Monitoring geomagnetic activity is essential for predicting and mitigating the impacts of space weather on our planet. Damages to infrastructure, GPS failures, communication disruptions, and electrical power blackouts, as well as enhanced decay of satellites' orbits, may all be a consequence of intense geomagnetic storms. To be able to mitigate geomagnetic storms impact, we can study magnetospheric equatorial currents by monitoring storms effect at low latitudes and ground level. In this paper, we calculate Local Disturbance indices (LDi) using data from two equatorial observatories (Ascension ASC and Fúquene FUQ) to use them as Dst-index proxies. We find that the LDi response to geomagnetic storms is different depending on the observatory's local time at the storm onset. In order to explore this local time influence on the measurements on the ground at low latitudes, we build new proxies using two observatories located at approximately the same longitude. The average of the longitude pairs exhibit strong correlation to the Dst index (≥ 0.88) during active periods and a moderate correlation (≥ 0.5) during quiet periods. We find that the storm intensity is associated with local time. We confirm that the fastest variation in the geomagnetic field during the storm is recorded between dusk and midnight, while the region between dawn and noon records more moderate variations, sometimes missing the storm effects altogether. Our results show an azimuthal asymmetry of the magnetospheric ring current, becoming most intense on the night side of the dusk terminator during active periods. We suggest that a global index is not enough to characterise the risk from geomagnetic storms. A local-time dependent index could be used, and good local time coverage of the equatorial magnetic field is important to better quantify and forecast possible impacts to infrastructure on Earth and space.