## 4 Data and Methods
### Cloud Simulation  
The simulation of cloud cover is one of the two major steps within this study. For the sake of comparability, simulated cloud cover in multi-spectral imagery has numerous advantages. Besides the opportunity to evaluate the quality of the cloud-filled multi-spectral image, due to the availability of a perfectly cloud-free reference, the control of the percentaged amount of cloud cover is very useful in terms of estimating the potential of SAR data for a reasonable cloud removal. Clouds doubtlessly can take on an infinite number of different shapes due the underlying processes while their development, in the course of wind shear, whilst merging of clouds _etc._[24]. Therefore the main focus of a cloud cover model must be the usage of geometric shapes representing the natural circumstances the best possible. Moreover, the geometric shape must not be an additional source of uncertainty, since the usage of very complex geometric models could be a source of certain errors. Considering these facts, the geometric shapes used in this study to simulate clouds are ellipses. In literature concerning clouds as 2-D objects, ellipses are very common to describe and abstract the shape of clouds [9, 20, 25, 26]. A huge variety of parameters such as water vapor content, particle size, particle size distribution and optical thickness seem important to describe cloud cover. In addition to these optical and microphysical properties, the size and distribution are the most important factors under consideration. Obviously, for the sake of removing cloud cover from remote sensing imagery, the knowledge of its microphysical properties can be regarded as dispensable. Only the optical thickness is of interest since it affects the ground signal. Within this study, only optical thick clouds are considered in the simulation. As a consequence, the information beneath a cloud can be regarded as lost and therefore must be reconstructed autonomous from the information at the specific spatial location. Hence, the only need for parameterization that arises from this section is the amount of cloud cover (%) within the multi-spectral image [27]. Regarding cloud cover as missing information required parameters of considerable significance are the size of clouds on the one hand, and their spatial distribution on the other hand. Based on these simple assumptions, an approximate model of cloud cover can be established using only three basic parameters, namely:  
* cloud cover fraction (%),
* mean cloud size (m),
* spatial distribution ( ).  
The mean cloud size is defined here as the diameter of the horizontal cloud. According to the findings from Section 2.1.2, the modal cloud sizes of cumulus clouds range in 1-2 km [24, 28, 29]. Since the test area is comparatively small, the mean cloud size in this study is fixed at a horizontal cloud diameter of 1 km. There are numerous indications that the consideration of the spatial pattern of clouds is very important [26, 29, 30, 31, 32]. For a practical solution, an index for the description of spatial organization is necessary in support of meaningful cloud simulation software. The measure used in this study is a spatial aggregation index \(R\) defined by [33]. The range of values of \(R\) is from 0 (maximum clustering) over 1 (perfectly random distribution) to 2.1491 (strictly hexagonal distribution) [33, 34].