Calculation of sand mining volumes and refilling rates

To separate mining sites from the surrounding bathymetry, the optimal robust separator (ORS) algorithm⁵² was applied. Before filtering of the original surveyed bathymetry, empty depth cells landward of the land-water interface were padded with zeros. The bank line from January 29, 2017, which was extracted from satellite images, was therefore used to define the land-water interface. The height for remaining empty depth cells was linearly interpolated. Afterwards, the original bathymetry was filtered by means of a median filter using the Generic Mapping Tools (GMT) (version 6.0.0) function grdfilter. Different filter widths wi were used, incrementally increasing the diameter by 100 m. For each diameter, the resulting regional bathymetry fi(x,y) was subtracted from the observational dataset s(x,y) to calculate a residual signal di(x,y). A depth contour of −1 m was then chosen to identify polygons reflecting the sand mining sites within these residual datasets. Resulting polygons with an area <2,500 m2 were neglected, since the associated mining sites could not always be clearly identified. Additional polygons were deleted during visual inspection. The ORS was then used to calculate the residual height hi¯ as follows:

where Ai is the area of the residual bathymetry enclosed by the −1 m depth contour and Vi is the volume under the residual for this area. For each mining site, suitable regional bathymetries were selected for the separation of the mining site from the surrounding bathymetry. In order to achieve this, the regional bathymetry leading to the maximum residual height as well as the ones associated with the next smaller and larger diameters were considered suitable candidates. In some cases, the increase in filter diameter led to a residual bathymetry, where single mining sites conflicted with adjacent bathymetric features, e.g. bedforms or scour holes. Since the spatial extent of mining sites could not be determined in such cases, the concerned regional bathymetries were neglected as possible candidates. Using the approach by ref. ⁵³, the separation of a mining site from the surrounding regional bathymetry was afterwards achieved by following procedure: First, the final regional bathymetry for a location fm(x,y) was obtained by calculating the median of all selected candidates fc(x,y) as follows:

To assess the sensitivity of the results to different filter diameters, the median absolute deviation (MAD)⁵⁴ σ*(x,y) was calculated as:

The final residual bathymetry dm(x,y) was obtained by subtracting the final regional bathymetry from the observational data and using the MAD to provide uncertainty bounds:

The extraction volume for each mining site was then estimated based on the volume under dm enclosed by the −1 m depth contour of this final residual bathymetry. The detailed procedure is also shown in Fig. 7. The recovery time, i.e. the duration of the refilling process of local sand mining sites, was calculated by means of a supplementary numerical model using the software Delft3D⁵⁵. A detailed description of the set-up, validation and the results of this model can be found in the Supplementary Material S¹.

Procedure for calculating extracted sand volume for all mining sites within the study area. Illustration was generated using Matlab 2018a (http://mathworks.com).