Geographical Information System

Spatial data model

A spatial data model is a way of representing real-world geographic features digitally so they can be stored, analysed and displayed in a GIS. The two main models are vector and raster.

Vector data model

Features are represented by discrete geometric objects defined by coordinates:

• Points – single (x, y) locations, e.g. wells, schools, towns.
• Lines (arcs) – ordered series of points, e.g. roads, rivers.
• Polygons – closed areas bounded by lines, e.g. land parcels, districts, lakes.

Attributes are linked to each feature in tables. Advantages: precise boundaries, compact storage, good topology, high quality map output. Disadvantages: complex data structure and slower overlay for continuous surfaces.

Applications: cadastral and land-ownership mapping, road and utility networks, administrative boundaries, route analysis.

Raster data model

The area is divided into a regular grid of cells (pixels); each cell holds a value for the phenomenon at that location. Resolution depends on cell size. Advantages: simple structure, fast overlay and map algebra, suits continuous data and satellite images. Disadvantages: large files, less precise boundaries, blocky appearance.

Applications: satellite imagery and aerial photographs, elevation models (DEM), land cover, temperature and rainfall surfaces, suitability analysis.

GIS (Geographic Information System) is a computer-based system for capturing, storing, managing, analysing and displaying spatially referenced (geographic) data together with attribute data. It answers questions about where things are and how they are related.

Components of GIS

1. Hardware – the computers (desktops, servers), input devices (digitizers, scanners, GPS), output devices (plotters, printers) and storage on which GIS runs.
2. Software – GIS programs providing tools to input, store, manipulate, analyse and display geographic data, plus the DBMS and a user interface (e.g. ArcGIS, QGIS).
3. Data – the most important component, consisting of spatial data (vector and raster) and attribute (tabular) data, collected in-house or obtained from sources.
4. People – the users and managers who design, operate and interpret GIS: GIS specialists, analysts, database administrators and decision makers.
5. Methods (procedures) – the well-designed plan and business rules, standards and analysis procedures under which the GIS operates.

A successful GIS needs all five components working together.

Remote sensing is the science and technology of acquiring information about the Earth's surface or objects without direct physical contact, by recording reflected or emitted electromagnetic radiation using sensors on platforms such as satellites, aircraft or drones.

Components of remote sensing

1. Energy source or illumination (A) – provides electromagnetic energy to the target; the sun (passive) or the sensor itself (active, e.g. radar, LiDAR).
2. Radiation and the atmosphere (B) – energy passes through the atmosphere on its way to and from the target, and is affected by scattering and absorption.
3. Interaction with the target (C) – the energy is absorbed, transmitted or reflected, depending on the target's properties, producing a spectral signature.
4. Recording of energy by the sensor (D) – the sensor on a platform collects and records the radiation.
5. Transmission, reception and processing (E) – data are sent to a ground receiving station, and processed into images.
6. Interpretation and analysis (F) – the image is interpreted visually or digitally to extract information.
7. Application (G) – the information is used to solve a problem, e.g. land use mapping, flood monitoring, forestry, and urban planning.

The platform (satellite, aircraft, drone) and the sensor type (optical, thermal, microwave) are also key parts of the system.

The figure is not reproduced here, so the method is given along with the coding rule.

Quadtree

A quadtree recursively divides the square study area into four quadrants until each cell is either wholly inside or wholly outside the feature (or a minimum cell size is reached). Quadrants are numbered in a fixed order, normally 0 = NW, 1 = NE, 2 = SW, 3 = SE.

Steps

1. Divide the whole grid into four quadrants (level 1).
2. A quadrant fully covered by the feature is shaded and not divided further; one with no feature is left empty; a mixed quadrant is divided again.
3. Repeat until all cells are homogeneous or the finest resolution is reached.
4. The tree has the root at the top, each internal node has four children, and leaves are shaded or empty.

Spatial index code

Each shaded leaf gets a code made by concatenating the quadrant numbers from the root to that leaf. For example, a leaf in the SE quadrant (3), then its NW sub-quadrant (0), then its NE sub-quadrant (1) has the code $301$. The shaded feature is indexed by the list of such codes of all its leaf cells, for example 0, 12, 13, 301. Larger shaded leaves have shorter codes.

This gives an efficient spatial index because a query for a location needs only to follow the path of digits down the tree.

Model Builder is a visual programming environment (in ArcGIS) in which geoprocessing workflows are built as diagrams. A model is a sequence of processes (tools) linked together, where the output of one becomes the input of the next. Elements are input data (blue ovals), tools (yellow rectangles) and output data (green ovals).

Example: finding suitable sites for a new school

1. Input: roads, rivers, land use and population layers.
2. Buffer roads (500 m) and rivers (200 m).
3. Select land use = barren/vacant.
4. Erase the river buffer from the area, then Intersect with road buffer and vacant land.
5. Output: a polygon layer of candidate sites.

Uses in GIS applications

• Automates repetitive tasks and saves time.
• Documents the workflow so it can be reproduced and shared.
• Allows parameters to be changed to run what-if scenarios (e.g. a buffer distance).
• Allows batch processing and building new tools without programming.
• Used in suitability analysis, hydrological modelling, environmental impact assessment and urban planning.

GIS programs may be open source (free to use, with source code available for modification) or commercial (proprietary software sold under licence).

Open-source GIS suits low-budget organizations, education and developing countries such as Nepal, while commercial products suit large enterprises needing guaranteed support and complete solutions.

A shapefile is a popular vector data format developed by Esri for storing geometry and attributes. It consists of at least three files: .shp (geometry), .shx (index) and .dbf (attributes).

Main advantages

1. Widely supported – readable by almost all GIS software, so it is a standard for data exchange.
2. Simple structure – easy to understand, create and manage.
3. Fast display and processing of features because the data structure is simple and compact.
4. Stores attributes in dBASE format, which can be edited in spreadsheet and database tools.
5. Supports points, lines and polygons (and multipart features).
6. Easy sharing and copying since files are small and independent of any database server.
7. Good for editing and easy to convert to other formats.
8. Free and open specification, with large amounts of free data available as shapefiles.

(a) Spatial interpolation

Spatial interpolation estimates unknown values at unsampled locations from known values at sample points, based on the principle that nearby places are more alike than distant ones (Tobler's first law). It is used to create continuous surfaces such as elevation, rainfall or temperature from point measurements.

Methods include:

• Nearest neighbour (Thiessen polygons)
• Inverse Distance Weighting (IDW) – the estimate is a weighted average where weights fall with distance: $\hat{z}=\dfrac{\sum z_i/d_i^p}{\sum 1/d_i^p}$
• Spline and Trend surface
• Kriging – geostatistical method using a semivariogram.

(b) Map scale vs scale factor

Map scale is the ratio of a distance on the map to the corresponding distance on the ground, e.g. $1:50{,}000$ means 1 cm on the map equals 50,000 cm (500 m) on the ground. It is a property of the whole printed or displayed map and is shown as representative fraction, verbal or graphic scale.

Scale factor is the ratio of the distance on the projection (map) to the distance on the reference globe, at a particular point or along a line, because map projections distort distance. It is 1 where the projection is true to scale (e.g. along a standard line) and differs from 1 elsewhere, e.g. 0.9996 for the central meridian of UTM. Thus map scale is the nominal reduction ratio, while scale factor measures local distortion in the projection.

Topology is the mathematical study of the spatial relationships (connectivity, adjacency and containment) between geographic features that remain unchanged when the features are stretched or deformed. In GIS, topology is stored explicitly as part of the data model, so that arcs, nodes and polygons know their neighbours.

Elements

• Connectivity – arcs connect at nodes.
• Area definition – polygons are bounded by a set of arcs.
• Contiguity – each arc has a left and a right polygon, so adjacency is known.

Importance in GIS

1. Data validation and quality control – detects errors such as gaps, overlaps, dangles, undershoots and overshoots in digitizing.
2. Spatial analysis without coordinates – supports network analysis (shortest path, routing), adjacency queries and overlay.
3. Efficient processing – operations like dissolve and polygon building are faster.
4. Ensures data integrity – shared boundaries are stored once, so edits keep adjacent polygons consistent.
5. Enables complex queries such as "which parcels are adjacent to this lake?".

A buffer zone is a polygon created around a point, line or area feature that contains all locations within a specified distance of that feature. It is a proximity analysis tool, e.g. a 100 m buffer around a river for flood-risk or protection zones.

Three variations of buffering

1. Variable (distance by attribute) buffers – the buffer width differs per feature according to an attribute value, e.g. wider buffers around larger rivers or higher-order roads.
2. Multiple ring buffers – several concentric buffers at different distances around the same feature (e.g. 100 m, 200 m, 500 m around a hazardous facility) to show graded zones.
3. Single-sided or non-dissolved/dissolved buffers – buffers can be drawn on one side only of a line (for example only the riverbank side), and buffers that overlap can be merged (dissolved) into one polygon or kept separate. Rounded or flat line ends are also options.

Other variations include buffers around donut shapes (inside/outside a polygon) and buffers that account for travel cost rather than straight distance.

Focal raster operations are neighbourhood operations in which the output value of each cell is computed from the values of that cell and its surrounding neighbours within a defined moving window (e.g. $3\times3$ or circular), which moves across the entire raster.

Common focal statistics: mean, sum, minimum, maximum, range, majority, variety, median. Focal operations also include slope and aspect, filtering and smoothing.

Example

Take a $3\times3$ window with the cell values $\begin{matrix}2&4&6\\3&5&7\\1&8&9\end{matrix}$ For the centre cell, the focal mean is $(2+4+6+3+5+7+1+8+9)/9 = 45/9 = 5$ and the focal maximum is 9. The output cell takes this value, then the window moves one cell and repeats.

Uses: smoothing noisy images (low-pass filter), edge enhancement, finding the highest elevation in a neighbourhood, computing slope from a DEM, and density calculations.

Overlay is a GIS operation that combines two or more spatial layers to produce a new layer whose features and attributes come from the inputs, based on their spatial location. Vector overlay types include Union, Intersect, Identity, Erase and Symmetrical Difference.

Union operation

Union combines the geometry and attributes of both input polygon layers. The output contains all areas from both layers, including areas that appear in only one of them, and areas where they overlap are split into new polygons carrying attributes of both. Where only one layer is present, the other layer's attribute fields are empty.

Example: Union of a soil layer and a land-use layer gives polygons for every combination of soil type and land use, plus the parts that are only soil or only land use.

Formally it is the Boolean OR: $A\cup B$. Both inputs must be polygon layers. It is used for suitability studies and combining administrative and environmental zones, but it can create many small sliver polygons that must be cleaned.