Series distance – an intuitive metric to quantify hydrograph similarity in terms of occurrence, amplitude and timing of hydrological events

By Uwe Ehret, E. Zehe. 2011

86 citations recorded by the source corpus.

Abstract. Applying metrics to quantify the similarity or dissimilarity of hydrographs is a central task in hydrological modelling, used both in model calibration and the evaluation of simulations or forecasts. Motivated by the shortcomings of standard objective metrics such as the Root Mean Square Error (RMSE) or the Mean Absolute Peak Time Error (MAPTE) and the advantages of visual inspection as a powerful tool for simultaneous, case-specific and multi-criteria (yet subjective) evaluation, we propose a new objective metric termed Series Distance, which is in close accordance with visual evaluation. The Series Distance quantifies the similarity of two hydrographs neither in a time-aggregated nor in a point-by-point manner, but on the scale of hydrological events. It consists of three parts, namely a Threat Score which evaluates overall agreement of event occurrence, and the overall distance of matching observed and simulated events with respect to amplitude and timing. The novelty of the latter two is the way in which matching point pairs on the observed and simulated hydrographs are identified: not by equality in time (as is the case with the RMSE), but by the same relative position in matching segments (rise or recession) of the event, indicating the same underlying hydrological process. Thus, amplitude and timing errors are calculated simultaneously but separately, from point pairs that also match visually, considering complete events rather than only individual points (as is the case with MAPTE). Relative weights can freely be assigned to each component of the Series Distance, which allows (subjective) customization of the metric to various fields of application, but in a traceable way. Each of the three components of the Series Distance can be used in an aggregated or non-aggregated way, which makes the Series Distance a suitable tool for differentiated, process-based model diagnostics. After discussing the applicability of established time series metrics for hydrographs, we present the Series Distance theory, discuss its properties and compare it to those of standard metrics used in Hydrology, both at the example of simple, artificial hydrographs and an ensemble of realistic forecasts. The results suggest that the Series Distance quantifies the degree of similarity of two hydrographs in a way comparable to visual inspection, but in an objective, reproducible way.

Subfields: Global and Planetary Change, Water Science and Technology

View Paper: https://www.semanticscholar.org/paper/e334ef97ed2473a924ed71c6f99c69cf6a18e097

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Global and Planetary Change

In Water Science and Technology

Citations in the corpus

Comparing expert judgement and numerical criteria for hydrograph evaluation (2015, methodology): “Ehret and Zehe (2011) proposed the Series Distance criterion, in which they paired and compared the timing and amplitude of observed and simulated events on the rising and recession limbs of hydrographs separately using a regular mathematical criterion.”
Characterising performance of environmental models (2013, background): “In recent years, some authors have proposed a new family of visual performance measures that are based on attempts to mimic how the eye evaluates proximity between curves (Ewen, 2011; Ehret and Zehe, 2011).”
On typical range, sensitivity, and normalization of Mean Squared Error and Nash‐Sutcliffe Efficiency type metrics (2011, background): “Similarly, Ehret and Zehe [2011] point out that the MSE metric (and its various normalized forms) merges timing and bias errors into a single measure, which is problematic as these may have quite different practical impacts.”
From R-squared to coefficient of model accuracy for assessing "goodness-of-fits" (2020, methodology): “(2009), Ehret and Zehe (2011), Legates and McCabe (1999), and Legates and McCabe (2013)).”
Rating curve estimation under epistemic uncertainty (2015, methodology): “…in common with other ‘human-driven’ performance measures such as hydrograph evaluation measures that mimic visual interpretation of hydrograph fit (Ehret and Zehe, 2011; Ewen, 2011; Crochemore et al., 2014) and more broadly with the recognition that validation includes both objective and…”