Digital terrain modeling of small stream channels with a total-station
theodolite
Richard F. Keim
a,*, Arne E. Skaugset
a, Douglas S. Bateman
baOregon State University, Forest Engineering Department, 215 Peavy Hall, Corvallis, OR 97331, USA bOregon State University, Forest Science Department, 026 Forest Sciences Laboratory, Corvallis, OR 97331 USA
Received 7 May 1998; received in revised form 12 December 1998; accepted 3 February 1999
Abstract
A Digital Terrain Model (DTM) is an alternative to traditional measures of stream channel morphology that allows for ex-traction of many dierent types of data. This paper describes a method of creating high-resolution Digital Terrain Models of stream channels using an electronic, digital, total-station theodolite and standard methods of land surveying, and also includes consid-erations unique to hydrological application. Included is a detailed description of one application in Oregon, and also suggestions of how to apply the method in other research of morphology. Ó 1999 Elsevier Science Ltd. All rights reserved.
Keywords:Digital terrain model; Mapping; Channel morphology
1. Introduction
Quanti®cation of channel morphology is a require-ment for a variety of subdisciplines within surface hydrology and geomorphology. Morphological charac-terizations taken from data collection in the ®eld com-monly are limited in scope, are not useful for multiple objectives, and often suer from low precision or poor accuracy. For example, wildland hydrologists have used many dierent methods to quantify the shape of small, headwater streams, including cross sections (e.g. Refs. [14,16,18]), longitudinal pro®les (e.g. Refs. [10,15,19]), or qualitative delineation of aquatic habitat units such as pools and ries (Refs. [1,10]). Most of these methods collect two-dimensional data, although the processes and conditions they seek to describe are three-dimen-sional. Qualitative data, which some methods collect, are insucient to quantitatively link hydrological processes in the channel to morphology (Ref. [8]).
In research of channel morphology, the most broadly useful information is a three-dimensional model of the stream channel. One such model is a Digital Terrain Model (DTM), which is a digital representation of a surface designed to show topographic dierence. The
digital format is usable in many software packages, in-cluding geographic information systems (GIS), so mul-tiple quantitative analyses are possible and data may be extrapolated for multiple research objectives. Precision and accuracy of DTMs are limited only by the amount of eort expended during collection of data, so can be as high as required for nearly any application.
Digital terrain models provide a quantitative basis for analyses of many aspects of channel morphology, in-cluding sediment transport, local scour and ®ll, and bank stability. A time series of DTMs allows changes in the channel to be measured precisely without prior designation of exact sample points. A single DTM serves as a base for research of microtopographic eects on velocity, turbulence, and scour. Also, companion data may be easily incorporated to a DTM using a GIS. These may be the object of research that must be con-sidered in the context of the DTM, or they may simply enhance the usefulness of the DTM. As an example, Ref. [22] and Keim et al. (in preparation) describe movement of coarse debris in channels using a chronosequence of DTMs.
We have developed a method to collect data for the creation of DTMs by making topographic surveys of stream channels using a total-station theodolite (``total station''). A total station collects data electronically and incorporates an electronic distance-measuring device that eliminates the need for manual measurements of
*Corresponding author. Tel.: 0515; fax: 001-541-737-4316; e-mail: [email protected]
distance. While others have made maps of streams, using taped distances from a baseline (Ref. [3]), dumpy level and range ®nder (Ref. [9]), or survey by stadia with a theodolite (Refs. [4,11,12]), these methods result in either an imprecise DTM or a less complete model, and are subject to a large amount of error from bias by personnel and are very susceptible to mistakes during collection of data (Ref. [6]). Using a total station elim-inates many of these problems, and is also faster than other mapping methods capable of producing compa-rable data.
A DTM may be generated from source data by a variety of methods, but for traditional land surveys, the most common is creation of a Triangular Irregular Network (TIN) (Ref. [2]). A TIN is, in general, a con-tinuous network of triangles connecting points of data within a set. In this application, the vertices of the tri-angles in the TIN are de®ned by critical points on the ground that describe breaks in slope (Ref. [5]). The data in a topographic survey consist of three-dimensional coordinates of the critical points that will later become vertices of the triangles in the TIN.
Despite the substantial requirements of equipment and time, a DTM and topographic map made with a total station is a useful research tool for intensively measuring local channel features and processes. It can also be used to assess the accuracy and precision of other methods that measure channel morphology. In this paper, we present the methods we used to create DTMs and topographic maps of small, headwater stream channels using a total station. We also recom-mend ways to use the method for hydrogeomorphic research.
2. Topographic surveying of mountain streams
We selected reaches of three small (second and third order from USGS 7.5 min maps), headwater streams in the Oregon Coast Range for our research of channel morphology. The approach was to delineate control and experimental reaches, apply a treatment to the experi-mental reaches, and then study eects of treatment with a chronosequence of DTMs generated using data col-lected with a total station. We were speci®cally inter-ested in quantifying changes in physical aquatic habitat for salmonid ®sh, but could have used the data for many other uses.
2.1. Layout of topographic survey
After the reaches for the experiment had been se-lected, we established control points for the topographic survey along each reach, outside the active channel. We situated the control points about 50±100 m apart, so that the views from them collectively aorded a view of
the entire experimental reach. Reaches were 460±700 m long, requiring seven to ten control points each. The control points were 2.5 cm´5 cm (1 in ´2 in) wooden
stakes (``hubs'') or 1.25-cm (0.5 in) diameter steel bars driven into the ground.
We established a local coordinate system for each survey, assigning an arbitrary elevation and north and east coordinates for the ®rst control point (hereafter: point of beginning [POB]). A second control point was set due north of the POB at the longest practicable distance from the POB for use as a reference backsight. Once we had established coordinates for the POB and backsight, we traversed through the control points to establish their coordinates and elevations.
2.2. Topographic mapping procedures in the channel
Using a Leica T1010 electronic digital theodolite equipped with a Leica DI1001 electronic distance mea-suring device (Leica AG, Heerbrugg, Switzerland), we took radial side ``shots'', composed of a horizontal an-gle, vertical anan-gle, and slope distance, from each control point to points in and adjacent to the stream. With this information, the coordinates of each point were deter-mined relative to the POB. Along with coordinates, each point was given a description and a unique point iden-ti®er. The points were selected as local minima and maxima that would best describe the ground surface when used to create a TIN.
We strati®ed the density of side shots by location relative to the idealized cross section illustrated in Fig. 1, so that the highest density of shots would be within the area of greatest interest. Between the toes of slope (the area of maximum interest), we took shots at a density sucient to describe features larger than 15 cm (0.5 ft) in size. A greater number of shots would increase the resolution of the resulting DTM, but would require more time. We took side shots outside the channel only at gross topographic breaks in slope to roughly depict the riparian area outside the channel on the resulting maps.
To describe the banks, we took shots along the top of both banks and at the toe of each slope. We rarely took
shots between the top of the bank and the toe of slope on each bank. Where breaks in slope occurred so that large features lay between the top of the bank and the toe, we moved the toe of slope shot upslope to describe the feature and used thalweg shots to describe the true toe. Exceptions were when unusual features such as uprooted trees occurred between the top and toe of the slope; these were captured with supplementary shots.
We used ``breaklines'', which force the terrain-mod-eling algorithm to triangulate between points such that triangle axes lie along breaks in slope, to connect shots along the banks. The top of each bank and the toe of each slope, corresponding to the idealized cross-section in Fig. 1, were each described by a breakline because they are natural boundaries in our streams. The channel did not always conform to our idealized cross section, but we continued all breaklines through non-standard reaches so we could use them as boundaries between areas of dierent sampling intensities. In practice, we usually chose locations of breaklines based on both the breaks in slope and areas of ¯uvial activity. For
exam-ple, breaklines de®ning the top of bank were always outside of any obvious recent changes in morphology, even if the most distinct break in slope was nearer the thalweg.
Overhanging banks present a special problem in to-pographic mapping (Fig. 2), because there is no stan-dard method for representing an empty space below the surface of the ground on a topographic map (Ref. [2]). It is nearly impossible to take shots beneath most over-hanging banks. The most common option is to place the rod at an estimated, oset position. We used several methods to try to solve this problem, and each method had tradeos in accuracy (Table 1). We settled on a method (option 4 from Table 1) that ignored overhangs that consisted primarily of roots and vegetation. Un-dercuts were also ignored if, in our judgment, including them would have resulted in a signi®cant error in mea-surement of volume of the bank. To describe banks with ignored undercuts, we estimated oset positions of the rod for shots below the overhangs. Most of the over-hangs we ignored consisted primarily of vegetation, and the undercuts we ignored were minor compared to stream volume.
2.3. Non-topographic features
Some features of the stream channel and the adjacent ¯ood plain were included in the survey but not the DTM. We included the location of large woody debris in our surveys (Fig. 3). We also took shots at the estimated limits of aquatic habitat units (Ref. [1]) to help describe the relationship between morphology and habitat.
Fig. 2. Potential errors in measurement due to overhanging banks. Breaks in slope that cannot be represented without an oset shot are indicated byX.
Table 1
Options of protocols for measurement of overhanging banks (refer to Fig. 2)
Protocol Advantages Disadvantages Recommendations
1. Allow breaklines to follow true toe slope and top of bank
Most accurate measurement of both stream bottom and bank
Results in breakline that cross horizontally - must be manually edited for accurate model; must estimate oset positions of the rod for shots below overhangs; still ignores other vertical breaks in slope within overhangs
Use when the higher accuracy is important enough to warrant increased complexity in analysis of data
2. Ignore overhangs; treat as a vertical bank
Accurate measurement of stream bottom; precise
Volume of bank underestimated; must estimate oset position of the rod for shots below overhangs (prone to error)
Use when measurements of the bank are less important than mea-surements of the stream bottom
3. Ignore undercuts; treat as a vertical bank
Accurate measurement of top of bank; precise; no estimations of oset position of rod necessary
Measurement of stream bottom inaccurate; volume of stream underestimated; overestimate volume of bank
Use when measurements of the bank are more important than measurements of the stream bottom
4. Ignore selected undercuts or measure some undercuts dierently than others; based on forming agents and morphology
Compromise between accuracy and precision; most eective way to distinguish between overhangs of vegetation and those of soil and rock
Criteria for selection of which undercuts to include is dicult to de®ne, therefore this is an imprecise method; potential for bias from observers; must estimate some oset positions of the rod for shots below overhangs (prone to error)
2.4. Terrain modeling and data analysis
We used Leica's LISCAD Plus Surveying and Engi-neering Environment software (Leica AG and LIStech, Boronia, Vic., Australia) and Surfer (Golden Software, Golden, CO) to process the data from surveys, and to create a DTM and a topographic map of the channels (Figs. 3 and 4). To create a DTM, this software forms a TIN by triangulating between points and interpolating elevations linearly along the axes of the triangles. The breaklines are important in this process, since the al-gorithm will not triangulate across a breakline. Once triangulation is complete, the software draws contour lines to connect extrapolated points of equal elevation.
Once the DTMs were complete, we were able to use LISCAD and other software to calculate depths or volumes of pools, sinuosity of the channel, ratios of width to depth, and other measures of morphology. Repeat topographic surveys of the same stream reaches enabled us to quantify such processes as local scour and ®ll and make reach-level assessments of aggradation, degradation, and stability of banks.
2.5. Repetition of surveys
We repeated the topographic survey of each stream channel once per year at periods of low ¯ow (Fig. 4); some changes in channel morphology occurred much more frequently than once annually, but the changes
that were relevant to our objectives occurred on an an-nual or semi-anan-nual frequency. For example, Fig. 4 shows a small pool developing under a piece of large woody debris, caused by local scour. This scour does not occur during summer low-¯ow, but the eects of higher ¯ows from the previous winter persist and constitute the physical aquatic habitat for much of the following year.
3. Recommendations
3.1. Survey setup
Before establishing a network of control points, re-searchers should decide whether to orient the network of control points to true north, property boundaries, or sea level. True north can be important if, for example, solar angles or topographic shading of the stream are to be included in the research. Orientation to boundaries usually is important only when boundaries of ownership are involved. If orientation is necessary, it can be ac-complished by a solar shot, star shot, section survey, or by using a Global Positioning System (GPS) device. It may be important to establish elevation relative to mean sea level if, for example, tides or ¯ood levels are integral to research objectives. In establishing elevation, greatest accuracy can be achieved by referencing the network of control points to a benchmark of known elevation, though a rough estimate from a topographic map may suce. A survey-grade GPS unit can be used to establish elevation, but inexpensive mapping-grade units may not be accurate enough for ®ne work.
There should be enough control points to allow un-obstructed views of the entire channel. However, there should not be more than necessary, because increasing the number of control points increases the potential for errors (Ref. [6]). We recommend closing the traverse if possible (i.e. including the ®rst control point in the network as the last as a check). Even if the traverse is not closed, frequently checking the backsight will reduce systematic error by operators. Leaving the traverse open can lead to many problems in reduction of data and deduction of errors, which are common when the work is done by people with limited surveying experience.
It is important to place control points where they will not be disturbed by maintenance of roads, vandalism, high stream ¯ow, or channel meanders. Recording at least three ties (measurements to established secondary marks such as nails in trees or secondary monuments in the ground) to control points reduces the chance that a control point will be lost, or if lost can be re-established. In our experience, steel bars are preferable to wooden stakes as control points because they are more durable and easier to use when setting up the instrument.
Control points should be established either where vegetative growth will not block the view in subsequent
surveys or where vegetation can be easily removed. Not all control points must be permanent, however. If needed, additional control points may be set temporarily for convenience in an individual survey.
3.2. Intensity of surveys
The choice of appropriate temporal and spatial in-tensity for topographic surveys should be based on
ob-jectives of the research, available resources,
characteristics of the channel, and the processes of
in-terest (Ref. [13]). Inappropriate intensity can lead to data that are not useful for the objectives of the research.
Choosing an appropriate temporal scale for repeti-tion of surveys requires knowledge of the stream and processes being examined. The appropriate scale might range from decades to minutes or even less. For exam-ple, we surveyed once year to measure characteristics that change primarily during storms in the winter and remain relatively stable during the summer. Ref. [8] surveyed a channel up to three times per day to measure
scour and ®ll in a glacial-outwash stream where mor-phology changed signi®cantly hourly. Ref. [7] suggested that an initial sampling to capture multiple temporal scales of change allows researchers to make more in-formed decisions about selecting an appropriate tem-poral scale. For example, conducting a pilot study of weekly, then monthly, then yearly surveys would allow better understanding of the temporal scale of the pro-cesses of interest if this is not already known.
The processes being studied help de®ne the appro-priate density of shots by de®ning the size of changes in the channel that are to be measured. It is important to de®ne spatial resolution by the sizes of the eects or by some threshold of size above which the changes are important, because incorrectly matching spatial scale or measurement to processes can lead to erroneous or spurious interpretations (Ref. [21]). For example, we did not attempt to measure small changes in morphology outside of the most ¯uvially active parts of the channel, because we assumed that such changes would be largely due to non-¯uvial forces such as animals or vegetation. Even within the channel, we limited interpretation of
channel changes to changes in morphology of P15 cm,
because we made no attempt to measure features smaller than this.
Besides the processes of interest, the appropriate density of shots is de®ned by the size of particles in the stream channel (Ref. [8]). As the size of substrate increases, the practically achievable resolution of sur-veys decreases; it would be necessary to map individ-ual particles for an accurate model if the desired resolution is ®ner than the dominant substrate in the channel.
Strati®cation of density of shots allows greater reso-lution where it is most useful. Reduced density can be useful when there are predictable regions of less ¯uvial activity or of larger substrate. Fig. 4 is an example of the eect of stratifying spatial intensity of surveying. Out-side the banks, low density of data is useful as little more than a suggestion of the landform. The banks them-selves are more precisely described, but there has been no eort to describe ®ne changes. Only between the banks are data dense enough to discern changes as small as 15 cm, which was the minimum spatial scale that was considered in this application.
Selection of temporal and spatial intensity should be linked. Since smaller features are more ephemeral, the appropriate density of shots increases as frequency of surveys increases. Practical considerations limit surveys as well. Our maximum speed was 240 shots per hour, equal to that reported in Ref. [8], though due to dense vegetation and time spent traveling to our research sites, some 300-m experimental reaches required up to six days to survey. Researchers planning large, detailed surveys should be aware that they require large invest-ments in time.
3.3. Methods of topographic mapping
Using breaklines when creating DTMs increases ac-curacy considerably (Ref. [2]). Examples of where breaklines are particularly useful are at still logs, linear features in bedrock, ridges in gravel bars, and areas of maximum depth in trench pools. For example, we used breaklines to help de®ne the banks, and imposing ad-ditional breaklines in the bottom of the channel would have increased accuracy. Breaklines should be de®ned concurrently with collection of data, since they are im-possible to impose during analysis of data without very speci®c descriptions of shots. Another option is to im-pose breaklines during proo®ng of topographic maps in the ®eld.
One way to make application of breaklines easier and more consistent in the ®eld is to match them to repeated features of channels. Often, these repeated features demarcate areas of dierent channel-forming processes that are important when describing morphology. For example, the cross-sectional representations that Rosgen [17] used to classify channel morphology could easily be adopted as standard cross-sections for a topographic survey.
When deciding upon a method for measuring un-dercut banks, it is important to remember that it is not possible to measure all con®gurations of overhanging banks using any of the methods listed in Table 1. Spaces with complex shapes and attributes often exist where undercut banks combine with roots or underground channels. The spatial and temporal variability of these features makes accurate measurements of the bank dif-®cult. Choosing a method to measure undercut banks involves deciding which characteristics of the bank should be measured most accurately, and should be based on which features are most important for objec-tives of a particular study.
Surveyors should identify and reduce error (Table 2). When inexperienced crews are involved, it is important to concentrate on reducing undetectable errors. Re-searchers who are unfamiliar with equipment can reduce random errors and blunders by attending training, or by hiring professional surveyors, though this can be ex-pensive.
3.4. Equipment and software for analysis of data
the nearest ®ve seconds or one second, so are suitable for almost any desired density of shots.
Many dierent software packages will reduce raw survey data, though software is usually designed spe-ci®cally for each data collector. Total stations that col-lect data internally are usually useful only with software for reduction that was designed for use with that in-strument. Instruments that send data to external col-lectors allow the used more choices of software for reduction of raw data, but can be less convenient to use in the ®eld.
Software for creating DTMs is sometimes packaged with the survey data reduction software, but there are other packages besides those speci®cally designed for applications in surveying. Software used for creation of DTMs uses a variety of algorithms (Ref. [2]), and cor-rect interpolation between points is dependent on a set of data that were collected for that speci®c algorithm. For example, using an algorithm that creates a TIN assumes that data were collected such that there are no breaks in slope between any shots, that shots were taken at local minima and maxima of elevation, and that the shots were spaced in a pattern that takes advantage of the algorithm's method of maximizing the eciency of the triangulation (Ref. [5]). By contrast, algorithms based on kriging expect data in somewhat regularly spaced intervals, and local minima and maxima are in-ferred instead of measured (Ref. [20]). When designing a survey, it is essential that researchers understand which method of interpolation will be used in the analysis. Inaccurate DTMs may result if created by an algorithm designed for a dierent type data than was collected.
Once data from the ®eld have been reduced, the data are three-dimensional coordinates that can be used by many programs designed for analysis of DTMs. The structure of the data enables a large number of strategies
of analysis and applications related to stream channel morphology. This versatility represents the major strength of an exhaustive set of data.
Acknowledgements
The authors thank Liz Dent, John Donahue, Jim Schroeder, and Vanessa Stone for helping develop the method in the ®eld. The Coastal Oregon Productivity Enhancement (COPE) program of the Oregon State University College of Forestry funded this research.
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Table 2
Errors associated with the method (modi®ed from [8])
Error type Examples of speci®c errors Detectability
Random (precision) Incorrect entry of manually recorded control network information
Detectable if the control network is designed to provide data redundancy or if the traverse is closed
Measurements associated with radial observations
Undetectable since there are no repeat observations, but minimized through the use of electronic data collection
Systematic (accuracy) Incorrect measurement of instrument, rod, or traverse target height
Undetectable unless procedures are heavily standardized or errors are gross and interpretable
Systematic and random Measurements associated with the control network
Detectable if observations are repeated during the control survey or if traverse is closed
Incorrect use of the instrument or rod: Out of level, incorrect backsight procedure, incorrect foresight procedure
Gross errors usually detectable, but ®ne errors undetectable
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