Determining the Volume of Your Lake
September 2004Barb Liukkonen, Water Resources Education Coordinator, University of Minnesota Extension Service and Minnesota Sea Grant, (612) 624-9256
How much water is there in your lake? Knowing this value may prove to be useful. Maybe you want to figure out the residence time of water in your lake (see the next article). Maybe you need to determine the proper application of an aquatic herbicide (or check on your contractor’s calculations). Maybe you just want to impress your lake association members or neighbors. Whatever your reason, here is a method you can use. It does require that you refresh your arithmetic skills and round up a bathymetric map, a measuring tool, and a calculator.
A bathymetric map shows contours, or lines connecting points of equal depth, in a lake. You can get bathymetric maps for many Minnesota lakes from local sporting goods stores or the Internet (e.g., go to the Minnesota Department of Natural Resources Lake Finder Web site). You can create your own if you have a GPS unit, a depth finder, and a lot of spare time. Contour intervals on bathymetric maps are usually in 5- or 10-foot increments.
Typical bathymetric map.
A formula is used to determine the volume of your irregularly shaped lake. The formula treats your lake like a series of layers, each layer shaped like a cone with the bottom chopped off (called a “frustrum”). You need to know the height and area of each layer in order to use the formula to calculate volume. Look at the depth zones drawing, which shows a 3D view of the bathymetric map above. Area 1 (A1) is equivalent to the 0 ft contour line, or the area of the whole lake. Area 2 (A2) is equivalent to the area encompassed by the 10 ft contour line, and so on. The difference in depth between two successive layers is the height (H) of that layer (in this example, 10 feet).
Depth zones in lake.
Your first task is to calculate the surface area within each contour line to plug into the formula. You can do this in a number of ways, depending on what tools you have available.
- Trace around the contour lines with a mechanical planimeter.
- Use a computer program such as ArcView.
- Cut out the contours and weigh them to determine the relative percentage of the total area made up of each successive contour in the lake. The weighing method is quite accurate, but requires a sensitive balance, such as would be available in a high school science laboratory.
- The simplest method is to transfer your bathymetric map to graph paper and count how many squares fall within each contour line. This may reduce accuracy because you often have to estimate by half- or quarter-squares, but it works.
Consider making a table with rows for each contour interval (e.g., 0-10 feet, 10-20 feet, 20-30 feet, etc.), and columns for your measurements, surface area (in acres and/or square feet), and volume. The number of rows in your table will depend on how deep your lake is – you need a row for each contour interval. A table like this may help you manage the numbers you’re going to generate. Sample determinations are included for a few layers.
| (Use these columns for methods 3 and 4 above) | |||||
|---|---|---|---|---|---|
| Contour Interval (H) | Relative area of each contour interval | Area of 0′ contour (square feet) | Area of contour interval (square feet)* | Acres (43,560 square feet/acre) | Volume in cubic feet or acre-feet (calculated from the formula) |
| 0′-10′ | 1 | 2,178,000 | 2,178,000 | 50 | 396 acre-feet |
| 10′-20′ | .6 | 2,178,000 | 1,306,800 | 30 | 221 acre-feet |
| 20′-26′** | .3 | 2,178,000 | 653,400 | 15 | |
| Total | |||||
* The conversion factor you’ll need to use will depend on the scale of your map.
** See instructions below for calculating the area of the lowermost layer.
Use the formula below to calculate the volume of water in each contour band of the lake (i.e., between 0 and 10 feet deep, between 10 and 20 feet, and so on). If your map has 5-foot contour lines, follow the same procedure (0-5 feet, 5-10 feet, 10-15 feet, etc.). The formula is:
- V = H/3 (Al + A2 + /(Al x A2))
- V = volume of water in each contour band
- H = difference in feet between two contour depths
- Al = area of the lake within the outer contour
- A2 = area of the lake within the inner contour
Depending on the scale of your bathymetric map, you may want to convert to acres for ease of calculation. There are 43,560 square feet in one acre. If you use acres for surface area and feet for depth, the volume you calculate will be in acre-feet. An acre-foot of water is one acre of water one foot deep, i.e., 43,560 cubic feet (~326,000 gallons).
**The calculation for the lowermost layer (in this example – 20-26 ft) uses a geometric cone formula: volume = 1/3(HxA). This formula assumes that the maximum depth of 26 feet occurs in one small area. So, in our example, the height would be 6 feet and the area would be the area of the 20 foot contour interval.
Note: If the maximum depth of 26 feet stretches over a broad area (determined by studying the bathymetric map, then encircle this area with a contour line, determine its area with a one of the methods described above, and use the frustum formula to calculate volume of the 20-26 foot zone.
This article is partially based on: Taube, C.M. 2000. Instructions for winter lake mapping. Chapter 12 in Schneider, J.C. (ed.). Manual of Fisheries Survey Methods II: With Periodic Updates. Michigan Department of Natural Resources, Fisheries Special Report 25, Ann Arbor.
