## 2 The definition of scale and relevant terminologies
### Notions of scales
It can be defined either as spatial extent (the lifetime), period (cycle) or the correlation length (integral scale), depending on the nature of the process [5]. Here, if the operational scale is smaller than the modeling scale, the variability lower than the modeling scale may be lost and the process may not be observed or found. 4. Geographic scale, which is also called \"coverage\", refers to the spatial extent of research. It determines the biological organization level on which the surface property is observed, such as the leaves (a few centimeters), the canopy (10 to 100 m), the landscape (100 m to a few kilometers) or the region (about 100 km) [19]. A larger geographic scale study involves a larger spatial area, and a smaller geographic scale study only contains a smaller spatial area. The ratio between geographic scale and measurement scale often determines data volume and constrains storage and processing capacities. \begin{table}
\begin{tabular}{c c c} \hline Operational scale & The scale of action at which a certain process is supposed to operate. & Depending on the nature of the process. Variability lower than modeling scale may be lost if the operational scale is smaller than the modeling scale. \\ \hline Geographic scale & The spatial extent of research & A larger geographic scale study involves a larger spatial area and a smaller geographic scale study only contains a smaller spatial area. \\ \hline Policy scale & The scale at which the decisions are made or the policy is implemented & In order to infer a reliable conclusion, the policy scale should be larger than the operational scale. \\ \hline Cartographic scale & The ratio between distance on the map and on the ground & A smaller cartographic scale corresponds to a larger geographic scale and may show fewer instances of features or less detail. \\ \hline \end{tabular}
\end{table} 
Table 1: Cont. (5) Policy scale is the scale at which the decisions are made or the policy is implemented [15]. For example, whether the crop yield of one specific village is reduced or not, may be judged on village level on the basis of one year. In order to infer a reliable conclusion, the policy scale should be larger than the operational scale. (6) Cartographic scale is defined simply as the ratio between distance on the map and on the ground. It is often used to represent the spatial distribution of research results. Generally speaking, a smaller cartographic scale corresponds to a larger geographic scale and may show fewer instances of features or less detail when compared to a larger cartographic scale. The six meanings of scale described above are mutually related. It is indispensable to determine the desirable scale before investigation. But, how do you select the suitable scale in remote sensing? Generally speaking, the choice of scale may only depend on the goals of the study if you do not take other factors (i.e., manpower, finance and time) into account. Commonly, the policy scale is determined first. And then, the operational scale is decided based on the previous knowledge of the research. Due to the fact that the policy scale is selected by the decision-making department and the operational scale is the natural characteristic of the process, they may have nothing to do with remote sensing. Remote sensing may only be used to provide knowledge to reveal the actual operational scale. By comparion, the observation scale, modeling scale and geographic scale are more closely related to remote sensing. They are more or less determined by the application of remote sensing. The smaller observation scale is not always correct. For example, the optimum observation scale for classification in land use and land cover is the scale where the variability within classes is at its minimum and the variability between classes is at its maximum. On the whole, the geographic scale should be large enough to characterize the image spatial variability or structures.