Does age matter? Controls on the spatial organization of age and life expectancy in hillslopes, and implications for transport parameterization using rSAS

Hillslopes have been extensively explored as a natural fundamental unit for spatially-integrated hydrologic models. Much of this attention has focused on their use in predicting the quantity of discharge, but hillslope-based models can potentially be used to predict the composition of discharge (in terms of age and chemistry) if they can be parameterized terms of measurable physical properties. Here we present advances in the use of rank StorAge Selection (rSAS) functions to parameterize transport through hillslopes. These functions provide a mapping between the distribution of water ages in storage and in outfluxes in terms of a probability distribution over storage. It has previously been shown that rSAS functions are related to the relative partitioning and arrangement of flow pathways (and variabilities in that arrangement), while separating out the effect of changes in the overall rate of fluxes in and out. This suggests that rSAS functions should have a connection to the internal organization of flow paths in a hillslope.Using a combination of numerical modeling and theoretical analysis we examined: first, the controls of physical properties on internal spatial organization of age (time since entry), life expectancy (time to exit), and the emergent transit time distribution and rSAS functions; second, the possible parameterization of the rSAS function using the physical properties. The numerical modeling results showed the clear dependence of the rSAS function forms on the physical properties and relations between the internal organization and the rSAS functions. For the different rates of the exponential saturated hydraulic conductivity decline with depth the spatial organization of life expectancy varied dramatically and determined the rSAS function forms, while the organizaiton of the age showed less qualitative differences. Analytical solutions predicting this spatial organization and the resulting rSAS function were derived for simplified systems. These analytical solutions were used to examine basic relationships among physical properties, the internal organization, and the rSAS function. This examination showed that it is possible in principle to parameterize the rSAS function from physically measurable parameters, at least for idealized hillslopes.