| Transit time distributions (TTD) offer a powerful tool for characterizing ‘lumped’ hydrologic
transport (i.e. with few parameters, and without resolving the internal dynamics), but their
general application for transport modeling has been hampered by the challenge of dealing
with time-variable TTD. A way forward has emerged with the development of
the ‘age function’ approach, but it has not been clear how to parameterize the age
function, or how to interpret it physically and compare it to perceptual models. It also
requires specification of the total storage, which is not possible in many cases of
interest.
This paper presents a more general formulation for TTD modeling that addresses these
limitations. Transport is parameterized in terms of a probability density function
Ω that represents the relative contribution of age-ranked water in storage to the
flux out. Other frameworks are shown to be a special case of this one if the total
storage is known. A new equation is obtained describing the time-evolution of the
TTD that does not require specification of the total storage. In fact, the storage can
be indefinitely large, allowing pdfs with semi-infinite support to parameterize Ω.
Classical equations for random-sampling (‘completely mixed’) and piston-flow type
transport fall out as special cases of Ω at steady-state. Other choices for Ω yield TTD
capable of replicating observed transport phenomena like heavy tails and fractal
1-f-noise. Application of the model to long term and high frequency passive tracer
datasets demonstrates its promise as a framework for new models of transport in
time-variable landscape hydrologic systems with a unique ability to capture these important
features. |