Exploring Hydrological Connections: A Threshold and Complex Network Based Approach&#160;
Authors: Nanda Aliva , Sen Sumit 
Published: March 2021

&lt;p&gt;The non-linear behaviour of soil moisture and rainfall influences the hillslope runoff generation mechanism and its thresholds. Inherent complexities of the hydrological processes at micro- to macro-scale hydrological systems need to be studied for identifying dominant connections. In this context, complex network theory is a beneficial tool to deal with all kinds of hydrological connections. To understand the practical implication of complex network theory and to explore out the runoff thresholds of infiltration-excess hillslope, we have selected two experimental hillslopes under two different landuse conditions i.e., agro-forested (AgF) and Grassed (GA) hillslopes. The hillslopes are situated at the Lesser Himalayan region of India. These are instrumented with ten soil moisture and water level sensors for capturing spatio-temporal variation of soil moisture and hillslope runoff at the outlet, respectively. After analyzing 59 rainfall events, we found that runoff generation in GA hillslope is significantly triggered when the 5-min peak rainfall intensity and initial soil moisture conditions exceed 50 mm/h and 0.25 m&lt;sup&gt;3&lt;/sup&gt;/m&lt;sup&gt;3&lt;/sup&gt;, respectively. The runoff generation in AgF hillslope is triggered when the 5-min peak rainfall intensity and initial soil moisture condition exceeds the mark of 12 mm/h and 0.20 m&lt;sup&gt;3&lt;/sup&gt;/m&lt;sup&gt;3&lt;/sup&gt;, accordingly. High intensity with very less duration event cannot generate any runoff at hillslope outlet; however, a low intensity with long duration (&gt; 15h) event could generate small runoff volume at both the hillslopes. After analyzing the runoff threshold, we used complex network theory to understand the connection between runoff and soil moisture for different runoff generating groups. Further, events having high rainfall intensity and high soil moisture condition show the more robust network connectivity between the runoff and the soil moisture points and moderate connectivity among the soil moisture stations. Primarily, in high-intensity events, the strongly connected soil moisture and the runoff nodes represents less runoff from that zone in an infiltration-excess dominated hillslope. The low-intensity rainfall of both the hillslope shows stronger network connectivity among the soil moisture, and the weak network connectivity between the runoff points and the soil moisture points as the events result in less runoff. Networks often contain clusters among the nodes and to measure the local density of these nodes, we calculated the global clustering coefficient (GCC). The GCC of all the selected events declines with an increase in correlation threshold (CT) values which indicate a decrease in network connectivity between the nodes for higher CT. For CT&amp;#8805; 0.8, the GCC values for the low-intensity events were higher than the high-intensity events, as the soil moisture networks are strong and dense during low-intensity events for high CT values. This study shows the first-time application of network theory to understand the linkage between network topology and hillslope runoff behaviour. However, we encourage the researchers to explore similar approaches in saturation-excess dominated hillslopes where the twining between soil moisture and runoff are different.&lt;/p&gt;