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

Recent virtual and experimental investigations have shown that the young water fraction F-yw (i.e. the proportion of catchment outflow younger than circa 2-3 months) increases with discharge in most catchments. The discharge sensitivity of F-yw has been defined as the rate of increase in F-yw with increasing discharge (Q) and has been estimated by the linear regression slope between F-yw and Q, hereafter called DS(Q). The combined use of both metrics, F-yw 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 F-yw 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: F-yw 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 that expresses how F-yw varies with discharge. The exponential parameter (S-d) approximates DS(Q) at moderate discharges where F-yw is well below 1; however, the exponential equation and its discharge sensitivity metric better capture the non-linear relationship between F-yw and Q and are robust with respect to changes in the range of sampled discharges, allowing comparisons between catchments with strongly contrasting flow regimes.