Onset and Withdrawal of Indian Monsoon as Phase Transition: A Climate Network Perspective

The onset of the Indian monsoon is associated with the northward migration of the Inter-Tropical Convergence Zone (ITCZ) from the southern tip of India, specifically over the state of Kerala. Therefore, the Indian Meteorological Department (IMD) defines the onset of the Southwest monsoon over India as the Monsoon onset over Kerala (MoK), which is also considered a large-scale onset over India. The MoK is based on three different criteria that should be satisfied after 10th May: (i) the amount of rainfall value at 14 locations in Kerala must be greater than or equal to 2.5 mm for two consecutive days, (ii) the presence of westerlies in the geographical region from the equator to 10^◦N & 55^◦E - 80^◦E upto 600 hPa with a zonal wind speed of the order of 10-15 knots at 925 hPa in the region 5^◦N - 10^◦N & 70^◦E - 80^◦E, and (iii) the Outgoing Longwave Radiation (OLR) should be below 200 Wm⁻² between 5^◦N - 10^◦N & 70^◦E - 75^◦E. However, the above definition is unable to capture the large-scale phenomena associated with the onset of the monsoon, especially the onset over Northeast India, which occurs prior to the MoK, which the IMD criteria does not account for. Further, this approach is not well suited to predict the local onset over different states in the country. However, the relationship of this large-scale onset with the local onsets throughout the Indian peninsula remains unclear. Therefore, it is essential to develop an objective methodology to predict both the local as well as large-scale onset of the Indian monsoon.

Using the framework of complex networks, we present the climatological progression of the onset and withdrawal of the Indian monsoon and unravel the association of large-scale onsets to the local-scale onsets across the Indian subcontinent. We consider the spatiotemporal precipitation data from the fifth-generation ECMWF atmospheric reanalysis dataset. The data has a spatial resolution of 0.25^◦ × 0.25^◦ and a daily temporal resolution. We compute the onset and withdrawal at each grid point over India using the daily cumulative precipitation anomaly, using the annual mean climatology over the past 83 years from 1940 to 2022. We construct time-varying spatial proximity complex networks where the geographical locations are nodes, and they are connected only if they are adjacent and have undergone onset simultaneously. We show that the Indian Monsoon undergoes a hybrid phase transition with two abrupt jumps associated with the onset of monsoon over Northeast India and Southwest India, followed by a continuous transition over North and Northwest India.

We study the spatiotemporal evolution of the connected components of the network. The characteristics of the components explain the spatiotemporal evolution of the Indian monsoon. The onset of the Indian monsoon occurs in fragments, which are small-scale onsets. As the monsoon progresses, these clusters coalesce to form large clusters, indicating the occurrence of large-scale onsets over the country. The formation of the largest connected component, the giant component (GC) of the network, marks the setting up of the monsoon over the entire India. The components over Northeast India
and Southwest India merge, eventually leading to an abrupt jump in the network phase diagram, indicating an abrupt phase transition. We then use the information of the size of the GC to identify the large-scale onset and withdrawal of the monsoon at different stages. We observe that the number of connected components decreases with an increase in average size as the monsoon peaks, signifying the presence of one large-scale dominant component responsible for the monsoon all over the country. During the withdrawal of the monsoon, the giant component breaks into different fragments across different regions, indicating that the monsoon has withdrawn on a large scale over those regions. We find that the monsoon starts to withdraw over East Rajasthan at a latitude of 29^◦ N.

The emergence of a giant component after the average degree of the network exceeds one is reminiscent of a phase transition. We find that during the onset phase, the fraction of nodes in the giant component increases abruptly with the average degree of the network in two stages: (i) the first jump is associated with the large-scale onset over Northeast India when the components over the Bay of Bengal and Myanmar merge with the small components over Northeast India and (ii) the second abrupt jump corresponds to merging of components from Northeast and Southwest India, after which we find that there is a continuous increase in the size of the GC over North and Northwest India indicating a continuous phase transition. We use the difference in the node fraction of the GC to determine the large-scale onset and withdrawal over various regions in the grid over India.