ were simultaneously high (compare CI along patches around $10^\circ$N and $85^\circ$E in central BoB region in (a-e)).