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  • Maps are used as the languages of simple geography. Importance of map making is recognised long¬†ago. Surveyors went round the land and prepared maps. Data required for locating and calculating¬†extent of a place/region is called spatial data.

    Physical properties and human activities related to a place/region are stored in the form of tables,  charts and texts. This information is called attribute data.
    Referring to maps/plans and then to attribute data stored in hard copies like books is time consuming updating and managing the data is difficult.
    This problem is overcome by combining spatial data and attribute data of the location by appropriate data base management in computers. The location information (spatial data) is digitised from available maps and stored in computers. For this data structure used is either raster data or vector  pickcells are associated with the spatial information, while in vector data structure coordinates are associated with each region and sub-regions. Over the spatial data attribute data is overlayed and stored. Once this geographical information system is developed, the user can access the attribute data of any place by clicking over the spatial data of that place. The user can utilise the information for further analysis, planning or for the management. For example, if land records of a village is developed as GIS data, the user can click the state map to pick up the district map and then access taluka map. Then he will access it to pick up the village map. Then land record of that village can
    be obtained and property map of any owner can be checked and printed. All this can be achieved in a very short time from any convenient place.
    Remote sensing and GIS go hand in hand, since lot of data for GIS is from remote sensing.
    Remote sensing needs GIS for data analysis. Some of the areas of GIS application are:
    1. drainage systems 2. streams and river basins management
    3. lakes 4. canals
    5. roads 6. railways
    7. land records 8. layout of residential areas
    9. location of market, industrial, cultural and other utilities
    10. land use of different crops etc.
    The above information helps in planning infrastructural development activities such as planning roads, rail routes, dams, canals, tunnels, etc. It helps in taking steps to check hazards of soil erosion and environmental pollution. Monitoring of crop pattern and condition helps in taking necessary action to the challenges in future.


  • Remote sensing may be defined as art and science of collecting informations about objects, area or
    phenomenon without having physical contact with it. Eye sight and photographs are common examples
    of remote sensing in which sunlight or artificial light energy from electricity is made to strike the object.
    Light energy consists of electromagnetic waves of all length and intensity. When electromagnetic wave
    falls on the object, it is partly
    1. absorbed 2. scattered
    3. transmitted 4. reflected.
    Different objects have different properties of absorbing, scattering, transmitting and reflecting the energy. By capturing reflected waves with sensors, it is possible to identify the objects. However this remote sensing has its own limitations in terms of distance and coverage of area at a time.
    Photographic survey, in which photographs taken from aircrafts are used for map making, fall under this category of remote sensing. Using electronic equipments, this basic remote sensing technique is extended to identifying and quantifying various objects on the earth by observing them from longer distances from the space. For this purpose, geostationary satellites are launched in the space, which rotate around the earth at the same speed as earth. Hence the relative velocity is zero and they appear stationary when observed from any point on the earth. Depending upon the property of the object, the electromagnetic waves sent from the satellite reflected energy is different. The reflected waves in the bandwidth of infrared, thermal infrared and micro waves are picked up by sensors mounted on satellite.
    Since each feature on the earth has different reflection property, it is possible to identify the features on

    the earth with satellite pictures. Data obtained from satellites are transferred to ground stations through
    RADARS where user analyses to find out the type of object and the extent of it. This is called image
    processing. For quantifying the objects computers are used. India is having its own remote sensing
    satellites like IRS-series, INSAT series and PSLV series.

    Application of Remote Sensing
    Various applications of remote sensing may be grouped into the following:
    1. Resource exploration 2. Environmental study
    3. Land use 4. Site investigation
    5. Archaeological investigation and 6. Natural hazards study.
    1. Resource Exploration: Geologists use remote sensing to study the formation of sedimentary rocks and identify deposits of various minerals, detect oil fields and identify underground storage of water. Remote sensing is used for identifying potential fishing zone, coral reef  mapping and to find other wealth from ocean.

    2. Environmental Study: Remote sensing is used to study cloud motion and predict rains. With satellite data it is possible to study water discharge from various industries to find out dispersion and harmful effects, if any, on living animals. Oil spillage and oil slicks can be studied using remote sensing.

    3. Land Use: By remote sensing, mapping of larger areas is possible in short time. Forest area, agricultural area, residential and industrial area can be measured regularly and monitored. It is possible to find out areas of different crops.

    4. Site Investigation: Remote sensing is used extensively in site investigations for dams, bridges, pipelines. It can be used to locate construction materials like sand and gravel for the new projects.

    5. Archaeological Investigation: Many structures of old era are now buried under the ground and are not known. But by studying changes in moisture content and other characteristics of the buried objects and upper new layer, remote sensors are able to recognise the buried structutures of archaeological importance.

    6. Natural Hazard Study: Using remote sensing the following natural hazards can be predicted to some extent and hazards minimised:
    1. Earthquake 2. Volcanoes
    3. Landslides 4. Floods and
    5. Hurricane and cyclones.

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  • The following three methods are available for computation of volumes:
    (i) From cross-sections (ii) From spot levels and
    (iii) From contours.
    First method is useful for computing earth work involved in road/rail/canal/sewage works. Second method is useful for finding earth work in foundations of large building and the last method is useful for finding capacity of reservoirs.

    Computation of Volume from Cross-sections
    To compute earth work, profile levelling is carried out along the centre line of the alignment of the project and cross-sectional levels are taken at regular intervals. Then the volume of earth work can be found, if the cross-sections are determined.
    First the calculation of cross-sectional area is discussed.
    (a) If section is level (Fig. 18.9)

    Let ‚Äėh‚Äô be the depth at the centre line of the alignment and 1 : n be the side slopes. Then

    w = b + 2nh
    ‚ąī A =¬†1 /2¬†(w + b) h
    = 1 / 2 (b + 2nh + b) h
    = (b + nh) h


    (b) If it is a multilevel section [Fig. 18.10]

    Let the coordinates of points be (x1, y1), (x2, y2), …, (xn, yn), then arrange the coordinates in the following order

    Then area of the figure
    =¬†1 /2¬†[ ő£ Product of pair of coordinates connected by continuous lines ‚Äď ő£ Product of coordinates¬†connected by dotted lines] ‚Ķ(18.9)
    The above formula can be easily proved by taking a simple example of a quadrilateral [Ref. Fig.
    18.11]. Let the coordinates of A, B, C and D be (x1, y1), (x2, y2), (x3, y3) and (x4, y4). Then area of ABCD¬†= Area of a AB b + Area of b BC c + Area of c CD d ‚Äď Area of a AD d.

    =¬†1 /¬†2¬†(x1+ x2) (y2 ‚Äď y1) +¬†1 /¬†2¬†(x2 + x3) (y3 ‚Äď y2) +¬†1 /¬†2¬†(x3 + x4) (y4 ‚Äď y3) ‚Äst1 /¬†2¬†(x1 + x4) (y4 ‚Äď y1)

    Calculation of Volumes
    Once cross-sectional areas at various sections are known volume can be found from trapezoidal or prismoidal rule as given below:
    Trapezoidal Rule

    Prismoidal Rule

    Computation of Earth Work from Spot Levels
    This method is used to calculate volume of earth work for the elevations of basements, large tanks and borrow pits. In this method the whole area is divided into a number of rectangles or triangles (Fig. 18.13).
    The levels are taken at corner points before and also after excavation. The depth of excavation at each corner point is measured. Then for each simple figure (rectangle or triangle).

    It may be noted that in Fig. 18.13 (a), in total volume calculations depth of some corners appear once, some twice, some of them 3 times and some 4 times. If
    ő£h1 = some of depths used once
    ő£h2 = sum of depths used twice
    ő£h3 = sum of depths used thrice
    ő£h4 = sum of depths used four times.

    Computation of Volume from Contours
    Figure 18.15 shows a dam with full water level of 100 m and contours on upstream side. Capacity of reservoir to be found is nothing but volume of fill with water level at 100 m. The whole area lying within a contour line is found by planimeter. It may be noted that area to be measured is not between two consecutive contour lines.

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  • If map of an area is available its area can be found by the following methods:
    (i) Approximate methods (ii) Using planimeter.

    Approximate Methods
    The following three approximate methods are available for calculating area from the map:
    (a) Give and take method (b) Subdivisions into squares
    (c) Subdivisions into rectangles.
    (a) Give and take method: In this method irregular boundary is approximated with straight
    lines such that area taken in is equal to the area given out. Accuracy depends upon the judging capacity of the engineer. Then the area with straight edges is divided into a set of simple figures, like triangles and trapezoids and the area of map is found using standard expressions.
    Figure 18.5 shows such a scheme.


    (b) Subdivisions into squares: Similar to a graph sheet, squares are marked on a transparent tracing sheet, each square representing a known area. Full squares are counted. Fractional squares are counted by give and take approximation. Then the number of squares multiplied by area of each square gives the area of the map Fig. 18.6 shows such a scheme. Finer the mesh better is the accuracy.

    (c) Subdivisions into rectangles: In this method, a set of parallel lines are drawn at equal spacing on a transparent paper. Then that sheet is placed over the map and slightly rotated till two parallel lines touch the edges of the tap. Then equalising perpendiculars are drawn between the consecutive parallel line. Thus given area is converted to equivalent set of rectangles and then area is calculated (Ref. Fig. 18.7).

    Computing Area Using Planimeter
    Planimeter is a mechanical instrument used for measuring area of plan. The commonly used planimeter is known as Amsler planimeter (Fig. 18.8). Its construction and uses are explained in this article.

    The essential parts of a planimeter are:
    1. Anchor: It is a heavy block with a fine anchor pin at its base. It is used to anchor the instrument at a desired point on the plan.
    2. Anchor arm: It is a bar with one end attached to anchor block and the other connected to an integrating unit. Its arm length is generally fixed but some planimeters are provided with variable arms length also.
    3. Tracing arm: It is a bar carrying a tracer point at one end connected to the integrating unit at the other end. The anchor arm and tracer arms are connected by a hinge. The length of this arm can be varied by means of fixed screw and slow motion screw.
    4. Tracing point: This is a needle point connected to the end of tracer arm, which is to be
    moved over the out line of the area to be measured.
    5. Integrating unit: It consists of a hard steel roller and a disc. The axis of roller coincides with the axis of tracer arm hence it rolls only at right angles to the tracer arm. The roller carries a concentric drum which has 100 divisions and is provided with a vernier to read tenth of roller division. A suitable gear system moves a pointer on disc by one division for every one revolution of the roller. Since the disc is provided with 10 such equal divisions, the reading on the integrating unit has four digits:
    (i) Unit read on the disc
    (ii) Tenth and hundredth of a unit read on the roller
    (iii) Thousandth read on the vernier.
    Thus if reading on disc is 2, reading on roller is 42 and vernier reads 6, then the total reading F = 2.426

    Method of Using Planimeter
    To find the area of a plan, anchor point may be placed either outside the plan or inside the plan. It is placed outside the plan, if the plan area is small. Then on the boundary of the plan a point is marked and tracer is set on it. The planimeter reading is taken. After this tracer is carefully moved over the outline of the plan in clockwise direction till the first point is reached. Then the reading is noted. Now the area of the plan may be found as

    Area = M (F ‚Äď I + 10 N + C)

    where M = A multiplying constant
    F = Final reading
    I = Initial reading.

    N = The number of completed revolutions of disc. Plus sign to be used if the zero mark of the dial passes index mark in clockwise direction and minus sign if it passes in anticlockwise direction.
    C = Constant of the instrument, which when multiplied with M, gives the area of zero circle.
    The constant C is added only when the anchor point is inside the area.
    Multiplying constant M is equal to the area of the plan (map) per revolution of the roller i.e., area
    corresponding to one division of disc.
    Multiplying constant M and C are normally written on the planimeter. The user can verify these values by
    (i) Measuring a known area (like that of a rectangle) keeping anchor point outside the area
    (ii) Again measuring a known area by keeping anchor point inside a known area.
    The method is explained with example.
    The proof of equation 18.7 is considered as beyond the scope of this book. Interested readers can see the book on surveying and levelling.


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  • If the area is bound by straight edges, it can be subdivided in a set of convenient figures and area¬†calculated. But in most of the cases the boundary may have irregular shape. In such cases major area is¬†subdivided into regular shape and area is found. The smaller area near the boundary is found from¬†taking offset from a survey line [Ref. Fig. 18.1].

    Computation of Areas of Regular Figures
    The following expressions for calculating areas may be noted:

    Areas of Irregular Shapes
    For this purpose from a survey line offsets are taken at regular intervals and area is calculated from any one of the following methods:
    (a) Area by Trapezoidal rule
    (b) Area by Simpson’s rule.
    (a) Area by Trapezoidal Rule:
    If there are ‚Äėn + 1‚Äô ordinates at n equal distances ‚Äėd‚Äô, then total length of line is L = nd, Area of¬†each segment is calculated treating it as a trapezium. Referring to Fig. 18.2,

    Area by Simpson’s Rule

    In this method, the boundary line between two segment is assumed parabolic. Figure 18.3 shows the first two segments of Fig. 18.2, in which boundary between the ordinates is assumed parabolic.
    ‚ąī Area of the first two segments
    = Area of trapezium ACFD + Area of parabola DEFH

    It is to be noted that the equation 18.6 is applicable if the number of segments (n) are even, in other words, if total number of ordinates’s are odd.

    If n is odd, then for n ‚Äď 1 segments area is calculated by Simpson‚Äôs rule and for the last segment¬†trapezoidal rule is applied.
    Trapezoidal rule gives better results if the boundary is not irregular to great extent. Simpson’s rule should be used if the boundary is highly irregular. This rule gives slightly more value compared to trapezoidal rule, if the curve is concave towards the survey line and gives lesser value, if the boundary is convex towards survey line.
    In both methods accuracy can be improved if the number of segments are increased.

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