Establishing the Downscaling and Spatiotemporal Scale Conversion Models of NDVI Based on Fractal Methodology

Scale effect is a crucial scientific problem in quantitative remote sensing (RS), and scholars attempt to solve it with scale conversion models, which can characterize the numerical relationship of RS land surface parameters at different resolutions (scales). As a significant land surface parameter, scale conversion of normalized difference vegetation index (NDVI) has been studied for a long time. Therefore, taking NDVI as an example, the development of scaling research is described and analyzed in the paper, and based on fractal theory, the development trends are discussed for land surface parameters in quantitative remote sensing. These are our conclusions: it will be the new trend to establish downscaling models based on fractal theory for land surface parameters in quantitative remote sensing; additionally, it still is the hotspot to establish spatiotemporal scale conversion models for land surface parameters in quantitative remote sensing in the future, and addressed on that, the multi-fractal scaling methodology is proposed, and its availability is analyzed in the paper, which presents significant potential

Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling

With the development of quantitative remote sensing, scale issues have attracted more and more the attention of scientists. Research is now suffering from a severe scale discrepancy between data sources and the models used. Consequently, both data interpretation and model application become difficult due to these scale issues. Therefore, effectively scaling remotely sensed information at different scales has already become one of the most important research focuses of remote sensing. The aim of this paper is to demonstrate scale issues from the points of view of analysis, processing and modeling and to provide technical assistance when facing scale issues in remote sensing. The definition of scale and relevant terminologies are given in the first part of this paper. Then, the main causes of scale effects and the scaling effects on measurements, retrieval models and products are reviewed and discussed. Ways to describe the scale threshold and scale domain are briefly discussed. Finally, the general scaling methods, in particular up-scaling methods, are compared and summarized in detail

Fractal Analysis

Fractal analysis is becoming more and more common in all walks of life. This includes biomedical engineering, steganography and art. Writing one book on all these topics is a very difficult task. For this reason, this book covers only selected topics. Interested readers will find in this book the topics of image compression, groundwater quality, establishing the downscaling and spatio-temporal scale conversion models of NDVI, modelling and optimization of 3T fractional nonlinear generalized magneto-thermoelastic multi-material, algebraic fractals in steganography, strain induced microstructures in metals and much more. The book will definitely be of interest to scientists dealing with fractal analysis, as well as biomedical engineers or IT engineers. I encourage you to view individual chapters

Quantifying scale relationships in snow distributions

2007 Summer.Includes bibliographic references.Spatial distributions of snow in mountain environments represent the time integration of accumulation and ablation processes, and are strongly and dynamically linked to mountain hydrologic, ecologic, and climatic systems. Accurate measurement and modeling of the spatial distribution and variability of the seasonal mountain snowpack at different scales are imperative for water supply and hydropower decision-making, for investigations of land-atmosphere interaction or biogeochemical cycling, and for accurate simulation of earth system processes and feedbacks. Assessment and prediction of snow distributions in complex terrain are heavily dependent on scale effects, as the pattern and magnitude of variability in snow distributions depends on the scale of observation. Measurement and model scales are usually different from process scales, and thereby introduce a scale bias to the estimate or prediction. To quantify this bias, or to properly design measurement schemes and model applications, the process scale must be known or estimated. Airborne Light Detection And Ranging (lidar) products provide high-resolution, broad-extent altimetry data for terrain and snowpack mapping, and allow an application of variogram fractal analysis techniques to characterize snow depth scaling properties over lag distances from 1 to 1000 meters. Snow depth patterns as measured by lidar at three Colorado mountain sites exhibit fractal (power law) scaling patterns over two distinct scale ranges, separated by a distinct break at the 15-40 m lag distance, depending on the site. Each fractal range represents a range of separation distances over which snow depth processes remain consistent. The scale break between fractal regions is a characteristic scale at which snow depth process relationships change fundamentally. Similar scale break distances in vegetation topography datasets suggest that the snow depth scale break represents a change in wind redistribution processes from wind/vegetation interactions at small lags to wind/terrain interactions at larger lags. These snow depth scale characteristics are interannually consistent, directly describe the scales of action of snow accumulation, redistribution, and ablation processes, and inform scale considerations for measurement and modeling. Snow process models are designed to represent processes acting over specific scale ranges. However, since the incorporated processes vary with scale, the model performance cannot be scale-independent. Thus, distributed snow models must represent the appropriate process interactions at each scale in order to produce reasonable simulations of snow depth or snow water equivalent (SWE) variability. By comparing fractal dimensions and scale break lengths of modeled snow depth patterns to those derived from lidar observations, the model process representations can be evaluated and subsequently refined. Snow depth simulations from the SnowModel seasonal snow process model exhibit fractal patterns, and a scale break can be produced by including a sub-model that simulates fine-scale wind drifting patterns. The fractal dimensions provide important spatial scaling information that can inform refinement of process representations. This collection of work provides a new application of methods developed in other geophysical fields for quantifying scale and variability relationships

Entropy-scaling search of massive biological data

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

Coupled modelling of land surface microwave interactions using ENVISAT ASAR data

In the last decades microwave remote sensing has proven its capability to provide valuable information about the land surface. New sensor generations as e.g. ENVISAT ASAR are capable to provide frequent imagery with an high information content. To make use of these multiple imaging capabilities, sophisticated parameter inversion and assimilation strategies have to be applied. A profound understanding of the microwave interactions at the land surface is therefore essential. The objective of the presented work is the analysis and quantitative description of the backscattering processes of vegetated areas by means of microwave backscattering models. The effect of changing imaging geometries is investigated and models for the description of bare soil and vegetation backscattering are developed. Spatially distributed model parameterisation is realized by synergistic coupling of the microwave scattering models with a physically based land surface process model. This enables the simulation of realistic SAR images, based on bioand geophysical parameters. The adequate preprocessing of the datasets is crucial for quantitative image analysis. A stringent preprocessing and sophisticated terrain geocoding and correction procedure is therefore suggested. It corrects the geometric and radiometric distortions of the image products and is taken as the basis for further analysis steps. A problem in recently available microwave backscattering models is the inadequate parameterisation of the surface roughness. It is shown, that the use of classical roughness descriptors, as the rms height and autocorrelation length, will lead to ambiguous model parameterisations. A new two parameter bare soil backscattering model is therefore recommended to overcome this drawback. It is derived from theoretical electromagnetic model simulations. The new bare soil surface scattering model allows for the accurate description of the bare soil backscattering coefficients. A new surface roughness parameter is introduced in this context, capable to describe the surface roughness components, affecting the backscattering coefficient. It is shown, that this parameter can be directly related to the intrinsic fractal properties of the surface. Spatially distributed information about the surface roughness is needed to derive land surface parameters from SAR imagery. An algorithm for the derivation of the new surface roughness parameter is therefore suggested. It is shown, that it can be derived directly from multitemporal SAR imagery. Starting from that point, the bare soil backscattering model is used to assess the vegetation influence on the signal. By comparison of the residuals between measured backscattering coefficients and those predicted by the bare soil backscattering model, the vegetation influence on the signal can be quantified. Significant difference between cereals (wheat and triticale) and maize is observed in this context. It is shown, that the vegetation influence on the signal can be directly derived from alternating polarisation data for cereal fields. It is dependant on plant biophysical variables as vegetation biomass and water content. The backscattering behaviour of a maize stand is significantly different from that of other cereals, due to its completely different density and shape of the plants. A dihedral corner reflection between the soil and the stalk is identified as the major source of backscattering from the vegetation. A semiempirical maize backscattering model is suggested to quantify the influences of the canopy over the vegetation period. Thus, the different scattering contributions of the soil and vegetation components are successfully separated. The combination of the bare soil and vegetation backscattering models allows for the accurate prediction of the backscattering coefficient for a wide range of surface conditions and variable incidence angles. To enable the spatially distributed simulation of the SAR backscattering coefficient, an interface to a process oriented land surface model is established, which provides the necessary input variables for the backscattering model. Using this synergistic, coupled modelling approach, a realistic simulation of SAR images becomes possible based on land surface model output variables. It is shown, that this coupled modelling approach leads to promising and accurate estimates of the backscattering coefficients. The remaining residuals between simulated and measured backscatter values are analysed to identify the sources of uncertainty in the model. A detailed field based analysis of the simulation results revealed that imprecise soil moisture predictions by the land surface model are a major source of uncertainty, which can be related to imprecise soil texture distribution and soil hydrological properties. The sensitivity of the backscattering coefficient to the soil moisture content of the upper soil layer can be used to generate soil moisture maps from SAR imagery. An algorithm for the inversion of soil moisture from the upper soil layer is suggested and validated. It makes use of initial soil moisture values, provided by the land surface process model. Soil moisture values are inverted by means of the coupled land surface backscattering model. The retrieved soil moisture results have an RMSE of 3.5 Vol %, which is comparable to the measurement accuracy of the reference field data. The developed models allow for the accurate prediction of the SAR backscattering coefficient. The various soil and vegetation scattering contributions can be separated. The direct interface to a physically based land surface process model allows for the spatially distributed modelling of the backscattering coefficient and the direct assimilation of remote sensing data into a land surface process model. The developed models allow for the derivation of static and dynamic landsurface parameters, as e.g. surface roughness, soil texture, soil moisture and biomass from remote sensing data and their assimilation in process models. They are therefore reliable tools, which can be used for sophisticated practice oriented problem solutions in manifold manner in the earth and environmental sciences