05 Feb 2021

05 Feb 2021

Review status: a revised version of this preprint is currently under review for the journal HESS.

Numerical daemons of hydrological models are summoned by extreme precipitation

Peter T. La Follette1, Adriaan J. Teuling1, Nans Addor2, Martyn Clark3, Koen Jansen1, and Lieke A. Melsen1 Peter T. La Follette et al.
  • 1Hydrology and Quantitative Water Management Group, Wageningen University, Wageningen, Netherlands
  • 2Geography, College of Life and Environmental Sciences, University of Exeter, Exeter, UK
  • 3Coldwater Laboratory, University of Saskatchewan, Canmore, Alberta, Canada

Abstract. Hydrological models are usually systems of nonlinear differential equations for which no analytical solutions exist and thus rely on approximate numerical solutions. While some studies have investigated the relationship between numerical method choice and model error, the extent to which extreme precipitation like that observed during hurricanes Harvey and Katrina impacts numerical error of hydrological models is still unknown. This knowledge is relevant in light of climate change, where many regions will likely experience more intense precipitation events. In this experiment, a large number of hydrographs is generated with the modular modeling framework FUSE, using eight numerical techniques across a variety of forcing datasets. Multiple model structures, parameter sets, and initial conditions are incorporated for generality. The computational expense and numerical error associated with each hydrograph were recorded. It was found that numerical error (root mean square error) usually increases with precipitation intensity and decreases with event duration. Some numerical methods constrain errors much more effectively than others, sometimes by many orders of magnitude. Of the tested numerical methods, a second-order adaptive explicit method is found to be the most efficient because it has both low numerical error and low computational cost. A basic literature review indicates that many popular modeling codes use numerical techniques that were suggested by this experiment to be sub-optimal. We conclude that relatively large numerical errors might be common in current models, and because these will likely become larger as the climate changes, we advocate for the use of low cost, low error numerical methods.

Peter T. La Follette et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-28', Jasper Vrugt, 23 Feb 2021
    • AC1: 'Reply on RC1', Peter La Follette, 23 Feb 2021
    • AC2: 'Reply on RC1', Peter La Follette, 04 Mar 2021
  • RC2: 'Review #2', Martina Kauzlaric, 24 Apr 2021
    • AC3: 'Reply on RC2', Peter La Follette, 26 Apr 2021
    • AC4: 'Reply on RC2', Peter La Follette, 29 Apr 2021
  • RC3: 'Comment on hess-2021-28', Anonymous Referee #3, 11 May 2021
    • AC5: 'Reply on RC3', Peter La Follette, 11 May 2021

Peter T. La Follette et al.

Data sets

Data for La Follette et al (Numerical Daemons and extreme precipitation) Peter La Follette

Peter T. La Follette et al.


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Short summary
Hydrological models are useful tools that allow us to predict distributions and movement of water. A variety of numerical methods are used by these models. We demonstrate which numerical methods yield large errors when subject to extreme precipitation. As the climate is changing such that extreme precipitation is more common, we find that some numerical methods are better suited for use in hydrological models. Also, we find that many current hydrological models use relatively inaccurate methods.