the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
On the use of streamflow transformations for hydrological model calibration
Guillaume Thirel
Olivier Delaigue
Charles Perrin
Abstract. The calibration of hydrological models through the use of automatic algorithms aims at identifying parameter sets that minimize the deviation of simulations from observations (often streamflows). It is a widespread technique that has been the subject of much research in the past. Indeed, the choice of objective function (i.e. the criterion or combination of criteria to optimize) can significantly impact the parameter set values identified as optimal by the algorithm. Besides, the actual goal of the model application (flood or low-flow estimation, for instance) influences the way calibration is undertaken. This article discusses how mathematical transformations, which are sometimes applied to the target variable before calculating the objective function, impact model simulations. Such transformations, for example square root or logarithmic, aim at increasing the weight of errors made in specific ranges of the hydrograph. Typically, a logarithmic transformation tends to increase the fit of streamflows to lower values, compared to no transformation. We show in a catchment set that the impact of these transformations on the obtained time series can sometimes be different from what could be expected. Extreme transformations, such as squared or inverse of squared transformations, lead to models that are specialized for extreme streamflows, but show poor performance outside the range of the targeted streamflows and are less robust. Other transformations, such as the power 0.2, the Box–Cox and the logarithmic transformations, can be qualified as more generalist, and show a good performance for the intermediate range of streamflows, along with an acceptable performance for extreme streamflows.
Guillaume Thirel et al.
Status: open (until 30 Jun 2023)
-
RC1: 'Comment on egusphere-2023-775 - Contribution could be more fundamental', Anonymous Referee #1, 23 May 2023
reply
The use of data transformation has a long tradition in the context of hydrologic model calibration, which makes this an interesting topic to review and analyse as the authors do. Here are some comments to further improve the study and its context.
[1] In lines 36-46, the authors cite a lot of literature where transformations have been used. I find this paragraph very difficult to read. Would it not be useful to place all these papers in a table and simply report percentages of time a particular transformation has been used? It is quite difficult to find the non-reference text in this paragraph.
[2] More explanation would be helpful in places to be clearer about what previous authors found and what the state of knowledge is. The authors cite studies, but it is not clear what relevance the conclusions of these papers have. A couple of examples:
"Peña-Arancibia et al. (2015) showed that a squared root transformation with the Nash–Sutcliffe efficiency leads to a better calibration and a reduced parameter uncertainty than no transformation or a logarithmic transformation." – In how far did it lead to better calibration? What does better calibration mean in this context? A better NSE value?
"Sadegh et al. (2018) investigated the role of several transformations in three catchments and two models and deduced that data transformations might be more helpful for evaluation and analysis of model behaviour than model inference." – Why did they conclude that? Why the difference in result for evaluation and inference? Is this conclusion not in conflict with the conclusion of Peña-Arancibia et al.? What does ‘analysis’ mean in this context.
[3] Why do the authors select these objective functions shown in section 2.3. The authors state that they analyze the following: ‘in order to estimate how transformations impact the simulated time series’ . But this is not really what the authors do. They assess performance difference with respect to a couple of popular metrics, they do not analyze how the actual time series changes beyond assessing model performance.
[4] I am a bit confused by the transformations introduced in section 2.4. Aren’t some of the transformations included in others? E.g. the log transformation is a specific case of the Box-Cox transformation. Why not use the minimum number of transformations and then test the influence of the scaling parameter used in the transformation. Using just the Box-Cox transformation and a Q^x transformation with lambda and x varying would capture most and would allow for a more general analysis. You could use the two flexible transformations and plot the result against the lambda and x values used and against the streamflow percentiles to get a better fundamental overview about what is happening!?
[5] What lambda value has been used for the Box-Cox transformation? The result should be dependent on that choice given that the transformation is flexible. Previous studies suggested a lambda value of 0.3 to suitable for streamflow data to gain a more balanced calibration results (e.g. Vrugt et al. (2006), Journal of Hydrology, doi: 10.1016/j.hydrol.2005.10.041). How much does the result depend on that choice?
[6] In line 245 you state: "In addition, the transformations that show the best average rank are not widely used in the literature (0.2, log and boxcox)."– Are you sure about this? Log and BoxCox (lambda of 0.3) transformations are such a standard to reduce the focus on high flows. They might not have been a focus in very recent years, but certainly from the late 90s to some years ago, they were widely used.
Some (random) examples:
Lerat et al. (2020). Journal of Hydrology, doi.org/10.1016/j.jhydrol.2020.125129
van Werkhoven et al. (2008). Water Resour. Res., doi:10.1029/2007WR006271
Huang et al. (2023). Journal of Hydrology, doi.org/10.1016/j.jhydrol.2023.129347
[7] For section 4.3, could the authors not organize the catchments into those dominated by slow and fast behavior, e.g. using the (central) slope of the flow duration curve or some other signature metric? There might be different reasons why a catchment varies in this regard (snow, pervious geology, …), which might not be easily captured by the characteristics available.
All in all, an interesting study, though I think the authors could (should?) provide some more fundamental insight still. For example by varying the parameter of the Box-Cox or other flexible transformations.
Citation: https://doi.org/10.5194/egusphere-2023-775-RC1
Guillaume Thirel et al.
Guillaume Thirel et al.
Viewed
HTML | XML | Total | BibTeX | EndNote | |
---|---|---|---|---|---|
266 | 91 | 6 | 363 | 5 | 3 |
- HTML: 266
- PDF: 91
- XML: 6
- Total: 363
- BibTeX: 5
- EndNote: 3
Viewed (geographical distribution)
Country | # | Views | % |
---|
Total: | 0 |
HTML: | 0 |
PDF: | 0 |
XML: | 0 |
- 1