Engineer Surveying Geo-Spatial Information cheat sheet

Deflection of the vertical: angle between the ellipsoid normal and the geoid normal; it has two components (meridian and prime vertical) and is typically < 1 arc-minute, but can reach tens of arc-seconds in mountainous regions.

Geoid undulation N relates ellipsoidal height h and orthometric height H by h = H + N; GNSS gives h, leveling gives H, so N is needed to connect them.

Curvature correction for leveling: c = d^2 / (2R), where d is the sight length and R is Earth's radius; at 100 m the correction is about 0.8 mm.

Refraction and curvature combined correction: c = 0.0675 d^2 (d in meters, c in meters) for a single sight; use the difference of squared distances for unequal sights.

Reduction of a measured distance to the ellipsoid: S = s * (1 - h/R + N/R) approximately, where s is horizontal distance at elevation h and N is geoid undulation; scale factor must also be applied for map projection.

Traverse closure: linear misclosure = sqrt((sum of dE)^2 + (sum of dN)^2); relative precision = misclosure / total traverse length; adjust by compass rule (Bowditch) or transit rule depending on angular vs linear accuracy.

Resection (three-point problem): the position of an unknown point is determined from angles measured to three known points; the danger circle is the locus of points where the three points subtend a constant angle, causing indeterminate solutions.

Vertical angle refraction coefficient k is typically 0.13 (or 0.14); the combined correction for curvature and refraction is (1 - k) d^2 / (2R) = 0.0675 d^2 for k = 0.13.

GNSS positioning modes: absolute (point) positioning uses code pseudoranges; relative (differential) positioning uses carrier-phase or code differences between receivers to cancel common errors; RTK requires a data link and gives cm-level accuracy within 10–20 km of the base.

PDOP (Position Dilution of Precision) = sqrt(PDOP^2 = HDOP^2 + VDOP^2); GDOP includes time; lower values indicate better satellite geometry; PDOP < 6 is generally acceptable for surveying.

Total station accuracy specification: angular accuracy (e.g., 2" or 5") and distance accuracy (e.g., ±(2 mm + 2 ppm)); ppm error is proportional to distance and must be added to the constant error.

Terrestrial laser scanning: point spacing at a given range = range × angular resolution; registration of multiple scans uses targets or cloud-to-cloud matching; accuracy is typically 2–6 mm at 10–50 m.

UAV photogrammetry: ground sample distance (GSD) = (pixel size × flying height) / focal length; overlap of 60–80% forward and 40–60% sidelap is typical for mapping; ground control points (GCPs) are required for absolute accuracy.

LiDAR: pulse repetition frequency (PRF), scan frequency, and flying height determine point density; multiple returns allow penetration of vegetation; intensity is a measure of return strength and can be used for classification.

Leveling: differential leveling uses a level and staff; the collimation error is checked by the two-peg test; misclosure is distributed proportionally to the number of setups or distance.

Hydrographic surveying: multibeam echosounder (MBES) swath width depends on depth and beam angle; sound velocity profiles correct for refraction in the water column; tide corrections reduce soundings to a chart datum.

Vector overlay operations: union, intersection, identity, and erase; the output attribute table combines attributes from both input layers; topological errors (slivers, gaps, overlaps) must be resolved before analysis.

Raster analysis: map algebra uses local, focal, zonal, and global functions; focal statistics (e.g., mean, sum) operate on a moving window; zonal statistics summarize raster values within polygon zones.

Spatial interpolation methods: inverse distance weighting (IDW) is deterministic and exact at data points; kriging is geostatistical and provides a variance surface; spline is a smooth interpolator; natural neighbor uses Voronoi polygons.

Buffer distance in a projected coordinate system is in linear units; in a geographic coordinate system, buffer distance is in degrees, which is inappropriate for most analyses; geodesic buffers should be used for large areas.

Network analysis: shortest path, service area, and closest facility; impedance can be distance, time, or cost; turn restrictions and one-way streets must be modeled in the network dataset.

Spatial join transfers attributes from one layer to another based on spatial relationship (intersects, contains, within, nearest); it does not modify geometry.

Topology rules: must not overlap, must not have gaps, must not have dangles; topology validation identifies errors; fixing errors requires editing the geometry or marking exceptions.

Geodatabase: feature dataset stores features with a common coordinate system; relationship classes manage associations; domains and subtypes enforce attribute integrity; versioning allows multiple editors.

Electromagnetic spectrum regions used in remote sensing: visible (0.4–0.7 µm), near-infrared (0.7–1.3 µm), shortwave infrared (1.3–3 µm), thermal infrared (3–14 µm), and microwave (1 mm–1 m); atmospheric windows are wavelength bands with high transmission.

Spectral signatures: vegetation has high NIR reflectance and low red reflectance (red edge); water absorbs NIR and appears dark; soil reflectance increases with moisture content up to a point, then decreases.

Photogrammetric scale: S = f / H, where f is focal length and H is flying height above ground; for a digital camera, GSD = (pixel size × H) / f.

Relief displacement: d = (r × h) / H, where r is radial distance from nadir, h is object height, and H is flying height; displacement is radial from the nadir point.

Stereo photogrammetry: vertical exaggeration = base-to-height ratio (B/H); overlap of 60% forward and 30% sidelap is typical; parallax difference yields elevation.

Orthophoto: rectified image with uniform scale; requires a digital elevation model (DEM) to remove relief displacement; orthorectification differs from simple georeferencing.

Satellite orbits: sun-synchronous (polar) orbits provide consistent illumination and global coverage; geostationary orbits provide continuous coverage of a fixed region; revisit time depends on orbit and swath width.

Image classification: supervised classification uses training samples; unsupervised classification clusters pixels (e.g., k-means, ISODATA); accuracy assessment uses a confusion matrix, overall accuracy, producer's accuracy, and user's accuracy.

Map scale: representative fraction (RF) 1:24,000 means 1 unit on map equals 24,000 units on ground; large scale shows more detail (e.g., 1:1,000), small scale shows less detail (e.g., 1:1,000,000).

Projection properties: conformal preserves angles (e.g., Mercator, Transverse Mercator); equal-area preserves area (e.g., Albers, Lambert Azimuthal Equal-Area); equidistant preserves distance from a point or along a line; azimuthal preserves direction from a center point.

Universal Transverse Mercator (UTM): 60 zones, each 6° wide; central meridian scale factor 0.9996; false easting 500,000 m; false northing 0 m (north) or 10,000,000 m (south); coordinates are in meters.

State Plane Coordinate System (SPCS): uses Transverse Mercator for north-south zones, Lambert Conformal Conic for east-west zones; zones are defined by state; units are feet or meters; scale factor varies within zone.

Map projection distortion: Tissot's indicatrix shows distortion of a small circle; the shape and size of the indicatrix indicate conformality and area distortion; scale factor is the ratio of map distance to ellipsoid distance.

Grid convergence: angle between grid north and true north; it varies with longitude within a zone; azimuths must be corrected for convergence when converting between grid and geodetic bearings.

Vertical datums: orthometric heights (e.g., NAVD88) are referenced to the geoid; ellipsoidal heights are referenced to the ellipsoid; the difference is the geoid undulation; tidal datums (MLLW, MHW) are used for nautical charts.

Map design: visual hierarchy, figure-ground relationship, and balance; color use should consider color blindness; typography should be legible; generalization (simplification, smoothing, aggregation) reduces detail at smaller scales.

Boundary evidence hierarchy: natural monuments, artificial monuments, reference monuments, courses and distances, area, and coordinates; this order is commonly used when evidence conflicts.

Adverse possession: requires actual, open, notorious, exclusive, hostile, and continuous possession for a statutory period; title by prescription is similar but based on easement use.

Riparian boundaries: boundary between land and non-navigable water typically follows the ordinary high water mark; for navigable waters, the state may own the submerged lands; accretion, reliction, erosion, and avulsion have different legal effects.

Easements: appurtenant easements benefit a dominant tenement and burden a servient tenement; easements in gross are personal; prescriptive easements require use that is open, notorious, adverse, and continuous for the statutory period.

Land tenure systems: cadastral surveys define parcel boundaries for taxation and ownership; Torrens system provides title registration with a state guarantee; general boundary systems (e.g., in England and Wales) do not guarantee exact boundary location.

PLSS (Public Land Survey System): divides land into townships (6 miles square), ranges, and sections (1 mile square, 640 acres); section numbering starts at northeast corner and snakes; fractional lots occur along boundaries.

Metes and bounds: describes boundary by courses (bearing) and distances from a point of beginning (POB); errors in bearing or distance can be adjusted by compass rule; natural monuments prevail over courses and distances.

Boundary retracement: the surveyor must follow the original survey evidence, not create new lines; evidence includes original monuments, field notes, and plats; the goal is to locate the original boundary as it was established.

Metadata standards: ISO 19115 (geographic information metadata) and FGDC CSDGM; metadata should include identification, data quality, spatial reference, entity and attribute, distribution, and metadata reference information.

Data quality elements: positional accuracy, attribute accuracy, logical consistency, completeness, and lineage; these are defined in ISO 19157 and FGDC standards.

Spatial data formats: vector (Shapefile, GeoJSON, GML, File Geodatabase), raster (GeoTIFF, JPEG2000, MrSID), and point cloud (LAS, LAZ); each has limitations (e.g., Shapefile field names limited to 10 characters, no null support).

Coordinate reference system (CRS) definition: includes datum, ellipsoid, prime meridian, and projection; EPSG codes provide standardized identifiers (e.g., EPSG:4326 for WGS84 geographic, EPSG:32633 for UTM zone 33N).

Topological quality: check for gaps, overlaps, dangles, and self-intersections; topology rules depend on feature class; validation should be performed before analysis or publication.

Positional accuracy standards: ASPRS positional accuracy standards for digital geospatial data (e.g., RMSE for horizontal and vertical); accuracy is reported at 95% confidence level (1.7308 × RMSE for horizontal, 1.9600 × RMSE for vertical).

Data conversion: raster to vector (vectorization) and vector to raster (rasterization); resampling methods (nearest neighbor, bilinear, cubic convolution) affect output; nearest neighbor preserves original values, bilinear and cubic smooth.

Versioning and archiving: geodatabases support versioning for multi-user editing; archiving tracks changes over time; backups and metadata records are essential for long-term preservation.

Professional ethics: surveyors must hold paramount the safety, health, and welfare of the public; practice only in areas of competence; maintain confidentiality; avoid conflicts of interest; and provide truthful and accurate reports.

Licensure: professional surveying licensure typically requires education, experience, and examinations (e.g., Fundamentals of Surveying, Principles and Practice of Surveying); continuing education is required for renewal in many jurisdictions.

Standards of care: the surveyor must exercise the degree of care and skill ordinarily exercised by reputable surveyors under similar circumstances; negligence is a breach of that standard.

Contracts: scope of services, deliverables, schedule, and fee should be clearly defined; limitations of liability and indemnification clauses are common; errors and omissions insurance covers professional liability.

Boundary surveys: must be performed under the responsible charge of a licensed surveyor; the surveyor should research public records, field evidence, and legal descriptions; a survey does not transfer title.

Regulations: many jurisdictions have laws defining the practice of surveying, minimum standards for surveys, and penalties for unlicensed practice; the surveyor must be familiar with local statutes and administrative rules.

Plats and records: survey plats must be filed with the appropriate agency (e.g., county recorder) as required by statute; field notes and records should be retained for the period specified by law.

Conflict of interest: a surveyor should not accept compensation from multiple parties for the same service without disclosure; should not bid on a project where they have a financial interest; should avoid using confidential information for personal gain.

UAV/drone mapping: Structure from Motion (SfM) photogrammetry generates point clouds and orthomosaics; accuracy depends on GCPs, camera calibration, and flight planning; regulations (e.g., FAA Part 107) govern commercial use.

LiDAR applications: topographic mapping, forestry (canopy height, biomass), bathymetry (green wavelength), and infrastructure inspection; full waveform LiDAR records the entire return signal, enabling better vegetation penetration.

InSAR (Interferometric Synthetic Aperture Radar): measures ground deformation with mm to cm precision; uses phase difference between SAR images; applications include subsidence, landslides, and earthquake monitoring; limitations include vegetation and temporal decorrelation.

GNSS modernization: multi-constellation (GPS, GLONASS, Galileo, BeiDou) and multi-frequency signals improve accuracy and availability; PPP (Precise Point Positioning) provides cm-level accuracy without a base station.

Indoor mapping and BIM: integration of GIS and Building Information Modeling (BIM) enables facility management; indoor positioning uses Wi-Fi, Bluetooth, or UWB; point clouds from laser scanning are used for as-built BIM.

Real-time kinematic (RTK) and network RTK: network RTK uses multiple reference stations to model atmospheric errors; accuracy is typically 1–3 cm horizontal; requires cellular or radio link.

Geospatial artificial intelligence: machine learning for feature extraction (e.g., building footprints, roads), land cover classification, and change detection; deep learning models require large training datasets and validation.

Digital twins: virtual replicas of physical assets and environments; integrate sensor data, GIS, and BIM; used for urban planning, infrastructure management, and simulation; require continuous data updates.