## 5 Overview of general scaling methods
### The scaling methods for products
In conclusion, the method is easy to understand and operate. If the intra-pixel spatial heterogeneity can be successfully represented, it can give reasonable results. The disadvantage of TSEM is that it must satisfy some hypotheses. The model needs to be continuous and have at least up to second order continuous derivatives in the interval under consideration. If the model has strong non-linearity, the approximation would not be appropriate. When using complicated models with a large number of variables, it would be difficult to find the derivatives of the model [16]. Again, failure to include high order terms or interactive terms (covariance) may limit the application of this technique. Generally, the variance and covariance within one pixel are important for the traditional textural parameters that can capture the spatial variability of the surface. However, they are difficult to be estimated due to the fact that the concurrencies of high and low resolution images are often not available. In addition, they may not be used to discriminate the situations where the surface heterogeneity can be caused either by the cover type changes or by density change within the same cover type. If the surface heterogeneity is caused by cover type changes, the linear models which have different forms for different cover types may also cause scale effects. In contrast, if the surface heterogeneity is caused only by density change, the non-linearity of the model would generally cause very small scale effects [31, 32]. In short, TSEM would be useless when the model is discontinuous or piecewise against the measurements. In order to break through the limitations of using textural parameters, [PERSON] [31] proposed a different scheme, CPM. It took the contextual parameters (e.g., the fractions of subcomponents) as a bridge to quantify the scaling effects. [PERSON] _et al_. [55] tried to use such subpixel information to upscale NPP. The result showed that the correlation between the distributed NPP and lumped NPP was greatly improved. [PERSON] and [PERSON] [44] thought the scale effects resulted from the overlooking of sub-pixel variability of land surface characteristics and proposed a simple algorithm that used contextural parameters of vegetation, soil cover, and surface topography to correct evapotranspiration (ET) estimates. [PERSON] _et al_. [54] developed such algorithms to remove the biases in lumped LAI maps using sub-pixel land cover-type information and correct coarse resolution products of LAI. Here the fractions can be estimated either by the sub-pixel land cover masks at high resolutions or the linear unmixing method. [PERSON] _et al_. [77] used the Bayesian-regularized artificial neural network with combined MODIS-MISR data to estimate sub-pixel land cover fractions and yielded a quantitative improvement result over spectral linear unmixing of single-angle, multispectral data. The result is promising. However, contexture-based methods are usually model-dependent. They cannot provide a general method to compensate for scaling effects. The mapping function needs to be redefined when the model is changed. When the model has several variables, the mapping functions become very hard to be derived. Therefore, contexture-based methods are not alternatives to texture-based methods. They are new attempts to solve scaling effects. In practice, we need to choose the corresponding scaling methods according to actual requirements. SFSM is based on the simple scaling and multiscaling characteristics of products. [PERSON] _et al_. [78] have found the log-log linearity relationship between the statistical moment and the scale factor, and the non-linear dependence of scaling exponents with order moment. That is to say, the statistical properties (moments) of process can be extended from one scale to the other scale. [PERSON] _et al_. [47] analyzed the statistical characterization of soil moisture retrieved from remotely sensed passive microwaves.