DC WRRC Report No. 162

FIELD MEASUREMENTS OF GROUNDWATER AND RIVER WATER LEVELS & CALIBRATION AND VERIFICATION OF

THE GROUNDWATER NUMERICAL MODEL

FINAL REPORT

(Reporting Period: August 1, 1990 to July 31, 1991)

H. P. Pao and S. C. Ling

Department of Civil Engineering The Catholic University of America

Washington, DC 20064

Supported by

Geological Survey The U. S. Department of the Interior

Reston, Virginia 22092

December 1991

TABLE OF CONTENTS

Abstract ii

1. Introduction 1

2. Selection of Measuring Gauges 1

3. Low-Pass Traveling-Wave Filter for Noise Attenuation 4

3.1 Concerns 4

3.2 The Principle of Low-Pass Filter - Theoretical Background 4

3.3 Hardware Implementation

4. Design and Fabrication of the New Automated Bubbler Tide Gauge 9

5. Laboratory Testing 9

6. Field Installation of Gas Outlet Orifice 15

7. Superior Features of the New Automated Bubbler Tide Gauge 15References 17

FIELD MEASUREMENTS OF GROUNDWATER AND RIVER WATER LEVELS & CALIBRATION AND VERIFICATION OF

THE GROUNDWATER NUMERICAL MODEL

FINAL REPORT

H. P. Pao and S. C. Ling

ABSTRACT

The primary objective of this study is to investigate and identify techniques and

instrumentations for field measurements of groundwater and river water levels and to carry out these

field measurements so that pertinent data inputs will be available to the numerical model for its

calibration and verification. In the first phase of this project, a new automated bubbler tide gauge

was selected, designed, fabricated, and laboratory tested. The key innovation is the development of

an effective low-pass traveling wave filter for the pressure waves along the transmission line. With

proper design, the filter damps out the noise above a selected cut-off frequency. The superior

features of this new tide gauge excel other gauges in many respects and, therefore, will be a good

candidate in the future for wide use in the field water-level measurement applications.

1. Introduction

The primary objective of this study is to investigate and identify techniques and instrumentations for field measurements of groundwater and river water levels and to carry out these field measurements so that pertinent data inputs will be available to the numerical model for its calibration and verification.

There are several types of gauges available to measure the river stages and groundwater tables. In this study, a newly available technology is used to carry out field measurements of groundwater and river water elevations accurately, reliably, automatically and at an affordable cost. Since the water quality of the Anacostia River is poor, one of the objectives is to install an automated tide gauge and to monitor the surface elevation of the Anacostia River at a selected station. The work plan includes: selection of measuring gauges; site selection; design and fabrication of the river stage gauge; installation and testing of the gauge; measurement of river stage; data collection and analysis; modification of the gauge for measuring groundwater elevation; installation and testing the groundwater gauge; field measurement, data collection and analysis of groundwater levels; calibration and verification of the numerical model for groundwater. The work will be carried out in two phases. In the first phase, the river stage gauge is to be designed, fabricated, and installed. In the second phase, the gauge is to be modified for measuring groundwater tables.

2. Selection of Measuring Gauges

A brief literature review on available gauges and techniques for field measurements of groundwater and river water levels has been carried out. It was decided in the beginning that same type of gauges will be selected for measuring both groundwater and river water levels. The requirements for measuring river water levels are more demanding and complex. Therefore, the selection of the gauges is mainly dictated by those for measuring river water. The more critical requirements for measuring groundwater levels are those during pumping tests where the water level fluctuates rapidly due to water splash and turbulence. The criteria of selection are based on reliability, accuracy, ruggedness, durability, maintainability, portability, availability, and cost. Requirements for automatic data recording and transmission are also major considerations. The selection was narrowed down to two gauges before the final selection was made. The two gauges made into final selection are (1) Aquatrak Air Acoustic Water Level Sensor, and (2) Automated Bubbler Gauge. These are two most recently developed gauges.

(1) The air acoustic sensor must be installed inside a protective well and the water level is

determined by measuring the time interval between the transmitting and returning acoustic echo. Aquatrak Model 3000 is manufactured by Sutron Corporation of

Herndon, Virginia. The sensor uses a pulsed acoustic, time-of travel technique and is self-calibrating for variations in the velocity of sound. It has a measurement range up to 35 feet, with a resolution of ± 0.01 ft. The sensor sampling rate is nominally five per second. The National Ocean Service is presently developing a Next Generation Water Level Measurement System (NGWLMS). The primary data collection platform is a modular system based on the Sutron 9000 Remote Terminal Unit (RTU) and the 9000 RTU family of modules. It is seen that the above system is only suitable for a network of gauges. The initial cost is beyond the reach of our present project. Moreover, the complex system is not suitable for our rather simple requirements. It should be noted that the system is still under development, therefore, its reliability and accuracy are still to be proven. Furthermore, freezing of water inside the protective well during cold winter days may cause operational problems for the air acoustic sensors. It is also noted that its sensitive electronic systems are generally installed in a sheltered house.

(2) Automated Bubbler Gauges. The pneumatic bubbler gauges are widely used for water level measurements by the National Ocean Service (NOS) in coastal waters, and by U.S. Geological Survey (USGS) in the inland waters and estuaries. Basically, it consists of a long pneumatic tube, a gas (typically nitrogen) supply, and an analog recorder. While in operation, a small steady amount of gas is fed into the tube to keep it dry at all time. Excess gas is bubbled away at the submerged end of the tube. The pressure in the tube then represents the hydrostatic pressure of the water level, which can be detected at a remote location on land, safe from adverse sea or river environment. Since all the electronic components are located on shore, there are minimal environmental and fouling problems. The bubbler gauge is suitable for water level measurement along open coast, in remote locations, and in harsh environments where other instruments cannot be easily deployed. However, existing gauges suffer from several operational problems such as (1) clogging of dampening valves, (2) gas leakage, (3) gas line flooding, (4) errors due to improper orifice design, (5) recorder's chart speed variation and (6) inaccuracy arising from severe noises due to background wind-waves and other short period surface fluctuations. Furthermore, the analog output is not compatible with present and future data processing requirements. Very recently, in-depth theoretical and experimental analyses of the bubbler gauge. were performed by Ling and Pao. Under the sponsorship of NOAA in the past several years, significant hardware improvements of existing bubbler gauges have been made. The key innovation is the development of an effective low-pass traveling wave filter for the pressure waves along the transmission line. With proper design, the filter damps out the noise above a selected cut-off frequency. The remarkable improvement is shown in Figure 1, where the background noise of wind-waves has been effectively filtered out. Other deficiencies of the existing bubbler gauge were also corrected through proper design, improved fittings and proper fabrication procedures. Since late 1987, seven modified and upgraded units of bubbler tide gauges have been installed at

(a) Output from existing gage

(b) Output from upgraded gage

Figure 1 . Comparison of analog outputs between existing and upgraded bubbler gage

NOAA/NOS tide stations for long term evaluation. Recent review of all the test data indicated that these units are working as well as originally expected. The upgraded bubbler gauge has been further improved by Ling and Pao very recently, by interfacing with a small digital data acquisition device so that the unit can read and store the data digitally every four minutes (or any specified interval). The case for the instrument package is about the size of an attached case with a weight of approximately 14 kg. It is, therefore, very portable and convenient to transport for field use. The digital data in the data acquisition unit can easily be transferred to any PC computer for further processing and analysis. If desired, the data can also be transmitted by a near real-time telemetry technique. For the measurement of groundwater levels, bubble-tube method has been widely employed. This technique is essentially the same as the bubbler gauges used for water level measurements in rivers and oceans. It is especially suitable for draw down measurements in pumped wells where water splash and turbulence may invalidate other techniques. The basic units of this newly developed automated bubbler gauge will be made available to this research project.

Based on the above review of water level measuring gauges, the bubbler gauge has been selected as the gauge for the measurement of both groundwater and river water levels for this project. It is seen that the bubbler gauge is the only one that is suitable for both groundwater and river water measurements. It is portable enough so that only one unit needs to be fabricated for measuring the river water levels as well as the groundwater levels. The unique and superior characteristics of the bubbler gauges have met our requirements remarkably well.

3. Low-Pass Traveling-Wave Filter for Noise Attenuation

3.1 Concerns

High frequency noises, mostly due to wind waves and disturbances such as ship traffic, often degrade the data quality and render the data processing task rather difficult.

Existing bubbler gauges use a needle valve as noise dampening device. However, in order to be effective, the valve has to be adjusted to a very fine closure. This often causes valve clogging and subsequently requires maintenance operations.

3.2 The Principle of Low-Pass Filter - Theoretical Background

The principle of the low-pass filter was based on the theoretical and experimental study by Ling and Pao [Ref #1] of a long pneumatic pipe line. The present problem involves the propagation of very low frequency pressure waves in a long tube with small bore. Pressure fluctuation due to waves, swells, surges, and tides covers a range of wave periods T from 2s to 45,000s. The resultant oscillatory breathing flow developed in the

tube is generally within the laminar flow range, hence the oscillatory flow profile in the tube is governed by the a parameter

a = D/2(JT/2n)1/2

where D is the diameter of the tube, and t1 the kinematic viscosity of gas. For the present problem, it can be shown that a is smaller than 1. Hence, the flow profiles are always fully developed and parabolic in form. Consequently, the frictional stress in the tube is essentially in phase with the flow [Ref #2]. Due to the relatively large amplitudes of waves under high sea states, the kinematic viscosity of gas in the tube can no longer be considered as constant. It should vary with the mass density of gas p , and thus also with the pressure P. Since the flow resistance in the tube is an odd function of P, any oscillatory pressures in the tube can contribute to a mass positive pressure error. The conservation of momentum within a ex element of the tube with uniform cross-sectional area A can be expressed as

Δx/Δt [qx(t)-qx(t-Δt)] + qx(t)/2 [Ux+Δx(t) – Ux-Δx(t)] + 32μΔx/D2ρ(px) * qx(t) = -A/2 [Px+Δx(t) – Px-Δx(t)], (2)

where t is the time, q=APU the mass flow rate, U the mean sectional velocity of gas flow, and p the viscosity of the gas. The first term of Eq. 2 is the local rate of change of momentum in the dx element. The second term is the convected momentum into the element. Due to uniform tube diameter and very long pressure waves, this term is very small with respect to the other terms. Hence, for this problem it may be deleted from the equation. The third term is the frictional force on the element due to laminar flow, and the last term represents the external pressure forces. The conservation of mass in the tube element can be expressed as

2 A Δx *ΔP/Δt + [qx+Δx(t) – qx-Δx(t)] = 0 (3)

That is, the rate of change of the mass inside the tube element is equal to the net mass flow into the element. Due to both the long period of pressure wave and small tube size, the equation of state for the gas can be taken to be isothermal and expressed as

Δρ/ΔP = ρa/Pa (4)

where the subscript a represents the value at standard atmospheric conditions. Substituting Δp of Eq.4 into Eq.3, we have

- Pa/2ρaΔxA [qx+Δx(t) – qx-Δx(t)] Δt = Px(t) – Px(t-Δt) (5)

We further define the following nondimensional variables and parameters as: n =x/Δx, N=l/Δx, Δr=Δt/T, P=P/IPw,,I

ρ(Px)/ρa = (Pa+Ps)/Pa [ 1 + Px(t)/Pa+Ps] , Q= 128μlPa/ πPwD4ρa(Pa+Ps) *q

S= T (Pa+Ps)D2/ 32π l2 , and E = ρa/Pa [(Pa+Ps)D2/ 32π l2]2

where P is the mean hydrostatic pressure of the gauge, IPw) is the moduTus of the input wave pressure, and ,1 is the total length of the tube. Finally Eqs. 2 and 5 can be expressed in the normalized forms as

E/NsΔr [Qn(r)-Qn(r-Δr)] + Qn(r) / N[1+ PwPn(r )/ Pa+Ps] = -1/2 [Pn+1(r ) – Pn-1 (r )] (6) - NSΔr/2 [Qn+1(r ) – Qn-1 (r )] = Pn(r) – Pn(r – Δr) (7) and

Boundary conditions for the problem are the input pressure Pwsin2nt at the inlet and closed tube at the output end.

The numerical solutions for Egs.6 and 7 are given in Figs. 2,3, and 4. In Fig.2 the normalized attenuation of the output pressure Po= P0/Pw is plotted as functions of the normalized wave period S and system characteristic parameter E. Note that for S>3, the signal attenuation is minimal, while signal cutoff is very sharp at S<0.1. The E parameter only affects small period waves. To obtain good high frequency cutoff characteristic, it is necessary to make E<0.002. The general wave and swell periods cover a period band of 2s to 15s. Hence, it is desirable to place the 5s period wave at S=0.05 in order to obtain a good signal attenuation for these waves. Since the tide has a mean period of 45,000s, the corresponding S value is 450. From Fig.2, one notes that there will be no attenuation for the tide signal, and the corresponding phase lag o is only -0.40. Hence, the system will provide accurate tide data. Fig.3 gives the normalized breathing mass flux Qi at the inlet and its phase angle 0 with respect to the input pressure Pw. This information is needed for the design of a larger diameter breathing cylinder to be attached to the inlet end of the tube. Note that Qi decreases as 1/S for S>3. Since the net breathing mass or volume per period is proportional to SQi, the breathing volume per period is a constant and maximum for S>3. Hence, to prevent flooding of the pneumatic tubing, the volume of the breathing cylinder should be made larger than the maximum breathing volume of the tube plus the breathing volume of the breathing cylinder itself. For Si ,2 the net breathing volume per period will decrease and vary as S It can be shown that the breathing effect can contribute to a mean negative pressure error. Figure 4 shows the normalized mean pressure error Pe/1Pw1 due to tube friction. It is plotted as functions of S and E parameters. For S<1 the error is a maximum and essentially a constant. Since the tube breathing effect generally contributes to a negative mean pressure error, while frictional effect contributes to a mean positive error, these errors can be made to cancel each

Figure 2- Normalized pressure response plot.

Fig. 4. Normalized mean pressure error due to pipe friction 'Fe Vs. S and E parameters.

other with a proper diameter for the breathing cylinder. The above analytical results have been verified experimentally.

From the results presented in Figs. 2 to 4, it is seen that the complex operating characteristics of a pneumatic transmission line is fully parameterized. From the present data, one can readily obtain the optimum design for a specific tide gauge; and many undesirable manual adjustments and correction factors for the gauge are thus eliminated. This has, in fact, paved the way for the automation of the tide gauge in this project.

3.3 Hardware Implementation

The results of mathematical model simulation led to the development of an effective low-pass filter, which is analogous to the traveling wave filter in modern radio and television sets. With proper design, the filter will damp out the noises above a selected cut-off frequency. In the gauge hardware this was implemented by a coil of micro-bore plastic tubing.

4. Design and Fabrication of the New Automated Bubbler Tide Gauge

Based on the results of theoretical and experimental investigations, a completely new bubbler gauge has been designed and fabricated for this project. The new gauge is equipped with a high precision pressure transducer, a properly designed filter coil, a leakage-proof tubing system, and an automated data acquisition and control unit. Thus, the gauge is completely automated and compatible with many standard digital data acquisition systems.

A schematic diagram showing the detail of the layout of the tide gauge is given in Fig.5. A picture of the front control panel of the tide gauge is shown in Fig.6. The data recording system as shown in Fig.7 can read and store data digitally. It is portable and convenient to transport for field use. A picture of the prototype of the new automated tide gauge is shown in Fig.8 in both open and closed positions. It is seen that the size of the new tide gauge in closed position is about the size of an attached case.

The recorded digital data can easily be transferred to any PC computer for further processing and analysis. With modification, the system can transmit data, through a telephone line by using a modem, to a central station at any time.

5. Laboratory Testing

Laboratory tests of the new prototype water level gauge have been carefully carried out, using our unique tide simulator. The simulator, as shown in Fig.9, can give a water level fluctuation with a period of 12 hours. The tide gauge has been checked with respect to accuracy, stability, and reliability. It has performed

N2

Input

Dampling Wave 223'long valve filter ;25J

"

Signal output

Figure 5. Schematic diagram showing detailed layout of the tide gauge.

Figure 6. Front control panel of tide gauge.

Figure 7. Data recording system.

-12-

Figure 8. A picture of the prototype of the new automated tide gauge. (a) Open position; (b) Closed position.

-13-14

respect to accuracy, stability, and reliability. It has performed almost flawlessly during the one-month period of testing. The high-precision Paroscientific Digiquartz pressure transducer with temperature correction is highly accurate which provides a water level resolution better than 1 mm.

6. Field Installation of Gas Outlet Orifice

A copper cup which will be used as a gas outlet orifice has been designed and fabricated. It was so designed that the positive pressure error contributed by the frictional effect is essentially cancelled by the negative pressure error due to the tube breathing effect. A drawing showing the details of field installation for the gas outlet orifice is shown in Fig.10. The installation of the new tide gauge is to take place as soon as the site is selected on the Anacostia River.

7. Superior Features of the New Automated Bubbler Tide Gauge

We now summarize the superior features of our new automated bubbler gauge as follows:

Sensing and recording components separated from pressure measuring point (in water) - all electronic components are located on shore, there are minimal environmental and fouling problems.

* No protective well is needed.

* Front-end filtering of noises

equipped with an effective low-pass traveling-wave filter damps out noises above a selected cut-off frequency flexibility for selecting filters.

Versatile data logger (called SQLOG)

4-minute data acquisition rate or any pre-selected time interval allows sleeping mode (energy-saving feature) so that one 9-V battery can last for two months no external power source is needed digital data stored in SQLOG module can easily be transferred to any PC computer for further processing and analysis.

* Easily adapted to a telemetric data transmission

With modification, the data logger can transmit data, through a telephone line by using a modem, to a central station at any time.

* High-precision pressure transducer with temperature correction

-15-

Stainless

steel 3/4" 0

Concrete

pier

HeavyPVC3/8"0 O.D.

Figure 10. Drawing of bubbler tide gauge gas outlet orifice installation at a concrete piling (assuming 1-ft diameter).

-16-

* Highly accurate and reliable - better than 1 mm water-level resolution

* Small, portable and easy to install - dimension: 31 cm x-41 cm x 17 cm

* Can be serviced easily

* Especially suitable for water level measurement along open coast with large tide range in remote hard-to-reach locations in harsh environments where other instruments cannot be easily deployed.

* An in-situ density determination feature can be included

one of the applications for this feature is to measure sediment concentration in water.

It is noted here that the superior features of this new tide gauge excel other gauges in many respects and, therefore, will be a good candidate for wide use in the field water-level measurement applications in the future.

References

1. Ling, S. C. and Pao, H. P. (1984). "Mechanics of A Pneumatic Tide Gage," Proc. Fifth Engineering Mechanics Div. Specialty Conference, ASCE, A.P. Boresi and K.P. Chang (Ed.), pp 807-810.

2. Schlichting, H. (1968). Boundary Layer Theory, McGrow-Hill, N.Y., pp 419-421.