Trinh @ Bath

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students_summer2026 [2026/06/01 12:31]
trinh 		students_summer2026 [2026/06/01 12:47] (current)
trinh
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 Chapter 20 covers an introduction to the basic model (though focussing on a special model known as the Probability Distributed Model). It is pitched at the audience of an undergraduate Engineering course (actually this is delivered as a fourth-year or MSc-level year), but it is generally not too sophisticated and can be understood with some help. I like how there is a little Matlab script to try.  Chapter 20 covers an introduction to the basic model (though focussing on a special model known as the Probability Distributed Model). It is pitched at the audience of an undergraduate Engineering course (actually this is delivered as a fourth-year or MSc-level year), but it is generally not too sophisticated and can be understood with some help. I like how there is a little Matlab script to try. 
 +
 +The initial model that is used in that chapter is as simple as this [from (20.7)]: 
 +$$
 +\frac{dS}{dt} = q_p - E_a - q_s,
 +$$
 +where the goal is to solve for the storage $S = S(t)$. 
 +
 +To do this, you take in precipitation rate, $q_p$ (provided by data), the actual evapotranspiration rate $E_a$, given by [eqn (20.11)]:
 +$$
 +E_a = H(S) E_p, 
 +$$
 +where $E_p$ is a potential evapotranspiration rate (provided by data), and $H$ is a Heaviside function, which is $1$ if $S > 0$ and zero otherwise. Finally, the runoff, $q_s$, is the key quantity to be obtained, which is modelled by:
 +$$
 +q_s = H(S - c) q_p.
 +$$
 +In other words, if the storage $S$ inceeds some capacity, $c$, all of the rain $q_p$ goes into runoff. In theory, $c$ is chosen by calibration, but if you read around Sec. 20.2.3.1 in the reference, it discusses graphs for the case of c = 80mm. This is the kind of graph that you produce for the storage. 
 +
 +{{ :flooding:smathias_chap20_storage.png?nolink&600 |}}
 +
 +You can read in that chapter why this is a poor model and how it is then improved. 
 +
 +==== Getting the right answers for the right reasons ====
 +
 +The next reference I want to provide is just a general review of the state of hydrology given by James Kirchner in 2006: 
 +
 +//Kirchner, J. W. (2006). Getting the right answers for the right reasons: Linking measurements, analyses, and models to advance the science of hydrology. Water Resources Research, 42(3). https://doi.org/10.1029/2005WR004362
 +//
 +
 +There is not much to add to this. I think it is a nice article to begin to understand why model differentiation and complexity are difficult topics in the area of hydrology. 
 +
 +==== A workshop on hydrological modelling ====
 +
 +The last reference I want to share is this one: 
 +
 +//Knoben, W. J. M., & Spieler, D. (2022). Teaching hydrological modelling: Illustrating model structure uncertainty with a ready-to-use computational exercise. Hydrology and Earth System Sciences, 26(12), 3299–3314. https://doi.org/10.5194/hess-26-3299-2022
 +//
 +
 +In this article, they discuss how a teaching exercise was designed to investigate some issues of hydrological modelling and uncertainty. The toolbox here is the excellent [[https://github.com/wknoben/marrmot|MARRMoT Matlab Toolbox]].
 +
 +As part of your investigations, I would like you to experience the little exercise that is discussed in the 2022 article, which is [[https://github.com/wknoben/Dresden-Structure-Uncertainty|then shared in this code here]].
  
Last modified: 2026/06/01 12:47