Streambeds are critical hydrological interfaces: their physical properties regulate the rate, timing, and location of fluxes between aquifers and streams. Streambed vertical hydraulic conductivity (K v) is a key parameter in watershed models, so understanding its spatial variability and uncertainty is essential to accurately predicting how stresses and environmental signals propagate through the hydrologic system. Most distributed modeling studies use generalized K v estimates from column experiments or grain-size distribution, but K v may include a wide range of orders of magnitude for a given particle size group. Thus, precisely predicting K v spatially has remained conceptual, experimental, and/or poorly constrained. This usually leads to increased uncertainty in modeling results. There is a need to shift focus from scaling up pore-scale column experiments to watershed dimensions by proposing a new kind of approach that can apply to a whole watershed while incorporating spatial variability of complex hydrological processes. Here we present a new approach, Multi-Stemmed Nested Funnel (MSNF), to develop pedo-transfer functions (PTFs) capable of simulating the effects of complex sediment routing on K v variability across multiple stream orders in Frenchman Creek watershed, USA. We find that using the product of K v and drainage area as a response variable reduces the fuzziness in selecting the "best" PTF. We propose that the PTF can be used in predicting the ranges of K v values across multiple stream orders. Water scarcity is among the most pressing issues to humanity. Intensive water consumption, driven by a growing population and changing climate, places the world's limited water supplies under increasing pressure. These stresses often propagate throughout a hydrologic system, because streams, rivers, and lakes are connected to underlying aquifers. For these reasons, the interaction between groundwater and surface water is of much interest to water managers. The water exchange or interaction pattern depends on substrate permeability 1-4. K v is one of the major parameters controlling stream-aquifer interactions. There are several reach-scale and watershed-scale variables which influence the spatial variation and distribution of K v along and across stream reaches. These factors can be geological, hydrological, anthropogenic, or biological 5-11. Some geologic factors that mostly influence streambed K v are sediment particle size, underlying geology, heterogeneity of the substratum, thickness of bed material, channel geometry, hydraulic radius variations, and roughness due to natural and anthropogenic alterations 8. In hydrological modeling studies, homogeneity of K v is usually assumed for practical reasons even though it may lead to more uncertainty in streamflow modeling 12,13. Since it is not practical to measure K v at every location along a stream course, modelers often rely on literature values or few measurements, and assume K v does not vary across the watershed. Owing to lack of detailed information ab...
