## 5 Overview of general scaling methods
### The scaling methods for products
They found these properties and suggested a deviation from simple scaling and the possible presence of multiscaling [49, 79]. [PERSON] and [PERSON] [50] argued that the scaling exponent of soil moisture during dry-down suggests a transition from simple scaling (in wet fields) to multiscaling (in dry fields) behavior. However, the fluctuation parts of soil moisture, which is decomposed by wavelet transforms, showed a simple scaling characteristic which implied the possibility of scaling soil moisture. In addition to soil moisture, other products also behave with self-similarity characteristics, such as NDVI and radiometric temperature [80]. Based on the multiple moments scaling law, the wish of scaling between different scales without other prior knowledge may be realized. Table 3 summarizes the general scaling methods discussed above. Besides these methods, we can use other methods for scaling the products, such as disaggregation-aggregation combined methods[81], process simulation methods [9] and so on. Again, additional information provided by optical and thermal sensors can be used as auxiliary knowledge to assist the scaling. [PERSON] [82] utilized such information and proposed the DisTrad technique to estimate subpixel variation of surface temperature. On the whole, scaling methods for products have already become a universally recognized problem. Its development needs the development of cross-disciplines in order to achieve theoretical and technical innovation. \begin{table}
\begin{tabular}{c c c c} \hline
**Categories** & **Methods** & **Advantages** & **Disadvantages** & **Ref.** \\ \hline \multirow{4}{*}{Scaling methods for measurements} & \multirow{2}{*}{AWM} & - Simple principle. & \multirow{2}{*}{- May be only suitable for flat regions.} & [22] \\  & & - Easy usage. & & \\ \cline{2-4}  & \multirow{2}{*}{FRPM} & - Simple principle. & - The representative parameters may have no & \\  & & - The analytical & specific physical meanings. & \\  & & solution to scale & - It is difficult to get representative parameters & \\  & & measurements. & when facing a large number of input arguments. & \\ \hline \multirow{4}{*}{Scaling methods for retrieval models} & \multirow{4}{*}{CGM} & - Regardless of whether or not & - Does not take into account the actual & \\  & & - Regardless of & distribution of parameters. The weights for & \\  & & whether or not & lower and upper bounds of a retrieval model & [4] \\ \cline{1-1}  & \multirow{2}{*}{CGM} & retrieval models & may be inappropriate. & [16] \\ \cline{1-1}  & & are continuous or & - Needs a large amount of computing time and a & [68] \\ \cline{1-1}  & & derivable. & special algorithm to retrieve convex hull, when & \\ \cline{1-1}  & \multirow{2}{*}{PSM} & - More accurate. & - It is difficult to derive when facing a large & [11] \\ \cline{1-1}  & & - Easy usage. & - Less accurate. & [53] \\ \cline{1-1}  & & & - The retrieval model and its derivatives must be & \\ \cline{1-1}  & \multirow{2}{*}{TSEM} & - Better basis of & - It may cause greater error when the model is & [16] \\ \cline{1-1}  & & - Easy usage. & strongly non-linear. & [33] \\ \cline{1-1}  & & & - The model needs to use the local variance as & \\ \cline{1-1}  & & & input, which may usually not be available. & \\ \hline \end{tabular}
\end{table} 
Table 3: Summaries of general scaling methods used in remote sensing.