Accuracy of U.S. Geological Survey manometer and pressure-sensor bubble gages

In Reply Refer To:                                July 30, 1991
WGS-Mail Stop 415


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