## 3 Mechanism analyses of scale effects
### Main causes of scale effects  
The main causes of scale effects can be summed up in three main reasons from the perspective of analysis, processing and modeling. The first reason is the limitation of measurement. Any measurement equipment has its own scale representation. It can only reflect the specific information within the scope of observation. An infrared radiometer at ground level can merely represent the temperature at the scale of points; however, the Large Aperture Scintillometer (LAS) can reflect the exchange of energy at the scale of a region. [PERSON] _et al_. [23] have shown that the criterion for judging whether the surface temperature is isothermal or not may only be dependent on the spatial scale or the spectral scale through experimental verification. Along with the change of scale, the isothermal surface could become non-isothermal. The second reason is the scale applicability of the retrieval models. The retrieval models do not explicitly express the characteristics of scale; however, they may be suitable for homogeneous surface or point measurements [4]. [PERSON] _et al_. [24] pointed out that it is not appropriate to use relationships between model and observational variables developed and calibrated at a local scale for application at a larger scale just by scaling the parameters. As a result, they need to be simplified or re-parameterized to adapt to the new circumstances since the driving force or mechanism may be totally different at various scales. It is difficult to imagine that models at the scale of leaves are still applicable to the scale of canopy. Consequently, the models or algorithms proposed at one scale would be neither effective, nor similar, or need to be revised at any other scale. Therefore, the first step of scale research is to investigate the impact of scale on the mechanism of physical models and algorithms. At present, the scale applicability of [PERSON]'s assumption [25], [PERSON]'s law [26], [PERSON]'s reciprocity principle [27], and Planck's Law [28, 29] have already been discussed at the pixel scale in remote sensing applications. The results showed that we need to carefully consider the scale's applicability for retrieval models when using them at different scales. The third reason is the heterogeneity of land surface and the characteristics of linearity or nonlinearity of the retrieval models. These two factors affect the scale effects together. If the measurements are homogeneous, it would not cause scale effects no matter whether the retrieval models are linear or not. The heterogeneity could be thought of as the inherent nature of land surfaces, which are a mosaic of different cover types. In other words, heterogeneity would be considered as the surface properties vary over the observed scene [19]. When observing through sensors, it may be very heterogeneous, especially in the case of coarser spatial resolution sensors. As the resolution decreases, the possibility that one pixel contains more than one cover type would increase. Therefore, heterogeneity is the most fundamental characteristic of all landscapes [30]. If land surface measurements or media properties vary in observation unit (space), it can be thought of as heterogeneity [5]. The surface heterogeneity is often of great concern when deriving surface parameters using remotely sensed data [31]. Here, the heterogeneity may be caused either by the change of density or the discontinuity that means the contrast change between cover types. The scale effects due to density change are usually smaller and can be negligible [31, 32]. On the whole, the term heterogeneity is a relative concept. The homogeneous canopy may still cause the heterogeneity of temperature due to the shade. In order to limit the influence of heterogeneity on the description of land surface processes, [PERSON] _et al_. [19] suggested two strategies. One is to quantify the intra-pixelspatial heterogeneity. The other is to define the proper pixel size to capture the variability of data and minimize the intra-pixel variability.