Water Science and the Environment – HWR 201 – Spring 2017
Homework 5
Distributed: 18 April 2017
Due: 25 April 2017, in class
Stream stage and flow, rating curve; soil porosity and water content
Problem 1. Creating own rating curve from field measurements of flow and water level.
Flow velocities were measured using the floater method during different water levels. The following
measurements were obtained: travel time (t), of the floater over distance L (from which the
water velocity can be computedusing this formula: v = L/t*0.85; the constant 0.85 converts surface
velocity that was measured to average velocity in water profile), water depth (d), and water
width (w) (from depth and width the cross-sectional area can be computed: A = d*w), and water
level (h)(stream stage). All measurements were made on a number of segments at the same point
in the stream (see diagram for details). In this exercise we use these measurements to compute the
total flow rate of the stream, and then relate this total flow rate to the water stage. Several flow
rate – water stage points can be used to define the rating curve.
The data are here:
Date segment depth, d width, w distance, L time, t
i ft ft ft s
Point #1 1 0.79 1.6 15 56
06‐Aug‐16 2 0.82 1.6 15 64
Stage: 1.09 ft 3 0.85 1.6 15 30
4 1.02 1.6 15 33
5 1.05 1.6 15 19
6 1.05 1.6 15 20
7 1.15 1.6 15 20
8 1.02 1.6 15 24
9 1.08 1.6 15 23
10 1.08 1.6 15 25
Point #2 1 0.33 1.64 15 25
07‐Aug‐16 2 0.49 1.64 15 12
Stage: 1.21 ft 3 1.02 1.64 15 18
4 1.02 1.64 15 24
5 0.98 1.64 15 19
6 1.08 1.64 15 19
7 1.31 1.64 15 10
8 1.31 1.64 15 12
9 1.35 1.64 15 12
10 1.18 1.64 15 14
11 0.89 1.64 15 10
12 0.85 1.64 15 14
13 0.66 1.64 15 26
14 0.46 1.64 15 28
Point #3 1 1.15 1.64 15 11.3
11‐Aug‐16 2 2.10 1.64 15 6.3
Stage: 1.50 ft 3 2.03 1.64 15 8.1
4 2.20 1.64 15 7.1
5 2.23 1.64 15 5.4
6 2.07 1.64 15 7.5
7 1.84 1.64 15 7.4
8 1.21 1.64 15 8.3
9 1.05 1.64 15 11.2
Point #4 1 0.92 3.28 15 31
12‐Aug‐16 2 1.20 3.28 15 13
Stage: 1.19 ft 3 1.29 3.28 15 10
Required:
(a) Compute flow rate in each segment in the table. Each line should have its own flow rate. Then
add up segments withing each point; this will be total flow rate at that time. Make a table
showing flow rates and river stage; you should have six entries, one for each point.
(b) Plot the data and fit a line (put stage on the horizontal axis and flow rate on the vertical axis).
This is your rating curve for the Sabino Creek. You will be asked to compare this with USGS
rating curve in Problem 2.
Problem 2. Reconstructing (reverse engineering) rating curve from USGS data on water
level and flow rate.
Use USGS stream gauge data to reconstruct the rating curve for the Sabino Creek.
The data are here: http://waterdata.usgs.gov/az/nwis/uv?site_no=09484000
Required:
(a) Download data for time period between 10 January 2017 and 30 January 2017 (this period
includes the highest flow rate in the past several years). Plot water level (on x axis) vs. flow
rate (on y axis).
(b) Fit a line through the data; this is the rating curve. What function best approximates the data?
(c) Compare with your rating curve from Problem 1. How similar or different are the two?
Explain briefly.
4 1.22 3.28 15 12
5 1.21 3.28 15 13
Point #5 1 0.95 2.95 15 33
15‐Aug‐16 2 0.98 2.95 15 35
Stage: 1.06 ft 3 0.92 2.95 15 32
4 0.56 2.95 15 62
Point #6 1 1.61 3.28 15 18
08‐Sep‐16 2 1.67 3.28 15 10
Stage: 1.36 ft 3 1.87 3.28 15 9
4 1.80 3.28 15 9
5 1.67 3.28 15 12
Extra credit: 25%
Problem 3. Soil properties and water content.
A soil sample was collected using a tube 5 cm long and 5 cm in diameter. The wet soil sample
weighs 165.9 g. After oven drying the mass of the sample was 151.2 g. The soil grains are made
of mineral quartz with grain density of 2.65 g/cm3
.
(a) Compute the volumetric soil water content (volume of water divided by volume of sample),
the wet bulk density of the soil (mass of wet soil divided by volume), and the dry bulk density.
(b) Compute the porosity of the sample (volume of pores divided by total v