Impact of simplifications on numerical modelling of the shallow subsurface at city-scale and implications for shallow geothermal potential.

Anthropogenic infrastructures in the shallow subsurface, such as heated basements, tunnels or shallow geothermal systems, are known to increase ground temperatures, particularly in urban areas. Numerical modelling helps inform on the extent of thermal influence of such structures, and its potential uses. Realistic modelling of the subsurface is often computationally costly and requires large amounts of data which is often not readily available, necessitating the use of modelling simplifications. This work presents a case-study on the city centre of Cardiff, UK, for which high resolution data is available, and compares modelling results when three key modelling components (namely ground elevation, hydraulic gradient distribution and basement geometry) are implemented either 'realistically', i.e. with high resolution data, or 'simplified', utilising commonly accepted modelling assumptions. Results are presented at a point (local) scale and at a domain (aggregate) scale to investigate the impacts such simplifications have on model outputs for different purposes. Comparison to measured data at individual locations shows that the accuracy of temperature outputs from numerical models is largely insensitive to simplification of the hydraulic gradient distribution implemented, while changes in basement geometry affect accuracy of the mean temperature predicted at a point by as much as 3.5 °C. At the domain scale, ground temperatures within the first 20 m show a notable increase (approximately 1 °C volume-averaged and 0.5 °C surface-averaged), while the average heat flux over the domain is about 0.06 W/m2 at 20 m depth. These increased temperatures result in beneficial conditions for shallow geothermal utilisation, producing drilling cost savings of around £1700 per typical household system or about 9% increase in thermal energy potential. Simplifications of basement geometry and (to a lesser degree) the hydraulics can result in an overestimation of these temperatures and therefore over-predict geothermal potential, while the elevation simplification showed little impact.

The effect of bed roughness uncertainty on tidal stream power estimates for the Pentland Firth.

Uncertainty affects estimates of the power potential of tidal currents, resulting in large ranges in values reported for sites such as the Pentland Firth, UK. Kreitmair et al. (2019, R. Soc. open sci. 6, 180941. (doi:10.1098/rsos.191127)) have examined the effect of uncertainty in bottom friction on tidal power estimates by considering idealized theoretical models. The present paper considers the role of bottom friction uncertainty in a realistic numerical model of the Pentland Firth spanned by different fence configurations. We find that uncertainty in removable power estimates resulting from bed roughness uncertainty depends on the case considered, with relative uncertainty between 2% (for a fully spanned channel with small values of mean roughness and input uncertainty) and 44% (for an asymmetrically confined channel with high values of bed roughness and input uncertainty). Relative uncertainty in power estimates is generally smaller than (input) relative uncertainty in bottom friction by a factor of between 0.2 and 0.7, except for low turbine deployments and very high mean values of friction. This paper makes a start at quantifying uncertainty in tidal stream power estimates, and motivates further work for proper characterization of the resource, accounting for uncertainty inherent in resource modelling.

The effect of uncertain bottom friction on estimates of tidal current power.

Uncertainty affects estimates of the power potential of tidal currents, resulting in large ranges in values reported for a given site, such as the Pentland Firth, UK. We examine the role of bottom friction, one of the most important sources of uncertainty. We do so by using perturbation methods to find the leading-order effect of bottom friction uncertainty in theoretical models by Garrett & Cummins (2005 Proc. R. Soc. A 461, 2563-2572. (doi:10.1098/rspa.2005.1494); 2013 J. Fluid Mech. 714, 634-643. (doi:10.1017/jfm.2012.515)) and Vennell (2010 J. Fluid Mech. 671, 587-604. (doi:10.1017/S0022112010006191)), which consider quasi-steady flow in a channel completely spanned by tidal turbines, a similar channel but retaining the inertial term, and a circular turbine farm in laterally unconfined flow. We find that bottom friction uncertainty acts to increase estimates of expected power in a fully spanned channel, but generally has the reverse effect in laterally unconfined farms. The optimal number of turbines, accounting for bottom friction uncertainty, is lower for a fully spanned channel and higher in laterally unconfined farms. We estimate the typical magnitude of bottom friction uncertainty, which suggests that the effect on estimates of expected power lies in the range -5 to +30%, but is probably small for deep channels such as the Pentland Firth (5-10%). In such a channel, the uncertainty in power estimates due to bottom friction uncertainty remains considerable, and we estimate a relative standard deviation of 30%, increasing to 50% for small channels.