Watershed Ecology, Spring 2002
Homework #2 – due Thursday 31 January 2002
Hydrology and Scale
Please show all your work, and please staple or clip your homework pages. And try
to have fun!
1) (5 points) Precipitation is typically measured as a volume (L3) per unit area (L2) which
has dimensions of length (L). In the United States, the average annual precipitation
varies from a minimum at Death Valley, CA (1.6 inches) to a maximum on Mt. Waialeale
on the island of Kauai in Hawaii (460 inches). What is the average annual precipitation
(in millimeters, mm) at each of these locations?
2) (5 points) In the U.S., stream discharge is often measured in units of cubic feet per
second, (ft3s-1, or “cfs”). In most other countries, discharge is measured in cubic meters
per second (m3 sec-1). What is the equivalent flow (in m3 s-1) of 18.2 ft3 s-1?
3) (5 points) In an average year, 1.0 m of precipitation falls on a catchment with an area
of 1000 (or 103) km2. What is the volume of water received during an average year in
cubic meters? In gallons?
4) (5 points) In an average year, a small (area = 3.0 km2) agricultural catchment receives
950 mm of precipitation. The catchment is drained by a stream, and a continuous record
of stream discharge is available. The total amount of surface water runoff for the year,
determined from the stream discharge record, is 1.1x106 m3.
a) What is the volume of water (in m3) evapotranspired for the year (assume no
change in water stored in the catchment)?
b) What is the depth of water (in mm) evapotranspired for the year (again, assuming
no change in water stored in the catchment?
c) What is the runoff ratio or water yield (runoff/precipitation) for the catchment?
5) (10 points) For this question, you will need to use Excel or other spreadsheet
program. The relationship between stage (stream height) and discharge in a stream or
river is taken to be of the form
Q = a Sb,
where Q is discharge, S is stage, a & b are fitting coefficients or parameters.
a) Write the logarithmic transformation (in base 10) of the equation Q = a Sb. This
yields an equation that is in linear form ( y = slope*X + intercept).
b) Using the data below, make a rating curve that describes the relationship between
S and Q. Record all data in metric (stage in m, discharge in m3/sec). Plot log10(Q) on
the y axis. Plot log10(S) on the x axis. Label the axes properly. Hint: you can cut
and paste the data set directly into Excel. If you do not know the proper command for
calculating logarithms in base 10 in Excel, search for it in Help.
c) Fit a least-squares line to this graph. Hint: in Excel, you right-click on a data
point on the graph, select “Add Trendline” from the menu, and then under “Options”
check the “Display equation on chart” and the “Display R2 value on chart” options.
Show the equation of this line. You would use this equation to predict discharge
based on a measured value of stream stage (e.g., log10 Q = ?). Include the R2 value,
showing the goodness of fit of our predicted line versus the observed data.
d) Describe the equation in c) in the form of Q = a Sb. (i.e., what are the values of
the parameters a and b)?
S, ft
Q, cfs
observed observed
Stage
discharge
0.12
0.566
0.16
0.588
0.16
0.678
0.15
0.679
0.12
0.706
0.18
0.753
0.18
0.951
0.21
1.05
0.21
1.056
0.24
1.424
0.2
1.453
0.31
2.19
0.31
2.457
0.3
2.56
0.38
3.438
0.38
3.522
0.37
3.92
6. (5 points) Using a pen or pencil, please delineate the small watershed draining into
Ellis Pond on the following map (arrow points to the mouth of its stream outlet). It will
help you if you print Pages 4 and 5 at your printer’s best quality setting.
7. (5 points) The scale at which we measure things can actually affect some of our
results. Here is an exercise to show this to you. Below are two maps of the eastern end
of Long Island. They are made at different scales.
A
B
Question 7, continued.
a) Using a string with the appropriate scale units marked off on it, or using a planimeter
if you have one, measure the perimeter of the land mass indicated in the dotted red
squares on each map. Use the metric scale (Kilometers).
Perimeter of land mass, Map A = _______ KM
Perimeter of land mass, Map B = _______ KM
b) Extra credit – 5 points. Using either the method of counting squares in a grid, or the
method of weighing, estimate the area of the land mass whose perimeter you just
measured in each map.
Area of land mass, Map A = ______ KM2
Area of land mass, Map C = ______ KM2
Which measurement, perimeter or area, seems more sensitive to the scale at which it is
measured?