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This is to certify that the

thesis entitled

A Bubbler System for Water Table Monitoring

presented by
Kurt Goebel

has been accepted towards fulfillment
of the requirements for

M- S - degree in Agricultural Engineering

/

ajor professor

Date yd? //) /j%

0-7839 MS U is an Aflimau've Action/Equal Opportunity Institution

 

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RETURNING MATERIALS:
}V153I_) P1ace in book drop to
LJBRARJES remove this checkout from
m. your record. FINES will
, be charged if book is
returned after the date
stamped below.

 

 

 

 

A BUBBLER SYSTEH FUR UGTERTABLE NONITDRING

89

Kurt flichael Boebel

fl THESIS

Submitted to
flichiaan State University
in partial fulfillment of the requirements
for the degree of

"ASTER OF SCIENCE

Department of Agricultural Engineering

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427—1474 7

nesrRacr
n BUBBLER svsrrn FDR wnIERIABLE MONITORING
Bu

Kurt flichael Boebel

The bubbler system is an electronic data acquisition system
to monitor and record the position of the watertable for
drainage and subsurface irrigation research. It uses a
small diameter observation well to minimize the time lag
between the actual watertable and the water level in the
observation well. Nitrogen gas bubbles slowly through
smaller diameter spaghetti tubing which is in the
observation well. A pressure transducer connected to the
spaghetti tubing senses the pressure required to force a
bubble out of the bubbler tube. thereby sensing the water
level surrounding the tube. a pressure transducer converts
the pressure into a voltage. a datalogger changes the
voltage from the pressure transducer to a digital output.
The data acquisition equipment is located in one central
location from which the spaghetti tubing fans out to the
observation wells. Data is stored in the datalogger and

transferred to floppy diskette for further analysis.

approved: /§Z:*L$£>/S§%;22;ZAVU\
:::or P ofe::::;aéi/ ,
Approved: é? I <9ngL//

Department Chairman

 

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ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my committee
chairman, Dr. George Herve, for the advice, help. and
encouragement given during the course of my studies and

research.

I am also grateful for the help and guidance offered by the
other members of my committee, Dr. Ted Loudon, Dr. John

Berrish, and Gary Peterson.
I would also like to thank Bill Presson for his friendship.

finally, a special thanks to my wife. Pam, and daughter,
Kristen, for supporting me through each of the deadlines for

the completion of this thesis which came and went.

11

TQBLE OF CONTENTS

I. Introduction

II. Literature Review

a. Non-recording methods
of water level monitoring

B. Recording methods
of water level monitoring

C. Problems with current
water level monitoring devices
III. System Design
A. Design objectives
8. Proposed system
C. Selection of components

D. Data transfer

1U. Development of system
a. Test system I
8. Test system II
c. Field system installation

D. Results of field test

iii

18

80
BO
22
25

EB

32
37

U. Error Analysis
A. Statistical method used
8. Calibration of components
C. Bubbler system calibration
D. Lag time determination

E. Analysis of system

01. Recommendations
A. Field system II

B. Other suggestions

UII. Other Applications
A. monitoring pump output

3. Run-off and pollutant monitoring (with
Campbell Scientific Hodel 81X micrologger)

C. watertable monitoring at 6% locations

0111. Conclusions

APPENDICES

A. Component specifications and prices

8. Sample BASIC program and datalogger commands
C. Component calibration data

D. System calibration data

E. PLDT-IT output for regression
lines forced through the origin

F. PLDT-IT output for Figure 28
G. Bibilography

H. Index of authors

iv

H5
H7
52
57
73

82

SO

SB
108
10%
110

182
127
136
133

Table 1:
Table 2:
Table 3:
Table %:

Table 5:

Table 6:

LIST OF TABLES

Equations used for the statistical analysis. SS
Summary of the pressure transducer calibration. 51
Summary of the bubbler system calibration. SS

Bubbler tube length versus slope of time
to equilibrium line. 71

Best fit equations for the curve in
Figure 27 as determined by PLDTIT. 73

maximum water level rate of change for
the tested bubbler tube lengths. SO

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

10:

11:

13:

13:

1‘1:

15:

15:

LIST OF FIGURES

Proposed bubbler system.

The transfer of information from
observation well to floppy diskette.

Test system I.

A one hour sample of the data from the test
system I data as recorded by a strip chart
recorder.

Test system II using a datalogger to
collect the data.

Fifteen hours of data from test system II.

The first field system showing the
datalogger, portable computer, and
observation well.

Bubbler system test field showing
the observation well sites.

Bubbler tube installation into a
observation well.

Fluctuations in the reference pressure
transducer output. The uncorrected and
corrected data sets are from observation
well site *6.

Sample of corrected date compared to
float-type chart recorder data.

Excitation voltage versus output voltage
for a pressure transducer.

Calibration curve for the pressure transducer

Determination of the temperature coefficient.

Temperature versus output voltage.

Time versus water depth for the
30.5 meter bubbler tube.

Time versus water depth for the
158.& meter bubbler tube.

vi

81

25

BS

30

31

3E

35

35

38

H1

$3

HS
50

53

58

SS

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure
Figure
Figure

Figure

Figure

17:

18:

13:

30:
31:

32:

E3:

2"}:

85:

ES:
37:

38:

ES:

30:

31:

33:

3"}:

Time versus
305.6 meter

water depth for the
bubbler tube.

Time versus
557.2 meter

water depth for the
bubbler tube.

Time versus
605.6 meter

water depth for the
bubbler tube.

Comparison of Figures 16 - 15.

versus time
30.5 meter bubbler tube.

mater depth change
to equilibrium for

versus time
152.5 meter bubbler tube.

water depth change
to equilibrium for

versus time
305.6 meter bubbler tube.

mater depth change
to equilibrium for

versus time
$57.2 meter bubbler tube.

Mater depth change
to equilibrium for

versus time
608.6 meter bubbler tube.

water depth change
to equilibrium for

Comparison of Figures 28 - 85.

Bubbler tube length versus slope of time
to equilibrium line.

First and second order response to step
input and the actual output curve.

First order response to a terminated
ramp and the actual output curve.

Determination of the time constant.
Difference amplifier.
Uariable voltage regulator.

The bubbler system layout using a Campbell
Scientific Hodel 21X micrologger.

Schematic of bubbler system instrumentation
and solenoid banks to monitor 6% observation
wells for a watertable management research
project.

vii

80

81

82
83

65

87

SS
70

78

75

77
78
83
85

SE

85

NOTE

Mention of specific manufactured products in this thesis is
made in the interest of clarity, and in no way implies
endorsement of these products by the author or Michigan
State University.

viii

I. Introduction

Research in the area of soil and water has not kept
pace with the electronic technology available for data
collection. An example is something as simple as monitoring
a water level. A record of water level versus time is very
important for many parameters used in soil and water
research. Some examples of these are the position of a
water table for subsurface irrigation research, rate of
change of position for the calculation of hydraulic
conductivity, actual depth in a flume to calculate flow, or

stage of a river.

Both non-recording and recording methods have been used
to measure water levels. Non-recording methods use a
calibrated tape, rod, or tube inserted into an observation
well until the water surface is reached. The manual,
non-recording method of water level data collection is
adequate only if frequent readings are not necessary or if

simultaneous readings are not required at multiple sites.

many techniques have been devised to monitor and record
water level. A popular and widely used chart recorder is
the Steven’s meter which utilizes a float-type system

consisting of a beaded cable that passes over a pulley. The

8

cable is equipped with a float on one end and a
counterweight on the other. The float follows the rise or
fall of the water surface and the stage or level may be read
from the tape, or from a recorder connected to the pulley
producing graphic records of water surface elevation with
time. The float-type chart recorder is probably the most
common method used to produce a water level-time
relationships. To analyze float-type data, values have to
be read from the chart either manually or through the use of
a digitizer and entered into a computer, a time consuming

task.

The increased use of the personal computer allows more
data to be analyzed to better describe an event or
management practice. To take more data, reliable
instrumentation to record water level readings at each site,
and methods for easy or automatic transfer of the data to

computer for analysis must be used.

To facilitate computer analysis, techniques to get the
information to a computer have been developed. Several
attempts at converting a float-type meter to give an
electrical output have been tried. One method used a
potentiometer connected to the float drive shaft to give a
linear DC voltage output dependent on the vertical position
of the float. Another method used a water level sensing
probe. The sensor activates microswitches that control the

electric motor to move the sensor up or down to determine

3

the water surface. A potentiometer gives as output a linear
DC voltage dependent on the vertical position of the sensor.
An inherent problem with a motorized probe device is that it
is expensive, requires frequent maintenance, and the
electric potential on the probe causes direct current flow

through the groundwater resulting in electrolysis.

Another method measured water level using platinum
electrodes connected in parallel and placed at given
intervals along a probe inserted into an observation well.
The presence of water at a given electrode level provides a
pathway for signal to flow to a common electrode running the
length of the probe. The data is stored on a strip-chart
recorder. This has the limitation of not being easily
modified to give analog output as well as the above
mentioned problem with electrolysis. To avoid electrolysis
and rapid deterioration of the probe contacts, the above
system was modified to use an AC input signal to energize
the probe. The AC signal was converted to DC prior to being

recorded.

The system proposed in this work uses a small water
table observation well, approximately Bl!” I.D., to minimize
the time required for the water level in the observation
well to reach the actual water table level following a
change in the actual water table level. Into the
observation well a smaller diameter bubbler tube (1/6” I.D.)

connected by flexible tubing to a tank of compressed

5

nitrogen gas is inserted. Nitrogen gas is used to retard
the growth of algae. The nitrogen gas is allowed to bubble
slowly through the tubing into the observation well. A
pressure transducer connected to the supply line senses the
pressure required to force a bubble out of the bubbler tube,
hence, sensing the water level surrounding the bubbler tube.
The bubbling rate is controlled by an in-line needle valve.
The pressure transducer converts the pressure required to
force a bubble out of the supply line into a voltage. A
datalogger, which converts a voltage into a digital output,
is connected to the pressure transducer and a reading is

taken at some time interval depending on the circumstances.

II. Literature Review

A. Non-recording methods of water level monitoring

The non-recording method of monitoring a water level
uses a calibrated tape, rod, or tube lowered until the water
surface is reached. flany methods have been devised to make

water level monitoring easier and more accurate.

Reeve (1965), as stated by flacUicar (1676), describes
two typical methods for locating water level in an
observation or stilling well. The first requires the user
to blow through a graduated tube and lower it until a
bubbling sound occurs. The second utilizes a brass bell
connected to a graduated tape which is lowered until the
bell is heard hitting the water surface. The United States
Bureau of Reclamation’s, fl33g;_ngggy;§mgn;_flgnygl,(1575)
describes two general types of non-recording gages that are
in use for river stage measurements: staff gages and chain
or wire gages. A staff gage can be vertical or inclined and
the stage readings are taken directly from the gage. The
chain or wire gage is usually mounted at some fixed
elevation above the water and the weight or float lowered
until the water surface is reached. The water level is then

read from the chain or wire index on a horizontal scale.
5

This type of gage measures from a fixed point and is
affected by settling and/or frost heave of the structure
that supports it, temperature changes, changes in the chain
length due to wear, and wind which may not allow the weight
or float to hang vertically. The wire weight gage is
similar to the chain gage but wire or small cable is wound
on a reel. The reel is graduated to tenths and hundredths

of a foot.

To get a field measurement of the hydraulic
conductivity of a soil below the watertable using the auger
hole method, the change of water level in an auger hole must
be monitored. Uan Beers (1666) used a simple apparatus to
follow the water rise in an auger hole. It consisted of a
vertical standard which was pressed into the ground a preset
distance and to which a ruler was attached. A light weight
steel tape, equipped with a pointer to show position on the
ruler, was connected to a float. After the water in the
auger hole was bailed out, readings were taken at a time
interval of 5 seconds to several minutes dependent on the

soil’s hydraulic conductivity.

To make an instrument easier to read and use, devices
have been developed to use electrical output to locate a
water level. An example is an electrical point gage, the
distance to the water surface is measured using a plumb bob
connected to a graduated tape. The bob is lowered until it

reaches the water surface, contact of the bob with the water

7

surface completes an electric circuit causing current to
flow through the circuit. Uilm and Collet (1651) designed a
compact and simple instrument using a flashlight case as the
main body. A milliammeter used to detect contact with the
water surface, was mounted in place of the lens and bulb.
The device was supported by a plug-in socket mounted at some
reference point with a ground wire going from the socket to
the water. Three standard 1-1/2 volt flashlight batteries
were connected in series with a 5000 ohm resistor and the
milliammeter. The negative side of the circuit was
connected to the ground wire, while the positive side was
connected to a steel measuring tape graduated in feet,
tenths, and hundredths. The bob was lowered until the
needle on the milliammeter deflected, signaling that the
water surface had been reached. The depth was read from the
steel measuring tape. Russel (1656) developed a similar
probe consisting of a graduated copper probe rod, and a
sensing circuit consisting of a 55 volt battery, a SOD-ohm
resistor, and a small milliammeter. A wire was connected to
a small brass machine screw embedded in a rubber insulator
and inserted into the bottom end of the copper tube, the
other end of the wire was soldered to the sensing circuit.
The probe was inserted into the observation well until the
milliammeter showed current flow, implying the water level
had been reached. The distance to the water level was
recorded from the scale on the copper tubing. Lissey (1667)

used a variation of a Fisher n-Scope electrical tape

modified by replacing the original wire with two conductor
shielded phono-pickup wire, color-coded footage tags were
attached to the wire to facilitate measurement. The probe
used two splicing sleeves to separate the upper and lower
electrodes and a fishing line leader with attached weights.
The electrodes were lla inch apart and the outside diameter
of the probe was 1/6 inch at the electrodes. The upper
electrode was connected to the outer metallic shielding
while the lower electrode was connected to both insulated
conductors. The probe was lowered until the meter on the
fl-Scope reel deflected. The distance to the water surface
was determined using the color-coded footage tags.

Uan Everdingen (1666) used pressure transducers to determine
the piezometric pressures in confined aquifers in South
Saskatchewan, Canada. The pressure transducers were
variable-reluctance type with a range of 0 to 100 pounds per
square inch absolute (p.s.i.a.). The pressure transducers
were installed in the bottom of the piezometers in specially
constructed waterproof housings. fleasurements of the water
levels in the piezometers were taken monthly using a battery
powered read-out instrument. The meter was adJusted so that
it read 0 for atmospheric pressure and 65 for 100 p.s.i.a.
Hater readings were converted to actual pressures using the

calibration curves.

Not all non-recording devices are this straightforward.
Inouye, Bernstein, and Seal (1670) discuss an advanced

electromagnetic technique for deducing the depth of a

watertable. The technique used the interaction of
low-frequency electromagnetic waves with the earth. The
two-coil tilt-angle electromagnetic method for measuring
watertable depths was used to obtain field data. The
ES-turn, 36 inch diameter, magnetic dipole transmitter was
driven between 3 kHz and 800 kHz with a square wave
generator. A E5-turn, 15 1/2 inch diameter, rotatable
receiver was adjusted for a null output for each coil
separation at several spot frequencies. The rotating axis
of the receiving coil was horizontal and normal to the line
between the transmitter and receiver. Signal frequency and
transmitter-receiver spacing were varied to obtain the best

data from the pertinent physical quantities.

The manual, non-recording methods of water level data
collecting are adequate if frequent readings are not
necessary or if readings are not required at multiple sites.
However, the increased use of the personal computer allows
more data to be analyzed to better describe an event or
management practice. To take more data, reliable
instrumentation to record water level readings at each site
and methods for easy or automatic transfer of the data to a

computer for analysis must be used.

B. Recording methods of water level monitoring

fleny techniques have been devised to monitor and record

a water level. Important advantages of recording gages over

10

non-recording gages are: (1) a continuous record of
fluctuations is provided, (a) maximum and minimum values and
the time of their occurrence are definitely recorded, and
(3) records can be obtained at points where observers are
not always available. One of the simplest recording methods
was developed by Ferguson (1652). It consisted of a 2 inch
stilling well fastened to some support, a removable inside
staff, and a marking substance (such as fine regranulated
cork) that will float on water. The maximum stage height
was shown by the highest level of cork dust. In addition
the cork also marked successively lower crests, leaving a
sharp, distinct line of grains at each crest stage. About 1

cubic inch of cork dust was used.

A popular and widely used water level recording system
is the float-type chart recorder. The United States Bureau
of Reclamation’s, ug;g:_flgggy;gmgn§_flgnygl,(1675) defines a
float-type chart recorder as consisting of a tape or cable
that passes over a pulley equipped with a float on one end
and a counterweight on the other. The float follows the
rise or fall of the water surface and the stage or level may
be read from the tape, or from a recorder connected to the
pulley producing graphic or punched paper tape records of
water surface elevation with time. Ing_flg;gg_nggayzgmgn;
flany31,states that, in general, graphic recorders consist of
two main elements: a clock mechanism actuated by a spring,
weight, or electric motor; and a gage height element

actuated by a float, cable or tape, and counterweight. A

11

gear reduction mechanism is usually also necessary in the
height element. Four types of recorders use these elements.
In a horizontal drum recorder the clock positions the pen
along the drum axis and the gage height element rotates the
drum. The vertical drum recorder, the time element again
operates parallel to the drum axis and the height element
rotates the drum according to the changes in stage. The
third type of recorder also has a vertical drum, but the
time and height elements have been reversed so that the
clock mechanism rotates the drum and the water stage becomes
a function of displacement along the drum axis. The above
recorders are usually operated by 6-day spring driven
clocks. For a continuous record of up to 6 months without
changing the chart paper, a fourth type of graphic recorder
can be used. The time element consists of a compensated,
balanced, weight-driven clock which drives two parallel
rolls, one of which holds the supply of paper. The float
activates a pen which moves parallel to the axis of the
rolls so that 1 inch of travel represents a change in the

water level of one foot.

In addition to the graphic type recorder, a digital
recorder may be used. The digital recorder is a paper-tape
punch which records 5-digit numbers on a paper tape at
preselected time intervals. Electronic translators are used
to convert the tapes into suitable input for digital

computers. To increase the time between rewinding the clock

1E

and changing the charts on a float-type recorder, Curtis
(1660) developed an automatic triggering device to begin
operation only when water begins to flow past the measuring
station. Clocks need to be rewound and charts changed only
after periods of flow. Hoff (1616) discusses the
'evapormeter”, a device used to monitor the change of the
water surface in an evaporation tank to an accuracy of 0.01
inches. It resembles a vertical drum float-type recorder.
The pen-point movement is ten times that of the float. The
pressure on the pen required for a continuous record would
put a load on the float which in consequence could not move
gradually as the water surface does. To eliminate this
problem, a rocker arm was developed. The rocker arm
controls the pressure of the pen arm against the chart drum.
Once every five minutes the rocker arm moves the pan from
its normal position, in which it does not touch the chart,
to the chart paper to make a mark as the cylinder moves.

The pen arm remains free to move subject only to the float’s

action.

The float-type chart recorder is probably the most
common method used to produce a water level-time
relationship. However, to analyze the data, values have to
be manually read from the chart or punched tape and entered
into a computer, a time consuming task. For this reason,
techniques to get the information to a computer
automatically were developed. Several attempts at

converting a float-type meter to give an electrical output

13

have been tried. Boon and Harrison (1671) used a float-type
system attached to a precision potentiometer to monitor
watertable cycles in a tidal beach. The output voltage was
proportional to the float position. A strip chart was used
to record output voltage versus time. A large observation
well was used but the high permeability of the beach sands
minimized the time between the actual watertable and the
water level in the observation well. Tromble and Enfield
(1671) used the same idea with a vertical drum recorder. A
5K ohm, 10 turn linear potentiometer was connected to the
float drive shaft of the recorder through a system of clock
gears. Using a 5:7 gear ratio the full scale deflection was
17.5 feet. Uan der Userd (1677) designed a float-type
system with an electrical output using thin nylon wire to
transfer the float movement to the precision potentiometer.
The wire is kept taut by means of a counterweight attached
to a wire that runs over a smaller diameter pulley, keeping
its vertical movement so small that it can be contained in a
short tube built inside the meter case. The meter has a
range of 1.85 meters and an accuracy of 0.5 centimeters, but
can be increased with a larger diameter float. Talman
(1663) developed a device consisting of a long float housed
in a ”self-contained” stilling well. Large variations in
water level are reduced using a spring attached to the float
so any range of water level can be recorded on any size
clock drum and chart by changing the spring constant or the

float size. The spring limits movement of the float and

15

reduces the change of water level to a smaller change of
float position while retaining a linear relationship. Data
is stored in analog form on a chart recorder and digital
form on a cassette tape. The biggest drawback of the system
is the installation. Since the stilling well is
self-contained, the 1500 millimeter range model requires an
auger hole of 8650 millimeters, a potential problem in soils
with high stone content. The mechanical impedance of the
float-type system requires a large float and observation or
stilling well which increases the time between the actual

watertable and the water level in the observation well.

Another way to monitor and record a fluctuating water
level is to use an electromechanical probe to physically
follow the movement of the water surface. The probe can be
connected to a chart recorder for a graphical output, or to
a potentiometer for an electrical output. The observation

walls can also be much smaller diameter.

Allman, Uilliams, and Stephenson (1666) used a
commercially available Keck water level sensing device, with
a precision of 0.003 foot, attached to a chart recorder for
continuous output. The probe was small enough to fit inside
a 5/16 inch pipe. Lovell at al. (1676) used a water level
sensing probe consisting of a sensor and electric circuitry
to control a 66 UDC permanent-magnet reversible EE-rpm
electric motor that moves the sensor vertically. The sensor

had three electrodes to activate microswitches that control

15

the electric motor which moved the sensor up or down to
determine the water surface. A 10-turn 50K ohm
potentiometer gave a linear DC voltage out dependent on the

vertical position of the sensor.

Nest and Black (1670) reported that the technique of
measuring soil oxygen flux with the stationary bare platinum
microelectrode has been applied to locating the watertable
level in the field. with a potential of -0.5 volts to
insure oxygen was the only element or compound reduced, near
zero oxygen flux has been found at shallow depths while at a
small distance above the saturated zone, the flux values
were relatively high. From this the watertable level can be

estimated.

Holbo, Harr, and Hyde (1675) measured water level using
32 platinum electrodes connected in parallel and placed at
given intervals along a probe inserted into an observation
well. The presence of water at a given electrode level
provided a pathway for signal to flow to a common electrode
running the length of the probe. The data was stored on a
strip-chart recorder. This had the limitation of not being
easily modified to give analog output as well as a problem

with electrolysis.

Durham and Kohlmeier (1673) discuss the use of
ultrasonic transducers to record the water level in
observation wells during aquifer pumping tests. The device

was placed in the bottom of the well and a sound pulse sent

18

upward. The time required for the sound to be reflected
back was measured, translated into a distance, and punched
into paper tape at each site. Carter et al. (1665)
introduced a device called a capacigage consisting of a
stainless steel probe connected to a bridge circuit to
measure the capacitance between the probe and a 5-cm
diameter, perforated, galvanized pipe to be used as a
stilling well. As the water level rose in the pipe, air,
which has a lower dielectric constant than water, was
displaced causing an increase in capacitance. The device
was designed to output 5 to 60 milliamps, but was modified

to output a DC voltage.

Bevier and Fausey (1676) tried placing a pressure
transducer in a perforated cone machined from delrin
inserted into the soil below the watertable. The
perforations allowed the head from the watertable to be
sensed by the pressure transducer. Some problems under
field conditions were encountered, the perforations plugged
and the transducers were damaged by overpressure during
installation. The transducers were not hermetically sealed
and displayed erratic results when exposed to humidity.
flacUicar and waiter (1665) designed a probe similar to
Holbo, Harr, and Hyde (1675) with the following goals in
mind: simple, continuous operation, inexpensive, ”large” DC
signal out and low output impedance, and small in size to
utilize a small observation well and minimize the time

between the actual watertable and the water level in the

17

observation well. The probe featured a series of resistors
regularly spaced over the depth to be monitored and a ground
wire opposite the contacts covering the same range of
depths. To avoid electrolysis and rapid deterioration of
the probe contacts, an AC input signal used to energize the
probe was converted to DC prior to being recorded. A linear

relationship between inverse resistance and depth was found.

A device to relate pressure in a tube to water level,
called a bubble gage, was described by Barron (1660),
Reinhart and Pierce (1665), and the United States Bureau of
Reclamation’s yg;g;_flgggy:gmgn§_flgny31,(1675). The bubble
gage was a mechanical instrument consisting of a pressurized
gas supply, a sensitive pressure control system, a tube
extending into the water, and either a non-recording or
recording method of measuring the pressure in the tube. The
non-recording method utilized a manometer to measure the
pressure in the tube. The recording method automated the
procedure using a servomotor that sensed the gas pressure
and converted it into a shaft rotation was connected to a
water stage recorder. The bubbler gage eliminated the need

for a large stilling well and float. The principle of the
ones is explained bu the Ways]. (1975).

18

”The gas is fed into the tube and it bubbles freely from the
open lower and which is fixed at a known level under water.
The gas pressure will be essentially equal to the head of
water on the tube outlet and is read on the mercury-filled
manometer.” Barron (1660) claimed a sensitivity of 0.005
foot using a mercury manometer and a range of more than 130

feet.
C. Problems with current water level monitoring devices

The devices which utilize a float to monitor the
watertable require a large observation well which increases
the time between water level in the well and the actual
watertable. All of the above devices output either an
analog or digital signal at the observation well. From the
observation well, the data must be transferred to a central
location or one datalogger must be dedicated to each well.
This is satisfactory if there are few sites or they are
close together. when there are many sites spread apart in
the field two choices exist, either one datalogger must be
used at each site and the observer must walk to that site
when the data needs to be dumped, or, wires must be run from
each site to a central location at which the datalogger is
located. The former would be very expensive and still time
consuming. The latter appears more feasible, but shielded
wire is expensive and the probability of picking up noise

and transient electrical surges with a long data

— m --.-=s-—--—=-A-— A

18

transmission wire is high. An inherent problem with a

motorized probe device is that it is expensive, requires
frequent maintenance, and the electric potential on the
probe causes direct current flow through the groundwater

resulting in electrolysis.

host soil and water research is still done using a
float-type chart recorder with the data either read off and
entered into a computer by hand or through the use of a

digitizer. Both are expensive and time consuming.

III. SYSTEM DESIGN

A. Design Objectives

The objective of this research was to design and test
an electronic data aquisition system for collecting
watertable elevation data with the following requirements:
1) low cost, a) direct input of data into a computer for
analysis, 3) a DC sensor output in the 5 volt range, 5) user
error tolerant, 5) relatively simple and quick to assemble,
6) durable and reliable, 7) a majority of off the shelf
items, 6) capability of monitoring watertable at eight
locations, 6) a watertable elevation range of about 0 to
768 mm (0 to 30 inches), and 10) an overall accuracy of

about :3 mm (10.1 inches).

6. Proposed System

Following recommendations by Herve and Fausey (1665)
the system (Figure 1) used a small watertable observation
well, approximately 161 mm (3/5 inches) I.D., to minimize
the time between the actual watertable and the water level
in the observation well. Into the observation well, a
smaller diameter bubbler tube, 3.16 mm (1/6 inches) 1.0.
connected by flexible spaghetti tubing to a tank of

pressurized nitrogen gas was inserted. Nitrogen gas was
20

a1

PPESSUI‘E SEI'ISOI‘

air supply—9 ——L

‘1" '5’ "l" ‘1’ "V ‘t’

 

water table 1;:

 

 

 

 

iMPE’I‘V i 005 l 398?

 

 

\\\\\{{<<{<\\\

Figure 1: Proposed bubbler system.

88

used in the system because it is comparatively cheap and is
inert and inorganic to retard algae growth at the end of the
bubbler tube. The nitrogen gas was allowed to bubble slowly
through the tubing into the observation well. The bubbling
rate was controlled through an in-line needle valve. A
pressure transducer connected to the supply line near the
nitrogen gas source sensed the pressure required to force a
bubble out of the bubbler tube, thereby sensing the water
level surrounding the tube. The pressure transducer
converted the pressure into a voltage. A datalogger
converted the voltage from the pressure transducer into a

digital output at some predetermined time interval.

C. Selection of Components

Components were chosen for the data aquisition system
(DAS) because of their low cost, simplicity, reliability,
and availability. The DAS had to be capable of monitoring
at least eight pressure transducers, a range of
approximately 0 to 762 mm (0 to 30 inches) of water pressure
with a system accuracy of about :3 mm (10.1 inches). A
brief description of the components is offered here (details

of component specifications are given in Appendix A).

83

The pressure transducer chosen was a differential type
with a range of 0 to 703 mm (0 to 27.7 inches) and a
accuracy of :1 mm (10.05 inches). Internal signal
conditioning produced a direct, linear output between 1 and
6 volts DC. Temperature compensation resulted in a
predictable performance over the specified temperature

ranges.

The data were logged on an 6 channel datalogger with 6
bit resolution resulting in a precision of 12.6 mm (10.11
inches). The datalogger had both analog(0 to 5 UDC) and
digital input and digital output capabilities. The internal
2K bytes of random access memory (RAH) had the capacity of
storing 1675 data points. The sampling interval was
adjustable from 1 second to 16.2 hours. The datalogger
utilized an R6232C port to initiate the data acquisition

process and to retrieve the stored data.

A small, briefcase type, portable computer was used to
communicate with the datalogger. The computer chosen had a
screen, constant memory, an RS232 port, and built-in
floating point BASIC. In addition, other built-in software
including word processing and telecommunications, allowed
the user to take notes, or send and receive information via

a telephone line while in the field.

85

D. Data Transfer

1. water level to pressure transducer

The position of the water level in the observation well
was transferred to the pressure transducer via the 3.16 mm
(1/6 inch) spaghetti tubing (Figure 2). As the water level
in the observation well changed, the pressure needed to
force a bubble out of the tube changed. When the water
level increased, the pressure in the spaghetti tubing, which
is sensed by the pressure transducer also increased. The
pressure transducer continuously converted the pressure in

the tube to a voltage.
2. Transducer to datalogger

The pressure transducer had a voltage output which
varied linearly as the pressure changed from 0 to 6.66 kPa(0
to 1 psi or 0 to 27.7 inches of water). The datalogger
converted the voltage (analog signal) to a digital number
between 0 and 255. The numbers were stored in the 2K bytes
of internal memory in the datalogger. A problem was
encountered when matching the output of the pressure
transducer with the input range of the datalogger. The
datalogger converted a voltage in the range of 0 to 5 000,
but the transducer had an offset of approximately one volt
giving a full range output of 1 to 6 UDC. This meant the

effective range of the pressure transducer and the

25

 

 

IBH transfer data to analyze I Radio Shack
compatible { Nodal 100
computer and store on floppy disk [portable computer

A

 

 

 

 

Starbuck initializing data acquisition

 

 

6232 {
datalogger and retrieving data from Starbuck

 

analog data from
pressure transducer

 

pressure
ltransducer

a

 

 

 

 

pressure data

 

 

observation well]

 

Figure 2: The transfer of information from
observation well to floppy diskette.

28

datalogger together was 1 to 5 UDC C0 to 563.6 mm (0 to 22.2
inches) of water]. This problem is addressed in more detail

in the ”Recomendations” section of the text.

3. Datalogger to portable computer

Uith 6 channels, and a total of 1675 data points
available in the datalogger, there were 256 data points
available for each channel. The time interval used was 30
minutes, so the data had to be collected from the datalogger
at least every 5 days. There were two possible methods to
communicate with the datalogger using the portable computer.
The first was with the memory based communication program.
In this approach, the communication parameters (baud rate,
data word length, parity, and stop bits) were set up the
same as in the datalogger. The communication program worked
well, but the operator had to manually enter each command.
Since this technique allowed operator induced error, the
second approach was used. In this approach, the datalogger
was accessed from a BASIC program (Appendix B), where the
operator needed only to ”RUN” the program after connecting
the computer to the datalogger. This allows statements in
the BASIC program to make communication with the datalogger
as user error tolerant as possible. The data from each
channel was written to a separate file on the portable
computer. It was then taken from the field to the office

and transferred to a larger computer for further analysis.

E7

5. Portable computer to IBfl compatible computer

when the portable computer was connected to an 16"
compatible computer to transfer data through the-RS232C
port, two problems were encountered. The first was that
both computers wanted to send and receive information on the
same wires. To solve this problem, the send wire on one
computer was connected to the receive wire of the other
computer and visa-verse. The second problem was that the
ID” compatible expected a voltage on pin #6 of the RS232C
connector(carrier detect). The portable computer did not
use that pin and the IBfl compatible never recognized that it
was hooked up. To solve this problem, a wire was jumpered
from pin #20 on the portable computer to pin #6 on the IBn
compatible. The data could then be uploaded to the personal

computer for further analysis.

Note: The IBM compatible computer needed a
communication package to ”talk” to the portable

computer.

IU. Development of System

A. Test system I

To test the above system in the laboratory, a bubbler
tube, consisting of a piece of spaghetti tubing taped on a
meterstick, was inserted into a 5 gallon pail designed to
fill to a predetermined level and then drain by siphon thus
simulating watertable fluctuations (Figure 3). A Bausch 6
Lomb 0.0.". 5 strip chart recorder was initially used to log
the data. The purpose of this test was not to determine the
accuracy of the system but to check the system’s ability to
follow a fluctuating water level. The test was run for 16

days and the results were very encouraging (Figure 5).

6. Test system II

The second version of the test system (Figure 5)
utilized an analog to digital converter (Starbuck 6232
datalogger) to record the data using the same test system
described above. The test was run for about 10 days and the
upper and lower as well as several intermediate values were
checked with a meterstick to be within 2.5 mm(0.1 inches) of
the recorded values. The results are shown in Figure 6.

Both short (16 meters (50 feetJJ and long (325 meters (1000
26

 

ES

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

analog, S'tl‘iP
chart
in-line pressure
valve transducer
' bUbbler tube
water /
in f
——3 ~ siphon
. / tube
N2 . -~ 1:
, wa er
gas . out
_—.A—

 

 

 

 

 

Figure 3: Test system I.

3O

 

Figure 5: A one hour sample of the data from the test

system I data as recorded by a strip chart
recorder.

31

 

 

 

datalogger
. _ . pressure
‘33};2e transducer

 

bubbler tube

  
 
  
   

 

--9 ‘ siphon;
ll / tube
H2
... "25:"
.u.—.— —— , i—

 

 

 

 

 

Figure 5: Test system II using a datalogger to collect the
data.

3E

 

 

 

 

01 -o
-10-
.21? : ”‘5
4-! L.
83 ., ,.
U Q) J L
LE "'20:
firE . ‘
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0 00 6:00 12 00 18 00
16 JULY .
time
Figure 6: Fifteen hours of data from test system II.

(seuouo
:41de 13mm

33

feet)] bubbler tubes were tested with no noticeable

difference in the accuracy of the system.

C. Field system installation

The data acquisition system (Figure 7) was installed in
a 15 ha (37 acre) corn field being subsurface irrigated
(Figure 6). The field was split in half so the watertable
level could be controlled separately, allowing two
management practices (a high and a low watertable level) to
be tested. It was desired to monitor the watertable over a
subsurface irrigation line and between a subsurface
irrigation line on each end of the field for both management
practices. The instrumentation equipment was housed in a
pump house located between the two management practices on
the edge of the field. The maximum length of a bubbler tube
required for any observation well was about 366 meters (1200

feet).

The observation tubes were constructed from 25.5 cm
(1 inch) 0.0. PUC pipe with holes drilled randomly to admit
water. The PUC pipe was wrapped in polyester cloth to
retard soil accumulation in the pipe. The observation wells
were drilled to a depth below the lowest expected watertable

level using a 3 inch soil auger.

35

 

 

 

 

   

 

 

 

in-line
valve Starbuck 8232
If: datalogger
\
___{:} g; .....
pressure //
transducer 8
"2 bubbler 1
gas tube \-
W' 5’ 5’ “Y ”Y
i" observation
wel 1
water table 7

 

 

 

iHPEPViOUS layer
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Figure 7: The first field system showing the datalogger,
portable computer, and observation well.

35

 

heat
flu flu

 

3“ e 7i:

 

 

 

 

 

 

 

 

 

 

 

 

=Ihl

 

 

 

 

house
Ditch

 

Figure 6: Bubbler system test field showing the
observation well sites.

 

38

The bubbler tube consisted of 3.16 mm (1/6 inch) I.D.
spaghetti tubing used in trickle irrigation. It was
unrolled from the instrumentation station to each
observation well. The bubbler tubes were inserted into the
observation wells after the system was calibrated. Each

tube was labeled to aid identification.

To set the bubbling rate for each bubbler tube, a
calibration tube (a piece of spaghetti tubing about 163
meters (500 feet) long) was connected to the in-line valve
of the bubbler tube to be adjusted. The other end of the
calibration tube was inserted into a can of water. The
in-line valve was opened until the bubbling rate was
approximately one bubble every second. The actual bubbler
tube was then reconnected to the in-line valve. The voltage
reading at each of the pressure transducers was checked and
recorded. This voltage was the transducer offset and
differed depending on the transducer and bubbler tube
length. The deviation in the offset is due to
manufacturer's variations in the pressure transducers and
slight differences in friction for different bubbler tube
lengths. Finally, each observation well was checked to be
sure it was bubbling. If not, the calibration spaghetti
tubing was reconnected and the rate of bubbling was
increased slightly. If this was done, it was necessary to

recheck and record the new offset.

37

The bubbler tubes were installed in the observation
walls by first determining the anticipated lower limit of
the watertable from the soil surface. A #3 rubber stopper
held in place with tygon tubing and hose clamps kept the
bubbler tube at a constant depth below the soil surface.
The rubber stopper was inserted into the observation tube
and the distance from the top of the stopper to the end of
the bubbler tube was measured and recorded as ”b”

(Figure 6). The distance from the top of the rubber stopper
to the soil surface was measured and recorded as ”a”. The
depth of the bubbler tube below the soil surface or (b - a)
was recorded for each observation well. The value ”c” in
Figure 6 is the pressure transducer reading minus the
offset. The equation for the distance to the watertable

from the soil surface (”d”) is therefore:
d - ((b - a) - c)

The system was now ready for data collection. The
information recorded in the user's field manual was the
value of (b - a), the offset for each pressure transducer,

and the starting time and date of data aquisition.
D. Results of Field Test
1. Problems with Field System I

The data acquisition system was field tested for
approximately three months. During this time, several

things were learned about the system. The pressure

38

bubbler tube-*'_._tygon tubing
hose c1anp.___

 

 

 

 

 

 

rubber a: ,,
stopper 3
Y Y 1' Y Y
_spaghetti
tubing
d
observation
. l vel 1
watertable 1‘ 27
C
J. .1.

 

 

 

impervious layer
\ \.'\ T'T‘T‘Y‘Y—TT-R——Kf'\ \ \ \

 

 

Figure 6: Bubbler tube installation into an observation
well.

38

transducer’s offsets remained constant. The bubbler tubes
in the observation wells had to be moved down midway through
the season when the watertable went below the estimated
lower limit of the watertable. The new distance to the
bottom of the bubbler tube was recorded and used later in

the analysis of the data.

The first field system was powered completely from a
120 UAC powerline. The datalogger was plugged directly into
the powerline while the pressure transducer’s D.C.
excitation voltage was supplied by a Heathkit IP-2716
Tri-power supply. The bubbler tube was strung on top of the
ground to each observation well. Three problems arose from
this set-up. The first was fluctuations in the pressure
transducer’s output. A pressure transducer was left open to
atmospheric pressure as a reference. The output should have
been a straight line, instead, the output was a diurnal-type
fluctuation. A probable cause of this problem was powerline
voltage variations. Since the pressure transducer output is
linearly related to the excitation voltage at a constant
pressure, powerline variations affected the pressure
transducer's output directly. A software solution was used
to solve this problem. The difference between each
individual pressure transducer output and the output from
the atmospheric reference transducer was taken to give the

COPT‘BCC output Of BBCI‘I DI‘BSSUT’B transducer .

50

The second power problem, power failure, affected both
the pressure transducers and the datalogger. The output
from the pressure transducers during a power outage was
zero. The datalogger had no internal back-up batteries to
power the memory, during a power failure all data and any
program stored in memory were lost. The problem was solved
by powering the datalogger with a 12 volt automotive battery
kept charged by a battery charger. The battery would
operate the datalogger for about a month without having to
be recharged, but in most cases, the power outages lasted

only for several hours at a time.

A third problem encountered was that rodents chewed on
the bubbler tubes, puncturing or severing the tube. The
problem could be checked for in the field and was indicated
by a low reading as compared to the readings in nearby
observation wells. To solve the problem the tubes were

buried under one or two inches of soil.

A pressure transducer was left open to the atmosphere
as a reference. The daily fluctuations, probably due to
powerline voltage changes can be seen in the output
(Figure 10). These fluctuations were subtracted from the

raw data to give the corrected data.

51

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-- fluctuations
-- raw data
—— corrected data ‘

 

 

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14 . 15 16 17
tIme and date (August 1984)

Fluctuations in the reference pressure
transducer output. The uncorrected and

corrected data sets are from observation well
site #6.

(seuouo
yidep alqopaioM

58

2. Bubbler data compared to Steven’s meter data

Data from a new system is not very meaningful unless it
can be verified using another method. In the test field,
float-type chart recorders (Steven’s meters) were installed
in the same area as were the bubbler tubes. Figure 11 shows
the comparison between the bubbler system and the Steven’s
meter data sets. The difference in the extremes of the data
is due to the greater sensitivity in the bubbler tube. This
is a result of a smaller observation well for the bubbler
system (1 inch versus 3 inch) which minimizes the time
between the actual watertable level and the water level in
the well [Herve and Fausey (1665)]. The diurnal
fluctuations as well as the downward trend of the watertable
can be seen in both Figures 10 and 11. The difference in
the watertable depths between the two figures is due to the
different management tests. Figure 10 is from the higher
watertable side and Figure 11 is from the lower watertable

side.

Centimeters below
the"Soil surface

Figure

53

Comparison of data from bubbler system
and float—type chart recorder.

 

— Float- -type recorder (3” observation well)

 

-- Babbler system (1" observation welll)

 

11:

TII 'II‘ITI I IIIW

12.00

(1)200 12: 000500 12: 000 00 12: 000 00
time and date 1(August 1984)

Sample of corrected data compared to float-type
chart recorder data.

U. ERROR QNHLYSIS

The error analysis performed on the bubbler system was
mainly concerned with the static calibration of the system
and to determine the lag time of the system as a function of
bubbler tube length. Lag time is the it takes for the
system to reach equilbrium after an increase of water depth
at the end of the bubbler tube. A static calibration was
chosen rather than a dynamic calibration because most
watertable levels monitored in agricultural research tend to
change slowly or a static change. The datalogger and
pressure transducer were calibrated separately first, then
together as a system with 5 different bubbler tube lengths
(30.5, 152.5, 305.6, 557.2, and 606.6 meters). The
datalogger and pressure transducer were kept at a constant
temperature while the different bubbler tube lengths were
tested at three different temperatures above 20°C (66'F). A
constant bubbling rate of approximately one bubble per

second was used for the entire calibration process.

55

55

A. Statistical method used

The data from the calibration of both the components
and the system was statistically analyzed using the least
squares method to determine the slope (H) in centimeters per
datalogger unit or centimeters per volt and y intercept (YI)
in centimeters. Data was colleced by the Starbuck 6232
datalogger and a Keithley 175 digital multimeter (DUN). In
the calibration, datalogger reading or voltage was plotted
on the x-axis and water depth on the y-axis. The
calibration equation was used to calculate a Y value, in
centimeters, given datalogger and ann readings. The
calculated Y value was subtracted from the measured Y value
to give the residual. The bubbler tube was mounted on a
meterstick and the measured y values were determined to the
nearest millimeter. The residual squared was summed over
the data set to yield the error sum of squares (SSE). The
varience(s) and standard error with a 65% confidence
interval were calculated for the slope (SE N), the y
intercept (SE YI), the calculated y value (SE Y) using
Student's t-distribution. An average standard error (SE Y
Ave) and percent error of full scale (2 arr) for the
calculated y were also determined. The complete data set
and statistical output from the calibration can be seen in
Appendix C. The data set and statistical output from the
system calibration can be seen in Appendix D. The equations

used in the statistical analysis are found in Table 1.

55

TRBLE 1

Equations used for the statistical analysis

n — -
ccx1 - v1) - (n - x - Y)

 

 

 

 

1-1 _ _
N ' -- v1 - v - n s x
n
scxia) — (hie)
1-1
n SSE
SSE - 1': (Y1 - Y1 ‘ r1 . X138 32 I ......
i-l n - 2
3 -a
s 1 X
33h - — —— seYI - c- + - ) - :3
D _ n n _
2 (x1 - X)a scx1 - X)?
1-1 1-1
1 (x - i)?
93v - (1 + - + 3 m ,2
n n
2 (x1 - X)?
1-1
SE [1 " $32" . tn_a’ssz SE VI " ISEYI . tn-a’ssz
SE v
SE Y - tsaY . tn_a 852 3‘ arr I 1 ——————— U 100
' 70.3 cm

(full scale reading)

n - number of data points s - variance

X - datalogger or voltage reading fl - slope of line

Y - water depth YI - y-intercept

t - Student’s t distribution SE - standard error
for n-2 points and a X - average of X
65% confidence interval _ values

2 err - percent error Y - average of Y

values
X1 and Y1 - any given value of X and Y

 

57

6. Calibration of Components

1. Datalogger

The “factory-calibration" of the datalogger's full
scale reading was checked by connecting a variable power
supply and increasing the voltage until the datalogger
output was just 255 units. The digital multimeter (DNN)
reading was 5.667 UDC which agreed with the operator’s
manual indicated value of 5.00 10.02 UDC. Once the full
scale reading was established, the datalogger was calibrated
over the full range using a 5 1/2 digit, 12 bit resolution,
Xeithley 175 Autoranging DNN which is more accurate than the
datalogger. The datalogger utilizes an analog to digital
converter with 6 bit resolution. The expected full scale
accuracy was (1/256) - 10.3622 or 10.0166 UDC. The voltage
was increased from about 1.25 to 5.00 UDC then decreased
over the same range. The lower limit of the voltage range
was chosen because of the power supply used. The average
percent error over the full range was 10.2602 or

10.0150 UDC.

2. Pressure transducer

The pressure transducer is capable of operating from a
single, positive excitation voltage ranging from 7 to 16
UDC. At a given excitation voltage, the offset (output
voltage at zero pressure) varies up to 152 depending on the

pressure transducer.

58

Each of the eight pressure transducers put in the field
were calibrated separately. The difference was in the
offset and not the slope of the calibration curve. Each
pressure transducer used in the system should be calibrated.
This error analysis was performed on one presure transducer.
The pressure transducer was calibrated with an excitation
voltage of 6 UDC, as suggested by the manufacturer. At this
excitation voltage, the offset can vary from 0.65 to 1.05
UDC depending on the pressure transducer. The offset of the
pressure transducer tested was 1.002 UDC. The output of the
pressure transducer is dependent on the excitation voltage.
The linear relationship between excitation voltage and

output voltage at a constant pressure is shown in Figure 12.

The pressure transducer was calibrated by connecting a
column of water above it. The water level in the column was
increased and then decreased at approximately 50 mm
intervals over the transducer range. The output voltage was
monitored both by a 5 1/2 digit Xeithley 175 Autoranging
digital multimeter(DNN) as well as the calibrated

datalogger.

Using the least squares method, the calibration curve
(Figure 13) for the pressure transducer was determined from
the DNN data. The slope, Y intercept, and the standard
error for both the datalogger and the DNN are summarized in

Table 2. The calibration equation for the pressure

transducer when using the datalogger was:

5S

 

 

2.001
1.805
81 1.603
B a
T) .
>* 1,40.
4-3) .1
CL
y .
3 1.20-
(D .
1.00;
0.80‘
Figure 12:

fi I l
10 15

excitation voltage

Excitation voltage versus output voltage for a
pressure transducer.

20

80.;
70:5

5 1
4a .
0 60.1
'0? 1
Eb 50:
H44 "
O 0 :
a E 40.31
13:3 :
c: .

93 a) .30.-
: o :
mv .
8 20.-§
E a
10.1

0 .

 

50

  
 
   

water depth(cm) -
(14.267toutput voltage) - 22.149

3.2 - 0.025 centimeters
excitation voltage = 8 VDC

Indap JGIDM paJnsoeuJ

63'
:1
9
~15 m
t m
v
~10.
I

 

 

Figure 13:

be 11) 20 3b 4”) so so

'f'.'I'TYIVIV'WYTr'V'V'VVVVI VWTIII'VTVIYTT'I'I‘VV'V'I'UI'

output voltage

Calibration curve for the pressure transducer.

51

water depth (cm) - ((0.276 ' datalogger reading) -
21.675) [Meter depth (inches) - ((0.110 * datalogger
reading) - 6.612)].

Uhen the output voltage is monitored, the equation was:
water depth (cm) - ((15.267 * voltage reading) - 22.156)
[water depth (inches) - ((5.617 ' voltage reading) -
6.720)].

TABLE 8

Summary of the pressure transducer calibration
I

D. ELL! 11. mm a
Datalogger
up 0.276 0.002 -21.730 0.337 0.267 0.115

down 0.878 0.008 '88.051 0.388 0.315 0.180
both 0.878 0.008 -81.875 0.351 0.503 0.178

Digital multimeter (DNN)
up 15.260 0.037 -22.010 0.170 0.202 0.066

both 15.357 0.050 -22.156 0.317 0.335 0.157

N - slope (cm/datalogger unit or cm/volt)

SE N - 662 standard error in the slope

YI - Y intercept (cm)

SE YI - 65% standard error in the Y intercept

65 Y Ave - average standard error (65%) in calculated Y (cm)
s - variance

58

3. Temperature effect

The temperature of the pressure transducer-datalogger
system was changed from 20°C (66°F) to 60°C (150°F) at a
constant excitation voltage and input pressure. The
temperature range was chosen based on approximated field
conditions and available labratory facilities. The output
voltage changed 0.03 volts over this temperature change
(Figure 15). From the slope of the line, the temperature
coefficient for the system was calculated to be 713.33(10'5)
volts per degree Celsius increase from 20°C. A temperature
coefficient should be determined for each datalogger-

pressure transducer combination put into the field.

C. Bubbler system calibration

The system, consisting of a portable computer,
datalogger, pressure transducer, and bubbler tube, was
calibrated using 5 different bubbler tube lengths at 3
temperatures using both the datalogger and the DNN to
collect the data. A bubbling rate of one bubble per second
was used for the entire error analysis. Nitrogen gas was
bubbled through the bubbler tube which was rolled up into a
60 centimeter diameter roll. Each bubbler tube length was
inserted into a oven. The end of the bubbler tube was taped
to a meterstick and inserted into a 2 liter glass graduated
cylinder. The end of the bubbler tube, the pressure

transducer, the datalogger, and the portable computer were

53

temperature coefficient =
713.3(10‘6) volts/degree Celsius

output voltage

 

 

10 20 3O 4O 50 60 7O

temperature (Celsius)

Figure 15: Determination of the temperature coefficient.
Temperature versus output voltage.

55

outside the oven and at room temperature about 20°C. Water
was added quickly into the graduated cylinder to increase
the depth about 5 to 15 centimeters each time. The measured
depth was taken from the meterstick. The increase in
pressure in the bubbler tube was moniitored by the
datalogger and the DNN until it reached an equilibrium.

This value was used for the calibration of the system.

The slope (N), standard error of N (SE N), y intercept
(YI), standard error of Y1 (SE YI), average standard error
of the calculated y value (SE Y Ave), and variance (s) were
calculated for each temperature and bubbler tube length.
The calibration values were averaged over the temperature
range for a given bubbler tube length. Dverall averages
were determined for N, SE N, SE Y Ave, and s. The values for
Y1 and SE YI were excluded from the overall average since
they change based on bubbler tube length and the bubbling
rate. The slope and calculated y values are independent of
tube length and bubbling rate and should remain constant.
The summary of the calibration output is given in Table 3.
Note that the slope of line stays relatively constant for
the different bubbler tube lenghts and temperatures. The y
intercept stays constant over the temperature range, but
becomes more negative as the bubbler tube length increases.
The reason the y intercepts are less for the 606.6 meter
bubbler tube than the 557.2 meter bubbler tube is that the
in-line valve was adjusted for the 606.6 meter tube to set

the bubbling rate to 1 bubble per second.

55

TABLE 3

Summary of the bubbler system calibration

DATALDSBER

[1

am

b.1111.

30.5 meter bubbler tube

88°C
55°C
55°C

0.878

0.005

0.878 0.008

0.878

0.003

Average 0.276 0.003

‘15.530
“15.332
“15.795

152.5 meter bubbler tube

88°C
37°C
51°C

0.878
0.877
0.877

Average 0.277

0.003
0.003
0.005
0.003

-18.718
-18.883
-18.858
-18.888

305.6 meter bubbler tube

85°C
38°C
50°C

0.877
0.878
0.878

Average 0.277

0.008
0.001
0.003
0.008

-18.815
-18.818
-18.087
~18.878

557.2 meter bubbler tube

88°C
38°C
53°C

0.881
0.880
0.878

Average 0.260

0.008
0.003
0.008
0.008

-80.088
-80.080
-80.513
-80.155

606.6 meter bubbler tube

81°C
88°C
35°C
53°C

0.878
0.877
0.878
0.881

Average 0.276

Dverall

Average 0.276

0.008
0.003
0.005
0.003
0.003

0.003

-1S.707
-18.101
-18.558
-80.818
'18.818

CI...

0.578
0.383
0.580
0.575

0.558

0.757
0.530

0.585
0.805
0.558
0.333

0.305
0.588
0.380
0.377

0.388
0.553
0.888
0.518
0.588

0.507
0.885
0.888
0.388

0.338
0.308
0.588
0.358

0.887
0.155
0.518
0.888

0.833
0.358
0.878
0.885

0.318
0.355
0.585
0.338
0.388

0.388

0.108
0.081
0.078
0.085

0.080
0.080
0.115
0.088

0.078
0.051
0.111
0.078

0.088
0.088
0.078
0.075

0.138
0.085
0.185
0.080
0.118

0.080

TABLE 3 (cont’d.).

DH”

58

30.5 meter bubbler tube

88°C
55°C
55°C

15.
15.
15.

073
033
083

Average 15.056

0.105
0.075
0.033
0.071

-15.885
-15.531
-15.837
-15.811

152.5 meter bubbler tube

88°C
37°C
51°C

15.
15.
1%.

055
037
108

Average 15.061

0.187
0.088
0.118
0.118

-15.857
-18.558
“18.851
-18.515

305.6 meter bubbler tube

85°C
38°C
50°C

15.
15.
15.

130
088
058

Average 15.061

0.053
0.088
0.185
0.088

-18.550
-18.758
-18.888
-18.077

557.2 meter bubbler tube

88°C
38°C
53°C

15.260 0.150
15.161 0.057
15.163 0.135
Average 15.205 0.111

-80.008
-18.888
-80.330
-80.088

606.6 meter bubbler tube

81°C
88°C
35°C
53°C

15.
15.
15.
15.

158
083
188
808

Average 15.156

Overall

Average 15.113

N
SE N
YI
SE YI

SE Y Ave

- slope (cm/datalogger unit or cm/volt)

- average standard error (65%) in calculated Y (cm)

0.083
0.075
0.088
0.085
0.078

0.083

-18.587
-18.075
-18.557
-18.888
-18.588

0....

0.300
0.817
0.105
0.807

0.508
0.810
0.388
0.378

0.188
0.315
0.503
0.300

0.585
0.158
0.558
0.358

0.885
0.835
0.818
0.888
0.850

.0.

0.818
0.170
0.083
0.158

0.388
0.187
0.885
0.881

0.188
0.838
0.303
0.880

0.371
0.113
0.335
0.873

0.857
0.185
0.158
0.188
0.183

0.817

652 standard error in the slope
- Y intercept (cm)
652 standard error in the Y intercept

varia

“CB

0.057
0.055
0.017
0.050

0.105
0.055
0.080
0.070

0.038
0.083
0.080
0.058

0.088
0.030
0.088
0.073

0.118
0.058
0.038
0.050
0.088

0.081

57

D. Lag time determination

During the calibration of the system, the datalogger
was programmed to store a voltage reading from the pressure
transducer every 10 seconds. These data made it possible to
calculate the rate of change of pressure in the bubbler tube
for a water level change at the end of the bubbler tube.
Data showed that time to equilibrium when the water level
was being decreased was approximately halved as compared to
when it was being increased. In most applications, the
water level fluctuates both up and down so the increase
would be limiting. For that reason, only the increasing
water levdl was analyzed. Figures 15 to 16 show the
relationship between the water depth changes and time for
the pressure in the bubbler tube to equilibrate at 3
temperatures. Each step on the curve represents the
addition of water to the graduated cylinder. Each
temperature-bubbler tube combination was tested separately
and the depth of each step was varied from about 5 to 15
centimeters. The flat part of the curves is when pressure
in the bubbler tube is at a constant value. A change in the
temperature of the bubbler tube did not noticably affect the
rate of change of pressure (slope of the increasing line)
for a given bubbler tube length as seen in Table 3. As the
bubbler tube length increased, the time to equilibrium for a
given change in water level also increased. Figure 20 shows
the comparison between the five bubbler tube lengths at the A

lowest temperature. For a given water depth change

58

IndIcoted. water
depth(cent1meters)
CA
‘3

 

 

 

1
101‘ ,I —— 55 °c
: f -- 44°C
- ’ - - - 29 °C
0 u [ 1 g . l ' l ‘ l
0 100 200 300 400 500

time (seconds)

Figure 15: Time versus water depth for the 30.5 meter
bubbler tube.

58

 

 

 

607
.c 507
4" .1
0- .
m .
'02? 40-:
5.93
1" (1)
gig; i305
.044 ..
33 5 1
08, 20~
.9 I
‘0 .
.E 1
‘0‘. -— 51’c
j -- 37°C
. -- 29°C
0 ' I r I ' I ' I r I
0 200 400 600 800 1000

time (seconds)

Figure 16: Time versus water depth for the 152.5 meter
bubbler tube.

80

 

 

 

601
.c 50‘.
H 4
Q II
(D/—\ ‘
Us 401
$3 4
H0) ‘
gé 30:
+4 .
E8 :
.53 2°:
'8 3 .
._ ‘0‘: "" — 50°C
:0, -— 32°C
0 . 25°C
....,....,
0 500 1000 1500

time (seconds)

Figure 17: Time versus water depth for the 305.6 meter
bubbler tube.

81

 

 

 

601
.c 50'?
+4 .
O- I
a)“ .
13 E! ‘¢0j
333 1
“m
o
gg 301
+4 .
E33 :
08, 20-
.9 ;
“O .
E J ..
' 10f ’ -—- 53°C
3 ' -- 39°C
- 28°C
0 ....,....,....,....,....,
0 500 1000 1500 2000 2500

time (seconds)

Figure 16: Time versus water depth for the 557.2 meter
bubbler tube.

88

 

 

 

601
.c: 50‘.
+J 4
o. .
<D/_\ .
‘09 40'.
33.2 i
“‘50) .
2E SO-j
a: .
E5 1
of; 20-
.9. 2
U 1
.E '

‘0‘." — 53°C

1 -- 35°C

«P’ 28°C

0 e,,-,-,
O 1000 2000 3000 4000

time (seconds)

Figure 16: Time versus water depth for the 606.6 meter
bubbler tube.

63

01
CD
4

 

504.8 meter
1 30.51%2eiiermet" 457.2 meter 609.6 meter

_C 501
+4 I
0- .
0A "
‘0 ‘3 40-
:3 a)
+J4J
C30)
3 E 30‘
“815,
*5 U excitation voltage a 8 VDC

v
.9 lowest temperature was plotted
"g for each bubbler tube length

 

 

 

('3' ' ' 1560' ' '1'o'ob' 'isroT' 'éo'obT iés'o'o' 3600

time (seconds)

Figure 30: Comparison of Figures 16 - 19.

65

Figure 80 shows that as the bubbler tube length increase so
does the time for the system to come ina equilibrium. The
curves do not start at zero centimeters of water because the
offset of the system is shown in the curves and it is

different for each bubbler tube length.

To determine a relationship between water depth change
and time for the system to come into equilibrium for each
bubbler tube length, the data points on the slope of the
calibration curve were extracted from the three temperatures
for a given bubbler tube length, and the equation of a line
forced through the origin was determined for the composite
data set using the statistical-plotting program PLDTIT..
Figures 81 through 25 show the regression line and the data
point scatter for each of the five bubbler tube lengths,
while Figure 26 compares the regression lines for the five
tube lengths. Table & summarizes the slope (seconds per
centimeter of water depth change) and coefficient of
determination (R3) for the bubbler tube lengths. The output

file from PLOTIT for these data can be seen in Appendix E.

* PLDTIT is a trademark of Computer Resource
Services Holt "1

65

30.5 meter bubbler tube
slope = 5.35 seconds/centimeter

R2 = 0.93

  
  

 

 

1007
80-1
E
.2 4
BA
2:? (D 60-
DE
0'
a) o
8
.833 40-
a)
.E
*" zoe
0
Figure 81:

I

5 . . . . 1E) . . . . ‘15

water depth change
(centimeters)

Mater depth change versus time to equilibrium
for the 30.5 meter bubbler tube.

86

152.4 meter bubbler tube
slope = 11.24 seconds/centimeter
R2 = 0.97

 

 

 

3001
E .
:3
'C 2001
JD/*\
5.8 4
as
“’ 5.3
.9 m 4
v
Q) 1004
.§
-§—’
J
0
Figure 23:

5 ' ' 1b 1 f j ' 1'5
water depth change
(centimeters)

water depth change versus time to equilibrium
for the 152.! meter bubbler tube.

 

67

304.8 meter bubbler tube
slope = 20.79 sec/cm

R2 = 0.99

  

 

3007
4
E
:3
"C 200-
JD/*\
35%
3%
¢>83 .
.93 J
a) 1001
.E i
4.1
0
Figure 23:

' V V r

5 ' 10
water depth change
(centimeters)

water depth change versus time to equilibrium
for the 30%.8 meter bubbler tube.

15

  
   

 

 

6001
5003 457.2 meter bubbler tube '
E slope = 37.15 sec/cm
:3 . R2 = 0.98
'C 400-
DA 1
25.8 3
3 u
38 300-
8 i
.93 g
a) 200d °
.E
4., 4
100j
o‘...-r...-......l...,
O 5 10 15 20

water depth change
(centimeters)

Figure 2%: water depth change versus time to equilibrium
for the $57.2 meter bubbler tube.

 

 

 

800?
; 609.6 meter bubbler tube . '
7001 slope = 72.13 sec/cm
: 2 =
E 600-} R 0.99
.2 .
L- i
2:”); 5004:
3c: «
0' -1
(”3(3) 400:
0 : «-
44$ 300‘: ' '°
‘1’ i
E, 200.;
100-j
0‘ . . . . , . . . . , . . . -.
0 5 10 15

water depth change
(centimeters)

Figure 25: Water depth change versus time to equilibrium
for the 609.6 meter bubbler tube.

 

7O

    

 

 

 

 

 

8001
3 609.6 meter
7001
:E) 600‘: 457.2 meter
‘C :
2373‘ 5001
3 I
C .
8'0 400:
O J
03’, 1
:v 300‘. 304.8 meter
E l
1:: 2002‘ 152.4 meter
100-3 flak»
0‘ ..—:. , . . . . , . -. .,
0 5 10 15
water depth change
(centimeters)
Figure 85: Comparison of Figures ea - ES.

71

TRBLE Q

Bubbler tube length versus slope of time to equilibrium line

slope
Bubbler tube (seconds per centimeter
length (meters) water depth change)

30.5 (Figure 88) 5.35 0.93
158.9 (Figure 83) 11.8% 0.97
309.6 (Figure 8%) 80.79 0.99
957.8 (Figure 85) 37.15 0.96
609.6 (Figure 86) 78.13 0.99

The lag time for a change in water level is given bu
the product of the water level change and the appropriate
slope as determined above. The relationship between the
slope and bubbler tube length is shown in Figure 87. PLDTIT
was used to determine the equation of the best fit. Table 5
summarizes the results. The output file from PLOTIT for

these data is in appendix F.

80d
E .
3’3? 70
L ‘1

CF
52 g ‘
3 C 60~
m 0 .
(3&3 5C%*
4—1 8' 4
§§13 4{)s
£5 ‘
045 304
E 3 .
u— (D 20..
C>23
0) Y3 i
gig: 1C}:
(0
0

Figure 87:

 

7E

 

r U f I T

' 100 ' 200 300 400 500 600 700
tube length (meters) '

Bubbler tube length versus slope of time to
equilibrium line.

TABLE 9
Best fit equations for the curve in Figure 87 as determined
by PLUTIT

Equation ' R2
v - 0.030x 0.99
v - 0.039x - 9.996 0.90
Y - 0.197(10‘*)xa - 0.571x + 7.975 0.99
v - 0.119(10‘73x3 - 0.17ac10“*)xa + 0.aaax + 9.099 0.99
v - -11.977(10‘3)/c-1.999c103) + X) 0.93
v - (36.56%X)/(636.016+X) 0.93
v - xxc33.55 + (0.229(10‘33x33 0.02
v - s.aosc1.001x) 0.99
v - 0.106(x5-331) 0.90

 

E. Analysis of system

The analysis of the system was performed using the data
from one water depth increase (about 9 centimeters) from the
time lag determination for the 609.6 meter (8000 foot)
bubbler tube at 53°C. This data set was chosen since the
609.6 meter bubbler tube was the longest tested and would be
the worst case. The following procedure could be used for
any bubbler tube length. The order of the system was

determined based on information given by Berrish (1966). and

9 personal communication

7H

Doebelin (1975). The order of an instrument gives an
indication of it’s dynamic characteristics. a zero order
instrument responds instantaneously to an input and no
dynamic characteristics exist. A first order instrument has
one dynamic characteristic, a time constant. The time
constant of a system is the physical time required to
transmit signals from input to output. A second order has
two dynamic charactteristics, a damping ratio and a natural
frequency. The analysis of a second order instrument is
much more complex than the analysis of a zero or first order
instrument. Initially, the pressure transducer, datalogger,
and total bubbler tube length, were considered together as
the system. The system was tested by applying a step
function at the end of the bubbler tube. a step function
assumes the system is initially at equilibrium, the input
quantity (water level in this case) is increased instantly
an amount to give a ”step”. Figure 86 shows the expected
output of a first and second order instrument after one step
input (one water depth increase) and the actual output
curve. The Jagged line in the actual output curve is due to
the resolution of the datalogger. The response is similar
to the second order curve, but is different enough to
Justify further analysis to determine the order of the

system and the test input function.

The next approach assumed the pressure transducer and
datalogger to be the data acquisition system, the bubbler

tube being used only as an information transfer system. In

unitless depth

75

I — output data

- - 2nd order response
--- lst order response

 

Figure 88:

UV"IT’"'T'ij'vril'thr‘Vf"V'erT'VVr'

1 2 3 4 5 6 7 8 910

unitless time

First and second order response to step input
and the actual output curve.

76

this case, even though a step input was applied at the end
of the bubbler tube, the data acquisition system ”saw” a
terminated ramp because of the bubbler tube’s limitation of
the flow of information. a terminated ramp assumes the
system is initially in equilibrium then the input starts to
change at a constant rate. At some value the ramp is
terminated and the input is held at a constant value. A
terminated ramp is shown as the dashed line in Figure 89.
The output curve is very similar to the expected response to
a terminated ramp function for a first order instrument
(Figure 89). The terminated ramp at the data acquisition
system was obtained by first applying a step change to the
end of the bubbler tube. Immediately following the step
input, water intruded into the end of the tube a distance
equal to the step change minus some amount dependent on the
tube length and the compressibility of the nitrogen gas.
The distance is greater for a longer tube and less for a
shorter tube. The pressure in the tube increased linearly
until the first bubble was expelled from the end of the
tube. From that time, water intruded less and less while
the bubbling rate increased until at some time (equal to the
time constant) very little or no water intruded into the

tube and the bubbling rate remained constant.

Based on the above assumptions, the time constant was
calculated as follows (Figure 30). The lower part of the
actual data curve was assumed to have the same constant

slope as the input ramp only offset by the time constant.

77

 

1.0 '..---;;;.--=_ __
0.9 ’ '
0.8 ,

0.7 ,
0.6 / '
0.5 I
0.4

0.3 .
0.2

/ - - - input function

0.0, —— output data
—-- expected output

0.0jIUIIVTIrv—rTllIr'vvv'm'vfr'rrr'rvfi Ifi IT!

I"'I"'rr*TI l l'j'l
01234 6789101112131415

unitless depth

unitless time

Figure 89: First order response to e terminated ramp and
the actual output curve.

units of depth

401

AIJJAI

78

   

-— Input function
— Output curve

 

 

 

- - Constant slope line

0 5160 ' 200 ' 300 ' 400 ' 500 5600 ' 700

' time (seconds)

Figure 30: Determination of the time constant.

73

The slope was assumed to be constant from 0 to 80 units.

For this constant slope, a line was extended to 33 units.
The point where the output curve deviated from this line was
considered to be the termination of the ramp and the time
the first bubble emerged. From the termination of the ramp,
a line parallel to the lower portion of the output curve was
constructed. The distance between the two lines along the x
axis was considered to be time constant and was found to be

equal to 5% seconds.

The length of the bubbler tube, not the pressure
transducer-datalogger combination, is the limiting factor in
the response time of the system. when using the complete
system, a more practical time constant other than that
calculated above would be one relating the time to
equilibrium to bubbler tube length for the whole system. A
way to look at this is to determine the maximum rate of
pressure change for a bubbler tube of a given length. The
data used for the lag time determination and system analysis
was the maximum rate since a large depth change was applied
to the end of the bubbler tube and the system could not
respond instantaneously. The maximum rate for each length
was calculated by multiplying 3600 seconds per hour by the
reciprocal of the slope (seconds per centimeter) of the
lines in Figure 87. This gave a maximum rate of rise or
fall of the field watertable in centimeters per hour. If
the maximum rate is exceeded, the effects of lag time would

be apparent in the output data. Table 6 summarizes the

80

results. In the worst case, the 609.6 meter tube, the
maximum rate of water level change is 99.9 centimeters per
hour (19.7 inches per hour). This should not present a
problem since most applications in watertable management do
not exceed this rate. The slope of_the output data,
however, should be compared to the critical slope to be sure

lag time is not affecting the data.

TflBLE 6

maximum water level rate of change for the tested bubbler
tube lengths

maximum rate

tube length (meters) cm/hrCin/hr)
30.5 678.9(869.9)
158.9 380.3(186.1)
309.9 173.8( 66.8)
957.8 96.9( 36.8)

508.6 98.9( 18.7)

81

1. Bubbling rate

The bubbling rate is an important parameter of the
bubbler system, affecting the lag time of the system, offset
of the calibration curve, and nitrogen gas use. The effect
of altering the bubbling rate was not tested. The bubbling
rate used for the entire error analysis was approximately 1

bubble per second.

A relationship between bubbling rate, bubble tube
length, maximum expected rate of change in water level, and
desired nitrogen gas use could be developed to give the
optimum bubbling rate given the three other parameters. The
maximum bubbling rate would be limited by excessive nitrogen
gas use and turbulence at the bubbler tube outlet. The
minimum bubbling rate would affect the time to equilibrium
of the system. a change in bubbling rate should not alter
the slope of the calibration curve, but it will move the
curve up or down on the y axis by changing the pressure

transducer offset at zero water depth.

The above analysis assumes a constant bubbling rate
prior to the change in water level. In some applications,
it might be beneficial to know the time to equilibrium from
zero pressure in the bubbler tube. This could also be
related to tube length and bubbling rate, as well as the

starting head of water.

UI. RECDNHENDATIDNS

a. Field system II

In the first version of the bubbler system, two
problems related to power were discovered. The first was
matching the output of the pressure transducer with the
input of the datalogger. As mentioned before, the
datalogger converts a voltage in the range of 0 to 5 volts,
but the transducer has an offset of one volt giving an
output of 1 to 6 volts. This means the effective range of
the pressure transducer was 1 to 5 volts E0 to 563.9 mm(O to
88.8 inches) of water]. Since this was a prototype version
of the system, this range was determined to be adequate and

no further attempts were made to correct the problem.

To take care of this problem, preliminary testing has
been done using a difference amplifier (Figure 31). a
difference amplifier utilizes an operational amplifier to
output the difference between two voltages (Ua-Ul-Uo). U2
is the actual signal voltage from the transducer, 01 is a
reference voltage equal to the pressure transducer offset,
and ”o is the voltage, with the offset subtracted, which
goes to the datalogger. ”8 ranges from 1 to 6 volts, 01 is

approximately equal to 1 volt, and Uo ranges from 0 to 5
68

83

 

 

 

 

U out

 

 

 

 

 

 

Figure 31: Difference amplifier.

89

volts. Two sources for a reference have been used. The
first was a variable voltage regulator (Figure 38) connected
to U1 and adjusted until ”o is zero at zero pressure. Since
the offset changes with different pressure transducers and
different bubbler tube lengths, the voltage regulator can be
adjusted to give the maximum range with any bubbler tube
length. The other reference voltage used another pressure
transducer’s output as U1. This has the advantage of
subtracting out fluctuations due to atmospheric pressure and
slight input voltage changes but is a disadvantage since the
offset is different for each transducer or ”8'01 - 0 10.05
volts. The user must record the remaining offset(the
voltage at ”o at zero pressure) so it can be subtracted from

the raw data before analysis.

The second problem encountered had to do with powerline
voltage fluctuations and power outages. The pressure
transducer output is linearly related to the input voltage
at a constant pressure. Since any changes in input voltage
are directly transmitted to the output, the input voltage
must be held relatively constant (10.01 volts) to achieve

accurate results.

Power outages affected both the pressure transducers
and the datalogger. The pressure transducers did not output
data during a power failure, while the datalogger lost all
data and any program stored in memory even if the power went

off for only a fraction of a second. The ”quick fix”

85

 

 

 

 

 

 

 

 

 

LM317T
"i" "a"11: 35+
' fldj
ti.
‘1- 1 UP . ZZBKQ

 

L" 10 of
,f' 5K0 T

Figure 38: Uariable voltage regulator.

solution was to connect the datalogger to a 18 volt
automotive battery. The battery was kept charged with an AC
battery charger to preserve the datalogger memory. The
pressure transducer’s output was zero for the duration of

the power outage.

a better solution to both powerline fluctuations and
power failures would be to power the entire data acquistion
system using a 18 volt automotive battery to power two
variable voltage regulators, one for the pressure
transducers and one for the datalogger. Then the system
could be installed at a remote site where ac power was not
available. The pressure transducers require a maximum of 80
milliamps each and the datalogger requires about
500 milliamps, so a system with eight pressure transducers
and one datalogger would require 660 milliamps or 0.66 amps.
The proposed, modified system was not tested, but a fully
charged battery should operate the system for at least a
month. If AC power were available, a battery trickle
charger could be used to keep the battery charged, and the

battery would be used only when the ac power went off.

6. Other suggestions

There are several additional suggestions that would
improve the system but have not been implemented or tested.
First, it would be convenient to be able to set the bubbling

rate at the instrumentation site rather than having to go

87

out to each observation well to check it. This could be
done by using a very accurate 0 to 1 psi pressure gauge

connected to the in-line flow control valve. The in-line
valve would be adjusted to a predetermined pressure for a

given bubbler tube length.

A copper or stainless steel tube, smaller diameter than
the bubbler tube, could be inserted into the observation
well and connected to the bubbler tube. This would have the
advantage of a straight tube which would be easier to
install and would not curl up in the observation well. The
smaller diameter tube might also decrease the amount of
nitrogen gas used. The smaller tube would also allow the
use of a smaller diameter observation well thereby
decreasing the lag time between the actual watertable and

the water level in the well.

Nitrogen gas was chosen because it is inert and
inhibits algae growth at the end of the bubbler tube. The
use of pressurized air in place of the nitrogen gas may be
advantageous. An air compressor installed at the site would
elimininate the need for transferring nitrogen gas tanks to
the site. The potential problem with air is the time for
algae to form at the end of the bubbler tube. Tests could
be conducted to determine that time or some additive could

be used occasionally to deter the growth of algae.

No test data has been developed for the operation of
the system in cold weather. A possible effect is the
increase in the time to equilibrium for a given bubbler tube
length. The effects could be minimized by burying the
bubbler tube to keep it at a relatively constant temperature
all year long. The instrumentation mounted in an insulated
box with a light bulb attached to a thermostat would keep it

at a temperature above freezing.

UII. OTHER RPPLICATIDNS

The bubbler system was originally designed to simplify
monitoring a watertable in the field, but the use of the
bubble system is not limited only to monitoring a
watertable. Several modified versions of the bubbler system
were used to aid data collection at Michigan State
University.

.

A. monitoring pump output

Pump flow was monitored using an orfice meter. A
pressure transducer was connected in place of the piezometer
to measure the water pressure in the discharge pipe. The
voltage from the pressure transducer was converted to a
digital number and recorded in the datalogger. The digital
number was converted to gallons per minutngpm) in the field

by the portable computer using the following equation:

88

80

0 - 6.08KAChO'S)

where:
0 is flow rate in gallons per minute.
K is the discharge factor dependent on the
ratio of orifice size to pipe diameter.

A is orifice area in square inches.
h is head in inches.

A problem encountered was fluctuations in the data due
to slight variations in pumping rate. Since the pumping
rate was relatively constant, the data values were averaged

giving good results.

6. Run-off and pollutant monitoring

The instrumentation to monitor water flow and trigger
pollutant samplers was improved using the bubbler system.
The purpose of the research was to determine the nature of
field pollutant losses from agricultural land where
conventional tillage practices (moldboard plow) and
conservation tillage practices (chisel plow) were used.
Tile flow and surface runoff at the field site was measured
utilizing flumes designed such that the volume of flow
passing through the flume was uniquely related to the depth
of flow in the flume. Tile flows were measured using three
U-flumes while surface runoff was measured using two

H-flumes.

81

In the past, float-type chart recorders were used to
monitor depth of flow in the flumes. ISCO flow meters,
based upon an air bubbling technique similiar to the bubbler
system were used to totalize the flow through the flumes and
initiate the pollutant samplers at a preset total. Both
systems were troublesome and required chart readings to
determine flow quantities. A modification of the bubbler
system was used to monitor flow depth in both the tile and
surface runoff flumes and trigger the pollutant samplers
(Figure 33). Water level in the outlet ditch and a
raingauge were also monitored. The system remained inactive
until 0.85 or more inches of rain was received in the
raingage. The ditch level was monitored to insure the tile
outlets were not submerged. Instead of the portable
computer and datalogger, a Campbell Scientific hodel 81X
micrologger was used to monitor the output voltage from the
pressure transducers. The micrologger was used because of
the ability to store many more points and the ease of
connecting the system to a modem for data transfer over a
phone line. when the rain gauge indicated over 0.85 inches
of rainfall, the depth of water running through the flumes
was stored and converted into a flow quantity using the
appropriate equation for each flume. Individual pollutant
samplers were triggered based on a preset cummulative flow

quantity.

88

 

110 UAC Surge Battery 18 UDC

 

 

Protection Charger Battery

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18 UDC
Regulated Campbell .
Power Scientific H Auto-answer
Supply flodel 81X flodem
A
6 UDC analog
data
Bubbler [Pressure
Transducer Phone Surge
Tubes [Box
_ Line Protection
Surge l Control lines
Flow
Control ProtectionJ to ISCO samplers
Ualves
Nitrogen
6as

 

Figure 33: The Bubbler System layout using a Campbell
Scientific Hodel 81X micrologger.

83

Time of day, day of year, raingage depth, ditch level,
flow depth, actual flow, and cumulative flow were stored in
the micrologger at five minute intervals. The system was
reset if the flow through the flumes went below a given

value.

The micrologger was capable of storing up to 83,396
data points. A telephone line installed at the site
provided the ability to call the micrologger to monitor the
system operation, check the number of samples taken, change
the micrologger program, or retrieve the stored data. The
data was retrieved from the micrologger approximately every
9 days. The use of the Campbell Scientific 81x micrologger
was advantageous to the system for several reasons. The 81X
has 13 bit precision while the other datalogger used has
only 6 bit precision so that the accuracy of the system was
limited by the accuracy of the pressure transducers rather
than by the datalogger. The data storage capability was
increased from 1975 to 83,396 data points and the system
could easily be called to monitor operation or retrieve
data. A disadvantage is the 81X must be programmed in a
language similar to machine language, making the program
harder to understand since no comment statements are
allowed. The portable computer it replaced uses the familiar
BASIC language which allows REflark statements to document
the procedure within the program. Also, the 81x micrologger
is about twice the cost of the other system. If accuracy is

the most important criteria, the 81X system is recommended.

89

C. Watertable monitoring at 69 locations

This application is currently being developed. It
involves monitoring the watertable at 69 locations in a 90
acre water management project. It is planned to develop the
system using one 6 channel, 6 bit datalogger, 6 pressure
transducers, 69 solenoid switches, and a portable computer.
The entire system will be powered using a 18 volt automotive
battery and will utilize difference amplifiers to subtract
the transducer offset from the raw output. The nitrogen gas
lines will be connected to the correct observation walls
using eight banks of eight solenoids (A to H in Figure 39)
switched sequentially by the digital output of the Starbuck
B838 datalogger. A set of solenoids consisting of one
solenoid from each of the eight banks, e.g. all the A
solenoids, will be opened to allow the nitrogen gas to
bubble out. One pressure transducer will be connected to
each of the eight solenoid banks so the pressure read by the
pressure transducer is the pressure at the open solenoid.
Each set of solenoids will be opened until all 69
observation sites are read. It will be designed to take a
set of data points every 30 minutes. The data will first be
stored in the datalogger, then transferred to the portable

computer, and finally to a cassette tape.

85

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

121nm
AUTmfin1VE
BATTERY
v V v v v
REED {— STARBUCK 6232 $; RADIO SHACK —} CASSETTE REELLATED
RELAYS DATALOGGER MODEL 100 RECORDER POWER
ermtv
analog data with Vic
offsets subtracted B to
digital data I ~diiferenca pressure
to solenoids neaplifiers transducers

 

 

 

l analog datafiroa
presmuwrtranmmuers

 

NINKEE

 

r—PTl —PT2 —PT3 —PT4 —PT5 h—PTb HT7 r—PTB

 

 

 

 

 

 

 

 

 

 

 

 

E

:h——4

E
—i——n
—Fl—--—-
_.’1'

 

 

 

 

 

 

 

 

unll
Illllllll

Bubblar tubes to
observation wells

0 -> Flow control valves
PTn >Presw etransdum
A-H -> Eight solenoids per bank

Figure 39: Schematic of bubbler system instrumentation
(top) and solenoid banks (bottom) to monitor 69
observation wells for a watertable management
research project.

UIII. CONCLUSIONS

The bubbler system is an electronic data acquisition
system to measure the position of the water table for
drainage and subirrigation. It uses a very small diameter
observation well into which a smaller diameter bubbler tube
connected by flexible tubing to a pressurized nitrogen gas
tank is inserted. A pressure transducer connected to the
supply line senses the pressure required to force a bubble
out of the bubbler tube. The data acquisition equipment can
be located in one central location with the bubbler tube
transferring the water level information from the
observation well to the pressure transducer. Data is stored
in a datalogger and transfered to floppy diskette for

further analysis and plotting.

The accuracy of the float-type chart recorders
previously used was approximately :3 mm (0.1 inches), so the
bubbler system was designed to have about the same accuracy.
The search for components was started by finding the
pressure transducer, than the datalogger, and finally the
computer. A flicro Switch Model 168PC01D pressure
transducer, Starbuck 6838 datalogger, and a Radio Shack
hodel 100 portable computer were the components chosen for

the data acquisition system.
96

87

The system was tested in the labratory and found to
perform well. It was then installed in the field for
further testing. Float-type chart recorders were installed
along with the bubbler tubes for comparison of the data.

The data from the bubbler system followed the digitized data
from the chart recorder accurately. The difference was due
to the increased time lag between the actual watertable and
the water level in the observation well caused by a larger
observation well diameter. The bubbler system used a 1 inch
observation well while the float-type recorder used a 3 inch

diameter well.

The datalogger and a single pressure transducer were
calibrated separately, then the complete system was
calibrated using five different bubbler tube lengths (100,
500, 1000, 1500, and 8000 feet) and three different
temperatures above 80'C(66'F). The error analysis indicated
that temperature had little effect on the system. Bubbler
tuba length did not effect the slope of the calibration
curve, but the offset increased slightly as the tube length
increased. There is a significant time delay from a given
change in water level until the system is equillibrated.
The time to equilibrium increases expotentially as the

bubbler tube length increases.

APPENDIX A: Component specifications and prices.

88

W
(Costs are typical retail prices in East Lansing, "I, 1966)

Radio Shack nodal 100 portable computer(89K model) 8600.00

Starbuck 6838 datalogger 990.00
micro-Switch Model 168PC01D pressure transducer 66.00
Bubbler tube(1/6” spaghetti tubing) per 1000 feet 19.68
In-line needle valve 10.97
Pressure regulator 69.00
Nitrogen gas (230 fta) 9.92
06-85 ribbon cable for communications between

Hodel 100 and Starbuck datalogger 80.00
niscellanous tubing connections 10.00

W

(All information given is based on 1966 data.)
Pressure Transducer (micro-Switch Nodal 168PCOlD)

“Size
59.6(8.35) x 30.0(1.16) x 86.5(1.19) mm(inches)

' Range 1
0 to 1 pound per square incthsi) or 0 to 87.66
inches of water. The output from the transducer is

between 0 and 6 volts DC, with a one volt offset,
and is linear over the full range.

88

9 Percent Error
Repeatability and hysteresis error of 10.152 of
full scale or 11.05 mm of water (10.0915 inches of
water).

9 Temperature compensated

will operate accurately in temperatures from -90'C
to +65'C (-65'F to +857'F).

Datalogger (Starbuck nodal 6838)

9 Size
886.6(9.0) x 879.9(11.0) x 50.6(8.0) mm(inches)
9 Analog input range
0 to 5 volts.
9 Resolution
Eight bit conversion with 11 least sign ficant
bit(LSB) means precision of 1 part in 8 (856)
which equals (1/856)9100 - 0.39%. This gave an
accuracy of 18.79 mm (30.11 inches) water.
9 Number of channels

6 analog and 6 digital channels in and 6 digital
channels out.

9 Stand alone operation -- data transfer
The datalogger is independent of another device
after the data collection process is started.
Data collection is initiated via the R9838C port
on a computer.

9 Time interval control

Time base scene or time interval between data
points is variable from 1 second to 16.8 hours.

9 Local (internal) storage

It has the ability to store up to 1975 data points
in the 8K of internal RAH.

100

Computer (Radio Shack model 100)

9 Size and weight

300(11.6) x 815(6.9) x 50.6(8.0) mm(inches)
1.361 kilograms(3 pounds 13.5 ounces).

9 Temperature and humidity

S’C to 90'CC91’F to 109'F) and 802 to 85% RN

9 Screen

An 6 line 90 column (890 x 69 full dot matrix)
screen.

9 Portable-Constant memory

Rechargeable batteries protect the memory 90 days
with ax model and 10 days with 38K model. The
operating batteries last 80 hours with all
input/output devices disconnected.

9 R5838C communications

An RS838C port, accessible from a BASIC program,
to communicate with the datalogger and the ability
to upload or download information to or from an
IBH compatible computer is supplied.

9 Permanent memory based programs
This computer has a word processor, a schedule and
address organizing program, and a communication
package.

9 Floating point BASIC

The Nodal 100 has an enhanced version of Microsoft
BASIC available for possible field data
manipulation.

101

9 Communication capability

It has a built-in modem with an automatic dialer.
The Model 100 can communicate through the modem
and R5838C port over a wide range of parameters.
The baud rate can be varied from 75 to 19800 bits
per second, the word length from 6 to 6 bits,
ignore, add, even, or no parity, 1 or 8 stop bits,
and telephone parameters of line status enable or
disable and a pulse rate of either 10 or 80 pulses
per second.

9 Bar code reader
The built-in bar code reader interface along with
an optional bar code reader allows the reading of
product marking-code identifications.

9 Cassette player interface
The cassette interface to allow direct connection
to a cassette player, for reading and writing
programs and data, is also built-in.

9 Parallel printer
A parallel printer interface is built-in.

9 Programmable function and cursor control keys
There are eight fully programmable function keys.
The flodel 100 has individual cursor control keys
and four command keys.

9 Clock

There is a real time clock, using military time,
and a calendar with both day and date.

9 Full size keyboard

It also has a full size keyboard and a 10 key
number pad.

APPENDIX 6: Sample BASIC program and datalogger commands.

108

BASIC program for Radio Shack hodel 100 to retrieve a set of
data points from Starbuck 6838 datalogger.

100
105

110
115

OPEN 'COH:37E1D' FOR INPUT AS 8

REM Open communications for data received from
datalogger.

OPEN 'COH:37E10” FOR OUTPUT AS 1

RE" Open communications for data transmitted to
datalogger.

PRINT 91,CHRS(87):”01";

REH Start communications with datalogger.

PRINT #1, "H6P3";

REh Bet number of data points on channel 3.

INPUT 98,AS:LE2 - LEN(A8):A9 - RIGHTS(A8,LE2-3)

A - UAL(AS)

I2 - INT((A-1)/10)+1

REH Number lines of data stored.

J2 - A-109(I2-1)

REH Number of points in last line.

J2 - 99J2

REM Characters in the last line.

PRINT 91,"flD3”;

REM Start data transmission.

INPUT 98,68

RE" Throw away unit identification response.

FOR L2 - 1 TO I2

IF L2 - I2 AND J2 <> 0 THEN AS(L2)-INPUTS(J2,8):60TO 890

A8(L2) - INPUTSC90,8)

NEXT L2

103

Sample communication session between Starbuck 6838 and Radio

Shack flodel 100.

Communications with

W

:90 01 ca'
01:

"R on

01:
"Bl-6:100 CR

01:
fill-9:80 CR

01:
"15-8:800 CR

01:
"SI-8 CR

01:
ESC CR

ESC 01 CR

01:
HBPI CR

01:100
"8P5 CR

01:8
NOS CR
01:

data data data

Definitions and/or

explanation.

Start communications.
Starbuck 6838 response.
Reset monitor routine.

Set aside 100 locations for each
channel.

One minute(60 second) time interval for
channels 1-9.

15 minute(900 second) time interval for
channels 5-6.

Start acquiring data on all eight
channels.

Stop communications -- talk to you
later!
No response.

Two hours later -- resume
communications.

How many points have been acquired on
channel 1?

100 points have been acquired.

How many points have been acquired on
channel 5?

9 points have been acquired.

Display the points on channel 5.

(9 data points)

'CR means press carriage return or enter key.

APPENDIX C: Component calibration data.

109

datalogger calibration (increasing water level)

X - datalogger reading (Units) Y - onn reading (Uolts)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
69.0 1.897 1.896 0.001 0.0000 0.0196
90.0 1.760 1.757 0.003 0.0000 0.0137
107.0 8.099 8.091 0.003 0.0000 0.0137
189.0 8.580 8.583 -0.003 0.0000 0.0137
158.0 8.969 8.975 -0.011 0.0001 0.0137
179.0 3.905 3.907 -0.008 0.0000 0.0137
196.0 3.699 3.639 0.010 0.0001 0.0137
805.0 9.019 9.016 0.003 0.0000 0.0137
839.0 9.565 9.566 -0.001 0.0000 0.0137
895.0 9.600 9.608 -0.008 0.0000 0.0137
853.0 9.953 9.959 -0.006 0.0000 0.0137
859.0 9.967 9.979 0.006 0.0001 0.0137
855.0 9.997 9.996 -0.001 0.0000 0.0137
n - 0.080 SE n - 0.000 YI - -0.011
S YI - 0.010 SE Y Ave 9 0.0136 2 err - 0.8760
s 9 0.006 SSE - 0.000 t(952) 9 8.801

datalogger calibration (decreasing water level)

X 9 datalogger reading (Units) Y 9 Dflfl reading (Uolts)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
859.0 9.888 9.889 0.009 0.0000 0.0138
898.0 9.793 9.798 90.005 0.0000 0.0138
833.0 9.575 9.578 0.009 0.0000 0.0138
810.0 9.189 9.180 0.009 0.0000 0.0138
188.0 3.888 3.885 90.003 0.0000 0.0188
173.0 3.388 3.389 90.008 0.0000 0.0188
198.0 8.881 8.809 90.013 0.0008 0.0188
115.0 8.851 8.855 0.005- 0.0000 0.0188
88.0 1.898 1.898 0.000 0.0000 0.0138
80.0 1.770 1.755 0.005 0.0000 0.0138
78.0 1.533 1.530 0.003 0.0000 0.0138
59.0 1.858 1.855 90.003 0.0000 0.0138
n 9 0.080 SE n 9 0.000 Y! 9 90.001
5 Y1 9 0.008 SE Y Ave 9 0.0135 2 art 9 0.870
s 9 0.005 SSE 9 0.000 t(852) 9 8.888

105

datalogger calibration (both data sets)

X 9 datalogger reading (Units) Y 9 DH" reading (Uolts)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED 5E Y
59.0 1.897 1.858 90.005 0.0000 0.019
80.0 1.750 1.758 90.008 0.0000 0.019
107.0 8.089 8.085 90.001 0.0000 0.019
188.0 8.580 8.587 90.007 0.0001 0.019
158.0 8.859 8.878 90.015 0.0008 0.019
179.0 3.905 3.910 90.005 0.0000 0.019
185.0 3.898 3.898 0.007 0.0000 0.019
805.0 9.018 9.018 0.000 0.0000 0.019
839.0 9.585 9.588 90.003 0.0000 0.019
895.0 9.800 9.809 90.009 0.0000 0.019
853.0 9.853 9.881 90.008 0.0001 0.019
859.0 9.887 9.881 0.005 0.0000 0.019
855.0 9.887 5.000 90.003 0.0000 0.019
859.0 9.888 9.881 0.007 0.0001 0.019
898.0 9.793 9.795 90.008 0.0000 0.019
833.0 9.575 9.558 0.008 0.0001 0.019
810.0 9.189 9.117 0.007 0.0000 0.019
188.0 3.888 3.881 0.001 0.0000 0.019
173.0 3.388 3.381 0.001 0.0000 0.019
198.0 8.881 8.800 90.008 0.0001 0.019
115.0 8.851 8.858 0.008 0.0001 0.019
88.0 1.898 1.838 0.009 0.0000 0.019
80.0 1.770 1.758 0.008 0.0001 0.019
78.0 1.533 1.585 0.007 0.0000 0.019
59.0 1.858 1.858 0.000 0.0000 0.019
n 9 0.080 SE n 9 0.000 YI 9 90.005
5 Y1 9 0.007 SE Y Ave 9 0.019 2 err 9 0.880
s 9 0.005 SSE 9 0.001 t(852) 9 8.079

Temperature data [Uin - 6 UDC and constant pressure]

TemperatureC'C) Uout
80 1.008
85 1.006
30 1.009
35 1.011
90 1.016
95 1.080
50 1.083
55 1.085

80 1.030

105

Uin/Uout

X 9 voltage in Y 9 voltage out

CALCULATED RESIDUAL

X Y Y - RESIDUAL SOUARED SE Y
7.09 0.903 0.987 -0.089 0.001 0.093
7.53 0.951 0.966 -0.015 0.000 0.093
6.01 1.008 1.006 -0.006 0.000 0.098
6.56 1.059 1.057 0.008 0.000 0.098
9.05 1.109 1.100 0.009 0.000 0.091
10.09 1.809 1.198 0.017 0.000 0.091
11.00 1.893 1.878 0.081 0.001 0.091
18.06 1.366 1.365 0.083 0.001 0.091
13.03 1.963 1.951 0.018 0.000 0.091
19.06 1.536 1.598 90.006 0.000 0.098
19.99 1.619 1.689 90.010 0.000 0.099
15.99 1.663 1.707 -0.089 0.001 0.095

n 9 0.066 SE n 9 0.009 YI 9 0.308

S YI 9 0.099 SE Y Ave 9 0.098

s 9 0.0175 SSE 9 0.003 t(952) 9 8.886

pressure transducer calibration with onn
(increasing water level)

X 9 Dhfl reading Y 9 water depth (cm)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
8.158 8.00 8.881 0.178 0.038 0.813
8.975 13.30 13.889 0.015 0.000 0.808
8.783 17.85 17.818 0.031 0.001 0.805
3.877 89.55 89.781 90.071 0.005 0.800
3.509 88.30 88.389 90.089 0.007 0.188
3.815 33.80 33.818 90.018 0.000 0.187
9.885 38.80 38.859 90.059 0.003 0.185
9.558 98.80 98.803 90.003 0.000 0.185
9.855 97.30 97.381 90.081 0.007 0.185
5.018 98.35 98.953 90.113 0.013 0.187
5.397 59.15 59.890 90.080 0.008 0.188
5.559 58.80 58.750 0.090 0.008 0.801
5.889 53.55 53.955 0.089 0.007 0.809
5.309 58.00 57.887 0.113 0.013 0.807
5.995 58.85 58.888 0.058 0.003 0.808

107

H 9 19.850 SE H 9 0.037 YI 9 988.010
5 Y1 9 0.170 SE Y Ave 9 0.808 2 err 9 0.887
s 9 0.088 SSE 9 0.100 t(852) 9 8.150

pressure transducer calibration with Dhn
(decreasing water level)

X 9 DH" reading Y 9 water depth (cm)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
5.906 68.10 61.966 0.118 0.0189 0.891
5.616 57.90 57.687 0.073 0.0053 0.865
5.399 59.00 53.951 0.099 0.0089 0.860
5.066 50.05 99.969 0.061 0.0036 0.876
9.969 96.70 96.691 90.191 0.0365 0.875
9.659 99.00 99.117 90.117 0.0137 0.878
9.895 36.90 39.000 90.100 0.0101 0.871
3.919 33.70 33.571 0.189 0.0166 0:871
3.961 87.00 87.115 90.115 0.0131 0.879
3.867 89.30 89.350 90.050 0.0085 0.876
8.666 16.60 16.663 90.063 0.0090 0.868
8.966 13.90 13.819 0.161 0.0387 0.869
8.856 10.00 9.970 0.030 0.0009 0.896
n 9 19.585 SE n 9 0.061 Y! 9 988.811
5 Y1 9 0.868 SE Y Ave 9 0.861 2 err 9 0.399
s 9 0.166 SSE 9 0.159 t(952) 9 8.801

pressure transducer calibration with DNN (both data sets)

X 9 nun reading Y 9 water depth (cm)

CALCULATED RESIDUAL

X Y Y RESIDUAL SOUARED 8E Y
8.158 8.00 8.587 0.303 0.0881 0.395
8.975 13.30 13.158 0.138 0.0180 0.390
8.783 17.85 17.588 0.151 0.0888 0.337
3.877 89.55 89.509 0.095 0.0081 0.338
3.509 88.30 88.870 0.030 0.0008 0.330
3.815 33.80 33.707 0.083 0.0087 0.388
9.885 38.80 38.199 0.055 0.0038 0.388
9.558 98.80 98.785 0.105 0.0111 0.388
9.855 97.30 97.875 0.085 0.0005 0.330
5.018 98.35 98.358 90.008 0.0001 0.330

108

5.397 59.15 59.137 0.013 0.0008 0.338
5.559 58.80 58.550 0.190 0.0187 0.335
5.889 53.55 53.358 0.188 0.0338 0.338
5.309 58.00 57.781 0.808 0.0938 0.398
5.995 58.85 58.808 0.198 0.0818 0.399
5.808 58.10 88.191 90.091 0.0017 0.338
5.515 57.80 57.875 90.075 0.0058 0.335
5.399 59.00 59.089 90.089 0.0088 0.338
5.055 50.05 50.188 90.078 0.0051 0.331
9.888 98.70 98.088 90.388 0.1085 0.330
9.559 99.00 99.850 90.850 0.0585 0.388
9.885 38.80 38.188 90.888 0.0580 0.388
3.819 33.70 33.588 0.008 0.0001 0.388
3.951 87.00 87.888 90.888 0.0585 0.331
3.857 89.30 89.958 90.158 0.0851 0.338
8.858 18.50 18.758 90.158 0.0885 0.335
8.985 13.90 13.318 0.081 0.0055 0.390
8.858 10.00 10.055 90.055 0.0099 0.393
n 9 19.857 SE fl 9 0.098 Y! 9 988.198
5 Y1 9 0.817 SE Y Ave 9 0.335 2 err 9 0.9755
s 9 0.157 SSE 9 0.593 t(852) 9 8.055

pressure transducer calibration with datalogger
(increasing water level)

X 9 datalogger reading Y 9 water depth (cm)

CALCULATED RESIDUAL

X Y Y RESIDUAL SOUARED SE Y
110.0 8.00 8.885 0.109 0.0108 0.315
185.0 13.30 13.350 90.050 0.0085 0.303
198.0 17.85 17.805 0.095 0.0080 0.883
157.0 89.55 89.755 90.115 0.0133 0.885
189.0 88.30 88.988 90.188 0.0385 0.889
188.0 33.80 33.575 0.185 0.0155 0.885
815.0 38.80 38.130 0.070 0.0050 0.881
838.0 98.80 98.853 0.037 0.0019 0.301
898.0 97.30 97.317 90.017 0.0003 0.319
n 9 0.878 SE fl 9 0.008 YI 9 981.730
8 Y1 9 0.337 SE Y Ave 9 0.887 2 err 9 0.983
s 9 0.119 SSE 9 0.081 t(852) 9 8.355

108

pressure transducer calibration with datalogger
(decreasing water level)

X 9 datalogger reading Y 9 water depth (cm)

CALCULATED RESIDUAL

X Y Y . RESIDUAL SOUARED SE Y
859.0 96.70 96.799 90.099 0.0089 0.335
837.0 99.00 99.011 90.011 0.0001 0.380
816.0 36.90 36.716 0.169 0.0390 0.309
800.0 33.70 33.699 0.001 0.0000 0.308
176.0 87.00 87.010 90.010 0.0001 0.300
167.0 89.30 89.508 90.808 0.0906 0.301
196.0 16.60 16.699 90.099 0.0089 0.309
187.0 13.50 13.359 0.196 0.0813 0.381
115.0 10.00 10.010 90.010 0.0001 0.330
n 9 0.87 SE n 9 0.008 YI 9 988.091
5 Y1 9 0.369 SE Y Ave 9 0.319 2 err 9 0.9967
s 9 0.180 SSE 9 0.101 t(952) 9 8.365

pressure transducer calibration with datalogger
(both data sets)

X 9 datalogger reading Y 9 water depth (cm)

CALCULATED RESIDUAL

X Y Y RESIDUAL SOUARED 5E Y
110.0 8.00 8.750 0.890 0.0575 0.918
185.0 13.30 13.815 0.089 0.0070 0.908
198.0 17.85 17.578 0.178 0.0315 0.901
157.0 89.55 89.535 0.015 0.0008 0.389
189.0 88.30 88.358 90.058 0.0098 0.383
188.0 33.80 33.597 0.853 0.0591 0.385
815.0 38.80 38.003 0.187 0.0388 0.388
838.0 98.80 98.737 0.153 0.0859 0.905
898.0 97.30 97.183 0.107 0.0119 0.915
859.0 98.70 98.859 90.159 0.0870 0.918
837.0 99.00 99.130 90.130 0.0158 0.908
818.0 38.80 38.838 0.058 0.0038 0.900
800.0 33.70 33.885 90.185 0.0157 0.385
175.0 87.00 87.191 90.191 0.0188 0.389
157.0 89.30 89.535 90.335 0.1180 0.389
195.0 18.50 18.788 90.185 0.0397 0.388
187.0 13.50 13.985 0.005 0.0000 0.907
115.0 10.00 10.153 90.153 0.0833 0.915
N 9 0.878 VI 9 981.875 SE n 9 0.008
5 Y1 9 0.351 SE Y Ave 9 0.903 2 err 9 0.573
s 9 0.175 SSE 9 0.985 t(852) 9 8.180

APPENDIX 0: System calibration data.

110

DATALOBGER DATA

X 9 datalogger reading Y 9 measured water level (cm)

30.5 meter (100 foot) bubbler tube

88°C (89.8'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SDUARED SE Y
100 11.8 11.885 90.085 0.007 0.918
111 15.8 15.055 0.195 0.081 0.385
188 80.0 80.078 90.078 0.005 0.381
158 88.8' 88.173 0.087 0.001 0.383
808 98.9 98.908 90.008 0.000 0.958
n 9 0.878 SE H 9 0.009 YI 9 915.885
5 Y1 9 0.57 SE Y Ave 9 0.907 2 err 9 0.578
s 9 0.108 SSE 9 0.035 t(852) 9 3.188

99'C (111.8'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
89 10.9 10.980 90.080 0.000 0.888
109 13.8 13.180 0.080 0.000 0.878
185 18.3 18.853 0.097 0.008 0.855
179 38.9 38.509 90.109 0.011 0.875
810 9 .5 98.993 0.057 0.003 0.318
N 9 0.875 SE n 9 0.008 YI 9 915.530
5 Y Ave 9 0.889
s 9 0.075 SSE 9 0.017 t(852) 9 3.188

SE YI 9 0.353

2 err 9 0.909

111

55°C (131'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
106 13.6 13.613 90.013 0.000 0.310
133 81.1 81.136 90.036 0.001 0.879
199 85.7 85.597 0.103 0.011 0.871
163 35.0 35.079 90.079 0.005 0.868
811 98.9 98.676 0.088 0.000 0.316
n 9 0.879 SE n 9 0.003 YI 9 915.938
S YI 9 0.960 SE Y Ave 9 0.898 2 err 9 0.915
s 9 0.076 SSE 9 0.016 t(952) 9 3.168
158.9 meter (500 foot) bubbler tube
89°C (69.8'F)
CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
98 6.9 6.653 0.097 0.008 0.356
119 16.9 16.357 0.093 0.008 0.387
136 81.5 81.636 90.136 0.019 0.316
191 36.9 36.366 0.038 0.001 0.335
813 98.5 98.963 0.017 0.000 0.361
n 9 0.876 SE n 9 0.003 YI 9 916.716
5 Y1 9 0.996 SE Y Ave 9 0.339 2 err 9 0.968
s 9 0.090 SSE 9 0.089 t(952) 9 3.168

37°C (88.5'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
69 6.0 7.995 0.005 0.000 0.319
103 11.9 11.677 0.083 0.001 0.305
156 86.6 86.579 0.086 0.001 0.865
176 38.0 38.180 90.180 0.019 0.898
815 93.0 98.939 0.066 0.009 0.389
n 9 0.877 SE n 9 0.003 Y! 9 916.663
S Y! 9 0.366 SE Y Ave 9 0.306 2 err 9 0.935
s 9 0.061 SSE 9 0.080 t(952) 9 3.168

51'C (183.8'F)

118

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
105 18.5 18.991 0.058 0.009 0.981
151 85.1 85.188 90.088 0.008 0.903
170 30.5 30.955 0.095 0.008 0.388
188 35.5 35.780 90.180 0.015 0.918
818 98.8 98.085 0.105 0.011 0.998
n 9 0.877 SE n 9 0.009 YI 9 915.558
5 Y1 9 0.757 SE Y Ave 9 0.988 2 err 9 0.510
s 9 0.119 SSE 9 0.038 t(852) 9 3.188

309.6 meter (1000 foot) bubbler tube

85'C (77'F)
CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
103 9.8 9.877 90.0766 0.006 0.309
135 16.8 16.186 0.0717 0.005 0.877
169 87.6 87.533 0.0666 0.009 0.866
803 36.9 36.936 90.0361 0.001 0.860
885 93.0 93.089 90.0837 0.001 0.308
n 9 0.87798 fl 9 0.008 YI 9 919.815
5 Y1 9 0.989 SE Y Ave 9 0.867 2 err 9 0.906
s 9 0.076 SSE 9 0.017 t(952) 9 3.168
38°C (69.6'F)
CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
69 6.0 5.969 0.0306 0.001 0.166
181 19.6 19.609 90.0066 0.000 0.199
156 85.0 85.030 90.0897 0.001 0.193
163 31.9 31.936 90.0357 0.001 0.196
880 98.8 98.157 0.0939 0.008 0.166
n 9 0.876 SE n 9 0.001 YI 9 9 16.616
5 Y1 9 0.805 SE Y Ave 9 0.159 2 err 9 0.819
s 9 0.091 SSE 9 0.005 t(952) 9 3.168

113

50'C (188'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
97 7.9 7.638 0.066 0.005 0.937
119 13.6 13.939 90.190 0.019 0.907
158 83.8 83.101 0.099 0.010 0.366
199 36.1 36.199 90.099 0.008 0.911
880 98.0 91.979 0.081 0.000 0.990
n 9 0.876 SE n 9 0.003 V! 9 919.097
SE Yl 9 0.556 SE Y Ave 9 0.916 2 err 9 0.598
s8 9 0.111 SSE 9 0.037 t(952) 9 3.168

957.8 meter (1500 foot) bubbler tube
86'C (68.9'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SQUARED SE Y
87 7.3 7.858 0.038 0.001 0.893
111 11.8 11.801 90.001 0.000 0.838
158 85.5 85.551 90.051 0.003 0.815
189 39.5 39.559 90.059 0.003 0.887
888 98.5 98.938 0.058 0.005 0.897
n 9 0.881 SE n 9 0.008 YI 9 980.088
5 Y1 9 0.309 SE Y Ave 9 0.833 2 err 9 0.331
s 9 0.058 SSE 9 0.018 t(852) 9 3.188

38'C (108.8'F)

CALCULATED RESIDUAL

X Y Y RESIDUAL SOUARED 5E Y

99 6.8 6.867 90.067 0.009 0.369

138 17.0 16.699 0.106 0.011 0.330

197 81.1 81.066 0.018 0.000 0.388

801 36.1 36.169 90.069 0.006 0.391

888 98.1 98.068 0.036 0.001 0.366
N 9 0.860 SE n 9 0.003 YI 9 980.080
5 Y1 9 0.966 SE Y Ave 9 0.396 2 err 9 0.998
s 9 0.098 SSE 9 0.085 t(952) 9 3.168

53°C (187.9'F)

119

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
81 5.0 5.008 90.008 0.000 0.888
189 19.3 19.888 0.071 0.005 0.859
155 85.5 85.585 90.085 0.007 0.858
188 33.8 33.888 90.088 0.001 0.858
885 98.5 98.998 0.051 0.003 0.888
N 9 0.878 SE n 9 0.008 YI 9 980.913
8 Y1 9 0.350 SE Y Ave 9 0.878 2 err 9 0.387
s 9 0.078 SSE 9 0.015 t(852) 9 3.188

609.6 meter (8000 foot) bubbler tube
81'C (69.6'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
118.0 11.50 11.593 0.057 0.003 0.383
187.0 15.85 15.788 0.188 0.015 0.315
193.0 80.10 80.188 90.088 0.008 0.311
158.0 89.90 89.378 0.088 0.001 0.310
173.0 88.50 88.553 0.037 0.001 0.318
188.0 33.00 33.087 90.087 0.001 0.315
805.0 37.80 37.981 0.308 0.085 0.385
881.0 98.00 91.855 0.099 0.008 0.335
803.0 35.70 35.833 90.833 0.059 0.383
188.0 38.70 38.798 90.098 0.008 0.315
171.0 88.00 88.005 90.005 0.000 0.311
158.0 89.90 89.378 0.088 0.001 0.310
193.0 80.00 80.188 90.188 0.037 0.311
188.0 15.00 15.007 90.007 0.000 0.315
111.0 11.10 11.859 90.159 0.087 0.389
88.0 5.00 9.895 0.159 0.089 0.390
fl 9 0.878 SE fl 9 0.008 YI 9 918.707
5 Y1 9 0.388 SE Y Ave 9 0.318 2 err 9 0.959
s 9 0.138 SSE 9 0.871 t(852) 9 8.150

115

88°C (88.9’F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
87.0 5.00 9.889 0.005 0.000 0.378
117.0 13.30 13.308 90.008 0.000 0.399
150.0 88.50 88.991 0.058 0.003 0.330
185.0 38.00 38.135 90.135 0.018 0.393
880.0 91.80 91.888 0.078 0.005 0.388
N 9 0.877 SE n 9 0.003 YI 9 918.957
5 Y1 9 0.953 SE Y Ave 9 0.355 2 arr 9 0.505
s 9 0.085 SSE 9 0.087 t(852) 9 3.188
35’C (SS'F)
CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
108.0 8.00 8.883 0.007 0.0000 0.509
135.0 18.90 18.973 90.073 0.005 0.998
170.0 88.00 87.858 0.098 0.008 0.931
803.0 37.30 37.153 0.197 0.088 0.955
883.0 98.50 98.788 90.188 0.017 0.987
”‘9 0.878 SE n 9 0.009 YI 9 918.995
5 Y1 9 0.588 SE Y Ave 9 0.955 2 err 9 0.558
s 9 0.189 SSE 9 0.095 t(852) 9 3.188
53’C (187.9'F)
CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
105.0 8.50 8.539 0.055 0.009 0.359
190.0 18.85 18.078 90.188 0.015 0.389
178.0 88.10 88.050 0.090 0.008 0.318
803.0 35.80 35.751 0.038 0.008 0.388
885.0 93.80 93.817 90.017 0.000 0.359
N 9 0.881 SE n 9 0.003 YI 9 980.818
5 Y1 9 0.518 SE Y Ave 9 0.335 2 err 9 0.978
s 9 0.080 SSE 9 0.089 t(852) 9 3.188

115

DIGITAL HULTIHETER (DNN) DATA

X 9 Dflfl reading Y 9 measured water level (cm)

30.96 meter (100 foot) bubbler tube

88'C (89.8’F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.858 11.8 11.880 0.00878 0.000 0.815
8.188 15.8 15.191 0.05888 0.003 0.807
8.538 80.0 80.057 90.0557 0.009 0.188
3.118 88.8 88.888 90.0888 0.001 0.800
9.189 98.9 98.373 0.08787 0.001 0.891
n 9 19.073 SE n 9 0.109 YI 9 915.555
5 Y1 9 0.300 SE Y Ave 9 0.818 2 err 9 0.308
s 9 0.057 SSE 9 0.010 t(852) 9 3.188

99’C (111.8'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.898 10.9 10.908 90.008 0.000 0.173
8.099 13.8 13.153 0.097 0.008 0.157
8.985 18.3 18.398 90.098 0.008 0.158
3.918 38.9 38.935 90.035 0.001 0.155
9.133 98.5 98.958 0.031 0.001 0.187
N 9 19.033 SE n 9 0.075 YI 9 915.531
5 Y1 9 0.817 SE Y Ave 9 0.170 2 err 9 0.898
s 9 0.095 SSE 9 0.008 C(852) 9 3.188

117

55’C (131’F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
8.078 13.5 13.500 0.000 0.000 0.057
8.513 81.1 81.110 90.010 0.000 0.051
8.838 85.7 85.580 0.080 0.000 0.058
3.508 35.0 35.018 90.018 0.000 0.051
9.158 98.8 98.883 0.007 0.000 0.058
N 9 19.053 SE n 9 0.033 Y! 9 915.537
5 YI 9 0.109 SE Y Ave 9 0.053 2 err 9 0.080
s 9 0.017 SSE 9 0.001 t(852) 9 3.188

158.9 meter (500 foot) bubbler tube

88’C (89.8'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.758 8.8 8.885 90.085 0.007 0.911
8.883 15.9 15.358 0.091 0.008 0.378
8.551 81.5 81.387 0.113 0.013 0.355
3.787 38.9 35.500 90.100 0.010 0.388
9.158 98.5 98.958 0.031 0.001 0.918
O 9 19.095 SE n 9 0.157 YI 9 915.897
5 Y1 9 0.508 SE Y Ave 9 0.388 2 err 9 0.558
s 9 0.109 SSE 9 0.033 t(852) 9 3.188
37°C (88.5'F)
CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.798 8.0 8.005 90.005 0.000 0.179
8.089 11.8 11.855 0.039 0.001 0.157
3.075 85.5 85.518 90.018 0.000 0.155
3.958 38.0 38.051 90.051 0.003 0.150
9.838 93.0 98.858 0.098 0.008 0.180
n 9 19.037 SE H 9 0.058 YI 9 915.598
5 Y1 9 0.810 SE Y Ave 9 0.157 2 err 9 0.838
s 9 0.099 SSE 9 0.005 t(852) 9 3.188

118

51°C (183.8'F)

CALCULATED RESIDUAL

X Y Y RESIDUAL SOUARED 5E Y

8.060 18.5 18.961 0.019 0.000 0.858

8.960 85.1 85.178 90.078 0.005 0.811

3.353 30.5 30.938 0.066 0.005 0.809

3.781 35.6 35.688 90.088 0.001 0.815

9.167 98.8 98.193 0.007 0.000 0.835

n 9 19.108 SE n 9 0.119 YI 9 916.651
9 Y1 9 0.396 SE Y Ave 9 0.889 2 err 9 0.319
s 9 0.060 SSE 9 0.011 t(952) 9 3.168

309.6 meter (1000 foot) bubbler tube

85'C (77'F)
CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
8.033 8.8 8.175 0.08375 0.001 0.138
8.578 18.8 18.805 90.0053 0.000 0.118
3.390 87.5 87.599 90.0991 0.008 0.113
3.885 35.8 35.888 0.00077 0.000 0.118
9.985 93.0 98.875 0.08988 0.001 0.188
N 9 19.130 SE n 9 0.053 YI 9 918.550
8 Y1 9 0.188 SE Y Ave 9 0.188 2 err 9 0.179
s 9 0.038 SSE 9 0.003 t(852) 9 3.188

38'C (88.5'?)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.757 5.0 5.855 0.0997 0.008 0.859
8.381 19.8 19.873 90.0739 0.005 0.888
3.118 85.0 85.015 90.0153 0.000 0.818
3.587 31.8 31.838 0.0585 0.009 0.885
9.335 98.8 98.818 90.0185 0.000 0.859
n 9 19.055 SE n 9 0.088 YI 9 918.758
5 Y1 9 0.315 SE Y Ave 9 0.835 2 err 9 0.335
s 9 0.053 SSE 9 0.018 t(852) 9 3.188

50'C (188'F)

118

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.808 7.8 7.881 0.008 0.000 0.317
8.388 13.8 13.798 0.058 0.003 0.887
3.007 83.8 83.313 90.113 0.013 0.881
3.813 35.1 35.038 0.051 0.009 0.888
9.338 98.0 98.008 90.008 0.000 0.380
n 9 19.095 SE n 9 0.185 YI 9 918.888
5 Y1 9 0.903 SE Y Ave 9 0.303 2 err 9 0.931
s 9 0.080 SSE 9 0.018 t(852) 9 3.188

957.8 meter (1500 foot) bubbler tube
86'C (68.9'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.808 7.3 7.873 0.087 0.001 0.387
8.185 11.8 11.817 90.017 0.000 0.370
3.188 85.5 85.953 0.037 0.001 0.399
3.889 39.5 39.537 90.137 0.018 0.351
9.358 98.5 98.911 0.080 0.008 0.383
n 9 19.888 SE n 9 0.150 YI 9 980.005
5 Y1 9 0.989 SE Y Ave 9 0.371 2 err 9 0.588
s 9 0.088 55E 9 0.088 t(852) 9 3.188

38°C (108.8'?)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.897 5.8 5.887 90.087 0.001 0.181
8.505 17.0 15.851 0.038 0.008 0.108
8.887 81.1 81.085 0.009 0.000 0.105
3.858 35.1 35.181 90.081 0.000 0.111
9.380 98.1 98.085 0.009 0.000 0.180
n 9 19.151 SE n 9 0.097 YI 9 918.888
5 Y1 9 0.158 5E Y Ave 9 0.113 2 err 9 0.151
s 9 0.030 SSE 9 0.003 t(852) 9 3.188

180

53’C (187.9'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.788 5.0 9.808 0.081 0.008 0.351
8.951 19.3 19.389 90.089 0.007 0.389
3.895 85.5 85.599 90.099 0.008 0.311
3.788 33.8 33.835 90.035 0.001 0.383
9.931 98.5 98.988 0.078 0.005 0.355
N 9 19.153 SE n 9 0.135 YI 9 980.330
5 Y1 9 0.998 SE Y Ave 9 0.335 2 err 9 0.977
s 9 0.088 SSE 9 0.089 t(852) 9 3.188

609.6 meter (8000 foot) bubbler tube
81'C (69.6'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
8.809 11.50 11.518 90.018 0.000 0.851
8.508 15.85 15.831 0.018 0.000 0.855
8.809 80.10 80.105 90.005 0.000 0.851
3.105 89.90 89.381 0.018 0.000 0.850
3.907 88.50 88.598 90.098 0.008 0.858
3.717 33.00 33.030 90.030 0.001 0.855
9.035 37.80 37.595 0.859 0.055 0.858
9.357 98.00 98.080 90.080 0.008 0.871
3.883 35.70 35.785 90.085 0.008 0.851
3.580 38.70 38.598 0.058 0.003 0.855
3.358 88.00 87.858 0.038 0.001 0.851
3.111 89.90 89.958 90.058 0.003 0.850
8.785 80.00 18.878 0.081 0.001 0.851
8.518 15.00 15.078 90.078 0.005 0.855
8.188 11.10 11.301 90.801 0.090 0.851
1.783 5.00 9.809 0.185 0.038 0.875
N 9 19.155 SE n 9 0.083 YI 9 918.587
5 Y1 9 0.859 SE Y Ave 9 0.857 2 err 9 0.355
s 9 0.118 SSE 9 0.177 t(852) 9 8.150

88'C (88.9“?)

181

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
1.710 5.00 9.973 0.087 0.001 0.195
8.301 13.30 13.869 0.016 0.000 0.176
8.961 88.50 88.566 90.066 0.009 0.170
3.633 38.00 38.016 90.016 0.000 0.177
9.333 91.90 91.660 0.090 0.008 0.196
n 9 19.063 SE n 9 0.075 YI 9 919.079
5 Y1 9 0.839 SE Y Ave 9 0.169 2 err 9 0.868
s 9 0.099 SSE 9 0.007 t(952) 9 3.168
35°C (SS'F)
CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
8.006 9.00 6.965 0.035 0.001 0.159
8.675 16.90 16.993 90.093 0.008 0.137
3.351 86.00 86.081 90.081 0.000 0.138
9.009 37.30 37.878 0.086 0.001 0.139
9.360 98.60 98.600 0.000 0.000 0.199
n 9 19.166 SE n 9 0.068 YI 9 919.957
5 YI 9 0.818 SE Y Ave 9 0.198 2 err 9 0.808
s 9 0.036 SSE 9 0.009 t(952) 9 3.168

53'C (187.9'F)

CALCULATED RESIDUAL
X Y Y RESIDUAL SOUARED SE Y
8.080 8.50 8.581 0.018 0.000 0.803
8.798 18.85 18.885 90.035 0.001 0.181
3.381 88.10 88.053 0.037 0.001 0.179
9.000 35.80 35.857 90.057 0.003 0.183
9.999 93.80 93.159 0.035 0.001 0.187
N 9 19.805 SE n 9 0.089 YI 9 918.858
5 Y1 9 0.888 SE Y Ave 9 0.188 2 err 9 0.857
s 9 0.050 SSE 9 0.007 t(852) 9 3.188

APPENDIX E: PLOT-IT output for regression lines forced
through the origin.

188

30.5 meter bubbler tube

M E A N A N D S U H S T A 8 L E

 

Mean Sum Sum of Squares 55 Deviations
Y 96.57193 660.0000 39800.000000 1171.93000
X 6.198657 119.7000 1110.9100000 171.199900

 

Cross Product 5998.0000 Cor. Cross Product 370.95730
R E 6 R E S S I O N S T A T I S T I C S

 

Regression Standard Student’s T Confidence Limits
Coefficient Error Ualue Sig Lower Upper
6(0) 5.396766 .90915 13.07 .00 9.965 6.833

 

Model: Y 9 8(0) 9 X REGRESSION LINE FORCED THROUGH ORIGIN

 

Coefficient of: Determination .989 Correlation .969

A N A L Y S I S O F U A R I A N C E

 

 

Source of Degrees of Sum of Mean F
variation Freedom Squares Square Ualue
Regression 1 31798.390000 31768.3600 170.9
Residual 13 8917.6880000 195.970900

Total 19 39800.000000 Sig. of F Ualue: .0000

 

A N A L Y S I S O F R E S I D U A L S

 

Number of positive residuals: 6
Largest positive residual: 85.3957
Number of negative residuals: 6
Largest negative residual: 915.9585
Number of sign runs: 6
Significance of sign runs test: .6987
Average absolute residual: 10.5138
Residual sum of squares: 8917.68
Residual mean square: 165.971
Residual standard deviation: 13.6371
Durbin-Uatson statistic: .397197

Auto-correlation coefficient: .759

157.9 meter bubbler tube

183

 

M E A N A N D S U M S T A B L E
Mean Sum Sum of Squares 55 Deviations
Y 100.6333 1810.000 131050.00000 9091.66900
X 9.591667 108.5000 1006.6300000 133.109800

 

Cross Product 11337.500
R E 6 R E S S I

Cor. Cross Product 1008.0930

O N S T A T I 8 T I C 8

Regression Standard
Coefficient Error Ualue Sig Lower
.57099 19.70

8(0) 11.89098

.00 8.885

Student’s T Confidence Limits

Upper
18.50

 

 

 

 

 

Model: Y 9 6(0) 9 X REBRESSION LINE FORCED THROUGH ORIGIN
Coefficient of: Determination .978 Correlation .966
A N A L Y S I S O F U A R I A N C E

Source of Degrees of Sum of Mean F
Uariation Freedom Squares Square value
Regression 1 187939.10000 187939.100 366.8
Residual 11 3610.6910000 386.868600

Total 18 131050.00000 Sig. of F value: .0000

 

A N A L Y S I 5 O F

R E S I D U A L S

 

Number of positive residuals:
Largest positive residual:

Number of negative residuals:
Largest negative residual:

Number of sign runs:
Significance of sign runs test:

Average absolute residual:
Residual sum of squares:

Residual mean square:
Residual standard deviation:

Durbin-Uatson statistic:
Auto-correlation coefficient:

8
30.0750

9

983.5959

8
.0091

15.3550
3510.88

388.853
18.1180

1.01085
.908

309.6 meter bubbler tube

189

 

M E A N A N D S U M S T A B L E
Mean Sum Sum of Squares 55 Deviations
Y 161.9831 8365.000 999085.00000 13776.9900
X 6.607693 111.9000 1018.5100000

98.3081900

 

Cross Product 81051.000

Cor. Cross Product 693.60790

O N S T A T I S T I C S

 

R E G R E S S I
Regression Standard
Coefficient Error
6(0) 80.79091 .78385

Student’s T Confidence Lim
Ualue Sig Lower Upper
89.75 .00 19.88 88.37

its

 

 

 

 

 

Model: Y 9 6(0) 9 X REGRESSION LINE FORCED THROUGH ORIGIN
Coefficient of: Determination .966 Correlation .993
A N A L Y S I S O F U A R I A N C E

Source of Degrees of Sum of Mean F
variation Freedom Squares Square value
Regression 1 937669.90000 937669.900 686.9
Residual 18 6355.6190000 589.639900

Total 13 999085.00000 Sig. of F Ualue: .0000

 

A N A L Y S I S

O F

R E S I D U A L S

 

Number of positive residuals:
Largest positive residual:

Number of negative residuals:
Largest negative residual:

Number of sign runs:
Significance of sign runs teat:

Average absolute residual:
Residual sum of squares:

Residual mean square:
Residual standard deviation:

Durbin-Uatson statistic:
Auto-correlation coefficient:

8
37.3335

9
937.1188

9
.0785

18.3387
5355.59

588.537
83.0138

1.07333
.388

185

957.8 meter bubbler tube

H E A N A N D S U H S T A 8 L E

Mean Sum Sum of Squares 55 Deviations
Y 386.8193 9595.000 1683985.0000 115860.900
X 9.919867 117.6000 1197.9800000 156.617000

 

Cross Product 98691.500 Cor. Cross Product 3977.6590
R E G R E S S I O N S T A T I S T I C S

 

Regression Standard Student’s T Confidence Limits
Coefficient Error value Sig Lower Upper
6(0) 37.19999 1.6886 88.99 .00 33.69 90.66

 

"0061: Y 9 8(0) 9 X REGRESSION LINE FORCED THROUGH ORIGIN

 

Coefficient of: Determination .976 Correlation .996
A N A L Y S I S O F U A R I A N C E ‘

 

 

Source of Degrees of Sum of Mean F
Uariation Freedom Squares Square value
Regression 1 1599131.0000 1599131.00 589.1
Residual 13 39893.660000 3088.60500

Total 19 1683985.0000 Sig. of F value: .0000

 

A N A L Y S I S O F R E S I D U A L 5

Number of positive residuals: 6
Largest positive residual: 99.8501
Number of negative residuals: 6
Largest negative residual: 971.8999
Number of sign runs: 9
Significance of sign runs test: .0861
Average absolute residual: 97.3671
Residual sum of squares: 39893.6
Residual mean square: 3088.60
Residual standard deviation: 59.9761
Durbin-Uatson statistic: .686666

Auto-correlation coefficient: .585

185

609.6 meter bubbler tube

H E A N A N D S U H S T A 8 L E

Mean Sum Sum of Squares 55 Deviations
Y 537.5633 6951.000 3797003.0000 389053.000
X 7.916667 69.00000 788.90000000 68.7167900

 

Cross Product 58135.500 Cor. Cross Product 9890.5630

R E G R E S S I O N S T A T I 5 T I C S

 

Regression Standard Student’s T Confidence Limits
Coefficient Error Ualue Sig Lower Upper
6(0) 78.18991 8.1919 33.66 .00 67.98 76.69

 

Model: Y 9 8(0) 9 X REGRESSION LINE FORCED THROUGH ORIGIN

Coefficient of: Determination .990 Correlation .995

A N A L Y S I S O F U A R I A N C E

 

 

 

Source of Degrees of Sum of Mean F
Uariation Freedom Squares Square Ualue
Regression 1 3760589.0000 3760589.00 1139.
Residual 11 36979.300000 3315.69500

Total 18 3797003.0000 Sig. of F Ualue: .0000

 

A N A L Y S I S O F R E S I D U A L 5

Number of positive residuals: 6
Largest positive residual: 113.369
Number of negative residuals: 6
Largest negative residual: 975.8391
Number of sign runs: 7
Significance of sign runs test: .6190
Average absolute residual: 95.6156
Residual sum of squares: 36979.0
Residual mean square: 3315.68
Residual standard deviation: 57.5638
Durbin-watson statistic: 8.96690

Auto-correlation coefficient: 9.873

APPENDIX F: PLOT-IT output for Figure 88.

187

Curve fitting for Figure 86

M E A N A N D S U H S T A 8 L E

Mean Sum Sum of Squares 55 Deviations
Y 89.33880 196.6610 7170.0970000 8669.80600

X 1080.000 5100.000 7510000.0000 8308000.00

Cross Product 886931.90 Cor. Cross Product 77337.170

R E G R E S S I O N S T A T I S T I C 5
Regression Standard Student’s T Confidence Limits
Coefficient Error Ualue Sig Lower Upper
6(0) .3081783E901 .388786908 9.36 .00 .8186E901 .3916E901

Model: Y 9 8(0) 9 X REGRESSION LINE FORCED THROUGH ORIGIN

 

Coefficient of: Determination .956 Correlation .976

A N A L Y S I S O F U A R I A N C E

 

Source of Degrees of Sum of Mean F

 

 

Uariation Freedom Squares Square value
Regression 1 6657.8390000 6657.83900 97.67
Residual 9 318.65910000 76.8195300

Total 5 7170.0970000 Sig. of F Ualue: .0007

 

A N A L Y 5 I S O F R E S I D U A L 5

Number of positive residuals: 8
Largest positive residual: 11.6955
Number of negative residuals: 3
Largest negative residual: 99.98683
Number of sign runs: 3
Significance of sign runs test: .5939
Average absolute residual: 7.09650
Residual sum of squares: 318.956
Residual mean square: 76.8196
Residual standard deviation: 9.99390
Durbin-watson statistic: 1.96656

Auto-correlation coefficient: 9.895

188

 

 

M E A N A N D S U M S T A B L E
Mean Sum Sum of Squares 55 Deviations
Y 89.33880 196.6610 7170.0970000 8666.80600
X 1080.000 5100.000 7510000.0000 8309000.00
Cross Product 886931.90 Cor. Cross Product 77337.170
R E G R E S S I O N S T A T I S T I C S

 

Regression Standard Student’s T Confidence Limits
Coefficient Error Ualue Sig Lower Upper
6(0)-9.996878 7.7969 9.63 .56-89.51 19.61
5.30

8(1) .3350831E901 .53889E908 .01 .13385901 .5353E901

 

Model: Y 9 8(0) 9 8(1) 9 X INTERCEPT 9 8(0), SLOPE 9 8(1)

 

 

 

 

Coefficient of: Determination .909 Correlation .951
A N A L Y S I S O F U A R I A N C E

Source of Degrees of Sum of Mean F

variation Freedom Squares Square value

Mean 1 9301.6910000 9301.99100

Regression 1 8591.9390000 8591.93600 86.09

Residual 3 876.76680000 98.8560900

Total 5 7170.0970000 Sig. of F Ualue: .0131

 

O F R E S I D U A L S

A N A L Y S I S

 

Number of positive residuals:
Largest positive residual:

Number of negative residuals:
Largest negative residual:

Number of sign runs:
Significance of sign runs test:

Average absolute residual:
Residual sum of squares:

Residual mean square:
Residual standard deviation:

Durbin-watson statistic:
Auto-correlation coefficient:

8
8.85855

3
98.85518

3
.5939

.5.78159
875.758

88.8553
8.50501

1.58815
9.189

188

 

M E A N A N D S U M S T A B L E
Mean Sum Sum of Squares 55 Deviations
Y 89.33880 196.6610 7170.0970000 8666.80600
X 1080.000 5100.000 7510000.0000 8306000.00

 

Cross Product 886931.90

R E G R E S S I

O N

Cor. Cross Product 77337.170
5 T A T I S T I C S

 

Upper
83.35
.3070E901

Regression Standard Student’s T Confidence Limits
Coefficient Error Ualue Sig Lower
6(0) 7.376336 3.7189 1.99 .1996.599
B(1)-.6719135E908 .66963E-08 9.77 .589.9913E901
6(8) .1917730E909 .90116E905

Model: Y 9 8(0) 9 8(1) 9 X 9 8(8) 9 X 9' 8

9.78 .09 .18155905 .3599E909

 

 

 

Coefficient of: Determination .998

A N A L Y S I S O F U A R I A N C E
Source of Degrees of Sum of Mean F
variation Freedom Squares Square Ualue
Mean 1 9301.9910000 9301.69100
Regression 8 8695.9380000 1988.96600 187.6
Residual 8 88.879190000 11.1370900
Total 5 7170.0970000 Sig. of F Ualue: .0076

 

A N A L Y S I S

O F

R E S I D U A L S

 

Number of positive residuals:
Largest positive residual:

Number of negative residuals:
Largest negative residual:

Number of sign runs:
Significance of sign runs test:

Average absolute residual:

Residual

sum of squares:

Residual mean square:

Residual

standard deviation:

Durbin-watson statistic:
Auto-correlation coefficient:

3
8.98791

8
93.30905

9
.8850

1.89058
88.8787

11.1389
3.33757

8.59910
9.958

130

 

M E A N A N D S U M S T A B L E
Mean Sum Sum of Squares 55 Deviations
Y 89.33880 196.6610 7170.0970000 8969.80600
X 1080.000 5100.000 7510000.0000 8306000.00

 

Cross Product 886931.90
R E G R E S S I

Cor. Cross Product 77337.170

0 N S T A T I S T I C S

 

 

 

 

 

Regression Standard Student's T Confidence Limits

Coefficient Error Ualue Sig Lower Upper
6(0) 3.099960 .73919 9.19 .1596.898 18.99
6(1) .8860799E901 .35187E908 6.99 .10-.8163E901 .6799E-01
6(8)-.1715763E909 .90963E905 99.89 .159.6957E-09 .39866-09
6(3) .1199531E907 .18658E906 9.09 .079.9560E906 .8757E907
Model: Y 9 6(0) 9 6(1) 9 X + 6(8) 9 X 99 8 + 6(3) 9 X 99 3
Coefficient of: Determination 1.000

A N A L Y S I S D F U A R I A N C E

Source of Degrees of Sum of Mean F
variation Freedom Squares Square Ualue
Mean 1 9301.6910000 9301.69100
Regression 3 8667.9990000 955.961800 3693.
Residual 1 .86899130000 .868991300
Total 5 7170.0970000 Sig. of F Ualue: .0188

 

A N A L Y S I S O F

R E S I D U A L S

 

Number of positive residuals:
Largest positive residual:

Number of negative residuals:
Largest negative residual:

Number of sign runs:
Significance of sign runs test:

Average absolute residual:
Residual sum of squares:

Residual mean square:
Residual standard deviation:

Durbin-Uatson statistic:
Auto-correlation coefficient:

3
.595575

8
9.910908

5
.8880

.309138
.519389

.519389
.783885

3.58559
9.837

131

M E A N A N D S U M S T A 8 L E

 

Mean Sum Sum of Squares 55 Deviations
Y .7895607E901 .3697909 .96099670000E-01 .199608700E901

X 1080.000 5100.000 7510000.0000 8308000.00

Cross Product 179.37790 Cor. Cross Product-198.70960
R E G R E S S I O N S T A T I S T I C S

 

Regression Standard Student’s T Confidence Limits
Coefficient Error Ualue Sig Lower Upper
6(0) .1561890 .87117E-01 5.63 .01 .7168E901 .8999

8(1)-.8398588E909 .88185E909 93.77 .039.1538E9039.1308E909

Model: Y 9 A / (8 + X) WHERE A 9 1/8(1) AND 8 9 8(0)/8(1)

Coefficient of: Determination .686 Correlation 9.909

A N A L Y S I S O F U A R I A N C E

 

 

Source of Degrees of Sum of Mean F
variation Freedom Squares Square value
Mean 1 .86619900000E901 .866199000E901
Regression 1 .16090910000E901 .160909100E-0119.89
Residual 3 .339996800006908 .118995900E908

Total 5 .96099670000E901 Sig. of F value: .0386

 

A N A L Y 8 I S O F R E 8 I D U A L S

 

Number of positive residuals: 8
Largest positive residual: .371769E901
Number of negative residuals: 3
Largest negative residual: 9.879159E901
Number of sign runs: 3
Significance of sign runs test: .5939
Average absolute residual: .8396336901
Residual sum of squares: .3369666908
Residual mean square: .118995E908
Residual standard deviation: .336199E901
Durbin-Uatson statistic: 1.59670

Auto-correlation coefficient: 9.885

138

M E A N A N D S U M S T A B L E
Mean Sum Sum of Squares 55 Deviations
Y .7895607E901 .3697909 .96099670000E-01 .1999087006901
X .86333336-08 .1916667E901 .10569990000E903 .655555600E909

 

Cross Product .81809030E908Cor. Cross Product .10666300E908
R E G R E S S I O N S T A T I S T I C 9

Regression Standard Student’s T Confidence Limits
Coefficient Error Ualue Sig Lower Upper

6(0) .8599990E901 .18536E901 8.07 .139.1391E901 .65666901
6(1) 16.57677 8.7865 6.06 .01 7.908 85.86

 

Model: Y 9 A 9 X / (8 9 X) A 9 1/8(0) AND 8 9 8(1)/8(0)

 

Coefficient of: Determination .985 Correlation .968

A N A L Y S I S O F U A R I A N C E

 

 

 

Source of Degrees of Sum of Mean F
Uariation Freedom Squares Square Ualue
Mean 1 .86619900000E901 .866199000E901
Regression 1 .16016310000E901 .160193100E90136.97
Residual 3 .19619690000E908 .997381500E903

Total 5 .960996700006901 Sig. of F Uelue: .0069

 

A N A L Y S I S O F R E S I D U A L S

 

Number of positive residuals: 8
Largest positive residual: .896176E901
Number of negative residuals: 3
Largest negative residual: 9.809109E901
Number of sign runs: 3
Significance of sign runs test: .5939
Average absolute residual: .191907E901
Residual sum of squares: .1961968908
Residual mean square: .967319E903
Residual standard deviation: .880753E901
Durbin-Uatson statistic: 1.96919

Auto-correlation coefficient: .187

133

M E A N A N D 5 U M S

T A 8 L E

Mean Sum Sum of Squares 55 Deviations
-Y 35.67596 179.3779 7090.9970000 605.836300
X 1080.000 5100.000 0000 8306000.00

7510000.

 

Cross Product 166889.00

Cor. Cross Product 5868.9990

R E G R E S S I O N 5 T A T I S T I C S

 

Regression Standard

Coefficient Error Ualue
6(0) 33.59955 11.399 8.96

8(1) .88803875908 .885588908 .85

Student’s T Confidence Limits

Sig Lower Upper
.0698.558 69.65
.68-.8716E901 .3179E901

 

Model: Y 9 X / (A + (8 9 X))

Coefficient of:

UHERE A 9 8(0) AND 8 9 8(1)

Determination .080 Correlation .191

A N A L Y S I S O F U A R I A N C E

 

 

 

Source of Degrees of Sum of Mean F
variation Freedom Squares Square Ualue
Mean 1 6935.8510000 6935.85100

Regression 1 18.001390000 18.0013900 .6069E901
Residual 3 593.83500000 197.795000

Total 5 7090.9970000 Sig. of F Ualue: .6813

A N A L Y S I 5 O F R E

S I D U A L S

 

Number of positive residuals: 3
Largest positive residual: 18.8679
Number of negative residuals: 8
Largest negative residual: 915.0685
Number of sign runs: 3
Significance of sign runs test: .5939
Average absolute residual: 10.1960
Residual sum of squares: 593.835
Residual mean square: 197.795
Residual standard deviation: 19.0688
Durbin-Uatson statistic: 1.50609

Auto-correlation coefficient: 9.160

139

 

M E A N A N D S U M S T A B L E
Mean Sum Sum of Squares 55 Deviations
Y 1.305005 6.585087 9.8997330000 .773536700
X 1080.000 5100.000 7510000.0000 8306000.00

 

 

 

 

 

 

 

 

 

Cross Product 7967.8750 Cor. Cross Product 1331.7960
R E G R E S S I O N S T A T I S T I C 5
Regression Standard Student’s T Confidence Limits
Coefficient Error Uelue Sig Lower Upper
6(0) .7169515 .33868E901 81.59 .00 .6106 .6883
6(1) .5770136E903 .87190E909 81.86 .00 .9906E903 .6639E903
Model: Y 9 A 9 B 99 X WHERE A 9 10996(0) AND B 9 1099B(1)
Coefficient of: Determination .993 Correlation .597
A N A L Y S I S O F U A R I A N C E
Source of Degrees of Sum of Mean F
Uariation Freedom Squares Square Ualue
Mean 1 6.5151960000 6.51519600
Regression 1 .76993650000 .766936500 958.0
Residual 3 .51001690000E908 .170005500E908
Total 5 9.8667330000 Sig. of F Ualue: .0008
A N A L Y S I 5 O F R E S I D U A L 5
Number of positive residuals: 8
Largest positive residual: .956966E901
Number of negative residuals: 3
Largest negative residual: 9.9569038901
Number of sign runs: 3
Significance of sign runs test: .5939
Average absolute residual: .8610868901
Residual sum of squares: .509993E908
Residual mean square: .169996E908
Residual standard deviation: .918306E901
Durbin-Uatson statistic: 8.00005

Auto-correlation coefficient: 9.365

135

 

 

M E A N A N D S U M S T A B L E
Mean Sum Sum of Squares 55 Deviations
Y 1.305005 6.585087 9.8667330000 .773536700
X 8.635816 19.17609 91.866790000 1.07697700
Cross Product 19.366890 Cor. Cross Product .66691970

R E G R E S S I O N

S T A T I S T I C S

 

Student’s T Confidence Limits

 

 

 

 

 

Regression Standard

Coefficient Error Ualue Sig Lower Upper
6(0)-.9769580 .99189 98.81 .1198.361 .9879
6(1) .6096613 .15360 5.89 .01 .3160 1.899
Model: Y 9 A 9 X 99 B UHERE A 9 1099B(0) AND B 9 6(1)
Coefficient of: Determination .908 Correlation .999

A N A L Y 5 I S O F U A R I A N C E

Source of Degrees of Sum of Mean F
Uariation Freedom Squares Square Ualue
Mean 1 9.5151960000 6.51519600
Regression 1 .69739370000 .697393700 87.96
Residual 3 .76198990000E901 .853976600E901
Total 5 9.8967330000 Sig. of F Ualue: .0135

 

A N A L Y S I S O F

R E S I D U A L 5

 

Number of positive residuals:
Largest positive residual:

Number of negative residuals:
Largest negative residual:

Number of sign runs:
Significance of sign runs test:

Average absolute residual:
Residual sum of squares:

Residual mean square:
Residual standard deviation:

Durbin-Uatson statistic:
Auto-correlation coefficient:

8
.178187

3
9.199590

3
.5939

.108978
.751889E901

.8538888901
.158370

1.38587
9.087

APPENDIX 6: Bibliography

135

Allman, 0.0., R.E. Williams, and 6.R. Stephenson. 1969.
Design and operation of an inexpensive sensitive
piezometer with short lag time. Groundwater 9 Drinking
7(6).

“Barron, 8.6. 1960. New instruments of the Surface water
Branch, U.S.G.S. A description of the bubbler gage.
Western Snow Conference Proceedings 86: 38936.

Bethea, R.M., 6.5. Duran, T.L. Boullion. 1965. Statistical
methods for engineers and scientists. Marcel Dekker,
Inc. New York. 8nd edition. p. 301916.

'Bevier, 6.R., N.R. Fausey. 1979. Strain Gage Pressure
Transducers for Continuous water Table Measurements.
ASAE Paper Number 7998076.

Boon, J.D. and U. Harrison. 1971. Instrumentation for
measurement of water-table fluctuations. In:
Investigation of the water table in a tidal beach.
Uirginia Institute of Marine Science Special Scientific
Report No. 60: 1919.

Carter, C.E., F.T. Uratten, U. McDaniel, B. Halverson.
1979. Hydraulic Conductivity Measured Electronically
in an Auger Hole. Transactions of ASAE 87(5):
1900-1909.

Curtis, N.R. 1960. An automatic trigger device for use on
F091 water level recorders. Journal of Forestry 59:
9199681. October.

Doebelin, E.O. 1975. Measurement systems: application and
design. McGraw-Hill. New York. Chapter 3.

.Durham, H.J. and R. Kohlmeier. 1973. Digital recording of
water levels with the aid of acoustics and its
application to hydrological pumping tests.
International Association of Hydrological Sciences
publication 99, Uol. 1: 11930.

Ferguson, G.E. 1998. Gage to measure crest stages of
streams. Civil Engineering 18: 5709571.

'Gerrish, J. 1666. Personal communication.

.Goebel, K.M., G.E. Merva. 1995. Bubbler system for
watertable monitoring. ASAE paper number 6598563.

137

Hoff, E.J. 1916. Sensitive water level recorder.
Engineering News 76:979-979.

Holbo, H.R., R.D. Harr and J.D. Hyde. 1975. A
multiple-well water level measuring and recording
system. Journal of Hydrology 87:199-806.

Inouye, G.T., H. Bernstein, and R.A. Gael. 1970.
Electromagnetic depth sounder. I.E.E.E. Transactions
Uolume GE6(9): 336-393.

Lissey, A. 1967. The use of reducers to increase the
sensitivity of piezometers. Journal of Hydrology 5:

Lovell, A.D., J.U. Ellis, R.R. Bruce and A.U. Thomas. 1976.
Remote sensing of water levels in small diameter wells.
Agricultural Engineering 59(10):99-95.

MacUicar, T.K., M.F. Walter. 1969. An electronic
transducer for continuous water level monitoring.
Transactions of the ASAE 87(1):105-109.

'MacUicar, T.R. 1979. A solid state transducer for
recording piezometer systems. M.S. Thesis, Cornell
University, Ithaca, NY.

'Merva, G.E., N.R. Fausey. 1969. Finite element analysis
of water table observation well behavior. ASAE paper
number 99-8061.

Reeve, R.C. 1965. Hydraulic Head. In: Methods of soil
analysis. C.A. BlackCEd), American Society of Agronomy.
Madison, 01, Mono. No. 9, pp. 160-196.

Reinhart, X.G., R.S. Pierce. 1969. Stream-gaging stations
for research on small watersheds. Forest Service, 0.5.
Department of Agriculture. Handbook Number 866: 89-33.
May.

Russel, M.B. 1995. A probe for establishing the position
of the water surface in standpipes. Journal of American
Society of Agronomy 37: 900.

Talman, A.J. 1963. A Device for Recording Fluctuating
Water Levels. Journal of Agricultural Engineering
Research 86:873-877.

Tromble, J.M., C.G. Enfield. 1971. Adapting Analog Water
Stage Recorders to Digital Data Acquisition Systems.
Agricultural Engineering 58(8):90-61. February.

138

US Bureau of Reclamation 0ater Measurement Manual, 8nd

edition. 1979. Department of the Interior. Chapter
UI: 137-155.

.Uan Beers, 0.J.F. 1956. The auger hole method. Bulletin
1. International Institute for Reclamation and
Improvement. 0ageningen, The Netherlands.

Uan der 0eerd, B. 1977. A registration unit for drain
outflow, groundwater depth, and precipitation. Journal
of Hydrology 39: 363-369.

Uan Everdingen, R.O. 1966. Use of pressure transducers for
the determination of piezometric pressures in confined
aquifers under the South Saskatchewan Reservoir,
Canada. Journal of Hydrology 9: 70-79.

Uest, 0.0. J.D.F. Black. 1970. Determination of a water
table in a soil profile using a platinum oxygen
cathode. Soil Science. 110(8): 119-183.

011m, H.G., M.H. Collet. 1991. A portable electric
water-depth gage. Civil Engineering 11: 305.

' unrefereed papers or personal communication.

APPENDIX H: Index of authors.

138

60500:.

Allman, 0.0., R.E. Uilliams, and 6.R. Stephenson
Barron, E.G.

Bevier, 6.R., N.R. Fausey.

Boon, J.D. and 0. Harrison.

Carter, C.E., F.T. 0ratten, U. McDaniel, B. Halverson
Curtis, 0.R.

Doebelin, E.O.

Durham, H.J. and R. Kohlmeier

Ferguson, G.E.

Gerrish, J.

Hoff, E.J.

Holbo, H.R., R.D. Harr and J.D. Hyde

Inouye, G.T., H. Bernstein, and R.A. Gaal
Lissey, A.

Lovell, A.D., J.0. Ellis, R.R. Bruce and A.0. Thomas
MacUicar, T.K., M.F. 0alter

MacUicar, T.R.

Merva. G.E., N.R. Fausey

Reeve, R.C.

Reinhart, K.G., R.S. Pierce

Russel, M.B.

Talman, A.J.

Tromble, J.M., C.G. Enfield

19
17
15
13
15
18
79
15
.10
73
18
15,15

19
15

80,98
5

17

7

13

13

US Bureau of Reclamation 0ater Measurement Manual 5,10,17

Uan Beers, 0.J.F.

190

Uan der 0eerd, B.
Uan Everdingen, R.D.
0est, 0.0. J.D.F. Black

011m, H.G., M.H. Collet

13

15

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