For simulations of future climate to be reliable, clouds must be represented as realistically as possible. However, most radiation schemes in climate models currently make a number of simplifications when accounting for clouds, one of the most important being the removal of horizontal inhomogeneity (the "plane-parallel" approximation). This has significant effects on the interactions of the clouds with radiation. In this thesis, a new scheme called "Tripleclouds" is presented that attempts to account for the neglected inhomogeneity by using two regions of cloud in each vertical layer of the model as opposed to one. One of these regions represent the optically thinner cloud in the layer, and the other represents the optically thicker cloud. Furthermore, the scheme uses a ''decorrelation'' overlap method that improves on more conventional "maximum-random'' overlap by overlapping vertically continuous cloud with increasing randomness for pairs of layers with larger vertical separation.