Integrating Network Science for Spatial Diffusion and Resilience Modelling to Renewable Energies: A Theoretical Background.

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2.1.1 Neoclassical and Behavioural Approaches in Urban Theory
The development of models to explain human activities at urban and economic perspective has mainly European and American origins. For example, Hotelling (1929) was interested in industrial location and competitiveness, developing the principle of minimum differentiation. Reilly (1927) worked about retail gravitation, which is the cornerstone of spatial interaction theory (SIT) and Converse (1949) proposed a new model based on Reilly’s work, doing notorious empirical tests and modifications to Reilly’s original model (Converse, 1943, 1949). Converse work, although less known that the prominent CPT from Christaller (1933) has been used for retail planning policies at international level (Dawson, 1980; Araldi, 2019).
Within the SIT, the concept of potential has been a recurrent approach used in human geography. Gravity or potential models are designed to capture and measure the potential interaction between different entities such as cities, enterprises or social-economic groups which are spatially located in different points. The nature of these interactions is diverse, by way of illustration we could name social media messages, goods, services, ideas, merchandise flows or circular migration. In order to understand the concept of demographic gravity models it is necessary to refer to its origins. In the early 1940’s, when the astronomer John Q. Stewart noticed a peculiarity in the composition of his class at Princeton University, students mainly came from the region and the proportion of students coming from somewhere else reduced when the distance increased as a distance decay effect. His seminal works were published (Stewart; 1941, 1942) and built the bases for demographic gravitation. His observation prompted him to apply physics concepts to demographic studies, he would then at some extent compare census data to catalogues of stars or tables of spectroscopic wave lengths (Stewart, 1948). The figure below is probably the first potential map done by Stewart in 1947 in New York.

2.1.3 Urban Systems Dynamics and Simulation

Forrester published his book Urban Dynamics in 1969, which is an integration of his previous work on industrial dynamics and his collaboration with former Boston Mayor John Collins who was then a professor at MIT and was interested in urban issues related to aging cities (Cambien et al. 2007). The urban system proposed by Forrester was built with three main dimensions: population, jobs, and housing but the space was not explicitly considered in this model.
These three variables interact with each other generating the emergence of intelligent behaviour: feedback loops. For example, when the population increases, the availability of housing and jobs decrease. While this is happening, an increase of housing price and less jobs will in return discourage more people to move in the area, diminishing its attractiveness. This is what is known as feedback loops in this model whose right construction, representation and interpretation embodies one of the most important features in SD. Figure 46 shows how mental models of the real world are the fundamental basis for strategies, structure and decision rules. This structure leads to decision-making processes, which influence the real world and consequently generate a feedback on decision-making processes in return.

2.1.4 Spatial Urban Dynamics

Sanders & Sanders (2004) did a review of the main aspects that were object to the criticism and also discussed about the implications of the lack of the spatial dimension, which generated some limitations to perform a validation of the model from an urban perspective. They did apply the spatial dimension to the Dutch city of Rotterdam that was struggling in the beginning of the 2000’s with urban decay issues, where housing decline and underemployment were present in an important proportion of the urban area. Hence, the Forrester’s urban dynamics model of would have a transition to ‘spatial urban dynamics’.
Forrester’s model involved two markets, housing and labour associated to population dynamics. The feedback mechanisms are represented as follows. Figure 48 illustrates the systemic relation between the variables in an urban system.
The figure above shows that as the population increases, jobs and housing availability decreases. When there is a low job availability, the area becomes less attractive due to the high rents and low salaries. If there is a low job availability, more unemployed people will be willing to work for low salaries. Underemployment generates less attractiveness leading to out migration and if there is a high house availability prices will fall, so less houses will be built. The interconnectedness and interplay of the system systematically triggers the variables accordingly with the interactions between them. Forrester (1971) showed that when industrial buildings age employment opportunities decrease. When residential building age, lower-income population use them in high densities, which means that there is not a housing shortage but an excess of low-income housing. Forrester suggests that aging buildings are the cause of decreasing job availability and a population increase. Consequently, he argued that an excess on low-cost housing attracts low-income groups and unemployed people at the extent that a limit is attain when all available jobs are taken so the life quality is affected and the inflow ceases.
Before introducing the spatial urban dynamic aspects, it is important to establish the basics of the original model of Forrester. For Forrester, a system (a city) is endogenously driven, this means that the dynamics of the city take place inside of the city with little intervention of the environment. However, the population can vary depending on the attractiveness of the city in comparison with other cities, which are outside of the system. To distinguish which variables are part of the system it is important to identify the three following elements: specific area, relative attractiveness, limitless environment. The specific area relates to the boundaries of the system (see Figure 49), where its limits determine the contours including the variables that represent the theoretical aspects of interest. The specific area of interest let us know the interactions within the system, in the Forrester model that is the intertwined relations of labour, housing and population. It is assumed that the urban model provides information about what happens inside that restricted world without considering the surroundings and it is small enough to not affect the outside environment (Forrester, 1969).
Forrester’s model assumes that the environment does not substantially influence the system and the system does not influence the environment, an issue called the boundary problem (see Alfeld, 1995). The basis of the argumentative criticism is related to the lack of interactions between the cities and the suburbs, which are not accounted for in the model, so a consequence of this assumption is that the dynamics of the system are endogenously driven (Gray et al., 1972; Rochberg 1972; Graham, 1974). A related paper on the interconnectivity of cities was also proposed by Berry (1964). The ‘environment’ creates a second set of structural conditions in the urban model that are relative to the system. The model shows thus, how attractive is the city regarding its environment, allowing the inflow of population for example when the attractiveness is high or the outflow when it is low. Forrester’s model was criticized concerning the characteristic limitless environment given that it has not size or boundaries, suggesting that the environment could be the universe (Sanders & Sanders, 2004). The spatial component was not considered and the recognition of the amount of people living in cities in the US prompted scholars to argue that the environment should be seen as a collection of cities that are in competition one to another (Babcock, 1972; Gray et al, 1972). So, this approach is focused on local optimization (for example a city) but do not support national optimization processes for instance, a group of cities.
Moreover, as mentioned before some of the model’s assumptions are not based on the scientific literature, this means that the model simulates a hypothetical city. Then some authors argue that the model’s results cannot be validated if hypothetical data is used to setup the parameters of the simulation (Gray et al., 1972) and there are not evidences to support some of the assumptions of the model (Garn & Wilson 1972). Regarding the data problem, Forrester’s answer was that when a variable’s data is not available is better to use an estimation than not using the variable at all (Forrester 1969; Forrester: 1980). The criticism to Forrester model was addresses by different scholars over the time, to some authors the most critical issue was the boundary problem, so Schroeder (1975) introduced a model that accounted for the interactions between the city and the suburbs. The inclusion of the suburb areas introduces the spatial dimension in the model but its complexity as well.
Schroeder (1975) developed two urban dynamic models, one was for the city and the other for the suburbs where the migration is a function of the attractiveness of the city and its suburbs as a whole in comparison with its environment. The migration is distributed around the city and its suburbs based on the attractiveness of the zones under the assumption that people who live in a location also work in that area. This model was the target of the same critics as the Forrester’s model since the city and the suburbs are not influenced by the environment, it means that Schroeder added a layer (the suburbs) but the environment still does not have a considerable impact on the dynamics of the system. Other similar improvements to tackle the problems of the Forrester model were achieved by Kadanoff & Weinblatt (1972) Laudet & Fournier (1979) and Fournier (1986). The model proposed by Kadannof considers some interaction between the city and the suburbs, but they are judged to be somehow ‘primitives’. This paradoxical situation which is characterized by the simplistic and at the same time complexity in systems modelling is a recurrent inconvenient in SD. The Figure 49 shows the evolution of the spatial dimension in SD. Furthermore, Burdekin (1979) divided the area in 16 zones, which enhanced the analysis in a spatial perspective where construction rates and types of housing were considered. The migration flows in the system are analysed in a city perspective however the population is not studied in each area.

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2.1.5 Land-Use Change Modelling

Land change is the consequence of multiple human-environment interactions, which are developed across scales (Manfredo et al., 2014). Some scholars have focused on land-use change models (LCM), which have multiple usage such as the assessment the impact of land-use on biophysical processes, ecosystems stability, climate change, land degradation (Veldkamp & Lambin, 2001) and also for urban purposes (Loubier et al., 2017). Since a land-use change model was implemented in the framework of this dissertation in order to verify if it was possible to determine any impact of the RET diffusion on the landscape, we will introduce this approach.
Predicting land-use allows to observe the dynamical behaviour of the parameters of interest and test the sensitivity of territories’ trajectories in order to anticipate the changes and the interactions between ecological and social systems (Veldkamp & Lambin, 2001; Veldkamp & Verburg, 2004). While it is not possible to predict spatial change, it is feasible to detect the trends in a territory and its propensity to change based on the historical developments (Voiron-Canicio & Fusco, 2020). Spatial change discontinuity can be modelled through the usage of cellular automata (CA), which were developed by John von Neumann and Stanislaw Ulam at the national lab in Los Alamos. This approached can be coupled with Markov chains and it is used to perform simulation of systems that can be characterised by a succession of states.
Now we will briefly identify the main properties and definitions of Markov analysis. Since the approach is applied in different fields such as financial markets to perform credit ranking for enterprises, which is done by agencies like Standard & Poor’s or Moody Fitch’s among others, we will review the method from a land-change modelling perspective. We will focus on the mathematical aspects of the approach and its application in geography, which will help to better underpin our understanding of the model developed in section 5.5.3. Markov analysis is particularly suitable for simulating the dynamics of a global system such as a landscape mosaics or ecosystems. This methodology is often used by geographers to try to predict the evolution of land-use in a given territory. Markov’s analysis is based on the observation of a system that may be in a certain state among a finite list. It is therefore necessary to know the classes of land-used in order to build a model capable of describing:
i) How these possible states interconnect with each other.
ii) How to switch from one state to another via a link and a probability rule
An effective way to carry out a Markov analysis is to first make a graph and then transform it into a transition matrix. The figure below shows an example of Markov Chain construction to deal with the possible states that can describe the evolution of the territory. A real simulation was performed in the region of Valais in Switzerland for 2048, the land-used was classified in 9 classes. The spatial units’ resolution was of 250 sqm. The complete procedure is discussed on section 5.3.

Table of contents :

Acknowledgements
Abstract
Résumé
Introduction
Introduction (Français)
Part 1 An Overview on Innovation Studies and Urban Innovation Networks 
Partie 1 (Français) Un aperçu sur les études sur l’innovation et les réseaux d’innovation urbaine.
1 An Overview on Innovation: A Path Towards Environmental and Societal Challenges.
1.1 First Period of Innovation Policy Framework – Post WW II to 1980’s: Innovation for Growth
1.2 Second Period of Innovation Policy Framework – 1980’s to 2000’s: National Systems of Innovation
1.3 Third and Current Framing of Innovation Policy: Transformative Change
1.4 Diffusion of Innovations
1.5 Conclusion Chapter 1
2 Theoretical and Modelling Approaches for the Dynamics of Complex Urban Systems and Diffusion of Innovations
2.1 Urban Systems Modelling
2.1.1 Neoclassical and Behavioural Approaches in Urban Theory
2.1.2 Systems Dynamics Modelling
2.1.3 Urban Systems Dynamics and Simulation
2.1.4 Spatial Urban Dynamics
2.1.5 Land-Use Change Modelling
2.2 Innovation Diffusion as a Spatial Process
Time and Space
2.2 Resilience: A Review of Theoretical Conceptualizations in Urban Studies and Business Management
2.3.1 Conceptual Views on Resilience
2.3.2 Regional Resilience
2.3.3 Business Continuity Management: An Attempt to Integrate Resilience in Business Management.
2.3.4 Urban Resilience and Sustainability Transition
2.3.5 Sustainability Transition: A Theoretical Review on Multiscale Modelling of Urban Resilience Under a Network Approach.
2.3.6 Overview of Research Questions
2.4 Conclusion Chapter 2
3 Study Area and Data
3.1 Urban and economic context in the Swiss region: the canton of Valais-Wallis
3.1.1 Demography
3.1.2 Economy
3.1.3 Nature, Climate Change and Spatial Planning in Valais
3.2 A rationale to Choose Renewable Energy Technologies as Innovation Indicators.
3.3 The Energy Transition Context in Valais – Wallis
3.4 Swiss Data
3.5 The Urban and Economic Context in the South Region of France.
3.5.1 Demography and Economy
3.5.2 Nature and Climate Change in the South Region of France
3.6 The Energy Context in the South Region
3.7 French Data
3.8 Conclusion Chapter 3
4 Integrating Network Science for Spatial Diffusion and Resilience Modelling to Renewable Energies: A Theoretical Background.
4.1 Preferential Attachment vs Randomness
4.1.1 Thresholds and Phase Transitions in Evolving Networks
4.1.2 Scale-free Networks: The Barabasi-Albert model.
4.2 Conclusion Chapter 4
4.3 Conclusion Part 1
4.4 Conclusion Part 1 (Français)
Part 2 Modelling and Simulation of Spatial Diffusion of Innovations and Urban Resilience to Energy Transition.
Partie 2 (Français) : Modélisation et Simulation de la Diffusion Spatiale des Innovations et de la Résilience Urbaine à la Transition Energétique.
5 Modelling Framework for Innovation Diffusion: A Multiscale Geospatial Network Approach for Renewable Energy Technologies Diffusion in the Swiss Alps.
5.1 Objectives
5.2 Design of the General System of Simulation.
5.3 Phase 1A: A Spatial Diagnosis of the Major Land-Use Trends in Valais-Wallis Via the SLEUTH Approach.
5.3.1 Data
5.3.2 Transition Matrix for Years 2006-2018 and Markov Chains
5.3.3 Trend Scenarios for Years 2006 – 2048
5.4 Geoprospective: Spatial Interaction Modelling for the Swiss Alps region.
5.4.1 Potential Fields
5.4.2 Attractiveness
5.4.3 Data
5.4.4 Spatial Representation of the Potential Fields of Innovation
5.4.5 Population Dynamics Simulation Under a Multi-paradigm Approach: System Dynamics and Agent-based Modelling.
5.4.5.1 System Dynamics Model
5.4.5.2 Population dynamics in the canton of Valais via the integration of a spatial interaction model and agent-based modelling.
5.5 Multi-scale Spatial Network Diffusion Modelling for Renewable Energy Technologies in the Swiss Alps.
5.5.1 Data
5.5.2 Exploratory Data Analysis of Renewable Energy Technologies
5.5.2.1 Solar Photovoltaics and Space: A Multiscale Statistical Analysis in the Swiss Alps . 214
5.5.2.2 Solar Photovoltaics, Space and Time: A Multiscale Spatial Analysis of the Distributional Changes in the Diffusion of Renewable Energy Technologies in the Swiss Alps. 218
5.5.2.3 Electric and Hybrid Vehicles, Space and Time: A Multiscale Spatial Analysis of the Distributional Changes in the Diffusion of Innovations in the Swiss Alps.
5.5.3 Spatial Preferential Attachment: A Network Modelling Approach for Diffusion of Innovations and Geography of Sustainability Transitions in Switzerland.
5.5.3.1 A Scale-free Network Spatially Explicit for Renewable Energy Technologies Diffusion: Solar PV in the Swiss Alps.
5.5.3.2 A Scale-free Network Spatially Explicit Approach for Renewable Energy Technologies Diffusion: Electric and Hybrid Vehicles in Switzerland.
5.6 Conclusion Chapter 5
6 A Multiscale Geospatial Network Approach for Renewable Energy Technologies Diffusion in the South Region of France.
6.1 Objectives
6.2 Multi-scale Spatiotemporal Modelling Framework for Geography of Sustainability Transitions: Application of the Spatial Preferential Attachment Model in the South Region of France.
6.2.1 Data
6.2.2 Exploratory Data Analysis of Renewable Energy Technologies in the South Region of France
6.2.2.1 Solar Photovoltaics and Space: A Multiscale Spatial Analysis of Energy Production in the South Region of France
6.2.2.2 Solar Thermal Collectors and Space: A Multiscale Spatial Analysis of Energy Production in the South Region of France
6.2.2.3 Solar Photovoltaics, Space and Time: A Multiscale Spatial Analysis of Energy Production in the South Region of France
6.2.2.4 Solar Thermal Collectors Space and Time: A Multiscale Spatial Analysis of Energy Production in the South Region of France
6.2.3 Spatial Preferential Attachment: A Network Modelling Approach for Diffusion of Innovations and Geography of Sustainability Transitions in France.
6.2.3.1 A Scale-free Network Spatially Explicit for Renewable Energy Technologies Diffusion in the South Region of France: The Case of Solar Photovoltaics and Solar Thermal Collectors. 253
6.2.3.2 An application of the Spatial Preferential Attachment Model for Energy Production for Electricity Based on a Technology Mix of: Wind Power, Small and Big Hydroelectric Power Plants, Biogas and Solar Pho
6.2.3.3 An application of the Spatial Preferential Attachment Model for Energy Production for Heating Based on a Technology Mix of: Biomass and Solar Thermal Collectors.
6.2.3.4 An application of the Spatial Preferential Attachment to the Energy Produced for Electricity and Heating Based on a Technology Mix of: Wind Power, Small and Big Hydroelectric Power Plants, Solar Photovo
6.2.3.5 Sensitivity Analysis
6.3 Conclusion Chapter 6
7 Network Science as a Conceptual Instrument for Urban Resilience to Innovation Diffusion: A Geospatial Simulation for Sustainability Transition
7.1 Objectives
7.2 Urban Resilience to Innovation Diffusion: A Simulation on Sustainability Transition.
7.2.1 Model
7.2.1.1 Urban Resilience to Renewable Energy Technologies at 300 Square Meters: Size Matters.
7.2.1.2 Urban Resilience to Renewable Energy Technologies at 600 and 1200 Square Meters: Where Fractality Begins.
7.3 Discussion: Resilient Systems are Fractal, but is Really Resilience Fractal?
7.3.1 Bridging Sustainability Transition Pathways and Resilience Modelling
7.4 Conclusion Chapter 7
7.5 Conclusion Part 2
7.6 Conclusion Part 2 (Français)
Conclusion and New Perspectives
Conclusions et Nouvelles Perspectives
References

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