DIGITAL TERRAIN MODELS
Digital Terrain Model Specifications are for three-dimensional coordinates of points taken in a specified pattern and recorded on a computer-compatible media.
Grid is a type of a digital terrain model which consist of elevations taken at regularly spaced intervals in two horizontal coordinate directions. These two horizontal directions should coincide with the northing and easting of the specified project coordinate system. Grids are advantageously used for measuring original and final terrain of borrow areas for quantity purposes.
Cross Sections are measured perpendicular to and at regular intervals and on low and high points along a centerline or baseline. Each cross section or baseline, measured for each significant break in the terrain. This type is used for defining the original terrain along the proposed line for the highway.
Re-measurement defines the terrain after earthwork is completed. Original measurement may have been in grid or cross-section pattern; re-measurement extends only as far as construction operations changed the terrain, and it includes measurement of the same grid points or along the same cross section lines, plus significant breaks in the surface as altered by construction.
Critical Points define the topography of an area using three coordinate. From such data other descriptions of the topography can be derived, such as contours or cross sections along any chosen alignment.
The digital terrain model shall be grid, cross section, re-measurement or critical point type, whichever will be specified and applicable to the particular project. For grid digital terrain models, the maximum spacing shall be fifteen (15) meters, and likewise the same maximum space for cross section, re- measurement or critical points. For cross sections the spacing shall be measured along the centerline or base line.
NJDOT shall show on a map the area to be included in the digital terrain model by outlining it or by drawing a centerline or base line and specifying the width of coverage. A written description of the area in question may further define the area.
Master Units = meter (M)
Sub Units = millimeter (MM)
Resolutions = 10 positional units per millimeter (MM)
The Root-Mean-Square-Error (RMSE) which is defined as the square root of the quotient of the sum of the squares of the errors divided by the number of measurements, or
RMSE = [(S e2)/n]1/2
in which “e” is the error at each point (the difference between the value used as a standard and the value being tested) and “n” is the total number of points tested. The elevations, in meters, of all points tested shall not exceed the limit specified by NJDOT for the work. (Refer to Section 6-06 to discussions and procedures for the selection of RMSE limits). No individual error shall exceed three(3) times the specified limit for root-mean-square error. The average error (the algebraic sum of the individual test point errors, taking into consideration their signs, divided by the number of test points) shall not exceed three-tenths the specified limit for root-mean-square error.
The root-mean-square- error and the average error for any individual cross section or any individual group of grid points shall not exceed twice the limits established for the entire digital terrain model.
The first consideration for a photogrammetrically produced digital terrain model is the relationship of the average depth of excavation and the needed accuracy. The average depth of excavation is the square meters of surface in the excavation areas divided by the number of cubic meters of materials to be excavated in the same areas. The root-mean-square-error for pay quantities should not exceed the average depth of excavation multiplied by the factor 0.03, but even in the heaviest excavation, the root-mean-square-error should not exceed 0.30 meters. If preliminary quantities only are being computed which will not be used for pay, the factor may be relaxed to 0.10 and the maximum to 0.45 meters. With the average depth of excavation estimated, this gives the root-mean-square-error to specify for ground surveyed digital terrain models and serves as a guide as to limits of usefulness of the photogrammetric method.
The second consideration for photogrammetrically produced digital terrain models is the capability of the stereoplotters. On open ground (no interfering cover) with uniform slopes, a double projection stereoplotter should be capable of producing elevations with a root-mean-square-error as small as 1/6 000 of the flight height; and an optical train stereoplotter, as small as 1/10 000 of the flight height. With irregular slopes, these reduce to about 1/5 000 and 1/8 000, and, with interfering ground cover, to about 1/3 000 and 1/5 000. This tells us that, considering the minimum flight height of 270 meters satisfactory pay quantities can be produced by a double projection instrument if the average depth of excavation is as small as (270/(6 000 x 0.03) = 1.5 meters, and by an optical train stereoplotter if the average depth of cut is as small as (270/10 000 x0.03) = 0.90 meter. For preliminary quantities for design, the minimum depth of excavation using a double projection stereo-plotter is as small as (270/6 000 x 0.10) = 0.45 meter, and using an optical trained stereoplotter, as small as (270/(10 000 x 0.10) = 0.27 meter. Photogrammetric quantities are usually more accurate and less costly for moderate and heavier work, but for very light work, ground surveys are necessary.
Since average depth of cut is only an estimation when planning a photogrammetric mission, and flight height may be the quantity to define, a third consideration is the accuracy required for the use to be made of the quantities and types of terrain. Pay quantities where the slopes are uniform, i.e. flat to rolling terrain, require a root-mean-square-error of 0.06 meter or less, and where slopes are irregular, i.e. rugged terrain, require a root-mean-square error of 0.20 meter or less. For preliminary quantities, flat to rolling terrain with no interfering ground cover requires a root-mean-square-error of 0.20 meter or less, and rugged terrain with interfering cover requires 0.50 meter or less.
A digital terrain model for computing earthwork quantities for pay shall not be accepted until at least four (4) percent of the grid points or of the cross sections have been compared with ground surveyed data and have met specifications requirements. Grid points shall be in groups of 20 to 40 contiguous points. Cross sections shall be complete sections. No more than two (2) adjacent sections may be included at any location. These single sections, pairs of sections, or groups of points shall be distributed over the project area so as to be representative of the whole digital terrain model. A digital terrain model for computing preliminary earthwork quantities for design only may be accepted when the agency has made enough ground surveyed or stereoplotter tests to assure that the work meets all specification requirements.