The ionospheric convection electric field is often assumed to be a potential field. This assumption is not always valid, especially when the ionosphere changes on short time scales $T \lesssim 5$~min. We present a technique for estimating the induction electric field using ground magnetometer measurements. The technique is demonstrated on real and simulated data for sudden increases in solar wind dynamic pressure of $\sim$1 and 10 nPa, respectively. For the real data, the ionospheric induction electric field is 0.15$\pm$0.015 mV/m, and the corresponding compressional flow is 2.5$\pm$0.3 m/s. For the simulated data, the induction electric field and compressional flow reach 3 mV/m and 50 m/s, respectively. The induction electric field can locally constitute tens of percent of the total electric field. Inclusion of the induction electric field increased the total Joule heating by 2.4\%. Locally the Joule heating changed by tens of percent. This corresponds to energy dissipation that is not accounted for in existing models.