Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Semivariogram based method (SVM) <s> This text provides the applied scientist, engineer or statistician with an introduction to geostatistics stressing the multivariate aspects. Geostatistics offers a variety of models, methods and techniques for the analysis, estimation and display of multivariate data distributed in space or time. The book presents a brief review of statistical concepts, an introduction to linear geostatistics and an account of three basic methods of multivariate analysis. Moreover, it presents an advanced presentation of linear models for multivariate spatial or temporal data, including the recent bilinear model of coregionalization, and an introduction to non-stationary geostatistics with a special focus on the external drift method. <s> BIB001 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Semivariogram based method (SVM) <s> Abstract The appropriate spatial scale for a distributed energy balance model was investigated by: (a) determining the scale of variability associated with the remotely sensed and GIS-generated model input data; and (b) examining the effects of input data spatial aggregation on model response. The semi-variogram and the characteristic length calculated from the spatial autocorrelation were used to determine the scale of variability of the remotely sensed and GIS-generated model input data. The data were collected from two hillsides at Upper Sheep Creek, a sub-basin of the Reynolds Creek Experimental Watershed, in southwest Idaho. The data were analyzed in terms of the semivariance and the integral of the autocorrelation. The minimum characteristic length associated with the variability of the data used in the analysis was 15 m. Simulated and observed radiometric surface temperature fields at different spatial resolutions were compared. The correlation between agreement simulated and observed fields sharply declined after a 10×10 m 2 modeling grid size. A modeling grid size of about 10×10 m 2 was deemed to be the best compromise to achieve: (a) reduction of computation time and the size of the support data; and (b) a reproduction of the observed radiometric surface temperature. <s> BIB002 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Semivariogram based method (SVM) <s> Global NDVI data are routinely derived from the AVHRR, SPOT-VGT, and MODIS/Terra earth observation records for a range of applications from terrestrial vegetation monitoring to climate change modeling. This has led to a substantial interest in the harmonization of multisensor records. Most evaluations of the internal consistency and continuity of global multisensor NDVI products have focused on time-series harmonization in the spectral domain, often neglecting the spatial domain. We fill this void by applying variogram modeling (a) to evaluate the differences in spatial variability between 8-km AVHRR, 1-km SPOT-VGT, and 1-km, 500-m, and 250-m MODIS NDVI products over eight EOS (Earth Observing System) validation sites, and (b) to characterize the decay of spatial variability as a function of pixel size (i.e. data regularization) for spatially aggregated Landsat ETM+ NDVI products and a real multisensor dataset. First, we demonstrate that the conjunctive analysis of two variogram properties – the sill and the mean length scale metric – provides a robust assessment of the differences in spatial variability between multiscale NDVI products that are due to spatial (nominal pixel size, point spread function, and view angle) and non-spatial (sensor calibration, cloud clearing, atmospheric corrections, and length of multi-day compositing period) factors. Next, we show that as the nominal pixel size increases, the decay of spatial information content follows a logarithmic relationship with stronger fit value for the spatially aggregated NDVI products (R2 = 0.9321) than for the native-resolution AVHRR, SPOT-VGT, and MODIS NDVI products (R2 = 0.5064). This relationship serves as a reference for evaluation of the differences in spatial variability and length scales in multiscale datasets at native or aggregated spatial resolutions. The outcomes of this study suggest that multisensor NDVI records cannot be integrated into a long-term data record without proper consideration of all factors affecting their spatial consistency. Hence, we propose an approach for selecting the spatial resolution, at which differences in spatial variability between NDVI products from multiple sensors are minimized. This approach provides practical guidance for the harmonization of long-term multisensor datasets. <s> BIB003
The semivariogram is often used as a tool to measure the difference in property values at two sample locations as a function of the distance between these locations. It provides the mean characteristics of spatial heterogeneity at the image scale. There are three features to characterize the semivariogram: nugget, sill and range. These features can be used to characterize and quantify the spatial heterogeneity of a land surface  . The nugget is the discontinuity of the semivariogram at the origin. It can be used to judge if uncorrelated noise (measurement error) exists or spatial structures are smaller than the pixel size. The sill is the value that the semivariogram may reach when the distance heads toward infinity. It can be an indicator of the spatial variability of the data. The range is the distance at which it reaches a sill. It can be used to characterize the image spatial structures. Artan et al. BIB002 used the semivariogram and the characteristic length calculated from the spatial autocorrelation to determine the scale of variability of the remotely sensed data. In order to account for the multiple length scales of data, Wackernagel BIB001 and Garrigues et al.  proposed a linear combination of elementary variogram models to model the semivariogram. Then, the structural parameters of the semivariogram model can be generalized into a single parameter: the integral range ( A ). Here, its square root c D is a weighted average of several range parameters and quantifies the mean length scale of data. Based on Shannon's theorem, the spatial sampling frequency must be larger than 2 / c D , therefore, the pixel size must be smaller than / 2 c D to retain the major part of spatial variability. Here, either A or c D can be used to judge whether the geographical scale is large enough to detect the length scales of the landscape. In addition, the rate of data regularization can be used to characterize the rate of the loss of image spatial variability at a given spatial resolution. Tarnavsky et al. BIB003 applied variogram modeling to evaluate the difference in spatial variability at different scales and characterize the impact of scale. Based on the analysis, an approach for selecting the spatial resolution is proposed. Subsequently, Garrigues et al.  proposed to use multivariate, red and near infrared spectral properties to quantify the landscape spatial heterogeneity by direct and crossvariograms modeled together with the geostatistical linear model of co-regionalization. The result showed it to be more powerful than univaritate variogram modeling.