Geographic Information System

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This section defines a GIS and its components, traces its historical development, and covers georeferencing, common data formats, the elements of data quality, and topology and spatial relationships.

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Definition and Functions A Geographic Information System is an organised system of hardware, software, data, people and procedures for the capture, storage, management, retrieval, analysis, modelling and display of spatially referenced data about the Earth.

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Its defining ability is to relate different layers of information by location and to answer questions that a non-spatial database cannot.

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Question the GIS answers Function used Location — what is at this place? Identify / query by pointing Condition — where does this condition occur? Attribute query and selection Trend — what has changed since…? Change detection, temporal overlay Pattern — what spatial pattern exists? Spatial statistics, clustering Routing — what is the best way? Network analysis Modelling — what if…? Suitability modelling, simulation Components of a GIS Component Content and remarks Hardware Computers, servers, storage, GNSS receivers, scanners, digitisers, plotters, mobile devices Software GIS engine with data input, storage (DBMS), analysis and display modules — ArcGIS, QGIS, GRASS, MapInfo, ERDAS Data Spatial (geometry) + attribute (thematic) + metadata; the costliest and most enduring component, typically 60–80 % of total project cost People GIS managers, analysts, database administrators, operators and end users — the component that decides success Methods / procedures The plans, standards, workflows and business rules under which the system is operated Historical Development • Roots:

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John Snow's 1854 cholera map of London — mapping as spatial analysis; overlay of transparent thematic sheets in landscape planning (Ian McHarg, Design with Nature, 1969). • 1960s — the Canada Geographic Information System (CGIS), developed by Roger Tomlinson ("the father of GIS") for the Canada Land Inventory, is regarded as the first true GIS; the Harvard Laboratory for Computer Graphics produced SYMAP, GRID and ODYSSEY. • 1970s–80s — commercialisation:

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ESRI (ARC/INFO, 1982) introduced the georelational model, Intergraph and MapInfo followed; the US Census DIME files and later TIGER established topological data structures. • 1990s — desktop GIS on the PC, the rise of remote sensing integration, and the Open GIS Consortium (1994, now OGC) for interoperability. • 2000s onward — internet and web GIS, Google Earth/Maps (2005), spatial databases (PostGIS), open-source GIS (QGIS, GRASS), mobile and volunteered geographic information (OpenStreetMap), and today cloud GIS, big geospatial data and geospatial AI. • Nepal — the Survey Department began digital mapping and the national topographic base (1:25,000 and 1:50,000) in the 1990s;

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GIS is now used in cadastre, municipal planning, forestry, disaster management and infrastructure.

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Georeferencing • Georeferencing is the process of establishing the relationship between image or map coordinates (row/column, digitiser units) and a real-world coordinate system, so that data from different sources overlay correctly. • Systems of geographic reference: geographic coordinates (latitude, longitude, height on an ellipsoid), projected coordinates (easting, northing — in Nepal the Modified UTM (MUTM) zones on Everest 1830 and UTM/WGS84), grid references (MGRS), linear referencing (chainage along a route), and indirect references (postal codes, ward numbers, place names resolved by geocoding). • Practical georeferencing of a scanned map or image uses ground control points and a polynomial (or spline/rubber-sheet) transformation, with quality judged by the RMSE of the residuals at the control points — see 8.3 for the transformation types. • Every GIS layer must carry its CRS/SRID; mixing layers with different datums without transformation produces systematic shifts (a classic exam trap:

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Everest 1830 vs WGS84 differ by hundreds of metres in Nepal).

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Data Formats Type Common formats Vector ESRI shapefile (.shp/.shx/.dbf/.prj), geodatabase (file/enterprise), GeoPackage (.gpkg, OGC), GeoJSON, KML/KMZ, GML, DXF/DWG, TopoJSON Raster GeoTIFF (and Cloud-Optimised GeoTIFF), IMG (ERDAS), NetCDF/HDF, JPEG2000, ASCII grid, GRID (ESRI), BIL/BIP/BSQ Database / web PostGIS, Oracle Spatial, SpatiaLite;

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WMS, WFS, WCS, WMTS and tile services (see 8.6) Point cloud / survey LAS/LAZ (lidar), E57, CSV of coordinates, RINEX for GNSS observations • Shapefile limitations worth remembering: multi-file, 2 GB size limit, 10-character field names, no topology, no true null values and one geometry type per file — hence the OGC GeoPackage (a single SQLite file) is the modern open alternative. • Raster storage may be BIL (band interleaved by line), BIP (by pixel) or BSQ (band sequential); compression may be lossless (LZW, DEFLATE, run-length encoding) or lossy (JPEG).

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Data Quality Element (ISO 19157) Meaning Positional accuracy Closeness of coordinates to true position — absolute and relative; reported as RMSE or CE90/LE90 Attribute (thematic) accuracy Correctness of the non-spatial values; for classifications, the confusion matrix and kappa Completeness Omission (missing features) and commission (extra features) Logical consistency Conformity to rules — topological, domain, format and conceptual consistency Temporal accuracy / currency Correctness of time attributes and how up to date the data are Lineage The source, processing history and custodians of the data (part of metadata, not strictly a quality element) Usability / fitness for purpose Whether the data meet the requirements of the intended application • Sources of error: source data (survey, digitising, classification), processing (transformation, generalisation, overlay sliver polygons, rasterisation), and use (wrong scale, wrong interpretation).

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Errors propagate and accumulate through each analytical step. • Accuracy vs precision: accuracy = closeness to the true value; precision = repeatability and the number of digits recorded.

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Data may be precise but inaccurate.

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Resolution and scale limit the detail: the minimum mapping unit and the rule that a 0.25 mm line at 1:25,000 is about 6 m on the ground.

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Topology and Spatial Relationships • Topology is the set of spatial properties that remain unchanged under continuous deformation (stretching, bending) of the map — it does not depend on coordinates or distance.

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The three classic topological properties are connectivity (arcs meet at nodes), adjacency/contiguity (polygons share an edge — left and right polygon of each arc) and containment/area definition (a polygon is bounded by a set of arcs). • Benefits: data validation (no undershoots, overshoots, dangles, slivers or unclosed polygons), efficient storage of shared boundaries, and support for network tracing, adjacency and polygon overlay.

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Cost: topology must be built and rebuilt after editing, and simple formats such as the shapefile are non-topological (spaghetti). • Topological errors to name: dangle (a line end not connected), undershoot and overshoot, sliver polygon, gap and overlap between polygons, duplicate geometry, and unclosed polygon; cleaning uses a tolerance (snapping/fuzzy tolerance). • Spatial relationships fall into: topological (touches, crosses, within, contains, overlaps, disjoint, equals — the eight/nine Egenhofer relations formalised by the DE-9IM matrix), metric/distance (near, within 500 m, distance decay), and directional (north of, upstream of, left/right).

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This section covers where GIS data come from, metadata and standards, the vector and raster data models, the field-based and object-based views of geographic space, and the TIN and grid representations of a surface.

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Data Sources Category Examples Primary (directly captured) Ground survey (total station, level), GNSS, aerial photography and photogrammetry, satellite imagery, lidar, UAV, echo-sounding, field questionnaires and mobile data collection Secondary (derived from existing records) Digitising or scanning of existing maps, cadastral records, census and statistical tables, addresses/geocoding, toponym registers, existing digital datasets Volunteered / crowd-sourced OpenStreetMap, GPS traces, social-media geotags — cheap and current but variable in quality Web services WMS/WFS/WCS feeds, national geoportals, open-data platforms (see 8.6) • Data capture methods: manual digitising (tablet or on-screen head-up digitising over an image), scanning plus automatic vectorisation (raster-to-vector, needing editing), direct coordinate entry (COGO) from survey observations or a deed, photogrammetric stereo-compilation, and import/conversion of an existing dataset. • In Nepal the principal public sources are the Survey Department (topographic base maps, cadastral maps, control, the national geoportal), the Central Bureau of Statistics (census with ward boundaries), Department of Roads, Department of Hydrology and Meteorology, and the Forest Research and Training Centre.

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Metadata and Standards • Metadata are "data about data": what the dataset contains, who made it, when, how, at what accuracy, in what CRS, under what licence, and how to obtain it.

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Without metadata a dataset is unusable by anyone but its author. • The international standard is ISO 19115 (geographic information — metadata) with the XML encoding ISO 19139; for services, ISO 19119; for quality, ISO 19157.

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The older American standard is the FGDC CSDGM.

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Catalogues are searched through the OGC CSW (Catalogue Service for the Web). • Metadata are used at three levels: discovery (does a suitable dataset exist?), exploration (is it fit for my purpose?) and exploitation (how do I access and use it correctly?). • Other relevant standards: the OGC Simple Feature Access (geometry), GML (transfer), GeoPackage (container), and the ISO 19100 series generally.

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Field-Based and Object-Based Views Field (continuous) view Object (discrete) view Concept Every location has a value of some variable Space is empty and populated by discrete entities Examples Elevation, temperature, rainfall, soil pH, pollution Parcels, buildings, roads, wells, administrative units Usual model Raster / grid (also TIN, contours, point samples) Vector (points, lines, polygons) Boundaries Gradual, fuzzy Crisp, well defined Typical question What is the value here? Where is this object and what are its attributes? The Vector Data Model • Geographic features are represented by points (0-dimensional), lines/polylines (1-D) and polygons (2-D) defined by coordinate pairs, plus optional multi- forms and 3-D surfaces/solids.

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Each feature is linked to a row of attributes by a feature ID. • Structures: spaghetti (independent, non-topological — shapefile, GeoJSON) and topological arc-node (arcs with from- and to-nodes, left and right polygons — coverage, PostGIS topology).

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The georelational model holds geometry in files and attributes in tables; the modern object-relational model holds both in the database (see Chapter 7). • Strengths: compact storage, precise geometry and boundaries, good cartographic output, explicit topology and network analysis, attributes easily handled.

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Weaknesses: complex data structure, overlay and buffering are computationally heavy, poor for continuous phenomena, and simulation/image integration is awkward.

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The Raster Data Model • Space is divided into a regular grid (tessellation) of cells (pixels), each holding one value.

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The grid is defined by the origin, cell size (resolution), number of rows and columns, CRS and NoData value.

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Resolution and file size trade off against each other: halving the cell size multiplies the number of cells by four. • Values may be nominal/categorical (land cover class) or continuous (elevation, reflectance).

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One layer holds one theme; multi-band rasters hold several (e.g. spectral bands). • Compression / storage: run-length encoding, chain codes, block codes, and the quadtree (recursive subdivision into four quadrants until each block is homogeneous) — efficient for large homogeneous areas. • Strengths: simple structure, easy and fast map algebra and overlay, natural for imagery, remote sensing and surface modelling, and well suited to simulation.

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Weaknesses: large storage, boundaries appear stepped (the staircase/jagged effect), loss of detail below cell size, mixed pixels, topology and network analysis are difficult, and results depend on the cell size chosen. • Conversion: vectorisation (raster to vector) needs thinning, line-following and smoothing; rasterisation (vector to raster) assigns cells by a rule such as cell-centre or maximum-area, and always loses some positional detail.

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TIN and Grid Grid (raster DEM) TIN Structure Regular square cells with one elevation each Irregular network of non-overlapping triangles from sample points Sampling Uniform, regardless of relief Adaptive — dense where relief is complex, sparse where flat Storage Implicit position; large for a fine cell size Explicit coordinates and topology; efficient for variable terrain Breaklines Cannot be enforced directly Enforced as triangle edges — ridges, streams, road edges Processing Simple, fast map algebra; standard for slope, aspect, hillshade More complex algorithms; exact within each facet Best for Regional analysis, integration with imagery Engineering surfaces, earthwork volumes, detailed sites • A TIN is normally built by Delaunay triangulation, which maximises the minimum angle of the triangles and so avoids long thin slivers; its dual is the Voronoi (Thiessen) diagram.

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The empty-circumcircle property is the standard definition: no sample point lies inside the circumcircle of any triangle. • Each TIN facet has a constant slope and aspect, computed from the plane through its three vertices; elevation inside a facet is obtained by linear interpolation.

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This section covers geometric transformation and resampling of layers, database query, overlay and network analysis, geospatial measurement, geovisualization with data-driven techniques, and the Styled Layer Descriptor.

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Geometric Transformation Transformation Parameters Preserves Conformal / similarity (4-parameter) 2 translations, 1 rotation, 1 uniform scale Shape and angles Affine (6-parameter, 1st-order polynomial) Translation, rotation, two scales, skew Straight lines and parallelism Projective (8-parameter) Affine plus two perspective terms Straight lines only 2nd / 3rd-order polynomial 12 / 20 coefficients Nothing — warps to fit; needs many well-spread GCPs Rubber sheeting / spline Local, piecewise Exact fit at control points • Minimum control points:

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2 for conformal, 3 for affine, 4 for projective, 6 for second-order and 10 for third-order; in practice use considerably more, well distributed, and judge the fit by the RMSE.

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A high-order polynomial with few points fits the control exactly but distorts badly between them. • Resampling assigns values to the new cells after transformation: nearest neighbour (fastest, keeps original values — the only choice for categorical data), bilinear (weighted mean of 4 cells, smoother), and cubic convolution (16 cells, sharpest-looking but alters values most).

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See 8.5 for their use in DEM resampling.

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Database Query • Attribute query selects records by their values using SQL and logical operators — SELECT * FROM parcel WHERE area > 500 AND land_use = 'residential'; the Boolean operators are AND, OR, NOT, XOR. • Spatial query selects features by their location or relation to other features: intersect, within, contains, within a distance of, completely contains, touches, crosses — implemented as the DE-9IM predicates of Chapter 7. • The two are combined in practice ("schools within flood-prone wards and with enrolment > 200"), and the selection may then be exported, summarised or used as the input to further analysis.

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Selection methods: new selection, add to, remove from, and select from the current selection.

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Overlay Analysis Vector operation Result Intersect Only the area common to both layers; attributes of both (logical AND) Union The full extent of both layers, split at every boundary; attributes of both, with nulls (logical OR) Identity Keeps the whole input layer, adding the attributes of the identity layer where they coincide Erase (difference) The part of the input outside the erase layer (logical NOT) Symmetrical difference The parts belonging to one layer only (XOR) Clip Cuts the input to the boundary of the clip layer; attributes of the input only Update / split / spatial join Replaces, divides or transfers attributes between layers by location • Overlay may be point-in-polygon, line-in-polygon or polygon-on-polygon; the last is the most demanding and the one that creates slivers along boundaries digitised twice. • Raster overlay is map algebra on coincident grids: local (cell by cell — arithmetic, Boolean, reclassification, weighted sum), focal (a neighbourhood window — mean, majority, the 3 × 3 filters of 8.4), zonal (statistics within zones of another layer) and global (distance, cost-distance, viewshed over the whole grid). • Suitability modelling reclassifies each criterion to a common scale, weights the layers (often by the Analytic Hierarchy Process) and sums them — the standard method for site selection, landslide susceptibility and land-capability mapping. • Buffering creates a zone of specified distance around features; it may be constant, variable (attribute-driven), multi-ring, or one-sided, and buffers of adjacent features are normally dissolved.

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Network Analysis • A network is a connected set of edges (links) and junctions (nodes) carrying impedance (length, travel time, cost), turn tables, one-way and restriction rules, and connectivity rules; correct topology is essential. • Standard problems: shortest/least-cost path (Dijkstra's algorithm, or A* with a heuristic), closest facility, service area / isochrone, origin-destination cost matrix, vehicle routing (travelling salesman), location-allocation, and tracing upstream/downstream in utility and river networks. • Applications: emergency response and ambulance routing, school and health-facility catchments, solid-waste collection routes, utility and pipeline management, and accessibility studies.

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Geospatial Measurement • Basic measures: distance (Euclidean on a projected plane, great-circle/geodesic on the ellipsoid, Manhattan, and network distance), length and perimeter, area (from the coordinates by the shoelace/trapezoidal rule), centroid, and direction/bearing. • Shape and pattern: compactness ratios, fragmentation and landscape metrics, density (simple and kernel density), nearest-neighbour index (R < 1 clustered, R = 1 random, R > 1 dispersed), quadrat analysis, and the spatial autocorrelation measures of Chapter 7 (Moran's I, Geary's C, Getis-Ord Gi*). • Caution: measurements must be made in a projected CRS suitable for the property being measured — an equal-area projection for areas, and never degrees for distances; results are also affected by the scale/generalisation of the data (the coastline paradox) and by the MAUP (modifiable areal unit problem) when data are aggregated into arbitrary zones.

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Geovisualization and Data-Driven Techniques • Geovisualization uses interactive, exploratory graphics to reveal patterns rather than merely to present a finished map — linked views (map, table, chart), brushing, dynamic classification, animation of time series, 3-D and virtual globes, and dashboards. • Thematic map types: choropleth (rates or densities in enumeration units — never raw counts), proportional/graduated symbol (totals), dot density, isarithmic/isopleth (contours of a continuous field), cartogram, flow map and heat (kernel density) map. • Data-driven styling means the symbol is computed from the attribute values: classification methods equal interval, quantile, natural breaks (Jenks), standard deviation, geometric interval and manual; the number of classes is usually 4-7; colour schemes are sequential (ordered data), diverging (deviation about a midpoint) and qualitative (categories), with ColorBrewer the standard reference. • The visual variables (Bertin) — position, size, shape, value (lightness), hue, orientation, texture — must match the level of measurement: size and value for ordinal/quantitative data, hue and shape for nominal data.

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Styled Layer Descriptor (SLD) • SLD is an OGC XML standard that describes how a map layer is to be symbolised, so that styling can be applied to a web service by the client rather than fixed on the server.

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It is used chiefly with WMS (and stored styles in GeoServer), and works together with Symbology Encoding (SE), which defines the symbolizers themselves. • Structure: a StyledLayerDescriptor contains NamedLayer/UserLayer → UserStyle → FeatureTypeStyle → Rule, and each Rule holds an optional Filter (OGC Filter Encoding) and/or scale denominators (MinScaleDenominator, MaxScaleDenominator) plus one or more symbolizers. • The symbolizers are PointSymbolizer, LineSymbolizer, PolygonSymbolizer, TextSymbolizer and RasterSymbolizer.

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Rules with filters give data-driven, class-based styling (for example a different fill for each land-use code), and scale denominators give scale-dependent rendering. • A WMS request can carry SLD= (a URL to an SLD document), SLD_BODY= (the XML inline) or STYLES= (a named style held on the server); the capabilities document advertises whether the server supports user-defined styles.

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This section covers the derivatives of a terrain surface computed from a DEM — slope, aspect and curvature — together with hillshade, viewshed, watershed delineation and surface intersection, their algorithms and applications.

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The 3 x 3 Moving Window Nearly all surface derivatives are computed by passing a 3 × 3 window over the grid and fitting a surface to the nine elevations.

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Labelling the cells a b c / d e f / g h i with cell size C, the standard third-order finite-difference (Horn) estimates of the partial derivatives at the centre cell e are: • dz/dx = [(c + 2f + i) − (a + 2d + g)] / (8C) — the rate of change in the x (east) direction • dz/dy = [(g + 2h + i) − (a + 2b + c)] / (8C) — the rate of change in the y (north) direction • Cells at the edge of the grid have no complete window, so a one-cell border of NoData appears in every derived surface.

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Slope • Slope is the maximum rate of change of elevation, the first derivative of the surface: tan(slope) = √[(dz/dx)² + (dz/dy)²], hence slope (degrees) = arctan √[(dz/dx)² + (dz/dy)²].

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It is expressed in degrees (0-90°) or as a percentage (rise/run × 100, unbounded); a 45° slope equals 100 %. • Slope is scale dependent: a coarser DEM smooths the terrain and systematically underestimates steep slopes.

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Algorithms differ (Horn's third-order, Zevenbergen-Thorne, simple maximum-drop among the 8 neighbours), and a TIN gives one constant slope per facet. • Applications: landslide and erosion susceptibility (with the USLE LS factor), road and canal alignment, terracing and land capability, building-site selection, avalanche and runoff modelling, and as a criterion layer in suitability models.

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Aspect • Aspect is the compass direction of the steepest downslope, measured clockwise from north, 0-360°, computed as aspect = arctan2(dz/dy, −dz/dx) converted to the compass convention.

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A perfectly flat cell has no aspect and is coded −1. • Because aspect is circular data, it must not be averaged arithmetically (the mean of 350° and 10° is 0°, not 180°); it is usually reclassified into the eight or sixteen compass sectors. • Applications: solar radiation and insolation modelling, snowmelt timing, vegetation and habitat distribution, siting of solar panels and orchards, and in Nepal's mountains the marked contrast between sunny south-facing slopes and shaded north-facing slopes.

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Surface Curvature • Curvature is the second derivative of the surface — the rate of change of slope.

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It is obtained by fitting a quadratic polynomial to the 3 × 3 window and is reported in units of 1/100 m. • Profile (vertical) curvature is measured in the direction of the steepest slope and controls acceleration and deceleration of flow: a negative value marks a convex, accelerating slope, a positive value a concave, decelerating slope where deposition occurs. • Plan (contour) curvature is measured perpendicular to the slope and controls convergence and divergence of flow: positive means a diverging ridge, negative a converging hollow. • Total (general) curvature combines both; zero curvature everywhere means a planar surface.

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Applications: soil moisture and erosion/deposition zones, landslide initiation (convergent hollows), geomorphological classification into ridges, slopes and valleys, and smoothing quality checks on a DEM.

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Hillshade (Analytical Relief Shading) • Hillshade gives a grey-scale 0-255 image of how an illuminated surface would appear, computed from slope, aspect and the position of a hypothetical light source defined by an azimuth (default 315°, i.e. north-west) and an altitude (default 45°). • Hillshade = 255 × [cos(zenith)·cos(slope) + sin(zenith)·sin(slope)·cos(azimuth − aspect)], where zenith = 90° − altitude; negative values are set to 0 (in shadow). • The north-west convention is used because a light source from the lower right produces relief inversion — ridges appear as valleys to most viewers.

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A vertical exaggeration (z-factor) is applied for gentle terrain, and the z-factor must convert units when elevations are in metres but the horizontal units are degrees. • Applications: backdrop for thematic and topographic maps, visual detection of DEM artefacts and lineaments, geomorphological and archaeological interpretation, and shadow analysis.

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Viewshed (Intervisibility) • A viewshed identifies the cells of a DEM that are visible from one or more observer points, by tracing a line of sight and comparing the required vertical angle with the maximum angle reached so far along the ray.

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The binary result (1 visible, 0 not) becomes a cumulative viewshed when several observers are used. • Parameters: observer and target offsets (OFFSETA, OFFSETB) for the height of the instrument and the target, azimuth limits, vertical angle limits, search radius, and corrections for Earth curvature and atmospheric refraction (usually 0.13). • Limitations: it uses a bare-earth DEM, so buildings and forest (present in a DSM) are ignored unless a surface model is used; results are sensitive to DEM resolution and error. • Applications: siting of telecommunication and radio masts, control-point and total-station intervisibility in survey network design, watch-towers and security, visual-impact assessment of towers, quarries and wind farms, scenic route planning and military defilade.

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Watershed Delineation • The standard raster workflow is: fill sinks → compute flow direction → compute flow accumulation → define the stream network by a threshold → snap pour point → delineate the watershed → derive stream order and basin parameters. • Flow direction is usually the D8 algorithm: flow from each cell goes entirely to the one of its eight neighbours with the steepest descent, coded 1, 2, 4, 8, 16, 32, 64, 128 clockwise from east.

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Multiple-flow-direction and D-infinity algorithms divide the flow among several neighbours and model divergent slopes better. • Filling sinks (internal depressions, usually DEM errors) is essential, otherwise flow paths terminate; flow accumulation counts the cells draining into each cell, so high values trace the channels. • Terminology: watershed/catchment/basin (the area draining to an outlet), divide/ridge line (its boundary), pour point/outlet, and Strahler stream order.

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Applications: hydrological and flood modelling, soil-erosion estimation, reservoir and micro-hydro siting, water-supply and irrigation planning, and integrated watershed management — all widely applied in Nepal's river basins.

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Surface Intersection • Surface intersection is the computation of the line or region where two surfaces meet — for example an existing ground surface and a proposed design (formation) surface.

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The difference raster (design − existing) gives cut where negative and fill where positive, and the zero contour of that difference is the intersection line, the daylight or catch line. • The same idea gives earthwork volumes (sum of the difference times the cell area, or the prismoidal/average-end-area formula on a TIN), inundation and flood-extent mapping (intersection of the DEM with a water-level plane), reservoir capacity curves, and geological modelling of the outcrop where a bedding plane meets the topography. • On a TIN the intersection is computed exactly facet by facet; on a grid it is approximate and depends on cell size.

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This section covers deterministic and geostatistical interpolation, resampling, spatial dependence and the semivariogram, ordinary and universal kriging, point-based moving-average models, and the DSM, DEM and DTM with their breaklines and applications.

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Principle of Spatial Interpolation Spatial interpolation estimates the value of a variable at unsampled locations from measurements at sampled locations.

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It rests on Tobler's First Law of Geography: "everything is related to everything else, but near things are more related than distant things".

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Estimating outside the range of the data is extrapolation and is far less reliable.

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Basis of classification Types Approach Deterministic (mathematical function only) vs geostatistical/stochastic (uses a model of spatial correlation and gives an error estimate) Extent of data used Global (all points — trend surface) vs local (points in a neighbourhood — IDW, spline, kriging) Fit at data points Exact (surface passes through the samples — IDW, spline, ordinary kriging) vs inexact/approximate (trend surface, smoothing splines) Abruptness Gradual (smooth, e.g.

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IDW) vs abrupt (Thiessen polygons, barriers) Deterministic Methods Method Principle and remarks Thiessen (Voronoi) polygons Nearest-neighbour: each location takes the value of the closest sample; abrupt, exact, used for rainfall areal averaging Inverse distance weighting (IDW) z = Σ(zi/di p) / Σ(1/di p); exact, local; the power p (usually 2) controls how fast influence falls off; produces bull's-eyes around isolated samples and can never exceed the data range Moving average / moving window Simple or weighted mean of the samples inside a fixed radius or of the k nearest points; smooths, inexact; the basis of IDW Trend surface (polynomial regression) Global least-squares polynomial; inexact, shows regional trend only, with residuals analysed separately Spline (thin-plate, regularised, tension) Piecewise polynomial minimising surface curvature; exact and very smooth; may overshoot beyond the data range near abrupt changes Natural neighbour Weights from the areas stolen from surrounding Voronoi cells; exact, smooth, stays within the data range Triangulation (TIN, linear) Exact within each Delaunay facet; used for engineering surfaces Resampling • Resampling changes the grid geometry (cell size, origin, projection).

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Nearest neighbour keeps the original values and is mandatory for categorical data; bilinear takes a distance-weighted mean of the 4 surrounding cells; cubic convolution uses 16 cells and gives the visually sharpest result but alters values most.

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Majority (mode) is used when aggregating categorical grids. • Upsampling to a finer cell size does not create new information — the detail is only apparent; downsampling (aggregation) loses detail and, as noted in 8.4, systematically flattens slope.

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Spatial Dependence and the Semivariogram • Spatial dependence (autocorrelation) is the tendency for values at nearby locations to be more alike than values far apart.

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It is quantified by the semivariance: γ(h) = (1/2N(h)) Σ [z(xi) − z(xi + h)]², the half mean squared difference between all pairs of points separated by the lag distance h. • The plot of γ(h) against h is the experimental semivariogram; a model (spherical, exponential, Gaussian, linear or power) is fitted to it, and its parameters feed the kriging equations. • Kriging assumes stationarity: the intrinsic hypothesis requires the mean to be constant and the semivariance to depend only on the separation vector h.

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Parameter Meaning Nugget (C0) The intercept at h = 0 — measurement error plus variation at distances shorter than the sample spacing; theoretically γ(0) = 0 Sill (C0 + C) The plateau the semivariance reaches — equal to the total variance of the data Partial sill (C) Sill minus nugget — the structured, spatially dependent part of the variance Range (a) The lag at which the sill is reached — beyond it points are no longer correlated and add nothing to the estimate Nugget-to-sill ratio Strength of spatial dependence: < 25 % strong, 25-75 % moderate, > 75 % weak Anisotropy Range (and sometimes sill) varying with direction — modelled with a directional semivariogram Kriging • Kriging is the Best Linear Unbiased Estimator (BLUE): the estimate is a weighted linear combination of the neighbouring samples, ẑ(x0) = Σ λi z(xi), in which the weights λi are chosen from the semivariogram so that the estimate is unbiased (Σλi = 1) and the estimation variance is minimised.

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Alone among the common methods it delivers a kriging variance (error) surface alongside the prediction. • The weights account for distance, the clustering of samples (declustering) and anisotropy, which is why kriging outperforms IDW where the sampling is uneven. • Ordinary kriging — the commonest form — assumes an unknown but locally constant mean and no trend.

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Simple kriging assumes the mean is known and constant.

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Universal kriging (kriging with a trend / KT) assumes a deterministic trend (drift) that is modelled as a polynomial of the coordinates, with ordinary kriging applied to the residuals; it is used when the variable shows a clear regional gradient. • Other variants: co-kriging (uses a correlated secondary variable), indicator kriging (probability of exceeding a threshold), block kriging (estimates an average over an area) and regression kriging. • Validation uses cross-validation (leave-one-out) or a withheld test set; the diagnostics are the mean error (bias, should be ≈ 0) and the RMSE (should be as small as possible), with the standardised RMSE near 1 if the kriging variance is realistic.

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DEM, DTM, DSM and Breaklines Term Definition DEM (digital elevation model) A grid of elevations of the terrain; often used as a general term but strictly bare earth DTM (digital terrain model) The bare-earth surface together with breaklines and morphological features such as ridges, channels and spot heights DSM (digital surface model) The first reflective surface — tops of buildings, canopy and other objects (a lidar first return, or image matching) nDSM / CHM DSM − DEM — normalised heights of objects above ground; used for building and canopy heights Breakline A line along which the slope changes abruptly — ridge, stream, road edge, retaining wall, kerb.

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Hard breaklines mark a sharp break in slope; soft breaklines add detail without changing the slope • Sources of DEM/DSM: photogrammetric stereo matching, lidar (first return → DSM, last return/ground classification → DEM), InSAR (SRTM 30 m, TanDEM-X), optical stereo satellites (ASTER GDEM 30 m, ALOS World 3D), digitised contours, and ground/UAV survey.

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Global free DEMs in common use are SRTM, ASTER GDEM, ALOS AW3D30 and Copernicus DEM. • Structures for storing a DTM: regular grid, TIN, contour lines and profiles; accuracy is reported as RMSE in height or LE90, and is typically judged against independent check points on open, flat ground. • Applications of a DTM: derivation of slope, aspect, curvature, hillshade, viewshed and watersheds (8.4); contour generation; cut-and-fill and earthwork volumes for roads, canals and levelling; route and alignment design with profiles and cross-sections; flood inundation and dam-break modelling; landslide susceptibility; line-of-sight and telecommunication planning; orthorectification of imagery (a true orthophoto needs a DSM);

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3-D city modelling; solar-potential mapping; and geomorphometric terrain classification. • Errors: voids in radar DEMs (steep Himalayan terrain and water), vegetation bias in DSM-derived DEMs, striping artefacts, interpolation error between contours, and edge effects between tiles.

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This section covers open standards and open-source GIS software, the GeoServer architecture, the OGC web services WMS, WFS and WCS, and web-based data visualization and applications.

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Open GIS, Open Source and Open Data • OpenGIS / Open Geospatial Consortium (OGC): an international consensus body (founded 1994) that publishes open, vendor-neutral interface standards so that different systems can exchange and process geospatial data. "Open" here means an open specification, not free software — a proprietary product may be fully OGC-compliant. • Open-source software means the source code is available under a licence (GPL, LGPL, MIT, Apache) permitting use, study, modification and redistribution; the geospatial projects are coordinated by OSGeo. • Open data means the data themselves are free to use and redistribute (e.g.

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OpenStreetMap under ODbL, government open-data portals).

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The three ideas are independent and are often confused in exam questions.

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Software Role QGIS Full desktop GIS — viewing, editing, analysis, cartography, plugins, Python (PyQGIS) GRASS GIS Powerful raster, vector, imagery and terrain analysis engine; strong hydrology and geomorphometry PostgreSQL / PostGIS Open-source spatial database (Chapter 7) GeoServer / MapServer Server software publishing OGC web services GDAL/OGR The universal raster/vector translation and processing library behind almost every GIS OpenLayers / Leaflet JavaScript libraries for web mapping clients SAGA, gvSIG, ILWIS, Orfeo Toolbox, QField Analysis, desktop, image processing and field data collection OpenStreetMap Global open, crowd-sourced spatial database • Advantages of open source: no licence fee, transparency and auditability, freedom to modify and localise, no vendor lock-in, rapid community development, and open formats.

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Limitations: support depends on the community or paid third parties, interfaces and documentation vary, training and staff capacity are needed, and some specialised modules are less mature.

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GeoServer • GeoServer is a Java-based open-source server that publishes spatial data from many sources as OGC web services — WMS, WMTS, WFS, WFS-T, WCS and WPS — and is the reference implementation of WFS and WCS. • Architecture: data store / coverage store (PostGIS, shapefile, GeoTIFF, GeoPackage, WFS…) → layer → layer group, organised in workspaces, with styles (SLD) attached to layers and a web administration interface plus a REST configuration API.

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GeoWebCache is built in for tile caching, and security is set per workspace, layer and service. • A typical publication workflow: create a workspace → add a store pointing at the data → publish the layer, setting its name, title, CRS (declared/native) and bounding box → upload and assign an SLD style → preview with the Layer Preview (OpenLayers) → consume the WMS/WFS URL in QGIS, a web client or a mobile app. • MapServer (C-based, CGI, mapfile configuration) is the main alternative; the client side is usually OpenLayers or Leaflet, and the catalogue GeoNetwork (CSW).

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The OGC Web Services Service Returns Core operations WMS (Web Map Service) A rendered map image (PNG/JPEG) — a picture, not the data GetCapabilities, GetMap, GetFeatureInfo (+ GetLegendGraphic, DescribeLayer) WFS (Web Feature Service) The vector features themselves, usually as GML (also GeoJSON, shapefile) GetCapabilities, DescribeFeatureType, GetFeature (+ LockFeature, Transaction in WFS-T) WCS (Web Coverage Service) The coverage (raster) values themselves — a GeoTIFF or NetCDF usable for analysis GetCapabilities, DescribeCoverage, GetCoverage WMTS Pre-rendered map tiles from a fixed tile matrix — very fast GetCapabilities, GetTile, GetFeatureInfo WPS The result of a geoprocess run on the server GetCapabilities, DescribeProcess, Execute CSW Metadata records from a catalogue GetCapabilities, GetRecords, GetRecordById • Key exam distinction:

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WMS gives you a picture you can only look at;

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WFS gives you features you can query, edit and analyse;

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WCS gives you the raster values you can compute with.

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A WMS layer therefore cannot be edited or have its attributes analysed locally, and a WFS-T is required for editing over the web. • Typical WMS GetMap parameters:

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SERVICE=WMS, VERSION=1.3.0, REQUEST=GetMap, LAYERS, STYLES, CRS (SRS in 1.1.1), BBOX, WIDTH, HEIGHT, FORMAT, TRANSPARENT; and SLD/SLD_BODY for user styling (8.3).

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In version 1.3.0 the BBOX axis order follows the CRS definition, so EPSG:4326 is min-lat, min-lon, max-lat, max-lon — a classic source of a blank map. • GetCapabilities is the first request to any OGC service: it returns the XML document listing the layers, their CRSs, bounding boxes, styles, formats and the operations supported. • Related standards:

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GML (the XML encoding of features), Filter Encoding (queries in WFS), SLD/SE (portrayal), KML, GeoPackage, GeoSPARQL, and the newer, REST/JSON-based OGC API — Features, Tiles, Maps and Coverages, which are gradually replacing the WxS family.

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Data Visualization and Applications • Web GIS architecture: a client (browser with OpenLayers, Leaflet or MapLibre; or a desktop GIS; or a mobile app) → application/web server → map server (GeoServer) → spatial database (PostGIS), with a catalogue (GeoNetwork) for discovery.

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Tiling and caching (GeoWebCache, XYZ tiles, vector tiles) give the responsiveness users expect. • Visualization techniques on the web: base map plus overlays, layer switching and opacity, pop-ups driven by GetFeatureInfo, time sliders for temporal data, clustering of dense points, heat maps, swipe and side-by-side comparison, 3-D terrain and building views, and dashboards combining map, chart and table. • Applications: national and municipal geoportals, cadastral and land-records viewers, utility and road asset management, disaster risk and real-time flood/earthquake response, health and epidemic mapping, environmental and forest monitoring, agriculture advisory services, tourism and navigation, and participatory mapping. • In Nepal, open-source web GIS underpins the Survey Department's national geoportal, municipal spatial data portals, OpenStreetMap-based disaster mapping (widely used after the 2015 earthquake), and open data from the Department of Hydrology and Meteorology and the Central Bureau of Statistics. • Benefits: low cost, wide reach without specialist software, a single authoritative copy of the data, interoperability across agencies, and easier maintenance.

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Challenges: bandwidth and infrastructure, data currency and quality, licensing and privacy, sustainability of funding and staff, and standards compliance.