Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> A geometric-optical forest canopy model that treats conifers as cones casting shadows on a contrasting background can explain the major portion of the variance in a remotely sensed image of a forest stand. The model is driven by interpixel variance generated from three sources: 1) the number of crowns in the pixel; 2) the size of individual crowns; and 3) overlapping of crowns and shadows. The model uses parallel-ray geometry to describe the illumination of a three-dimensional cone and the shadow it casts. Cones are assumed to be randomly placed and may overlap freely. Cone size (height) is distributed lognormally, and cone form, described by the apex angle of the cone, is-fixed in the model but allowed to vary in its application. The model can also be inverted to provide estimates of the size, shape, and spacing of the conifers as cones using remote imagery and a minimum of ground measurements. Field tests using both 10-and 80-m multispectral imagery of two test conifer stands in northeastern California produced reasonable estimates for these parameters. The model appears to be sufficiently general and robust for application to other geometric shapes and mixtures of simple shapes. Thus it has wide potential use not only in remote sensing of vegetation, but also in other remote sensing situations in which discrete objects are imaged at resolutions sufficiently coarje that they canot be resolved individually. <s> BIB001 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> Abstract Measurements of gap probability, defined as the probability that a photon of direct illumination at a given zenith angle will penetrate a tree canopy, were made for some moderate-sized, open-grown conifers of varying species in the National Arboretum, Washington, D.C. The measurements were collected by ratioing the standardizing readings in red and near-infrared bands of two radiometers with 6° fields of view that were pointed directly at the sun. One radiometer was located within the shadow of the conifer tree; the other was placed outside of the shadow. The path length associated with each radiometric measurement was calculated by fitting a simple conical geometric model to each tree from measurements of tree height and width. The radiometric measurements are best fit by a binomial model in which sunlight is either unobstructed or fully attenuated, and analysis show that the gap probability, which is taken as the mean of the binomial, fits a negative exponential function of path length quite well. The conifer shadow, then, is an object of almost uniform darkness with some bright holes or gaps that are found near the shadow's edge but rapidly disappear toward the shadow's center. <s> BIB002 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> Abstract Models used in remote sensing are based mostly on a relationship between a parameter and the measured reflectance at a given wavelength. They are generally built on the basis of physical considerations at a scale enough small enough so that the media can be considered to be homogeneous. The general practice in remote sensing is to apply these models to reflectances measured from satellites on heterogeneous surfaces, without considering making any correction in order to compensate for the change of scale. It is shown that this usual practice generates errors, the lower and upper bounds of which are given in the form of two functions associated with the physical model. Finally, a general method is proposed to build a new model connected to the physical one, reducing the error introduced by the heterogeneity of the analysed surface. An application to the role of resolution change for the quantification of covered area is also considered. <s> BIB003 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> Whether the reciprocity principle can be applied to the field or satellite observations of directional reflectance of land surface has been a question important to both theory and practice of land surface remote sensing. Under the assumption that every point on ground follows reciprocity, this paper explains why the heterogeneity of land surface can still yield apparent failure of the principle at the scale of remote sensing pixel. <s> BIB004 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> The issue of using remotely sensed surface temperature to estimate the area-average sensible heat flux over surfaces made up of different vegetated patches has been investigated. The performance of three aggregation procedures, ranging from physically based through semi-empirical, to entirely empirical has been assessed by comparing measured and simulated area-average sensible heat flux. The results show that the physically based scheme perform very well. The performance of the entirely empirical scheme was reasonable but that of the semi-empirical scheme, which actually takes full advantage of remotely sensed data, was very poor. This result suggests that unlike the case of surface fluxes, it is not appropriate to use relationships between model and observational variables (here radiative and aerodynamic surface temperature) that were developed and calibrated at a local/patch scale, for an application at a larger/grid scale just by scaling the parameters. Therefore, future research should be directed towards building robust relationships between model and observational variables directly at the large-scale. <s> BIB005 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> Abstract A major goal of landscape ecology is to understand the formation, dynamics, and maintenance of spatial heterogeneity. Spatial heterogeneity is the most fundamental characteristic of all landscapes, and scale multiplicity is inherent in spatial heterogeneity. Thus, multiscale analysis is imperative for understanding the structure, function and dynamics of landscapes. Although a number of methods have been used for multiscale analysis in landscape ecology since the 1980s, the effectiveness of many of them, including some commonly used ones, is not clear or questionable. In this paper, we discuss two approaches to multiscale analysis of landscape heterogeneity: the direct and indirect approaches. We will focus on scale variance and semivariance methods in the first approach and 17 landscape metrics in the second. The results show that scale variance is potentially a powerful method to detect and describe multiple-scale structures of landscapes, while semivariance analysis may often fail to do so esp... <s> BIB006 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> Leaf area index (LAI) is one of the surface parameters that has importance in climate, weather, and ecological studies, and has been routinely estimated from remote sensing measurements. Canada-wide LAI maps are now being produced using cloud-free Advanced Very High-Resolution Radiometer (AVHRR) imagery every 10 days at 1-km resolution. The archive of these products began in 1993. LAI maps at the same resolution are also being produced with images from the SPOT VEGETATION sensor. To improve the LAI algorithms and validate these products, a group of Canadian scientists acquired LAI measurements during the summer of 1998 in deciduous, conifer, and mixed forests, and in cropland. Common measurement standards using the commercial Tracing Radiation and Architecture of Canopies (TRAC) and LAI-2000 instruments were followed. Eight Landsat Thematic Mapper (TM) scenes at 30-m resolution were used to locate ground sites and to facilitate spatial scaling to 1-km pixels. In this paper, examples of Canada-wide LAI maps are presented after an assessment of their accuracy using ground measurements and the eight Landsat scenes. Methodologies for scaling from high- to coarse-resolution images that consider surface heterogeneity in terms of mixed cover types are evaluated and discussed. Using Landsat LAI images as the standard, it is shown that the accuracy of LAI values of individual AVHRR and VEGETATION pixels was in the range of 50–75%. Random and bias errors were both considerable. Bias was mostly caused by uncertainties in atmospheric correction of the Landsat images, but surface heterogeneity in terms of mixed cover types were also found to cause bias in AVHRR and SPOT VEGETATION LAI calculations. Random errors come from many sources, but pixels with mixed cover types are the main cause of random errors. As radiative signals from different vegetation types were quite different at the same LAI, accurate information about subpixel mixture of the various cover types is identified as the key to improving the accuracy of LAI estimates. D 2002 Elsevier Science Inc. All rights reserved. <s> BIB007 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> Three definitions of emissivity for non-isothermal pixels are evaluated, and their differences are analysed. On the basis of the experimental data and numerical simulation, a generalized formula is established to scale for land surface emissivity, reflectance, and other variables between pixel scale and sub-pixel scale. Finally, it is pointed out that isothermal concept of land surface temperature and homogeneous concept of some other parameters in one spatial scale are relative according to humans' capability of measurement, and that the heterogeneity in a spatial scale is absolute in the natural world. <s> BIB008 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Main causes of scale effects <s> The monitoring of earth surface dynamic processes requires global observations of the structure and the functioning of vegetation. Moderate resolution sensors (with pixel size ranging from 250 m to 7 km) provide frequent estimates of biophysical variables to characterize vegetation such as the leaf area index (LAI). However, the computation of LAI from moderate resolution remote sensing data induces a scaling bias on the LAI estimate if the moderate resolution pixel is heterogeneous and if the transfer function that relates remote sensing data to LAI is non-linear. This study provides a model to evaluate and correct the scaling bias. The model is built first for a univariate semi-empirical transfer function relating LAI directly to NDVI. The scaling bias is a function of (i) the degree of non-linearity of the transfer function quantified by its second derivative and (ii) the spatial heterogeneity of the moderate resolution pixel quantified by the variogram of the high spatial resolution (20 m) NDVI image. Then, the model is extended to a bivariate transfer function where LAI is related to red and near infrared reflectances. The scaling bias depends on (i) the Hessian matrix of the transfer function and (ii) the variograms and cross variogram of the red and near infrared reflectances. The scaling bias is investigated on several distinct landscapes from the VALERI database. Adjusting for scaling bias is critical on crop sites which are the most heterogeneous sites at the landscape level. Regarding the univariate transfer function, the magnitude of the scaling bias increases rapidly with pixel size until this size is larger than the typical spatial scale of the data. For the bivariate transfer function, it results from the addition of several components that may add up or cancel each other out. It is thus more difficult to analyze. The accuracy of the model to estimate the scaling bias is discussed. It depends mainly on the ability of the variograms and cross variogram to represent the local dispersion variances and covariance within the moderate resolution pixel. The model is generally highly accurate at 1000 m spatial resolution for the univariate transfer function and less accurate for the bivariate transfer function. <s> BIB009
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. Zhang et al. BIB008 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 BIB003 . Chehbouni et al. BIB005 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 reparameterized 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 Lambert's assumption BIB001 , Beer's law BIB002 , Helmholtz's reciprocity principle BIB004 , and Planck's Law   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  . 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 BIB006 . If land surface measurements or media properties vary in observation unit (space), it can be thought of as heterogeneity  . The surface heterogeneity is often of great concern when deriving surface parameters using remotely sensed data  . 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  BIB007 . 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, Garrigues et al.  suggested two strategies. One is to quantify the intra-pixel spatial heterogeneity. The other is to define the proper pixel size to capture the variability of data and minimize the intra-pixel variability. Besides the heterogeneity of the land surface, the characteristics of linearity or nonlinearity of the retrieval models is the other factor. We cannot arbitrarily draw the conclusion that the linear retrieval models would not cause a scale effect or that the nonlinear retrieval models would cause a scale effect. The linear retrieval models could also incur scale effects when the retrieval models for different cover types are quite different  . The nonlinear retrieval models may also cause no scale effects when the medium is homogeneous, which has been successfully demonstrated by the Taylor series expansion  BIB009 . Chen  suggested that nonlinear algorithms applied to pixels mixed with different land cover types may be the major cause of scaling errors. Considerable scale effects may be expected for mixed pixels where the mixture is unknown, as radiative signals from different cover types can be very different for the same measurements BIB007 . Generally speaking, the linear retrieval models may cause smaller scale effects than nonlinear ones in such a situation  .