A new method of generating two‐dimensional and three‐dimensional cloud fields is presented, which share several important statistical properties with real measured cloud fields. Well‐known algorithms such as the Fourier method and the Bounded Cascade method generate fields with a specified Fourier spectrum. The new iterative method allows for the specification of both the power spectrum and the amplitude distribution of the parameter of interest, e.g. the liquid water content or liquid water path. As such, the method is well suited to generate cloud fields based on measured data, and it is able to generate broken cloud fields. Important applications of such cloud fields are e.g. closure studies. The algorithm can be supplied with additional spatial constraints which can reduce the number of measured cases needed for such studies. In this study the suitability of the algorithm for radiative questions is evaluated by comparing the radiative properties of cloud fields from cloud resolving models of cumulus and stratocumulus with their surrogate fields at nadir, and for a solar zenith angle of 0° and 60°. The cumulus surrogate clouds ended up to be identical to the large eddy simulation (LES) clouds on which they are based, except for translations and reflections. The root mean square differences of the stratocumulus transmittance and reflectance fields are less than 0.03% of the radiative budget. The radiances and mean actinic fluxes fit better than 2%. These results demonstrate that these LES clouds are well described from a radiative point of view, using only a power spectrum together with an amplitude distribution.