Accuracy of U.S. Geological Survey manometer and pressure-sensor bubble gages
In Reply Refer To: July 30, 1991
WGS-Mail Stop 415
OFFICE OF SURFACE WATER TECHNICAL MEMORANDUM NO.91.09
Subject: Accuracy of U.S. Geological Survey manometer
and pressure-sensor bubble gages
Concerns recently have been expressed about the accuracy of stage
measurements made with U.S. Geological Survey (USGS) gas-purge
manometer and pressure-sensor systems (bubble gages). One concern
is the effects of temperature variations. A second concern is the
effects of the weight of the purge gas in long bubble-delivery
lines. The purpose of this memorandum is to provide information on
the magnitude and practical significance of these effects.
Various systems are used to monitor water levels by sensing pressure
and applying a pressure-stage conversion relation to produce stage
readings. Such systems include balance-beam manometers and various
types of pressure transducers, as well as the USGS Stacom mercury
manometer. Although these systems differ in the details of how the
pressure is sensed, the relations between pressure and stage are
substantially the same for all of them. The theory and practical
operation of the USGS gas-purge manometers are described in Water-
Supply Paper (WSP) 2175 and Techniques of Water-Resources
Investigation Report Book 8, Chapter A2 (TWRI 8A2). Similar
principles apply to other pressure-sensor systems that use gas-purge
systems to transmit pressure to the sensor.
The usual operating environment for USGS bubble gages is on a
stream bank, with water depths less than about 50 ft over the
orifice, with negligible wave or surge action, and with the
instrumentation located no more than about 100 ft above the bubble
orifice. Most available USGS documentation and experience relates
to this operating environment. Proper interpretation of bubble
gage records from reservoirs with large ranges of stage, estuaries
with heavy wave action, and other unusual environments requires
specialized analyses. (See, for example, W. Smith, WRD Bulletin,
1974, and Beck and Goodwin, WSP 1869-E, 1970. Smith's 1974 article
has been revised slightly and included in WSP 2340, Selected Papers
in the Hydrologic Sciences, which is now in press.)
Bubble gages that are not subject to heavy wave action or other
dynamic effects can be analyzed using elementary hydrostatic
principles and the ideal-gas law. Such analyses have been carried
out by Smith (1974, 1991) and Kirby (1991, Water-Resources
Investigation Report 91-4038, in press). The key elements of these
analyses are proper accounting for the weights of gas in the
bubble-delivery tube and in the atmospheric column during the
formulation and subsequent mathematical manipulation of the
hydrostatic equations. These analyses clarify the significance of
facts about bubble-gage performance that are noted but given little
emphasis in WSP 2175 and TWRI 8A2.
TWRI 8A2 states that the Stacom manometer has a temperature
sensitivity of 0.01 percent per degree Fahrenheit, due to change
in the density of mercury. Daily maximum and minimum temperatures
commonly depart from the seasonal mean by 10! F or more. A 20! F
temperature change induces a 0.20 percent change in manometer
reading, which amounts to 0.10 ft at a 50-ft height (stage) of
water over the orifice and to 0.01 ft at a 5-ft stage. Since USGS
manometers ordinarily are not equipped to compensate for diurnal
temperature changes, these changes ordinarily will appear as
variations in the recorded stage. The degree to which such
variations will affect the discharge records depends on the
frequency and duration of large temperature changes, the frequency
and duration of high stages, and the slope of the stage- discharge
rating. Because the slope of stage-discharge ratings typically is
between 1.5 and 3 on log-log paper, a 0.3 percent fluctuation in
manometer reading would result in a 0.5-1.0 percent fluctuation in
computed instantaneous discharge; errors due to daytime high
temperatures would tend to be cancelled by nighttime lows in the
calculation of daily-mean discharge. A limited informal survey of
data chiefs in 1986 suggested that there was a consensus that
bubble-gage errors due to orifice plugging, stagnation, and other
problems often can have a magnitude of tenths of a foot, which is
quite large relative to the temperature effect.
WSP 2175 (p. 74) and TWRI 8A2 (p. 1) both acknowledge that the
weight of pressurized gas in the bubble-delivery tube will make
the gas pressure at the gage house slightly less than that at the
orifice. This pressure differential is offset partially by the
weight of the atmospheric column between the water surface and the
gage house. Gas weights affect both mercury manometers and all
other types of pressure sensors that operate with gas-purge bubble
systems. Calculations using the ideal gas law show that the gas-
weight effect increases nearly linearly with increasing stage and
height of the instrument above the orifice. For installations at
sea level and at moderate atmospheric temperatures, the results
(Smith, 1974, and Kirby, 1991) may be illustrated as follows:
___________________________________________________________________________
Height of instrument Water depth Gas weight head (ft of water)
above over for indicated bubble gas
orifice (ft) orifice (ft) N2 CO2
-------------------- ------------- -------- -------
30 0 0 -.02
10 - .02 -.05
30 - .07 -.11
100 0 0 -.06
10 - .04 -.13
30 - .14 -.27
230 0 + .01 ----
50 - .46 ----
150 -1.39 ----
___________________________________________________________________________
These results depend on barometric pressure, air temperature,
bubble-gas temperature, and other factors, but for the normal
range of environmental conditions (barometric pressures of 29 to
30.5 inches of mercury, temperatures of 250 to 300 degrees Kelvin
[about -20 to +30 degrees Celsius]), these factors are of
secondary importance relative to instrument and water-surface
heights. See the references for details.
The effect of gas weights on stage measurement by bubble gage
depends on the magnitude of the gas-weight head relative to the
water depth over the orifice and on how the pressure-stage
calibration for the gage is established.
If the calibration is based on theoretical calculations that
neglect gas weight (for example, by using a nominal unit weight of
62.4 pounds per cubic foot to convert pressure to depth of water),
then the computed gas-weight heads represent errors in the stages
indicated by the bubble gage. Such errors are likely to be
present in "off-the-shelf" factory-calibrated manometers and other
pressure sensors, especially if gage elevation, instrument height
above orifice, and bubble-gas composition are not specified in the
order for the instrument.
On the other hand, if the bubble gage has been field-calibrated to
agree with direct measurements of stage throughout the range of
stages, then the gas weights are automatically accounted for. Such
calibration can be accomplished by means such as field adjustment of
the gage or application of a correction factor to the gage readings.
For calibrated gages, gas weights may be of interest as a
theoretical explanation for all or part of the empirically
determined calibration, but they do not represent a residual source
of error.
WSP 2175 (p. 74) notes that the gas-weight error and a number of
other bubble-gage errors vary linearly (or nearly so) with stage and
that such errors can be corrected by adjusting the manometer slant
angle, gear ratios, or other physical dimensions of the mechanism.
For "smart" pressure sensors with embedded microprocessors, additive
and linear corrections to stage can be applied easily by changing
the values of bias and scale factors that are provided in the
microprocessor software.
Theoretical pressure-stage calibrations for bubble gages always
are subject to the shortcomings of any theoretical analysis of
real physical phenomena. Calibrations or adjustments based on
actual field data can be performed by comparing bubble-gage
readings with corresponding direct measurements of stage made by
reading outside gages, such as wire-weight or staff gages. High-
water marks and crest-stage gages are helpful for obtaining direct
high-stage measurements, which are especially important for
defining the slope of the relation between bubble-gage reading and
water-surface elevation.
The foregoing considerations underscore the importance of
obtaining independent, direct measurements of stage at all bubble
gages. Longstanding USGS policy calls for collection and preser-
vation of records of actual water-surface stages at gaging
stations. Longstanding OSW policy also calls for use of crest-
stage gages in addition to outside staff or wire-weight gages at
all bubble-gage sites and for reading all gages, inside and out,
on every visit. This memorandum reiterates these policies.
The normal process of analyzing stream-gage data should include
checks to ensure that the stage records agree with true water-
surface elevations in the stream at all stages. These checks are
especially important for bubble gages. Agreement may be achieved
either by proper adjustment of the stage-sensing instruments or by
application of appropriate gage-height corrections, which may vary
with stage. For quality assurance, the annual station records
should include documentation of (a) the comparison of recorded
stages with true water-surface elevations and (b) the derivation
of any necessary corrections.
Please bring this information to the attention of all personnel in
your office who collect, analyze, or review stage records based on
bubble-gage data.
Charles W. Boning
Chief, Office of Surface Water
DISTRIBUTION: Regional Surface-Water Specialists, FO