Technical note: An improved discharge sensitivity metric for young water fractions

Abstract

Abstract. Recent virtual and experimental investigations have shown that the young water fraction Fyw (i.e. the proportion of catchment outflow younger than circa 2–3 months) increases with discharge in most catchments. The discharge sensitivity of Fyw has been defined as the rate of increase in Fyw with increasing discharge (Q), and has been estimated by the linear regression slope between Fyw and Q, hereafter called DS(Q). The combined use of both metrics, Fyw and DS(Q), provides a promising method for catchment inter-comparison studies that seek to understand streamflow generation processes. Here we explore the discharge sensitivity of Fyw in the intensively sampled small Mediterranean research catchment Can Vila. Intensive sampling of high flows at Can Vila allows young water fractions to be estimated for the far upper tail of the flow frequency distribution. These young water fractions converge toward 1 at the highest flows, illustrating a conceptual limitation in the linear regression method for estimating DS(Q) as a metric of discharge sensitivity: Fyw cannot grow with discharge indefinitely, since the fraction of young water in discharge can never be larger than 1. Here we propose to quantify discharge sensitivity by the parameter of an exponential-type equation expressing how Fyw varies with discharge. The exponential parameter (Sd) approximates DS(Q) at moderate discharges where Fyw is well below 1; however, the exponential equation and its discharge sensitivity metric better capture the non-linear relationship between Fyw and Q and are robust with respect to changes in the range of sampled discharges, allowing comparisons between catchments with strongly contrasting flow regimes.

Investigating young water fractions in a small Mediterranean mountain catchment: Both precipitation forcing and sampling frequency matter

“…First, we estimated F yw for different quantiles of the flow regime (similar to Figure 7 in von Freyberg et al, 2018). Second, we assumed that F yw was not a fixed value but that it increased with discharge up to a limit value of 1, following an exponential-type equation (Gallart et al ., 2019):…”

“…where F 0 (1) is the Y-intercept or virtualF yw for Q =0 and S d (unit of Q -1 ) is the discharge sensitivity metric. These metrics can be obtained by non-linear fitting of the equation (Gallart et al ., 2019):…”

“…2016;Lutz et al , 2018). Nevertheless,F yw is basically non-stationary and climate factors seem to overwhelm catchment physiographic characteristics:F yw is known to usually increase with stream discharge due to the activation of faster flow paths when the wetness of the catchment increases (Kirchner 2016a, b;von Freyberg et al , 2018;Gallart et al, 2019).…”

Investigating young water fractions in a small Mediterranean mountain catchment: both precipitation forcing and sampling frequency matter

“…First, we estimated F yw for different quantiles of the flow regime (similar to Figure 7 in von Freyberg et al, 2018). Second, we assumed that F yw was not a fixed value but that it increased with discharge up to a limit value of 1, following an exponential-type equation (Gallart et al ., 2019):…”

Technical Note: Revisiting the Procedure for Quantification of the Young Water Fraction Based on Seasonal Tracer Cycles

“…One of the challenges when using Fyw estimated from the seasonal tracer concentrations in precipitation and streamflow using the procedure proposed by Kirchner (2016) is that the estimated τyw will vary between catchments depending on the actual shape of the TTD. Still, the actual τyw values are often not reported in inter-catchment comparisons using Fyw (Gallart, von Freyberg, et al, 2020;Lutz et al, 2018;von Freyberg et al, 2018). Therefore, it is unclear how we can evaluate the effects of climate and catchment properties on Fyw among catchments if they correspond to different τyw values.…”