Registered Surveyor cheat sheet

Priority of evidence in retracement: undisturbed original monuments outrank measurements, then bearing trees and other calls, then courses and distances, then area; quantity yields to quality.

Rule of harmonization: when a deed call is ambiguous, interpret it so all calls are given effect; specific calls control general calls, and natural monuments control artificial ones.

Adverse possession generally requires actual, open and notorious, exclusive, continuous, and hostile possession for the statutory period; color of title and payment of taxes extend or shorten periods in many statutes.

Boundary by acquiescence rests on a recognized line treated as the boundary by adjoining owners for the limitations period, regardless of the record location.

Parol evidence is admissible to resolve latent ambiguities, locate monuments, and prove practical location, but not to vary an unambiguous deed description.

Easements: a prescriptive easement requires use that is open, notorious, adverse, and continuous for the statutory period; it is not exclusive in the adverse-possession sense.

Riparian and littoral boundaries: boundaries on meandered non-navigable streams move with gradual accretion and reliction; avulsion (sudden change) leaves the boundary where it was.

Retracement procedure: recover the record, identify the controlling monuments, evaluate evidence quality, then compute; never set new corners from record distances alone when original evidence exists.

Junior-senior rights: where a tract is conveyed by the same grantor and a conflict arises, the senior (earlier) conveyance generally prevails over the junior conveyance.

Ellipsoid parameters: flattening f = (a − b)/a; first eccentricity e² = 2f − f²; GRS80 has a = 6,378,137 m and 1/f = 298.257222101.

Radius of curvature in the meridian M = a(1 − e²)/(1 − e² sin²φ)^(3/2); in the prime vertical N = a/(1 − e² sin²φ)^(1/2).

Geoid undulation N relates ellipsoidal and orthometric heights: h = H + N; a geoid model converts GNSS ellipsoid heights to orthometric heights.

Deflection of the vertical is the angle between the ellipsoid normal and the gravity vertical; it affects astronomic azimuth and zenith angle reductions.

Refraction and curvature combined correction for a level sight of length d: approximately 0.0675 d² m with d in km, subtracted from the rod reading.

Scale factor and elevation factor combine into a combined factor: CF = grid scale factor × elevation factor, where elevation factor ≈ R/(R + H).

Least-squares adjustment: normal equations N = AᵀPA, solution x = N⁻¹AᵀPl; residuals v = Ax − l; a posteriori variance σ₀² = vᵀPv/(n − u).

Error propagation: for y = f(x), the covariance propagates as Σy = J Σx Jᵀ, with J the Jacobian of the transformation.

State Plane Coordinate System: Lambert Conformal Conic for east-west states, Transverse Mercator for north-south states; each zone has its own false easting and northing.

Geodetic to grid: grid azimuth = geodetic azimuth − convergence angle γ; convergence is positive east of the central meridian for TM.

UTM: 60 zones of 6° longitude, central meridian scale factor 0.9996, false easting 500,000 m, false northing 0 m (north) or 10,000,000 m (south).

Vincenty's inverse formula gives geodesic distance and azimuths on the ellipsoid; it iterates and may fail to converge for near-antipodal points.

ECEF to geodetic: iterate φ from tan φ = (Z + e²N sin φ)/p until convergence, where p = √(X² + Y²); height h = p/cos φ − N.

Datum transformation: a 7-parameter Helmert transformation applies three translations, three rotations, and a scale factor between reference frames.

Grid to ground: ground distance = grid distance ÷ combined factor; grid distance = ground distance × combined factor.

Forward geodetic problem on a short line can use the reduction: Δφ = s cos α/M, Δλ = s sin α/(N cos φ), with s the ellipsoidal distance.

Total station: horizontal and vertical circle readings give direction and zenith angle; slope distance is reduced to horizontal and vertical components using the zenith angle.

EDM accuracy is typically stated as ±(a mm + b ppm); the ppm term scales with distance, so long shots carry larger uncertainty.

Traverse closure: linear misclosure = √(ΔE² + ΔN²); relative precision = misclosure ÷ perimeter; adjust by compass (Bowditch) or transit rule.

Bowditch adjustment distributes the closure proportional to course length; the transit rule distributes proportional to the coordinate change magnitude.

Differential leveling: elevation difference = backsight − foresight; misclosure must be within the allowable limit for the order of the survey before adjustment.

GNSS RTK requires a fixed integer ambiguity solution for centimeter accuracy; a float solution is decimeter-level and must be flagged in the record.

Three-point resection: the instrument occupies an unknown point and observes angles to three known points; a weak geometry (points near a circle through the station) amplifies error.

Setup and centering error, instrument leveling error, and target plumbing error are systematic sources that do not average out with repeated observations.

Metes and bounds descriptions rely on monuments, courses, distances, and adjoiners; the order of calls and the closing call are legally significant.

The Public Land Survey System uses principal meridians and baselines, townships of 36 sections, and section subdivision; aliquot parts are described by half and quarter divisions.

PLSS corners are classified as standard, closing, meander, and special; original government corners are the highest evidence in a retracement.

Lot and block descriptions reference a recorded plat; the plat and its surveyor's certificate are part of the record and control over unrecorded measurements.

Recording acts: race, notice, and race-notice statutes determine priority among competing purchasers; a race-notice jurisdiction requires both prior recording and lack of notice.

A cadastral parcel identifier is a stable administrative key; it does not by itself define the legal boundary, which remains the recorded description.

Torrens (registration) systems make the registered title conclusive against most claims, subject to statutory exceptions such as fraud and government takings.

Chain of title and title search must reconcile every conveyance; a gap or a wild deed can break the chain even when each individual deed is valid.

Conformal projections preserve local angles and shapes at the cost of area; equal-area projections preserve area at the cost of shape.

Mercator is conformal with scale factor sec φ; it is unsuitable for area comparison and exaggerates high-latitude areas.

Transverse Mercator scale factor: k = k₀(1 + x²/(2R²) + …), where x is the distance from the central meridian; k increases away from the central meridian.

Lambert Conformal Conic uses two standard parallels; scale is exact along the standard parallels and between them, and is larger outside them.

Map scale as a representative fraction (1:24,000) is dimensionless; one inch on a 1:24,000 map represents 2,000 feet on the ground.

Contour interval selection depends on terrain relief and map scale; index contours are emphasized every fifth contour.

Map generalization includes selection, simplification, smoothing, aggregation, and displacement; it is required when source detail exceeds the display scale.

A graticule shows latitude and longitude lines; a measured grid shows projected coordinate lines, which are not the same as a graticule.

Vector topology encodes adjacency, connectivity, and containment; it enables network tracing and polygon overlay without duplicate coordinates.

Raster resolution sets the minimum mappable unit; a cell is assigned one value, so mixed classes within a cell are lost (mixed-pixel problem).

Overlay operations: union keeps all areas, intersect keeps the overlap, identity keeps the input extent with the overlay attributes; each requires matching coordinate systems.

Coordinate system mismatch is the most common GIS error; reprojection changes the coordinate values, not the underlying datum unless a datum transformation is applied.

Metadata should record source, datum, projection, accuracy, currency, and lineage so a derived product can be evaluated and reproduced.

A digital elevation model stores elevation per cell; slope and aspect are derived from the local gradient, and flow direction from the steepest descent.

Spatial query and selection by attribute are distinct operations; a buffer uses a distance tolerance that must be expressed in the layer's coordinate units.

Data quality elements include positional accuracy, attribute accuracy, completeness, logical consistency, and temporal accuracy.

Scale of a vertical aerial photograph: S = f/H, where f is focal length and H is flying height above the terrain; relief displacement increases away from the principal point.

Stereo parallax p = x_left − x_right; flying height H = B·f/p, where B is the air base, so parallax gives elevation.

Ground sample distance: GSD = (pixel size × flying height)/focal length; smaller GSD means finer detail.

Overlap requirements: about 60% endlap for stereo and 20–30% sidelap for full coverage; excessive overlap raises the base-to-height ratio problem.

Orthorectification removes relief displacement and tilt by using a DEM and camera model; a rectified image without a DEM retains relief error.

Bundle block adjustment solves camera poses and object points together using tie points and ground control points.

LiDAR produces a point cloud with intensity and return number; classification separates ground from vegetation to build a bare-earth DEM.

Remote sensing indices: NDVI = (NIR − Red)/(NIR + Red); values near 1 indicate healthy vegetation, near 0 or negative indicate non-vegetation.

A surveyor's seal and signature certify that the work was performed and reviewed by the licensee; sealing another's work without review is a violation.

Standards of care: the surveyor must meet the ordinary skill and care of the profession; a written contract cannot disclaim liability for negligence in most jurisdictions.

Conflict of interest must be disclosed; accepting compensation from two parties for the same boundary determination compromises independence.

Boundary retracement opinions should be documented with the evidence relied on, the reasoning, and the basis of the conclusion.

Records, field notes, and computations are professional records and are generally subject to retention requirements and to discovery in litigation.

Liability to third parties may arise from foreseeable reliance on a survey, plat, or certification even without privity of contract.

Statutes of limitations and repose limit exposure; the surveyor should know the jurisdiction's period and the effect of concealed defects.

Unauthorized practice includes offering survey services without a license; supervision of unlicensed staff must comply with the jurisdiction's rules.

Random errors follow a distribution with mean near zero and are reduced by redundancy; systematic errors bias every observation and are not reduced by repetition.

Standard deviation of the mean: σ_x̄ = σ/√n; precision improves with the square root of the number of observations.

Weights are inversely proportional to variance: w = 1/σ²; a weighted mean is x̄ = Σw x/Σw.

Propagation for a sum: σ² = σ₁² + σ₂² + 2ρσ₁σ₂; independent terms drop the covariance.

Error ellipse: semi-major and semi-minor axes from the eigenvalues of the 2×2 covariance matrix; it describes positional uncertainty at a stated confidence.

Chi-square test of a variance: χ² = (n − 1)s²/σ₀²; compare with critical values to test whether the observed scatter matches the expected precision.

Blunder detection uses residuals and standardized residuals; a residual much larger than expected signals a mistake rather than random error.

Significant figures: carry extra digits through computation and round only the final result; a distance reported to 0.01 ft implies precision that the field work must support.