# Temperature model

One of the most decisive factors that determine the geothermal potential is the aquifer temperature. ThermoGIS uses a temperature model to determine the average temperature of the aquifers at each XYZ location (Békési et al. (2020); (Bonté et al., 2012); Gies et al. (2021)). The model consists of a three-dimensional grid with 1000x1000x200-metre cells. Each cell holds an estimate of the temperature. The basis of the model is formed by a layer model that is a combination of the ThermoGIS aquifer layer model and REGIS (the REgional Geohydrological Information System, Hummelman et al. (2019); Vernes & van Doorn (2005)), supplemented by the depths of the Namurian, Westphalian, Dinantian and those of the Upper and Lower Crust.

The model is calculated in a number of steps, initially in a grid with cells of 3000x3000x200 metres down to a depth of 10 kilometres and 3000x3000x3000 metres to a depth of 100 kilometres. In a subsequent step this is refined to 1000x1000x200 metres down to a depth of 10 kilometres.

Initially, porosity, vertical thermal conductivity and radiogenic heat production are assigned to all layers of the coarse grid based on expected rock content and textbook values (Hantschel & Kauerauf (2009)). Temperature boundary conditions are imposed at the bottom and top of the model: 10°C at the top (0 m) and 1200°C at the base (100 km depth). A temperature for each cell is determined by solving the heat equation in 1D ('multi-1D'). Vertical conduction is the heat transport mechanism in this step. Then, in the second step, the calculations are refined by solving the heat equation in 3D using the results obtained in the first step as prior estimate. The calculated temperatures are compared with a database of temperatures measured in the subsurface. Then, in steps 3 and 4, the predetermined thermal properties autigenic heat production and vertical thermal conductivity are iteratively adjusted to minimise the difference between the calculated and measured temperatures (ES-MDA: Ensemble Smoother - Multiple Data Assimilation).

Finally, the model is limited to a depth of 10 kilometres, and refined to cells of 1000x1000x200 metres. The results of step 4 are adopted, and steps 1, 2 and 4 are repeated on the refined grid.

In this way, temperature estimates of the Dutch subsurface are generated that correspond to temperature measurements, and are based on realistic estimates of subsurface thermal properties, and heat flow.