the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note: Hydrograph separation: How physically based is recursive digital filtering?
- University of Applied Sciences Weihenstephan-Triesdorf, Weidenbach, 91746, Germany
- University of Applied Sciences Weihenstephan-Triesdorf, Weidenbach, 91746, Germany
Abstract. Recursive digital filtering of hydrographs is a widely used method to identify the groundwater-borne portion of streamflow. In this context, a distinction is often made between physically based and non-physically based algorithms. The algorithm of Furey and Gupta (2001), for example, is counted among the former. In this paper, it is contrasted with the algorithm of Eckhardt (2005). This algorithm represents a whole class of recursive digital filters based on the assumption that the aquifer is a linear reservoir. It is shown that the algorithm of Eckhardt (2005) is not merely a low-pass filter, but that it is largely identical to the aforementioned physically based algorithm of Furey and Gupta (2001). The algorithm of Eckhardt (2005) differs from the algorithm of Furey and Gupta (2001) only in the time delay assumed between precipitation and the exfiltration of groundwater into surface waters, and in the fact that two parameters are combined into one, BFImax. This parameter can thus be interpreted physically and an approach for its calculation emerges.
Klaus Eckhardt
Status: open (until 10 Aug 2022)
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CC1: 'Comment on hess-2022-186', Keith Beven, 23 Jun 2022
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A very long time ago (in 1991) I published a review of hydrograph separation methods. The review had been requested for a meeting of the British Hydrological Society. It included a section on Choosing a Hydrograph Seperation method. That section consisted of a single word: "Don't." The reason for that was mostly to avoid the types of problems represented by this paper - particularly the inference that some mathematical filter can be used to decide what is groundwater or not. The author appears to think that baseflow and groundwater are equivalent. This is particularly ironic when he references the use of tracer information to support the lack of a time delay in his own function on the basis that tracers show that there can be "a rapid release of so-called pre-event-water". But just why should that pre-event water be baseflow (or groundwater)? The tracer data generally undermine the whole idea of baseflow separation. To suggest that something might be physically-based by comparing one mathematical function to another mathematical function based on a linear store is surely naive at best, and downright misleading at worst. We might perhaps want to use a consistent mathematical filter to produce some "baseflow index" as a characteristic of catchment response but please do not relate it to any superficial process interpretation. Better still, please do not choose a baseflow separation method at all but try to understand the actual processes of catchment response.
Reference.
Beven, K.J. (1991), Hydrograph Separation?, Proc.BHS Third National Hydrology Symposium, Institute of Hydrology, Wallingford, 3.1-3.8.
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AC1: 'Reply on CC1', Klaus Eckhardt, 28 Jun 2022
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Keith Beven writes that the point of this article is to "to suggest that something might be physically-based by comparing one mathematical function to another mathematical function". Apparently, he does not concede the approach of Furey and Gupta (2001) to be physically based. I see it differently. In my view, their algorithm is physically based. One can argue about how accurate the physical basis is. However, a fundamental debate on whether hydrograph separation is useful or not goes far beyond the purpose of this technical note. There are, after all, a variety of methods of hydrograph separation and they are used. For more than four decades, recursive digital filtering has been one of them. The present contribution thus does exactly what HESS associates with a technical note: "Technical notes report [...] novel aspects of [...] theoretical methods and techniques which are relevant for scientific investigations within the journal scope." (https://www.hydrology-and-earth-system-sciences.net/about/manuscript_types.html).
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CC2: 'Reply on AC1', Keith Beven, 28 Jun 2022
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OK, I will accept the argument that physically-based can be defined in terms of mathematics derived from explicit assumptions and you are certainly correct about the technical note. I am not in any way disputing that, only the utility of such analyses. The danger, as ever, is thinking that those assumptions represent the actual physics of the catchments we are interested in, as you seem to do when you equate baseflow and groundwater, and when you invoke tracer evidence for fast groundwater responses when surely that very information suggests that contributions of pre-event water are quite different from baseflow defined by those mathematics. That therefore suggests to me that the assumptions of the mathematics are wrong in terms of being a physically-based description of the actual processes. So create a baseflow index if you wish, but please do not call it groundwater (or even better, explicitly differentiate them to avoid others making a similar false equivalence).
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CC2: 'Reply on AC1', Keith Beven, 28 Jun 2022
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AC1: 'Reply on CC1', Klaus Eckhardt, 28 Jun 2022
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Klaus Eckhardt
Klaus Eckhardt
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