Abstract
Abstract. This technical note deals with the mathematical representation of concentration–discharge relationships. We propose a two-sided affine power scaling relationship (2S-APS) as an alternative to the classic one-sided power scaling relationship (commonly known as “power law”). We also discuss the identification of the parameters of the proposed relationship, using an appropriate numerical criterion. The application of 2S-APS to the high-frequency chemical time series of the Orgeval-ORACLE observatory is presented here (in calibration and validation mode): it yields better results for several solutes and for electrical conductivity in comparison with the power law relationship.
Highlights
The relationship between solute concentrations and river discharge is an age-old topic in hydrology
This technical note presents a two-sided affine power scaling relationship that can be seen as a generalization of the power law
As our main objective in this note is to compare the performance of two relationships, we divided our dataset into two parts to perform a split-sample test (Klemeš, 1986): we used June 2015 to July
Summary
The relationship between solute concentrations and river discharge ( on “C–Q relationship”) is an age-old topic in hydrology (see among others Durum, 1953; Hem, 1948; Lenz and Sawyer, 1944). Many complex models have been proposed to represent C–Q relationships, from the tracer mass balance (e.g., Minaudo et al, 2019) to the multiple regression methods (e.g., Hirsch et al, 2010). Moatar et al (2017) present an extensive typology of shapes (in log–log space) for the French national water quality database, which shows that the power law must be modified to represent the C–Q relationship for dissolved components as well as for particulate-bound elements. This technical note presents a two-sided affine power scaling relationship (named “2S-APS”) that can be seen as a generalization of the power law. We do not wish to claim that it can be universally applicable, we argue here that it allows for a better description and modeling of the C–Q relationship of some solutes as a natural extension of the power law
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