Calibration
and use of
a dual-energy gamma system,
pressure transducers,
and thermocouples
to determine
volumetric water content,
dry bulk density,
soil water pressure head,
and temperature
in soil columns
A gronomy and Soils Departmental Series No. 101
Alabama Agricultural Experiment Station
Auburn University Auburn University, Alabama
Gale A. Buchanan, Director September 1985

Calibration and Use of a Dual-energy 
Gamma System,
Pressure Transducers, and 
Thermocouples to Determine
Volumetric Water Content, 
Dry Bulk Density, Soil
Water Pressure Head, and Temperature 
in Soil Columns
J.W. Hopmans and J.H. Dane
Graduate Assistant and 
Associate Professor
of Agronomy and Soils
TABLE OF CONTENTS
Page
SUMMARY .. 4
INTRODUCT ION ........................................... 5
THEORY GAMMA MEASUREMENTS .......... ..................... 5
INSTRUMENTATION i0......................10
1. Gamma-unit .....................................10
2. Pressure transducers ........................... 13
3. Thermocouples .............. 13
CALIBRATION ............................ 17
1. Gamma-system ............. ............ 17
2. Pressure transducers ........................... 26
3. Thermocouples ................................... 27
DATA ACQUISITION ........................................ 37
MEASUREMENT ERRORS ................. ..................... 39
LITERATURE CITED ............ ................. 44
Appendix A ....................................... 45
SAS-program to Determine Regression Coefficients
of Polynomial
Appendix B .............................................. 46
SAS-program to Plot Count Intensity Ratio versus
Resolving Time for 3 Absorber Thicknesses
Appendix C .................................. 48
FORTRAN-program to Determine Calibration Constants
Appendix D .............................................. 53
BASIC-program for Simultaneous Gamma, Pressure,
and Temperature Determinations
Appendix E .............................................. 59
Additional BASIC-programs
Information contained herein is available to all regardless
of race, color, sex, or national origin.
LIST OF FIGURES AND TABLES
Page
Figure 1. Schematic presentation 
of photomultiplier ..... 15
Figure 2. Function diagram 
for electronics of gamma-system 
16
Figure 3. Energy spectrum 
of Cs-137 
28
Figure 4. Energy spectrum 
of Am-241 ..................... 
29
Figure 5. Cs-intensity 
in the low-energy band plotted
against observed Cs-intensity 
in the high energy
range ......................................... 
30
Figure 6. Plot of adjusted 
Cs-count intensity ratios
versus resolving time (T) for 
3 different
absorber thicknesses .......................... 
31
Figure 7. Plot of adjusted 
Am-count intensity ratios
versus resolving time (T) for 
3 different
absorber thicknesses .......................... 
32
Figure 8. Dry bulk densities 
at 38 points along container
computed from Am and Cs radiation 
intensities . 33
Figure 9. Example of calibration 
curve of pressure
transducer (Type: Bell & Howell) 
............... 34
Figure 10. Relation between 
temperature (F) and output
(mVolt) of copper-constantan thermocouples 
..... 35
Figure 11. Standard deviation 
in e and p for
counting times of 60 and 300 s ................. 
42
Table 1. Partial listing of 
calibration constants(U) for
both the Cs(c) and Am(a) and 
for both water(w)
and soil solids(s) in the container 
........... 36
Table 2. Standard counts of 
Am and Cs as a function of
time ............................................
43
SUMMARY
Bulk density and volumetric water content of a 
porous
medium can be determined by concurrent measurement of count
intensities at two gamma energy levels. 
In utilizing a
dual-energy gamma system it is necessary to know the 
mass
attenuation coefficients of water and the specific 
soil
used. A new technique is presented that allows determination
of the calibration constants (product of pathlength 
and mass
attenuation coefficient), without having to know 
the exact
bulk density at each measurement point. The operation 
of
the gamma system is outlined. A description of the 
operation
and calibration technique of pressure transducers 
and ther-
mocouples is added so that in addition to measurements 
of
bulk density and volumetric water content, soil water 
pres-
sure head and temperature can also be determined.
5
INTRODUCTION
The use of pressure transducers and copper-constantan
thermocouples, together with the dual-energy gamma system,
allows the simultaneous measurement of volumetric water con-
tent, dry bulk density, soil water pressure head, and 
temp-
erature. Bulk density and volumetric water content 
of a
porous medium can be determined by concurrent measurement 
of
count intensities at two gamma energy levels. Gamma sources
that are often used for this purpose are Am-241 (60 keV-
peak) and Cs-137 (662 keV-peak). In utilizing a dual-energy
gamma system it is necessary to know the resolving time as
well as the mass attenuation coefficients for water and soil
at the two gamma energy levels. Because compton scattering
caused by the high energy Cs radiation is detected in the
Am-band, Am-count rates need to be corrected for this so-
called low-energy Cs.
THEORY OF GAMMA MEASUREMENTS
Gamma radiation travels, like all electro magnetic
radiation, with the speed of light. Its energy is contained
in photons which have zero "rest" mass. The attenuation of
gamma radiation in matter is affected by both the chemical
composition and concentration of matter, and varies with 
the
radiation energy level. For a dry soil with unchanging
chemical composition, the dry bulk density can be deter-
mined, provided the mass attenuation coefficient of the 
soil
6
is known for the gamma energy level used. Water content 
can
be determined, if the bulk density remains constant and the
mass attenuation coefficient of water is known. If the
ratio of attenuation coefficients of soil and water differs
appreciably at two different gamma energies, then both bulk
density and water content can be determined from concurrent
measurements at these two different gamma energies, 
provided
the chemical composition of the attenuating medium remains
constant.
Gamma sources that are generally used for this purpose
are Americium-241 (Am energy peak at 0.060 MeV) and Cesi-
um-137 (Cs energy peak at 0.66 MeV). Both gamma energy lev-
els are such that attenuation will mainly occur through
Compton scattering and photoelectric absorption. The Compton
effect involves a collision between a photon and an electron
in which part of the energy of the photon is imparted to the
electron. The photon emerges from the collision in a new
direction with reduced energy. The photoelectric effect
occurs principally at low photon energies. Through the ine-
lastic collision of a photon with an electron, all the pho-
ton's energy is carried over to the electron, thereby eject-
ingth electronq fro -w -%m its-rbit.%
7
attenuation coefficient 
p (cm
2 
g-1) of the absorber:
dI = -PabPIdX . [1]
Integration of this equation 
between I, the intensity of 
the
Io
emergent beam, and I
o
, the intensity of the incident 
beam,
and between X=O and X, the thickness 
of the absorber, yields
In(I/Io) = -PabPX . [2]
Expanding the term on the right 
to include a combination 
of
absorbers, e.g., soil(s), water(w), 
air(a), and column
walls(c) yields
I'
ln(I/Io)=-xwPwPw -xsPsPs-XaPaPa
-xcPcPc 
, 
[3]
where x denotes path length through 
each individual absor-
ber, and p
5 
is the particle density of the soil's solid
phase. Rearranging Eq. [3] 
while omitting the contribution
of air (PaPa is small relative 
to other components) and
assuming pw=
1
, yields
8
I,
I=Ioexp{X(-O8w-pps) 
- xcPcpc) , [4]
where p is the dry bulk density of the soil, and X is the
soil thickness perpendicular to the gamma-beam. Including
If
the contribution of the wall into I
o
, results in:
I = Ioexp{-X(Op
w 
+ Pps)} , [5]
if
where Io = Ioexp(-xcpcc)
If both e and p are unknown, the use of Eq. [5]
requires two radioactive sources, each with a different
energy level and each with different mass attenuation coef-
ficients. Writing Eq. [5] for two radio-active sources
allows e and p to be calculated from
0={Usaln(Ioc/Ic) - Uscln(Ioa/Ia)}/k 
[6]
p=(Uwcln(Ioa/Ia) - Uwaln(oc/Ic)}/k , [7]
where U = IX, k = UsaUwc - UscUwa, and the subscripts a and
c refer to gamma energies of Americium-241 and Cesium-137,
respectively.
9
One of the most efficient 
counters for y photons
(detector) is a thallium activated 
sodium iodide crystal in
which the absorption of a 
y-photon gives rise to a light
pulse which is detected by 
a sensitive photomultiplier. The
resultant electrical pulse 
is amplified and counted 
by a
scaler. The intensity of the 
light pulse is a function 
of
the y-photon energy. The detector 
will count photons with a
spectrum of energies, however, 
by means of electronic selec-
tion (pulse height analyzer) it 
is possible to identify and
measure only those y-photons 
that remained unchanged in
energy. The ratio of the incident 
to emergent y-intensity
is a measure of the attenuation.
For good resolution, it 
is further necessary to
restrict measurements 
to the energy of the highest 
energy
peak of the y-source.
10
INSTRUMENTATION
1. Gamma-unit
Gamma-ray photons are emitted by a 200 mCi Am-241 and a
200 mCi Cs-137 radio-isotope ( 1 Curie is defined as that
quantity of any radioactive nuclide in which the number of
disintegrating atoms per second is 3.7*1010). The two
source capsules are mounted coaxilly with the Cs-source in
the center of a 0.17-m-long and 0.14-m-diameter lead shield.
The Am-source is contained in a brass holder, 10 mm thick,
and 40 mm in diameter, and is placed at the front end of the
lead shield. This arrangement minimizes the absorption of
the low- energy gamma rays from Am-241 prior to their reach-
ing of the soil sample.
Another cylindrical shield (1=0.11 m and d=0.14 m)
encloses the scintillation crystal with photomultiplier tube
(detector). The principle of operation of a scintillation
detector is the production of a small flash of visible light
(a scintillation) when radiation interacts with certain
substances called fluors. For y-radiation detection, the
fluor consists of a thallium activated sodium iodide crys-
tal. The photocell to detect the small scintillations is
called a photomultiplier, figure 1. In this photomultiplier,
electrons dislodged from a cathode by a photon of light are
11
increased in number by as much as 1 million times by a
system of electrodes (dynodes) within the multiplier tube. A
high voltage supply is necessary for the operation of the
photomultiplier. The voltage supply must be very stable, as
amplification is dependent on the high voltage. An increase
in voltage causes smaller pulses from less energetic gamma
rays to be detected and accounted for, while higher pulses
may be discriminated.
Collimation is provided by 6-mm cylindrical holes in
both lead shields and the brass holder. Two mounting plat-
forms, which support the detector and source-holders, can be
moved both horizontally and vertically by stepping motors,
thereby positioning the dual-energy gamma-ray beam at any
position of interest with a precision of ca 0.1 mm.
A block diagram showing the components of the gamma
system is presented in figure 2. Pulses emitted by the pho-
tomultiplier of the detector (4S4) are first amplified by a
preamplifier (NB-28) and an amplifier (NA-17), and then lin-
early transmitted through an automatic gain control unit
(NA-22) to a single channel pulse height analyzer (NC-22).
The preamplifier is located as close to the photomultiplier
as possible. The NA-22, which contains a built-in single
channel pulse height analyzer, permits stabilization of the
gain. Both the NA-22 and NC-22 are used in their differen-
tial mode and are connected to a scaler (NS-30) to determine
the Cs- and Am count, respectively. The pulse height ana-
12
lyzer discriminates pulses according to their amplitude or
voltage. Since pulse height is proportional to the incident
radiation energy, the pulse height analyzer is analyzing the
radiation energy. The base line setting E of the analyzer
establishes the lower discrimination level. Pulses with an
amplitude less than E do not appear at the analyzer output.
The window AE establishes the range of pulse amplitudes
greater than E which will be passed by the analyzer and will
appear at the analyzer output. Pulses with an amplitude
greater than E + AE are also rejected. Thus, of all pulses
appearing at the analyzer input, only those with an ampli-
tude between E and E +AE are transmitted to the scaler or
ratemeter.
A timer (NT-29) is used to determine the counts over
preset time intervals, while a linear ratemeter(NR-30) is
connected to either the NA-22 or NC-22, mainly for approxi-
mate peak determinations. Both scalers are connected to a
data transmitter (NE-30), which in turn is connected to a
desk top computer (HP-9845T) through a RS232C-HPIB transla-
ter (Aston Model 807). This arrangement allows for complete
automation of resetting the scalers and the timer, starting
the count readings and storage of data on magnetic tape.
Simultaneous movement of the sources and detector car-
rying platforms also occurs under computer control. The GPIB
actuator (Aston Model 800) allows for selection of either
one of the stepping motor control units (Superior Electric,
13
Model SPl55A), the number 
of steps or half steps to be
taken, and the direction 
of movement.
2. Pressure transducers
Two different types of pressure 
transducers are avail-
able to measure water or air 
pressure. The Statham (Model
PMl31TC+15-350) transducers 
allow only gauge pressures 
to be
measured, while the Validyne (Model 
DP-15) and Bell & Howell
(Model 4-351-0051) transducers 
can also be used to measure
pressure differentials. Transducer 
excitation and amplifica-
tion of the transducer output 
signal are provided by a 
set
of strain gauge conditionars 
(Vishay 2100) for the Statham
and Bell & Howell models and a set of 
carrier demodulators
(Validyne model CD-18) for 
the Validyne pressure transduc-
ers. The analog signals 
are digitized by an analog 
to digi-
tal converter (Aston Model 
805).
3. Thermocouples
Temperatures can be measured 
by 15 copper-constantan
thermocouples. An HP3497A - acquisition system with built-
in Option 020 allows temperatures 
to be measured at 20 chan-
nels. The Option 020 is provided 
with hardware compensation
since the voltage measured by the 
3497A without this compen-
sation technique is different than 
the actual thermocouple
14
voltage due to junction voltages. The voltage output is
therefore the true thermocouple voltage and can be used
directly with a standard table to determine equivalent temp-
erature.
15
- Light-tight Window
FIG. 1. Schematic presentation of 
photomultiplier.
El)
0
El)
--)
0
44)
E
rH$
C:
0
u
N
*'4
0
C
O
*H
17
CALIBRATION
i. Gamma-system
The first step in the calibration of the gamma unit
consists of determining the energy spectrum of both sources
so that the output signals from the detector can 
be discrim-
inated. This energy spectrum is determined by using a
lucite absorber as the attenuating medium. The base line
setting of the pulse height analyzer is indicated in volts.
For a given high voltage and amplifier gain adjustment, 
the
base line voltage is proportional to the energy of the 
inci-
dent radiation. It is hereby convenient to adjust the ampli-
fier gain or the high voltage so that the base line reading
and the energy (MeV) are related by a multiple of 10. The
base line calibration is carried out by connecting the NA-22
to the ratemeter (NR-30), and setting the energy level 
of
the NA-22 on 6.6, which is approximately 10 times the 
maxi-
mum energy level of the Cs in MeV. The high voltage supply
(NV-25A) and/or gain is increased until a maximum count
intensity is observed in the window of the ratemeter. The
resulting high voltage should not be disturbed, as a chang-
ing voltage will alter base line settings and energy levels.
The energy spectrum of the Cs-137 can now be determined. The
18
NA-22 is connected to a scaler 
(NS-30) and E and AE are set
to 4.6 and 0.2, respectively, while 
the toggle switch of the
NA-22 is set in the disabled mode. 
Consecutive 1-minute
counts are obtained after increasing 
the E-setting by 0.1.
An example of the Cs-energy spectrum 
is shown in figure 3.
From this spectrum the correct window 
setting can be deter-
mined (E=5.5 and AE=2.1). The 
same procedure is repeated to
determine the energy spectrum 
and window setting of the 
Am
(NC-22). The toggle switch of 
the NA-22 is now set to
track, to stabilize the gain by preventing 
a shift of the
Cs-window in either direction. 
Figure 4 shows the Am-spec-
trum with E=0.35 and AE=0.50. 
The small peak in the begin-
ning of the spectrum does not 
originate from the Am and
should not be included in the window 
setting. None of the
settings should be changed during 
subsequent measurements.
The second step in the calibration 
procedure involves a
correction of the Am count-intensity. 
Compton scattering of
the high energy Cs-source causes 
low energy photons to be
detected in the Am-spectrum. It 
is believed that the amount
of this type of scattering is independent 
of the sample
material. To determine the amount 
of low energy Cs, a brass
plate thick enough to block all Am radiation is placed
between the sources and detector. 
Changes in amount of back
and side scatter may occur 
for different sources-absorber-
detector geometries. Subsequent 
calibration measurements are
therefore preferably carried 
out for the same geometry as
19
used later in the actual experiment. Count rates in the 
low
energy window (Cslow) are plotted against those of the high
energy window (Cs) for an increasing number of optical 
glass
plates serving as absorber, figure 5. After fitting the data
points by a third degree polynomial, subsequent corrected
count rates in the Am window are obtained by subtracting the
low-energy Cs from the observed Am count rate. A SAS-pro-
gram that calculates the regression coefficients for this
polynomial is provided in Appendix A. The referred analysis
yielded the following relationship (all count intenstities
are in counts per second):
Cslow=-9.1607751+0.2582747Cs-2.315935*10-5Cs
2
+ 5.5831407*10-
9
Cs
3 
. [8]
After accounting for the Cs-interference in the Am-win-
dow, it is further necessary to apply resolving time correc-
tion to the count intensities of both sources (third step).
Resolving time of a gamma-ray counting system is the minimum
time that can separate two consecutive recorded gamma-ray
photons. A photon that arrives at the scintillation crystal
before the minimum time has elapsed will not be recorded. 
An
observed count rate can be corrected for resolving time 
(T)
with the equation
20
I = R/(l-TR) , [9]
where
I: true count intensity, cps,
R: observed count intensity, cps,
T: resolving time, s count
-
1
.
This correction, but not T, varies 
with the count rate (the
difference between I and R increases with 
increasing count
rate).
Fritton (1) was able to determine 
T by minimizing the
sum of squares of the differences 
between measured data
points, corrected for given T-values, 
and the linear rela-
tionship fitted through these points. 
Different count inten-
sities were obtained by changing the 
absorber thickness.
Since this method appeared to be unsuccessful 
in our situ-
ation, we instead used a variation 
of the method described
by Stroosnijder and de Swart (4). 
Stroosnijder and de Swart
determined the T-value from count 
rates obtained with (R)
and without an absorber (Ro) for 
3 different distances
between source and detector. Adjusting 
the obtained count
rates for assumed T-values and plotting (R/Ro)-adjusted ver-
sus T for each source-detector distance resulted 
in 3 lines
intersecting at one point. The T-value corresponding 
to
this joint point was assumed to be the correct 
value.
21
Instead of changing the distance between sources and
detector, we placed additional absorbers (glass plates for
Am and brass plates for Cs) between sources and detector.
With this method, a resolving time of 2.5 ps was found for
both the Cs and Am count intensity. A SAS-program that
plots the various adjusted count intensity ratios versus
resolving time, figures 6 and 7, is presented in Appendix B.
The fourth and last step in the calibration procedure
involves the determination of the mass attenuation coeffi-
cients of water and soil for both gamma energies. Provided
one knows the exact chemical composition, these coefficients
could be calculated from the theoretical mass attenuation
coefficients of the individual elements at the specified
energy levels. However, experience has shown that better
results will be obtained if the attenuation coefficients are
experimentally determined. All measurements in this step of
the calibration must again be carried out for the same
sources-medium-detector geometry.
Designating I as the radiation intensity (the number of
counts per second detected by the detector) upon passing
through a soil with dry bulk density p (g cm
-3
) and volumet-
ric water content 0, the basic attenuation equation (Beer's
law) is written as
I = Ioexp(-pspX - wPwoX)
[10]
22
where I
o 
is the count intensity (counts per second,cps) 
with
only the empty container in the beam, X is 
the thickness
(cm) of the soil in the direction of the 
beam, Pw is the
density of water (g cm-3), and ps and pw are the 
mass atten-
uatio coefficients (cm
2 
g-
1
) of the soil and water, Writ-
ing Eq. [10] with subscripts a and 
c for the Am and Cs
yields
I
a 
= Ioaexp(-PsaPx - PwaPw6X) 
[11]
I
c
= Iocexp(-1scpx - pwcPweX) 
, [12]
where Ic and Ioc are corrected for resolving time, and I
a
and Ioa are corrected for both low energy 
Cs and resolving
time.
Measurement errors for the attenuation coefficients 
and
soil thickness are reduced by combining the 
two into one
variable, giving U
s 
=psx (cm
3 
g-
1
) and Uw = pwPwx (dimen-
sionless). Equations [11] and [12] can then 
be written as
Ia = Ioaexp(-Usap 
- Uwae) , 
[13]
i
c
Iocexp(-Usc
p
- UwcO) , [14]
or, in general, for location i along the soil 
column as
23
[n(Ioa/Ia)] = UaP + Uwa , [15]
[ln(Ioc/Ic)] = U~cP + U~c
i  
, [16]
where the various U-terms are defined as calibration con-
stants, and i=1,...,M (M is total number of locations).
For both the empty container and the container filled
with de-ionized water, 5-minute counts were obtained at 38
points with the centers spaced 5 mm apart in the vertical
direction. Each scanning cycle was replicated 20 times and
the average count intensity for each point i (i= 1,...,M =
38) was calculated. For the water filled container Eq. [15]
and [16] can be written as
[ln(Ioa/Ia) = U 
, [17]
Uwa 
[ln(Ioc/Ic)]w = Uwc , [18]
which allows the calibration constants Uwa and Uwc 
(i
1,...,M) to be calculated.
The container was subsequently filled with oven-dry
soil (Norfolk sandy loam), and again 20 5-minute counts were
obtained and averaged for each point.
For e = 0, the attenuation equation for Am reduces to
[in(Ioa/Ia)] 
= U ap
[19]
24
The calibration constants U~a (i=l,...,M) can only be
directly calculated from Eq. [19] if the density at each
measurement point is known. As this is not the case, a
method was developed to reduce the number of unknown vari-
ables in Eq. [19].
If measurements are always carried out at the same
locations, it seems reasonable to assume that relative
changes in calibration constants with position will be simi-
lar for soil and water. Therefore,
U1a sUa 1 iii, ,[20]
U = Uwa/ Uwa = a , =
Since a
i 
can be calculated from measurements through the
water filled container (Eq. [17]), the number of unknowns is
reduced to M+l, while having M equations of the type
[ln(Ioa/Ia)] = Usa pi / a
1  
, [21]
or
pi - ai[ln(Ioa/Ia) / Ula
, i=l,...,M . [22]
25
An additional equation can 
be obtained by assuming that 
the
bulk density values at the M measurement 
points represent
the average bulk density of the 
medium in the container,
i.e.
M
(l/M) p
1 
= , [23]
i=1
where p is the average dry bulk 
density of the medium, cal-
culated from the dry mass of soil 
and the volume of the con-
tainer. Eq. [22] and [23] represent 
(M+1) equations and
(M+1) unknowns (U1a and p, i=l,...,M), 
which were solved by
iteration on Usa. The correct 
value for Ua, and therefore
for pi, is obtained when Eq. [23] 
is satisfied. Equation
[20] is then used to calculate 
the soil's calibration con-
stants at the other (M-l) points. 
A similar procedure was
used to determine the calibration 
constants for the Cs-
source (Usc, i=l,...,M) with the 
corresponding dry bulk den-
sities (replace subscript a by 
c in Eq. [19] through [22].
An example of bulk density profiles 
calculated from the
information obtained from the two sources 
is shown in Fig.
8. The two density profiles are almost identical, indicating
the usefulness of the outlined 
procedure. The FORTRAN pro-
gram that is used to determine 
the calibration constants is
listed in Appendix C. A partial 
listing of calibration con-
stants determined for the same 
soil on which the density
26
profiles in figure 8 apply, is given in table 1. It is
obvious from figure 8 and table 1 that no single value for
the dry density or for any of the calibration constants
would have sufficed. Additional information on this calibra-
tion technique can be found in Hopmans and Dane (3).
The stepping motors can move the mounting platforms,
which support the detector and sources-holder, both horizon-
tally and vertically, thereby positioning the dual-energy
beam at any position. Choosing a reference point as the ori-
gin (usually the location where standard counts are taken),
a point in the X-Y plane can be defined by the number of
steps or half steps that the platforms have to be moved in
order to reach that point. In defining the origin, it is
emphasized that the platform should at least move 1 cm in
the downward direction before reaching the origin. The GPIB
Actuator (Model 800), that serves as an interface between
the stepping motor control units and the computer, can be
set in LOCAL-mode so that the movement of the platforms can
be regulated manually.
2. Pressure transducers
27
strain gauges can be found in their respective manuals. Both
models allow zero and span control adjustment. The A/D-con-
verter Model 805 can be set to LOCAL mode, so that voltage
readings can be directly read from the display on the
805-unit. An example of a calibration curve of a Bell &
Howell pressure transducer is shown in figure 9. The rela-
tion between output voltage and actual pressure is strictly
linear. The calibration line in figure 9 also shows zero
voltage at zero gauge pressure and an adjustment of the span
control such that a pressure difference of 50 cm corresponds
to 1 V. It is advised to flush the pressure transducers
every few days with de-aired water. Recalibration will only
require adjustment of the zero control switch.
3. Thermocouples
The relation between a copper-constantan thermocouple
voltage and temperature has the following unique relation-
ship:
T = 32.02814 + 46.397395V - l.072966V
2
, [24]
where T is in OF and V in mVolt, figure 10.
28
May, 1984
5.0 5.8
Voltage Vy)
FIG. 3. Energy spectrum of Cs-137.
79,000
59,000
, 39,000
0
19,000
0
29
200,000
150,000
3 100A00 0May, 1984
0
50,000
10,000
I I I II
0 0.2 0.4 0.6 0.8 1.
Voltage (V)
FIG. 4. Energy spectrum of Am-241.
1,200
1,100
1,000
900
800
700
600
500
400 -
300
200
I I I I I I !
1250 1750 2250 2750 3250 3750 4250
High-energy 
Cs intensity, counts 
sec-
1
FIG. 5. Cs-intensity in the low-energy band plotted against
observed Cs-intensity in the high-energy range.
30
cubic polynominal
for glass
(A
U
o
(A
U)
UE
0
(1)
LM
U,
0
31
0.662
0.661
0.660'
0.659
0.658'
0.657
0.656'
0.655
0.654
0.653
CESIUM
0
0A
0
0.652 ...
0.0
0
1.5
I
I 0
4
0
0
S
0
A
A
0
0
A
0
0
3.0 4.5 6.0
Resolving time, ipsec
FIG . 6. Plot of adjusted Cs-count intensity ratios versus
resolving time (T) for 3 different absorber thicknesses.
0
0 O
m
0
(0
4l)
r I
... , i l
32
0,31251
0,3100
0.3075
0.3050-
0.3025-
0.3000-
0.2975-
0.2950-
0.2925-
0 29001
0.28751
0.28501
Af
AMERICIUM
0
0 0
L 
"
A 
o
I 10
0
h'0
A
0
A
0
A
A
0
0
0.0 1.5 3.0 4.56.
Resolving time, psec
FIG. 7. Plot of adjusted Am-count intensity ratios versus
resolving time (T),for 3 different absorber thicknesses.
0
0
U-
Cl,
0
0
Cl,
ff I aI T
33
Position along column, m
Ul
C'
0 C,'
0
0
0
W-4
tjl
0
U'
0
0
U'
01-
0
CA)
FIG. 8. Dry bulk densities at 38 points along container com-
puted from Am and Cs radiation intensities.
1)
0
0
34
75-
50-
*
25
*
*
*
0- *
*
P ,
R -25
S
S
U -50- *
R
E
I -75-
N *
C
M -100-
0
F
-125-
w
A
E -1I50
R
*
-175- *
*
-200-
-225-
-250
II I I
-5 -3 -1 1
PTX 2,DCV IN VOLT
FIG. 9. Example of calibration curve of pressure transducer
(Type: Bell & Howell).
35
T 120-
R 110-
A **
T**
R
E 100-
I
N
D 90-
E
G
R
E
E 80-
F
A
H
R 70-
E
N
H **
E
1 60-
T
50-
40-
0.0 0.4 0.8 1.2 1.6 
2.0 2.4
DCV IN MVOL
FIG. 10. Relation between temperature (OF) and output
(mVolt) of copper-constantan thermocouples.
36
Table 1.
Both the
Solid(s)
Partial Listing of Calibration Constants(U) for
Cs(c) and Am(a) and for Both Water(w) and Soil
in the Container.
At Position
point along Uwa 
Usa Uwc Usc
container,
cm
1 19.75 1.16194 1.51283 0.51590 0.47053
5 17.75 1.15885 1.50880 0.51543 0.47010
10 15.25 1.15811 1.50784 0.51507 0.46978
15 12.75 1.15844 1.50827 0.51451 0.46926
20 10.25 1.15861 1.50849 0.51464 0.46939
25 7.75 1.15784 1.50749 0.51458 0.46933
30 5.25 1.15910 1.50912 0.51658 0.47115
35 2.75 1.16080 1.51134 0.51654 0.47112
38 1.25 1.16565 1.51765 0.51668 0.47124
37
DATA ACQUISITION
The following BASIC statements are required:
1. To fetch gamma readings from the Cs and Am channel
50 PRINT "PRESS RESET AND THEN START ON NE-30"
OUTPUT 702;"START"
CALL Gamma(Y1,Y2)
STATUS 702;X6
DISP X6
IF X6=10 THEN GOTO 50
CONTINUE
I
SUB Gamma(A,B)
DIM B$(10)
A=0
PRINTER IS 16
B$="0"
ABORTIO 7
WAIT 500
ENTER 702;A
WAIT 500
ENTER 702 USING"%,6A";B$
B=VAL(B$)
SUBEND
2. To move the platform
in vertical direction: OUTPUT 700;"SMO,MR-0050000"
in horizontal direction: OUTPUT 700;"SMl,MR-0050000"
OUTPUT 700;"SMO,MA+0000000"to origin:
38
3. To fetch time and date
OUTPUT 9;"R"
ENTER 9;T$
PRINT T$
4. To obtain pressure transducer 
readings
OUTPUT 701;"RIO1"
ENTER 701;V
PRINT V,"voltage at channel 
01"
5. To obtain temperature readings
Ch=l
CLEAR 709
OUTPUT 709;"VFl"
OUTPUT 709;"Al";Ch
ENTER 709;V
PRINT "Volt",V,"at channel",Ch
A BASIC-program that has been 
used to obtain gamma,
pressure transducer, and temperature 
readings at 13 measur-
ment points along a soil column is 
presented in Appendix D.
This program can be found on Prog. 
tape 3:T15 (temp3.prog).
Other programs that may be 
useful are listed in Appendix 
E.
39
MEASUREMENT ERRORS
It is interesting to know how the counting 
time affects
the precision of the water content 
and/or dry bulk density
determination.
Gardner and Calissendorf (2) showed 
that, due to the
random emission of photons, the 
variance in the dry bulk
density and volumetric water content 
can be written as,
var(8) = (Usa/k)
2
(1/Nc+l/Noc) + (Usc/k)
2
(1/Na+l/Noa)
[25]
var(p) = (Uwc/k)
2
(1/Na+l/Noa) + (Uwa/k)
2
(1/Nc+l/Noc)
1 [26]
where N denotes the number of counts 
over a given time
period. Assuming Noa and Noc to be large as compared to Na
and Nc (large counting times were used 
for the Io-counts to
compensate for random error), and using 
Eq. [13] and [14],
the variances due to random emission can 
be approximated by
var(e) = (Usa/k)
2
/{tlocexp(-Uscp - Uwce)}
+ (Usc/k)
2
/{tloaexp(-Usap - UwaO)} , [27]
40
var(p) = (Uwc/k)
2
/{tIoaexp(-Usap - Uwae)}
+ (Uwa/k)
2
/{tIocexp(-Uscp 
- Uwce)} , 
[28]
where t denotes the counting time in seconds. 
These last
two equations were used to calculate the theoretical 
stan-
dard deviations in 0 and p from gamma measurements 
of the
same soil as used for the calibration. The results 
are shown
in figure 11 for counting times of 60 and 300 seconds. For
a given dry bulk density (solid lines), 
the standard devia-
tion in 0 can be found by selecting a particular value 
for e
on the bottom x-axis. Similarly, for a given volumetric
water content (dashed lines), the standard deviation 
in den-
sity can be found by selecting a particular density 
on the
top x-axis. The variances decrease with increasing 
counting
time and count rates (Eq. [27] and [28]). 
Figure 5 indi-
cates that, if 5-minute count readings 
are taken at each
measurement point, the standard deviation 
in both 0 and p is
smaller than 0.01.
To check for possible changes in the electronic 
set-
tings, standard counts must be taken at regular time 
inter-
vals. Table 2 shows standard count readings 
over a 10-month
interval. It appears from these data 
that there is a slow
decrease in count intensity in the Cs-window. 
This decrease
in the Cs-intensity is attributed to 
the relative short
halflife time (tl/
2
) of the Cs. Theoretically tl/
2
-Cs is 30
years, whereas the tl/
2
calculated from the count intensi-
41
ties in table 2 yields a value of ca 33 years. It is there-
fore suggested to adjust the Cs-count rates 
proportional to
the ratio of standard count at the time of gamma-unit 
cali-
bration to the standard count at the time 
of measurement
during the experiment.
1.2
42
pMg rn-
3
1.4
Norfolk sandy loam
1.6 1.8
in_ E
in p
60 sec.
e = .4. p=1.4
-. 0-0
o 
logo-050-WO
6= -000000-
P=1.8
p=1.4 
300 sec.
P=1.0
e =.4 
e=.2 
=.0
n n I I
.10 .30
.40
FIG. 11. Standard deviation in e and p for counting 
times of
60 and 300 seconds.
1.0
0.025-
0.020-
0.05
0.0101
43
Table 2. Standard Counts of Am and Cs as a Function of 
Time
Date Standard counts (counts per minute)
Cesium Americium
July 1984 275084 83263 3
August 1984 274312 835575
September 1984 274400 835600
November 1984 273500 836000
December 1984 273300 836500
January 1985 272300 836300
May 1985 270600 835100
44
LITERATURE CITED
(1) Fritton, D.D. 1969. Resolving 
Time, Mass Absorption
Coefficient and Water Content with 
Gamma-ray Attenua-
tion. Soil Sci. Soc. Amer. Proc. 33:651-655.
(2) Gardner, W.H. and C. Calissendorff. 
1967. Gamma-ray and
Neutron Attenuation in Measurement 
of Soil Bulk Density
and Water Content. pp. 101-113. In Isotope 
and radia-
tion techniques in soil physics and irrigation 
studies.
Symposium Proc., Istanbul, Turkey. IAEA 
Vienna, Austria.
(3) Hopmans, J.W. and J.H. Dane. Determination 
of Multiple
Point Calibration Constants for Dual-energy 
Gamma Atten-
uation in a Soil. Submitted to Water Resources
Research.
(4) Stroosnijder, L. and J.G. de Swart. 
1974. Column Scan-
ning with Simultaneous Use of 241Am 
and 137Cs Gamma
Radiation. Soil Sci. 118(2):61-69.
45
APPENDIX A
SAS-program to Determine Regression Coefficients 
of
Polynomial
//CSLO1 JOB (AYL59,124),'JAN HOPMANS',NOTIFY=AYL59JH,MSGCLASS=P
/*ROUTE PRINT RMT4
/*JOBPARM LINES=4K,TIME=010
// EXEC SAS,REGION=220K,PLTFORM=1111
//SYSIN DD *
GOPTIONS DEVICE=CALCOMP;
* DETERMINATION OF THE COEFICIENTS OF THE POLYNOMIAL;
TITLE Y=BO + B1*X + B2*X**2 + B3*X**3;
DATA D1;
INPUT XX YY ;
Y=YY/60; X=XX/60; * CONVERSION TO 
CPS;
LIST;
CARDS;
2867-41 77750
271369 71758
256206 66212
241610 61094
226851 56294
213021 51762
201558 48194
189394 44976
179682 42257
168391 39308
158745 37078
149644 34807
141955 32719
133684 30800
126288 29034
118216 27235
PROC PRINT;
PROC GLM DATA=D1;
MODEL Y=X X*X X*X*X/P;
OUTPUT OUT=D3 PREDICTED=PY RESIDUAL=RY;
PROC PLOT;
PLOT Y*X='*' PY*X='.' / OVERLAY;
TITLE LOW ENERGY CESIUM VERSUS HIGH ENERGY CESIUM.;
LABEL Y = LOW ENERGY CESIUM IN CPS
X = HIGH ENERGY CESIUM IN CPS;
SYMBOL V=STAR I=RC;
PROC GPLOT;PLOT Y*X;
/*
46
APPENDIX B
SAS-program to Plot Count Intensity Ratio 
Versus Resolving
Time for 3 Absorber Thicknesses
GOPTIONS DEVICE=CALCOMP;
* SAS PROGRAM WHICH WILL FIND THE OPTIMUM DEAD TIME;
* FOR THE AMERICIUM AND CESIUM RADIATION;
* BY A METHOD SIMILAR AS DESCRIBED BY STROOSNYDER;
DATA Dl;
INPUT I01 II 102 I2 103 13;
LIST;
I01=I01/60;
I02=IO2/60;IO3=I3/60;
Il=Il/60; I2=I2/60; I3=I3/60;
*A=-9.16077510;
*B=+0.25827473;
*C=-2.315935E-05;
*D=+5.5831407E-9;
*YCL=A + B*YC + C*YC**2 + D*YC**3 ; *LOW CS-COUNT IN CPS;
*T =YA-YCL;
DO DT=0.0 TO 6.OE-06 BY 5.OE-07;
DN1=IO1/(1-DT*IO1); DN2=IO2/(1-DT*IO2); DN3=IO3/(1-DT*IO3);
N1=Il/(1-DT*Il); N2=I2/(1-DT*I2); N3=I3/(1-DT*I3);
R1=N1/DN1; R2=N2/DN2; R3=N3/DN3;
OUTPUT;
END;
CARDS;
336511.4 222648.8 192123.6 126797.1 148408.9 
97804.5
PROC PRINT ;
TITLE CESIUM FOR POINT CS;
PROC GPLOT;
PLOT R1*DT='1' R2*DT='2' R3*DT='3'/ OVERLAY;
PROC PLOT;
PLOT R1*DT='1' R2*DT='2' R3*DT='3'/ OVERLAY;
DATA D2;SET D1;
INPUT 104 14 105 15 106 16;
LIST;
I04=IO4/60;
I05=IO5/60;
I06=IO6/60;
-4=I4/60; 15=15/60;
16=16/60;
A=-9.160 77510;
B=+0 .25827473;
C=-2 .315935E-05;
D=+5. 5831407E-9;
47
YCLIO1=A + B*IO1 + C*IO1**2 + D*IO1**3 ; *LOW CS-COUNT IN CPS;
I04= IO4-YCLIO1;
YCLIO2=A + B*102 + C*102**2 + D*102**3 ; *LOW CS-COUNT IN CPS;
I05= IOS-YCLIO2;
YCLIO3=A + B*1I3 + C*1I3**2 + D*103**3 ; *LOW CS-COUNT IN CPS;
I06= IO6-YCLIO3;
YCLI1=A + B*I1 + C*I1l**2 + D*I1l**3 ; *LOW CS-COUNT IN CPS;
14= I4-YCLI1;
YCLI2=A + B*I2 + C*I2**2 + D*I2**3 ; *LOW CS-COUNT IN CPS;
15= 15-YCLI2;
YCLI3=A + B*13 + C*13**2 + D*13**3 ; *LOW CS-COUNT IN CPS;
I6= 16-YCLI3;
DO DT=0.0 TO 6.OE-06 BY 5.OE-07;
DN4=IO4/(1-DT*IO4); DN5=IO5/(1-DT*IO5);
DN6=IO06/(1-DT*IO6);
N4=I4/(1-DT*I4); N5=IS/(1-DT*I5);
N6=I6/(1-DT*I6);
R1=N4/DN4; R2=N5/DN5; R3=N6/DN6;
OUTPUT;
END;
CARDS;
1583967 957700 1061910 640600 664312 402476
PROC PRINT ;
TITLE AMERICIUM FOR POINT CS;
PROC GPLOT;
PLOT R1*DT='1' R2*DT='2' R3*DT='3'/ OVERLAY;
PROC PLOT;
PLOT R1*DT='1' R2*DT='2' R3*DT='3'/ OVERLAY;
48
APPENDIX C
FORTRAN-program to Determine Calibration 
Constants
// EXEC LIST
//* data file specified in next 
line contains the input data
//SYSIN DD DSNAME=AYLS9JH.STAT.LIB(DATIN2) 
,DISP=SHR
// EXEC FTVVCLG 
0009
//*EXEC FORTHCLG,PARM='XREF,MAP' 
0010
//FORT.SYSIN DD * 
0011
C this fortran program allows for determinination 
of the calibration
C constants of cs and am at all specified 
measurement points.
INTEGER I(38,6)
REAL C(38,6),LWC(40),LSC(40),A(40),DD(40),U(40),LWA(40),LSA(40)
REAL DDD(40),UU(40),Z(40)
WRITE(6,6)
6 FORMAT(' determination of att. coef. for both water and 
soil',
11(/),' for the c e s i u m ',5(/))
N=11
C give positions of measuring 
points.
Z(1) = -19.75
DO 9 II=2,N
Z(II) = Z(II-1)+1.5
9 CONTINUE
C -- if soil sample has some low volumetric 
water content--
TH = 0.0004
C -- correction of count intensity Am for low 
Cs-interference--
AO = -9.1607751
Al = 0.25827473
A2 =-2.315935E-05
A3 = 5.5831407E-09
READ(3,7)
7 FORMAT(2(/))
DO 100 K=1,N
READ(3,l0) (I(K,J),J=l,6)
10 FORMAT(6I10)
DO 30 J=1,6
C(KJ)=I(K,J)/60.
30 CONTINUE
WRITE(6,21) K,(C(KJ),J=l,6)
DO 50 L=1,5,2
CL = AO + Al*C(K,L) + A2*C(KL)**2 + A3*C(KL)**3
C(KL+1)=C(K,L+1) - CL
50 CONTINUE
WRITE(6,22) K, (C(K,J) ,J=1,6)
21 FORMAT(lX,'original cps at',I3,2X,6(FlO.2,2X))
22 FORMAT(lX,'corrected cps at',I3,2X,6(FlO.2,2X))
23 FORMAT(lX,'Uw-cs at point',I3,' = ',F1O.5)
49
100 CONTINUE
WRITE(6,0ll)
101 FORMAT(5(/))
C -- Calculation of calibration 
constants of water for Cs --
DO 200 K=1,N
C--if a hypothetical resolvingtime 
correction is applied--
Cc- resolving time cs= 
dcs
DCS=2.5E-06
Pl=DCS*C(K,1)
P2=DCS*C(K,3)
P3=DCS*C(K,5)
C(K,1)=C(K,1)/(1-Pl)
C(K,3)=C(K,3)/(1-P2)
C(K,5)=C(K,5)/(1-P3)
LWC(K)= ALOG(C(K,1)/C(K,3))
LSC(K)= ALOG(C(K,1)/C(K,5)) -TH*LWC(K)
WRITE(6,23) K,LWC(K)
200 CONTINUE
DO 300 K=2,N
A(K) = LWC(K)/LWC(l)
300 CONTINUE
C -- AD: give average bulk density of total soil sample--
AD = 1.663
A(1)=1.
WRITE(6,26)
26 FORMAT(3(/),' U-est at point 1 rho-average rho-estimat 
error')
Cc -- Iteration on Usoil-Cs of first measurement 
point--
DO 600 IS=38000,42000,200
US=IS/l00000.
DO 400 J=1,N
DD(J) = LSC(J)/(US*A(J))
400 CONTINUE
ED=O
DO 500 K=1,N
ED=ED+DD(K)
500 CONTINUE
ED = ED/N
C-- ERR: difference between measured and 
calculated average density--
C-- to achieve minimum ERR, readjust IS-values above--
ERR = AD - ED
WRITE(6,550) USADEDERR
550 FORMAT(lX,Fl0.5,8XF7.5,6XF7.5,4XFlO.6)
600 CONTINUE
WRITE(6,28)
28 FORMAT(3(/),' at point 
position uwc usc 
density')
C-- If ERR is small enough, substitute the 
corresponding IS-value--
C-- from above.--
C-- in this example: 0.475330 (=U-soil Cs 
for first measurement point-
DO 700 K=1,N
U(K)=A(K)*0.394760
DD(K) = LSC(K)/(0.394760*A(K))
C-- listing of the soil's calibration constants for Cs and dry --
50
C-- density values for all measurement points 
--
WRITE(6,650) KZ(K) ,LWC(K) ,U(K) ,DD(K)
WRITE(l,650) KZ(K),LWC(K),U(K),DD(K)
650 FORMAT(2X, 14,4X,2F0 .
5,FlO. 5,F9.4)
700 CONTINUE
C-- repeat procedure for the Am-source--
WRITE(6,8)
8 FORMAT(lH1' determination of 4tt. 
coef. for both water and soil',
L1(/),' for the a mn e r I c I 
u M '15(/))
DO 800 K=1,N
C--if a hypothetical resolvingtime correction 
is applied--
Cc- resolving time am= dam
DAM=2 .5E-06
Pl=DAM*C(K,2)
P2=DAM*C(K, 4)
P3=DAM*C(K,6)
C(K, 2)=C(K,2 )/( l-Pl)
C(K, 4)=C(K, 4)/( l-P2)
C(K,6)=C(K,6)/(l-P3)
LWA(K)= ALOC(C(K,2)/C(K,4))
LSA(K)= ALOG(C(K,2)/C(K,6))- TH*LWA(K)
WRITE(6,823) KLWA(K)
800 CONTINUE
DO 4000 L=1,N
WRITE(6,22) L, (C(L,J) ,J=l,6)
4000 CONTINUE
823 FORMAT(lX,'Uw-am at point',13,' 1 ,F10.5)
DO 900 K=2,N
A(K) =LWA(K)/LWA(l)
900 CONTINUE
AD = 1.663
A(l)1l.
WRITE( 6,26)
DO 1100 IS=124000,129000,200
US=IS/100 000.
DO 1000 J=lN
DDD(J) =LSA(J)/(US*A(J))
1000 CONTINUE
ED=O
DO 1040 K1,fN
ED=ED+DDD (K)
1040 CONTINUE
ED =ED/N
ERR =AD -ED
W. RIE(6,5%50) US7,ADEDnERR:)
51
WRITE(1,650) KZ(K) ,LWA(K) 
,UU(K) ,DDD(K)
1200 CONTINUE
C -- plot calibration constants 
and calculated density values-
C - for both gamma energies 
as a function of depth.
C GO TO 5000
CALL PLOTS(0,0,0)
IFLAG~l
IF (IFLAG.EQ.0) GO TO 2000
CALL PLOT(l.0r,0,-3)
DD(N+l)=1.50
DD(N+2)=0.02
DDD (N+1) =1. 5
DDD(N+2 )0 .02
U (N+ 1 )= 0.0
U(N+2 )0.25
UU (N+ 1) = 0.0
UU (N+2 )= 0 .25
LWC(N+l)0 .0
LWC(N+2 )=0 .25
LWA (N+ 1 )=0. 0
LWA (N+ 2 )= 0.25
Z (N+ 1 )= 0.0
Z(N+2 )=+2 .5
CALL AXIS(0.0,0.0,'CALIBRATION COEF',+16,8.0,0.0,U(N+l),U(N+2))
CALL AXIS(0.0,0.0, 'POSITION' ,-8,8.0,270.0,Z(N+l),Z(N+2))
CALL LINE(UZNfl,-lrl)
CALL LINE(UUZNrl,-l,2)
CALL LINE(LWCZ,Nfl,-l,3)
CALL LINE(LWAZNrl,-l,4)
CALL PLOT(0.0,0.0,-999)
CALL PLOT(l.0,9.0,-3)
CALL AXIS(0.0,0.0, 'DENSITY' ,+7,l0.0,0.0,DD(N+l) 
,DD(N+2))
CALL AXIS(0.0,0.0, 'POSITION' ,-8,8.0,270.0,Z(N+l) 
,Z(N+2))
CALL LINE(DDZNfl,+lfl)
CALL LINE(DDDZNfl,+l,2)
CALL PLOT(0.0,0.0,-999)
2000 CALL PLOT(0.0,0.0,+999)
STOP
END
//GO.FT0lFO0l DD DSNAME=AYL59JH.OUT.DATAUNIT=DISK, 
0317
/DISP=(NEWCATLG),SPACE=(TRK,(5,5),RLSE),LABEL=RETPD=31 
0318
/DCB=(RECFMFBfLRECL=8OBLKSIZE=6160) 
0319
/*the data file specified on the next 
line contains the input
/*data. that is it contains the count 
intensities of empty
//* container- , -containe -%-%* r. with- wat n4-e rnd co4r- nta =;iner v-f 
;1iled. w --Ith
52
input data file for FORTRAN-program
one minute counts for 38 points along the flowcell. the last
two colums correspond to counts through
io-cs
333554
334863
334590
334540
334496
334586.
334629
334451
334532
334459
334566
334368
334677
334487
334573
334426
334616
334517
334524
334426
334720
334667
334706
334962
334655
334812
334792
334975
335215
335174
335660
335493
335802
335665
335948
335911
335982
335387
io-am
1242831
1242486
1241006
1239981
1239797
1239868
1239342
1238787
1238734
1238556
1238464
1238601
1238782
1238573
1238448
1238903
1238911
1238881
1239132
1239372
1240151
1240799
1241370
1241846
1242151
1242594
1243212
1244116
1245130
1245654
1246647
1247558
1248027
1248933
1249677
1251115
1252091
1252654
water cs
201782
202479
202494
202335
202372
202414
202356
202566
202360
202291
202299
202371
202325
202305
202457
202489
202234
202443
202595
202467
202490
202675
202343
202393
202591
202505
202686
202642
202746
202616
202811
202800
202870
202913
202971
203151
202985
202855
water am
416324
417053
416725
"416 
49 
4
416397
416226
416363
416382
416228
416422
416525
416287
416214
416379
416340
416696
416513
416671
416748
416493
416824
417048
417253
417115
417543
417607
417620
417690
418011
418067
417974
418244
418482
418599
418770
418747
418676
418291
Norfolk
soil cs
170927
170196
167461
167624
165823
165190
168452
166490
167662
167184
166502
167559
169941
169408
171864
167688
169136
167946
168781
168719
166255
165127
165709
162322
163874
166794
168082
169668
169202
169385
168893
166741
169350
168615
167031
164902
162370
164730
sandy loam soil
soil am
171057
167777
160971
161951
155913
154450
164217
157711
161487
160353
158496
161090
167625
166194
173320
160703
165857
162149
164623
165410
157607
154643
157635
152160
158795
163095
168516
166358
167780
165440
158946
166429
163313
159772
154650.
147005
153871
53
APPENDIX D
BASIC-program for Simultaneous 
Gamma, Pressure and
Temperature 
Determinations
10 i:iPTION BASE 1
20 STATUS 702;X1
30 DISP . 1
40 PRINTER IS 16
50 PRINT "PRESS RESET AND THEN 
START O1 N E-30"
60 BEEF'
70 CALL Gama r.-X1 2
80 CALL G-a1mm -a IXI2
9 CALL G-a rmaX1,r2
100 STATUS 702;X3
110 FPRINT X3
120 IF 13=10 THEN GOTO 50
130 DIM Ptf'13),Ti(500),Gno(25)
140 SHORT Pu(1, 1)Th4 
h4,Ph13,Te(13
150 SHORT Ga40),GU(40),Stc,Sta.Hh(13'
160 I THESE DATA STATEMENTS REFER TO THOSE 
POINTS WHERE PRESSURE AND
170 AND TEMPERATURE MEASUREMENTS ARE 
REQUIRED.
180 DATA 2,4,6,9,12,162,2-4,28,313436-8
190 MA1HT READ Pt
191 AND THESE HARE THE MEASUREMENT 
PINT THAT NEED TO BE SKIPPED
200 DATA 1 5,5,7,8,10 1113,14, 15,17, 1 , 19,-21,22,23,25,26,2729,30323:3,3537
210 MAT READ Gno
220 PRINTER IS 16
230 INPUT "HOW MANY SECOfNDS I N A COUNT- ?? 
" ,Sec
240 INPUT "T HOW MANY POINTS DOES THE GAMMA UNIT 
MEASURE,-,"N
250 REDIM Ga(N),Gc (N), The(N),Rho 
(N
260 OUTPUT 700;"SO, ZA"
270 OUTPUT 700;"SM0qZP"
280 INPUT "HOW MANY GAMMA MEASUREMENTS 
DO OU WANT AT EACH POINT ",L
290 INPUT "HOW MANY TRIGGERS PER 
POINT FOR TEMP. PRESSURE?', T
300 INPUT "ARE THERE GAMMA MEASUREMENTS 
TO BE MADE ?",A$
310 IF A$="NO" THEN G=1
320 INPUT "ARE THERE PRESSURE MEASUREMENTS 
TO BE MADE ?",
330 IF A$="NO" THEN P=1
34iC INPUT "ARE THERE TEMPERATURE MEASUREMENTS 
TO BE MADE ?"
350 IF A$="NO" THEN T=1
360 MASS STORAGE IS "i:T14"
370 ASSIGN #1 TO "RAWEX3"
380 MASS STORAGE IS ":T151
390 ASSIGN #2 TO "CALEX3"
400 INPUT "IS THIS THE BEGINNING OF AN 
EXPERIMENT?",A$
410 IF A$="YES" THEN GOTO 540
420 INPUT "WHAT WAS THE LAST RUN IN 
THIS E::PERIMENT?"Nr
430 FOR I=1 TO Nr
4 6 0 READ #1;Nr, TSTiISt ct-a, Gc. , 
-a Li , T .
4940 READ #2;NiTSTi The ( *,Rhc';*.,Phr 
.',Tm)
500 NEXT I
91Lr PRINT "Las nume: "Hr, LIN'.1 .; "D.at: "; T4,LIN' 1'; "tc"
FF: PI NT NWI TN COR'FRESFPO NDINHG WATER COLNTENT PROFILE" ,LI N" 1 ;The( )
530 PRINT "MND VOLT FLIP TEMP: ";T'.'i
I4-WiFOE TO LiOME
5 !HERE AFTER COHMES THE TINE LLOOP
'I-A PRINT "LAST HF iiF THIS E FEFRIMENT" 
Nr LIIN'2)
570 iOULTPUT 9; "P'
580 ENTER 9;T$
590 PRINT T$
54
ION INT #9 GOSIB Neasure
: N TFR:13L MliSN ' ; 22
O~UTPUIT 9;"A
CARD' ENABLE -9
GIU Ptiu rin
OiU T PU T 9 ;" i t.-':-H -aI t UIni t.z-:= F.i 4t. f-- 1-4 Itt I 2 r ic-d 15 0 00. -ste c U ri t 213c-
IHE;:,*T FOLL' IDI I 111 EDOinALL THE MEAbUFI-IEtMEIIT :FROM THE PO-T TI
ITO THE TOP ''F THE FLOW CELL N flIN
60
6 1 0
6 i
6- IS H
710
711
720
740
741
850
70
7880
890
9 10
9828
9:38
841
86 0
890
920U
940
950lj
101 C,
112C
1 14c,
117C
1 ol.
11 2C
1 1
11 7
,3;TATEMNHT
M1
.1
4
j
.1
j
I N T HISC A' E T INPE -TEF rOF S -4 1NNIN 1L 4 HF:R
T I (N r+11.= C4
FOF. PNr+2 TI'40
II F 111I F FE RE lT T I ME S T EP I U E'1 A L-ri -I H A N 1E 24 IHN NE::T
NEXT P
PRINT "TINE' 1111CItTi 2
OUTPUT 
9; 11UI
ENTER 9;Ns
IPRINT Ms
T i rihrsNt F360000
WAIT 5088
PR INT Ns.. 10LIUIH"SECOI NDS" T i n1-rs;.HRS"
IF Ti rnhrs 005 THEN GOSLIB MeasuLre
P1""Ti(N-r)+ 8m1"
P2=Ti (Nr) 0012
IF (Tir mhrs F*Pit ND ( T i rihr .P12* THEN GOSLIB Measure
!TIME IN HOURFTI' HALT NEASUREMENTS -.EXAMPLE: 188 HRS)
IF Timrhrs<180U L THEN GOTO 758
! PROGRAM
PRINTER IS 16
GOTO 188
S TOP
END
NV-easure!NA INH NEASLIRENENTS F:E DONE I N TH IS SEGMENT
fLCRD ENABLE 9
H-4r = Hrt + 1
P R I N T " CYtC:L ENHF'WI1T H I N E'e" E R I -1ENHT ;H r
tUTPUT 9;"R"
ENTER 9;T$
IFIRST THE AVERAGING OF THE GANNA .:.TC F:RE A 11N GS
IaU LB NtO.gam
FPFI NT "HVERANIE STANDARDIt.~NS"S t
OUTPUT 7ULI NH liP 885888-
IF Iii Liii THEN FPFI NT "WENT OUT OF LUOP,* RESTART NOTOR"
IF Iii j5tU THEN GF~HTF:I 1888
WIT l1i00
LL 1
Co= 1
FLRIP I 1TO
GOIUB iEA'gam2
GOS~UB Ft Lheck
NEXT I
LIUTFUT 9l'Ult)
ENTERF9;,Hs
T iht I 688
T i riiT i Iii-P1I
LII I P iConvert
ItGOSUE. Tfhrho
GULB Ptrt
CARHD ENABLE 9
OUTFPUT ii8;, t118, A+00088
55
1 i -2l1
12 C I
1 C.
1 :,:. H
1 ,'7
1 -3H8c
1390
1420
1450
1460L
1430
1480
1490i
15001
1530
1541
15701
16111
1'-. 'LI
16V~30
16 4 U
1170
1710
174
H I FI NT':"
P ET U FRN
FH'. g -~ri1 A"'ERAGD I NC F GAMMA READ'I NG,
I j 1-U0
FOF 1=1 TO L
OUTPUT-12; 
"MTART'1
ATLLT1Ia ri aX
DI F 1
FNT'1. T 2
RE T I 1
A' '.- rii2 i-' A EFi]"HMMH FEHADICHG 
T THEI.
I F I =G i o'C c.T H EN 
]0T ' *j
FFR H T L I N'( 2 'HI LLrA T10tINC
FOR T 1 TU L
OUTFPUT 702; 
"' TFT"
CAHLL IGamma(I)- 
f,
FFR1INT 
k1,
DISP:6
NEX'T J
IaCc)=Hv/L
FPR I N T 1HA VER A GE S A N DIAHI R E,:P A T 
POCiI NT'I
IPRINT "C OUNTEF IS"; Cc
IF I=3 THEN GOTO 1610
IF I=G-(''Cc') THEN Coc'C.o+ 1
IF I '- s-THEN Cc'5
W I T 20U
I F 1I20THEN OUTPUT M 0 M 
R, -LC'O1- 4
WHIT 2000I
IF 11i =400i THEH PFFI HT "WENT FLI1IT 
0'F LOAF'.l P
IF Iii=4110 THEN GOTO 1 56.7-
FETURN
e c LIIIIo C H ELC T RA VE L B''-TEPPFEFR 
IlTOI
Iii =0
'-TATLI700;X
I i i =I i i+1I
PRINTER IS13*16
F I SP X 5
t'ISP Ii i
IF X~5=16 THEN GOTO 1720
I F I ii =400 THEN GOTO 1 720C.
GOTO 1640
F:ETURJF:N
Ft c:hec k CHECKS *'--FOF'P'ESSURE 
OF: TEIIPEF:
IF I =Pt (:Cc ' THEN mci B Pres-LOrE-
IF I =Pt (Cc ' THEN GOSUB TempE
IF I =Pt(Cc*.' THEN C: =Cc+ 1
RETUPRN
Pre-sure I TAii- ES'-'.OLT F:EAI'I NG3AT 
SP-FEC IF
y j-r
RFE,:;T A RT M11L TI:PR
ATURE FEAD'I NGS
I IC PO-jINHT
I :G (Cl: ) ::' i : c
P
56
1800 FOR 1 TO T
1810 IF Cc=1 THEN GOT0 
1 40
18:20 IF Cc 2 THEN uG Tn 
19G.I
18:30 IF Cc=3 THEN GOTH 1980
1840 IF Cc=4 THEN GiTO 2000
1850 IF Cc =5 THEN GOTO 2L20
1860 IF Cc =6THEN GOTO 204H
1870 IF CcT7 HENI IT'0 2 
0-
1 130 IF Cc= THEN GOTO 2080
1I 90 IF Cc-=9 THENI' iGT'; '100
1900 IF Cc= 10 THEN ifT1 212 
0
19310 IF F_:c=11 THEN G20Ti 2140
1,2190 IF i:c12 THENH GOTO 2161-
1 0 1IF Cc =13 THEN 11T :Tl1:110
1941 OJ UT PUT i T I ii
1950 GOTO 21190
1960 OUTPLIT H7011011
1970 GOTO 2190
1980 13 UTPUT U7 10 FI R17 -1
1990 GOTO 2190
2000 OUTPUT 781;11RI04"
2010 GOTO 2190
2020 OUTPUT 701;"R11
2030 GOTJ 2190
Q~ii iIITFIIT 111, F116
240 OiTPUTH 71;FIH6"
210 GOTO 210
2060 OUTPUT 701;11RI01
2130 ';OTO 2190
2080 0 LlT P UT 7 0 1 F' 10 I
2090 GOTO 2190
2140 OUTPUT 701;11RI, l
2110 GOTO 2190
2120 OUTPUT 701;"RIIO"
.10GOTO 2190
2140 OUTPUT 
71; .111"
2150 GOTO 2190
2160 OUTPUT 71;lF12
2170 GOTO 2190
2180 OLITPIJT 701 RF 11I
2200 VHi Y1
2210 NE IXT K
223 PRINT PvU'- )"'OLT P CHANNEL Cc
224U RETURN
22951 TempI: TA[KES 'CiiJT FEAD' I Nil AT SPEC.IF IC POI NT
26 CLEAR70
220 OUTPUT 709;1"YF11
s,300 FOR K=1 TiO T
2310LOUTFUT 7U911 HI ;Cc
232U ENTEF U09;
2340 NEX"T 1
2360PFR I NT Tv (I C c 13L T T C*HA N NE L"
2370 FETURN
U 38I0*i-r,,-i rt CI L-'NE R T!:-'.VULT FEAD' I NGS; FOR F AND T I NT':'AB:SOLUTE PRESSUFRE
2390HArD TEMPERATURE
2400 TEMFEFHTUFE --- CALIBRATION IS THE SAME FOR ALL THERMO COUPLES
2410
2420 FOIR Ji=l1 TI 13
2440a T1c, .- I =1 14fC-31 1+4.39 T'- T1t-1 i6*ult
57
T ern.Jj 5 . T e ru I--eI I
HNE:X:T 51
P R INT T ernm ; T EMP1F REHADINIGS"
PR FES S11R E H EHA
DATA -0. -2-4!1 +4"4'::4. 5,+ Cl. 0H7 + 4 '?. -1 .* 0. +49. 700 ++, 
. 05f:1 + 490 -00
DAT +. C :,-4 + 4-9.747,+0C1.125,+ 49 . +-: l , rr.029+ 4 9. +.0:27,4'?.79
DATA +LI. 14,4-4..+ C. Ci4 6.4 9. , L. Ci0 4,49 . 7 8,7--0.04L,-49.525
DATA +0.01,- 49-.71
R ES6-;TO0RE'25 1Cr
FFR S i=1 
TO 1'.
FEAD I nt.1
Tj 1 1 F 1
DIATA + 7. 5,9 .5, + ,1 l 12 514 . 51 
5-.+ 18.5-+ 2CI. 5 +22 . C-+ .2:.5 4.5 +:'C2
FOR Jj=l TO 13
READ D z
Ph -'.j )= Hh Jj - D
N IEX'.T Jsj
PR I N T P h PFRESS U R E HE A D SAMT S PE 
C. Pu I NT:"
R ET UR N
T he ho C~ALCULA TES THE TA AND 1 DENS 
I T''FF0ROM GAMMA MEASURFE MEN T,:
T H I SUB R 0:1LIT I N-lE F ET CH ES' T H E 11A MA 
R EAD11I NS
EAC H DATA L I NE CCRRESPONDS TO A MEA'SLI 
I NG PCI I NT THE F I F,:-T LI11.NE TI:0
POT N1-4T 1 BO13T TOM CI F CE L L.'T HE'SE 
6 HLUM BE R'SC RFFSPO;F,-lND11PES F' T C
LI I: ~ U to a Is a, I oc - A N D I o-at .H ASrn 
CP-' .
f E ST iR E 276Cr0
2460
2470 C
25 10U
252C,
2610
26701
2710L
A?7411111
2' 151C
2?0 i-1
2:D, 50.
y813 - 1
2389 C
'MiTHA ..5 15 22, .46,91 1 I ,D,:.51 -5 10Cl1 1,5 
5'81 .1 19 C1 2E. 6
I'DATR . 51 544. . 4 70 111 1 .15 751 9050, 35 57 5 
.- 7 1 7.7
FITA . 514,4 .457,1 1 1919 1 .509191 
5576. 4,1-D- ' .4
A .51477i . 41,8~, 1 597555 1 e. ..9
)iHTH . 5 101 : .
4 
65
7 4  
1 .15'8 24 1 .0:5:0L,,5 5 7. ., 9e.6
lATA .951 *39 E. . 4,27 7,1 .1574 1, 1 .5f.0 9 ,5 5 7- 
1:::: 70
A T A . 5 1464. . 4e,9 ::-.9 1. 1 5--'--.1 1 .95 l- 4 9 , 597 :i 
1' 9E:
nHTo-r to 45,15 42 rir10101r 0,I .91rj--:42,59 
7 ,19 01 1
HTH .5 1 '',-.2 -4 1 .1 :'-'94 1 . 5 0::'9 2 5:_-: 
2 4.191952
ilTt' .99-, 4, .? I , 1 1- 1 1 .C1 ~ 7 1,5594. 
.--:, 1 0 : 9.LC
Hl~THA.51-14 47017.- 1 . 16052, 1 .5107 
5594.4, 19 127. 1
IHTA.515ir 9 1 .16C2II. 5 1 :-.0 4 5 5 9ED. 5,1916 
1.
FBAH.5 1 E.-:: 4.7124 1 . 16G565 1 . 5 1765,55::,9. 
9,19 191 .5
FCI RP PI Ti0 N
GcP 'G c (P)ec
G -a F' 11Ca( F '', I CC:0N4V ERS2;10IN4FROM 
P1C FM PI TC CP
AOc=-. I1.07r751
Hi-.= 25::, 74,73 C:C, E F 
PO L~iNOM P I A L T0 D ET E RM I NHE L011W:-
A 2= 2 5 :3.5 E-9
A355:14A'E-"
CI 14.4' H+ AI+*G c'(P) +AMA c P.'.2A310c 
,P -3
G a .* )F 1-a )-I C. F I o
LiLLG (I c..Gc P.")
L '-HL.O (I-aL PF'"
L 3-I= Us -*IU w Ic- l*I U
The (P)'-=I('Us a*LI -s:L2 ./L3
Rho'( P) =-(II.,.*L2Hi,.a*LI /L3S
NEXT F
FPF I N T T h e44,T HE T A A T !:SULC CESS I Y 
E P C' I N T S
PR It-NT L I N: 2) Fhc-( "R'HOJ AT SUC CES!S I YE 
POINTS"
R ET U FR N
Pr ni.r : ! PRINTS DATA FIR.ST TO TAPE
PRINT "RET=l',F-n1
PRINT #;N ~ ra ~,S ,C:Ln'G'*,P(),T
PRINT "WHAT 
NE::T"
58
3 2 2 R PIT "rt= ,t
3 0 PRI NT #2 h, T, T ir,,Th- R T ho+FPh 4Tern(
3240 fR I TEF: IS
- H1 1T IEF4t- H- T im h c L4 t- s n: t rid-at, coLint"
3 -6- PRI NT "ST HAN D .TH FES."StcS taLINI
2"'0 PRINT CS C 0 TU N rT(S*)
3280 FIRI4T A rui CUNT H T S.IS
3290 PRINT "THETI; The(* *
3:300 PR I NT " Rh-o " ; Rh *- - ( * ) ; L I N 1
3310 PRINT "PRESSURE HEHD"; Ph(*
3 *1 PRINT "TEMPERATURE ;T I N (5.
3 3:30 PR I N T "HYI-DRALIC HEAD PROFILE" Hh
3340 P'RINTER IS 16
3350 FETLR N
3360
3370 'U B G amrfi ~a DB
3380 DIMi B$(10)
3390 A=O
3400 PRINTER IS 16
3410 B$=01
3420 UBORT I 0
3430 HA~IT 500
'3 4 40 ENt-4T ER 7 02;A
3450 WAIT 500
.3460 E N T E R 7 0 2U SI NGIS . A
3470 B =YAFiL ( $?
34830 LIB1:EN 11
3500
59
APPENDIX E
Additional BASIC-programs
1. Prog. tape 2: T-15
Program name
gmfreq
attsoi
calpt
vert
attso2
gmonly
trdul3
calall
final
Program function
to determine frequency distribution 
of
count intensities
to determine mass attenuation coefficients
of soil from gamma measurements 
through
compartmental box
for calibration pressure transducers
gamma- and pressure transducer 
readings
simultaneously at 4 soil 
columns
as attsoi
gamma readings at 4 soil 
columns
to obtain readings from 13 
pressure trans-
ducers
to be used to calibrate 13 
pressure trans-
ducers
to calculate volumetric water 
content and
dry density if mass attenuation 
coefficients
and pathlength are specified
60
2. Prog. tape 3: T-15
Program name
3497
reate3
tapeco
statgam
tempo
templ
temp2-
temp3
temp4
Program function
to fetch temperature readings
to read data from magnetic tape
to copy data from magnetic 
tape (HP) to
data cassette of Techtran 817A 
recorder
to average gamma measurements 
at one
specific point and to calculate
corresponding water content 
and density
to obtain long series of gamma 
readings
at one specific point
gamma-, pressure transducer-, and 
temperature
readings at 38 points along a column
as templ, but for only 32 points
as templ, but for only 13 points