| 13 Jan 2026
Variability and persistence of scour at bridges using stochastic simulations
Abstract. The stochastic and non-stochastic properties of the scouring process at bridges are analysed by coupling synthetic streamflow generations with a scour and fill model considering the upstream sediment supply. Streamflow was generated using the asymmetric moving-average (AMA) scheme that preserves the Hurst-Kolmogorov (HK) dynamics, the second-order dependence structure, time asymmetry, and the first four statistical moments of the marginal distribution. Stationarity, homogeneity, and ergodicity of the streamflow and scouring processes were assumed. Monte Carlo analyses covered 12,000 realisations for each of the three considered scenarios with different upstream sediment supply. Extreme scour events were assessed using annual maxima with GEV fitting and compared against the equilibrium scour. The dependence structure was identified with the climacogram and climacospectrum stochastic tools and fitted with a filtered HK model (FHK-CD). The obtained results show a multi-scale dynamics of the scouring process with rough and weak persistent behaviour (M ≈ 0.40; H ≈ 0.60), while envelopes span from antipersistent to strongly persistent scour regimes (H up to ≈ 0.86) depending on the upstream sediment supply. It is worth noting that the upstream sediment supply reduced the envelope variability and modified the extreme scour values. Additionally, synchronisation between extreme events of streamflow and scour showed a weak correspondence (Critical Success Index ≈ 0.15–0.60), indicating that streamflow extremes do not systematically translate into scour extremes. Finally, scour depths with a given return period (computed from scour time series) increase with upstream sediment supply.
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.