# Lidar Base Specification: Glossary

10 Nov.,2022

LiDAR Mapping Services

accuracy: The closeness of an estimated value (for example, measured or computed) to a standard or accepted (true) value of a particular quantity. See precision.

• accuracy, absolute: A measure that accounts for all systematic and random errors in a dataset. Absolute accuracy is stated with respect to a defined datum or reference system.

• accuracyr (ACCr): The National Standards for Spatial Data Accuracy (NSSDA) (Federal Geographic Data Committee, 1998) reporting standard in the horizontal component that equals the radius of a circle of uncertainty, such that the true or theoretical horizontal location of the point falls within that circle 95 percent of the time.

• ACCr = 1.7308 * RMSEr

• See RMSEr.

• accuracyz (ACCz): The NSSDA reporting standard in the vertical component that equals the linear uncertainty value, such that the true or theoretical vertical location of the point falls within that linear uncertainty value 95 percent of the time.
• ACCz = 1.9600 * RMSEz

• See RMSEz.

• accuracy, horizontal: The horizontal (radial) component of the positional accuracy of a dataset with respect to a horizontal datum, at a specified confidence level. See accuracyr.

• accuracy, local: The uncertainty in the coordinates of points with respect to coordinates of other directly connected, adjacent points at the 95-percent confidence level.

• accuracy, network: The uncertainty in the coordinates of mapped points with respect to the geodetic datum at the 95-percent confidence level.

• accuracy, positional:  The accuracy at the 95-percent confidence level of the position of features, including horizontal and vertical positions, with respect to horizontal and vertical datums.

• accuracy, relative: A measure of variation in point-to-point accuracy in a dataset. In light detection and ranging (lidar), this term may also specifically mean the positional agreement between points within a swath, adjacent swaths within a lift, adjacent lifts within a project, or between adjacent projects.

• accuracy, vertical: The measure of the positional accuracy of a dataset with respect to a specified vertical datum at a specified confidence level or percentile. See accuracyz.

aggregate nominal pulse density (ANPD): A variant of nominal pulse density that expresses the total expected or actual density of pulses located in a specified unit area resulting from multiple passes of the lidar instrument, or a single pass of a platform with multiple lidar instruments, over the same target area. In all other respects, ANPD is identical to nominal pulse density (NPD). In single coverage collection, ANPD and NPD will be equal. See aggregate nominal pulse spacing, nominal pulse density, nominal pulse spacing.

aggregate nominal pulse Spacing (ANPS): A variant of nominal pulse spacing that expresses the typical or average lateral distance between pulses in a lidar dataset resulting from multiple passes of the lidar instrument, or a single pass of a platform with multiple lidar instruments, over the same target area. In all other respects, ANPS is identical to nominal pulse spacing (NPS). In single coverage collections, ANPS and NPS will be equal. See aggregate nominal pulse density, nominal pulse density, nominal pulse spacing

aqueduct: A structure designed to transport domestic or industrial water from a supply source to a distribution point, often by gravity.

artifacts: An inaccurate observation, effect, or result, especially one resulting from the technology used in scientific investigation or from experimental error. In bare-earth elevation models, artifacts are detectable surface remnants of buildings, trees, towers, telephone poles, or other elevated features; also, detectable artificial anomalies that are introduced to a surface model by way of system specific collection or processing techniques. For example, corn-row effects of profile collection, star and ramp effects from multidirectional contour interpolation, or detectable triangular facets caused when vegetation canopies are removed from lidar data.

attitude: The position of a body defined by the angles between the axes of the coordinate system of the body and the axes of an external coordinate system. In photogrammetry, the attitude is the angular orientation of a camera (roll, pitch, yaw), or of the photograph taken with that camera, with respect to some external reference system. With lidar, the attitude is normally defined as the roll, pitch, and heading of the instrument at the instant an active pulse is emitted from the sensor.

bald earth: Nonpreferred term. See bare-earth.

bare-earth (bare earth): Digital elevation data of the terrain free from vegetation, buildings, and other man-made structures. Elevations of the ground.

blunder: A mistake resulting from carelessness or negligence.

boresight: Calibration of a lidar sensor system equipped with an Inertial Measurement Unit (IMU) and Global Positioning System (GPS) to determine or establish the accurate position of the instrument (x, y, z) with respect to the GPS antenna and orientation (roll, pitch, heading) of the lidar instrument with respect to straight and level flight.

breakline: A linear feature that describes a change in the smoothness or continuity of a surface. The two most common forms of breaklines are as follows:

• breakline, soft: Ensures that known z-values along a linear feature are maintained (for example, elevations along a pipeline, road centerline, or drainage ditch), and ensures that linear features and polygon edges are maintained in a triangulated irregular network (TIN) surface model by enforcing the breaklines as TIN edges. They are generally synonymous with 3-dimensional (3D) breaklines because they are depicted with series of x, y, z coordinates. Somewhat rounded ridges or the trough of a drain may be collected using soft breaklines.

• breakline, hard: Defines interruptions in surface smoothness (for example, to define streams, rivers, shorelines, dams, ridges, building footprints, and other locations) with abrupt surface changes. Although some hard breaklines are 3D breaklines, they are typically depicted as 2-dimensional (2D) breaklines because features such as shorelines and building footprints are normally depicted with series of x, y coordinates only, which are often digitized from digital orthophotos that include no elevation data. See mass point.

bridge: A structure carrying a road, path, railroad, canal, aircraft taxiway, or any other transit between two locations of higher elevation over an area of lower elevation. A bridge may traverse a river, ravine, road, railroad, or other obstacle. “Bridge” also includes but is not limited to aqueduct, drawbridge, flyover, footbridge, overpass, span, trestle, and viaduct. In mapping, the term “bridge” is distinguished from a roadway over a culvert in that a bridge is an elevated deck that is not underlain with earth or soil. See culvert, saddle.

calibration (lidar systems): The process of identifying and correcting for systematic errors in hardware, software, or data. Determining the systematic errors in a measuring device by comparing its measurements with the markings or measurements of a device that is considered correct. Lidar system calibration falls into two main categories:

• calibration, instrument: Factory calibration includes radiometric and geometric calibration unique to each manufacturer’s hardware and tuned to meet the performance specifications for the model being calibrated. Instrument calibration can only be assessed and corrected by the instrument manufacturer.

• calibration, data: The lever arm calibration determines the sensor-to-GPS-antenna offset vector (the lever arm) components relative to the antenna phase center. The offset vector components are redetermined each time the sensor or aircraft GPS antenna are moved or repositioned. Because normal aircraft operations can induce slight variations in component mounting, the components are normally field calibrated for each project, or even daily, to determine corrections to the roll, pitch, yaw, and scale calibration parameters.

calibration point: Nonpreferred term. See control point

cell (pixel): A single element of a raster dataset. Each cell contains a single numeric value of information representative of the area covered by the cell. Although the terms “cell” and “pixel” are synonymous, in this specification “cell” is used in reference to nonimage rasters such as digital elevation models (DEMs), whereas “pixel” is used in reference to image rasters such as lidar intensity images.

check point (checkpoint): A surveyed point (x, y or x, y, z) used to estimate the positional accuracy of a geospatial dataset against an independent source of greater accuracy. Check points are independent from, and may never be used as, control points on the same project.

classification (of lidar): The classification of lidar point cloud returns in accordance with a classification scheme to identify the type of target from which each lidar return is reflected. The process allows future differentiation between bare-earth terrain points, water, noise, vegetation, buildings, other man-made features, and objects of interest.

confidence level: The percentage of points within a dataset that are estimated to meet the stated accuracy; for example, accuracy reported at the 95-percent confidence level means that 95 percent of the positions in the dataset will have an error with respect to true ground position that are equal to or smaller than the reported accuracy value.

consolidated vertical accuracy (CVA): Replaced by the term vegetated vertical accuracy (VVA) in this specification, CVA is the term used by the National Digital Elevation Program (NDEP) guidelines for vertical accuracy at the 95th percentile in all land cover categories combined (NDEP, 2004). See percentile, vegetated vertical accuracy.

control point (calibration point): A surveyed point used to geometrically adjust a lidar dataset to establish its positional accuracy relative to the real world. Control points are independent from, and may never be used as, check points on the same project.

CONUS: Continental United States, the conterminous 48 States.

culvert: A tunnel carrying a stream or open drainage under a road or railroad or through another type of obstruction to natural drainage. Typically constructed of formed concrete or corrugated metal and surrounded on all sides, top, and bottom by earth or soil.

data void: In lidar, a gap in the point cloud coverage caused by surface nonreflectance of the lidar pulse, instrument or processing anomalies or failure, obstruction of the lidar pulse, or improper collection flight planning. Any area greater than or equal to four times the ANPS, squared, measured using first returns only, is considered to be a data void.

datum: A set of reference points on the Earth's surface against which position measurements are made, and (usually) an associated model of the shape of the Earth (reference ellipsoid) to define a geographic coordinate system. Horizontal datums (for example, the North American Datum of 1983 [NAD 83]) are used for describing a point on the Earth's surface, in latitude and longitude or another coordinate system. Vertical datums (for example, the North American Vertical Datum of 1988 [NAVD 88]) are used to measure elevations or depths. In engineering and drafting, a datum is a reference point, surface, or axis on an object against which measurements are made.

digital elevation model resolution: The linear size of each cell of a raster DEM. Features smaller than the cell size cannot be explicitly represented in a raster model. DEM resolution may also be referred to as cell size, grid spacing, or ground sample distance.

digital elevation model (DEM): See four different definitions below:

• A popular acronym used as a generic term for digital topographic and bathymetric data in all its various forms. Unless specifically referenced as a digital surface model (DSM), the generic DEM normally implies x, y coordinates and z-values of the bare-earth terrain void of vegetation and man-made features.

• As used by the U.S. Geological Survey (USGS), a DEM is the digital cartographic representation of the elevation of the land at regularly spaced intervals in x and y directions, using z-values referenced to a common vertical datum.

• As typically used in the United States and elsewhere, a DEM has bare-earth z-values at regularly spaced intervals in x and y directions; however, grid spacing, datum, coordinate systems, data formats, and other characteristics may vary widely.

• A “D-E-M” is a specific raster data format once widely used by the USGS. DEMs are a sampled array of elevations for a number of ground positions at regularly spaced intervals.

digital surface model (DSM): Similar to DEMs except that they may depict the elevations of the top surfaces of buildings, trees, towers, and other features elevated above the bare-earth. DSMs are especially relevant for telecommunications management, air safety, forest management, and 3D modeling and simulation.

digital terrain model (DTM): See two different definitions below:

• In some countries, DTMs are synonymous with DEMs, representing the bare-earth terrain with uniformly spaced z-values, as in a raster.

• As used in the United States, a “DTM” is a vector dataset composed of 3D breaklines and regularly spaced 3D mass points, typically created through stereo photogrammetry, that characterize the shape of the bare-earth terrain. Breaklines more precisely delineate linear features whose shape and location would otherwise be lost. A DTM is not a surface model and its component elements are discrete and not continuous; a TIN or DEM surface must be derived from the DTM. Surfaces derived from DTMs can represent distinctive terrain features much better than those generated solely from gridded elevation measurements. A lidar point dataset combined with ancillary breaklines is also considered a DTM.

discrete return lidar: Lidar system or data in which important peaks in the waveform are captured and stored. Each peak represents a return from a different target, discernible in vertical or horizontal domains. Most modern lidar systems are capable of capturing multiple discrete returns from each emitted laser pulse. See waveform lidar.

elevation: The distance measured upward along a plumb line between a point and the geoid. The elevation of a point is normally the same as its orthometric height, defined as H in the equation:

$$H = {h-N}$$,

where

$$h$$    is equal to the ellipsoid height and

$$N$$   is equal to the geoid height.

first return (first-return): The first important measurable part of a return lidar pulse.

flightline: A single pass of the collection aircraft over the target area. Commonly used incorrectly to refer to the data resulting from a flightline of collection. See swath.

fundamental vertical accuracy (FVA): Replaced by the term nonvegetated vertical accuracy (NVA), in this specification, FVA is the term used by the National Digital Elevation Program (NDEP) guidelines for vertical accuracy at the 95-percent confidence level in open terrain only where errors should approximate a normal error distribution. See nonvegetated vertical accuracy, accuracy, confidence level.

geographic information system (GIS): A system of spatially referenced information, including computer programs that acquire, store, manipulate, analyze, and display spatial data.

geospatial data: Information that identifies the geographic location and characteristics of natural or constructed features and boundaries of earth. This information may be derived from—among other things—remote-sensing, mapping, and surveying technologies. Geospatial data generally are considered to be synonymous with spatial data; however, the former always is associated with geographic or Cartesian coordinates linked to a horizontal or vertical datum, whereas the latter (for example, generic architectural house plans) may include dimensions and other spatial data not linked to any physical location.

ground truth: Verification of a situation without errors introduced by sensors or human perception and judgment.

hillshade: A function used to create an illuminated representation of the surface, using a hypothetical light source, to enhance terrain visualization effects.

horizontal accuracy: Positional accuracy of a dataset with respect to a horizontal datum. According to the National Standards for Spatial Data Accuracy (NSSDA), horizontal (radial) accuracy at the 95-percent confidence level is defined as ACCr. See accuracy, horizontal.

hydraulic modeling: The use of digital elevation data, rainfall-runoff data from hydrologic models, surface roughness data, and information on hydraulic structures (for example, bridges, culverts, dams, weirs, and sewers) to predict flood levels and manage water resources. Hydraulic models are based on computations involving liquids under pressure, and many other definitions of hydraulic modeling exist that are not associated with terrain elevations (for example, modeling of hydraulic lines in aircraft and automobiles).

hydrologic modeling: The computer modeling of rainfall and the effects of land cover, soil conditions, and terrain slope to estimate rainfall runoff into streams, rivers, and lakes. Digital elevation data are used as part of hydrologic modeling.

hydrologically conditioned (hydro-conditioned): Processing of a DEM or TIN so that the flow of water is continuous across the entire terrain surface, including the removal of all isolated sinks or pits. The only sinks that are retained are the real ones on the landscape. Although hydrologically enforced is relevant to drainage features that generally are mapped, hydrologically conditioned is relevant to the entire land surface and is done so that water flow is continuous across the surface, whether that flow is in a stream channel or not. The purpose for continuous flow is so that relations and (or) links among basins and (or) catchments can be known for large areas.

hydrologically flattened (hydro-flattened): Processing of a lidar-derived surface (DEM or TIN) so that mapped waterbodies, streams, rivers, reservoirs, and other cartographically polygonal water surfaces are flat and, where appropriate, level from bank to bank. Additionally, surfaces of streams, rivers, and long reservoirs demonstrate a gradient change in elevation along their length, which is consistent with their natural behavior and the surrounding topography. In traditional maps that are compiled photogrammetrically, this process is accomplished automatically through the inclusion of measured breaklines in the DTM; however, because lidar does not inherently include breaklines, a DEM or TIN derived solely from lidar points will depict water surfaces with unsightly and unnatural artifacts of triangulation. The process of hydro-flattening typically involves the addition of breaklines along the banks of specified waterbodies, streams, rivers, and ponds. These breaklines establish elevations for the water surfaces that are consistent with the surrounding topography and produce aesthetically acceptable water surfaces in the final DEM or TIN. Unlike hydro-conditioning and hydro-enforcement, hydro-flattening is not driven by any hydrologic and hydraulic (H&H) modeling requirements but solely by cartographic mapping needs.

hydrologically enforced (hydro-enforced): Processing of mapped waterbodies so that lakes and reservoirs are level and so that streams and rivers flow downhill; for example, a DEM, TIN, or topographic contour dataset with elevations removed from the tops of selected drainage structures (bridges and culverts) so as to depict the terrain under those structures. Hydro-enforcement enables hydrologic and hydraulic models to depict water flowing under these structures, rather than appearing in the computer model to be dammed by them because of road deck elevations higher than the water levels. Hydro-enforced TINs also use breaklines along shorelines and stream centerlines (for example, where these breaklines form the edges of TIN triangles along the alignment of drainage features). Shore breaklines for streams and rivers would be 3D breaklines with elevations that decrease as the stream flows downstream; however, shore breaklines for lakes or reservoirs would have the same elevation for the entire shoreline if the water surface is known or assumed to be level throughout.

intensity (lidar): For discrete-return lidar instruments, intensity is the recorded amplitude of the reflected lidar pulse at the moment the reflection is captured as a return by the lidar instrument. Lidar intensity values can be affected by many factors such as the instantaneous setting of the instrument’s Automatic Gain Control and angle of incidence and thus cannot be equated to a true measure of energy for discrete return systems. In full-waveform systems, the entire reflection is sampled and recorded, and true energy measurements can be made for each return or overall reflection. Intensity values for discrete returns derived from a full-waveform system may or may not be calibrated to represent true energy. Lidar intensity data make it possible to map variable textures in the form of a grayscale image. Intensity return data enable automatic identification and extraction of objects such as buildings and impervious surfaces and can aid in lidar point classification. In spite of their similar appearance, lidar intensity images differ from traditional panchromatic images in several important ways:

• Lidar intensity is a measure of the reflection of an active laser energy source, not natural solar energy.

• Lidar intensity images are aggregations of values at point samples. The value of a pixel does not represent the composite value for the area of that pixel.

• Lidar intensity images depict the surface reflectivity within an extremely narrow band of the electromagnetic spectrum, not the entire visible spectrum as in panchromatic images.

• Lidar intensity images are strongly affected by the angle of incidence of the laser to the target and are subject to unnatural shadowing artifacts.

• The values on which lidar intensity images are based may or may not be calibrated to any standard reference. Intensity images usually contain wide variation of values within swaths, between swaths, and between lifts.

For these reasons, lidar intensity images must be interpreted and analyzed with unusually high care and skill.

LAS: A public file format for the interchange of 3D point cloud data between data users. The file extension is .las. (ASPRS, 2011)

last return: The last important measurable part of a return lidar pulse.

lattice: A 3D vector representation method created by a rectangular array of points spaced at a constant sampling interval in x and y directions relative to a common origin. A lattice differs from a grid in that it represents the value of the surface only at the lattice mesh points rather than the elevation of the cell area surrounding the centroid of a grid cell.

lever arm: A relative position vector of one sensor with respect to another in a direct georeferencing system. For example, with aerial mapping cameras, lever arms are positioned between the inertial center of the Inertial Measurement Unit (IMU) and the phase center of the Global Positioning System (GPS) antenna, each with respect to the camera perspective center within the lens of the camera.

lidar: An instrument that measures distance to a reflecting object by emitting timed pulses of light and measuring the time difference between the emission of a laser pulse and the reception of the pulse’s reflection(s). The measured time interval for each reflection is converted to distance, which when combined with position and attitude information from GPS, IMU, and the instrument itself, allows the derivation of the 3D point location of the reflecting target’s location.

lidar systems: See calibration.

lift: A lift is a single takeoff and landing cycle for a collection platform (fixed or rotary wing) within an aerial data collection project, often lidar.

local accuracy: See accuracy, local.

mass point(s): Irregularly spaced points, each with x, y, z coordinates, typically (but not always) used to form a TIN.  When generated manually, mass points are ideally chosen to depict the most significant variations in the slope or aspect of TIN triangles; however, when generated automatically (for example, by lidar), mass point spacing and pattern depend upon the characteristics of the technologies used to acquire the data. Mass points are usually used in conjunction with breaklines. See breakline.

metadata: Any information that is descriptive or supportive of a geospatial dataset, including formally structured and formatted metadata files (for example, eXtensible Markup Language [XML]-formatted Federal Geographic Data Committee [FGDC] metadata), reports (collection, processing, quality assurance/quality control [QA/QC]), and other supporting data (for example, survey points, shapefiles).

monotonic: In mathematics, a function that varies such that it either increases or decreases, but never both. As used in this specification, it describes a hydrographic breakline that continuously flows either level or downhill, but never uphill.

nominal pulse density (NPD): A common measure of the density of a lidar dataset; NPD is the typical or average number of pulses within a specified areal unit. NPD is typically expressed as pulses per square meter. This value is predicted in mission planning and empirically calculated from the collected data, using only the first (or last) return points as surrogates for pulses. As used in this specification, NPD refers to single swath, single instrument data, whereas ANPD describes the overall pulse density resulting from multiple passes of the lidar instrument, or a single pass of a platform with multiple lidar instruments, over the same target area. NPD is more commonly used in high-density collections (greater than or equal to 1 pulses per square meter [pls/m2]), with its inverse, NPS, being used in low-density collections (less than or equal to 1 pls/m2). Assuming meters are being used in both expressions, NPD can be calculated from NPS using the formula NPD = 1/NPS 2. See aggregate nominal pulse density, aggregate nominal pulse spacing, nominal pulse spacing.

nominal pulse spacing (NPS): A common measure of the density of a lidar dataset, NPS is the typical or average lateral distance between pulses in a lidar dataset, typically expressed in meters and most simply calculated as the square root of the average area per first return point. This value is predicted in mission planning and empirically calculated from the collected data, using only the first (or last) return points as surrogates for pulses. As used in this specification, NPS refers to single swath, single instrument data, whereas ANPS describes the overall pulse spacing resulting from multiple passes of the lidar instrument, or a single pass of a platform with multiple lidar instruments, over the same target area. NPS is more commonly used in low-density collections (greater than or equal to 1 m NPS), with its inverse, NPD, being used in high-density collections (less than 1 m NPS). Assuming meters are being used in both expressions, NPS can be calculated from NPD using the formula NPS = 1/√NPD. See aggregate nominal pulse density, aggregate nominal pulse spacing, nominal pulse density.

nonvegetated vertical accuracy (NVA): Replaces fundamental vertical accuracy (FVA). The vertical accuracy at the 95-percent confidence level in nonvegetated open terrain, where errors should approximate a normal distribution. See fundamental vertical accuracy.

overlap: Any part of a swath that also is covered by any part of any other swath.

penstock: A structure designed to convey water into the turbine of a hydro-electric generating plant. Typically the main pipes within a large hydro-electric dam.

percentile: A measure used in statistics indicating the value below which a given percentage of observations (absolute values of errors) in a group of observations fall. For example, the 95th percentile is the value (or score) below which 95 percent of the observations may be found.  There are different approaches to determining percentile ranks and associated values. This specification recommends the use of the following equations for computing percentile rank and percentile as the most appropriate for estimating the vegetated vertical accuracy (VVA). Note that percentile calculations are based on the absolute values of the errors because it is the magnitude of the errors, not the sign, which is of concern. The percentile rank (n) is first calculated for the desired percentile using the following equation:

$$n=(((\frac{P}{100})*(N-1))+1)$$

where:

$$n$$    is the rank of the observation that contains the Pth percentile,
$$P$$    is the proportion (of 100) at which the percentile is desired (for example, 95 for 95th percentile), and
$$N$$   is the number of observations in the sample dataset.

Once the rank of the observation is determined, the percentile (Qp) can then be interpolated from the upper and lower observations using the following equation:

Qp = (A[nw] + (nd * (A[nw + 1] - A[nw])))

where:

Qp  is the Pth percentile; the value at ran n;
A    is the array of the absolute values of the samples, indexed in ascending order from 1 to N;
A[i]  is the sample value of array A at index i (for example, nw  or nd). i must be an integer between 1 and N;
n    is the rank of the observation that contains the Pth percentile;
nw  is the whole number component of n (for example, 3 of 3.14); and
nd   is the decimal component of n (for example, 0.14 of 3.14).

pixel: See cell.

playa: An undrained desert basin that periodically fills with water to form a temporary lake. Playas drain directly into the ground. They can often be identified by having apparent inlet channels but no outlets, and with flat and level floors.

point classification: The assignment of a target identity classification to a particular lidar point or group of points.

point cloud: One of the fundamental types of geospatial data (others being vector and raster), a point cloud is a large set of 3D points, typically from a lidar collection. As a basic geographic information system (GIS) data type, a point cloud is differentiated from a typical point dataset in several key ways:

• point clouds are almost always 3D,

• point clouds have an order of magnitude more features than point datasets, and

• individual point features in point clouds do not typically possess individually meaningful attributes; the informational value in a point cloud is derived from the relations among large numbers of features. See raster, vector.

• See raster, vector

precision (repeatability): The closeness with which measurements agree with each other, even though they may all contain a systematic bias. See accuracy.

point family: The complete set of multiple returns reflected from a single lidar pulse.

preprocessing: In lidar, the preprocessing of data most commonly refers to those steps used in converting the collected GPS, IMU, instrument, and ranging information into an interpretable X-Y-Z point cloud, including generation of trajectory information, calibration of the dataset, and controlling the dataset to known ground references.

postprocessing: In lidar, postprocessing refers to the processing steps applied to lidar data point clouds, including point classification, feature extraction (for example, building footprints, hydrographic features, and others), tiling, and generation of derivative products (DEMs, DSMs, intensity images, and others).

raster: One of the fundamental types of geospatial data (others being vector and point cloud), a raster is an array of cells (or pixels) that each contain a single piece of numeric information representative of the area covered by the cell. Raster datasets are spatially continuous; with respect to DEMs, this quality creates a surface from which information can be extracted from any location. As spatial arrays, rasters are always rectangular; cells are most often square. Co-located rasters can be stored in a single file as layers, as with color digital images. See raster, vector.

repeatability: See precision.

resolution: The smallest unit a sensor can detect or the smallest unit a raster DEM depicts. The degree of fineness to which a measurement can be made. “Resolution” is also used to describe the linear size of an image pixel or raster cell.

root mean square difference (RMSD): The square root of the average of the set of squared differences between two dataset coordinate values taken at identical locations. RMSD differentiates from root mean square error (RMSE) because neither dataset is known to be more or less accurate than the other, and the differences cannot be regarded as errors. RMSD is used in lidar when assessing relative accuracy, both intraswath and interswath. See root mean square error.

root mean square error (RMSE): The square root of the average of the set of squared differences between dataset coordinate values and coordinate values from an independent source of higher accuracy for identical points. The RMSE is used to estimate the absolute accuracy of both horizontal and vertical coordinates when standard or accepted values are known, as with GPS-surveyed check points of higher accuracy than the data being tested. In the United States, the independent source of higher accuracy is expected to be at least three times more accurate than the dataset being tested.

• RMSEr  The horizontal root mean square error in the radial direction that includes both x and y coordinate errors.
• $$\sqrt{(RMSE_x^2+RMSE_y^2)}$$
•
• where:
• RSMEx  is the RMSE in the x direction, and
• RSMEY  is the RMSE in the y direction.
• RMSEx  The horizontal root mean square error in the x direction (easting).
• $$\sqrt{\sum{\frac{(x_n-x_n')^2}{N}}}$$
•
• where:
• xn    is the set of N x  coordinates being evaluated,
• x'n   is the corresponding set of check point x coordinates for the points being evaluated,
• N     is the number of x coordinate check points, and
• n     is the identification number of each check point from 1 through N.
• RMSEy The horizontal root mean square error in the y direction (northing).
• $$\sqrt{\sum{\frac{(y_n-y_n')^2}{N}}}$$
• where:
• yn    is the set of N y  coordinates being evaluated,
• y'n   is the corresponding set of check point y coordinates for the points being evaluated,
• N     is the number of y coordinate check points, and
• n     is the identification number of each check point from 1 through N.
• RMSEz The vertical root mean square error in the z direction (elevation).
• $$\sqrt{\sum{\frac{(z_n-z_n')^2}{N}}}$$
• where:
• zn    is the set of N z  values (elevations) being evaluated,
• z'n   is the corresponding set of check point elevations for the points being evaluated,
• N     is the number of z check points, and
• n     is the identification number of each check point from 1 through N.

saddle: The lowest area between two opposing higher terrain features, usually connecting two areas of lower terrain, as in a mountain pass. Used in this specification to reference the area exposed by the removal or exclusion of a bridge deck from a DEM. See bridge.

siphon:  A structure designed to convey water by gravitational force over, or under, an obstruction. Often seen as vertical pipes in smaller ponds with earthen dams that convey overflow water under the dam.

spatial distribution: In lidar, the regularity or consistency of the point density within the collection. The theoretical ideal spatial distribution for a lidar collection is a perfect regular lattice of points with equal spacing on x and y axes. Various factors prevent this ideal from being achieved, including the following factors:

• instrument design (oscillating mirrors),

• mission planning (difference between along-track and cross-track pulse spacing), and

• in-flight attitude variations (roll, pitch, and yaw).

standard deviation: A measure of spread or dispersion of a sample of errors around the sample mean error. It is a measure of precision, rather than accuracy; the standard deviation does not account for uncorrected systematic errors.

supplemental vertical accuracy (SVA): Merged into the Vegetated Vertical Accuracy (VVA) in this specification, SVA is the NDEP guidelines term for reporting the vertical accuracy at the 95th percentile in each separate land cover category where vertical errors may not follow a normal error distribution. See percentile, vegetated vertical accuracy.

swath: The data resulting from a single flightline of collection. Swaths can be considered as one of five general types:

• project: Originally planned to cover the project area.

• cross-tie: Originally planned and within the project area, but intended for calibration/boresighting purposes only.

• calibration: Data collected for calibration/boresighting purposes only, usually over the base airport, and often not within the project area.

• fill-in: Additional swaths collected to fill unplanned gaps or areas of low data density discovered in the planned project area collection.

• other: Any swath that does not meet the above definitions.

• See flightline.

systematic error: An error whose algebraic sign and, to some extent, magnitude bears a fixed relation to some condition or set of conditions. Systematic errors follow some fixed pattern and are introduced by data collection procedures, processing, or given datum.

topology: The spatial relationship between geographic features in a common space. Examples particularly relevant to this specification include precise coincidence of ending and beginning vertices of lines in a continuous network (stream connectivity), and consistent line direction (from high to low) corresponding to streamflow direction.

triangulated irregular network (TIN): A vector data structure that partitions geographic space into contiguous, nonoverlapping triangles. In lidar, the vertices of each triangle are lidar points with x, y, and z values. In most geographic applications, TINs are based on Delaunay triangulation algorithms in which no point in any given triangle lies within the circumcircle of any other triangle.

uncertainty (of measurement): A parameter that characterizes the dispersion of measured values, or the range in which the “true” value most likely lies. It can also be defined as an estimate of the limits of the error in a measurement (where “error” is defined as the difference between the theoretically unknowable “true” value of a parameter and its measured value). Standard uncertainty refers to uncertainty expressed as a standard deviation.

vector: One of the fundamental types of geospatial data (others being raster and point cloud), vectors include a variety of data structures that are geometrically described by x, y, and potentially z coordinates. Vector data subtypes include points, lines, and polygons. A DTM consisting of mass points and breaklines is an example of a vector dataset; a TIN is a vector surface. See point cloud, raster.

vegetated vertical accuracy (VVA): Replaces supplemental vertical accuracy (SVA) and CVA. An estimate of the vertical accuracy, based on the 95th percentile, in vegetated terrain where errors do not necessarily approximate a normal distribution. See percentile, nonvegetated vertical accuracy.

waveform lidar: Lidar system or data in which the entire reflection of the laser pulse is fully digitized, captured, and stored. Discrete return point clouds can be extracted from the waveform data during postprocessing. See discrete return lidar.

well-distributed: For a dataset covering a rectangular area that has uniform positional accuracy, check points should be distributed so that points are spaced at intervals of at least 10 percent of the diagonal distance across the dataset and at least 20 percent of the points are located in each quadrant of the dataset (adapted from the National Standards for Spatial Data Accuracy of the Federal Geographic Data Committee, 1998). As related to this specification, these guidelines are applicable to each land cover class for which check points are being collected.

withheld: Within the LAS file specification, a single bit flag indicating that the associated lidar point is geometrically anomalous or unreliable and should be ignored for all normal processes. These points are retained because of their value in specialized analysis. Withheld points typically are identified and tagged during preprocessing or through the use of automatic classification routines. Examples of points typically tagged as withheld are listed below:

• spatial outliers in either the horizontal or vertical domains, and

• geometrically unreliable points near the edge of a swath.