## Assumed parameter range distribution for the Monte Carlo

Table 3.

The model comprises three steps. First, the heat flux of all individual AHFS sources in each pixel ij is determined using a Monte Carlo simulation. Second the anthropogenic heat flux per pixel ij is determined, which describes the average heat flux of the pixel. Third, the anthropogenic heat fluxes of all pixels are summed up to determine the heat flow, i.e. the BMS-794833 amount transported into the aquifer over the whole study area in the span of one year.

2.3.2. Anthropogenic heat flux from individual sources

The anthropogenic heat flux from individual sources represents the energy per square meter and second that each AHFS source transports into the groundwater. Most of the energy is transferred by conductive heat transport processes and can be determined using Fourier\'s law q = λ ⋅ ∇T = λ ⋅ ΔT/Δd. Here λ is the thermal conductivity and ∇T the thermal gradient that can be derived by dividing the difference in temperature ΔT by the distance Δd between two points. For the anthropogenic heat fluxes from elevated ground surface temperatures (qGST) the temperature gradient depends on the difference between GST (TGS) and GWT (TGW) as well as on the depth dGW of the water table (see Fig. 4). It can be calculated as follows:equation(1)qGSTij=λ⋅TGS−TGWij+δTGWdGWij+δdGW.