Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Characteristics of scales <s> [1] We analyzed spatial and temporal variograms of precipitation, runoff, and groundwater levels in Austria to examine whether characteristic scales exist and, if so, how big they are. In time, precipitation and runoff are stationary with characteristic scales on the order of a day and a month, respectively, while groundwater levels are nonstationary. In space, precipitation is almost fractal, so no characteristic scales exist. Runoff is nonstationary but not a fractal as it exhibits a break in the variograms. An analysis of the variograms of catchment precipitation indicates that this break is due to aggregation effects imposed by the catchment area. A spatial variogram of hypothetical point runoff back calculated from runoff variograms of three catchment size classes using aggregation statistics (regularization) is almost stationary and exhibits shorter characteristic space scales than catchment runoff. Groundwater levels are nonstationary in space, exhibiting shorter-scale variability than precipitation and runoff, but are also not fractal as there is a break in the variogram. We suggest that the decrease of spatial characteristic scales from catchment precipitation to runoff and to groundwater is the result of a superposition of small-scale variability of catchment and aquifer properties on the rainfall forcing. For comparison, TDR soil moisture data from a comprehensive Australian data set were examined. These data suggest that in time, soil moisture is close to stationary with characteristic scales of the order of 2 weeks while in space soil moisture is nonstationary and close to fractal over the extent sampled. Space-time traces of characteristic scales fit well into a conceptual diagram of Bloschl and Sivapalan [1995]. The scaling exponents z in T ∼ Lz (where T is time and L is space) are of the order of 0.5 for precipitation, 0.8 for runoff from small catchments, 1.2 for runoff from large catchments, 0.8 for groundwater levels, and 0.5 for soil moisture. <s> BIB001 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Characteristics of scales <s> The paper revises and clarifies definitions of the term scale and scaling conversions for imaging spectroscopy of soil and vegetation. We demonstrate a new four-dimensional scale concept that includes not only spatial but also the spectral, directional and temporal components. Three scaling remote sensing techniques are reviewed: (1) radiative transfer, (2) spectral (un)mixing, and (3) data fusion. Relevant case studies are given in the context of their up- and/or down-scaling abilities over the soil/vegetation surfaces and a multi-source approach is proposed for their integration. ::: Radiative transfer (RT) models are described to show their capacity for spatial, spectral up-scaling, and directional down-scaling within a heterogeneous environment. Spectral information and spectral derivatives, like vegetation indices (e.g. TCARI/OSAVI), can be scaled and even tested by their means. Radiative transfer of an experimental Norway spruce (Picea abies (L.) Karst.) research plot in the Czech Republic was simulated by the Discrete Anisotropic Radiative Transfer (DART) model to prove relevance of the correct object optical properties scaled up to image data at two different spatial resolutions. Interconnection of the successive modelling levels in vegetation is shown. A future development in measurement and simulation of the leaf directional spectral properties is discussed. ::: We describe linear and/or non-linear spectral mixing techniques and unmixing methods that demonstrate spatial down-scaling. Relevance of proper selection or acquisition of the spectral endmembers using spectral libraries, field measurements, and pure pixels of the hyperspectral image is highlighted. An extensive list of advanced unmixing techniques, a particular example of unmixing a reflective optics system imaging spectrometer (ROSIS) image from Spain, and examples of other mixture applications give insight into the present status of scaling capabilities. ::: Simultaneous spatial and temporal down-scaling by means of a data fusion technique is described. A demonstrative example is given for the moderate resolution imaging spectroradiometer (MODIS) and LANDSAT Thematic Mapper (TM) data from Brazil. Corresponding spectral bands of both sensors were fused via a pyramidal wavelet transform in Fourier space. New spectral and temporal information of the resultant image can be used for thematic classification or qualitative mapping. <s> BIB002
Although "scale" is a widely used term and has different meanings in various disciplines, in general, it can be thought of as having multi-dimensionality, complexity and variability. Firstly, scale has a multi-dimensional nature BIB002 . It can be expressed as the variability in space and the expansibility in time  . Consequently, the scale is divided into spatial scale and temporal scale, respectively, based on the different research targets or fields. As the observations of remote sensing are more specialized compared to conventional measurement methods, the scale notion can be extended to spectral scale, directional scale and polarization scale. The spectral scale expresses the ability to discriminate fine spectral differences and refers to the full width at half maximum (FWHM) of band. The directional scale describes the angular geometry of the sun-object-sensor system BIB002 . The polarization scale refers to the polarization direction of the signal. In general, the spatial and temporal scales are closely related. Then, within a specific discipline, the processes that operate over larger temporal scales may also operate over larger spatial scales due to the transport mechanisms between space and time  . Bloschl and Sivapalan  demonstrated a scheme to classify hydrological processes according to typical space and time scales. Skoien et al. BIB001 used the ratio of spatial scale and temporal scale to discriminate the different processes in a space-time coordinate system. In reality, all sensors boarded on spacecrafts are a kind of "hand-made" equipment. The spatial resolution, the bandwidth and the spectral response function are not the same. The difference between sensors must be analyzed first. That is to say, both spatial and spectral scaling is necessary when comparing the retrieval products of different sensors. Even if the resolutions of the sensors are close to each other, i.e., MODIS and AVHRR, spectral scaling is needed. Such a point of view may improve our understanding of scale effects. Secondly, scale has complex hierarchies. It is the reflection of the level of the organization of nature, which results in the research targets varying with scales. For example, small-scale hydrological studies may mainly focus on the scale of vegetation and soil; meso-scale studies may focus on the response of the hydrology unit to the changes of land surface; while large-scale studies may be mainly about the interaction of the atmosphere and the land surface. These phenomena and processes occurring at different scales may interact with each other, consequently, many regional or global changes, such as pollution, the greenhouse effect and biodiversity may be rooted in local scale or small-scale environmental problems. Similarly, large-scale changes (such as global climate change and ocean circulation anomalies), in turn, will influence small-scale phenomena and processes. This shows that both large-scale and small-scale studies are equally important. Large-scale describes the abstract features or macro-structure, and small-scale characterizes the details. On the one hand, we can understand the macro-changes and the general trend through large-scale studies; on the other hand, we may find the mechanism of the development of the process and give reasonable explanations through small-scale studies. Finally, scale may also have variability, that is, the targets at different scales will show different characteristics. The isothermal surface would become non-isothermal. The spectral curve of emissivity may become smoother when the spectral scale is coarser. It has increased the difficulty of scale analysis.