Understanding the spatial and temporal distribution of pumping activities is crucial for effective water resource management. However, obtaining accurate pumping records is often challenging, particularly in areas without efficient groundwater withdrawal permit systems. In this study, we propose a novel approach for identifying pumping activities and estimating their associated pumping rates across space and time. Our data-driven approach integrates empirical orthogonal function (EOF) and Hilbert-Huang transform (HHT) analyses on first-differenced head data to extract high-frequency head variations that are closely related to pumping activities. The identified pumping-associated head variations are used to estimate the on-and-off times of local pumping stations and their associated pumping-rate time series. We test our approach using a hypothetical aquifer with designed pumping and real precipitation time series. Our results show that the EOF analysis is able to distinguish pumping locations where distinct temporal head variabilities are present. HHT analysis is then able to effectively remove noise from the EOF-identified pumping-associated head variations. Compared to the designed pumping data, our results demonstrate that our proposed method is able to produce accurate pumping estimates in terms of both spatial and temporal distribution and total amounts. While our approach does have limitations, such as delayed and boundary effects, our results suggest that it can be an effective tool for pumping estimation in areas with relatively abundant head observations across space and time, which is a common scenario in Taiwan.