Climate-catchment-soil control on hydrological droughts in peninsular India

Most land surface system models and observational assessments ignore detailed soil characteristics while describing the drought attributes such as growth, duration, recovery, and the termination rate of the event. With the national-scale digital soil maps available for India, we assessed the climate-catchment-soil nexus using daily observed streamflow records from 98 sites in tropical rain-dominated catchments of peninsular India (8–25° N, 72–86° E). Results indicated that climate-catchment-soil properties may control hydrological drought attributes to the tune of 14–70%. While terrain features are dominant drivers for drought growth, contributing around 50% variability, soil attributes contribute ~ 71.5% variability in drought duration. Finally, soil and climatic factors together control the resilience and termination rate. The most relevant climate characteristics are potential evapotranspiration, soil moisture, rainfall, and temperature; temperature and soil moisture are dominant controls for streamflow drought resilience. Among different soil properties, soil organic carbon (SOC) stock could resist drought propagation, despite low-carbon soils across the Indian subcontinent. The findings highlight the need for accounting feedback among climate, soil, and topographical properties in catchment-scale drought propagations.


SI. 1.1 Determination of Seasonality in Drought Termination
The termination date of each drought event is plotted on the circle with unit radius, where the position of the event is defined by θi where T is the number of days in the year, D is the termination date which varies from 1 to 365 days in a non-leap year (366 days in a leap year), The position of the mean termination date can be determined using the angles, converting it to x and y coordinates: where qi = Deficit volume for the event 'i' The mean direction of the circular Data ( η ) is determined as: Mean Event Date can be calculated as: Where ω is the mean date of occurrence of the extreme events and η is computed using Eq. and φ =1 if all the events are terminating in the same month (high regularity) The variability in timing of drought termination is determined using circular variance (s 2 ):

SI 1.2 Drought Cluster Identification using Fuzzy Algorithm
Fuzzy C-means (FCM) algorithm was firstly proposed by which was further improved 1,2 . The FCM algorithm assigns the membership to each feature vector with respect to the euclidean distance between the feature vector and cluster center, and it is more generalized and useful to describe a point not by a hard clustering, but by its membership values with respect to all the clusters 3 . The higher the value of fuzzy membership stronger is the relationship of the feature vector with the specific cluster 4 . For a data set of M objects and p classes, if Xk is the feature vector of the k th object, where k = 1,2, 3…., M, the main aim of the FCM algorithm is to minimize the objective function as defined below: Where, uik is the membership value of k th data point in the i th cluster, ‖Yk−Ci‖ 2 is the Euclidean distance between feature vector k and a center point of i th cluster, Ci is the center value of the i th cluster and α is called as fuzzifier value, which can have any value which is greater than 1.
The value closer to 1 provides the cluster solution which is very similar to hard clustering (e.g., K-means clustering) algorithm. In general, fuzzifier value ranges from 1 to 2.5 5 .

Fuzzy c-means Algorithm Steps:
1. The number of clusters and the data vector of the cluster center is assumed at random.

Membership value matrix is calculated using
Where i= 1,2,…...c, k=1,2,…,M. j = 1,2.,….c 3. Using the updated membership values and equation, new values for the cluster center are calculated as below: Finally, the clustering process is stopped when it follows a certain stopping criterion. For our case, we stopped the clustering process when two successive iterations reached a value of objective function less than 0.001.         Table S1 with four different stages of drought namely; growth, duration, recovery and drought termination rate. The crosses show the significant correlation between the variables at 10% significance level. The figure is prepared in MATLAB R2020b (academic version) [Software].