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

Abstract

Abstract: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.

Concentration–discharge relationships describe solute and sediment mobilization, reaction, and transport at event and longer timescales

“…Williams () described more complex hysteresis patterns including the “single loop plus line” and double‐looped “figure eight” patterns and evaluated the role of concentration and discharge timing, skewness, and spread in generating these complex hysteresis patterns. Zuecco, Penna, Borga, and Meerveld () also classified hysteresis patterns into single and multiloop categories but further distinguished within these groups based on the dominant hysteresis rotation in multiloop categories and the direction (positive or negative) of the predominant axis. Using these characteristics, they developed a quantitative index to assess event hysteresis dynamics (Zuecco et al, ).…”

“…Zuecco, Penna, Borga, and Meerveld () also classified hysteresis patterns into single and multiloop categories but further distinguished within these groups based on the dominant hysteresis rotation in multiloop categories and the direction (positive or negative) of the predominant axis. Using these characteristics, they developed a quantitative index to assess event hysteresis dynamics (Zuecco et al, ).…”

Canopy-scale biophysical controls of transpiration and evaporation in the Amazon Basin

“…Although λE T and λE E estimates are interdependent on g C and g A (as shown in , the figures reflect the credibility of the conductances as well as transpiration estimates by realistically capturing the hysteretic behavior between biophysical conductances and water vapor fluxes, which is frequently observed in natural ecosystems (Zhang et al, 2014;Renner et al, 2016) (also Zuecco et al, 2016). These results are also compliant with the theories postulated earlier from observations that the magnitude of hysteresis depends on the radiation-vapor pressure deficit time lag, while the soil moisture availability is a key factor modulating the hysteretic transpiration-vapor pressure deficit relation as soil moisture declines (Zhang et al, 2014;O'Grady et al, 1999;Jarvis and McNaughton, 1986).…”

Runoff generation in mountain catchments: long-term hydrological monitoring in the Rio Vauz Catchment, Italy

“…Indeed, several studies have reported hysteretic relations between streamflow and other variables, such as sediment (e.g., Lawler et al, 2006;Aich et al, 2014) and solute concentrations (e.g., Evans and Davies, 1998;Butturini et al, 2006;Aubert et al, 2013;Lloyd et al, 2016a), subsurface hillslope flow (e.g., McGuire and McDonnell, 2010), storage (e.g., Davies and Beven, 2015;Pfister et al, 2017) and groundwater levels (e.g., Allen et al, 2010;Fovet et al, 2015). In the last two decades, both the qualitative interpretation of hysteresis (e.g., Evans and Davies, 1998) and the application of quantitative metrics (e.g., Aich et al, 2014;Lloyd et al, 2016b;Zuecco et al, 2016) for the description of the loops improved the knowledge of the mechanisms triggering runoff generation and displacement of sediments and contaminants.…”