Exploring the potential of transfer entropy for identifying similarity of catchment dynamics
Authors: Neri Mattia , Coulibaly Paulin , Toth Elena 
Published: March 2021

&lt;p&gt;Catchment classification is one of the essential steps for transferring information between similar watersheds, through the identification of the dominant hydrological processes and their main characteristics. The delineation of similar groups of basins is required for several regionalisation applications and how to assess the hydrological similarity generally depends on the specific purpose of the study and on the features to be regionalised. In some analyses, such as for example the regionalisation of rainfall-runoff models, the similarity should reflect the interaction between meteorological forcings and river streamflow time series, in particular at fine temporal scale, in order to reproduce the catchment behaviour in the rainfall-runoff transformation processes. Previous hydrological research has identified basins with similar meteorological forcings (i.e. similarity of climate) or with similar streamflow time-series (i.e. similarity of runoff response), but no studies have so far considered the interaction between the entire time-series of forcing data (e.g. precipitation) and streamflow, quantifying it through measures to be used as similarity metrics.&lt;/p&gt;&lt;p&gt;One of the approaches that may be applied for this purpose is the use of the concepts belonging to &lt;em&gt;information theory&lt;/em&gt;, that are based on the notion of &lt;em&gt;entropy&lt;/em&gt;, i.e. the content of information of a signal (as a time-series), or, in the multivariate case, the content of information shared between more variables. The present study proposes the use of a multi-variate entropy-based measure, the so-called&lt;em&gt; transfer entropy&lt;/em&gt;, a time-asymmetric quantity which analyses the interaction between different signals.&lt;/p&gt;&lt;p&gt;In this study, the concept of transfer entropy is applied for identifying the dominant hydrological processes occurring in a catchment, measuring the transfer of information from different meteorological forcings over the catchment (such as rainfall, snowmelt and evapotranspiration) to the corresponding streamflow time-series at the basin outlet. The resulting similarity measure is then used for grouping catchments with similar dynamics.&lt;/p&gt;&lt;p&gt;In a first step, the different amounts of information transferred from the meteorological forcing variables to observed runoff are estimated through the computation of the transfer entropy. The transfer entropy values are then used as signatures to characterise catchment dynamics, and a classification of the basins inside a study region is obtained assuming that similar values of transfer entropy for the considered forcing variables identify similar basins.&lt;/p&gt;&lt;p&gt;The methodology is tested for two study regions: the first is Austria, where a very densely-gauged set of catchments is available; the second is the conterminous US (CAMELS dataset), characterised by sparser gauging stations and a much higher hydroclimatic variability.&lt;/p&gt;&lt;p&gt;The outcomes of the approach are evaluated against a set of &amp;#8220;traditional&amp;#8221; catchment signatures, demonstrating the potential of transfer entropy as an additional promising instrument for assessing hydrological similarity and for quantifying the connection between different governing processes.&lt;/p&gt;