The shape of the active length vs streamflow relation in temporary streams

River networks are not static entities, as they dynamically respond to the time-variant climatic conditions in the surrounding landscape. Over time, rivers change in both the streamflow Q, as the hydrograph continuously peaks and recedes, and active length L, as the temporary (i.e. non perennial) reaches wet up and dry down. As such, a correlation between L and Q has long been recognized in literature, starting with the first empirical studies dating back to 1968. More recently, a few conceptual frameworks have attempted to explain the physical processes that relate L with Q, showing how the shape of the L(Q) relation is determined by the spatial distribution of the subsurface transport capacity along the network (i.e. the maximum specific flow by unit contributing area delivered downstream in the hyporheic region). Knowing the functional form of the L(Q) relation can be useful in a number of ways, including the following: a) it creates a link between the temporal dynamics of L and Q, allowing one to exploit widely available streamflow datasets to study temporary streams; b) it gives information on invisible subsurface properties of the hyporheic zone; and c) it may provide more reliable predictions of the configuration of the active portion of the network during hydrological conditions that have not been observed yet.

In this contribution, we studied the shape of the L(Q) relation in 45 different catchments around the world, spanning a wide range of climates, geology, morphology, and catchment area. We found that L(Q) relations can be split in 3 main categories: a) generally increasing relations, b) relations showing a plateau for the higher values of Q due to the presence of a maximum potential network that can't be exceeded, and c) relations with a sigmoid shape, when the network length is constant for the driest hydrological conditions e.g. because it is fed by a local perennial source. We speculate that, in most cases, the presence of a plateau or sigmoid shape might not be visible in the data due to the limited number of observations for the relevant high and low flow conditions. For each catchment we also tested different functional forms for the L(Q) relation and selected 3 analytical forms that are best suited to fit the available data (exponential, gamma, power-law). The power law generally performed reasonably well, even though it overestimated L for the largest values of Q in those cases in which a maximum potential wet network is observed. In most cases, the exponential distribution described the plateau quite well but has a reduced performance for the lower flowrates. The gamma distribution, instead, shows the best performance in describing L(Q) relations in all categories. The proposed contribution aims at identifying new general patterns common to all temporary streams, creating new modelling tools that enable large scale studies and giving new tools for the effective monitoring of dynamic river networks.