Hi, this is Megan Poff
and I'm the Field Office Chief
at the USGS in Las Vegas, Nevada.
In this video, I'll be discussing the background
and theory for the slope-area indirect measurement method.
Don't click off of this video yet!
It's important that you understand
why you're doing what you're doing
and knowing a little theory can help with your understanding
so you can collect the best data possible.
Slope-area measurements are the most common type
of indirect measurement method used by the USGS.
Generally if you hear someone
say that they were out running indirects,
they were likely referring to the slope-area method.
You can find more information on this topic in TWRI 3-A2:
Measurement of peak discharge by the slope-area method.
What is a slope-area measurement?
A slope-area measurement is a one-dimensional flow model
developed using a uniform flow equation
that accounts for channel geometry, channel roughness,
and the water-surface profile at the peak of the flood.
For the uniform flow equation,
the USGS uses a variation of Manning's equation,
which is defined as Q equals 1.486 over n
AR to the 2/3 S to the 1/2, where Q is discharge,
n is a roughness coefficient,
A is the area of the channel cross section,
R is the hydraulic radius,
and S is the slope or energy gradient.
Hydraulic radius R essentially is the mean depth of flow,
defined as area of the channel cross section
divided by the wetted perimeter.
Wetted perimeter is simply the perimeter of the channel
that is, well, wet.
Sometimes, Manning's equation is simplified
as Q equals KS to the 1/2,
and K is referred to as the conveyance.
Think of the conveyance
as a measure of channel carrying capacity.
In the slope-area method, the slope S is approximated
by the water-surface profile defined by high-water marks.
The slope-area method assumes you have conditions
close to steady and uniform flow.
These conditions are known as gradually varied flow.
Steady flow means that your flow isn't varying by time,
and uniform flow means that your flow
isn't varying spatially, so depth, area and velocity
are the same from section to section.
Generally, steady flow is a safe assumption
at the flood peak because we will have conditions
that approximate steady flow just at the end of the rise
and before the start of the recession.
However, we also need to choose a measurement reach
in which the channel geometry is fairly uniform throughout.
Take a look at a natural channel.
To me, this sure doesn't look
like completely uniform conditions.
See those areas of expansion and contraction?
As long as channel changes in the reach are not too drastic,
that is, they change gradually,
we can basically assume steady and uniform flow
in this reach by placing cross sections
at the major hydraulic changes,
which we will identify by assessing
the flood high-water marks
and resulting water-surface profile.
We'll get more into detail on the water-surface profile
in the slope-area surveying video.
Okay, I gave you a flow equation
and I gave you some definitions of steady and uniform flow.
What does all of this have to do
with a slope-area indirect measurement?
Manning's equation applied to several cross sections
in a stream reach is the basis
for a slope-area indirect measurement.
Remember I just mentioned that our simplified version
of Manning's equation is Q equals KS to the 1/2?
We can apply the equation to several cross sections
by using the geometric mean of the conveyances
at adjacent cross sections, because we're assuming
the conveyance varies gradually between sections.
Before you start panicking
and I start giving you more equations
to account for things like velocity head coefficients,
energy losses, and friction losses,
keep in mind that nobody does
a slope-area computation by hand anymore.
The USGS has developed a helpful computer program
called SAC, which stands for Slope-Area Computation,
it calculates discharge using the slope-area method
from a user-prepared input file
that includes the spacing between cross sections
along a longitudinal baseline,
the water-surface elevation at each cross section,
the X-Y geometry of each cross-section
starting from an arbitrary horizontal reference,
remember, this is a 1-D model,
and user-defined estimates of the roughness
at each cross section.
There are also Graphical User Interface, or GUI,
platforms like iRIC and SAC-GUI
that can help you create the input file;
the SAC executable program is integrated with these GUIs.
You can download a copy of the SAC executable program,
along with its user's guide
from https://water.usgs.gov/software/SAC.
Before attempting a slope-area indirect measurement,
please refer to the video that covers
survey requirements for a slope-area.
If you need help in the field,
call your supervisor, surface-water specialist,
or indirect measurement specialist.