1. Introduction
The aim of this study is to present and validate the attempt to analyze interactions between spatial, economic, social and ecological aspects of urban life primarily using mathematical graph simulative modelling based on the spatial urban configuration of a city. The following aspects of the research are highlighted:
A complex simulative model, even if based primarily just on spatial urban configuration data, creates a background for better understanding of the functioning of the urban fabric in terms of synergies between spatial, social, economic and ecological aspect.
Such a simulative model has a predictive power and could be used as an objective part of a decision support system by various stakeholders in urban development.
The model reflects the complex nature of a city as a system by demonstrating the “butterfly effect” when even relatively small and scattered infill development affects synergies between social, ecological, spatial and economic aspects of urban structure notably.
The availability of open data and various GIS based technologies means that the presented model can be seen as a part of wider ecosystem of urban planning technologies of the Smart City movement.
There are numerous various new constructions and renovations occurring in Kaunas as in many other cities annually. Under free market conditions, such processes are influenced in both bottom-up ways by various stakeholders (e.g., land and property owners, developers, other participants of the property market, etc.) and top-down ways (e.g., by city master plans). These bottom-up processes of construction and renovation may be seen as insignificant at a whole city scale, but even small changes in a complex system such as a city can cause significant shifts in urban networks. Although construction projects initiated by property developers are quite often primarily focused on economic benefits and lack long-term perspective in terms of sustainable city development, in such situations, it is very important to see and understand the effects of various infill developments in complex urban contexts, thus creating a background for top-down catalyzing actions, targeted support activities, the identification of either positive or negative synergies, etc.
The objective of the presented research is to present, validate and discuss a simulative model which would allow an analysis and prediction of the effects of urban regeneration and infill development on the complex functioning of a city based on open data.
As a city is a very complex phenomenon [
1], when we try to comprehend it and understand and model its changes, a systemic approach that allows us to understand the interconnectedness of all the city elements and components at different scales can be helpful. According to the theory of interdisciplinarity [
2,
3], a systems approach provides an orientation to looking at the whole problem and its relationship to its parts. Everything is interconnected and systems-based thinking emphasizes that problems have many dimensions. There are many factors involved in any problem, and there can be various types of connections between them. Applying this paradigm, a city can be divided into various “systemic layers” that have their own research theories, methods, and approaches, and at the same time, they are interconnected and integrated:
Public spaces. Public spaces are defined as spaces of street culture and encompass streets without intensive transport in the old town, pedestrian streets, squares, parts of green spaces near developments when they are cut by paths oriented to the attraction centers, pedestrian zones near important streets in which the formation of multi-functional corridors occurs similar to those according to models of New Urbanism [
4], public spaces near shopping centers, etc. [
5], i.e., these spaces are universally accessible and offer opportunities for people to meet other people and interact with them. Public spaces and their systems are analyzed from visual, spatial, compositional, social, functional, psychological, and other points of view in order to understand what makes a good public space [
6,
7,
8,
9].
Nature frame and green infrastructure. Nature frame is a concept developed in the middle of the 20th c. by geographers [
10], and landscape architects and ecologists [
11,
12]. The natural frame is an integral network of natural ecological compensation territories, which ensures the ecological balance of the landscape as well as natural connections between protected territories and other environmentally important territories or habitats and the migration of plants and animals between them [
10]. When analyzing urban morphology, natural determinants and human made determinants are designated, and natural areas are usually protected as eco-compensational areas intertwining with urbanized areas. Other concepts such as a green infrastructure [
13] and ecological services [
14] are also important in analyzing and planning cities and their renovation and regeneration, particularly to increase the ecological potential of urbanized areas and provide material and non-material benefits for human beings in cities.
Transport infrastructure, sustainable mobility. The characteristics of transport systems affect the morphological type, size of the urban structure, its liveability and its functioning [
15]. Sustainable mobility is one of sustainable development goals of every city in the world. In order to analyze and plan city transport infrastructure, many quantitative and qualitative indicators must be established and evaluated. The newest research [
16] attempts to integrate the development of transport and urban spaces systems by proposing sets of indicators describing sustainable transport and city development of, for example, the road system (turnover, infrastructure spatial features, public transport infrastructure, transport demand, modal split, etc.) or the space system (safety, comfort, use frequency, time, aesthetics, etc.).
Social context and social infrastructure. The social dimension is an important part of the sustainable development concept, and the social environment encompasses the immediate physical surroundings, social relationships, and cultural milieus within which defined groups of people function and interact [
17]. Social infrastructure includes culture, education, public health and safety, sports and wellness, recreation and tourism, religious sites, administrative areas, and other objects of public use [
15]. When measuring city sustainability [
18], the social aspect is represented by a range of indicators, e.g., education, sanitation, health, quality of public spaces, etc.
Urban frame, building typology and urban composition. The urban frame and urban composition represent the most functionally, spatially, and visually distinguishing part of the urban structure that helps to organize spatial environments into recognizable and unique coherent patterns. Building typology describes buildings according to their similarity of function and form. The research methods can be classified into the following types: methods evaluating the overall impression of the spatial patterns, and methods dividing it into parts, i.e., structural quantitative and qualitative methods, complex methods based on expert and non-expert judgement, etc. [
6,
15,
19,
20,
21].
Historical context and cityscape identity. The historical context of the city partially defines its identity and provides it with a historical background. However, a cityscape identity is a more complex phenomenon. To establish a city-scape identity, it is necessary to integrate subjective (human) and objective (physical) aspects, physical and virtual environments that represent it, etc. In the scientific literature, existential (place), spatial, personal, and cultural dimensions of the concept of landscape identity are distinguished [
22], which are important for the overall perception and evaluation of landscape identity. Considering this holistic approach [
23], cityscape identity is analyzed and evaluated using various theories and methods with different disciplinary origins. These include the theories of semiotics and cultural-historical artefacts [
24,
25] for distinguishing physical components as cultural symbols formed through history. The experience and perception of place is analyzed by sociological surveys applying the theories of K. Lynch [
26] of mental city images, the S. Shamai [
27] model of “sense of the place”, and the semantic differential measurement developed by Ch. Osgood [
28].
According to the above-mentioned, even simplified, representation of a city as a complex phenomenon, it is evident that there are many factors operating in a city that are difficult to model and study simultaneously. Therefore, we need theories and approaches allowing us to indicate, assess and model interrelated changes of different systems making up the city totality.
The structure of complex systems can be analyzed from many perspectives. Not all of them can be revealed or described as relationships between elements. There is, therefore, always a risk of overlooking important relationships on which the territorial organization of the system depends. It is even more difficult to analyze the functioning and dynamics of the system, even though it is possible to express all these aspects in terms of individual relationships. It is possible to take different approaches to the study of a single system (e.g., economic, geographical, sociological, etc.) by looking at only a particular section of the system, selecting the relevant characteristics according to the task at hand, and describing them in terms of relationships.
A system is generally considered to have a single structure, which can be analyzed from different angles, e.g., by building different models of the same system. Sometimes, for simplicity, these sections are referred to as different system structures, e.g., hierarchical, economic, etc.
The structure of system relationships is based on the concept of a system as a single object whose properties are the sum of the properties of its elements. The structure of relations in a territorial system is characterized by a particular diversity. Even in small and relatively homogeneous territorial systems, the nature, extent, importance, number of branches, etc., of the links vary considerably.
Linkages can be direct or reverse, cover all or part of a territory, be permanent or temporary, and be variable. Permanent links are links that do not change during the functioning of the system of a given structure, but which, if broken, cease to function and practically disintegrate. Variable (flexible) relationships can change as the system functions, which does not break down the structure of the system, so the system can adapt to certain changes. The purpose of the variable links in the system is to maintain a dynamic equilibrium and interaction with the outside of the system. The research of spatial systems is, therefore, a very complex task that requires the use of digital methods [
29,
30,
31].
The theoretical background of the presented research is based on three cornerstones. The first cornerstone is set by the actualization of the idea of a city as a network by Dupuy: “Urban networks, … are widely discussed, but there has hardly been debate on what constitutes an urbanism of networks. It is time to shift network urbanism from the realm of general debate to that of identifying the task-specific tools and techniques required for its implementation” [
32].
The second cornerstone is defined by a specific approach to modeling of complex systems which is well and fully presented by Michael Batty in his book
The New Science for Cities. He says that “In a world now dominated by communications and in a world where most people will be living in cities by the end of this century, it is high time we changed our focus from locations to interactions, from thinking of cities simply as idealized morphologies to thinking of them as patterns of communication, interaction, trade, and exchange; in short, to thinking of them as networks.” [
33]. The essential tool for modeling complex urban networks, according to Batty, is mathematical graph theory which can describe urban areas, or any network, as made of nodes and links. It is important to note that a mathematical graph model could be considered as a kind of simulative model suitable for description and modeling of complex systems. Such models demonstrate a very large number of elements and self-organization as cities do. Depending on the modeling purpose, a street, segment, crossroad, building, or cell of public space could be seen as a node and the functional or visual connections between them as links. The calculation of importance or centrality of the nodes is the essence of the Graph theory, as rooted in the proposals by Linton Freeman [
34], which he generated while analyzing social networks. The three centralities proposed by him are the following:
The degree centrality is the number of links with neighboring nodes. Nodes with a larger number of connections are considered as more important, e.g., the number of “friends” in social media networks or the number of intersecting streets in a city.
The closeness centrality is a sum of distances from each node to the rest of the network. A smaller sum indicates greater importance as it shows higher closeness of the node to the rest of the network.
The betweenness centrality is a sum of the shortest transit journeys between pairs of all nodes which choose the calculated node as a transit route. A higher value indicates greater importance of the node because of the larger transit flow it attracts.
The space syntax theory developed by Bill Hillier applies and develops the calculation of node centralities for urban analysis and further modeling [
35] by introducing more indicators, normalization of the results and offering simulative modeling rules for interpretation of calculated graph centralities as follows:
Symmetry is described as “… the property that if A is a neighbor of B, then B is neighbor of A” [
36]. Symmetrical relations between nodes mean that if they as spaces or buildings have symmetrical relations to each other created by short distance and direct links, they bring people, activities, functions together and create more multi-functional, diverse zones in a city.
Depth “… exists wherever it is necessary to go through intervening spaces to get from one space to another” [
36]. More depth creates more asymmetry, thus segregating people, activities, functions, etc.
Movement economy theory is “… built on the notion of natural movement, proposes that evolving space organization in settlements first generates the distribution pattern of busier and quieter movement pattern flows, which then influence land use choices, and these in turn generate multiplier effects on movement with further feedback on land use choices and the local grid as it adapts itself to more intensive development” [
35]. Patterns of various attraction zones could be identified using mathematical graph centralities.
Space syntax has attracted various criticisms [
37,
38] which should be taken into consideration, but because “all models are wrong, but some are useful” [
39], the most important question is if the space syntax model is working in the context of precise research. It should be noted as well that the criticisms were mainly addressed to the early forms of space syntax analysis focused on axial graphs [
40] which were later improved and replaced by segment graphs [
41]. However, the syntactic models used here are validated a few times during the research presented.
The third cornerstone is based on the theory of four urban capitals—an analytical theory of urbanism developed by Lars Marcus [
42] where he describes a city as the interaction of four capitals: spatial, social, economic, and ecological. “… spatial capital in this sense has a fundamental impact, not only on economic capital, but also on social and ecological capital” [
42] according to Marcus. We generalize the urban capital definition for further investigation as follows: capital is the potential for interaction between its “cells” (people and people, buildings and nature, land exchange values, buildings and public spaces), which is enabled by spatial structure and brings people, activities, and objects together. More potential interaction is by default seen as bigger capital. Definitions of the capitals are presented in
Figure 1. All four capitals could be described on the basis of networks: a network of spaces, a network of humans, a network of land plots, and a network of ecological areas.
Based on the general literature review presented in the introduction, we conclude that, for the investigation of transformations caused by infill urban development, the simulative modeling approach is best able to reflect the complexity of urban systems. The urban capitals concept is employed as a more specific form of application of the mathematical graph model.
4. Discussion
A city masterplan is often focused on large-scale zoning, infrastructure planning, heritage protection, etc. In reality, a master plan makes a general framework for relatively small-scale infill development which is initiated in a bottom-up way by various businesses and other stakeholders. A problem is created by the fact that such bottom-up initiatives may implement the vision of the master plan just in a fragmented way because of limiting factors, such as the number of inhabitants, speed of economic growth and other peculiarities of a specific city. If not understood, predicted, and catalyzed properly in a top-down way, such infill actions can create imbalances between social, economic, ecological and even cultural aspects of sustainable urban development. The main research question of the present study was formulated as follows: would it be possible based on the open data to analyze and predict the effect of various infill developments on sustainability of a city at the city level or at the level of the neighborhoods? Sustainability based on the concept of New Urbanism [
60], which supports multi-functionality, diversity, walkability, proximity of housing and commerce, etc., was addressed as a synergy between four urban capitals by Marcus [
42]: spatial, social, ecological, and economic.
Kaunas city was chosen for study due to its low top-down control of urban processes and strong dominance of private business interests in bottom-up development initiatives. A simulative modeling approach was chosen as it can reflect the complexity of urban functioning based on its configuration (e.g., street network, allocation of buildings, allocation of green areas). Several mathematical graph-based models have been used for this purpose, including space syntax [
35] and graph of buildings [
45]. Despite the availability of numerous tests of workability of mathematical graph models in urban settings, the models were additionally tested a few times during the current research. Various data from the open sources, such as the perimeter of buildings, density of inhabitants, and area of green recreational zones, were used as weightings in the model in order to reflect the ecological, economic, social, and spatial capitals.
The key findings of the study can be summarized as follows:
Simulative mathematical graph-based modeling was used successfully for the analysis of the potential transformations of the synergies between capitals, thus revealing that the chaotic infill development in Kaunas in some neighborhoods could be seen as a positive in terms of sustainability, but negative in the other ways. Despite the positive synergies in some neighborhoods, in general, the study reveals the quite accidental character of interaction of the capitals under the present planning situation in Kaunas and reveals a need for predictive, catalyzing top-down approach in the city master plan.
All the simulative models involved in the presented research were validated positively using independent open GIS data as density of points of interest based on the movement economy approach [
35].
The modeling results could be used at various scales of urban planning: at a level of the whole city, at a level of the neighborhood, and at a level of the single house. Such flexibility reveals the potential of the presented modeling approach as a decision support system for various stakeholders involved in urban development and planning.
The presented research, besides “traditional” space syntax analysis which focuses primarily on modeling and simulation of the movement of people, most often, just on a street network without consideration of the other urban factors as inhabitants’ density, morphology of buildings, allocation of recreational areas, etc., could be compared to some more complex views and studies of functioning of urban structures based on analysis of spatial characteristics.
Firstly, Urban Mixed-use Index (MXI) could be mentioned. It calculates the floor space of buildings with residential use as percentage of the total amount of floor space in the investigated area. It is argued by some authors that MXI “… in a dimensionless quantity that expresses a proportion analog to density, building percentage and open space ratio using physical parameters like floor space and plot size in a same manner.” [
61]. MXI, in this case, is seen as a neutral definition of multifunctionality of land use, which might differ significantly between different stakeholders of urban development and as a methodological tool for implementation of various models of New Urbanism. While agreeing with the importance of the proposed index and its potential usefulness in urban planning, the absence of the logistic dimension in the model should be noted. It is important to note that, even within the scope of New Urbanism concept, modelling of transit flows should be considered as an important aspect of urban corridors, which depending on their significance, can call for different MXI. The proposed model addresses aspects of logistics by using a mathematical graph model and adds an economic–ecological–social dimension to the analysis. On the other hand, it is possible to look for a way to use MXI as a part of weighting procedure in the calculations of centralities, thus making the model of spatial capital even more precise and more sensitive to specific functional mixes identified by the index.
The Space Matrix index is another concept which allows the quantification of such variables of urban structure as intensity, compactness, non-built space, and building height, and thereby differentiates urban form efficiently [
62]. The differentiation of the efficiency of urban form is classified based on statistical cluster analysis. The method utilizes possibilities for data analysis offered by GIS technologies in a similar way to the research presented in this article, but as in MXI case, the aspect of urban logistics is missing. At the same time, it should be noted that the application of cluster analysis in the identification of synergies between four urban capitals instead of calculations of correlations is a potential alternative which should be tested in future.
Van Ness [
63] addresses the common “weak point” of both the above-mentioned concepts by combining Space Syntax, MXI and Spacematrix in a GIS environment. This model differs from the proposed one as it is not assessing economic, social and ecological data directly, but its employment of GIS and a combination of Space Syntax models makes it similar to the research presented in the article, even if the syntactic modelling is constructed at the level of street segment but not building.
Within this theoretical context, the presented research on four urban capitals is an alternative or supplementary addition focused on practical implementation that further develops and tests the ideas of Marcus while applying the same mathematical graph model to all four capitals: spatial, ecological, economic and social.
Within the wider context, the capitals model could be seen as creating potential synergies with various GIS based visualized analysis, e.g., analysis of groundwater quality [
64], which could be related to ecological capital, or analysis of seismic risk in a specific geographical area [
65], which could be related to economic capital. The data for the presented research was obtained from OSM but it could be based on the other methods which allow the creation of vector data from orthophoto or photogrammetry [
66], thus expanding list of potential components of the four capitals in the model.
The results obtained first of all allow us to address various issues of urban planning related to changes in spatial configurations of the street network, changes in building density and allocation of new buildings from the perspective of sustainable urban development. Moreover, the presented methodology allows the use the obtained results as an expansion to various sustainability compass methodologies [
67] or could be used on their own as evidence in discussions between various stakeholders or even as a background for parametric urban design.
The proposed model may be limited by the availability of suitable open data for the modeling of economic capital. In the case of Kaunas, the necessary information was purchased from the state agency “Registrų centras”. At the moment, the model is limited just to validation in Kaunas, and its feasibility should be tested in other cities. In the Kaunas case, the positive synergies between spatial, economic, and social capital were revealed, whereas ecological capital produced negative correlations with the other three capitals. This result is quite logical when considering the traditional form of urban development when nature and urban zones of higher density do not overlap with each other, but in a wider context, possible positive synergies between all four capitals may show the way for a new paradigm of urban planning.
The presented research should be tested in more cities, and more options for normalization of the values of the four urban capitals should be tested as well as the synergy between them.