Status: this preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Streamflow elasticity as a function of aridity
Vazken Andréassian,Guilherme Mendoza Guimarães,Julien Lerat,and Alban de Lavenne
Abstract. Relating variations in annual streamflow to a climate anomaly, commonly referred to as streamflow elasticity to climate, is central for a rapid assessment of the impact of climate change on water resources. This elasticity is classically estimated via a multiple linear regression between anomalies in streamflow and climate variables. However, this approach does not explicitly account for the fact that elasticity depends on aridity as suggested by “Budyko-type” water balance formulas. Using a large dataset of 4,122 catchments from four continents, we first verify empirically the link between elasticity and aridity. Then, we propose a method to constrain elasticity coefficients with derivatives from a “Budyko-type” water balance formula, that allows introducing an explicit dependency between elasticity and aridity. We show that adding this dependency produces a regionalized elasticity formula with physically-realistic elasticity coefficients.
Received: 03 Oct 2025 – Discussion started: 05 Nov 2025
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The paper focuses on climate elasticity of streamflow, which is important to understand how vulnerable river flow is to changes in climate. The authors test if climate elasticity depends on the aridity index by using annual streamflow anomalies from a large data set. This dependency is clearly demonstrated. Further the authors propose a new form to estimate climate elasticity which takes account of the dependency of the climate elasticity to aridity as well as the synchronicity pf precipitation and potential evaporation.
While reading I asked myself if there is sufficient novelty to warrant publication in HESS. Going back to the seminal paper of Sankarasubramian et al. (2001) in WRR one can find quite a similar test if climate elasticity depends on aridity using data from 1200 catchments in the US. The dependency was also found and they also find a significant effect of the synchronicity of precipitation and potential evaporation. Yet in the present paper there is an explicit term on the synchronicity, which was also new to me. So in addition to the even larger data set, there is also a relevant climatic property explicitly addressed.
The second achievement of the present paper is trying to take account for aridity in the elasticity derivation. The proposed functional form seems a bit empirical and ad-hoc. It is validated by a better NSE fitting the annual anomalies than without account for this (Table 4). Here I have a few questions: (a) what is the significance of being better (could be shown by the distribution of NSE across catchments) (b) what would be the goodness of fit using the theoretical elasticity coefficients.
I also want to stress that interannual storage changes affect the annual anomalies of streamflow which cannot directly be estimated by climate variations. Also changes in catchment characteristics like vegetation, water management in a basin will affect annual anomalies. In addition there are also statistical issues like co-variation, trends and non-normal distributions which affect the quality of the empirical derived elasticity coefficients. These issues were not addressed in the present paper, but in the companion paper of the authors earlier this year.
To my mind these issues can lead to larger variation and even the non-physical values of the empirical elasticity coefficients. Therefore before reading the paper I would have rather used the theoretical derived climate elasticity when estimating the potential change of streamflow to changes in climate. Now I might try to use the new formula since I do like the explicit accounting for the synchronicity of precipitation and potential evaporation presented in the paper.
The quality of presentation and the clarity of writing is very high and I enjoyed reading the paper. I would recommend publication in HESS after addressing my remarks and a few minor comments below.
L313: please explain what you mean be mixed results
L358-9: In the discussion there is this sentence: „relationships were developed on catchments with limited interannual memory“ – to me this is a major methodological step (constraining the sample) which was not described in the methods. Please add explicitly, so readers have everything to apply the methods with their own data.
We study the variations in annual streamflow and explicit their dependence to climate variations, in order to understand their causes and to provide tools for a rapid assessment of the impact of climate change on water resources. By making explicit the dependency of streamflow elasticity to aridity, we are able to propose a regionalized elasticity formula with physically-realistic elasticity coefficients.
We study the variations in annual streamflow and explicit their dependence to climate...
The paper focuses on climate elasticity of streamflow, which is important to understand how vulnerable river flow is to changes in climate. The authors test if climate elasticity depends on the aridity index by using annual streamflow anomalies from a large data set. This dependency is clearly demonstrated. Further the authors propose a new form to estimate climate elasticity which takes account of the dependency of the climate elasticity to aridity as well as the synchronicity pf precipitation and potential evaporation.
While reading I asked myself if there is sufficient novelty to warrant publication in HESS. Going back to the seminal paper of Sankarasubramian et al. (2001) in WRR one can find quite a similar test if climate elasticity depends on aridity using data from 1200 catchments in the US. The dependency was also found and they also find a significant effect of the synchronicity of precipitation and potential evaporation. Yet in the present paper there is an explicit term on the synchronicity, which was also new to me. So in addition to the even larger data set, there is also a relevant climatic property explicitly addressed.
The second achievement of the present paper is trying to take account for aridity in the elasticity derivation. The proposed functional form seems a bit empirical and ad-hoc. It is validated by a better NSE fitting the annual anomalies than without account for this (Table 4). Here I have a few questions: (a) what is the significance of being better (could be shown by the distribution of NSE across catchments) (b) what would be the goodness of fit using the theoretical elasticity coefficients.
I also want to stress that interannual storage changes affect the annual anomalies of streamflow which cannot directly be estimated by climate variations. Also changes in catchment characteristics like vegetation, water management in a basin will affect annual anomalies. In addition there are also statistical issues like co-variation, trends and non-normal distributions which affect the quality of the empirical derived elasticity coefficients. These issues were not addressed in the present paper, but in the companion paper of the authors earlier this year.
To my mind these issues can lead to larger variation and even the non-physical values of the empirical elasticity coefficients. Therefore before reading the paper I would have rather used the theoretical derived climate elasticity when estimating the potential change of streamflow to changes in climate. Now I might try to use the new formula since I do like the explicit accounting for the synchronicity of precipitation and potential evaporation presented in the paper.
The quality of presentation and the clarity of writing is very high and I enjoyed reading the paper. I would recommend publication in HESS after addressing my remarks and a few minor comments below.
L313: please explain what you mean be mixed results
L358-9: In the discussion there is this sentence: „relationships were developed on catchments with limited interannual memory“ – to me this is a major methodological step (constraining the sample) which was not described in the methods. Please add explicitly, so readers have everything to apply the methods with their own data.