Friday, April 5, 2024

A series of talks and material on Transit (Travel) time, Residence time and Response Time

Here below we started a little series of lectures about a statistical way of seeing water movements in catchments that, while having a long history (e.g. Niemi, 1977, Rigon et al, 2016) has been largely renewed recently starting from Botter et al., 2010 and Botter et al., 2011. The material is the same prepared for the Hydrological Modelling class however grouped here separately for the readers convenience. 

An alternative perspective is presented here regarding their concepts. While certain passages may pose some challenges, the enhanced comprehension of flux formation processes at the catchment scale is, in my opinion, immensely valuable and well worth the effort. The proposed approach involves the following line of thinking: a) the collective fluxes within catchments result from the cumulative movements of numerous small water volumes (water parcels); b) parcels can be understood through three key distributions: the travel time distribution, the residence time distribution, and the response time distribution; c) the interrelations among these distributions are elucidated; d) linking these distributions to catchment processes is achieved through the formulation of age-ranked distributions within ordinary differential equations; e) the theory developed here represents a generalization of the unit hydrograph theory.

Some References
  • Benettin, P., Soulsby, C., Birkel, C., Tetzlaff, D., , G. and Rinaldo, A. (2017) Using sas functions and high resolution isotope data to unravel travel time distributions in headwater catchments. Water Resources Research, 53, 1864–1878. URL: http: //doi.org/10.1002/2016WR020117. 
  • Benettin, Paolo, and Enrico Bertuzzo. 2018. “Tran-SAS v1.0: A Numerical Model to Compute Catchment-Scale Hydrologic Transport Using StorAge Selection Functions.” Geoscientific Model Development Discussions, January, 1–19.
  • Benettin, Paolo, Nicolas B. Rodriguez, Matthias Sprenger, Minseok Kim, Julian Klaus, Ciaran J. Harman, Ype van der Velde, et al. 2022. Transit Time Estimation in Catchments: Recent Developments and Future Directions.†Water Resources Research 58 (11). https://doi.org/10.1029/2022wr033096.
  • Botter, Gianluca, Enrico Bertuzzo, and Andrea Rinaldo. 2010. “Transport in the Hydrologic Response: Travel Time Distributions, Soil Moisture Dynamics, and the Old Water Paradox.” Water Resources Research 46 (3). http://doi.wiley.com/10.1029/2009WR008371.
  • Botter, Gianluca, Enrico Bertuzzo, and Andrea Rinaldo. 2011. “Catchment Residence and Travel Time Distributions: The Master Equation.” Geophysical Research Letters 38 (11). http://doi.wiley.com/10.1029/2011GL047666.
  • Drever, Mark C., and Markus Hrachowitz. 2017. “Migration as Flow: Using Hydrological Concepts to Estimate the Residence Time of Migrating Birds from the Daily Counts.” Methods in Ecology and Evolution / British Ecological Society 8 (9): 1146–57.
  • Harman, Ciaran J. 2015. “Time-Variable Transit Time Distributions and Transport: Theory and Application to Storage-Dependent Transport of Chloride in a Watershed.” Water Resources Research 51 (1): 1–30.
  • Harman, Ciaran J., and Esther Xu Fei. 2024. Mesas.py v1.0: A Flexible Python Package for Modeling Solute Transport and Transit Times Using StorAge Selection Functions.†Geoscientific Model Development 17 (2): 477–95. https://doi.org/10.5194/gmd-17-477-2024.
  • Hrachowitz, M., Benettin, P., van Breukelen, B. M., Fovet, O., Howden, N. J. K., Ruiz, L., van der Velde, Y. and Wade, A. (2016) Transit times-the link between hydrology and water quality at the catchment scale: Linking hydrology and transit times. Wiley Interdisciplinary Reviews: Water, 3, 629–657. 
  • McDonnell, Jeffrey J. 2014. The Two Water Worlds Hypothesis: Ecohydrological Separation of Water between Streams and Trees? Wiley Interdisciplinary Reviews: Water, April. http://doi.wiley.com/10.1002/wat2.1027.
  • Niemi, Antti J. 1977. “Residence Time Distributions of Variable Flow Processes.” The International Journal of Applied Radiation and Isotopes 28 (10): 855–60.
  • Rigon, Riccardo, Marialaura Bancheri, and Timothy R. Green. 2016. “Age-Ranked Hydrological Budgets and a Travel Time Description of Catchment Hydrology.” Hydrology and Earth System Sciences 20 (12): 4929–47.
  • Rigon, R., and M. Bancheri. “On the Relations between the Hydrological Dynamical Systems of Water Budget, Travel Time, Response Time and Tracer Concentrations.” http://abouthydrology.blogspot.com/2020/05/equivalences-and-differences-among.html.
  • Sprenger, M., Stumpp, C., Weiler, M., Aeschbach, W., ST, A., Benettin, P., Dubbert, M., Hartmann, A., Hrachowitz, M., Kirchner, J., McDonnel, J., Orlowski, N., Penna, D., Pfahl, S., Rinderer, M., Rodriguez, N., Schmidt, M. and Werner, C. (2019) The demographics of water: A review of water ages in the critical zone. Rev. Geophys., 2018RG000633. 
  • Schwemmle, Robin, and Markus Weiler. 2024. Consistent Modeling of Transport Processes and Travel Times: coupling Soil Hydrologic Processes with StorAge Selection Functions. Water Resources Research 60 (1). https://doi.org/10.1029/2023wr034441.
  • Velde, Y. van der, 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): W06536–13.
  • Velde, Ype van der, Ingo Heidbüchel, Steve W. Lyon, Lars Nyberg, Allan Rodhe, Kevin Bishop, and Peter A. Troch. 2014. “Consequences of Mixing Assumptions for Time-Variable Travel Time Distributions.” Hydrological Processes 29 (16): 3460–74.
  • Wilusz, Daniel C., Ciaran J. Harman, and William P. Ball. 2017. “Sensitivity of Catchment Transit Times to Rainfall Variability Under Present and Future Climates.” Water Resources Research 53 (12): 10231–56.
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