Lake Basin Characteristics and Morphometry
11
Measure the area contained by each contour at least twice. The variance between readings should
be limited to 0.003 units or less, depending on the size of the figure and the accuracy. The
standard area should be measured at least five times to obtain a mean value. When the unknown
area is too large to be accommodated by the working area of the planimeter, it should be divided
into a number of fractional areas, the areas of each then are determined and summed. Areas of
islands or submerged lake mounts must be subtracted; areas of planes at equal depth but
separated (e.g., multiple depressions in a lake basin) must be added.
Volume (V). The volume of the basin is the sum of the volumes of the strata at successive depths
from the surface to the point of maximum depth. The volume is approximated closely by plotting
the areas of contours, as closely spaced as possible, against depth and integrating the area of this
curve by planimetry. Alternatively, the volume can be estimated by summation of a series of
truncated irregular cones of the strata:
where h = vertical depth (thickness) of the stratum, in meters; Al = area of the upper surface, in
m 2 , and; A2 = area of the lower surface of the stratum whose volume is to be determined.
It has been assumed commonly that the increase in benthic area below an area oflake surface
resulting from the slope of the lake or stream bottom is negligible. This assumption can be valid
for very shallow lakes or shallow areas of a littoral zone where the slope is slight. The error
increases significantly, however, with increasing degree of slope. Estimates of benthic area can be
made for smooth or rocky substrata [cf., Loeb et al. (1983)]. For example, benthic areas below
1 m 2 of lake surface for different bottom slopes (BO) are
Area of bottom below 1.00m 2 of lake surface
BO
Smooth slope
Rocky slope
1.04
1.10
1.22
1.44
Maximum Depth (zm). The greatest depth of the lake.
1.27
1.47
1.70
2.00
Mean Depth (Z). The volume divided by its surface area at zero depth:
V
i = -
Ao
Relative Depth (z.). The maximum depth as a percentage of the mean diameter [cf.,
Hutchinson (1957)]:
Most lakes have a Zr of less than 2 %, whereas deep lakes with small surface areas exhibit greater
resistance to mixing and usually have a Zr > 4%.
Shore Line (SL). The intersection of the land with permanent water is of nearly constant
length in most natural lakes. The length of the shore line can, however, fluctuate widely in
ephemeral lakes and in reservoirs in response to variations in amounts of precipitation and
discharge.
The length of the shore line can be determined directly by measurement or from maps with
map measures (chartometer, rotometer). These inexpensive devices measure the lengths oflines
11
Measure the area contained by each contour at least twice. The variance between readings should
be limited to 0.003 units or less, depending on the size of the figure and the accuracy. The
standard area should be measured at least five times to obtain a mean value. When the unknown
area is too large to be accommodated by the working area of the planimeter, it should be divided
into a number of fractional areas, the areas of each then are determined and summed. Areas of
islands or submerged lake mounts must be subtracted; areas of planes at equal depth but
separated (e.g., multiple depressions in a lake basin) must be added.
Volume (V). The volume of the basin is the sum of the volumes of the strata at successive depths
from the surface to the point of maximum depth. The volume is approximated closely by plotting
the areas of contours, as closely spaced as possible, against depth and integrating the area of this
curve by planimetry. Alternatively, the volume can be estimated by summation of a series of
truncated irregular cones of the strata:
where h = vertical depth (thickness) of the stratum, in meters; Al = area of the upper surface, in
m 2 , and; A2 = area of the lower surface of the stratum whose volume is to be determined.
It has been assumed commonly that the increase in benthic area below an area oflake surface
resulting from the slope of the lake or stream bottom is negligible. This assumption can be valid
for very shallow lakes or shallow areas of a littoral zone where the slope is slight. The error
increases significantly, however, with increasing degree of slope. Estimates of benthic area can be
made for smooth or rocky substrata [cf., Loeb et al. (1983)]. For example, benthic areas below
1 m 2 of lake surface for different bottom slopes (BO) are
Area of bottom below 1.00m 2 of lake surface
BO
Smooth slope
Rocky slope
1.04
1.10
1.22
1.44
Maximum Depth (zm). The greatest depth of the lake.
1.27
1.47
1.70
2.00
Mean Depth (Z). The volume divided by its surface area at zero depth:
V
i = -
Ao
Relative Depth (z.). The maximum depth as a percentage of the mean diameter [cf.,
Hutchinson (1957)]:
Most lakes have a Zr of less than 2 %, whereas deep lakes with small surface areas exhibit greater
resistance to mixing and usually have a Zr > 4%.
Shore Line (SL). The intersection of the land with permanent water is of nearly constant
length in most natural lakes. The length of the shore line can, however, fluctuate widely in
ephemeral lakes and in reservoirs in response to variations in amounts of precipitation and
discharge.
The length of the shore line can be determined directly by measurement or from maps with
map measures (chartometer, rotometer). These inexpensive devices measure the lengths oflines