Several hydrological signatures use the median for scaling. For example the high flow variabilty is defined as mean of annual maximum divided by the median flow (Jowett and Duncan, 1990). Now rivers in arid regions can run dry in extreme years, thus meaning their flow is 0. When this happens more than 50 % of the time the median flow is also 0. For the calculation above this would lead to an division by 0, which is obviously not a good idea. Thus it cannot be calculated. Still, I would argue this river should have high flow variability. Does anyone now a sound solution for this problem?
Hi Florian, dryland hydrology always brings unique challenges. I would suggest using a different metric for flow variation, since it can have the divide by 0 problem as you pointed out, but also because peak flow divided by the median is not necessarily the best measure of flow variance. CV or similar is very simple and can be very effective since it may use the full structure of the dataset more effectively. If you want more nuanced metrics of flow variability, I would recommend using components of the flow duration curve. You can see our paper using many of these, that successfully include many highly ephemeral catchments in Australia (link below).
There is also no hard and fast rule for when a system is sufficiently ephemeral to no longer be a river. If the channel network exists, then its a good bet it receives sufficient discharge at least on decadal timescales. This would be the case for many systems in the middle east (e.g. wadis). If you get at least some flow once a year then I would say it's a moderately active dryland system, and is characteristic of many dryalnd rivers in central Australia, the Sahel, Negev, etc.
Hope that helps
Josh
Article Linking the Budyko framework and the Dunne diagram
Thank for the suggestion. We considered this as well, as you stated it is a different signature then. Another idea would be to dividie by the median when median > 0 and by the mean when median < 0. This would lead to a step in solutions, which is not desirable.
Yet another solution would be to only consider days > 0 for the median, but this would also be a bit tricky as now mean and median draft from a different pool.
Or you could use only days > for both median and mean.
So my problem is that I have a range of bad options^^
You're right, but I am still not sure which option to use. What also crossed my mind is the following: At what point is a river no river any more? Is something a river when only 10 % of all the time there is any water in it? Are their rules to this?
Hello Florian,
since surface flow is the total of baseflow and quick flow, then for dry regions with no added inflows and no rainfall, the baseflow is the predictor and the controller. hydrological modelling should help you with this. GR4J and AWBM are less complex to estimate flow variability with different stats results. you can use SOURCE, eWATER software which can help you to run different Rainfall-Runoff models automatically. But you will need daily time step data and GIS maps for the catchment.
Hope this help.
Try googling "hydrologic signature". You'll get a lot of hits. You might find good coverage of your question in some of those papers.
The paper "Five guidelines for selecting hydrological signatures" - McMillan - 2017
https://onlinelibrary.wiley.com/doi/full/10.1002/hyp.11300
provides a number of general criteria.
You haven't stated the context of your question, which always raises the question of suitability for purpose. The five guidelines paper, in my opinion, incorporates approaches to suitability for purpose.
Thank you Fayha and Geoffrey for your answers. I already have my data (I use the CAMELS data set) and I know which signatures I want to use (the ones from Westerberg and McMillan in " Uncertainty in hydrological signatures"). The problem arises from several of the rivers being in very dry regions. Those "rivers" have a measured discharge of 0 for more than 50 % of the time. This leads to a median of 0, which is a case that is not considered in common signatures and I wonder how the signature equations could be modified to incorporate this in a sensible way.
Hi Florian, dryland hydrology always brings unique challenges. I would suggest using a different metric for flow variation, since it can have the divide by 0 problem as you pointed out, but also because peak flow divided by the median is not necessarily the best measure of flow variance. CV or similar is very simple and can be very effective since it may use the full structure of the dataset more effectively. If you want more nuanced metrics of flow variability, I would recommend using components of the flow duration curve. You can see our paper using many of these, that successfully include many highly ephemeral catchments in Australia (link below).
There is also no hard and fast rule for when a system is sufficiently ephemeral to no longer be a river. If the channel network exists, then its a good bet it receives sufficient discharge at least on decadal timescales. This would be the case for many systems in the middle east (e.g. wadis). If you get at least some flow once a year then I would say it's a moderately active dryland system, and is characteristic of many dryalnd rivers in central Australia, the Sahel, Negev, etc.
Hope that helps
Josh
Article Linking the Budyko framework and the Dunne diagram
Thank you Josh and Sina for your very useful answers. So I guess in conclusion, one could say that the hydrological signatures that divide by the median are simply not really applicable on ephemeral catchments. However, if you really want to use them, switching the median with the trimean might be a worthwhile approach.
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