A versatile index to characterize hysteresis between hydrological variables at the runoff event timescale

This study presents a versatile index for the quantification of hysteretic loops between hydrological variables at the runoff event timescale. The conceptual development of the index is based on a normalization of the input data and the computation of definite integrals at fixed intervals of the independent variable. The sum, the minimum and the maximum of the differences between integrals computed for the rising and the falling curves provide information on the direction, the shape and the extent of the loop. The index was tested with synthetic data and field data from experimental catchments in Northern Italy. Hysteretic relations between streamflow (the independent variable) and soil moisture, depth to water table, isotopic composition and electrical conductivity of stream water (dependent variables) were correctly identified and quantified by the index. The objective quantification of hysteresis by the index allows for the automatic classification of hysteretic loops and thus the determination of differences in hydrological responses during different events. The index was also used to examine the seasonal dynamics in the relation between streamflow and soil moisture and captured the switch in the direction of the loop with changes in event size and antecedent wetness conditions. The sensitivity of the index to the temporal resolution of the measurements and measurement errors was also tested. The index can successfully quantify hysteresis, except for very noisy data or when the temporal resolution of the measurements is not well suited to study hysteresis between the variables.