David J. Schwab

Diana L. Sellers

Great Lakes Environmental Research Laboratory

Ann Arbor, Michigan

March 1980

Revised January 1996

GLERL Contribution No. 212

Contents

Abstract

1. Introduction

2. Bathymetric Data

3. Shoreline Data

4. Geographical Conversions

5. Procedure For Obtaining Data

6. Acknowledgments

7. References

Appendix. Data Base Format

This report describes bathymetric grid data and digitized shorelines compiled for the five Great Lakes and Lake St. Clair. The bathymetric grids consist of an array containing the average lake depths in 2-km squares (1.2-km squares for Lake St. Clair). The digitized shorelines are lists of latitudes and longitudes for closed loops describing lake and island shorelines. Conversion equations for map-to-geographical and geographical-to-map coordinate transformations are given for all the bathymetric grids. An appendix details the format of the data base.

Bathymetric data for Lakes Ontario, Erie, Huron, and Superior on a 2-km grid as described in
Robertson and Jordan (unpublished) was obtained from the Canada Center for Inland Waters.
They superimposed 2-km grids on standard bathymetric charts and averaged a mean depth in
each grid square by eye. Depths are relative to the Great Lakes Datum of 1955 (Dohler,
1961). All grids are aligned with the central meridian of the bathymetric chart, except that
for Lake Erie, which is tilted 27.33° counterclockwise to obtain a better fit to the shoreline.
GLERL carried out a similar procedure for Lake St. Clair with a 1.2-km grid rotated 2.24°
clockwise from a central meridian of 82.67°. National Ocean Survey chart number 14850 was
used for Lake St. Clair depths. The chart scale is 1:60,000. For Lake Michigan, a 2-km grid
aligned with the 86.50° meridian was defined. A computer subroutine was written to interpolate
the 2-min grid depths of Hughes *et al. * to arbitrary latitude and longitude by bilinear
interpolation within each 2-min square. These data were used to calculate the average depth
in each 2-km grid square by averaging the depth at the center of the square and the four
depths at coordinates (.5,.5), (.5,-.5), (-.5,-.5), and (-.5,.5) km relative to the center of the
square. Depths at some grid squares near the shoreline were adjusted by hand so that they
better fit the actual lake shoreline. The data for Lake Michigan were then put into the same
format as those for the rest of the lakes. Statistics for the digitized bathymetric data of the
Great Lakes are presented in Table 1.

Table l. Statistics for Bathymetric Data ________________________________________________________________________________________ Grid East-West North-South Central Reference Surface area Volume Lake size (km) grids grids Meridian datum (m) (10**9 m**2) (10**12 m**3) ________________________________________________________________________________________ Superior 2 304 147 88.00° 182.88 82.2 11.82 Michigan 2 160 250 86.50° 175.81 59.9 4.79 Huron 2 209 188 82.75° 175.81 59.6 3.40 St. Clair* 1.2 35 36 82.67° 174.25 1.1 0.0039 Erie+ 2 209 57 81.00° 173.31 25.3 0.47 Ontario 2 152 57 78.00° 74.01 18.5 1.67 ________________________________________________________________________________________ * The Lake St. Clair bathymetric grid is rotated 2.24° clockwise. + The Lake Erie bathymetric grid is rotated 27.33° counterclockwise.

Table 2. Statistics for Shoreline Data __________________________________________________________________________________ Number of segments Shore length (10**6 m) Area (10**9 m**2) Number of __________________ ______________________ _________________ Lake islands lake islands lake islands lake islands __________________________________________________________________________________ Superior 41 1387 741 2.62 1.04 84.0 1.58 Michigan 21 1537 443 2.15 0.35 57.9 0.39 Huron 66 2473 1672 2.94 1.65 63.4 3.96 St. Clair 15 182 262 0.19 0.16 1.2 0.07 Erie 7 888 167 1.32 0.13 25.8 0.10 Ontario 16 1434 468 1.50 0.35 19.6 0.33 __________________________________________________________________________________

The bathymetric grids described above are based on charts with polyconic projections. To convert geographic coordinates (latitude and longitude) to grid coordinates (x and y) and vice-versa, one could use the exact polyconic projection formulas for the original charts, but these formulas are complicated and time-consuming to calculate even by computer. Conversion formulas with sufficient accuracy for most purposes (approximately 500 m) can be obtained by a simple expansion of the geographical coordinate in terms of the grid coordinate and vice-versa.

The formulas for the geographical-to-map coordinate transformation are

x = a Dlon + b Dlat + c Dlon Dlat + d Dlon**2 and y = e Dlon + f Dlat + g Dlon Dlat + h Dlon**2where x and y are the eastward and northward grid distances in kilometers from the base latitude and longitude of the grid, Dlat is latitude minus base latitude, Dlon is base longitude minus longitude, and a...h are the transformation coefficients. These values were determined for the Lakes Ontario, Erie, Huron, and Superior bathymetric grids by Rodgers (1969). A similar procedure was used at GLERL to determine the coefficients for Lakes St. Clair and Michigan. For grids oriented parallel to the central meridian, coefficients d and g are not used. This is equivalent to assuming a linear variation of x with longitude and a quadratic variation of y with longitude for a fixed latitude in these cases. The transformation coefficients a...h and base longitude and latitude for each bathymetric grid are given in table 3. These transformations were used to plot the shoreline digitizations on the bathymetric grid in figures 1-6.

Figure 1.Outline of digitized bathymetric grid and digitized shoreline for Lake Superior.

Figure 2.Outline of digitized bathymetric grid and digitized shoreline for Lake Michigan.

Figure 3.Outline of digitized bathymetric grid and digitized shoreline for Lake Huron.

Figure 4.Outline of digitized bathymetric grid and digitized shoreline for Lake St. Clair.

Figure 5.Outline of digitized bathymetric grid and digitized shoreline for Lake Erie.

Figure 6.Outline of digitized bathymetric grid and digitized shoreline for Lake Ontario.

Table 3. Geographical-to-map coordinate transformation coefficients. The equations are x = a Dlon + b Dlat + c Dlon Dlat + d Dlon**2 and y = e Dlon + f Dlat + g DlonDlat + h Dlon**2. Dlat is latitude minus base latitude. Dlon is base longitude minus longitude. x and y are in km. ________________________________________________________________________________________________ Grid Base longitude, a b c d Lake orientation base latitude e f g h ________________________________________________________________________________________________ Superior 0° 92.10275°W 7.70215E+1 5.84617E+0 -1.42494E+0 ---------- 46.31846°N -3.98892E+0 1.11176E+2 ---------- 4.86127E-1 Michigan 0° 87.94260°W 8.31831E+1 1.90171E+0 -1.31825E+0 ---------- 41.60766°N -2.07627E+0 1.11000E+2 ---------- 9.58685E-1 Huron 0° 84.6620°W 8.15869E+1 2.57588E+0 -1.34705E+0 ---------- 42.96603°N -1.85606E+0 1.11111E+2 ---------- 4.85354E-1 St.Clair 2.24°cw* 82.93158°W 8.22690E+1 -4.18687E+0 -8.92958E-1 5.49244E-1 42.30415°N 2.84351E+0 1.10232E+2 1.82918E-1 2.35336E-1 Erie 27.33°ccw+ 82.98345°W 7.40161E+1 5.29979E+1 -1.15249E+0 2.21791E-1 40.97000°N -4.01422E+1 9.76373E+1 5.95700E-1 4.29100E-1 Ontario 0° 79.81996°W 8.13204E+1 2.42939E+0 -1.33486E+0 ---------- 43.16554°N -1.76688E+0 1.11101E+2 ---------- 4.85416E-1 ________________________________________________________________________________________________ * Clockwise + Counterclockwise

The formulas for map-to-geographic coordinate transformation are

Dlon = Ax + By + Cxy + Dx**2 and Dlat = Ex + Fy + Gxy + Hx**2,where A...H are the map-to-geographic transformation coefficients. For each lake a series of 64 sets of geographic coordinate pairs covering the lake were converted to x and y values by the formulas given above. These sets of x, y, Dlat, and Dlon values were then used to determine A...H by least-squares fitting to the map-to-geographic coordinate transformation equations. Again, for grids parallel to the central meridian D and G were not used. The results of the least-squares procedure for A...H and the maximum errors for each lake are given in Table 4.

______________________________________________________________________________________ Table 4. Map-to-geographical coordinate transformation coefficients. The equations are Dlon = Ax + By + Cxy + DX**2 and Dlat = Ex + Fy + Gxy + Hx**2. Dlat is latitude minus base latitude. Dlon is base longitude minus longitude. x and y are in km. ______________________________________________________________________________________ A B C D Max. longitude deviation Lake E F G H Max. latitude deviation ______________________________________________________________________________________ Superior 1.29841E-2 -7.17624E-4 2.26882E-6 ---------- 9.63680E-4 4.77160E-4 8.98120E-3 ---------- -7.57848E-7 9.56804E-4 Michigan 1.20166E-2 -2.19428E-4 1.83917E-6 ---------- 9.52070E-4 2.41793E-4 9.00600E-3 ---------- -1.33547E-6 9.50140E-4 Huron 1.22482E-2 -2.97178E-4 1.92849E-6 ---------- 9.99598E-4 2.20311E-4 8.99372E-3 ---------- -7.02891E-7 9.79506E-4 St.Clair 1.21387E-2 4.62637E-3 1.10856E-6 -1.02938E-6 9.59513E-5 -3.13049E-4 9.05963E-3 -2.3882E-7 -2.79918E-7 9.46533E-5 Erie 1.03968E-2 -5.80515E-3 1.52086E-6 7.78340E-7 9.53751E-4 4.28786E-3 7.888811E-3 6.05812E-7 -4.81076E-7 9.53751E-4 Ontario 1.22965E-2 -2.74739E-4 1.85864E-6 ---------- 8.78075E-5 1.99237E-4 8.99770E-3 ---------- -6.74272E-7 8.78075E-5 ______________________________________________________________________________________

National Geophysical and Solar-Terrestrial Data Center

NOAA/EDIS/NASDC

Mail Code: D-621

Boulder, CO 80303

303-499-1000 ext. 6376 or 6338

- Dohler, G. C. (1961): The adoption of the International Great Lakes Datum, 1955, Canadian
Hydrographic Service, Surveys and Mapping Branch, Department of Mines and Technical Surveys,
Ottawa, Ont. 28 pp.
- Hughes, T. H., G. E. Birchfield, and M. T. Matthies (1972): A compilation of the average depths
of Lake Michigan and Lake Ontario on a 2-min grid, Report ANL/ES-10, Argonne National Laboratory,
Argonne, Ill. 94 pp.
- Robertson, D. G., and D. E. Jordan (unpublished): Digital bathymetry of Lakes Ontario, Erie,
Huron, Superior, and Georgian Bay, Canada Centre for Inland Waters unpublished report,
Canada Centre for Inland Waters, Burlington, Ont. 10 pp.
- Rodgers, G. K. (1969): Data atlas project, Project Report No. HO 83836, Great Lakes
Institute, University of Toronto, Toronto, Ont. 21 pp.

1. bathymetric data header records

2. bathymetric data records

3. lake shoreline header record

4. lake shoreline data records

5. island shoreline header records

6. island shoreline data records

For each lake there are six bathymetric data header records and one shoreline header record. The format of each record type and the card columns used are as follows:

FORTRAN Card format columns 1.1 Bathymetric data header record 1: lake name 50A1 1-50 blank 30X 51-80 1.2 Bathymetric data header record 2: number of east-west grid boxes I5 1-5 number of north-south grid boxes I5 6-10 base latitude F12.7 11-22 base longitude F12.7 23-34 grid size (m) I5 35-39 maximum depth (m) I5 40-44 blank 36X 45-80 1.3 Bathymetric data header record 3: geographic-to-map coordinate conversion coefficients for x. a E15.6 1-15 b E15.6 16-30 c E15.6 31-45 d E15.6 46-60 BLANK 20X 61-80 1.4 Bathymetric data header record 4: geographic-to-map coordinate conversion coefficients for y. e E15.6 1-15 f E15.6 16-30 g E15.6 31-45 h E15.6 46-60 BLANK 20X 61-80 1.5 Bathymetric data header record 5: map-to-geographic coordinate conversion coefficients for longitude. a E15.6 1-15 b E15.6 16-30 c E15.6 31-45 d E15.6 46-60 BLANK 20X 61-80 1.6 Bathymetric data header record 6: map-to-geographic coordinate conversion coefficients for latitude. e E15.6 1-15 f E15.6 16-30 g E15.6 31-45 h E15.6 46-60 BLANK 20X 61-80 2. Bathymetric data records: depths in meters 19I4 1-76 sequence number I4 77-80 3. Lake shoreline header record: blank 20X 1-20 lake name 60A1 21-80 4. Lake shoreline data: longitude, latitude pairs 4(2F9.5) 1-72 sequence number I8 73-80 5. Island shoreline header record: blank 20 1-20 island name 60A1 21-80 6. Island shoreline data: longitude-latitude pairs 4(2f9.5) 1-72 sequence number I8 73-80

**NOTES:**

- The depths on bathymetric data cards fill the bathymetric grid proceeding west to east and
then south to north. The following FORTRAN statements could be used to read the bathymetric
data cards:
READ 10, (NDEPTH(I,J), I = 1, IMAX), J = 1, JMAX) 10 FORMAT (19I4,4X)

where IMAX is the number of east-west grids and JMAX is the number of north-south grids as given in table 1. Zero depth indicates land. - The first and last longitude-latitude pair of each lake shoreline or island shoreline are the
same. If the last longitude- latitude pair is not the last pair in a record, the remaining pairs are
set to zero. If it is the last pair in a record, the next record will consist of eight zeros.

______________________________________________________________________________ Table 5. The number of bathymetric data and shoreline record in the data base for each lake. ------------------------------------------------------------------------------ Superior Michigan Huron St.Clair Erie Ontario Bathymetric data records 2352 2106 2068 67 627 456 Lake shoreline data records 348 385 619 46 223 359 Island shoreline header records 41 21 66 15 7 16 Island shoreline data records 221 129 478 78 48 131 ______________________________________________________________________________

*URL: https://www.glerl.noaa.gov/pubs/tech_reports/glerl-016/dr-016.html/*