36 research outputs found
Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland
Revealing spatiotemporal evolution regularity in the spatial diffusion of
epidemics is helpful for preventing and controlling the spread of epidemics.
Based on the real-time COVID-19 datasets by prefecture-level cities and date,
this paper is aimed at exploring the multifractal scaling in spatial diffusion
pattern of COVID-19 pandemic and its evolution characteristics in Chinese
mainland. The ArcGIS technology and box-counting method are employed to extract
spatial data and the least square calculation is used to calculate fractal
parameters. The results show multifractal distribution of COVID-19 pandemic in
China. The generalized correlation dimension spectrums are inverse S-shaped
curves, but the fractal dimension values significantly exceeds the Euclidean
dimension of embedding space when moment order q<<0. The local singularity
spectrums are asymmetric unimodal curves, which slant to right. The fractal
dimension growth curves are shown as quasi S-shaped curves. From these
spectrums and growth curves, the main conclusions can be drawn as follows.
First, self-similar patterns developed in the process of Covid-19 pandemic,
which seem be dominated by multi-scaling law. Second, the spatial pattern of
COVID-19 across China can be characterized by global clustering with local
disordered diffusion. Third, the spatial diffusion process of COVID-19 in China
experienced four stages, i.e., initial stage, the rapid diffusion stage, the
hierarchical diffusion stage, and finally the contraction stage. This study
suggests that multifractal theory can be utilized to characterize
spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be
instructive for further exploring natural laws of spatial diffusion.Comment: 22 pages,6 figures, 4 table
Multifractal scaling analyses of urban street network structure: the cases of twelve megacities in China
Traffic networks have been proved to be fractal systems. However, previous
studies mainly focused on monofractal networks, while complex systems are of
multifractal structure. This paper is devoted to exploring the general
regularities of multifractal scaling processes in the street network of 12
Chinese cities. The city clustering algorithm is employed to identify urban
boundaries for defining comparable study areas; box-counting method and the
direct determination method are utilized to extract spatial data; the least
squares calculation is employed to estimate the global and local multifractal
parameters. The results showed multifractal structure of urban street networks.
The global multifractal dimension spectrums are inverse S-shaped curves, while
the local singularity spectrums are asymmetric unimodal curves. If the moment
order q approaches negative infinity, the generalized correlation dimension
will seriously exceed the embedding space dimension 2, and the local fractal
dimension curve displays an abnormal decrease for most cities. The scaling
relation of local fractal dimension gradually breaks if the q value is too
high, but the different levels of the network always keep the scaling
reflecting singularity exponent. The main conclusions are as follows. First,
urban street networks follow multifractal scaling law, and scaling precedes
local fractal structure. Second, the patterns of traffic networks take on
characteristics of spatial concentration, but they also show the implied trend
of spatial deconcentration. Third, the development space of central area and
network intensive areas is limited, while the fringe zone and network sparse
areas show the phenomenon of disordered evolution. This work may be revealing
for understanding and further research on complex spatial networks by using
multifractal theory.Comment: 32 pages, 9 figures, 5 table
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Remote sensing of impervious surface growth: A framework for quantifying urban expansion and re-densification mechanisms
A substantial body of literature has accumulated on the topic of using remotely sensed data to map impervious surfaces which are widely recognized as an important indicator of urbanization. However, the remote sensing of impervious surface growth has not been successfully addressed. This study proposes a new framework for deriving and summarizing urban expansion and re-densification using time series of impervious surface fractions (ISFs) derived from remotely sensed imagery. This approach integrates multiple endmember spectral mixture analysis (MESMA), analysis of regression residuals, spatial statistics (Getis_Ord) and urban growth theories; hence, the framework is abbreviated as MRGU. The performance of MRGU was compared with commonly used change detection techniques in order to evaluate the effectiveness of the approach. The results suggested that the ISF regression residuals were optimal for detecting impervious surface changes while Getis_Ord was effective for mapping hot spot regions i n the regression residuals image. Moreover, the MRGU outputs agreed with the mechanisms proposed in several existing urban growth theories, but importantly the outputs enable the refinement of such models by explicitly accounting for the spatial distribution of both expansion and re - densification mechanisms. Based on Landsat data, the MRGU is somewhat restricted in its ability to measure re-densification in the urban core but this may be improved through the use of higher spatial resolution satellite imagery. The paper ends with an assessment of the present gaps in remote sensing of impervious surface growth and suggests some solutions. The application of impervious surface fractions in urban change detection is a stimulating new research idea which is driving future research with new models and algorithms
Uncovering inequality through multifractality of land prices: 1912 and contemporary Kyoto
Multifractal analysis offers a number of advantages to measure spatial economic segregation and inequality, as it is free of categories and boundaries definition problems and is insensitive to some shape-preserving changes in the variable distribution. We use two datasets describing Kyoto land prices in 1912 and 2012 and derive city models from this data to show that multifractal analysis is suitable to describe the heterogeneity of land prices. We found in particular a sharp decrease in multifractality, characteristic of homogenisation, between older Kyoto and present Kyoto, and similarities both between present Kyoto and present London, and between Kyoto and Manhattan as they were a century ago. In addition, we enlighten the preponderance of spatial distribution over variable distribution in shaping the multifractal spectrum. The results were tested against the classical segregation and inequality indicators, and found to offer an improvement over those
Computing Local Fractal Dimension Using Geographical Weighting Scheme
The fractal dimension (D) of a surface can be viewed as a summary or average statistic for characterizing the geometric complexity of that surface. The D values are useful for measuring the geometric complexity of various land cover types. Existing fractal methods only calculate a single D value for representing the whole surface. However, the geometric complexity of a surface varies across patches and a single D value is insufficient to capture these detailed variations. Previous studies have calculated local D values using a moving window technique. The main purpose of this study is to compute local D values using an alternative way by incorporating the geographical weighting scheme within the original global fractal methods. Three original fractal methods are selected in this study: the Triangular Prism method, the Differential Box Counting method and the Fourier Power Spectral Density method. A Gaussian density kernel function is used for the local adaption purpose and various bandwidths are tested. The first part of this dissertation research explores and compares both of the global and local D values of these three methods using test images. The D value is computed for every single pixel across the image to show the surface complexity variation. In the second part of the dissertation, the main goal is to study two major U.S. cities located in two regions. New York City and Houston are compared using D values for both of spatial and temporal comparison. The results show that the geographical weighting scheme is suitable for calculating local D values but very sensitive to small bandwidths. New York City and Houston show similar global D results for both year of 2000 and 2016 indicating there were not much land cover changes during the study period
The cooling intensity dependent on landscape complexity of green infrastructure in the metropolitan area
The cooling effect of green infrastructure (GI) is becoming a hot topic on mitigating the urban heat island (UHI) effect. Alterations to the green space are a viable solution for reducing land surface temperature (LST), yet few studies provide specific guidance for landscape planning adapted to the different regions. This paper proposed and defined the landscape complexity and the threshold value of cooling effect (TVoE). Results find that: (1) GI provides a better cooling effect in the densely built-up area than the green belt; (2) GI with a simple form, aggregated configuration, and low patch density had a better cooling intensity; (3) In the densely built-up area, TVoE of the forest area is 4.5 ha, while in the green belt, TVoE of the forest and grassland area is 9 ha and 2.25 ha. These conclusions will help the planners to reduce LST effectively, and employ environmentally sustainable planning
Multifractality applied to the study of spatial inequality in urban systems
This thesis investigates multifractality as a tool to analyse the spatial patterns emerging from urban inequality. In our context, inequality is defined as a difference between individuals in economic welfare (in the tradition of Dalton and Sen). As such, it considers the typical household income distribution, but also variables such as real estate and energy consumption. These variables can be transformed into mathematical measures which present diverse extent of self-similarities explained by the self-organisation processes resulting from an intense competition for space. The multifractal methodology can exploit these self-similarities to produce precise local statistical information even when the usual tools fail due to an excessive complexity. The analysis is performed on large geographical datasets for London, Paris, New-York and Kyoto. The main results are a decrease in multifractality with modernisation that can be understood as an arguably positive homogenisation, but also a negative loss of diversity; striking similarities in the independent evolution of the spatial repartition of land and housing prices across the globe during the 20th century; and discrepancies between income and the other measures, in accordance with the idea that income alone is not enough to fully characterize inequality. The most important result, however, is the validation after comparison with the traditional inequality and segregation measures that multifractality is a high-performing spatial inequality indicator. It is in particular able to extend the exposure and clustering dimensions of segregation to ordinal continuous variables