<p style="font-weight: 400;">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 (<em>M</em> ≈ 0.40; <em>H</em> ≈ 0.60), while envelopes span from antipersistent to strongly persistent scour regimes (<em>H</em> 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<span>–</span>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.