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