We found that cloud spatial structure manifests itself as spectral signature in shortwave irradiance fields – specifically in transmittance and net horizontal photon transport in the visible and near-ultraviolet wavelength range. In this paper, we demonstrate this through radiative transfer calculations with cloud imagery from a field experiment, and show that such three-dimensional effects may occur on scales up to 60 km. Neglecting net horizontal photon transport leads to a transmittance bias on the order of ±12–19 % even at the relatively coarse spatial resolution of 20 km, and of more than ±50 % for 1 km. This poses a problem for radiative energy budget estimates from space because the bias for any pixel depends on its spatial context in a non-trivial way. The key for solving this problem may lie in the spectral dimension, since we found a robust correlation between the magnitude of net horizontal photon transport (H) and its spectral dependence (slope). It is scale-invariant and holds for the entire pixel population of a domain. This was at first surprising given the large degree of spatial inhomogeneity, but seems to be valid for any cloud field. We prove that the underlying physical mechanism for this phenomenon is molecular scattering in conjunction with cloud inhomogeneity. On this basis, we developed a simple parameterization through a single parameter ε, which quantifies the characteristic spectral signature of spatial heterogeneities. In a companion paper, we will show that it is accompanied by spectral radiance perturbations, which can be detected from multi-spectral imagers and may be translated into bias reductions for cloud radiative effect estimates in the future.