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Register a new userScaling and Hierarchy in Urban Economies
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Authors
Cosma Rohilla Shalizi
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In several recent publications, Bettencourt, West and collaborators claim that properties of cities such as gross economic production, personal income, numbers of patents filed, number of crimes committed, etc., show super-linear power-scaling with total population, while measures of resource use show sub-linear power-law scaling. Re-analysis of the gross economic production and personal income for cities in the United States, however, shows that the data cannot distinguish between power laws and other functional forms, including logarithmic growth, and that size predicts relatively little of the variation between cities. The striking appearance of scaling in previous work is largely artifact of using extensive quantities (city-wide totals) rather than intensive ones (per-capita rates). The remaining dependence of productivity on city size is explained by concentration of specialist service industries, with high value-added per worker, in larger cities, in accordance with the long-standing economic notion of the hierarchy of central places.
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Urban scaling and Zipfs law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about the connection between these two laws using population and GDP data from almost five thousand consistently-defined cities in 96 countries. We empirically demonstrate that both laws are tied to each other and derive an expression relating the urban scaling and Zipf exponents. This expression captures the average tendency of the empirical relation between both exponents, and simulations yield very similar results to the real data after accounting for random variations. We find that while the vast majority of countries exhibit increasing returns to scale of urban GDP, this effect is less pronounced in countries with fewer small cities and more metropolises (small Zipf exponent) than in countries with a more uneven number of small and large cities (large Zipf exponent). Our research puts forward the idea that urban scaling does not solely emerge from intra-city processes, as population distribution and scaling of urban GDP are correlated to each other.
The increasing use and spread of low carbon technologies are expected to cause new patterns in electric demand and set novel challenges to a distribution network operator (DNO). In this study, we build upon a recently introduced method, called buddying, which simulates low voltage (LV) networks of both residential and non-domestic (e.g. shops, offices, schools, hospitals, etc.) customers through optimization (via a genetic algorithm) of demands based on limited monitored and customer data. The algorithm assigns a limited but diverse number of monitored households (the buddies) to the unmonitored customers on a network. We study and compare two algorithms, one where substation monitoring data is available and a second where no substation information is used. Despite the roll out of monitoring equipment at domestic properties and/or substations, less data is available for commercial customers. This study focuses on substations with commercial customers most of which have no monitored `buddy, in which case a profile must be created. Due to the volatile nature of the low voltage networks, uncertainty bounds are crucial for operational purposes. We introduce and demonstrate two techniques for modelling the confidence bounds on the modelled LV networks. The first method uses probabilistic forecast methods based on substation monitoring; the second only uses a simple bootstrap of the sample of monitored customers but has the advantage of not requiring monitoring at the substation. These modelling tools, buddying and uncertainty bounds, can give further insight to a DNO to better plan and manage the network when limited information is available.
We present a model for generating probabilistic forecasts by combining kernel density estimation (KDE) and quantile regression techniques, as part of the probabilistic load forecasting track of the Global Energy Forecasting Competition 2014. The KDE method is initially implemented with a time-decay parameter. We later improve this method by conditioning on the temperature or the period of the week variables to provide more accurate forecasts. Secondly, we develop a simple but effective quantile regression forecast. The novel aspects of our methodology are two-fold. First, we introduce symmetry into the time-decay parameter of the kernel density estimation based forecast. Secondly we combine three probabilistic forecasts with different weights for different periods of the month.
Urban areas play an unprecedented role in potentially mitigating climate change and supporting sustainable development. In light of the rapid urbanisation in many parts on the globe, it is crucial to understand the relationship between settlement size and CO2 emission efficiency of cities. Recent literature on urban scaling properties of emissions as a function of population size have led to contradictory results and more importantly, lacked an in-depth investigation of the essential factors and causes explaining such scaling properties. Therefore, in analogy to the well-established Kaya Identity, we develop a relation combining the involved exponents. We demonstrate that application of this Urban Kaya Relation will enable a comprehensive understanding about the intrinsic factors determining emission efficiencies in large cities by applying it to a global dataset of 61 cities. Contrary to traditional urban scaling studies which use Ordinary Least Squares (OLS) regression, we show that the Reduced Major Axis (RMA) is necessary when complex relations among scaling exponents are to be investigated. RMA is given by the geometric mean of the two OLS slopes obtained by interchanging the dependent and independent variable. We discuss the potential of the Urban Kaya Relation in main-streaming local actions for climate change mitigation.
Distribution network operators (DNOs) are increasingly concerned about the impact of low carbon technologies on the low voltage (LV) networks. More advanced metering infrastructures provide numerous opportunities for more accurate load flow analysis of the LV networks. However, such data may not be readily available for DNOs and in any case is likely to be expensive. Modelling tools are required which can provide realistic, yet accurate, load profiles as input for a network modelling tool, without needing access to large amounts of monitored customer data. In this paper we outline some simple methods for accurately modelling a large number of unmonitored residential customers at the LV level. We do this by a process we call buddying, which models unmonitored customers by assigning them load profiles from a limited sample of monitored customers who have smart meters. Hence the presented method requires access to only a relatively small amount of domestic customers data. The method is efficiently optimised using a genetic algorithm to minimise a weighted cost function between matching the substation data and the individual mean daily demands. Hence we can show the effectiveness of substation monitoring in LV network modelling. Using real LV network modelling, we show that our methods perform significantly better than a comparative Monte Carlo approach, and provide a description of the peak demand behaviour.
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