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Handling complexity to the smallest detail in atmospheric radiative transfermodels is unfeasible in practice. On the one hand, the properties of theinteracting medium, i.e., the atmosphere and the surface, are only availableat a limited spatial resolution. On the other hand, the computational cost ofaccurate radiation models accounting for three-dimensional heterogeneousmedia are prohibitive for some applications, especially for climate modelling andoperational remote-sensing algorithms. Hence, it is still common practice touse simplified models for atmospheric radiation applications.  Three-dimensional radiation models can deal with complex scenariosproviding an accurate solution to the radiativetransfer. In contrast, one-dimensional models are computationally more efficient, but introduce biases to the radiationresults.  With the help of stochastic models that consider the multi-fractal nature ofclouds, it is possible to scale cloud properties given at a coarse spatialresolution down to a higher resolution. Performing the radiative transferwithin the cloud fields at higher spatial resolution noticeably helps to improvethe radiation results.  We present a new Monte Carlo model, MoCaRT, that computes the radiative transfer in three-dimensionalinhomogeneous atmospheres. The MoCaRT model is validated by comparison with the consensus results of the Intercomparison ofThree-Dimensional Radiation Codes (I3RC) project.  In the framework of this paper, we aim at characterising cloud heterogeneityeffects on radiances and broadband fluxes, namely: the errors due tounresolved variability (the so-called plane parallel homogeneous, PPH, bias)and the errors due to the neglect of transversal photon displacements(independent pixel approximation, IPA, bias). First, we study the effect ofthe missing cloud variability on reflectivities. We will show that thegeneration of subscale variability by means of stochastic methods greatlyreduce or nearly eliminate the reflectivity biases. Secondly,three-dimensional broadband fluxes in the presence of realisticinhomogeneous cloud fields sampled at high spatial resolutions are calculatedand compared to their one-dimensional counterparts at coarser resolutions.We found that one-dimensional calculations at coarsely resolved cloudy atmospheres systematicallyoverestimate broadband reflected and absorbed fluxes and underestimate transmitted ones

Reduction of radiation biases by incorporating the missing cloud variability by means of downscaling techniques: a study using the 3-D MoCaRT model