Ocean Alkalinity Enhancement (OAE) is a method proposed for ocean-based Carbon-Dioxide Removal and describes the sequestration of CO₂ from the atmosphere through a deliberate increase in alkalinity in the ocean. In this study, we compare multiple approaches for the calculation of the CO₂ uptake efficiency for regional OAE using an Earth system model. We find that for regional alkalinity deployment at the European Atlantic coast the change in the global ocean inventories for dissolved inorganic carbon and alkalinity is not a feasible approach. The OAE-induced removal of CO₂ from the atmosphere leads to phase shifts in the large-scale climate pattern El Niño, but it does not influence its frequency or intensity. This alters the timing of interannual variations in global carbon fluxes, which obscures the detection of the immediate signal of alkalinity addition on ocean carbon uptake on annual to decadal timescales. Approaches that track the regional distribution of the added alkalinity or the OAE-induced regional strengthening of the air-sea CO₂ flux provide more robust estimates of CO₂ uptake efficiency, when the following criteria are taken into account: (i) ocean conditions in and close to the deployment region (e.g., circulation, upwelling and subduction) (ii) the natural variability of surface alkalinity and air-sea CO₂ flux, and (iii) the possible impacts on global climate modes such as El Niño.