Observations of sunlight reaching the Earth's surface are crucial for a range of applications, including accurate monitoring and nowcasting of solar energy. Satellite retrieval algorithms for global horizontal irradiance (GHI) are generally one-dimensional (1D), assuming horizontally independent and homogeneous pixels, called the independent pixel approximation (IPA) and plane-parallel approximation (PPA), respectively. In reality, clouds scatter radiation in three dimensions, introducing retrieval errors which – without prior knowledge of three-dimensional (3D) cloud structures – remain unknown. This study assesses the PPA and IPA validity in GHI retrievals for two highly variable cumulus cloud fields at spatial resolutions ranging from 0.05 to 12.4 km. Using accurate 3D Monte Carlo radiative transfer (RT) simulations, synthetic top-of-atmosphere reflectances are generated, from which GHI is retrieved. GHI calculated directly from the input using 1D and 3D RT serves as a reference. We explain how horizontal photon transport leads to GHI underestimations in clear-sky regions, while in cloud shadows GHI is overestimated. Furthermore, towards coarser spatial resolutions, the PPA introduces retrieval biases due to mixing of cloudy and clear-sky reflectances. Generally, domain-averaged biases are minimal at a resolution of 1 to 3 km. In terms of root mean square error, the largest disagreements are observed at the finest spatial scales, with IPA-related errors dominating for resolutions finer than about 2 to 6 km. The current generation of geostationary satellites already resolves these finer spatial scales. Therefore, this work emphasises the need to develop 3D RT parameterizations and corrections for GHI retrievals.