*2.5. Brier Skill Score*

In order to estimate the prediction capability of the different combinations of models objectively (granular stress and turbulence models), the Brier Skill Score (*BSS*) was used. It is a statistical approach used to measure the quality of an agreemen<sup>t</sup> between simulation results and experimental data. This statistical tool has been extensively used in the coastal engineering community [29–31]. It provides an estimation of a model's performance and is defined following the expression:

$$BSS = 1 - \frac{\sum\_{i}^{n} |y\_i^s - y\_i^e|^2}{\sum\_{i}^{n} |y\_i^0 - y\_i^e(x)|^2}. \tag{35}$$

The *BSS* compares the sum of the squared difference between the bed elevation *ys* from simulations and *ye* from experiments at point *i* (from 0–*<sup>n</sup>*, the total number of experimental points) with the mean squared difference between the initial bed elevation *y*0 and *ye* also at point *i*. The bed elevation *ys* in the simulations is the line of isoconcentration *φ* = 0.5. A *BSS* equal to one expresses a perfect agreemen<sup>t</sup> between simulation and experimental results. The agreemen<sup>t</sup> quality decreases with the *BSS*, whereas a negative *BSS* expresses simulation results further away from the experimental results than the initial bed elevation.
