DC Land Surveyor Exam cheat sheet

Priority of evidence in boundary retracement: natural monuments, artificial monuments, courses and distances, then area or quantity; written calls generally outrank measurements they contradict.

Ambiguity in a deed is construed against the grantor (contra proferentem); a call to a natural monument that can be located controls over a conflicting distance call.

Adverse possession generally requires actual, open and notorious, exclusive, continuous, and hostile possession for the statutory period; color of title and payment of taxes can shorten or extend the period depending on state statute.

Riparian boundaries: boundary of a non-navigable stream generally follows the thread (middle) of the channel; on navigable waters the state holds title to the ordinary high water mark, subject to state law.

Accretion (gradual, imperceptible deposit) adds to the riparian owner; avulsion (sudden, perceptible change of channel) does not move the boundary.

A prescriptive easement requires use that is open, notorious, adverse, continuous, and for the statutory period, but unlike adverse possession it need not be exclusive.

Parol evidence is generally inadmissible to contradict an unambiguous deed, but may be admitted to resolve latent ambiguities, explain monuments, or show fraud, mistake, or boundary agreement.

Record vs. occupation: junior-senior rights and recording acts (race, notice, race-notice) determine which of competing conveyances prevails; a surveyor must reconcile record title with possession evidence.

Ellipsoid parameters: GRS80 has a = 6,378,137.0 m and 1/f = 298.257222101; WGS84 has a = 6,378,137.0 m and 1/f = 298.257223563. NAD83 and WGS84 differ by roughly 1–2 m in CONUS.

Geodetic vs. geocentric latitude: geodetic latitude is the angle between the ellipsoid normal and the equatorial plane; geocentric latitude uses a line to the ellipsoid center; the difference is up to about 0.19°.

State Plane Coordinates: each zone uses a map projection (Lambert Conformal Conic or Transverse Mercator) with a scale factor; grid distance = ground distance × combined factor (ellipsoid factor × projection factor).

Elevation factor = R/(R+h), where R is the mean Earth radius (~6,371,000 m) and h is the ellipsoid height; projection scale factor for Lambert varies with longitude from the central meridian.

Geoid vs. ellipsoid: orthometric (mean sea level) heights differ from ellipsoid heights by the geoid undulation N; h (ellipsoid) = H (orthometric) + N.

Datum transformation: NAD27 to NAD83 shifts coordinates by roughly 10–100 m depending on location; use published NGS transformation tools (NADCON) rather than a simple translation.

UTM zones are 6° wide, numbered 1–60 eastward from 180° W; central meridian scale factor is 0.9996; coordinates are in meters with a false easting of 500,000 m.

Convergence angle: the difference between grid north and true north; it is zero on the central meridian and increases with longitude distance from it and with latitude.

Random vs. systematic error: random errors follow a normal distribution and are reduced by redundancy; systematic errors (refraction, instrument calibration) bias results and must be eliminated by procedure or correction.

Standard deviation of the mean = σ/√n; standard error of a single observation is estimated from residuals via σ = √(Σv²/(n−1)).

Least squares adjustment minimizes the sum of squared weighted residuals; the normal equations are N = AᵀWA and x = (AᵀWA)⁻¹AᵀWL.

Weights are inversely proportional to variance: w = 1/σ²; relative weights may be used because the adjustment is scale-invariant.

Error ellipse: semi-major axis a and semi-minor axis b derived from the covariance matrix; the 95% confidence ellipse uses a scale factor of 2.4477 for 2D (chi-square, 2 DOF).

Loop closure: for a closed traverse, angular misclosure is distributed by rule (equal or by angle weight); linear misclosure is checked against the allowed precision, e.g., 1:10,000 for ordinary traverses.

Compass (Bowditch) rule distributes latitude and longitude errors proportionally to line length; transit rule distributes proportionally to the absolute latitudes and departures.

Blunder detection: standardized residuals exceeding about 3σ, or a reference-factor test (a posteriori σ vs. a priori σ), indicate an outlier or misweighted observation.

Total station: horizontal angle from two face readings; zenith angle converted to vertical angle; slope distance reduced to horizontal with HD = SD·sin(zenith) and vertical difference VD = SD·cos(zenith).

EDM accuracy is typically stated as ±(a mm + b ppm × D); atmospheric correction uses temperature and pressure; a 10 °C error causes roughly 1 ppm error in distance.

GNSS RTK: typical horizontal accuracy 10 mm + 1 ppm, vertical 20 mm + 1 ppm; fix vs. float solution depends on integer ambiguity resolution; PDOP above about 6 degrades accuracy.

GNSS is subject to multipath, ionospheric and tropospheric delay; base-rover baseline length should generally be under 10–20 km for RTK accuracy.

Digital levels use bar-coded staffs and image processing to achieve ~0.3 mm/km double-run accuracy; level loops must be closed and adjusted.

Terrestrial laser scanning: point cloud registration uses targets or cloud-to-cloud matching; accuracy is typically 2–6 mm at 10–50 m; scan density depends on angular resolution and range.

UAV photogrammetry requires ground control points and checkpoints; GSD (ground sample distance) is calculated as pixel size × flying height / focal length.

Robotic total station and automatic target recognition (ATR) allow one-person operation; prism constants (e.g., 0 mm vs. −30 mm) must match the prism used or distances are biased.

A subdivision plat must typically show bearings and distances of all lot lines, curve data (R, Δ, L, LC, chord bearing), lot areas, monument locations, and dedication language.

Metes and bounds description begins at a point of beginning (POB) and returns to close; it should reference monuments, adjoiners, and the basis of bearings.

Curve formulas: L = R·Δ(radians); T = R·tan(Δ/2); LC = 2R·sin(Δ/2); M = R(1 − cos(Δ/2)); E = R(sec(Δ/2) − 1).

Area by coordinate method (shoelace): 2A = Σ(Xᵢ·Yᵢ₊₁ − Xᵢ₊₁·Yᵢ); area by DMD: 2A = Σ(DMD × departure).

Plat approval process generally involves preliminary plat, planning commission review, public hearing, final plat, and recording; local ordinances govern street widths, setbacks, and easements.

Easements must be described by width and centerline or by metes and bounds; a utility easement does not convey fee title but burdens the servient estate.

Lot area and frontage requirements come from zoning; nonconforming lots may be buildable under grandfathering provisions, but surveyors should not certify compliance without checking ordinances.

Monumentation requirements: set monuments at all corners and at curve PCs, PTs, and points of tangency; record the monument type, cap, and coordinates in the plat or description.

Construction stakeout: horizontal and vertical control are established, then offset stakes are set outside the work area; grade is referenced to a benchmark or laser plane.

Cut and fill: cut = existing elevation − design elevation (positive = cut); volume by average end area = L × (A₁ + A₂)/2, or by prismoidal formula V = L/6 × (A₁ + 4Aₘ + A₂).

Mass diagram: cumulative earthwork volume plotted along the alignment; the balance point indicates equal cut and fill; the ordinate difference between two stations is the volume between them.

Slope staking uses catch points where the design slope intersects existing ground; the horizontal distance to catch = (grade difference) / (slope difference).

Horizontal and vertical curves: vertical curve elevation y = y_PVC + g₁x + ((g₂ − g₁)/2L)x²; K = L/A where A is the algebraic grade change in percent.

As-built surveys verify that constructed improvements match design; deviations outside tolerance (e.g., ±0.05 ft for structures) require documentation and sometimes redesign.

Machine control and GPS grading use a digital terrain model; the design surface must be verified against the site datum before use.

Stormwater and utility layout: invert elevations, pipe slopes (typically 0.5%–2% for gravity sewers), and cover depths must be checked against design and local standards.

Surveyor licensure: NCEES Fundamentals of Surveying (FS) exam, then the Principles and Practice of Surveying (PS) exam; state boards set experience requirements and continuing education hours.

A professional seal and signature certify that work was performed by or under the direct supervision of the licensee; sealing work outside one's competence is an ethics violation.

Conflict of interest: a surveyor must disclose any financial interest in the property or transaction and must not accept compensation from more than one party for the same service without disclosure.

Boundary survey standards: ALTA/NSPS Land Title Survey standards define minimum requirements, including title commitment review, monumentation, and optional Table A items.

Contracts should define scope, deliverables, standard of care, limitations of liability, and fee; a surveyor is held to the standard of a reasonably competent practitioner, not to a guarantee of perfection.

Records retention and confidentiality: client information and survey records should be retained per state statute and released only with authorization or legal process.

Lien rights: many states allow a surveyor's lien for unpaid services; deadlines for filing and notice vary by jurisdiction.

Ethical advertising and expert testimony: a surveyor serving as an expert witness must base opinions on evidence and disclose the basis; advocacy must not distort technical facts.

Map scale: representative fraction (RF) 1:24,000 means 1 unit on the map equals 24,000 units on the ground; large scale = small denominator (more detail).

Horizontal accuracy standards (ASP RS/NMAS): at map scale 1:24,000, the 90% horizontal accuracy is typically 1/30 inch × scale, about 12.2 m (40 ft).

Raster vs. vector: rasters store values in a grid of cells; vectors store points, lines, and polygons; topology defines adjacency, connectivity, and containment.

Coordinate reference systems in GIS: a projected CRS (e.g., State Plane, UTM) vs. a geographic CRS (lat/long on a datum); mismatched datums cause feature shifts of tens of meters.

LiDAR point clouds are classified (ground, vegetation, buildings) to produce DEM/DTM; bare-earth DEMs are used for contours and hydrology.

Contours: index contours are typically every fifth contour and labeled; contour interval is the vertical distance between adjacent contours; hachures indicate depressions.

Metadata should document source, datum, accuracy, and date; FGDC/ISO 19115 standards define metadata content.

Spatial analysis: buffer, overlay (union, intersect), and spatial join; TIN and DEM interpolation methods include IDW, kriging, and natural neighbor.

Hydrographic positioning: soundings are referenced to a chart datum (often MLLW in the U.S.); depths are reduced by tide or water-level measurements during the survey.

Multibeam and single-beam echosounders measure depth using sound speed in water (~1,500 m/s); sound velocity profiles correct for temperature, salinity, and pressure.

Side-scan sonar images the seafloor for object detection; it does not give accurate depths without additional sensors.

Tidal datum: mean lower low water (MLLW) is the average of the lower of the two daily low waters; mean sea level (MSL) is the average of hourly heights over a 19-year epoch.

Topographic mapping: total station or GNSS RTK collects breaklines and spot elevations; contours are interpolated from a TIN or DEM.

Vertical datum: NAVD88 uses a fixed benchmark (Father Point, Quebec) and orthometric heights; NGVD29 is an older datum differing by up to about 1 m in places.

Hydrographic survey accuracy standards (IHO S-44) define orders: Special Order (a = 0.25 m, b = 0.0075), Order 1a (a = 0.5 m, b = 0.013), Order 1b, and Order 2.

Volume computations in dredging use pre- and post-dredge surfaces; payment is typically by in-situ or hopper volume, and the surveyor must document the method and datum.

A deed description that is ambiguous may be reformed by a court upon clear and convincing evidence of mutual mistake; a surveyor's opinion is evidence, not a judicial determination.

Unwritten rights: prescriptive easement, adverse possession, boundary by agreement, boundary by acquiescence, and estoppel can establish or move a boundary without a deed.

A boundary by agreement requires a dispute or uncertainty, an agreement, and performance or possession consistent with the agreed line.

Junior-senior rights: when a grantor conveys a portion of land and later conveys the remainder, the earlier (senior) conveyance generally prevails over the later (junior) one to the extent of any overlap.

Water boundary: meander lines are not boundary lines; they approximate the water's edge for area computation and do not control the boundary.

Monument evidence: a called-for monument that is found in place and undisturbed generally controls over a distance call; a monument set by the surveyor does not control over an original monument.

The surveyor's report should state the basis of bearings, datum, monument found/set, and any discrepancies between record and occupation.

Chain of title: a title search reveals recorded instruments affecting the parcel; unrecorded interests and prescriptive rights may not appear in the record.

Geodetic azimuth vs. grid azimuth: grid azimuth = geodetic azimuth − convergence (with sign convention depending on hemisphere and zone).

State Plane zones: some states have multiple zones (e.g., California has 6, Texas has 5); a project crossing a zone boundary requires transformation between zones.

Scale factor for Transverse Mercator: k = k₀(1 + x²/(2R²)) approximately, where x is the distance from the central meridian; k₀ = 0.9996 for UTM.

Ellipsoid height h can be obtained from GNSS; orthometric height H = h − N, where N is the geoid undulation from a model such as GEOID18.

Latitude/longitude to State Plane: use published projection equations or NGS software; do not interpolate between zones.

Datum realization: NAD83(2011) differs from NAD83(NA2011) and from WGS84 by up to about 1–2 m; always state the epoch and realization.

Great-circle distance: d = R·σ, where σ is the central angle from the spherical law of cosines or haversine formula; use for long baselines.

Azimuth from coordinates: α = atan2(ΔE, ΔN); quadrant must be resolved to a full 0°–360° bearing.

Traverse computations: latitude = distance × cos(azimuth); departure = distance × sin(azimuth); Σlatitude and Σdeparture should close to zero for a closed loop.

Angular misclosure for a closed polygon = sum of interior angles − (n − 2)×180°; distribute equally or by weighted rule.

Precision ratio = total linear misclosure / total traverse length; express as 1:N.

Error propagation: for a function f(x,y), σf² = (∂f/∂x)²σx² + (∂f/∂y)²σy² + 2(∂f/∂x)(∂f/∂y)σxy.

Chi-square test: computed χ² = vᵀWv / (n − u) compared to a table value at a chosen confidence level; a large value suggests a blunder or wrong weights.

Level loop adjustment: distribute misclosure proportionally to the number of setups or to the distance; check against the allowed misclosure (e.g., 0.05 ft√M for ordinary leveling).

Resection and intersection: resection determines an occupied point from known points; intersection determines an unknown point from two known stations.

Network design: redundancy (degrees of freedom) improves blunder detection; a minimally constrained adjustment fixes one station and one azimuth to define the datum.

Total station face-left and face-right readings: the mean of the two face readings eliminates collimation error and vertical index error.

Prism constant: a 0 mm prism and a −30 mm prism differ by 30 mm; using the wrong constant biases every distance by that amount.

Atmospheric correction: EDM distances are corrected using temperature, pressure, and humidity; the correction is typically ppm-level and can exceed 100 ppm in extreme conditions.

GNSS observation: static surveys require longer occupation for long baselines; rapid static uses short occupations (5–20 min) for baselines under about 10–15 km.

Coordinate transformation: a Helmert 7-parameter transformation (3 translations, 3 rotations, scale) converts between datums; a 4-parameter (2D) transformation is used for local grid shifts.

Digital terrain model: breaklines, spot shots, and mass points define the surface; check that the TIN honors breaklines and does not create spurious triangles.

Field data collection: coding and feature codes automate linework; check that codes match the feature table and that attributes are complete.

Quality control: repeat measurements, independent checks (e.g., a second occupation or a different instrument), and comparison to known control points.

Lot line adjustment: a minor reconfiguration of two or more lots that does not create additional lots; typically requires local approval and a recorded deed or plat.

Subdivision map act (California example) or state plat act: requirements for tentative map, final map, and parcel map vary by state and local ordinance.

Dedication: an offer of land for public use (streets, parks) that is accepted by the public entity; acceptance may be by resolution or by use.

Easement by necessity: arises when a parcel is landlocked and access is required; it terminates when the necessity ends.

Legal description by aliquot parts: e.g., the SW¼ of the NE¼ of Section 14, T3N, R2E; area = 40 acres (¼ × ¼ × 640).

Section subdivision: a section is 1 mile square (640 acres); quarter sections are 160 acres; quarter-quarter sections are 40 acres.

Plat review: check for closure, monumentation, easements, setbacks, and compliance with zoning; a plat should not be recorded until all signatures and approvals are obtained.

Corner monumentation: original government corners (GLO) are protected by law; destruction or removal may be a criminal offense in many states.

Grade: percent grade = (vertical difference / horizontal distance) × 100; a 2% grade over 100 ft rises 2 ft.

Cut/fill staking: mark the cut or fill at the stake; the grade rod reading minus the design grade gives the cut or fill.

Horizontal curve layout: deflection angle for a chord = (chord length / (2R)) in radians; set stakes by deflection from the tangent.

Vertical curve: the high or low point occurs where the grade is zero; x = −g₁L/(g₂ − g₁).

Earthwork: the prismoidal formula is more accurate than average end area for tapering volumes; use it for large grade changes.

Construction tolerances: foundations, utilities, and pavement each have specified tolerances; document as-built deviations.

Site layout: establish horizontal and vertical control, set benchmarks, and protect them from construction activity.

Machine guidance: verify the design model and the local coordinate system; check a known point before grading.

Standard of care: the degree of care and skill ordinarily exercised by members of the profession under similar circumstances; it is not a warranty of perfection.

Scope of services: a written contract should define the survey type (boundary, ALTA, topographic), deliverables, and exclusions.

Conflict of interest: disclose any relationship with a party that could impair objectivity; avoid contingent fees for boundary opinions.

Confidentiality: client information should not be disclosed without consent except as required by law or to defend against a claim.

Continuing education: most states require 15–30 hours per renewal cycle, with a portion in ethics or surveying law.

Seal and signature: only a licensee may seal work; sealing work not performed by the licensee or under their supervision is a violation.

Expert witness: testimony must be based on facts and accepted methods; a surveyor may testify about boundary evidence but the court decides the boundary.

Records: retain field notes, computations, and correspondence for the period required by state law; records may be discoverable in litigation.

Map projection: conformal projections preserve angles (Lambert, Transverse Mercator); equal-area projections preserve area (Albers); equidistant projections preserve distance from a point or along a line.

Scale: a 1:1,000 map is larger scale than a 1:24,000 map; the larger-scale map shows more detail.

Contour interval: choose based on map scale and terrain; a smaller interval shows more detail but can clutter the map.

GIS data quality: positional accuracy, attribute accuracy, completeness, logical consistency, and lineage are the five elements of spatial data quality.

Raster resolution: cell size determines the level of detail; a 1 m DEM cannot resolve features smaller than about 2 m.

Coordinate transformation in GIS: use the correct datum and projection; reprojecting from NAD27 to NAD83 without a datum transformation shifts features by tens of meters.

LiDAR: returns are classified; a bare-earth DEM is created from ground returns; check for vegetation and building artifacts.

Metadata: document source, date, accuracy, and processing steps; metadata supports data sharing and reproducibility.

Tide reduction: observed depths are reduced to chart datum by subtracting the predicted or observed tide height at the time of the sounding.

Sound speed: sound travels faster in warmer, saltier, and deeper water; a sound velocity probe measures the profile.

Multibeam coverage: swath width depends on depth and beam angle; overlap between adjacent lines ensures complete coverage.

IHO S-44 orders: Special Order, Order 1a, Order 1b, and Order 2; each specifies total vertical uncertainty (TVU) and horizontal uncertainty.

Topographic survey: collect breaklines at grade changes, edges of pavement, and water features; spot elevations supplement the breaklines.

Vertical datum: NAVD88 is the current U.S. vertical datum; local tidal datums (MLLW, MHW) are used for hydrographic charts.

Volume computation: use the same datum and method for pre- and post-dredge surveys; document the surface models and the method.

Hydrographic positioning: use RTK or DGPS for horizontal position; check the position against known control points.

Rules of construction: a deed is construed as a whole; specific calls control general calls; monuments control distances; and a call to an adjoiner may control over a distance.

A call for a natural monument (river, tree, rock) controls over a call for an artificial monument if the natural monument is more certain and permanent.

A call for an artificial monument (iron pin, stone) controls over courses and distances if the monument is identified and undisturbed.

Courses and distances control over area; area is the least reliable call and is used only as a check.

Ambiguity in a deed may be resolved by the parties' practical construction (their conduct) and by the surrounding circumstances.

Boundary by acquiescence: a long-standing line recognized by the parties may be enforced even without a dispute, depending on state law.

Prescriptive easement: use must be adverse, open, notorious, continuous, and for the statutory period; exclusivity is not required.

Adverse possession: possession must be hostile, actual, open, notorious, exclusive, and continuous; some states require payment of taxes or color of title.

Geoid model: GEOID18 provides geoid undulations in the U.S.; the model is referenced to NAD83(2011) and NAVD88.

Ellipsoid height from GNSS: h = H + N; if N is unknown, use a geoid model or a local benchmark.

State Plane coordinates: the combined factor = elevation factor × scale factor; grid distance = ground distance × combined factor.

Scale factor: for Lambert, the scale factor is 1 at the standard parallels and less than 1 between them; for Transverse Mercator, the scale factor is k₀ at the central meridian.

Convergence: the angle between grid north and true north; it is positive east of the central meridian in the northern hemisphere.

Datum transformation: use NGS tools (NADCON, HTDP) for accurate transformations; a simple translation is not sufficient for precise work.

UTM: the central meridian scale factor is 0.9996; the false easting is 500,000 m; the false northing is 0 m in the northern hemisphere and 10,000,000 m in the southern hemisphere.

Geodetic coordinates: latitude, longitude, and ellipsoid height; convert to ECEF coordinates using the ellipsoid parameters.

Least squares: the observation equations are A x = L + v; the normal equations are N x = AᵀWL; the solution is x = N⁻¹AᵀWL.

Covariance matrix: Σx = σ₀² N⁻¹; the standard deviations of the unknowns are the square roots of the diagonal elements.

A posteriori variance factor: σ₀² = vᵀWv / (n − u); it should be close to 1 if the weights are correct.

Error ellipse: the semi-major and semi-minor axes are the square roots of the eigenvalues of the covariance matrix; the orientation is given by the eigenvectors.

Confidence region: the 95% confidence ellipse uses a scale factor of 2.4477 for 2D; the 95% confidence interval for 1D uses 1.96.

Blunder detection: use the standardized residual or the data snooping method; a large residual indicates a blunder.

Traverse adjustment: the compass rule distributes errors proportionally to distance; the transit rule distributes proportionally to latitude and departure.

Leveling: the misclosure is distributed proportionally to the number of setups or to the distance; check against the allowed misclosure.

Total station: the horizontal angle is the mean of face-left and face-right readings; the vertical angle is the mean of the zenith angles.

EDM: the distance is corrected for atmospheric conditions, prism constant, and instrument offset; the correction is applied in ppm.

GNSS: the accuracy depends on the baseline length, the number of satellites, and the PDOP; a PDOP above 6 is generally unacceptable for precise work.

RTK: the rover receives corrections from a base station or a network; the fix solution requires integer ambiguity resolution.

Static GNSS: long occupations (30 min to hours) are required for long baselines; the accuracy is typically 5 mm + 1 ppm.

Digital level: the bar-coded staff is read automatically; the accuracy is typically 0.3 mm/km double run.

Laser scanning: the point cloud is registered using targets or cloud-to-cloud matching; the accuracy is typically 2–6 mm at 10–50 m.

UAV: the GSD is calculated as pixel size × flying height / focal length; ground control points are required for accurate mapping.

Metes and bounds: the description must close; the error of closure should be within an acceptable tolerance (e.g., 1:10,000).

Curve data: the plat should show R, Δ, L, LC, chord bearing, and the tangent bearing.

Area: the area of a lot is computed from the coordinates; the area should match the record area within an acceptable tolerance.

Easements: the description should show the width, centerline, and the burdened parcel; the easement should be recorded.

Subdivision: the plat should show all lots, streets, easements, and monuments; the plat must be approved and recorded.

Zoning: the lot must meet the minimum area, width, and setback requirements; a nonconforming lot may be buildable under grandfathering.

Monumentation: set monuments at all corners and at curve points; record the monument type and cap.

Legal description: the description should be sufficient to locate the parcel without reference to other documents; it should include the basis of bearings and the datum.

Cut and fill: cut = existing − design; fill = design − existing; the volume is computed by average end area or prismoidal formula.

Mass diagram: the ordinate is the cumulative volume; the balance point is where the cumulative volume is zero; the haul distance is the area under the mass diagram.

Vertical curve: the elevation at any point is y = y_PVC + g₁x + ((g₂ − g₁)/2L)x²; the high or low point is where the grade is zero.

Horizontal curve: the deflection angle for a chord is Δ/2; the chord length is 2R sin(Δ/2).

Slope staking: the catch point is where the design slope intersects the existing ground; the horizontal distance is (grade difference) / (slope difference).

Construction layout: establish control, set benchmarks, and protect them; check the design against the site datum.

As-built: verify the constructed improvements against the design; document deviations and their resolution.

Machine control: verify the design model and the local coordinate system; check a known point before grading.

Standard of care: the degree of care and skill ordinarily exercised by members of the profession; it is not a guarantee of perfection.

Contract: the scope, deliverables, schedule, fee, and limitations of liability should be in writing.

Conflict of interest: disclose any financial interest in the property or transaction; avoid contingent fees for boundary opinions.

Confidentiality: client information should not be disclosed without consent except as required by law.

Continuing education: most states require 15–30 hours per renewal cycle, with a portion in ethics or surveying law.

Seal and signature: only a licensee may seal work; sealing work not performed by the licensee or under their supervision is a violation.

Expert witness: testimony must be based on facts and accepted methods; the court decides the boundary, not the surveyor.

Records: retain field notes, computations, and correspondence for the period required by state law.

Map projection: conformal projections preserve angles; equal-area projections preserve area; equidistant projections preserve distance.

Scale: a 1:1,000 map is larger scale than a 1:24,000 map; the larger-scale map shows more detail.

Contour interval: choose based on map scale and terrain; a smaller interval shows more detail but can clutter the map.

GIS data quality: positional accuracy, attribute accuracy, completeness, logical consistency, and lineage.

Raster resolution: cell size determines the level of detail; a 1 m DEM cannot resolve features smaller than about 2 m.

Coordinate transformation: use the correct datum and projection; reprojecting from NAD27 to NAD83 without a datum transformation shifts features by tens of meters.

LiDAR: returns are classified; a bare-earth DEM is created from ground returns; check for vegetation and building artifacts.

Metadata: document source, date, accuracy, and processing steps; metadata supports data sharing and reproducibility.

Tide reduction: observed depths are reduced to chart datum by subtracting the tide height at the time of the sounding.

Sound speed: sound travels faster in warmer, saltier, and deeper water; a sound velocity probe measures the profile.

Multibeam coverage: swath width depends on depth and beam angle; overlap between adjacent lines ensures complete coverage.

IHO S-44 orders: Special Order, Order 1a, Order 1b, and Order 2; each specifies total vertical uncertainty and horizontal uncertainty.

Topographic survey: collect breaklines at grade changes, edges of pavement, and water features; spot elevations supplement the breaklines.

Vertical datum: NAVD88 is the current U.S. vertical datum; local tidal datums (MLLW, MHW) are used for hydrographic charts.

Volume computation: use the same datum and method for pre- and post-dredge surveys; document the surface models and the method.

Hydrographic positioning: use RTK or DGPS for horizontal position; check the position against known control points.

Monument controls over distance: a found original monument that is undisturbed generally controls over a distance call in the deed.

Natural monument controls over artificial monument: a river or tree call may control over an iron pin if the natural monument is more certain.

Courses and distances control over area: area is the least reliable call and is used only as a check.

Ambiguity is construed against the grantor: the grantor is responsible for the language and any ambiguity is resolved in favor of the grantee.

Practical construction: the parties' conduct over time may be used to interpret an ambiguous deed.

Boundary by acquiescence: a long-standing line recognized by the parties may be enforced even without a dispute, depending on state law.

Prescriptive easement: use must be adverse, open, notorious, continuous, and for the statutory period; exclusivity is not required.

Adverse possession: possession must be hostile, actual, open, notorious, exclusive, and continuous; some states require payment of taxes or color of title.

Geoid model: GEOID18 provides geoid undulations in the U.S.; the model is referenced to NAD83(2011) and NAVD88.

Ellipsoid height from GNSS: h = H + N; if N is unknown, use a geoid model or a local benchmark.

State Plane coordinates: the combined factor = elevation factor × scale factor; grid distance = ground distance × combined factor.

Scale factor: for Lambert, the scale factor is 1 at the standard parallels and less than 1 between them; for Transverse Mercator, the scale factor is k₀ at the central meridian.

Convergence: the angle between grid north and true north; it is positive east of the central meridian in the northern hemisphere.

Datum transformation: use NGS tools (NADCON, HTDP) for accurate transformations; a simple translation is not sufficient for precise work.

UTM: the central meridian scale factor is 0.9996; the false easting is 500,000 m; the false northing is 0 m in the northern hemisphere and 10,000,000 m in the southern hemisphere.

Geodetic coordinates: latitude, longitude, and ellipsoid height; convert to ECEF coordinates using the ellipsoid parameters.

Least squares: the observation equations are A x = L + v; the normal equations are N x = AᵀWL; the solution is x = N⁻¹AᵀWL.

Covariance matrix: Σx = σ₀² N⁻¹; the standard deviations of the unknowns are the square roots of the diagonal elements.

A posteriori variance factor: σ₀² = vᵀWv / (n − u); it should be close to 1 if the weights are correct.

Error ellipse: the semi-major and semi-minor axes are the square roots of the eigenvalues of the covariance matrix; the orientation is given by the eigenvectors.

Confidence region: the 95% confidence ellipse uses a scale factor of 2.4477 for 2D; the 95% confidence interval for 1D uses 1.96.

Blunder detection: use the standardized residual or the data snooping method; a large residual indicates a blunder.

Traverse adjustment: the compass rule distributes errors proportionally to distance; the transit rule distributes proportionally to latitude and departure.

Leveling: the misclosure is distributed proportionally to the number of setups or to the distance; check against the allowed misclosure.