© Author(s) 2016. Surface melt and mass loss of the Greenland Ice Sheet may play crucial roles in global climate change due to their positive feedbacks and large fresh-water storage. With few other regular meteorological observations available in this extreme environment, measurements from automatic weather stations (AWS) are the primary data source for studying surface energy budgets, and for validating satellite observations and model simulations. Station tilt, due to irregular surface melt, compaction and glacier dynamics, causes considerable biases in the AWS shortwave radiation measurements. In this study, we identify tilt-induced biases in the climatology of surface shortwave radiative flux and albedo, and retrospectively correct these by iterative application of solar geometric principles. We found, over all the AWS from the Greenland Climate Network (GC-Net), the Kangerlussuaq transect (K-transect) and the Programme for Monitoring of the Greenland Ice Sheet (PROMICE) networks, insolation on fewer than 40% of clear days peaks within ±0.5h of solar noon time, with the largest shift exceeding 3h due to tilt. Hourly absolute biases in the magnitude of surface insolation can reach up to 200W m-2, with respect to the well-understood clear-day insolation. We estimate the tilt angles and their directions based on the solar geometric relationship between the simulated insolation at a horizontal surface and the observed insolation by these tilted AWS under clear-sky conditions. Our adjustment reduces the root mean square error (RMSE) against references from both satellite observation and reanalysis by 16W m-2 (24%), and raises the correlation coefficients with them to above 0.95. Averaged over the whole Greenland Ice Sheet in the melt season, the adjustment in insolation to compensate station tilt is ∼ 11W m-2, enough to melt 0.24m of snow water equivalent. The adjusted diurnal cycles of albedo are smoother, with consistent semi-smiling patterns. The seasonal cycles and inter-annual variabilities of albedo agree better with previous studies. This tilt-corrected shortwave radiation data set derived using the Retrospective, Iterative, Geometry-Based (RIGB) method provide more accurate observations and validations for surface energy budgets studies on the Greenland Ice Sheet, including albedo variations, surface melt simulations and cloud radiative forcing estimates.