Evidence for the homothetic scaling of urban forms

2018 ◽  
Vol 47 (5) ◽  
pp. 870-888 ◽  
Author(s):  
Rémi Lemoy ◽  
Geoffrey Caruso
Keyword(s):  
Land Use ◽  
Population Density ◽  
Scaling Laws ◽  
Radial Distance ◽  
Three Dimensions ◽  
City Size ◽  
Cube Root ◽  
Radial Profiles ◽  
Population Grid ◽  
Urban Scaling

The size and form of cities influence their social and environmental impacts. Whether cities have the same form irrespective of their size is still an open question. We analyse the profile of artificial land and population density, with respect to the distance to their main centre, for the 300 largest European cities. Our analysis combines the GMES/Copernicus Urban Atlas 2006 land use database at 5 m resolution for 300 larger urban zones with more than 100,000 inhabitants and the Geostat population grid at 1 km resolution. We find a remarkable constancy of radial profiles across city sizes. Artificial land profiles scale in the two horizontal dimensions with the square root of city population, while population density profiles scale in three dimensions with its cube root. In short, cities of different size are homothetic in terms of land use and population density, which challenges the idea that larger cities are more parsimonious in the use of land per capita. While earlier literature documented the scaling of average densities (total surface and population) with city size, we document the scaling of the whole radial distance profile with city size, thus liaising intra-urban radial analysis and systems of cities. Our findings also yield homogenous spatial definitions of cities, from which we can re-question urban scaling laws and Zipf’s law for cities.

Inelastic wave propagation in sodium chloride

1982 ◽  
Vol 72 (6A) ◽  
pp. 2107-2130
Author(s):  
D. B. Larson
Keyword(s):  
Sodium Chloride ◽  
Scaling Laws ◽  
Shear Failure ◽  
Free Field ◽  
Radial Distance ◽  
Confining Pressure ◽  
Scale Model ◽  
Small Scale ◽  
Cube Root ◽  
Slant Range

abstract Explosion-induced free-field ground motion measurements in sodium chloride closely follow simple cube root scaling laws over 10 orders of magnitude of explosion energy (from 0.6 to 2.2 ×1010 kJ). This observation has important implications for the use of scale model experiments in simulating many of the effects associated with large chemical and nuclear explosions. Small-scale experiments in polycrystalline sodium chloride have been conducted using chemical explosives with energies between 0.6 and 300 kJ. Measurements at various confining pressures up to 32.2 MPa show that both cavity volume and free-field motion produced by explosions in pressed salt are independent of confining pressure. Within a scaled slant range (the radial distance to the center of the energy source) of about 80 m/kt1/3, the salt undergoes shear failure of the matrix (deformation which is both inelastic and nonlinear). Beyond 80 m/kt1/3 and to 250 m/kt1/3 (where these data end), the deformation continues to be strongly inelastic, but the magnitude of this inelasticity appears to decrease with range. Furthermore, measurement at a slant range of 168 m/kt1/3 of the combined signals produced by two simultaneous charges (separated by 191 m/kt1/3) shows little, if any, deviation from linearity.

scholarly journals How the geometry of cities determines urban scaling laws

2021 ◽  
Vol 18 (176) ◽  
Author(s):  
Carlos Molinero ◽  
Stefan Thurner
Keyword(s):  
Population Size ◽  
Scaling Laws ◽  
City Planning ◽  
Critical Density ◽  
Three Dimensions ◽  
Linear Scaling ◽  
Average Height ◽  
Urban Resilience ◽  
Practical Applications ◽  
Urban Scaling

Urban scaling laws relate socio-economic, behavioural and physical variables to the population size of cities. They allow for a new paradigm of city planning and for an understanding of urban resilience and economics. The emergence of these power-law relations is still unclear. Improving our understanding of their origin will help us to better apply them in practical applications and further research their properties. In this work, we derive the basic exponents for spatially distributed variables from fundamental fractal geometric relations in cities. Sub-linear scaling arises as the ratio of the fractal dimension of the road network and of the distribution of the population embedded in three dimensions. Super-linear scaling emerges from human interactions that are constrained by the geometry of a city. We demonstrate the validity of the framework with data from 4750 European cities. We make several testable predictions, including the relation of average height of cities and population size, and the existence of a critical density above which growth changes from horizontal densification to three-dimensional growth.

scholarly journals Constructing cities, deconstructing scaling laws

2015 ◽  
Vol 12 (102) ◽  
pp. 20140745 ◽  
Author(s):  
Elsa Arcaute ◽  
Erez Hatna ◽  
Peter Ferguson ◽  
Hyejin Youn ◽  
Anders Johansson ◽  
...  
Keyword(s):  
Population Density ◽  
Population Size ◽  
Scaling Laws ◽  
City Size ◽  
Scaling Analysis ◽  
Large Set ◽  
England And Wales ◽  
Universal Scaling ◽  
Definition Of ◽  
Nonlinear Correlations

Cities can be characterized and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al . have proposed that many of these urban measures can be predicted through universal scaling laws. We develop a framework to consistently define cities, using commuting to work and population density thresholds, and construct thousands of realizations of systems of cities with different boundaries for England and Wales. These serve as a laboratory for the scaling analysis of a large set of urban indicators. The analysis shows that population size alone does not provide us enough information to describe or predict the state of a city as previously proposed, indicating that the expected scaling laws are not corroborated. We found that most urban indicators scale linearly with city size, regardless of the definition of the urban boundaries. However, when nonlinear correlations are present, the exponent fluctuates considerably.

Urban scaling and the geographic concentration of inequalities by city size

2018 ◽  
Vol 46 (9) ◽  
pp. 1627-1644 ◽  
Author(s):  
Somwrita Sarkar
Keyword(s):  
Urban Policy ◽  
Scaling Laws ◽  
City Size ◽  
Urban Systems ◽  
Scaling Analysis ◽  
Middle Income ◽  
Income Distributions ◽  
Spatial Inequalities ◽  
Housing Costs ◽  
Urban Scaling

Urban scaling laws summarise how socio-economic behaviours of urban systems may be predicted from city size. While most scaling analysis rests on using aggregate quantities (total incomes, GDP, etc.), examining distributions of these aggregate quantities (e.g. income distributions) could shed light on how socio-economic inequalities may correlate or be causally linked to city size. In this direction, this paper examines how geographic distributions and spatial inequalities of income and housing costs vary by city size. The paper presents three principal results. First, it brings out qualitative implications of quantitative scaling by relating scaling of the distributions of income and housing costs to their specific geographic concentrations. Second, it shows that some small and medium sized cities are clear outliers, showing behaviour similar to the largest cities and starkly different from the behaviours of the bulk of small and medium sized cities. Third, this above observation explains why heteroscedasticity, or large and heterogeneous fluctuations, are frequently observed in urban indicator data when plotted as a function of city size. Putting together these three results, overall, it is shown that income distributions and housing costs scale and concentrate in cities by size in a predictable way, where the largest cities superlinearly/disproportionately agglomerate the highest income earners and the highest housing costs, and show relatively lower concentrations of low-middle income earners and low-medium housing costs. In contrast, most of the smaller and medium sized cities show a ‘flipped’ opposite trend. A few small and medium sized cities are outliers: they show trends that match those of the largest cities, due to specialisations of economic functions or concentrations of high-paying occupations in these cities. The empirical findings lead to a discussion on the objective and normative relationships between city size and urban inequalities. It is suggested that due to the concentrations of high income and high housing costs, largest cities may have a resulting housing market structure that will push out lower and medium income earners, thereby making affordability, diversity, and socio-spatial justice emerge as important urban policy issues.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

scholarly journals Correlating elements content in mosses collected in 2015 across Germany with spatially associated characteristics of sampling sites and their surroundings

2019 ◽  
Vol 31 (1) ◽  
Author(s):  
Stefan Nickel ◽  
Winfried Schröder
Keyword(s):  
Land Use ◽  
Population Density ◽  
Atmospheric Deposition ◽  
Vegetation Structure ◽  
Urban Areas ◽  
Explanatory Power ◽  
Spatial Density ◽  
Area Index ◽  
Explanatory Variables ◽  
Tree Layer

Abstract Background The aim of the study was a statistical evaluation of the statistical relevance of potentially explanatory variables (atmospheric deposition, meteorology, geology, soil, topography, sampling, vegetation structure, land-use density, population density, potential emission sources) correlated with the content of 12 heavy metals and nitrogen in mosses collected from 400 sites across Germany in 2015. Beyond correlation analysis, regression analysis was performed using two methods: random forest regression and multiple linear regression in connection with commonality analysis. Results The strongest predictor for the content of Cd, Cu, Ni, Pb, Zn and N in mosses was the sampled species. In 2015, the atmospheric deposition showed a lower predictive power compared to earlier campaigns. The mean precipitation (2013–2015) is a significant factor influencing the content of Cd, Pb and Zn in moss samples. Altitude (Cu, Hg and Ni) and slope (Cd) are the strongest topographical predictors. With regard to 14 vegetation structure measures studied, the distance to adjacent tree stands is the strongest predictor (Cd, Cu, Hg, Zn, N), followed by the tree layer height (Cd, Hg, Pb, N), the leaf area index (Cd, N, Zn), and finally the coverage of the tree layer (Ni, Cd, Hg). For forests, the spatial density in radii 100–300 km predominates as significant predictors for Cu, Hg, Ni and N. For the urban areas, there are element-specific different radii between 25 and 300 km (Cd, Cu, Ni, Pb, N) and for agricultural areas usually radii between 50 and 300 km, in which the respective land use is correlated with the element contents. The population density in the 50 and 100 km radius is a variable with high explanatory power for all elements except Hg and N. Conclusions For Europe-wide analyses, the population density and the proportion of different land-use classes up to 300 km around the moss sampling sites are recommended.

scholarly journals Landscape controls on riverine export of dissolved organic carbon from Great Britain

2021 ◽  
Author(s):  
Jennifer L. Williamson ◽  
Andrew Tye ◽  
Dan J. Lapworth ◽  
Don Monteith ◽  
Richard Sanders ◽  
...  
Keyword(s):  
Land Use ◽  
Great Britain ◽  
Population Density ◽  
Organic Carbon ◽  
Dissolved Organic Carbon ◽  
Forest Cover ◽  
River Systems ◽  
C Cycle ◽  
Global Land ◽  
Doc Export

AbstractThe dissolved organic carbon (DOC) export from land to ocean via rivers is a significant term in the global C cycle, and has been modified in many areas by human activity. DOC exports from large global rivers are fairly well quantified, but those from smaller river systems, including those draining oceanic regions, are generally under-represented in global syntheses. Given that these regions typically have high runoff and high peat cover, they may exert a disproportionate influence on the global land–ocean DOC export. Here we describe a comprehensive new assessment of the annual riverine DOC export to estuaries across the island of Great Britain (GB), which spans the latitude range 50–60° N with strong spatial gradients of topography, soils, rainfall, land use and population density. DOC yields (export per unit area) were positively related to and best predicted by rainfall, peat extent and forest cover, but relatively insensitive to population density or agricultural development. Based on an empirical relationship with land use and rainfall we estimate that the DOC export from the GB land area to the freshwater-seawater interface was 1.15 Tg C year−1 in 2017. The average yield for GB rivers is 5.04 g C m−2 year−1, higher than most of the world’s major rivers, including those of the humid tropics and Arctic, supporting the conclusion that under-representation of smaller river systems draining peat-rich areas could lead to under-estimation of the global land–ocean DOC export. The main anthropogenic factor influencing the spatial distribution of GB DOC exports appears to be upland conifer plantation forestry, which is estimated to have raised the overall DOC export by 0.168 Tg C year−1. This is equivalent to 15% of the estimated current rate of net CO2 uptake by British forests. With the UK and many other countries seeking to expand plantation forest cover for climate change mitigation, this ‘leak in the ecosystem’ should be incorporated in future assessments of the CO2 sequestration potential of forest planting strategies.

scholarly journals Changing Land Use and Population Density Are Degrading Water Quality in the Lower Mekong Basin

Water ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 1948
Author(s):  
Flavia Tromboni ◽  
Thomas E. Dilts ◽  
Sarah E. Null ◽  
Sapana Lohani ◽  
Peng Bun Ngor ◽  
...  
Keyword(s):  
Water Quality ◽  
Land Use ◽  
Population Density ◽  
Local Population ◽  
Reference Conditions ◽  
Mekong River ◽  
Land Use Impacts ◽  
Wet Season ◽  
Mekong Basin ◽  
Lower Mekong Basin

Establishing reference conditions in rivers is important to understand environmental change and protect ecosystem integrity. Ranked third globally for fish biodiversity, the Mekong River has the world’s largest inland fishery providing livelihoods, food security, and protein to the local population. It is therefore of paramount importance to maintain the water quality and biotic integrity of this ecosystem. We analyzed land use impacts on water quality constituents (TSS, TN, TP, DO, NO3−, NH4+, PO43−) in the Lower Mekong Basin. We then used a best-model regression approach with anthropogenic land-use as independent variables and water quality parameters as the dependent variables, to define reference conditions in the absence of human activities (corresponding to the intercept value). From 2000–2017, the population and the percentage of crop, rice, and plantation land cover increased, while there was a decrease in upland forest and flooded forest. Agriculture, urbanization, and population density were associated with decreasing water quality health in the Lower Mekong Basin. In several sites, Thailand and Laos had higher TN, NO3−, and NH4+ concentrations compared to reference conditions, while Cambodia had higher TP values than reference conditions, showing water quality degradation. TSS was higher than reference conditions in the dry season in Cambodia, but was lower than reference values in the wet season in Thailand and Laos. This study shows how deforestation from agriculture conversion and increasing urbanization pressure causes water quality decline in the Lower Mekong Basin, and provides a first characterization of reference water quality conditions for the Lower Mekong River and its tributaries.

Pemanfaatan Peta Tematik dalam Perencanaan Pembangunan Sarana dan Prasarana Pendukung Pariwisata Daerah di Kabupaten Pangandaran

Tunas Agraria ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 1-19
Author(s):  
Rizka Fakhrizatullah ◽  
Rochmat Martanto ◽  
Yendi Sufyandi
Keyword(s):  
Land Use ◽  
Data Collection ◽  
Population Density ◽  
Literature Review ◽  
Qualitative Method ◽  
Thematic Maps ◽  
Coastal Tourism ◽  
Factors Affecting ◽  
Regional Autonomy

Abstract: Pangandaran is a district with a coastline of 91 Km, so this district has the potential for coastal tourism that needs to be developed. As a new regency of regional autonomy, demands to carry out construction of facilities and infrastructure to support tourism need to be increased. This study aims to determine the distribution of facilities and infrastructure that need to be developed and to know the factors that influence the determination of the construction of facilities and infrastructure. This research uses qualitative method, data collection is done through literature review and interviews. The results of the study indicate that the factors affecting the distribution of infrastructure include land use, population density, tourism objects, land slope and disaster vulnerability. The analysis shows that the distribution of villages suitable for the development of infrastructure includes the villages of Wonoharjo, Babadan, Pananjang and Pangandaran Village.Keyword: tourism, facilities and infrastructure, thematic maps. Intisari: Pangandaran merupakan kabupaten dengan garis pantai sepanjang 91 Km, sehingga kabupaten ini memiliki potensi pariwisata pantai yang perlu dikembangkan. Sebagai Kabupaten yang baru melakukan otonomi daerah, tuntutan untuk melaksanakan pembangunan sarana dan prasarana guna mendukung pariwisata perlu ditingkatkan. Kajian ini bertujuan untuk untuk mengetahui sebaran sarana dan prasarana yang perlu dikembangkan serta mengetahui faktor-faktor yang mempengaruhi penentuan pembangunan sarana dan prasarana. Penelitian ini menggunakan metode kualitatif, pengumpulan data dilakukan melalui kajian pustaka dan wawancara. Hasil kajian menunjukkan bahwa faktor-faktor yang mempengaruhi sebaran sarana prasarana meliputi penggunaan lahan, kepadatan penduduk, obyek wisata, kemiringan lahan dan kerawanan bencana. Dari hasil analisis menunjukkan bahwa sebaran desa yang sesuai untuk pengembangan sarana prasarana meliputi Desa Wonoharjo, Babadan, Pananjang dan Desa Pangandaran.Kata kunci: pariwisata, sarana dan prasarana, peta tematik.

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