Abstract Estimating precipitation over large spatial areas remains a challenging problem for hydrologists. Sparse ground-based gauge networks do not provide a robust basis for interpolation, and the reliability of remote sensing products, although improving, is still imperfect. Current techniques to estimate precipitation rely on combining these different kinds of measurements to correct the bias in the satellite observations. We propose a novel procedure that, unlike existing techniques, (i) allows correcting the possibly confounding effects of different sources of errors in satellite estimates, (ii) explicitly accounts for the spatial heterogeneity of the biases and (iii) allows the use of non overlapping historical observations. The proposed method spatially aggregates and interpolates gauge data at the satellite grid resolution by focusing on parameters that describe the frequency and intensity of the rainfall observed at the gauges. The resulting gridded parameters can then be used to adjust the probability density function of satellite rainfall observations at each grid cell, accounting for spatial heterogeneity. Unlike alternate methods, we explicitly adjust biases on rainfall frequency in addition to its intensity. Adjusted rainfall distributions can then readily be applied as input in stochastic rainfall generators or frequency domain hydrological models. Finally, we also provide a procedure to use them to correct remotely sensed rainfall time series. We apply the method to adjust the distributions of daily rainfall observed by the TRMM satellite in Nepal, which exemplifies the challenges associated with a sparse gauge network and large biases due to complex topography. In a cross-validation analysis on daily rainfall from TRMM 3B42 v6, we find that using a small subset of the available gauges, the proposed method outperforms local rainfall estimations using the complete network of available gauges to directly interpolate local rainfall or correct TRMM by adjusting monthly means. We conclude that the proposed frequency-domain bias correction approach is robust and reliable compared to other bias correction approaches.