Use of thermal potentials for territory analysis

    An example of calculating the thermal potential for a street network in Nizhny Novgorod

    The territory of a city is a complex, heterogeneous system that is in constant change. It is possible to describe the territory and assess the urban environment using spatial objects (factors). The factors describing the territory are different in the nature of their influence (positive, negative) and geometric configuration (points, lines, polygons).

    It is often difficult to determine the degree of influence of each individual object on the level of development of the territory as a whole or some particular aspect of it. Today, the problem of defining and describing such concepts as “culture”, “social sphere”, “social tension”, “good life”, “economic development”, and “public health” is becoming increasingly relevant. The ambiguity of these concepts increases if we want to apply them to different social groups, populations of different ages and sexes.

    Also, it should be noted that the boundaries of the city in the modern concept are rather arbitrary. Daily population migration, transport accessibility of remote areas “blur the border” of the city even more. The widely used notion of agglomeration as a whole reflects the boundaries of the city, but at the same time makes the very concept of the boundaries of the city even more vague.

    Despite the problems described above, the analysis and assessment of territories today are some of the promising and interesting areas that allow solving many urgent problems of the urban environment.

    The article proposes to consider a method of analyzing the territory using the "thermal" model. The basis of this method is the study of potentials created by objects (factors) of various nature (point, linear and areal). Analysis of the territory using this method makes it possible to move from a set of spatial data (factors) describing the territory to an exact numerical (point) estimate at each point in the territory.

    The potentials studied as part of the analysis of the territory have a physical interpretation - the distribution of heat in media of different dimensions (2D, 3D). This phenomenon can be represented in the form of “thermal” images (“thermal” maps of the territory), giving an idea of ​​the degree of development of the territory depending on the color intensity of the image.

    Territory Factors

    The analysis of the territory involves the search and processing of information on factors of influence on the territory and their indicators. Factors of influence are objects that affect the surrounding territory, possessing a set of characteristics and spatial coordinates. Examples of influence factors include shops, industrial facilities, roads, forests, water bodies.

    Influence indicators are objects that reflect the influence of objects and also have a set of characteristics and spatial coordinates. Examples of impact indicators: ATMs, billboards, monuments.

    In the following presentation, we will use the concept of influence factors, combining both terms - factors and indicators of influence.

    The following is an example of spatial data that are influencing factors.

    One of the important stages of the work on the analysis of territories is the stage of collecting and processing initial information. Today, there is a lot of information about factors of influence on the territory of varying degrees of detail.

    Information can be obtained from open sources or sources of limited access. In many cases, open information is sufficient for analysis, although, as a rule, it needs a rather time-consuming processing.

    Among open sources, the leader, in our opinion, is the resource - OpenStreetMap (OSM). Information obtained from this source is updated daily around the world.

    OpenStreetMap (OSM) resource information is presented in the following formats:

    - OSM format. The basic format with the extension “.osm” is used to describe XML images - nodes, paths, relationships.

    - “Polish format”. A text format with the extension “.mp” is used for working with graphics.

    - PBF format. Data storage format with the extension ".osm.pbf".

    As sources of information you can also use:

    - 2GIS
    Resource contains high-quality, monthly processed information, with an excellent 3-level classifier for enterprises and organizations.

    - KML (Keyhole Markup Language) files
    KML (Keyhole Markup Language) files are a file format used to display geographic data in Google Earth, Google Maps, and Google Maps for mobile devices.

    Using KML files, you can:
    - set various icons and make captions to indicate locations on the Earth's surface
    - create different angles for selected objects by changing the position of the camera
    - use various overlays to
    define styles to define the display of the object, use HTML code to create hyperlinks and embedded images
    - use folders for hierarchical grouping of elements
    - dynamically receive and update KML files from remote or local hosts
    - receive KML data in accordance with changes in the three-dimensional viewing tool

    - Federal Service for State Registration, Cadastre and Cartography "Rosreestr"
    Information on the Rosreestr portal is valuable in its content and relevance, but, unfortunately, it does not make it possible to get a schedule for capital construction and land sites at no cost. The Rosreestra portal also contains a large amount of restricted information.

    - Statistical
    agencies Statistical data is a legitimate source of information about the territory, however, as of today, statistics from the statistical authorities are available only for a certain number of indicators, mainly in the reports of statistical agencies and reports of regional authorities.

    -Information systems of authorities.
    Qualitative information is contained in information systems of authorities, however, only a small part of them is published in the public domain and is available for analysis.

    The analysis of the territories does not impose any specific requirements on the composition of the information, in fact, you can use everything that you can find, information from open sources is interchangeable as a rule. However, it should be noted that even just the information received from the OSM resource is enough to make an analysis of an unfamiliar territory.

    Analysis of the territory using the "thermal" model. Physical interpretation of potentials

    As mentioned earlier, the analysis of the territory today is an urgent topic and a powerful tool for reasonably attracting investment in the development of infrastructure of various urban environments.

    The variety of tasks that can be solved by analyzing the territories can be combined into several major areas:

    - Obtaining the most interpreted and detailed assessment of the territory at each of its points.
    Solving this problem, you can get a set of point estimates at each point of the territory, giving an idea of ​​the level of development of the territory in general, as well as in some subject area. Such a subject area may be, for example, culture, industry, trade, etc.

    - Determination of the most advantageous places for placement of investment objects of a certain type (for example, banks, specialized stores, shopping and entertainment centers, etc.) in the selected territory.

    - Analysis of the most efficient use of the territory.
    This direction allows for a detailed study of the characteristics of the territory, the market situation prevailing in the study area, and identification of the options that are in demand.

    - Determining the contribution of one factor to the cost model, using the example of the emergence of new roads and new routes.

    - Analysis of different aspects of one territory and analysis of different territories (comparison of territories).

    The originality of the method of analyzing the territory proposed in the article using the “thermal” model consists in the use of indicators of the development of the territory — potentials presented in numerical terms and reflecting the degree of influence of the object (influence factor) on the territory.

    To understand the essence of the study, a few words should be said about the thermal potential itself, and give its physical interpretation.

    In physics, there are such concepts as a force field and a force function . The force field has the dimension of energy, the force function is the dimension of force.

    For the law of gravity, the force field is determined by the formula:

    $ F = k / r2 $where
    k is a constant;
    r is the distance between interacting objects.

    The force function ϕ is determined by the expression:

    $ dϕ = -F * dr $where
    ϕ is the force field potential;
    dϕ, dr are differentials;
    r is the distance between interacting objects,

    therefore$ ϕ = k / r $.

    The physical meaning of the force field potential ϕ is the work E performed by the force field when passing a certain path. In the case of the law of universal gravitation, when the distance to the object changes from r2 to r1, the force function is determined by the formula

    $ E = k * (1 / r1-1 / r2) $where
    E is the work performed by the force field when passing a certain path;
    r1, r2 - the initial and final position of the object.

    For the task of analyzing the territory, the influence of objects (factors) on the territory can be considered as strength ( power function ), and the level of development of the territory as the total thermal potential ( force field ) from all objects (factors). In the problems of physics, the thermal potential is the temperature, and in the problems of analyzing territories using the "thermal" model, the potential is the total effect of all factors influencing the point of the territory.

    Spatial data are points, lines, polygons. To calculate the potentials, extended spatial data are divided into small fragments. For each fragment, the potential from a point with a factor equal to the size of the fragment of the object (factor) is calculated.

    Data is divided into semantic groups according to the principle of close similarity. For example, objects of trade are combined by goods. There are groups of forest objects, water bodies, settlements, bus stops, etc. The meaningful groups are a factor. Passing through all the objects (factors), we obtain a set of thermal potentials suitable for further processing.

    The use of potentials (“heat maps”) allows you to move from spatial data to “thermal” images of objects (factors) of influence on the territory (visualization of potentials). Such a transition makes it possible to determine the degree of presence of the factor at each point in the territory and conduct further analysis, i.e. display different directions of development of the city in color. Thus, we obtain a glow of varying intensity for each point of the territory.

    Examples of "thermal" images of the territory of Nizhny Novgorod in the context of several factors are presented below.

    “Thermal” map of N. Novgorod reflecting the “Pharmacy Chain” factor “

    Thermal” map of N. Novgorod reflecting the factor “Polyclinics for adults”

    “Thermal” map of N. Novgorod reflecting the factor “Children's polyclinic”

    “Thermal” map of N. Novgorod, reflecting the “Industrial zones” factor.

    “Thermal” images of the territory allow determining the concentration of potentials from various objects of influence. Next, it is necessary to combine the obtained potentials into an integral characteristic that allows an assessment of the territory by a large number of factors. To do this, you need a method that allows you to analyze a large amount of information, recognize objects, and also reduce the dimensionality of data by losing the least amount of information. One such method is the principal component analysis (PCA). You can read more about this method on Wikipedia .

    The essence of the method is to find a linear combination of initial parameters, which changes most strongly in the field of analysis. For spatial data - the most variable across the territory.

    The method of principal components identifies objects (factors) that vary most strongly across the territory. As a result of the method’s work, new variables appear - the main components, which are more informative in comparison with the initial data, with the help of which it is easier to analyze, describe and visualize the territory, which makes it easier to build models.

    The main components are analytical expressions - the sum of the potentials of the initial factors with some coefficients. However, if any factor has a significant impact on the territory, but does not change in the analyzed territory, the principal component method will not include this factor in the composition of the main components.

    The main components are ordered in descending order of information - i.e. spread over the territory. The first main components carry much more information than individual factors, and well describe the territory. As a rule, when using about a hundred factors, the first main component carries about 50% of all information (dispersion) across the territory. The main components do not correlate with each other and can be used for models as characteristics of the territory at each point.

    The main component, as some abstractly calculated indicator of the territory, does not have a clear name and classification. However, the combination of factors strongly correlating with the main component allows interpretation of the main components. As a rule, the following factors correlate with the main components:

    - level of infrastructure development;
    - transport component of the territory;
    - climatic zones;
    - level of agricultural development;
    - economic potential of the territory.

    Further analysis, including clustering, comes with a few of the first significant main components.

    In the figures you can see a graphical display of the first major components in several cities of the Russian Federation.

    The first main component characterizing the level of urban infrastructure development in N. Novgorod

    The first main component characterizing the level of urban infrastructure development in Yekaterinburg

    The first main component characterizing the level of urban infrastructure development in Kazan

    The first main component characterizing the level of urban infrastructure development in Perm

    the first principal component, which characterizes the level of development of urban infrastructure in Samara

    the first principal component, which characterizes uro Shade urban infrastructure development in Khabarovsk

    Integral Features: Clustering

    The next stage of work on the analysis of territories is the search for urban areas of uniform quality. This search is based on an analysis of the values ​​of the main components at each point in the territory. The task of searching for these homogeneous zones can be solved using clustering - the process of grouping territories according to the principle of proximity of a set of characteristics.

    Clusterization of the territory has two goals:

    - creating a better perceived visualization of the territory;
    - allocation of areas for the compilation of individual models.

    Territories are clustered according to selected factors for analysis. These factors may be factors affecting pricing or factors describing some aspect of the development of a territory, for example, the social sphere.

    There are two common classical clustering methods: the K-means method and the dendrogram method. When working with territories, the K-means method has proven itself well, the peculiarity of which is the “growing" of the cluster by connecting new objects to the growth points. The advantages of the K-means method are the similarity of its work to the natural process of forming territories: integration of similar ones, rather than separation of dissimilar ones.

    The K-means method was used to calculate Nizhny Novgorod (Figure below).

    Correspondence of clusters to the level of development of the territory by the example of the city of N. Novgorod

    With the proposed approach, you can get an idea of ​​the territory on various topics. The topics of interest to us may be, for example, the level of development of urban infrastructure, the level of “elitism” of the territory, the level of development of culture, the social component of the development of the territory. These topics are poorly defined integral concepts, and consist of many interrelated factors.

    With some algorithm for selecting parameters for analysis (including with the involvement of experts), we will get thematic maps that give an idea of ​​one aspect of the development of the territory.

    Integral characteristics are understood as the first main components, first of all, the most informative first main component, and the clustering of the territory according to the selected parameters.

    Thematic maps of the first major components on various aspects of development are presented in the figures below.

    Thematic map “Cultural objects” on the example of N. Novgorod

    Thematic map “Social sphere” on the example of N. Novgorod

    Integral characteristics make it possible to understand the features of the territory, operating with many factors with minimal loss of information.

    In conclusion, it is worth noting once again that today, the analysis of territories is an extremely important stage in solving the problems of developing the urban environment, choosing places for investing in construction, and finding the most favorable location for new objects and other tasks.

    The method of analyzing the territory proposed in the article using the “thermal” model from factors of different nature is not critical to the set of factors, that is, it does not impose restrictions and requirements on the source information.

    The diversity and redundancy of the source information, as well as the ability to use open data provides unlimited prospects for the analysis of any territory of the world.

    In the following publications devoted to the problems of territorial analysis, we plan to reveal the features of compiling models using the main components and methods for their implementation for such tasks as:

    - choosing the best place when placing a new object;
    - building a price surface for a certain category of objects using market value;
    -assessment of the profitability of a certain type of activity depending on the location of objects.

    It is also planned to introduce methods of the inverse transition from the main components to factors, which in turn allows us to obtain a model of factors for a given territory.

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