Cartographic images of the earth's surface as they increase. Topo map.docx - Abstract of a lesson in geography on the topic "Topographic map" (grade 8). Globe - a model of the Earth

1.1. Cartography - subject and definition.

Obviously, certain types and types of maps are necessary in various areas of human activity. In industry and transport, in agriculture and cultural construction, they are not only necessary, but very often indispensable means for performing a complex of works.

Maps are needed to find new roads and power lines; The development of subsoil and mineral deposits begins with the study of the terrain using maps. It is necessary for the construction of cities and villages, land reclamation, navigation and air navigation, the study of land resources, land management and land cadastre.

Maps are a reliable guide, in military affairs they are one of the main sources of information about the terrain and an indispensable tool in command and control.

In addition to directly serving national economic needs, geographical and other maps make it possible to study the country in geological, soil, botanical, demographic and other respects, to predict various natural phenomena, such as climate or natural disasters. An important feature of modern cartography is the intensive development of its cognitive functions as a means of studying the objective world and acquiring new knowledge.

The science of cartography deals with the study of maps, methods of their creation and use.

The state standard for cartographic terms defines:

"Cartography is a field of science, technology and production, covering the study, creation and use of cartographic works."

1.2 Cartography structure

AT in its totality, cartography combines a number of scientific areas and disciplines:

- theoretical foundations of cartography (the doctrine of the map)– studies

and develops a theory map projections, generalization of the cartographic image, ways of displaying thematic content, issues of creating sign systems (map legends).

- mathematical cartography- studies and develops mathematical methods for depicting the surface of the Earth and other planets on a plane. It is the first step in the process of creating maps.

Cartometry - studies and develops methods for measuring various objects on maps to determine their quantitative characteristics (coordinates, distances, heights, areas, volumes, angles of inclination, etc.).

- design and mapping– studies and develops map projects, methods of their creation, basic principles of editorial management at all stages of map creation.

Mapping is the study of the types and properties of geographical maps, the history of cartography, and the methods of using maps.

Card design - the study and development of methods and means of colorful and graphic design maps (design) and preparing them for publication.

Map publishing is the development of methods for reproducing and reproducing maps.

- economics and organization of cartographic production– study of the methods of its most rational organization.

Cartography in its structure is closely related to a number of scientific

disciplines. These are: geodesy, astronomy, topography, geography and polygraphy, mathematics, photogrammetry, informatics and computer graphics. In its content, cartography is unthinkable without connection with such sciences as soil science, geology, demography, climatology, land management, etc.

Geodesy provides cartographers with accurate data on the shape, size and gravitational field of the Earth, coordinates of geodetic reference points.

Topography - provides primary cartographic sources - large-scale topographic maps that serve as the source material for the creation of all geographical maps.

Geography - explains the essence of natural and socio-economic phenomena, their origin, interconnection and distribution on the earth's surface.

From polygraphy - cartography borrows methods of making printing forms and reproduction of maps.

Since the birth of cartography, mathematics has been at the heart of it, mathematical cartography can be considered as a purely mathematical discipline. Introduction to cartography computer technology made it possible to develop new types of maps, calculate the most complex projections, enriched cartography with new methods of studying maps using the apparatus of mathematical statistics, and made it possible to automate the laborious process of creating maps to a large extent.

Photogrammetry develops methods for determining the position, size, and shape of objects on the earth's surface from aerospace surveys. At present, aerial photography makes it possible to obtain a map that is superior in accuracy to similar works obtained on the ground, in addition, to reduce ground geodetic and topographic work to a minimum.

The list of sciences with which cartography maintains the closest connection can, of course, include geoinformatics and geographical sciences (geomorphology, hydrology, etc.), the sciences of the nature of the Earth (botany, zoology), the national economy, economics, history, and many others.

Summarizing the above, we can single out the main directions for using maps for science and practice.

− general acquaintance with the area, region, country, mainland, their study on maps without visiting in kind;

− application as a guide (tourism, aviation, navigation

etc.);

− use as a basis for engineering use - transport, energy, industrial, agricultural, for the purposes of district planning, construction;

− research and transfer of projects to nature;

− military use;

− study and rational use of natural (including land) resources and environmental protection;

− integrated and rational development of economic regions;

− use as an information basis in the conduct of land management and land cadastre.

1.3 Map elements, other cartographic works.

We have repeated the word map many times, but so far we have not considered a map as a graphic document, we have not studied the elements of a map, its properties, we have not even given a clearly formulated definition.

The Cartographic Terms Standard defines:

“A map is a reduced, built in a cartographic projection, generalized image of the surface of the Earth, the surface of another celestial body or extraterrestrial space, showing the objects located on them in a certain system of conventional signs.”

This definition, which may not be entirely perfect, highlights three features of maps that are very important for understanding the features that distinguish a map from other images of the earth's surface, such as an aerial photograph or a landscape. It:

1. mathematically defined construction;

2. use of cartographic symbols (codes);

3. selection and generalization of the depicted phenomena.

The mathematically defined construction of maps provides for the establishment of a strict functional relationship between geographical and rectangular

coordinates of points of the same name on the terrain and on the map. Such a construction, as it were, includes two actions for the transition from the physical surface of the Earth to its image on a plane. One of them consists in projecting the earth's surface onto the mathematical surface of the earth - the geoid. This projection is carried out orthogonally, by plumb lines perpendicular to the mathematical surface. But due to its complexity, the geoid in cartography is replaced by a surface of an ellipsoid of revolution, which is very similar in shape, i.e. a figure obtained by rotating an ellipse around its minor axis (Fig. 1.1).

It is with respect to this ellipsoid that all geodetic calculations are performed and map projections are calculated.

Another action is to depict the surface of the ellipsoid on a plane. It is impossible to expand the surface of an ellipsoid on a plane without folds and breaks; various kinds of deformations will take place, which in cartography are called distortions. The transition from an ellipsoid to a plane is carried out using cartographic projections that express the relationship between the coordinates of points on the earth's surface and the coordinates of the same points on the plane (map sheet).

When such a dependence is known, it is possible to take into account the distortions of a flat image and, therefore, to determine the actual distances, areas, angles on the map with the necessary accuracy, that is, to obtain the correct data on the location, size and shape of the depicted objects from the maps.

The use of cartographic conventions becomes obviously beneficial when comparing a map with an aerial photograph of the same area. The initial impression may be unfavorable for the card. Indeed, an aerial photograph allows you to see the true picture of the earth's surface, while on a map

it is replaced by a system of signs, which, as it were, erase many of the individual features of the objects of the area and thereby impoverish the image. However, it can be noted that the use of cartographic signs allows:

1. Significantly reduce the image in order to cover a significant part of the earth's surface or the entire planet at a glance, while reproducing those objects that, due to reduction, are not expressed on the map scale. In aerial photographs, as the scale decreases, the details are difficult to distinguish, and then completely lost.

2. show the terrain on the map, for example, using contour lines.

3. show not only appearance object, but also indicate its internal properties, for example, give qualitative characteristics of agricultural land, show the temperature and salinity of water, the height and species of trees in forests, and much more.

4. show the propagation of phenomena that are not perceived by our senses, such as magnetic declination, distortion values, etc.

5. exclude insignificant aspects of objects and highlight their common and essential features. At the same time, the process of selection and generalization of the depicted phenomena is very important, a process that is called cartographic generalization. Generalization saves on the map only those phenomena that are important in a practical or theoretical sense, it focuses on the transfer of the most significant features of the displayed phenomenon, primarily based on their purpose of the map. It allows you to distinguish the main from the secondary on the maps, to find common patterns in single properties.

1.4 Geographic map elements

The study and development of maps requires an analytical approach to them, dividing them into constituent elements, the ability to understand their meaning, determine their place, and see their connection with each other.

The map distinguishes between a cartographic image, a mathematical basis, auxiliary equipment and additional data (Fig. 1.4.1).

Cartographic image and associated legend- the main part of any geographical map, contains information about the objects and phenomena shown on the map, their location, properties, relationships.

This information constitutes map content. In turn, the content of the map is divided into elements, both geographical and thematic. The complex of these elements is not the same on different maps. But one of the elements, namely hydrography, is mandatory on all maps. For example, on thematic maps, the main content elements can be minerals, flora or fauna, soils, etc. Content elements are depicted with the same detail on topographic maps.

The geometric laws for constructing maps are determined by its mathematical basis, the elements of which include: a cartographic projection, as well as a cartographic grid associated with it (a network of meridians and parallels), scale, reference geodetic network, nomenclature, map layout and layout.

The scale of the map indicates the overall degree of reduction of the earth's surface when depicted on a plane. It is characterized by the ratio of the length of a line on a map to the corresponding line on the earth's surface. There are 3 types (methods) of scale representation on maps:

− numerical (for example, 1:25000)

− natural (for example, there are 250 meters in 1 centimeter)

− linear (transverse, graphic), displayed as a graph.

AT Depending on the scale of the map and the size of the mapped area, the map can be displayed on one or more sheets.

The main elements of the mathematical foundation are map projection and associated map grid. Depending on the type of geometric surface on which the surface of the ellipsoid is projected, there are projections of cylindrical, conical, azimuthal and some others.

Layout - rational placement on the map sheet of the mapped territory, auxiliary and additional equipment.

Accessories- makes it easier to read the map and work with it. It includes the necessary explanations and graphs for measuring by maps, as well as the name of the map, information about the performers, reference and output data, etc.

To additional equipment include cards placed in the "air" or on

its fields additional cards, profiles, diagrams, textual and digital data that explain, complement and enrich the cartographic image.

General geographic maps

Additional information

The content of the article

MAP, a reduced generalized image of the surface of the Earth (or part of it) on a plane. Man has been creating maps since ancient times, trying to visualize the relative position of various parts of land and seas. A collection of maps, usually bound together, is called an atlas (a term coined by the Flemish Renaissance cartographer Gerardus Mercator).

A ball (sphere) with a cartographic image of the Earth applied to its surface is called a globe. This is the most accurate representation of the earth's surface. On all maps that give an image of a ball on a plane, there are certain distortions that cannot be eliminated. Nevertheless, maps have certain advantages over the globe. For example, a world map allows you to look at the entire earth's surface (i.e. its image), while on a globe from one point you can see no more than half the globe; therefore, maps are more convenient when considering the entire surface of the Earth. On the map, in addition, it is much easier than on the globe to measure angles and directions. At present, globes are rarely used for navigational purposes. The image on a spherical surface of territories that do not exceed the size of a subcontinent does not provide practically any advantages, therefore, in such cases, maps are used, rather than segments of the globe. Moreover, maps are much easier to make, transport and store (although some of these difficulties can be overcome by using inflatable globes).

MAIN FEATURES OF THE CARDS

With all the amazing variety of existing maps, most of them have some common features. Even contour maps, which are as unloaded as possible so that students can apply additional information on them of their choice, usually have a degree grid of coordinates, a scale, and basic elements (for example, coastlines). In addition, inscriptions and symbols are usually applied to the cards, and a legend is attached to them.

coordinate grid

is a system of mutually intersecting lines indicating latitude and longitude on a map or globe surface. Latitude lines run east-west parallel to the equator (which has a latitude of 0°); the latitude of the poles is considered to be 90° (North latitude for the North Pole and South latitude for the South Pole). Since these lines do not intersect and are mutually parallel, they are also called parallels. Of these, only the equator is the largest circle (the plane bounded by this line, passing through the center of the Earth, cuts the globe in half). The remaining parallels are circles, the length of which naturally decreases with distance from the equator. All lines of longitude - meridians - are halves of a large circle, converging at the poles. The meridians run in a north-south direction, from pole to pole; they count the angular distance from the initial meridian, denoted as 0 ° longitude, to the east and west to 180 ° (at the same time, longitudes that are measured in the east direction are indicated by the letters “east”, and in the west - “w. etc.") . Unlike the equator, which is equidistant from the poles along its entire length and, in this sense, is a “natural” reference point in determining latitude, the initial meridian from which longitude is measured is chosen arbitrarily. In accordance with international agreement, the meridian of the Greenwich Astronomical Observatory (now located in London) is taken as the origin of coordinates (0 ° longitude). However, before this agreement was reached, some cartographers used as the initial meridians of the Canary or Azores, Paris, Philadelphia, Rome, Tokyo, Pulkovo, etc.

On the surface of the globe, the lines of parallels and meridians intersect at an angle of 90°; as for maps, such a ratio is preserved on them only in some cases. Both on maps and on globes, a certain system of meridians and parallels (drawn through 5 °, 10 °, 15 ° or 30 °) is usually applied. In addition to this, maps and globes show the Northern Tropic, or Tropic of Cancer (23 1/2 ° N), the Southern Tropic, or Tropic of Capricorn (23 1/2 ° S), the Arctic Circle ( 66 1/2°N) and the Antarctic Circle (66 1/2°S). International Date Lines are often also shown on charts, which generally coincide with 180° longitude.

Scale

cards can be numerical (a ratio of numbers or a fraction, for example, 1:25,000 or 1/25,000); verbal or linear (graphic). In the example above, a unit of length on the map corresponds to 25,000 such units on the ground. The same ratio can be expressed by the words: "1 cm is equal to 250 m" or, even more briefly: "250 m in 1 cm". In some countries that traditionally use non-metric measures of length (USA, etc.), the scale is expressed in inches, feet and miles, for example, 1:63 360 or "1 mile in 1 inch". The linear scale is depicted as a line with divisions plotted at certain intervals, against which the corresponding distances on the earth's surface are indicated. The graphical representation of scale has certain advantages over the other two ways of expressing it. In particular, if the size of the map changes when it is copied or projected onto a screen, then only the graphical scale, which changes along with the entire map, remains correct. Sometimes, in addition to the length scale, the area scale is also used. Globes may use any of the above scale designations.

Basic elements and conventional cartographic signs.

The geographic base elements include the image of the coastline, watercourses, political boundaries, etc., which create a base against which the spatial distribution of the displayed phenomenon is shown. When compiling maps, many conventional signs are used, which are divided into several categories: off-scale, or point, used to depict "point" objects or such, scale which cannot be expressed on the map (for example, to show settlements - dots or circles, the size of which indicates a certain population); linear for objects of a linear nature, preserving the similarity of the outlines of the object (for example, the image of a permanent watercourse in the form of a line, the thickness of which increases downstream); areal, used to fill in the areas of objects that are expressed at the scale of the map (for example, hatching or filling with color to show the distribution of forests). Further, these three classes of signs can be subdivided according to whether the objects they represent are imaginary (for example, political borders) or real (roads); whether the signs themselves are homogeneous (points on the map, each of which corresponds to a certain number of inhabitants) or differentially representing the quantitative characteristics of objects (image of cities using circles of different sizes, corresponding to the population); whether they give a qualitative characteristic of the object (for example, the presence of a swamp) or contain quantitative information (for example, population density - the number of people per unit area).

The purpose of the legend is to inform the reader about the meaning of the symbols used. In old maps, the legend was placed in an elaborately ornamented frame in the form of a scroll, and now it is in a strict rectangular frame.

As an example, the legend to the geographical maps contained in the Encyclopedia Around the World is given.

Inscriptions and geographical names on maps.

In the past, all the inscriptions were applied by hand, which gave an individual character to each map, but now cartographers, as a rule, choose one of the standard fonts that best suits the nature of the depicted objects. Some types of fonts are traditionally used for certain groups of objects, for example, rivers, lakes, seas are usually in italics, and land features are indicated in roman type. The size of the letters depends on the significance (or size) of the object. Distances between letters and words in names can vary widely depending on the area or extent of a given object on the map.

The font design of the map includes a heading that reflects the content of the map and the territory to which it refers; for this, the largest font is used. A special place is occupied by geographical names, the selection and number of which depend on the purpose of the map (for example, a city plan contains many street names, and vegetation maps contain only a few of the most necessary names). It is customary to indicate the publishing organization, year of publication, sources used. The map is accompanied by a legend that deciphers conventions and sometimes notes.

Map Orientation

in relation to the cardinal points is determined by the lines of the cartographic grid within the frame of the map and represents an essential element of its layout. In the Middle Ages, both in Europe and in the Arab countries, maps were drawn in such a way that the east was located at the top (the term "orientation" itself comes from the Latin word oriens - east). In modern maps, north is usually located at the top of the map, although deviations from this rule are sometimes allowed. Reading a map, especially in the field, is greatly facilitated by its correct orientation relative to objects and directions on the ground. To indicate the cardinal points, a compass card is sometimes depicted on the map, but more often it is just an arrow pointing north.

TYPES OF CARD

Maps are divided into groups according to a number of characteristics - scale, subject, territorial coverage, projection, etc. However, any properly carried out classification must take into account at least the first two features. In the United States, three groups are distinguished by scale: large-scale maps (including topographic maps), medium-scale maps, and small-scale maps, or survey maps.

Large scale maps

are basic because they provide the primary information used in the preparation of maps of medium and small scales. The most common of these are topographic maps at a scale larger than 1:250,000.

On modern topographic maps, relief is usually shown using isogypses, or contour lines that connect points that have the same height above zero level (usually sea level). The combination of such lines gives a very expressive picture of the relief of the earth's surface and allows you to determine the following characteristics: the angle of inclination, slope profile and relative elevations. In addition to the image of the relief, topographic maps contain another useful information. Usually they show highways, settlements, political and administrative borders. Kit additional information(for example, the distribution of forests, swamps, loose sandy massifs, etc.) depends on the purpose of the maps and the characteristic features of the area.

No country in need of an assessment of its natural resources can do without topographic surveys, which are greatly facilitated by the use of aerial photographs. Nevertheless, there are still no topographic maps for many regions of the globe, which are so necessary for engineering purposes. Successes in solving this problem were achieved with the help of the so-called. orthophotomap. Orthophotomaps are based on computer-processed planned aerial photographs with increased color brightness and contour lines, boundaries, place names, etc. applied to them. Orthophotomaps and satellite images with topographic load elements raised on them are much less labor-intensive to manufacture than traditional topographic maps. Many thematic large-scale maps—geological, soil, vegetation, and land use—use topographic maps as a basis upon which a special load is applied. Other specialized large-scale maps, such as cadastral maps or city plans, may not have a topographic basis. Usually, on such maps, the relief is either not shown at all, or is depicted very schematically.

Medium scale maps.

Both large-scale topographic and medium-scale maps are usually produced in sets, each of which meets certain requirements. Most of the medium-scale ones are published for the needs of regional planning or navigation. The medium-scale International Map of the World and aeronautical charts of the USA are distinguished by the greatest territorial coverage. Both sets of maps are produced in 1:1,000,000 scale, the most common for medium scale maps. When preparing the International Map of the World, each country issues maps to its territory prepared in accordance with the given general requirements. This work is coordinated by the UN, but many of the maps are outdated and others are not yet complete. The content of the International Map of the World basically corresponds to the content of topographic maps, but is more generalized. The same applies to aeronautical charts of the world, but most of the sheets of these charts have an additional special load. Aeronautical charts cover the entire land. On a medium scale, some nautical or hydrographic charts are also compiled, on which Special attention is given to the image of reservoirs and the coastline. Some administrative and road maps are also medium scale.

Small-scale, or survey, maps.

On the maps small scale the entire surface of the globe or a significant part of it is shown. It is difficult to draw a precise line between small and medium scale maps, but the 1:10,000,000 scale definitely applies to survey maps. Most atlas maps are on a small scale, and thematically they can be very different. Almost all the above indicated groups of objects can also be reflected on small-scale maps, provided that the information is sufficiently generalized. In addition, maps of the distribution of various languages, religions, crops, climates, etc. are compiled on a small scale. As an illustrative example of special small-scale maps, well known to millions of people, one can point to weather maps.

Animated and computer cards.

For cartoon cards that can be projected onto a TV screen, the fourth coordinate is entered - time , allowing you to follow the dynamics mapped object . Computer cartography has now reached such a stage of development that almost all operations can be performed in digital form. As a result, it is much easier to make all kinds of corrections and clarifications. This method of creating maps of any type and scale, including cartoon maps, is designated by the special term "geographic information systems" (GIS).

MAIN TYPES OF PROJECTIONS

A map projection is a way of displaying the spherical surface of the globe on a plane. The associated image transformation inevitably leads to distortion. However, some characteristics of the cartographic grid applied to the surface of the globe can be stored on the map at the expense of other characteristics that will be distorted.

On the globe, all parallels and meridians intersect at right angles. A projection in which this property is preserved is called conformal, or conformal. In this case, the shape of areal objects is preserved, but the relative sizes change from place to place. With another method of transformation, it is possible to preserve the correct ratio of areas (corresponding to the original surface of the globe), but in these cases, distortion of the angles of intersection of the meridians and parallels is observed; right angles are preserved only in a limited area. Projections that maintain the correct ratio of the areas of individual cells of the degree grid are called equal; they are characterized by a greater or lesser violation of the similarity of the figures. The correct transfer of the configuration of objects, as well as the correct transfer of areas, are of great importance, especially if we are talking about small-scale overview maps. However, both of these characteristics cannot be combined on the same map: there is no projection that would be both equal-angle and equal-area. In addition, the correct display of distances and directions is very important. To some extent, this can be achieved by using certain projections.

Map projections can be classified according to the type of auxiliary geometric surface that can be used in its construction. Let's take a transparent globe with lines of meridians and parallels drawn on its surface and a point source of light. We can enclose a globe (with a light source located in the center of the ball) in a cylinder. In this case, the degree grid is projected onto the surface of the cylinder, which can then be deployed on a plane. The cylinder can be tangent and touch the globe only along one line (for example, the equator), or it can be secant. In the latter case, the surfaces of the sphere and the cylinder will coincide along two lines (for example, along 45 ° N and 45 ° S), and only along these lines the correct scale is preserved in this projection. By changing the position of the light source with respect to the surface of the ball, various projections of the cartographic grid onto the surface of a cylinder or other geometric figure can be obtained.

One such figure traditionally used in map projections is the cone. As in the previous case, the cone can touch the ball, or it can cut it. The lines along which these figures touch or cut one another (usually these are certain parallels) maintain the correct scale and are standard parallels. To reduce distortion, a series of truncated cones can be used instead of a single cone; in this case, the correct transfer of scales along a number of standard parallels will be achieved.

In the cases considered, a development on the plane of the cylinder or cone is necessary, but, of course, it is also possible to directly project the surface of the ball onto the plane. In this case, the plane can touch the ball at one point or cut it; in the latter case, the surfaces of the sphere and the plane will coincide along the line of the circle. This transformation of the degree grid is called the azimuthal projection; in it, the true scale is preserved only at the point of contact or at the line of intersection of the plane and the sphere. The configuration of the resulting grid on the projection depends on the position of the light source.

In accordance with the geometric figures used in the construction of the considered projections, the latter are called cylindrical (or rectangular), conic and azimuthal. In addition to those indicated, other transformations of the degree grid are possible, which are not reducible to these simple geometric shapes, but having a mathematical justification; they are usually called arbitrary. Many projections have been developed at various times, but only a few of them have come into widespread use. The task of the cartographer is to choose the projection that best suits the tasks of this map.

A distinctive feature of the stereographic projection is that all objects that are circles on the earth's surface are also depicted on the map as circles or, in some special cases, as straight lines. It is due to this property that the stereographic projection, invented in ancient times, is so widely used now, for example, to show the propagation of radio waves, etc.

The Mercator projection is conformal. Any straight line that intersects all meridians at the same angle on the earth's surface is transmitted in this projection by a straight line, which is called a loxodrome. This remarkable property makes the Mercator projection very useful for navigation charts. Unfortunately, this projection is often misused to show areas such as global population distribution, crops, and so on.

In such cases, it is most appropriate to choose equal projections, for example, a sinusoidal one. This projection, one of many developed for world maps, has a certain defect - both poles on it are located on ledges, and the areas adjacent to them turn out to be significantly deformed. On other maps of the world using equal-area projections, the poles are depicted as a straight line of various lengths (in cylindrical projections it is equal to the equator, in the Eckert IV projection - half the length of the equator, in the flat polar projection - a third of the equator), or even in the form of an arc (Mollweide projection ). The characteristics of some projections are given in the table ( see below). The list of projections placed in the table is far from complete and does not include, for example, polar equidistant and polar equidistant (both azimuthal), as well as some projections that allow you to most accurately reproduce the surface of the globe, for example, orthographic.

One of the most convenient projections, gnomonic, is unique in that any great circle of a sphere (and an arc of a great circle) is represented as a straight line in it. Since the arcs of great circles are the lines of the shortest distances on the map, then on a small-scale map drawn up in such a projection, one can easily find (by a ruler) shortcuts between two points; however, it must be borne in mind what the great circle arc does not correspond to the constant direction measured by the compass. As with other azimuth projections, in the gnomonic projection the image can be projected onto a plane tangent to the surface of the ball at any point, such as the pole or the equator, but the territorial coverage of such maps is very limited.

The equal area projection of Bonn is more suitable for depicting areas that are elongated in the meridional direction. If the mapped area is elongated in latitude, then the Lambert conformal conic projection is preferable for it. The polyconic projection is neither conformal nor equal area, but for small areas it gives little distortion; it is in this projection that the series of maps prepared by the US Geological, Surveying and Cartographic Service, as well as (with minor changes) the International Map of the World, are compiled. Another equal-area projection, developed for survey maps, combines the features of a sinusoidal (when transferring equatorial regions) and pseudocylindrical Mollweide projections (in polar regions). As in a number of other equal-area projections, the image in it can be given with breaks or in a compressed form.

Discontinuities arise if not one average (rectilinear) meridian is chosen, but several, and for each of them a part of the degree grid is built. An extreme case is the image of the entire surface of the globe in the form of segments of the globe. Maps in this projection also use a "compressed" image; compression is achieved due to the fact that parts of the image that are not needed for a given map (for example, water areas for a soil cover map) are "cut out" and the remaining ones are brought together; this makes it possible to use a larger scale while maintaining the same sheet area.

MAPPING METHODS

Once a projection has been chosen and the corresponding grid has been drawn, one can begin to draw up the basis and prepare the information that determines the content of the map. At the same time, aerial photographs are often used for large-scale maps. Theoretically, a planned aerial photograph contains all the elements of the landscape that can be shown on large scale map. Moreover, having photographs partially overlapping each other, it is possible to build relief maps in contour lines; this requires a stereoscope and various devices for measuring heights from images. The development of photogrammetry, a science that deals with measuring and mapping the earth's surface using aerial photographs, has made it possible to significantly speed up the compilation of maps and improve their accuracy. The use of aero and satellite images made it easier to update obsolete maps. Although aerial photographs good picture surfaces, they still cannot replace cards; they contain a lot of "unsorted" information, so they require interpretation. On the map, relatively less important data can be omitted, while other, more significant for the purposes of this map, on the contrary, are highlighted for easier reading. Moreover, both within the same image and on different images of the same series, there are various image distortions and violations of its scale. Therefore, in order to use images for compiling detailed maps, they must be brought to a single scale and corrected.

Some of the problems of mapping can be illustrated by the example of coastlines demarcating land and water areas. Since there are tides, the boundaries of the continents and oceans change in accordance with the change in the level of the World Ocean; usually maps show their position at mean sea level (i.e., the average between high and low tide levels). Moreover, even the largest scale maps cannot show all the details of the coastline; therefore, generalization is necessary.

The value of generalization, i.e. selection and generalization of details, increases as the scale of maps decreases; almost all elements of the basis and content of the map are subjected to generalization. For example, of the streams depicted on a large-scale topographic map, only a few can be preserved on a medium-scale map; when moving to overview maps, further selection and reduction in the number of elements is required. When selecting and generalizing, it is also necessary to establish the principles of selection - for example, when choosing criteria for displaying settlements, it is necessary to decide whether to be guided only by population or also take into account the political significance of cities; in the latter case, it is necessary to show all the capitals on the map, although their population may be low.

One of the most difficult tasks of mapping is the correct rendering of the terrain. In this case, methods such as hillshade, rendering of relief forms, isohypses, hatching and layered hypsometric coloring are used. Contours can be thought of as lines of intersection of a topographic surface by a series of equally spaced horizontal planes; the distance between these planes along the vertical is called the horizontal section. As a quantitative indicator, contour lines are very informative, but this method has some disadvantages - for example, small landforms may not be reflected on the map even with a small section, and, in addition, the relief in such an image is not very clear. In some cases, difficulties are overcome with the help of plastic hillshade - in addition to contour lines, shadows are applied to the relief image in accordance with the main skeletal lines, giving a qualitative characteristic, i.e. distribution of light and shadow for a given (oblique or vertical) illumination. A similar effect can be obtained when photographing an illuminated terrain model. Theoretically, even very small landforms can be shown with the help of shadow hillshading, if they are expressed at this scale at all. The combination of contour lines and hillshade achieves the most accurate, qualitatively and quantitatively, transfer of surface shapes.

The display of the relief by means of strokes differs in that the strokes are drawn along the dip of the slope (and not along the strike, like horizontal lines). The thickness of the strokes depends on the slope angle; the steeper the slope, the thicker the line, causing steeper slopes to appear darker on the map. Hatching can show sharp ridges and steep ledges; when drawing contours, even the most careful, these forms usually look smooth. The use of echo sounding makes it possible to perform detailed mapping of the topography of the ocean floor.

The oldest method of showing the outlines of the earth's surface is the use of perspective conventional signs, which are a stylized image of certain landforms in profile or in a 3/4 perspective. At the same time, their appearance, of course, differs from the planned image characteristic of the map, and, accordingly, some of them turn out to be displaced with respect to the true coordinates. Such a shift is tolerable on overview maps, but unacceptable for maps of large scales. Therefore, schematic signs depicting landforms are usually used only on small-scale maps. Previously, only the largest objects were transmitted in this way; small forms are also shown on modern physiographic maps. In this case, it is necessary to exaggerate the vertical scale compared to the horizontal one, since otherwise the relief forms look too flat and inexpressive.

The image of the relief on hypsometric maps is the highest degree of generalization of the contour lines method. Like the depiction of landforms with stylized perspective signs, this method is mainly used on overview maps. On hypsometric maps, each altitudinal zone is painted over with a certain color (or shade). A line can be drawn along the contact of two high-rise steps highlighted in different colors. At the same time, in each individual altitudinal belt, which sometimes spans hundreds of meters vertically, many details of the relief structure are not reflected on the map.

Traditionally, hypsometric maps used a specific color scale, in which shades of green, yellow and brown succeeded each other in ascending order of height; now some cartographers are refusing to do so. However, there is a tradition of depicting a number of mapped objects in a certain color. For example, brown is used for contour lines, blue for water features, red for settlements, and green for vegetation. The use of color not only makes the map more attractive, but also allows additional information to be presented.

statistical maps.

Small-scale statistical maps deserve special mention because of their increasing importance. These maps are usually based on quantitative sources such as census data. Among the methods of transmitting information, point methods, isopleth, choropleth (cartogram) and cartogram methods should be indicated. All of these methods can be used for the same data. Dot icons of the same size, each representing the same number of units of the depicted phenomenon , are plotted on the map according to the actual location of the phenomenon; the accumulation or sparseness of points shows the distribution (density) of the mapped phenomenon. Isopleths are isolines connecting points with the same values ​​of some relative indicator calculated on the basis of other indicators (and not measured directly). An example is the isolines of average monthly temperatures (calculated index). In the Horoplet system, a specific territorial statistical unit (for example, administrative District) is considered as homogeneous according to this statistical indicator; spatial differentiation is achieved by dividing the selected units into classes according to the size of the mapped feature and assigning a specific color to each class. On map diagrams, areas that are statistically homogeneous with respect to the selected attribute are shown regardless of the boundaries of territorial units, the data for which are the basis of the map.

Two more methods often used for statistical maps are signs, the size of which depends on the quantitative characteristic of the phenomenon depicted, and signs showing the direction of movement. In the first method, used in the case of precisely localized phenomena, such as the urban population, the point symbols have different weights; the size of signs is chosen proportional to their weight and has several gradations (for example, according to the number of city residents). Movement signs may also include a quantitative characteristic (for example, the volume of shipping). This effect is achieved by changing the thickness of the lines.

HISTORY OF THE DEVELOPMENT OF CARTOGRAPHY

The universality of the cards is evidenced by the fact that even the so-called. primitive peoples make maps that perfectly suit their needs. For example, the Eskimos, without any measuring instruments at their disposal, made maps of vast areas of northern Canada, which do not lose much when compared with maps of the same territories compiled using modern methods. Similarly, the nautical charts compiled by the inhabitants of the Marshall Islands provide exceptionally interesting examples of "primitive" cartography. In these maps, the "grid" is formed by the midribs of the palm leaves, representing the open sea, and the arcuate lateral veins correspond to the front of the waves approaching the islands; the islands themselves are marked with clam shells. There has been a growing interest in Aboriginal maps, including American Indians.

In addition to rock paintings, we have come down to ancient maps compiled in Babylon and ancient Egypt. Babylonian maps on clay tablets dated to about 2500 BC show features ranging in size from a single landholding to a large river valley. On the lid of one Egyptian sarcophagus is a stylized map of the roads of ancient Egypt. Chinese cartography also dates back to ancient times. In China, some very important techniques were developed a long time ago and independently of the West, including a rectangular cartographic grid used to determine the location of an object.

With regard to ancient Greece, although we have only a few examples of maps from this era, it is known from literary sources that the Greeks greatly surpassed other peoples in this area. Already in the 4th c. BC. the Greeks came to the conclusion about the sphericity of the Earth and divided it into climatic zones, from which the concept of latitude later arose. Eratosthenes in the 3rd c. BC. using simple geometric constructions, he amazingly accurately determined the dimensions of the Earth. He also owns a map of the world, on which lines of latitude and longitude were shown (although not in a modern ordered form). The representation of geographic coordinates in the form of a regular grid with equal intervals, attributed to the Greek astronomer Hipparchus, was used by the famous Greek cartographer Ptolemy, who lived in the 2nd century BC. AD in Alexandria. Ptolemy compiled a gazetteer that included ca. 8000 points with their coordinates, and developed a manual for the compilation of maps, from which, many centuries later, scientists were able to reconstruct some of the maps he compiled. After Ptolemy, cartography in the West fell into decline, although the Romans did a lot of land surveying. and compiling road maps.

Significant progress in cartography was made in China: compiled there in the 12th century. maps are superior to any other from this time. It is China that is credited with issuing the first printed map ca. 1150 ( see fig.). Meanwhile, the Arabs, using data from astronomical observations, learned to determine the latitude and longitude of any place much more accurately than Ptolemy could. Most of the maps drawn up in Europe in the Middle Ages were either extremely sketchy, such as road maps for pilgrims, or were overloaded with religious symbolism. The most common were cards like "T in O"; The earth was depicted on them in the form of a disk, and the letter "O" depicted the ocean surrounding the land; the vertical line of the letter "T" represented the Mediterranean Sea, and the rivers Nile and Don constituted, respectively, the right and left parts of the upper crossbar. These bodies of water separated Asia (located at the top of the map), Africa, and Europe on the map.

At the beginning of the 14th century a new type of map appeared in cartography. These were sea charts - portolans, which served navigational purposes; their creation became possible due to the appearance in Europe of a magnetic compass. Initially, these maps, embellished with a schematic representation of a compass and characterized by extremely detailed study of coastlines, were compiled only for the Mediterranean. In some respects, the pinnacle of medieval cartography is the small globe made by Martin Behaim in 1492, showing the world as it appeared before the discovery of America. This is the oldest globe.

Great geographical discoveries of Europeans in the second half of the 15th century. provided to the cartographers of the Renaissance new material. At the same time, scholars rediscovered and translated from ancient Greek the works of Ptolemy, the dissemination of which was made possible by printing. The development of printing has revolutionized cartography, making maps much more accessible. In particular, the production of maps has increased dramatically in the Netherlands. The central role in this process was played by Gerard Mercator (1512–1594), who clarified the position of many points on the world map, developed cartographic projections and created a major atlas, published after his death. The first atlas in the modern sense was a collection of maps published by the Flemish Abraham Ortelius under the title Spectacle of the globe (Theatrum orbis terrarum). The success of these ventures led to the flourishing of the card trade; in the centuries that followed, the industry declined due to a lack of new ideas.

A new impetus to the development of cartography was given in the 17th century. as a result of the activities of newly formed scientific societies, such as the Royal Society of London or the Royal Academy of Sciences in Paris. These organizations financed scientific expeditions, and also made a lot of efforts to more accurately determine the shape of the Earth and the location of individual points, which contributed to a significant progress in cartography. An important role in the development of topographic cartography was played by the invention of the theodolite, scale, barometer, and pendulum clocks, as well as by the development of new imaging methods (isolines, shading, etc.). Modern topographic survey on the scale of the whole country was begun in France in the 18th century.

In the 19th century there have been notable advances in small-scale mapping and especially in the development of quantitative cartography. At the end of the 19th century German geographer Albrecht Penk spoke at the International Geographical Congress with a proposal to create an International Map of the World. This project was carried out in the 20th century. In our century, the use of aerial photographs has become widespread. Ideas about the structure of the earth's surface and the shape of the Earth have been significantly enriched thanks to observations from artificial satellites, from which materials were obtained for mapping and other celestial bodies.

ORGANIZATIONS AND ENTERPRISES ENGAGED IN COMPILATION AND PUBLICATION OF MAP

Mapping the earth's surface has been and remains the lot of various international organizations. For example, the UN, in addition to financing the International Map of the World, allocates funds to mapping organizations. The international exchange of cartographic information is facilitated by the International Cartographic Association, which holds regular meetings and publishes a reference yearbook ( The International Yearbook of Cartography). Another international publication, the magazine Imago Mundi (translated as "The Image of the World"), is devoted to the history of cartography.

Topographic survey of the territories of individual countries is usually carried out by the forces of these countries. In many countries, national surveying and topographical work originally served military purposes; An example is the UK Film Service, responsible for the preparation of topographic maps of the territory of this country. In the US, there are more than a dozen federal organizations involved in topographic surveys in the country; the largest of these is the US Geological, Surveying and Mapping Service, whose main residence is in Washington. Surveying the US coastal zone and providing the necessary geodetic base for this are assigned to the US Coast and Geodetic Survey. Other US mapping organizations include the Department of Defense Surveying and Cartography Administration, which deals with topographic, hydrographic, and aerospace surveys. In many countries, national atlases are produced by various organizations, partly or wholly financed by the government.

In some countries, geographical societies occasionally issue thematic maps as supplements to their periodicals. The US Geographic Society, for example, features a variety of political and thematic maps in most issues of its popular magazine, National Geographic.

Commercial mapping companies often specialize in the production of a particular type of mapping product. Some issue road maps, others wall maps and atlases for schools, colleges and universities, others specialize in publishing cadastral maps for the needs of lawyers, tax inspectors, etc. The center for commercial map publishing in the United States is located in Chicago. In many countries, such enterprises are located in the capitals. Collecting cards, especially old ones, is widespread in the United States. For collectors, a special magazine "Card Collector" ("Card Collector") is published. The Map collector"). Many facsimile copies are commercially available. vintage maps and atlases.

In the United States, the most complete collection of maps and atlases, including both modern and ancient editions published in various countries, is located in the Cartographic Department of the Library of Congress in Washington. Copies of maps issued by the US federal agencies, as well as handwritten maps compiled by the same agencies, are stored at the National Archives and Records Administration in Washington. The same functions in Great Britain and France are carried out, respectively, by the cartographic department of the British Library in London and the National Library in Paris. The Vatican Library in Rome has a large collection of old and very valuable maps.

Literature:

Salishchev K.A. Cartology. M., 1976
Berlyant A.M. Cartographic research method. M., 1978
Brief Topographic and Geodetic Dictionary. M., 1979
Salishchev K.A. Cartography. M., 1982
Berlyant A.M. Image of space: map and informatics. M., 1986

Without certain distortions, it is impossible to depict on paper a significant part of the Earth's surface. Mathematical methods of image on the plane of the earth's surface are called map projection. In a map projection, meridians and parallels are represented by a system of straight or flat curved lines. Every projection has its inherent distortions. At the heart of any cartographic projection is one or another method of depicting a degree grid. The representation of a grid on a map is called a cartographic grid. Depending on the purpose of the map, a cartographic projection is selected. When compiling political maps of parts of the world, one must choose a projection that would give a fairly accurate idea of ​​the size of the territory of a particular state, which would make it possible to compare the territory of countries by area. Such projections, in which all areas are reduced by the same number of times (not distorted), are called equal-area. For navigation, conformal projections are convenient, in which the angles between different directions on the earth's surface are depicted in full size, although the relationship between areas is not preserved.

One can talk about the nature and magnitude of distortions on the map by placing a cartographic grid with the degree grid of the globe. On the globe, all meridians, parallels are placed at the same distance from each other. Therefore, all cells of the degree grid between two adjacent parallels have the same shape and size on the globe, and the cells between the meridians narrow and decrease in size to the north and south of the equator. Therefore, signs of map distortion are unequal shape and different cells between adjacent parallels (distortion of the area), different segments of meridians between parallels (distortion of the length of lines and unequal scale in different parts of the map), deviations from the right angle of the angles between the meridians and parallels on the map (angular distortion).

Depending on the methods of transferring the degree grid from the globe to the map plane, there are the following projections: azimuthal, cylindrical, conical.

If we attach a screen to the equator of the globe and project each of its points, we will get a map in the azimuthal equatorial projection. In this projection, maps of the hemispheres are built. When projecting a globe onto a screen located at the North or South Poles, an azimuthal polar projection is obtained. It gives a correct idea of ​​the polar regions. Distortion on these maps will increase with distance from the pole. Projecting a globe onto the sides of a cylinder will give a cylindrical projection. The distortion of the outlines of the earth's surface with a cylindrical projection increases with distance from the equator to the poles. Therefore, it is convenient for depicting countries located near the equator. Meridians and parallels in this projection are parallel lines that intersect at right angles.

For the image of countries of middle latitudes, a conic projection is used. It is obtained by designing a globe on the walls of a cone. In the conic projection, the meridians are depicted as straight lines that diverge as rays from one point, and the parallels are shown as arcs of circles with a common center at the point that was the top of the cone. In this projection, the exact scale is preserved on the parallel where the cone touched the globe. The farther from this parallel, the more the contours of the earth's surface are distorted on the map.

The surface of the globe cannot be depicted on a plane without distortion. Only on a spherical globe can the similarity and proportionality of the sizes of all parts of the earth's surface be preserved. But globes are inconvenient to use, and their scale is usually not large, for example, with a scale of 1 km in 1 cm (1: 100,000), the diameter of the globe would be 127.4 m.

There are various ways to depict the earth's surface on a plane. All of them are called map projections. Some of them are actually obtained by projecting the earth's surface onto a plane by rays emanating from a constant point of view located outside, on or inside the globe, others have a different geometric meaning. Each of these methods indicates a well-defined method of depicting the earth's surface on a plane and taking into account the inevitable distortions.

However, if you take an ordinary school globe 1: 50,000,000 scale (about 25 cm in diameter) and pin a small piece of paper 1 cm2 in size to its surface, it turns out that it almost completely coincides with the surface of the globe without wrinkles. This shows that in small areas we can consider the earth's surface flat and depict it on paper while maintaining the geometric similarity of the figures. Such images are often called plans. The use of projections loses its significance here, since even in different, but properly chosen, projections, the images of very small parts of the globe almost do not differ from each other.

When considering cartographic projections, the image on the plane of the earth's surface is practically replaced by the image on the plane of the geographic grid of meridians and parallels, which on the map is called the cartographic grid. This is permissible because, having built meridians and parallels on the map, we can plot any point according to its geographical coordinates. Therefore, in the following presentation, we are talking about a grid of meridians and parallels on the "mathematical surface" of the earth, for which we take the surface of the oceans, mentally continued under the continents, and about the image of this grid on a plane. For some projections, cartographic grids are built geometrically, but more often they use a different technique. First, the flat projections are calculated using the available formulas for the selected projection. rectangular coordinates points of intersection of the meridians and parallels, then these points are superimposed on the paper according to the coordinates and then connected by smooth curved lines depicting the meridians and parallels.

Each conditional image of the earth's surface on a plane, i.e., each projection, corresponds to a well-defined type of cartographic grid and well-defined permissible distortions. There are distortions of lengths, areas and angles.

It is known that on the earth's surface all meridians have the same length; segments of the same parallel between neighboring meridians are also equal. But only the middle meridian is shown as a straight line; the remaining meridians are curved lines, the length of which increases with distance from the middle meridian. Parallels are distorted to the same extent - their segments between neighboring meridians increase with distance from the middle meridian.

There are other projections that do not distort the length along certain, well-defined, directions. For example, equidistant cylindrical. On it, the meridians are rendered without distortion, since the lengths of the meridians on the grid are equal to the lengths of the meridians in nature, of course, with a reduction to the scale of the map. But the lengths of the parallels in this projection are distorted. On the grid, the segments of the parallels between two adjacent meridians remain constant at any latitude, while in nature they decrease as they approach the poles.

The expression "length distortion" means that the lengths are transmitted on the same map with different reductions, i.e., at different scales in different places on the map. In other words, the scale on the same map is not a constant value; it can change not only at different points, but even at one point in different directions.

The scale that is signed on the map is called the main one, it determines the ratio of the lengths on the map to the corresponding lengths in kind only in some parts of the map defined for each projection. The scales in its other parts are larger or smaller than the main one and are called private.

Such a projection, which would transmit without distortion any length in any direction, is impossible, since it would preserve the similarity and proportionality of all parts of the earth's surface, which can only take place on a globe.

Area distortions can be traced in the same figures. The surfaces of cells located between two adjacent parallels are in nature the same size, but they increase markedly to the east and west of the middle meridian. The surfaces of cells bounded by two meridians in nature decrease to the north and south of the equator; but they all have the same value.

However, there are numerous projections on which the dimensions of the surfaces are transmitted without distortion, all areas on such maps are proportional to the magnitudes of the corresponding surfaces in nature, although the similarity of the figures is violated. Such projections are called equal-area, equal-area, or equivalent.

Meridians and parallels, forming right angles between themselves in nature, remain perpendicular only along the middle meridian. Conversely, the cartographic grid is free of angle distortion. Such projections that preserve the magnitude of the angles are called conformal or conformal. Around each point of a conformal projection at infinitesimal distances, the scale can be considered constant.

There are many projections that are neither equal area nor equal angle (they are called arbitrary), but there is no one that combines both qualities.

___________
You can find the basic principles of diagnosis, prevention and treatment of such a serious joint disease as osteoarthritis (or arthrosis) on the site spina.net.ua, which is dedicated to diseases of the spine.

Since ancient times, a person has had a need to convey to other people information about where he was and what he saw. Today there are different kinds images of the earth's surface. All of them are small models of the world around us.

Cartography

Images of the earth's surface appeared earlier than writing. ancient man used mammoth tusk, stone or wood for the first sketches of the area. In the ancient world, images were made on papyrus and cloth, and later on parchment. The first mapmakers were real artists, and the maps were works of art. Ancient maps resemble fabulous paintings depicting unknown countries and their inhabitants. In the Middle Ages, paper and the printing press appeared, which made it possible to mass-produce maps. The creators of the maps collected information about the Earth from the words of numerous travelers. The contents of the cards became more and more diverse. The science of maps as a special way of depicting the earth's surface, their creation and use is called cartography.

Globe - a model of the Earth

The ancient Greeks proved for the first time that the Earth is spherical. To correctly display the shape of the Earth, a globe was invented. Globe (from the Latin word globe - ball) is a three-dimensional model of the planet, reduced by many millions of times. There is no surface distortion, so with its help they get a correct idea of ​​the location of the continents, seas, oceans, islands. But the globe is much smaller than the Earth, and it is impossible to show any area in detail on it. It is also inconvenient to use while traveling.

Plan and map

A plan is a drawing on which a small area of ​​the terrain is depicted in detail in a reduced form with conventional signs, so there is no need to take into account the curvature of the earth's surface.

A map is a generalized reduced image of the earth's surface on a plane using the system.

Geographic Maps have important properties. In contrast to the plans, they depict different areas but in coverage - from small areas of the earth's surface to the continents, oceans and the globe as a whole. When displaying the convex surface of the Earth on a flat sheet of paper, distortions inevitably occur in the image of its individual parts. Nevertheless, maps allow you to measure distances and determine the size of objects. They contain information about the properties of objects. For example, about the height of the mountains and the depth of the seas, the composition of the flora and fauna.

Atlases - collections of maps

An important step in the development of geographical images was the creation of atlases of map collections. These are real cartographic encyclopedias. It is believed that the first collection of maps appeared in the Roman Empire. Later, in the 16th century, the very concept of "atlas" was introduced. Geographical atlases are very diverse in terms of territorial coverage: world atlases, atlases
individual countries, regions and cities. According to their purpose, atlases are divided into educational, local history, road and others.

aerospace images

Progress in aviation and astronautics allowed man to photograph the Earth. Aerial photographs and space photographs provide a detailed image of all the details of the terrain. But the geographical objects on them have an unusual look for us. Recognition of images in pictures is called decoding.

Today, we increasingly use maps on a computer monitor or screen. mobile phone. They are created on the basis of space images using special computer programs.