## 2 Materials and Methods  
For the analysis, the data of the field experiment carried out in September-October 2007 in the Shkorpilovtsi settlement (Bulgaria) at a special experimental pier belonging to the Institute of Oceanology of the Bulgarian Academy of Sciences were used. The pier is located on the Kamchiya-Shkorpilovsky beach site on the Black Sea (Figure 1), which does not have a sediment budget deficit and has been relatively stable over the past 50 years. The study site has a rectilinear shoreline with almost parallel isobaths. During the experiment, the approach of the storm waves was almost perpendicular to the coastline, and the longshore current was either very weak or even absent, i.e., it can be assumed that the changes in the underwater topography and coastline were determined mainly by wave action and the cross-shore wave-driven currents, like undertow [28]. During the experiment, along the pier, with a length of 230 m, 15 string wave gauges were installed: seven are the capacitive type and eight are the resistance type. The free surface elevations (waves) were measured with sampling frequencies of 5 and 200 Hz, respectively (Figure 1). The length  
Figure 1: Location of the study site, sea bottom profile on 27 September 2007 and positions of wave gauges during the field experiment. of the series of measurements lasted from 20 min to 1 h. For analysis, long records were divided into 20 min sections corresponding to the quasi-stationary state of the wave regime. The sea bottom in the area is composed mainly of anisomeric sand, in which quartz components predominate (96%). The other 4% consists of fine shell particles. In the upper part of the underwater bottom profile (up to 2.5 m depth), over 95% of bottom sediments consist of coarse and medium sands (0.30/0.70 mm). With increasing water depth sediment, decreasing grain size and at depths greater than 8 m, the size over 90% of sediments is less than 0.25 mm [29]. Synchronously with the wave measurements, the seabed variations along the pier were measured using a special metal stick lowered from the pier deck every 2 m, from the shore to a depth of about 4 m. Point \"0\" was on the shore and corresponded to 30 m from the shoreline position. The accuracy of this kind of measurement for strong wave conditions does not exceed 10 cm, and for conditions of calm and moderate excitement it is significantly less [29; 30]. Despite such a simple method of measurement, it remains the only possible in situ measurement under storm conditions, since other modern methods require a calm sea. The seabed variation profiles were measured once or three times per day, depending on the wave regime. In total, 37 profiles and 65 wave records were obtained. The sea bottom profile during the experiment had one nearly stable bar, with its top located at a distance of 140-160 m. Sometimes, a second underwater bar was formed near the shore (up to 100 m) and existed for several days. To estimate the cross-shore sediment discharge, [PERSON]'s formula was used [8]:  
\[q=\frac{1}{2}f_{w}\rho\Big{(}\frac{\varepsilon_{b}}{\tan\sigma}\overline{u|u| ^{2}}+\frac{\varepsilon_{s}}{W_{s}}\overline{u|u|^{3}}\Big{)} \tag{2}\]  
where \(f_{w}\) = 0.01 is the coefficient of bottom friction, \(\rho\) is the sand density, \(\varepsilon_{b}\) = 0.1 and \(\varepsilon_{s}\) = 0.02 are the coefficients of turbulent viscosity and turbulent diffusion, respectively, tan 6 = 0.5 is the coefficient of particles' inner friction, where 6 is the sediment internal friction angle, \(w_{s}\) is the sediments fall velocity, and \(\overline{u|u|^{2}}\) and \(\overline{u|u|^{3}}\) are third and fourth moments of near-bottom velocity, respectively.