A MATLAB toolbox for the quantification of the discharge-sediment hysteresis process

Understanding the coupling between river discharge (Q) and suspended sediment concentration (SSC) is fundamental for understanding erosion, sediment connectivity, and sediment sources in a fluvial system. While direct correlation via rating curves provides a first-order approximation of the discharge-sediment relationship, it cannot capture the non-linear response of SSC to changes in Q during a hydrological event or on an annual timescale. Hysteresis process, i.e., the difference in SSC for a given Q during rising and falling limbs, is utilized for characterizing such nonlinearities in the Q and SSC relationship. While Hysteresis Loop (HL) is the graphical representation of the Q-SSC relationship, Hysteresis Index (HI) is the quantitative measure of the broadness of HL. HL and HI are frequently used to understand the time lags, sediment sources, and sediment transport capacity within river reaches. Several approaches to HI quantification are present in the literature, indicating methodological variability and data normalization techniques, whereas a systematic comparison is still required to understand the applicability of each model for specific research problems. This work presents a comprehensive review of major methodologies for calculating HI from Q and SSC data for different timescales. We employed daily Q and SSC data from the Monsoon-dominated Peninsular Indian region and Moravian-Silesian Region. Further, we used high-resolution (15-minute) Q and SSC data from the Rio Cordon catchment in the Eastern Italian Alps. The daily Q and SSC values were aggregated into mean monthly values to observe the annual-scale hysteresis patterns in Peninsular India. We developed a MATLAB toolbox, ‘Hysteresis Index Toolbox (HyInd)’, to standardize the normalization technique, rising and falling limb separation for hydrological events, and data visualization. The toolbox currently features six methods for HI calculation, which are suitable for all time scales (sub-daily, daily, or monthly). Our results suggest that data normalization is crucial for comparing sediment transport dynamics across drainage basins with varying drainage areas. Furthermore, our results also imply that quantification of the normalized area inside the HL presents the most robust result for simple to complex hysteresis processes. We also carried out sensitivity analyses to assess the influence of data noise on the quantification of HI. While sub-daily Q and SSC data inherently contain noise, we introduced stochastic perturbations into the daily and monthly average datasets. We observed that most existing HI calculation methods are not significantly affected by random noise. This study elucidates the strengths and weaknesses of each HI calculation method and provides practical guidance for selecting the proper model. Although the HyInd toolbox is primarily designed to understand the discharge-sediment hysteresis process, it can also be used to quantify hysteresis in other environmental parameters, i.e., soil moisture or water quality.