Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Mechanism analyses of scale effects <s> The problem of how the scale, or spatial resolution, of reflectance data impacts retrievals of vegetation leaf area index (LAI) is addressed in this article. We define the goal of scaling as the process by which it is established that LAI values derived from coarse resolution sensor data equal the arithmetic average of values derived independently from fine resolution sensor data. The increasing probability of land cover mixtures with decreasing resolution is defined as heterogeneity, which is a key concept in scaling studies. The effect of pixel heterogeneity on spectral reflectances and LAI retrievals is investigated with 1-km Advanced Very High Resolution Radiometer (AVHRR) data aggregated to different coarse spatial resolutions. It is shown that LAI retrieval errors at coarse resolution are inversely related to the proportion of the dominant land cover in such pixel. Further, large errors in LAI retrievals are incurred when forests are minority biomes in non-forest pixels compared to when forest biomes are mixed with one another, and vice versa. A physically based scaling with explicit spatial resolution-dependent radiative transfer formulation is developed. The successful application of this theory to scaling LAI retrievals from AVHRR data of different resolutions is demonstrated. These principles underlie our approach to the production and validation of LAI product from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Multi-angle Imaging Spectroradiometer (MISR) aboard the TERRA platform. <s> BIB001 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Mechanism analyses of scale effects <s> Abstract Land surface temperature (LST) is a key parameter in numerous environmental studies. Surface heterogeneity induces uncertainty in pixel-wise LST. Spatial scaling may account for the uncertainty, however, different approaches lead to differences in scaled values. Satellite-retrieved LST may be representative of the pixel-wise LST and useful for scaling analysis, but the limited accuracy of retrieved values adds uncertainty into the scaled values. Based on the Stefan–Boltzmann (S–B) law, this study proposed scaling approaches for LST over flat and relief areas to explore the combined uncertainties in scaling using satellite-retrieved data. To take advantage of simultaneous, multi-resolution observations at coincident nadirs by the Advanced Spaceborne Thermal Emission Reflection Radiometer (ASTER) and the MODerate-resolution Imaging Spectroradiometer (MODIS), LST products from these two sensors were examined for part of the Loess Plateau in China. 90-m ASTER LST data were scaled up to 1 km using the proposed approaches, and variation in the LST was generally reduced after scaling. Amongst the sources of uncertainties, surface heterogeneity (emissivity) and different scaling approaches resulted in very minor differences, with a maximum difference of 0.2 K for the upscaled LST. Terrain features, taken as an areal weighting factor, had negligible effects on the upscaled value. Limited accuracy of the retrieved LST was the major uncertainty. The overall LST increased 0.6 K on average with correction for terrain-induced angular effect and 0.4 K for both angular and adjacency effects over the study area. Accounting for terrain correction in scaling is necessary for rugged areas. With terrain correction, the upscaled ASTER LST achieved an agreement of − 0.1 ± 1.87 K and a root mean square error (RMSE) of 1.87 K overall with the 1-km MODIS LST rectified by Wan et al.'s approach [Wan, Z., Zhang, Y., Zhang Q., Li, Z.-L. (2002b), Validation of the land-surface temperature products retrieved from Terra Moderate Resolution Imaging Spectroradiometer data. Remote Sensing of Environment, 83 , 163–180]. Refining the rectification approach resulted in a better agreement of − 0.2 ± 1.57 K and a RMSE of 1.58 K. <s> BIB002
In order to analyze the mechanism of scale effects, firstly, we need to abstract the retrieval process from reality, which is concluded as follows: where measurements refer to the physical quantity measured by remote sensing; f refers to the retrieval model that is used to estimate products from measurements; products are the characteristic parameters of land surface, such as biophysical (e.g., leaf area index, fraction of photosynthetically active radiation absorbed by vegetation) or geophysical variables (e.g., albedo, emissivity). The measurements, retrieval model and products may not be the same at different scales. So they can be considered as scale-dependent. The relationships are demonstrated in Figure 1 . Here, n r or R   , f or F and n p or P   represent the measurements, retrieval models and products at the local or large scale, respectively. Apparently, if the retrieval models at both local scale and large scale are available, there is no scale effect yet. The products retrieved by remote sensing can be estimated by the corresponding models. However, only retrieval models at a local scale are usually proposed, as they can be easily validated in the laboratory or the testing field. Generally, the retrieval model may not be the same for different scales as the dominant factors or stated variables are variable at different scales. For example, both Lowtran and Modtran are radiative transfer models, however, they are only suitable for the low spectral scale and the moderate spectral scale, respectively. In such a situation, the scaling for the retrieval model is necessary. The first task of scale research in remote sensing is to determine the validation scope of retrieval models. Based on physical analysis, the retrieval models are simplified or re-parameterized to adapt to the new scale. If we do not scale retrieval models and only adopt the same form at different scales, there are two other alternative methods to compensate for the scale effects: the scaling of measurements and the scaling of products. If we assume the retrieval models are the same at any scale, there are two ways to estimate measurements or retrieve products at a large scale. One is to aggregate measurements and products directly using local scale data, thereby producing average measurements R   . It is difficult to determine which are best. We can only select the appropriate one by real situations. For example, the goal of scaling for leaf area index (LAI) is to make the values derived from coarse resolution sensor data equal to the arithmetic average of values derived independently from fine resolution sensor data BIB001 . If the retrieval model is proposed at local scale and the products estimated are associated with the unit area, such as LAI, 1 P   may be more suitable because it follows the law of conservation of matter. Otherwise, 2 P   may be more advisable. The product of temperature is an example. Here is the other thing we need to pay more attention to. The aggregation may not be area-weighted, the aggregation of radiance in a heterogeneous terrain region should consider both the area and the local slope angle effects BIB002 . Besides, not all the aggregation is scientifically reasonable. As the aggregation of temperature follows neither the law of conservation of energy nor the law of conservation of matter, consequently, it may not make sense. The discrepancy between 