"Sherlock Holmes Meets Hardy-Cross or Model Calibration in Austin

Go To Letter
Sherlock Holmes
Meets
Hardy-Cross
or Model Calibration
in Austin, Texas
Thomas M. Walski
Onewouldthink that water distribution modelcalibrationwouldbe a straightforward,
logical process.Sometimes,however,the besttools for modelcalibration consist of a lot
of detective work, a little intuition, and just a pinch of luck. Some anecdoteson model
calibration in Austin, Texas,illustrate this principle.
Maybe when you were a child you
wanted to be a detective. Sherlock
Holmes has always been your hero. You
can see yourself using your wits to
unravel hopelessly complicated mysteries. But, alas, you always did well in
math and you wanted a secure job, so
you ended up in civil engineering instead.
Don’t despair. There is an area in civil
engineering that requires the keen observation of a Sherlock Holmes and the
dogged determination of a Mike Hammer-pipe network model calibration.
One would ordinarily think that pipe
network model calibration would be a
straightforward logical processinvolving
finding out what is wrong with the
uncalibrated model and correcting the
error to make the model work. The
problem, however, lies in the fact that it
is virtually impossible to know what is
wrongwith agiven model with certainty.
Sure, any reasonably bright person can
spot gross errors like missing tanks, or
pipes with 12-ft lengths and 5,000~in.
diameters. But there are dozens of things
that can make a model inaccurate, and
sometimes it takes a great deal of effort
(which translates to agreat deal of time,
field data collection, and money) to isolate
the problem with any confidence.
This article is not about the kind of
model calibration in which the engineer
looks at a computer printout and concludes that as long as there are no
negative pressures or velocities in excess
of 20 fps, everything must be all right.
Model calibration, as done in Austin,
Texas, involves comparing predicted
heads and flow rates against accurately
measured values over a wide range of
flow conditions. Predicted and observed
heads should agree to within 10 ft,
although it may be necessary to settle
for 20 ft. Usually hydrant flow tests are
conducted as part of model calibration
data collection to provide data on heads
over a wide range of flows.
Researchers have been trying to develop simple cookbook procedures for
34 MANAGEMENTANDOPERATIONS
JOURNALAWWA
Copyright (C) 1990 American Water Works Association
model calibration for some time
now. This author has developed
an approach that enables an
engineer to back-calculate C-factors and water use from hydrant
flow test data.l.2 Ormsbee and
Wood,” Ormsbee,4 and Lansey”
developed optimization methods
for calculating C-factors based
on pressure measurements.
Bhave developed a modification
of this author’s approach that
includes the use of pump flowmeter data.fi The problem with
all of these approaches is that
they are based on the assumption
that all of the error in an uncalibrated model is a result of errors
in C-factor or possibly water use.
In reality, however, there are
simply too many other things
that can be at fault.
It would be easy to list some
typical problems that can be
found in uncalibrated models.
But the lessons will probably be
better rememberedby illustrating
them with some examples from
recent model calibration work
done at the Austin utility.
creates some problems in modeling in
that some lines are Austin lines, some
lines are shared lines, and some lines are
MUD lines. Therefore, when two lines
cross on a map, it is not safe to assume
that they are hydraulically connected.
Assigning C-factors to water mains is
also difficult because Austin softens its
water but does not recarbonate. This
results in a treated water with high
scaling potential. C-factors between 29
and 98 have been measured in older
pipes, with higher values occurring in
newer pipes.7 The utility’s policy is to
base pipe-sizing calculations on a Cfactor of 80. Typical literature C-factors
or pipe aging rates based on corrosion
are meaningless in Austin.
Clearly, model calibration in Austin is
a bit more difficult than it is for most
other systems. Some real detective work
was required to make any computer
model describe what was happening in
the Austin distribution system.
The model
Computer modeling work is performed
in the Systems Planning Division. At the
timeof this work, pump station and tank
operation was handled through the
Water Treatment Division. Operation of
The Austin water system
system valves is handled through the
Operation and Maintenance Division;
The Austin Water and Wastewater
installation of new pipes lies in the
Utility serves approximately a half
million people with water treated at purview of Project Management, which
three plants along the Colorado River in is in a separate department in the city
Texas. Austin is one of the hilliest cities government. Communication between
in Texas, and because of this the service thegroups is generally good, but it is not
area is divided into seven major pressure uncommon for modelers to ask three
zones with numerous small, reduced, or different individuals about the status of
boosted zones. In addition to pumping at a line or valve and get three different
the three treatment plants, there are answers.
nine major pumping stations and eleven
The computer model of the system
storage tanks, plus numerous additional
was originally set up by a private firm*
minor storage and pumping facilities.
during a master planning study in the
The service area covers approximately
early 1980s. The program is the WADSY
450 sq mi.
computer program, which the utility
Although Austin has a typical water runs on a MicroVAX II computer. There
system in most respects, it has some is actually one highly skeletonized “priunique problems and characteristics.
mary” model and seven more detailed
During the early to mid-1980s, Austin
“secondary” models corresponding to
was among the fastest-growing cities in the seven major pressure zones. The
the United States. System improvements secondary models are generally limited
have been installed at a rapid pace. The to pipes 12 in. or more in diameter,
Systems Planning Division of the utility
although some important pipes of smalle
must wage a constant battle to keep the diameter are included. There are roughly
mode1up todate. The problem is exacer- 200 nodes and links in each secondary
bated by the fact that the Maps and model. The primary model only contains
Records Group has experienced difficulabout 25 nodes in the system, although it
ties keeping system maps updated.
contains a great deal of detail in the
The city has also had difficulty funding pump stations. Calibr
improvements to keep up with this rapid work focused on the secgrowth. This has led to the creation of ondary models.
numerous Municipal Utility Districts
Calibration data
(MUDS) around the perimeter of Austin
to provide service to newly developed collection
areas. Many of these MUDS and water
Water use in Ausdistricts around Austin receive Austin
tin is highly dewater on a wholesale basis, although in pendent on the
s’
A
some instances Austin also provides nmnthnr
meter-reading and billing services. This period of
““C(ILIICI
.
hot, dry weather can result in water use
twice that of an average day. It is a better
test of model accuracy to check the
computer model against field data on
days in which head loss isgreatest. This
tends to magnify errors in C-factors and
water use. Therefore, data collection
was carried out during the third week of
August 1987, the week of peak water use
for that year.
Fire hydrant flow tests were carried
out at 31 locations throughout the system. These locations were characterized
as being far from tanks and pump
stations but still located near nodes in
the model. Enough hydrants were opened
during the flow tests to drop the pressure
at the residual hydrant by at least 10 psi.
American National Standards Institute
type A pressure gauges were used. They
were calibrated at the end of each day’s
work. During the field work, the crew
used a video camera to record the face of
the gauge and radio communications
during the test, as well as recording the
overall layout of each test.
The exact water levels in the tanks
and discharge settings of the pumps
were recorded at the time of each test.
During each test, the pressure record
from some remote pressure transmitters
was also noted. However, because the
elevation of these recording gauges are
not known exactly, the data from these
pressure points were used only as checks.
Before joining the staff at the Austin
utility, the author was involved in calibratinga sizable number of pipe network
models. In these instances, data collection for model calibration was a one-time
effort. Because of travel costs, it was
impossible to repeat the tests if there
were inconsistencies in the data. Therefore, some puzzles were never solved. In
Austin, modelers are able to rerun tests
with additional residual pressure gauges
or ferret out details.
Data collection should not be a onetime effort. Rather, engineers should be
free at any time tograb a pressuregauge,
hop in a car, and do some additional
checking. The benefits are not simply a
better-calibrated model but also engineers who have an improved understanding of how the system works.
*Metcalf
& Eddy Inc.. Woburn.
Mass.
Ll
MARCH 1990
THOMAS M. WALSKI
Copyright (C) 1990 American Water Works Association
35
meters began reading zero and new
meters showed up in their accounts.
Checking their accounts, the modelers
found that the MUD and its several
hundred customers had been moved into
the neighboring pressure zone. When
this was fixed, the models in both pressure zones worked better.
The puzzles
Some of the results of the flow tests
agreed with model results, with no additional adjustment of the model required.
But the norm was that the observed and
predicted heads were significantly different, indicating that the existing model
was not a very accurate representation
of thesystem. This is where thedetective
work began. The utility had todetermine
what was wrong with the model. In
some cases the problems were not easy
to find. Instead of simply spellingout the
problems that were found, the next section of the article encourages readers to
test their luck and knowledge of applied
hydraulics.
What’s the connection?
The puzzle. In one area, the model
consistently predicted much higher
heads than those that were observed in
the field. Because there was a 36-in. pipe
nearby, it appeared that there was a
closed valve between the pipe and the
flow test. Closing the valve between the
pipe and the test in the model, however,
still did not produce enough head loss.
Shutting off the 36-in. pipe in the model
produced too much head loss. A valve
crew checked the valves in the 36-in.
pipe and claimed that none were closed.
What happened?
The solution. The crew finally resorted
to a different kind of fire hydrant flow
test to track the path of the water in this
area. They ran the fire hydrant flow test
several times with several residual pressure gauges. In this way the crew was
able to fairly accurately reconstruct the
hydraulic-grade lines that existed during
the test. The 36-in. pipe was open and
not one but two valves between it and
the test location were closed. Water was
reaching the test hydrant through a
path that had not been thought to be
significant. The technique of running a
flow test with several residual hydrants
proved helpful in a number of instances.
It is superior to measuring static pressure at a number of locations because
during a hydrant flow test the head loss
is much greater, so that small errors in
reading gauges do not obscure the results. This technique is not only good for
model calibration but also for finding
closed valves.
Fire hydrants are the engineer’s windows
into what is happening underground.
the distribution maps. The model agreed
with field data once it was resolved
which lines were in place and how they
were connected.
Skeletons in the closet
The puzzle. In an older neighborhood,
the model predicted heads much lower
than those observed during tests. The
area had a rich mesh of 6- and &in. pipes,
but because the pipes were old, the Cfactors should have beenvery low. Where
did this neighborhood get its extra carry
ing capacity?
The solution. The key to resolving this
problem was realizing that pipes smaller
than 12 in. were not in the model, yet
here was an area with only two 12-in.
pipes. As the modelers began to fill in the
grid with smaller pipes, the model and
field results begin toconverge. The moral
is not to expect a skeletonized model to
work well in areas where most of the
water is carried in small pipes that are
not in the model.
The case of the moving MUD
The puzzle. Again the model predicted
much lower heads than were observed
The case of the fast-growing system
during the tests. The author’s equations
The puzzle. The heads predicted by the indicated that actual water use was less
model were less than those observed in than modeled water use. Because this
the system. The author’s equations’ test was near a pressure-zone boundary,
indicated that the C-factors neededto be valves werechecked toensure that water
much higher. But they were already was not spilling between adjoining zones.
very high. How could they be raised?
No open valves were found. Where did
The solution. As mentioned earlier, the the water users go?
Austin system is growing fast. After
The solution. Because there was a large
checking with construction inspectors, MUD near this test, the modelers checked
the modelers found that several new the water use through the MUD’s master
large lines had been placed in service in meters. Several months before the testthat area but had not yet shown up on ing was conducted, some of the MUD’s
A long way from anything
The puzzle. One of the flow tests was
conducted in a water district that buys
its water from Austin. Part of the water
district is connected to the Austin system
through several miles of 6-in. pipe. Pressures there are usually adequate because
of low elevation and limited water use.
During a hydrant flow test, the pressure
dropped below 20 psi even though the
hydrant was delivering less than 200
gpm. To make the model and field data
agree, it was necessary to significantly
increase water use in the area during
normal times and raise the C-factor to
get the right head during the fire hydrant
flow test. The modelers did not feel
comfortable doing this. What should
they have done instead?
The solution. Although the model was
adjusted to work, no one believed it
really described what was happening in
thedistrict. Several months later, utility
personnel were in a meeting with the
engineer for the water district when he
casually mentioned the “PRV [pressurereducing valve] in the 6-in. line.” The
utility’s response was, “What PRV?” A
few days later they drove out to the
water district and found the PRV that
had made it look as if there was more
water use during normal periods than
anyone had anticipated or believed. The
PRV had not been marked on any map.
The case of the floating
pressure recorder
The puzzle.In one pressure zone, it was
possible (within reason) to match the
heads at the test sites, but the measured
head at the pumping station (head = 740
ft) was always much higher than predicted by the model (head = 720 ft). No
one wanted to ignore the pressure reading at the pumps, but it would have
taken some hefty manipulating to force
enough head loss between the pumps
and the test locations. How could a
modeler justify increasing the discharge
head at the pump station?
The sulution. The modelers decided to
go to the treatment plant and check the
pressure recorder from which they were
obtaining the high heads. The operator
explained that there were twogauges on
the pump discharge line: one read 69 psi
and had elevation 582 ft stamped on it
(head = 741 ft), whereas the second read
59 psi and had elevation 555 ft stamped
on it (head = 691 ft). Stop and think
about this for a second.. . whoever says
the stamps on the recording charts had
36 MANAGEMENT AND OPERATIONS
JOURNAL AWWA
Copyright (C) 1990 American Water Works Association
been switched is correct. The heads now
made sense.
The ghost of the 944ti zone
The puzzle. At one time in the system’s
history, there was a pressure zone for
which the tank overflow was set at 944
ft above mean sea level. Recently that
pressure zone had been absorbed into
the 1,015-and 860-ft zones, depending on
theground elevation. Nevertheless, field
tests showed static heads of roughly944
ft in an area that corresponded to part of
the old 944.ft zone. The maps said the
area was in the 1,015-ft zone, the model
predicted heads closer to 1,015 ft than to
944 ft, and operations personnel said the
944-ft tank, although still standing, was
not only valved off from the system but
was empty. Was the ghost of the 944
zone stalking the streets of Austin?
The solution. Utility personnel measured quite a few pressures in the 1,015ft and 944-ft zones and concluded from
the data that there was a great deal of
head loss occurring-much more than
the model predicted. The modelers were
able to isolate the stretch of pipe responsible for the loss. The model contained a pipe that was installed but had
not been accepted or connected because
of some construction contract problems.
All of the flow to the old 944-ft zone was
going through a set of fairly small pipes,
and the head loss in those pipes reduced
the head from 1,015tosomewherearound
944. The 944-ft zone was indeed dead,
but the memory lingered on.
Pulling the plug on the system
The puzzle. In two of the tests, it would
have been necessary to increase the Cfactors to very high <alues to achieve
calibration, A number of small pipes
were added to the system to ensure that
the system wasn’t skeletonized too much,
but there was still a need for more
carrying capacity during the test. Both
tests were at low spots in hilly areas in
residential neighborhoods. Where did
the carrying capacity in these areas
come from?
The solution. The two tests in question
were characterized by fairly dramatic
drops in water pressure during the fire
hydrant flow tests. In these cases, the
modelers were not correct in simply
adding hydrant discharge to normal
water use to obtain total water use
during the test. In most of the other
tests, the modelers only dropped pressure
byabout lOto20psiduringthe test,and
thus water use did not change much.
That assumption did not hold here.
Instead, the modelers had to decrease
modeled water use during the hydrant
flow tests.
The end of the line
The puzzle. At one remote part of the
system, the heads could not be made to
match, The area had essentially two
systems-one was the utility’s, the other
a MUD supplied by the utility. When the
systems were modeled as separate, the
predicted heads were too low. When they
were connected, the heads were too high.
Were they connected or not?
The solution. The utility conducted
some followup flow tests with multiple
residual hydrants. They know now that
the utility and MUD lines are connected
in some places, but still haven’t been
able to identify exactly where because
hydrants in neighborhoods in this area
are attached to one system or another.
There is not a situation in which the
hydrants on one side of the street are in
one system and those on the other side
are in the other. During subsequent road
construction, some small (6-in.) connections were found.
Can you say “diurnal”?
The puzzle. In one large pressure zone
testing took the better part of the day,
rather than the few hours required for
smaller zones. Heads during normal
water use varied widely from the nominal
head expected for that zone. For some
tests, water use had to be increased and
in others it had to be decreased. What
was the pattern?
Thesolution.Water use in Austin varies
significantly during the day. There is a
high morning peak, with a low point
after lunch. Because this was a large
pressure zone, it was wrong to expect
water use to remain constant during
testing. By using different water-use
multipliers through the day as the crew
moved through the zone, the results
improved.
Sometimes you see a lot just by looking
The puzzle. As mentioned earlier, all
that was certain about C-factors was
that they were somewhere between 29
and 140. Based on utility policy, a default
value of 80 was used in initial runs of the
model, and the modelers were reluctant
to change this value because they knew
some pipes had lower values. In general,
the author’s methods indicated that Cfactors generally neededto be increased.
How did they justify increasing C-factors?
The solution. The crew had
seen samples of pipes with
severescale,and during some
hydrant flow tests in old
neighborhoods, chunks of
scale would break off the
pipes and fly into the street,
making it look as if someone
had dumped a bucket of
gravel. It seemedthat the Cfactors should be fairly low.
Oneday, however, theauthor
was jogging along a stretch
where some lo-year-old asbestos-cement pipe was be-
ing removed for a road relocation. Examining the pipe at work later showed the
pipe had some scale but much less than
in older pipes that had been tested. A
logical guess at the C-factor was 110.
Apparently scale was forming at a slower
rate in newer pipes. This was verified
with later C-factor testing. Therefore, it
was decided to raise the default C-factor
to 100, with values of 80 for older pipes
and 120 for brand new pipes. Overall
results improved significantly.
The case of the industrial revolution
The puzzle. In an industrial part of
town, the model predicted too high a
pressure during normal operation.
Because the results during fire hydrant
flow tests were acceptable, it appeared
that the initial water-use estimates were
low. The water-use estimates for large
industries were based on actual metered
use at those industries, and no one
wanted to change these values. This
area was near the boundary with another
(lower) pressure zone, and there was a
possibility that water was flowing into
the lower zone through a PRV. Where
was all this water going?
The solution. The PRV was not open
under normal conditions. Driving
through the neighborhood revealed some
things about the industries. They were
mostly new. Some of them may not have
been operating when the water usage
data had been collected. In addition, one
large user-thought to be on the lower
pressure zone-was found to be on the
higher pressure zone. When the model
was loaded with new water-use rates
based on more recent billing information, the results looked much better.
Every hour on the hour
The puzzle. In calibrating the
extended-period model, initial
MARCH 1990
Copyright (C) 1990 American Water Works Association
agreement was poor. It was not uncommon for tanks to overflow in the
model, even though tank water levels
remained reasonable in the system.
Pump operation was checked numerous
times, yet the model did not track tank
water levels well. Was the model wrong?
The solution. The model was set up so
that pumps could only be turned on and
off in the model at the beginning of each
time step, which corresponded to one
Knowing the exact locations at which
smaller pipes are tied to large mains is
important for loading the model.
hour. In reality, pumps were turned on
and off approximately, but not exactly,
at the hour or half hour. Rounding off
pump operation to the nearest hour
caused the differences between observed
and predicted tank water levels. In addition, the diurnal variation in water use
determined during the calibration day
was not used, but rather the modelers
used a “smoothed” diurnal-use curve.
This induced additional errors. “Unsmoothing” the water use improved the
calibration, but the problem of pumps
coming on during the hour could not be
resolved without reducing the time-step
size in the model, which is not desirable.
There is some discussion about repeating
the calibration of the extended period
model with the operators only changing
pump settings on the hour.
When is an open valve really open?
The puzzle. The crew conducted one
test on a 12-in. dead-end pipe that
branched off from a 24-in. pipe. The
crew expected very little head loss during
the fire hydrant flow test but experienced
a great deal. The test was repeated with
several residual hydrants, and virtually
no head loss was found in the 24-m. pipe
(as expected), but a considerable drop in
head was found in the first 100 ft of the
12-m. pipe. The crew concluded that the
valve in the 12-in. pipe at the junction
with the 24-in. pipe was partly closed. A
valve crew was sent out to check the
valve, and they reported that it was
open. What caused the head loss?
The solution. The crew returned to the
test site with the valve crew and repeated
the test (with the same results). The
38
author then directed the valve crew to
open the valve. Crew members tried and
said it was open. He then asked them to
close the 12-m. valve, and they found
that it closed in three turns. (The valve
had been almost completely closed for
some time.) When they reopened the
valve, they forced it past the point at
which it had apparently been stuck. The
test was repeated, and the results agreed
with the model.
Acknowledgment
The modeling work and data collection
was carried out by Damon Bresenham,
Allison Gephardt, Gail Hamrick-Pigg,
Teresa Lutes, and Melissa Triece. They
were assisted in the field work by Gerry
Aguirre, Randy Alexis, Richard Chaffee,
Jim Edwards, Tino Gonzales, V.M.
“Buster”Hearne, James Knox, Sylvester
Luna, Dong Nguyen, and Fred Sailor.
Water-use projections were prepared by
Craig Bell and Steve Rhoades. Modeling
work was supervised by Craig Bell and
was conducted under the general supervision of Marsha Slaughter.
An earlier version of this paper was
presented at the International Symposium on Computer Modeling of Water
Distribution Systems in Lexington, Ky.,
in May 1988.
Summary and conclusions
When done right, model calibration is
not quick or easy. The price for not doing
it right is basing pipe-sizing decisions on
a model that may be seriously in error.
This makes the cost of calibration look
small.
Conducting fire hydrant flow tests
with several residual pressure gauges is
References
the best way to resolve questions about
1. WALSKI,T.M. Analysis of Water Distribuvalvestatusorthe topology of thesystem.
tion Systems. Van Nostrand Reinhold,
It should be a routine part of hydrant
New York (1984).
flow tests for model calibration.
2. WALSKI,T.M. Case Study: Pipe Network
The experiences just described have
Model Calibration Issues. JOUY. Water
lead the author to conclude that it is
Resources Planning & Management
unlikely that a simple analytical proceDiv.-ASCE, 112:2:238(Apr. 1986).
dure or optimization technique to cali3. ORMSBEE,L.E. & WOOD, D.J. Explicit
brate a model will ever be developed.
Pipe Network Calibration. JOUY. Water
Resources Planning & Management
There are simply too many things that
Div.-AXE,
112:2:166(Apr. 1986).
can be incorrect in the initial, uncali4. ORMSBEE,L.E. & CHASE,D.V. Hydraulic
brated model, and there are too many
Network Calibration Using Nonlinear
sources of error in field data. The
Programming. Intl. Sym. on Computer
methods developed by the author and
Modelingof WaterDistribution Systems,
others shed some light on possible
Lexington, Ky., May 1988.
sources of error, but there is still a large
5. LANSEY, K.E. A Procedure for Water
gap that must be filled by detective
Distribution Network Calibration Conwork, intuition, and additional data
sidering Multiple Loading Conditions.
collection. Possibly some technique in
Intl. Sym. on Computer Modeling of
Water Distribution Systems, Lexington,
the area of expert systems may help
Ky., May 1988.
inexperienced engineers track down
6. BHAVE,P.R. Calibrating Water Distribuerrors in models, but development of a
tion Network Models. Jour. Envir. Engrg
cookbook procedure for model calibration
Div.-AXE,
1141 (Feb. 1988).
is unlikely. Ultimately, a good deal of
7. Metcalf & Eddy Inc. Water Master Plan:
detective work is needed.
Volume 3-Pitometer Trunk Main SurThis article also points out the imvey (1985).
portance of modelers communicating
with all groups in the utility. Some
discrepancies between model results and
field observations could only be resolved
by posing specific questions to valve
crew supervisors, construction inspectors, and operations personnel. The
experiences described in this article
should also illustrate the importance of
accurate, up-to-date maps of the distribution system. Several problems with
ten, he was an engineer with the Water
the model were a result of the lag between and Wastewater Utility in Austin, Texas.
installation of new mains and updating
He hasa PhDin environmentaland water
of system maps.
resources engineering from Vanderbilt
The payback for the time and effort
University (Nashville, Tenn.) and worked
invested in calibration is a consensus 12 years with the US Army Corps of
throughout the utility, not just among Engineers at the Waterways Experiment
the modelers, that the computer model Station in Vicksburg, Miss., beforejoining
of the system accurately reflects what is the Austin utility. Walski is a member of
occurring in the system. Without that
AWWA,
WPCF, and ASCE, and his
credibility, the most sophisticated and work has been published previously by
theoretically correct model that could be JOURNALAWWA, Water ResourcesBulledeveloped would not be effective in
tin, and Public Works, as well as several
helping plan a sound system.
others.
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Copyright (C) 1990 American Water Works Association