In this study, the Authors analyze the observed variability of the scour effect at bridges using stochastic simulation tools and schemes, by estimating and preserving vital stochastic properties of scour, such as the long-term persistence and the fractal behaviour, by using high-quality hourly streamflow timeseries with over 20 years of length, and calculating the scour effect through the BRISENT model; please see some (mostly minor) suggestions that I hope they can be helpful to the Authors to further highlight their innovative work:

1) In the Title of the manuscript (i.e., ": Variability and persistence of scour at bridges using stochastic simulations"), I would recommend keeping the "persistence" since if a process is considered persistent then it will also show high variability.

2) I would recommend replacing the "non-stochastic properties of the scouring process" to "deterministic properties of the scouring process".

3) I would recommend that "Observations" shown in Table 3 cannot be "Assumed stationary" and "Nonstationary" but rather the model used to simulate them can be either stationary or non-stationary (see for example, the work by Koutsoyiannis and Montanari, 2015; doi:10.1080/02626667.2014.959959, which describes exactly this issue and its consequences in stochastic simulation).

4)  Please note that the case H=0.0 shown in Table 3, can be very difficult to mathematically simulate it; I would recommend to replace it to the H>0 case.

5) Please consider further explaining in more detail the 3 key parameters in the BRISENT model (i.e., 𝜆, 𝑊, and 𝑆) since some Readers may not be familiar with these terms.

6) In the sentence "It is worth mentioning that rough dynamics (i.e., 𝑀 < 0.5) instead of a smooth one (i.e., 𝑀 > 0.5) is usual in many hydrological processes at the analysed hourly scale such as the cases of near-surface temperature, relative humidity, dew point, sea level pressure, wind speed, and precipitation (see, e.g., Dimitriadis et al., 2021b..."), I would recommend replacing the Dimitriadis et al., 2021b (which coincides with Dimitriadis et al., 2021a) to the more relevant study by Pizarro et al. (2022; doi:10.3390/hydrology9070126), where they also estimate important stochastic properties such as the fractal and Hurst parameters.

7) Please consider discussing the work by Vavoulogiannis et al. (2021; doi:10.3390/hydrology8020063), where the AMA model is applied and the asymmetry of streamflow is estimated as prominent at time scales up to four days.

Note: I have contacted the editor and NHESS twice because I feel unable to review a large part of this manuscript. However, I have received no reply. The hydrodynamic concepts and the stochastic tools that the authors refer to, are out of my domain. I am not able to judge the scientific correctness of their approach and would therefore advise to find another reviewer.

In lack of any response, I will now submit a partial review and will point out for which points an additional reviewer should be consulted. I regret the delay that this situation has caused the authors and apologize for any inconvenience my lack of knowledge in the field is causing the authors.

The authors present a framework for the investigation of scour dynamics. The data basis is increased by creating a large set of synthetic stream flow time series which are used to force a scour and fill model.

The manuscript has a good structure and is well written. However, the manuscript is highly technical. Advanced statistical methods and hydrodynamic scour modelling are constantly referred to and fill many consecutive pages in the methods section. Any reader who is just slightly in a different research field, will have a very hard time to understand the methods or find the manuscript simply unreadable. This aspect also reflects in the fact that the authors, apart from the introduction, mainly cite their previous work, which complicatest the independent validation of the underlying methods, as any unnoticed flaws in earlier work may be amplified through continued reliance on the same line of research. 

The study is very specialized. This should be in itself no problem but it is unfortunate for the authors. It would help the manuscript, if the authors were able to add short explanations why certain methods are used. E.g. climacographs, climacospectrums, generalised Cauchy-Dagum-type climacogram, Hurst and Mandelbrot parameters, FHK-CD model should be explained, as I doubt that every reader is aware of these concepts and is willing to dig in the references. I am certainly not. To this end, I wonder if this manuscript fits into the rather broad scope of NHESS.

See attached file for the full review.