Application of a new formulation for hydrologic transport using time-variable transit time distributions (Lina Stein)


The time that it takes a drop of water to travel from recharge to discharge areas – its transit time - is an important hydrological characteristic. It can be used e.g. to classify catchments according to its ability to degrade environmental pollutants (which is linked with the water residence time in a catchment) or as an estimate for the climate sensitivity of storage. However, the pathways that a drop of water can take are potentially infinite. To represent this multitude of paths, hydrologists apply “transit time distributions” (TTD) - a concept similar to a tracer breakthrough curve – to represent the spatially complex network of flow paths in the catchment. With TTDs, we map temporally variable climatic inputs (precipitation) to outputs (discharge). The challenge is to capture the catchment’s complexity in a simple, parsimonious distribution that distills the essential transport behavior.

Aims of the thesis

A new theoretical framework for modelling transport using transit time distributions has recently been suggested as a way forward. This framework introduces time variable transit time distributions that change its properties and parameters over time. Previous frameworks run under the assumption of time-invariance. This project would involve applying this new framework to datasets collected and applied for preceding modeling studies, and to evaluate its performance under different boundary conditions.


The new modeling framework will be provided in python or in C++ with an R interface. Similarly, datasets from different modeling studies will be provided ready-for-application. The student's task will be the application of the new framwork to the datasets, an evaluation of the obtained simulations, and a comparizon to the preceding modeling studies.


Andreas Hartmann, Benedikt Heudorfer, Ciaran Harman (Johns Hopkins University, USA)

Special notes

A visit to the second advisor at John Hopkins University is possible and support when applying for external travel funding (DAAD, International Office, Freunde der Universität, Förderverein, or similar) will be provided by Andreas Hartmann.

Recorded lectures from last year’s summer workshop about time-variant transit time distributions can provide an easy access to the topic.


Application of a novel modeling framework that has the potential to signficantly change the way hydrologic transport models are developed and applied.




Harman, C. J., and M. Kim (2014), An efficient tracer test for time-variable transit time distributions in periodic hydrodynamic systems, Geophys. Res. Lett.,41, 1567–1575.

Harman, C. J. (2015), Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed, Water Resour. Res., 51, 1–30.

van der Velde, Y., P. J. J. F. Torfs, S. E. A. T. M. van der Zee, and R. Uijlenhoet (2012), Quantifying catchment-scale mixing and its effect on time-varying travel time distributions, Water Resources Research, 48(6).10.1029/2011wr011310

Harman, C. (2014), Modeling unsteady lumped transport with time-varying transit time distributions, Geophysical Research Abstracts, Vol. 16, EGU2014-15510

Possible data sets:

Hartmann, A., J. A. Barberá, J. Lange, B. Andreo, and M. Weiler (2013), Progress in the hydrologic simulation of time variant recharge areas of karst systems – exemplified at a karst spring in Southern Spain, Advances in Water Resources, 54, 149-160.10.1016/j.advwatres.2013.01.010

Hartmann, A., T. Wagener, A. Rimmer, J. Lange, H. Brielmann, and M. Weiler (2013), Testing the realism of model structures to identify karst system processes using water quality and quantity signatures, Water Resources Research, 49, 3345–3358.10.1002/wrcr.20229

thesis/omegamodel.txt · Zuletzt geändert: 2016/11/01 09:43 von mweiler