Laboratory Exercise 1

Lake Morphometry

(This exercise has been modified from one developed by J. A. Holmes of the University of Toronto)

    Knowledge of depth, sediment area, area of water strata at various depths, volumes of strata between depth contours, shoreline characteristics and other morphological features of a lake or stream is important because the morphology affects nearly all major physical, chemical, and biological properties that we measure in lakes.  For example, information on morphometry is needed to investigate erosion, nutrient loading rates, chemical mass, heat content, thermal stability, biological productivity and growth, and other ecosystem structures and function in lakes. Hayes and Anthony (1964) found that for 150 North American lakes, fish productivity could be directly related to mean depth and surface area.  Schindler (1971) explained differences in the trophic status among a group of neighboring lakes in Ontario by differences in surface area, lake volume, and drainage area.

    The morphology of a lake or stream tends to reflect its geological origins. Most lakes in Pennsylvania were formed as a result of glaciation, either by glacial scouring or meltwater flows, or a block of melting ice (kettle lakes). Some useful parameters that you will be measuring and calculating are shown below. All of these parameters can be measured and calculated from topographic or hydrographic (showing lake bottom, i.e., depth contours) maps and should be completed before beginning work on a lake.

1. Lake surface area (Ao) is measured by digitizer or polar planimeter.

2. If you are lucky, lake volume (V) is calculated from bathymetric map.  If not, you may have to construct your own by making soundings (most easily done on frozen lakes) or using a 'fish-finder' to scan the bottom.   

Consider the lake as an irregularly shaped cone, divided into segments by the different depth contours. The upper and lower surfaces of each segment are delineated by sequential depth contours. The volume of the lake is calculated by summing the "surface area" of each depth contour and applying the formula for the volume of a cone. Thus, if there are two depth contours, the volume is calculated as

V = h/3[A1 + A2 + Ö( A1 x A2)]

where h is the difference between depth contours, A1 is the area of the upper depth contour, and A2 is the area of the lower contour. The last or bottom cone is calculated as

Volume = 1.047 x r2 x h

where r is the radius of the top of the cone and h is the depth, i.e., the difference between the last depth contour (top of the cone) and the maximum depth.

3. Limnological mean depth (˛) = V/Ao

4. Maximum depth (zmax) taken from bathymetric map.

5. Relative depth (zr) expresses the zmax as a percentage of the mean diameter of the lake. Most lakes have a zr < 2%. Some deep lakes with small surface areas may have zr values > 4% and these lakes tend to exhibit greater stability than those with a lower zr.

zr = 50 x zmax  x √π/√Ao

6. Mean depth:maximum depth ratio (˛: zmax) provides information on how lake shape differs from a cone and it describes the form of a basin relative to the development of its volume. A cone has a ratio of 0.33. Lakes with deep holes such as kettle lakes have values < 0.33. Fjord-type lakes have ratios > 0.5 while most lakes in Pennsylvania will have ratios between 0.33 and 0.5.

7. Fetch is the maximum distance on a lake surface between any two unobstructed points. This parameter is important for predicting wave height and thermocline depth.

8. Shoreline length (L) is a linear distance and is measured using a cartographic wheel.

9. Shoreline development (DL) is the degree of shoreline irregularity expressed as ratio of L to circumference of a circle of area equal to Ao. The closer this ratio is to 1, the more circular the lake. A larger ratio means the shoreline is more crenulated and hence the potential for littoral community development is greater. Shoreline development is calculated as

DL = L / (2 x √π x Ao

10. A hypsographic or depth-area curve describes the relationship between surface area and depth. The curve is plotted on graph paper and may be expressed in relative (%) or absolute units (m2, ha, km2). This curve only approximates the area of exposed lake bottom sediments between depth contours since areal measurements are related to the plane of the lake surface.

11. Drainage basin is the total land surface area drained by tributaries that feed the main channel of a stream.  This parameter is calculated for streams or lakes by outlining the height of land on a topographic map and using a polar planimeter of digitizer. The term watershed denotes the boundary between adjacent drainage basins and in practice it is used as a synonym of drainage basin.

Laboratory 1 Exercises

You will be given copies of hydrographic date for a local lake.  Each student should carry out the following morphometric calculations, and answer the following questions.

A. Lake Morphometry

1. Calculate the mean (˛) and relative depths (zr) and the ˛: zmax ratio for each lake. What do these values tell about the shape of each lake? Examine the maps and consider the scale of each in your answer. Based on the general relationship between mean depth and biological productivity, what can you say about the productivity of different trophic levels in these lakes?

2. Using a ruler, measure the fetch (in km) and estimate the depth of the summer thermocline (in m) for each lake. Remember to convert your fetch measurements to km using the scale on the maps (which are in m).  Do you think that these estimates are reasonable considering the morphometry of each lake?

3. Lake 239 has 4480 m of shoreline (L) and Lake 304 has 827 m of shoreline. Calculate shoreline development ratios (DL) and comment on the potential for littoral community development in each lake.

B. Hypsographic Curves

1. Use the area data on the bathymetric maps to plot a hypsographic curve for each lake. The curves should show cumulative % area vs depth. Remember that the x-axis is cumulative area and should be at the top of the curve while the y-axis shows depth, beginning at the top and increasing downward.

2. What do the hypsographic curves tell you about the bottom shape of each lake basin?

3. If rooted aquatic macrophytes grow to a height of 2 m in each lake, what portion (%) of the total lake area can be considered the littoral zone? Are your values consistent with your comments concerning shoreline development ratios in each lake?

C. Nutrient supply and Trophic Status

1.Lake 239 drains an area of 260 x 104 m2 and Lake 304 drains a land area of 33 x 104 m2. Schindler argued that lake productivity was proportional to the ratio of (A0 + A0)/V. Calculate these ratios and comment on the trophic status of each lake. Are these results what you expected considering your comments based on the hypsographic curves and DLs for each lake?

E. Lake Productivity Assessment

1. Lake trophic status is a function of edaphic (nutrient supply, e.g., Schindler’s ratio) and morphometric factors. Comment on this statement briefly, using the parameters that you’ve calculated in the previous sections to support your answer. Indicate which lake is the most productive and which is the least productive. If some of your calculations produce contradictory interpretations, try to explain how you might resolve the difficulty. NOTE: we are not asking for a strict classification into oligotrophic or eutrophic; rather we want your informed opinion as to what you would expect to find if you went to these lakes and sampled them.

Any graphs that you do for this course should be neat and well labeled (axes, including units, and a caption explaining what the graph is about). Hard copies from various graphics programs are acceptable but note that standard scientific labeling conventions should be followed (e.g., if your program will not label the y-axis vertically, you will have to do it by hand). Hand-drawn curves should be on graph paper and a ruler must be used.

Show your work for any calculations that you hand in for marking. We are interested in how you arrive at your answer as much as the result itself. Submission of a final answer only will not receive full marks for a question.

Hayes 1964.

Schindler 1971.