Marine Geodesy, 25:27– 36, 2002
C 2002 Taylor & Francis
Copyright °
0149-0419/02 $12.00 + .00
Digital Tide-Coordinated Shoreline
RONGXING LI
RUIJIN MA
KAICHANG DI
Department of Civil and Environmental Engineering and Geodetic Science
Ohio State University, Columbus, Ohio, USA
The shoreline is one of the most important features on earth’s surface. It is valuable to a
diverse user community. But the dynamic nature of the shoreline makes it difŽ cult to be
represented in a naturally dynamic style and to be utilized in applications. The ofŽ cially
used shoreline,for example in nauticalcharts,is the so-calledtide-coordinatedshoreline.
It is also the shoreline that makes the computation of shoreline changes and associated
environmentalchanges meaningful.Mapping of the tide-coordinatedshoreline has been
very costly. On the other hand, instantaneous shorelines extracted from different data
sources may be available. Also, high-resolutionsatellite and airborne imagery have the
capacity of stereo imaging and can be used to extract instantaneousshorelines at a high
accuracy and low cost. This article proposes an approach to derivation of digital tidecoordinated shorelines from (a) those instantaneous shorelines and (b) digital coastal
surface models and a digital water surface model. Some preliminary study results,
analysis, and the potential of the approach are discussed.
Keywords shoreline, tide-coordinatedshoreline, coastal terrain model, water surface
model
Shorelines are among the most important terrain features on earth’s surface. They are recognized by the International Geographic Data Committee (IGDC) as one of the 27 most
important features. The location and attributes of a shoreline are highly valued by a diverse user community (Lockwood 1997). Shorelines have never been stable in either their
long-term or short-term positions. The changes are caused by natural processes, human
activities, or both. Regardless of the causes, the shoreline changes impact their immediate environments either positively or negatively. Thus shoreline mapping and shoreline
change detection become critical to safe navigation, coastal resource management, coastal
environmental protection, sustainable coastal development, and planning.
By deŽ nition, a shoreline is a linear intersection of coastal land and the surface of a
water body (Figure 1). Because of the dynamic nature of the water body and the coastal land,
the shoreline changes all the time. Thus, this shoreline is usually called an instantaneous
shoreline. In a geographic information system (GIS) it is currently impossible to depict the
dynamic characteristics of the shoreline. In practice, the instantaneous shoreline cannot be
directly used for shoreline mapping and navigation, nor can it be employed for quantifying
Received 18 July 2001; accepted 12 October 2001.
We acknowledge funding from NSF Digital Government Program and Sea Grant—NOAA National Partnership Program and the Lake Erie Protection Fund (LEPF), and matching funding from the Coastal Service Center,
OfŽ ce of Coastal Survey, and National Geodetic Survey of NOAA.
Address correspondence to Rongxing Li, Department of Civil and Environmental Engineering and Geodetic
Science, The Ohio State University, Columbus, OH 43210-1275. E-mail: [email protected]
27
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R. Li et al.
FIGURE 1 A shoreline deŽ ned as a linear intersection between coastal land and a water
body.
shoreline changes. A shoreline that is deŽ ned based on a stable vertical datum can be treated
as a reference shoreline and used to differentiate shorelinechanges. Such a shoreline is called
a tide-coordinated shoreline, that is, the linear intersection between the coastal land and a
desired water level.
In the United States, internal shoreline mapping is the responsibility of the National
Oceanic and Atmospheric Administration (NOAA). The National Geodetic Survey (NGS)
of NOAA uses MHW (Mean High Water) and MLLW (Mean Lower Low Water) to deŽ ne
the tide-coordinated shorelines (Figure 2). MHW and MLLW are the averages of high and
lower low water levels, respectively, over a period of 19.2 lunar years. All high water heights
are included in the average of MHW, where the type of tide is either semidiurnal or mixed.
Where the type of tide is predominantly diurnal, only the higher high water heights are
FIGURE 2 The proŽ le of MHW and MLLW.
Digital Tide-Coordinated Shoreline
29
included in the average on those days when the tide is semidiurnal. The lower low water is
the lower of the two low water levels of any tidal day where the tide is of the semidiurnal or
mixed type. The single low water occurring daily during periods when the tide is diurnal is
considered to be lower low water (Shalowitz 1962). On NOAA nautical charts both MHW
and MLLW coordinated shorelines are shown on tidal areas. Figure 2 depicts the proŽ le of
MHW and MLLW.
A Review of Shoreline Mapping Techniques
The Ž rst shoreline mapping endeavor in the United States was in 1807, and the Ž rst shoreline survey was completed in 1834. Around the time of World War I, the entire U.S. coast,
except for Alaska, had been surveyed at least once. In the early years, the main device used
was the plane table, which can obtain a high accuracy. As control for shoreline mapping,
the surveying system was deŽ ned by a series of points with known latitudes and longitudes,
and this established the Ž rst geodetic surveying system. This geodetic system was called
the “line of sight” observation method in which each surveying point must be visible by at
least one other surveying point. This geodetic system evolved into more advanced surveying
methods like space-oriented observations, Bibly towers, electronic distance measurement
(EDM), and the Global Positioning System (GPS) (CSC 2001). In the early era of coastal
surveying, the mean high water line was delineated. The line was determined more from
physical appearance than precisely running spirit levels along the coast. What the topographer actually delineated were the markings left on the beach by the last proceeding high
water, barring the drift cast up by the storm tides (Shalowitz 1962). Plane table mapping
was replaced by photogrammetry during the onset of World War I. In 1919, an investigation
was started to evaluate the feasibility of aerial photography in compiling shoreline maps,
and by 1927 the full potential of photogrammetry to complement the production of charts
and maps was recognized. But until 1927, practically all the topographic surveys were
made by plane tables. Since 1927, aerial photographs and photogrammetric methods have
been utilized increasingly to provide the required topographic information along the coast
(Shalowitz 1962).
Analytical photogrammetry has been the primary technology for shoreline mapping.
With recent advances in digital photogrammetry, GPS, and other all-weather sensors, researchers have been exploring the potential of more efŽ cient and economic shoreline mapping techniques.Land vehicle based mobile mapping technologyin local shoreline mapping
uses GPS receivers and a beach vehicle to trace watermarks along the shorelines (Shaw and
Allen 1995; Li 1997). In contrast, regional and national shoreline mapping has been conducted by aerial photogrammetry and LIDAR (Light Detection and Ranging) depth data
(Slama et al. 1980; Ingham 1992). GPS technology has been applied to provide orientation
information and to enhance aerial photogrammetric triangulation (Lapine 1991; Merchant
1994; Bossler 1996). Recently, satellite-imaging systems have increasingly improved image resolution. A new generation of high-resolution (one-meter) satellite-imaging systems
has been or will be launched (Fritz 1996; Li 1998), including the IKONOS imaging system
with the capability of stereo imaging. Since the in-track stereo mode is provided, stereo
pairs that are necessary for deriving elevation information of objects can be formed in quasi
real time; the cross-track stereo requires additional time allowing the satellite to revisit
the same area from a neighboring track. An investigation of shoreline mapping using such
high-resolution satellite images demonstrated a promising shoreline mapping accuracy of
2 m and a great reduction of required ground control points (Zhou and Li 2000; Li et al.
2001).
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R. Li et al.
Digital Tide-Coordinated Shoreline
The objective of this article is to give the preceding review of shoreline mapping techniques
and to discuss new methods of tide-coordinated shoreline mapping. In current practice,
aerial photographs for shoreline mapping are taken when the water level reaches the desired
value (MLLW). This requires coordination between the water gauge reading and aerial photographing to make sure that the shoreline that appears in the images is the tide-coordinated
shoreline. We call this tide-coordinated shoreline physical tide-coordinated shoreline. In
the case of satellite imaging, the imaging technology has improved so much that the image
resolution is comparable to that of aerial photographs, and it also has stereo mapping capability. In principle, the images can be taken repeatedly within a short period. In addition,
it provides multispectral signals that are not available or are limited in the aerial imaging
case. However, it not realistic to arrange satellite imaging at the desired water levels. The
shorelines delineated from the satellite images are instantaneousshorelines. We believe that
there are relationships between the instantaneous shoreline and the tide-coordinated shoreline. We call the tide-coordinated shoreline thus derived digital tide-coordinated shoreline
(DTS).
Such a digital tide-coordinatedshoreline does not require the Ž eld coordinationbetween
the gauge reading and the aerial photography and can eliminate the associated costs. It
improves the shoreline mapping efŽ ciency by integrating instantaneous observations that
are more widely available and less costly. The tide-coordinated shoreline and shoreline
changes can be accurately computed, and future shorelines can also be generated through
scenarios. This shoreline mapping technology may mark the start of a new era of digital
shoreline mapping and coastal change detection and monitoring. Two approaches toward
generation of the digital tide-coordinated shoreline are discussed below.
Approach I: DTS from Instantaneous Shorelines
Figure 3 depicts the situation where instantaneous shorelines f (X ; Y ; Z )t 1 ; f (X; Y; Z )t2 ,
and f (X; Y; Z )t 3 at times t1 ; t2 , and t3 are derived from nontide-coordinated airborne or
satellite images. The objective is to compute the tide-coordinated shoreline F(X, Y, Z)
at the desired water level of MLLW. The lake shoreline in Figure 3 can be extended to
an open sea environment and should not affect the discussion in the remaining part of
the article. A simpliŽ ed model such as EPR (End-Point Rate) method may calculate a
recession/ advancing rate on each transect of the shoreline. The desired shoreline position
can then be estimated by a temporal interpolation or extrapolation. But the EPR method
assumes that the shoreline position changes in one direction and linearly, which does not
FIGURE 3 Instantaneous shorelines (t1 ; t2 , and t3 ) and the tide-coordinated shoreline.
Digital Tide-Coordinated Shoreline
31
match the situation in the real world. In Figure 3, the shoreline at t3 is between those at t1
and t2 , possibly because of the tidal effect. This demonstrates that an improved approach
should consider both the shoreline positions and water levels.
In principle, the general DTS function F(X, Y, Z) can be decomposed into
X D FX (Ä; 8; t );
Y D FY (Ä; 8; t ); and
(1 )
Z D FZ (Ä; 8; t );
which are functions of the coastland geometry Ä, water surface 8, and time t. The interaction
between Ä and 8 at a certain time t results in the DTS. To simplify the shoreline geometry,
we propose piece-wise polynomials to describe the shoreline in Figure 3. The particular
piece can be parameterized by a one-dimensional parameter s that starts from the beginning
and is measured along the shoreline. Equation (1) then becomes
X D FX (ao ; a1 ; a2 ; : : : ; an ; s; t );
Y D FY (bo ; b1 ; b2 ; : : : ; bn ; s; t ); and
(2 )
Z D FZ (co ; c1 ; c2 ; : : : ; cn ; s; t );
where ao (h); a1 (h); : : : ; cn (h) are temporal polynomial coefŽ cients that characterize the
geometric shape of the shoreline. They may themselves be represented as polynomials of
the water level h:
ao D ®oo C ®1o h C ®2o h 2 C : : : : : :
::: :::
(3 )
cn D ·on C ·1n h C ·2n h 2 C : : : : : :
The function F may take different forms according to characteristics of various coastal
areas. For example, we may adjust orders of a0 ; a1 ; : : : ; cn based on shoreline topography
( at, steep slope, bluff, wetland, etc.). We can change the order of s considering the long
shore topography; the detailed terms of the parameter h should represent the effect of the
tide and coastland change on the shoreline. Further, for each coefŽ cient in Equations (2)
and (3) a signiŽ cance coefŽ cient may be used to measure if the term is needed for this
particular piece of shoreline.
As observations, vertices of the instantaneous shorelines derived from satellite and
airborne images provide (X, Y, Z ) measurements in Equation (2) with given s and t. Gauge
station water level observationsare time series observations with locations. A preprocessing
of the gauge station data is needed to associate the locations of gauge stations with the
instantaneous shorelines, as well as times. These measurements contribute mostly to the
determination of the temporal relationships in Equation (3).
The entire shoreline is described by a collection of the polynomial pieces. There is
a need to investigate the ways and criteria for breaking the shoreline to pieces. We may
consider lengths, curvatures, topography, geological material types, hydrographic nature,
shoreline erosion rate, and other information from an existing coastal GIS. The overall
shoreline model requires that the shoreline pieces be continuous at the connections of
adjacent pieces, which should be enforced in an integrated adjustment of all observations.
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The coefŽ cients of Equations (2) and (3) are estimated using the Least Squares principle
in the global integrated adjustment. Finally, given the time and water level information, we
are able to determine the digital tide-coordinated shoreline.
In this way, the shoreline pieces are estimated globally in the least squares adjustment.
In addition to the temporal modeling, the overall shoreline shape, the detailed connection
between the neighboring pieces, and the internal shoreline topography within the pieces are
incorporated implicitly. This makes the new approach theoretically more comprehensive
and accurate than the existing point and change-rate-based models.
Approach II: DTS from Digital Models
The second approach toward generatinga DTS is to simulate the intersectionof the coastland
and the water surface. The coastland is represented by a coastal terrain model (CTM) that
contains topographic information in a narrow zone of the coast and near-shore bathymetry.
The topographic information can be derived from the one-meter resolution satellite stereo
imagery (for example, IKONOS) and airborne images. There is often a gap in the shallow
water area between the topographicmodel and the bathymetric data that are usually acquired
by a multibeam system and do not cover shallow water areas. LIDAR mapping seems to
Ž ll this gap very efŽ ciently. The CTM is then built by georeferencing and integrating the
topographic, data, LIDAR data, and bathymetric data in the same planimetric and vertical
datum. Given the date and time, the CTM at that time can be derived from the periodically
acquired CTMs. The water surface is depicted by a water surface model (WSM) that can be
produced by a hydrologicalmodeling system using meteorological data and coastal physical
environmental data as boundary conditions. The DTS is created digitally by an intersection
of the CTM and WSM.
Theoretically, the shoreline can be derived by a subtraction of the WSM from the
CTM, where the grid points with differential value of 0 represent the shoreline. Technically,
a number of issues need to be addressed before a quality digital shoreline can Ž nally be
obtained. A test run of our existing data set demonstrated great potential success if the
processing steps in Figure 4 are followed. The subtraction result of the CTM and WSM is
further smoothed so that the shorelines are continuous lines in the grid represented by grid
points with value 0. Also, spikes and ‘shoreline segments’ whose lengths are smaller than a
threshold are eliminated. Furthermore, a classiŽ cation based on the elevation/bathymetry
differential values is performed to delineate grid points into land, water, and land-water
FIGURE 4 Generation of a tide-coordinated shoreline from CTM and WSM.
Digital Tide-Coordinated Shoreline
33
interactionpointsand to create a thematicimage. Subsequently,a clump operation groups the
same kinds of grid points together to form clumps of land, water, and land-water interaction
areas. After a noise detection and deletion process, the reŽ ned clump image is used to Ž nd
the shoreline which is deŽ ned as one of the boundaries of the clump areas. In shoreline
detection, topological information indicating that a shoreline separates water from land is
also checked. The raster or grid shoreline is then converted to the vector shoreline. Finally,
after a visual inspection and editing process, the digital shoreline becomes available for
various applications. If the WSM represents the water surface at the desired MLLW time,
the derived shoreline is the required digital tide-coordinated shoreline.
Experimental Result and Discussion
In order to test the concept of the second approach, we performed an experiment in a Lake
Erie study area that covers a shoreline of 11 km from Sheldon Marsh to Oberlin Beach, Ohio
(Figure 5). A set of NOAA tide-coordinated aerial photographs, taken when the water level
reached the MLLW, was processed to produce a digital terrain model and an orthophoto of
the area. The tide-coordinated shoreline can be digitized directly from the orthophoto. This
shoreline is treated as a master shoreline because it is tide-coordinated and has a very high
accuracy.
The terrain model derived from the aerial photographs was integrated with bathymetric
data acquired by ODNR (Ohio Department of Natural Resources) to form a CTM. A WSM
of the same area was generated by the Great Lakes Forecasting System developed by OSU
(Bedford and Schwab 1991). A second WSM that has a water level difference of 80 cm
from the Ž rst one was generated by the same system.
Figure 6 shows the two digital shorelines in a marshland subarea located westmost in
Figure 5. Since the CTM is very  at in the marshland, the 80 cm water difference created a
signiŽ cant shoreline change. Since the WSM does not correspond to MLLW the shorelines
generated are not tide-coordinated. A comparison between the two digital shorelines and
FIGURE 5 DTS experiment in Lake Erie area.
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R. Li et al.
FIGURE 6 Two digital shorelines created from CTM and WSM.
the master shoreline indicated very small differences (Li et al. 2001). We will continue
our investigation on the integration of tide information in the hydrological modeling and
subsequent shoreline modeling, so that the digital shoreline produced in this way becomes
a DTS.
The accuracy of the above shorelines is affected by the accuracies of the CTM and
WSM. The CTM consists of a DTM derived from aerial photographs and a bathymetric
data set. The DTM has an accuracy of 2.1 m, while the bathymetric data have an estimated
accuracy of 40 m. When we merged these two data sets, the DTM grid points were chosen
in an overlapping area. If there is a gap between the two data sets, we interpolate at the
grid points in such a way that a normalized weight of 2/3 is used for DTM points, and 1/3
for bathymetric points. Thus, the interpolated points have a propagated standard deviation
of 13.4 m. Overall, the accuracy of the CTM ranges from 2.1 m to 13.4 m for the area of
land-water interaction where the digital shoreline was generated. The water surface data
is estimated to be accurate to several centimeters. Assuming a Ž ve-degree coastal slope,
a water surface error of 5 cm would theoretically produce a horizontal error of 0.6 m,
which can affect the accuracy of the generated digital shoreline. Therefore, the major
error source of the Ž nal digital shoreline comes from the CTM. The quality of the CTM
can be signiŽ cantly improved by better aerial image processing and LIDAR shallow water
mapping so that the land-water intersection area will have far better terrain information for
improved shoreline extraction operations.We expect that the digital shoreline thus produced
will have an accuracy of around 1 m.
To compare various techniques of shoreline mapping, we reviewed existing shoreline
maps in the study area, and the data and techniques employed to produce them. The master
shoreline used for comparison was extracted from orthophotos that are one of the products
of a bundle adjustment of the NOAA tide-coordinated aerial photographs. The DTM used
to produce the orthophotos has a horizontal error of 2.1 m. The difŽ culty in delineation
Digital Tide-Coordinated Shoreline
35
TABLE 1 Estimated Accuracy of the Shorelines in the Study Area Derived
from Various Sources
Shoreline
T-sheet
USGS DLG
Aerial orthophoto
Digital shoreline from CTM and
WSM
IKONOS 1 m simulated image
IKONOS 4 m image
Estimated standard deviation
2.5– 20 m depending on scale
12 m (1:24000)
2.6 m (considering DEM error)
2 – 13 m dep. on CTM / WSM
quality
2– 4 m
8.5 m
of the shoreline from the orthophotos may introduce an error of 1.5 pixels in the images.
Therefore, the master shoreline used in this study has an estimated error of 2.6 m.
An attractive data source is the IKONOS 1 m resolution satellite imagery. The accuracy
of the shoreline derived from the 1 m simulated IKONOS images is 2 – 4 m, considering
the fact that the accuracy of 3D ground points reaches 2 – 3 m and the identiŽ cation error
of conjugate shoreline points in a stereo image pair is about 1.5 pixels, about 1– 2 m (Zhou
and Li 2000; Li et al. 2001). The 4 m IKONOS multispectral images in the same area came
as Geo-product with an accuracy around 24 m. After a polynomial georectiŽ cation using
eight GPS ground control points, the improved images have an accuracy of 6 m estimated
from the differences between the GPS surveyed coordinates and the rectiŽ ed coordinates
at the ground control points. Taking the shoreline delineation difŽ culty into account, an
optimistic estimation of the shoreline accuracy derived from the 4 m IKONOS images in
this speciŽ c case is about 8.5 m.
NOAA T-sheets have large and medium scales from 1:5000 to 1:40000. Taking
0.5 mm on the map as the error source, the accuracy of the digitized shoreline from the
T-sheet is about 2.5 m to 20 m. Similarly, the shoreline extracted from the USGS DLG
(1:24000) data should have an error of 12 m. The ODNR map in the area has a scale of
1:12000 and the estimated error of the shoreline is about 6 m (Table 1).
Conclusions
A high-accuracy, tide-coordinatedshoreline is required in many applicationssuch as coastal
management, mapping, environmental monitoring and protection, and the insurance industry. In order to achieve efŽ cient and cost effective tide-coordinated shoreline mapping,
more research should be conducted in the generation of digital tide-coordinated shoreline
modeling. Based on the above results, the following conclusions can be drawn:
² High quality, digital instantaneous shorelines can be extracted from high-resolution images, such as IKONOS satellite images and airborne images. The instantaneousshorelines
derived from the CTM and WSM are capable of performing simulation and prediction
of shorelines.
² Tide-coordinatedshorelines should be used to calculate shoreline erosion rates and shoreline changes in order to take the dynamic nature of the shoreline into consideration.
² Further research efforts should be made in establishing and implementing mathematical
models for derivation of tide-coordinatedshorelines based on (a) instantaneousshorelines
observed from high-resolution remote sensing imagery, and (b) CTM and WSM.
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References
Bedford, K. W., and D. Schwab. 1991. The Great Lakes Forecasting System—Lake Erie
Nowcasts/Forecasts. Proc. of Marine Technology Society Annual Conference (MTS’91).
Washington, DC: Marine Technology Society, pp. 260– 264.
Bossler, J. D. 1996. Airborne Integrated Mapping System. GIM, July, pp. 32– 35.
CSC 2001. CSC/NOAA web page: http://www.csc.noaa.gov/shoreline/history.html; status: June 29,
2001.
Fritz, L. W. 1996. Commercial earth observation satellites, Intn. Archives of Photogrammetry and
Remote Sensing. ISPRS Com. IV: 273– 282.
Ingham, A. E. 1992. Hydrography for the surveyor and engineer. London: Blackwell ScientiŽ c
Publications.
Lapine, L. A. 1991. Analytical calibration of the airborne photogrammetric system using a priori
knowledge of the exposure station obtained by kinematic GPS techniques. Report No. 411,
1991, Department of Geodetic Science and Surveying, The Ohio State University.
Li, R. 1997. Mobile mapping: An emerging technology for spatial data acquisition. J. of Photogrammetric Eng. and Remote Sensing 63(9):1085– 1092.
Li, R. 1998. Potential of high-resolution satellite imagery for national mapping products. J. of Photogrammetric Eng. and Remote Sensing 64(12):1165– 1169.
Li, R., K. Di, and R. Ma. 2001.A comparativestudy on shorelinemappingtechniques,4th International
Symposium on Coastal GIS, Halifax, NS, Canada, June 18– 20, 2001.
Lockwood, M. 1997. NSDI Shoreline BrieŽ ng to the FGDC Coordination group, NOAA/NOS.
Merchant, D. C. 1994. Airborne GPS-photogrammetry for transportation systems. Proc. of ASPRS/
ACSM, pp. 392– 395.
Shalowitz, A. L. 1962. Shore and sea boundaries—with special reference to the interpretationand use
of coast and geodetic survey data. U.S. Department of Commerce Publication 10-1, Two Vols.
Washington, DC: U.S. GPO.
Shaw, B., and J. R. Allen. 1995. Analysis of a dynamic shoreline at Sandy Hook, New Jersey, using
a Geographic information system. Proc. of ASPRS/ACSM, pp. 382– 391.
Slama, C. C., C. Theurer, and S. W. Henriksen. 1980. Manual of Photogrammetry. American society
of photogrammetry, Falls Church, VA.
Zhou, G., and R. Li 2000. Accuracy evaluation of ground points from IKONOS high-resolution
satellite imagery. J. of Photogrammetric Eng. and Remote Sensing 66(9):1103– 1112.