Geomagnetically induced currents (GICs) have long been known to affect power systems adversely. Modelling these GICs usually involves consideration of a chain of coupled systems. The scope of the modelling chain spans multiple disciplines, from solar physics through to geophysics and power engineering. Most models split the chain into sequential and separate processes. Recent approaches focus on improving accuracy in the geophysical process and in network models to a transformer level. However, even complex models in the geophysical or engineering steps leave significant unmodelled uncertainties in the coupled systems. The focus of this work is to use data-driven approaches to probe the uncertainties and provide a framework for operational estimation from the geomagnetic field to GIC. Although the empirical approaches chiefly link measurements of geomagnetic fields and GICs, measured geoelectric fields and magnetotelluric surface impedance responses are also employed. Analysis is done in both the time and frequency domains. Various aspects of this novel empirical approach have been tested using datasets from power networks in four mid-latitude countries, with consistent results found across the different contexts. The novel empirical ensemble method shows improvements compared with previous empirical models, regardless of data fidelity or coverage. Frequency-related driving and filters are shown to have material effects on GIC modelling. The network parameters widely used to calculate GICs at nodes are shown to vary with the magnitude of the geomagnetic disturbance during an event. Modelling uncertainty can be quantified, and an operational level of modelling was possible across all cases. For GIC modelling in networks with sparse magnetic Field data coverage, the well-defined and often used planar spherical elementary current systems interpolation method is adapted to use low-cost variometers and describe mid-latitude current systems. For the first time, uncertainty is included in the results from this interpolation scheme. This research has direct applications for power system operators in mid-latitude regions. The use of variometers and low-cost GIC monitors supports the feasibility of large-scale data collection. The empirical modelling methods developed can augment existing approaches and inform decisions regarding operations, maintenance, planning and risk assessment.