Atmospheric processes are highly nonlinear. A small group at the METU in Ankara has been working on a fuzzy data driven generic model of nonlinear processes. The model developed is called the Middle East Technical University Fuzzy Neural Network Model (METU-FNNM). The METU-FNN-M consists of a Fuzzy Inference System (METU-FIS), a data driven Neural Network module (METU-FNN) of one hidden layer and several neurons, and a mapping module, which employs the Bezier Surface Mapping technique. In this paper, the percent cloud coverage (%CC) and cloud top temperatures (CTT) are forecast one month ahead of time at 96 grid locations. The probable influence of cosmic rays and sunspot numbers on cloudiness is considered by using the METU-FNN-M.