Von Thunen’s Legendre Transform: Urban rent and the Interaction Model
The von Thunen construction is a Legendre transform of travel distance to rent plus travel cost. ... more The von Thunen construction is a Legendre transform of travel distance to rent plus travel cost. Rent and travel cost can be identified within the standard maximum entropy derived transportation model. Rent plus travel cost equates to enthalpy and in the case of the linear rent curve the enthalpy is constant. A Legendre diagram can be drawn for the standard transportation model identifying a complete set of thermodynamic relationships including microcanical,canonical and grand canonical representations and the Maxwell relations.
Rent and Transport in the Polycentric City
The land rent analysis of von Thunen is shown to be embedded in the standard transportation model... more The land rent analysis of von Thunen is shown to be embedded in the standard transportation model in the form of a Legendre transform. This allows the estimate of von Thunen land rent in a polycentric setting, using only the data of a transportation model but reflecting a change in the effective distance. The effective distance changes are explored in relation to the complexity definitions of Emery and Trist and the role of coevolution in rent determination. The analysis links land use theory, location theory and spatial interaction modeling. This is demonstrated for an area covering London and part of South East England. The embedding of consumer and producer surplus in the spatial interaction model is examined. The potential benefits of the calculated rents lie in their use in the cost benefit analysis of transport investment and the integration of landuse planning with transport planning. The role of rents in the analysis of agglomeration economies in cities is pursued and it is ...
The Effect of Transport on Rent in the Polycentric City
The land rent analysis of von Thunen is shown to be consistent with and embedded in the standard ... more The land rent analysis of von Thunen is shown to be consistent with and embedded in the standard transportation model.. This allows the estimate of von Thunen land rents in a polycentric setting, using only the data of a transport distribution model. The analysis links land use, location and spatial interaction theory. The modelling of land rents is demonstrated for an area covering London and part of South East England and the effect of travel cost changes on land rent estimated. The analysis explores the use of the method in measuring development demand and in modifying the conventional logsum measure of consumer benefit.
The use of growth factor models for trip distribution has given way in the past to the use of mor... more The use of growth factor models for trip distribution has given way in the past to the use of more complex synthetic models. Nevertheless growth factor models are still used, for example in modelling external trips, in small area studies, in input-output analysis, and in category analysis. In this article a particular growth factor model, the Furness, is examined. Its application and functional form are described together with the method of iteration used in its operation. The "expected information" statistic is described and interpreted and it is shown that the Furness model predicts a trip distribution which, when compared with observed trips, has the minimum expected information subject to origin and destination constraints. An equivalent entropy maximising derivation is described and the two methods compared to show how the Furness iteration can be used in gravity models with specified deterrence functions. A trip distribution model explicitly incorporating information from observed trips, is then derived. It is suggested that if consistency is to be maintained between iteration, calibration, and the derivation of gravity models, then expected information should be used as the calibration statistic to measure goodness of fit. The importance of consistency in this respect is often overlooked. Lastly, the limitations of the models are discussed and it is suggested that it may be better to use the Furness iteration rather than any other, since it is more fully understood. In particular its ease of calculation makes it suitable for use in small models computed by hand.
The competition in space between rail and sea transport is of great significance to the integrati... more The competition in space between rail and sea transport is of great significance to the integration of Eurasia. This paper proposes a land and sea transport spatial balance model for container transport, which can extract a partition line on which transport costs by rail and sea are equal given a destination. Four scenarios are discussed to analyse the effects of different factors on the model. Then the model is empirically tested on current rail and sea transport networks to identify the transport competition pattern in Eurasia. The location of destinations, the freight costs, and time costs are the three main factors affecting the model. Among them, time costs are determined by the value of a container and its contents, the interest rate, and by time differences between land and sea transport. The case study shows that Eurasia forms a transport competition pattern with a land area to sea area ratio of about 1:2; this ratio, however, changes to 1:1 when time costs are considered. Further, the land and sea transport balance lines are consistent with the theories of geopolitics, which indicate that the same processes may exist in the spatial pattern of geo-economics and geopolitics in Eurasia. According to the balance lines, we get a spatial partition, dividing Eurasia into the land transport preferred area, the land-sea transport indifference area, and the sea transport preferred area. The paper brings a new perspective to the exploration of geopolitical economic spatial patterns of Eurasia and provides a practical geographic theory as an analytic basis for the implementation of the Belt and Road Initiative.
The current COVID-19 pandemic has profoundly impacted people's lifestyles and travel behaviours, ... more The current COVID-19 pandemic has profoundly impacted people's lifestyles and travel behaviours, which may persist post-pandemic. An effective monitoring tool that allows us to track the level of change is vital for controlling viral transmission, predicting travel and activity demand and, in the long term, for economic recovery. In this paper, we propose a set of Twitter mobility indices to explore and visualise changes in people's travel and activity patterns, demonstrated through a case study of London. We collected over 2.3 million geotagged tweets in the Great London Area (GLA) from Jan 2019-Feb 2021. From these, we extracted daily trips, origin-destination matrices, and spatial networks. Mobility indices were computed based on these, with the year 2019 as a pre-Covid baseline. We found that in London, (1) People are making fewer but longer trips since March 2020. (2) In 2020, travellers showed comparatively reduced interest in central and sub-central activity locations compared to those in outer areas, whereas, in 2021, there is a sign of a return to the old norm. (3) Contrary to some relevant literature on mobility and virus transmission, we found a poor spatial relationship at the Middle Layer Super Output Area (MSOA) level between reported COVID-19 cases and Twitter mobility. It indicated that daily trips detected from geotweets and their most likely associated social, exercise and commercial activities are not critical causes for disease transmission in London. Aware of the data limitations, we also discuss the representativeness of Twitter mobility by comparing our proposed measures to more established mobility indices. Overall, we conclude that mobility patterns obtained from geo-tweets are valuable for continuously monitoring urban changes at a fine spatiotemporal scale.
This paper explores a decentralisation initiative in the United Kingdom-the Northern Powerhouse s... more This paper explores a decentralisation initiative in the United Kingdom-the Northern Powerhouse strategy (NPS)-in terms of its main goal: strengthening connectivity between Northern cities of England. It focuses on economic interactions of these cities, defined by ownership linkages between firms, since the NPS's launch in 2010. The analysis reveals a relatively weak increase in the intensity of economic regional patterns in the North, in spite of a shift away from NPS cities'traditional manufacturing base. These results suggest potential directions for policy-makers in terms of the future implementation of the NPS.
The standard von Thunen construction for a monocentric city is shown to be a Legendre transform ... more The standard von Thunen construction for a monocentric city is shown to be a Legendre transform of the kind which underlies the statistical mechanical relationships of the standard maximum entropy transportation model. This allows the integration of the von Thunen analysis with the doubly constrained transportation model and shows the place of rents in the transportation model. This extension of the model clarifies its interpretation as a complete thermodynamic system for which the Maxwell relations may be derived.
Zenodo (CERN European Organization for Nuclear Research), Apr 6, 2021
In this paper we created a novel framework for understanding housing affordability in England usi... more In this paper we created a novel framework for understanding housing affordability in England using a linked house price dataset. Regional house price studies revealed that after the global economic crisis, there was an unprecedented regional house price divergence driven by faster price increases in London from 2009 onwards. To ease England's resulting housing affordability issues, we consider the scenario of a typical London homeowner to offer a new insight into local housing affordability by different property type in England and explore the best property search areas for homeowners moving out of London.
Peer review UCL Open: Environment is an open scholarship publication, all previous versions and o... more Peer review UCL Open: Environment is an open scholarship publication, all previous versions and open peer review reports can be found online in the UCL Open: Environment Preprint server at ucl.scienceopen.com
Most spatio-temporal studies of house price in the UK are carried out at national or regional sca... more Most spatio-temporal studies of house price in the UK are carried out at national or regional scale, but house prices differences could be better understood at finer spatial scales. Since England's house prices, standardised by the size of the property (£/m 2), have been shown to be somewhat clustered at local authority level and highly clustered at Middle Layer Super Output (MSOA) level, in the period 2009 to 2016, this research aims to further explore the nature of spatial and temporal variation in house prices at local authority level in England. Growth curve modelling offers a model-based description of the spatio-temporal patterns of local authority house price variation. This research explores local authority effects and three different time effects (quarter, half-year and year) on house price spatio-temporal variation. Results show that these three time effects are essentially identical and are extremely small, in comparison with local authority effects. Since annual effects provide the best fit, local authority annual house price trajectories between 2009 and 2016 are further explored. Local authorities with higher house prices in 2009 are found to have faster growing prices over the eight-year period than local authorities with lower house prices. Moreover, two clear geographic hubs of house price change over the period are observed, one centred on London, the other on Bristol.
The morphology of urban agglomeration is studied here in the context of information exchange betw... more The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Urban migration to and from cities is characterised as non-random and following non-random pathways. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements. In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy. Our analysis is based on a stochastic urban fractal model, which mimics urban growing settlements and migration waves. The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales.
We pose the central problem of defining a measure of complexity, specifically for spatial systems... more We pose the central problem of defining a measure of complexity, specifically for spatial systems in general, city systems in particular. The measures we adopt are based on Shannon's (in Bell Syst Tech J 27:379-423, 623-656, 1948) definition of information. We introduce this measure and argue that increasing information is equivalent to increasing complexity, and we show that for spatial distributions, this involves a trade-off between the density of the distribution and the number of events that characterize it; as cities get bigger and are characterized by more events-more places or locations, information increases, all other things being equal. But sometimes the distribution changes at a faster rate than the number of events and thus information can decrease even if a city grows. We develop these ideas using various information measures. We first demonstrate their applicability to various distributions of population in London over the last 100 years, then to a wider region of London which is divided into bands of zones at increasing distances from the core, and finally to the evolution of the street system that characterizes the built-up area of London from 1786 to the present day. We conclude by arguing that we need to relate these measures to other measures of
The current COVID-19 pandemic has profoundly impacted people’s lifestyles and travel behaviours, ... more The current COVID-19 pandemic has profoundly impacted people’s lifestyles and travel behaviours, which may persist post-pandemic. An effective monitoring tool that allows us to track the level of change is vital for controlling viral transmission, predicting travel and activity demand and, in the long term, for economic recovery. In this paper, we propose a set of Twitter mobility indices to explore and visualise changes in people’s travel and activity patterns, demonstrated through a case study of London. We collected over 2.3 million geotagged tweets in the Great London Area (GLA) from Jan 2019 –Feb 2021. From these, we extracted daily trips, origin-destination matrices, and spatial networks. Mobility indices were computed based on these, with the year 2019 as a pre-Covid baseline. We found that in London, (1) People are making fewer but longer trips since March 2020. (2) In 2020, travellers showed comparatively reduced interest in central and sub-central activity locations compar...
Understanding patterns and competitions of short‐ and long‐term rental markets: Evidence from London
Transactions in GIS
Exploring local authority travel time to London effects on spatio-temporal pattern of local authority house prices variation in England
The Bartlett Centre for Advanced Spatial Analysis, UCL, May 1, 2020
Von Thunen's Legendre Transform
The standard von Thunen construction for a monocentric city is shown to be a Legendre transform ... more The standard von Thunen construction for a monocentric city is shown to be a Legendre transform of the kind which underlies the statistical mechanical relationships of the standard maximum entropy transportation model. This allows the integration of the von Thunen analysis with the doubly constrained transportation model and shows the place of rents in the transportation model. This extension of the model clarifies its interpretation as a complete thermodynamic system for which the Maxwell relations may be derived.
House Price per Square Metre in England and Wales, 1995-2021
This house price per square metre dataset was created on 1/4/2021 and is based on the LR PPD, Dom... more This house price per square metre dataset was created on 1/4/2021 and is based on the LR PPD, Domestic EPCs and NSPL downloaded on the same day. It covers over 18 million transactions with 218 variables in England and Wales between 1/1/1995 and 26/2/2021. 16 of the 104 variables come from the LR PPD, 84 variables come from Domestic EPCs, one variable (lad21cd) from NSPL and three variables (i.e.id, classt, priceper) are created by the first author. Before the data linkage, a unique identifier (id) is created for all the unique EPCs after removing the individual lodgement identifier (i.e. LMK_KEY variable). During the data linkage, a variable named classt is created to identify 1:1 and 1:n linkage relationships. After the data linkage, a derived house price per square metre variable (i.e. priceper) is obtained through dividing the transaction price paid in the LR PPD with the total floor area variable in the EPC dataset. The NSPL (May 2021 version) is used to assign the local authori...
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