A 3-m deep temperature probe was installed at the campus of Indian Institute of Management, Ahmedabad in August, 1999. Probe has five resistance type device PT 100 sensors, mounted at 1-m interval. It was put in to the ground up to depth of 3-m. First sensor is at 3-m depth, second at 2-m depth, third at 1-m depth, fourth just 2 cm below the surface and the fifth 1-m above ground. Temperatures from all the sensors were noted one day on each month for a year. Readings were noted at hourly interval. In this paper, the results are presented. Motivation for this work was the need to know the diurnal and seasonal variation of temperature in deeper layers of soil in order to determine the level suitable for installation of earth tube heat exchangers.

Girja Sharan

Jadhav Ratan

English

Research Papers in Economics

Soil Temperatures Regime at Ahmedabad
Girja Sharan
Professor
Cummins-IIMA Lab
Centre for Management in Agriculture
Indian Institute of Management,
Ahmedabad
Ratan Jadhav
Project Officer
SEWA
Ahmedabad
Abstract
A 3-m deep temperature probe was installed at the campus of Indian Institute
of Management, Ahmedabad in August, 1999.  Probe has five resistance type
device PT 100 sensors,  mounted at  1-m interval.  It was put in to the ground
up to depth of 3-m.  First sensor is at 3-m depth,  second  at 2-m depth,  third
at 1-m depth,  fourth just 2 cm below the surface and the fifth  1-m above
ground.  Temperatures from all the sensors were noted one day on each
month for a year.  Readings were noted at hourly interval.  In this paper, the
results are presented.  Motivation for this work was the need to know the
diurnal and seasonal variation of temperature in deeper layers of soil in order
to determine the level suitable for installation of  earth tube heat exchangers.
Introduction
We have been developing earth tube heat exchangers (ETHE) for space cooling in parts
of Gujarat.  This required knowledge of soil temperature regime and the variation in it
through the year.  ETHE needs to be buried at a depth where diurnal as well as annual
fluctuations in temperature become small.  For ETHE meant for long hours of continuous
operation, greater depth is desirable. Temperature data of deep layers of soil is not
available for any site in Gujarat.  Measurements do exist for some other part of the
country,  for instance,  Jodhpur [1],  Pantnagar [2, 3],  and Ludhiana [4].  These  go  up  to2
the depth of 1.75  to 2.0 m. Our interest lies in deeper levels.  Accordingly, we developed
a 3-m deep  temperature probe and installed it  at the campus of IIM, Ahmedabad.  In this
paper we describe the construction of the probe, present the results and compare the
findings with what would be expected on the basis of a somewhat simplified but widely
used theory of penetration of temperature wave through the layers of soil.
The Probe
A schematic diagram of the probe installed at the campus of Indian Institute of
Management, Vastrapur, Ahmedabad in August 1999  is shown in figure-1.   It consists of
a 4-m long, 50-mm diameter PVC tube on which sensors are mounted.   Sensors are put
through a hole on the tube and protrude outside about 5 mm.  Probe has five sensors
(RTDs - PT 100). Length of lead wires of all five sensors has been kept equal (3.5 m). The
ambient air sensor is shaded to protect it from the direct sun. Sensors are connected to a
common digital indicator with a selector switch.  The sensors are placed at  3-m,  2-m,  1-
m  depth below ground.   One sensor is placed  1-m  above ground.  One is placed just  2-
cm below the surface.  After installation of sensors, tube was filled with granules of
thermocole to prevent convective transfer of heat from one level to another. Top end of
the tube was closed with tape to prevent entry of water. Bottom end is simply set on the
soil, but otherwise open. This was done to let water drain out by gravity in the event it
finds its way into the tube.  A pit was dug and probe installed. Pit was then backfilled
carefully to ensure that sensor tips protruding into the soil are not damaged.   All sensors
were checked in laboratory for calibration and accuracy before installation.3
Temperature Data
Temperatures were noted on hourly basis one day in each month, usually near the middle.
  Results
Diurnal Variation
Figure-2 shows the temperatures on August 20-21.  The ambient temperature varied from
a minimum of 22.7
oC to maximum of 31.5
oC.   The amplitude of fluctuation was  thus,
4.4
oC. Amplitude is half of the difference between the maximum and the minimum.   At
1-m  depth the temperature varied from 25.2
oC to 25.4
oC only.  The amplitude was
reduced to just 0.35
oC.  There was also hardly any fluctuation further down at  2-m and 3-
m depth. Table-1 shows the amplitude of diurnal fluctuation on a day in each month in the
ambient and in soil at various depths including the surface.  It can be seen that the same
pattern -  reduction in diurnal fluctuation with depth - was uniformly present through
twelve months.
Annual Variation:  Damping of Amplitude and Phase Lag with Depth
In order to see the variation through the twelve months,  hourly observations of a day were
averaged to get the daily mean.  Diurnal function is thus removed, leaving only the
fluctuations that occur over a longer period.   Table-2 shows the data.  Figure-3 shows the
same data graphically.  From table-2  (column-3),  it can be seen that the maximum
temperature on the soil surface during the year was  35.6
oC (April) and minimum was
15.5
oC (January).   The amplitude of annual variation at the soil surface was thus 10
oC. At
1-m depth it reduced to 4.6
oC,  at  2 m  to  3.2
oC and at 3 m  to  just  2.8
oC.  These values4
were normalised with that at the surface.  Normalised amplitudes at 1-m,  2-m  and  3-m
depth are 0.46, 0.32 and 0.28  respectively.  Attenuation of the annual wave is clearly
evident, as it penetrates into the soil.  It is also seen that the damping of amplitude with
depth is less rapid than in case of the diurnal wave.
From  figure-3,  it can also be seen that the peak of annual wave at the soil surface is in
early April.  As one moves deeper,  peak occurs later.  At the depth of one meter, it is near
the middle of June.  At  2-m   and  3-m it shifts further to the right.  July and August are
the usual rainy months in Ahmedabad.  It is because of this that the temperature lines
sometimes intercept each other.  But phase-lag associated with depth is visible.
Analytical Expression for Daily Mean Soil
Temperature at Ahmedabad
Consider a semi-infinite medium as shown below.  Consider further that the entire
medium is initially at a known constant temperature.  Surface of the medium is maintained
at a temperature that varies harmonically.
  Z+
Let
Z space coordinate  (here depth below surface, positive downward)  m
 t   time  (days)
T(z,t)  temperature  of  points at depth  z,     time  t   (
oC)
Surface5
Ta   temperature of  the medium initially (
oC),  constant
 A 0 amplitude of the temperature wave at the surface  (
oC)
ω angular frequency of the temperature wave at the surface (rad/day)
  k thermal diffusivity of  the material of which the medium is made (m
2/day)
Equation (1) describes one dimensional heat  flow through the semi-infinite (z>0) medium
Initial Condition ( at t = 0 )
T (z,0) = Ta               .......      (2)
Boundary condition  ( at z = 0 , t > 0 )
T(0, t)    =    Ta + Ao cos (ωt - ε)        ......     (3)
ε parameter to indicate the time origin
By a change of variable, initial and boundary conditions can be made simpler.
Let
θ  = T - Ta
Equation ( 1 ), initial condition ( 2 ),  and  boundary condition ( 3 ) can now be written as
  θ (z, 0 )  =  0          .  .  .  .  .  .  .      (5)
θ (0, t)  = A0 cos (ωt - ε)  .  .  .  .    (6)
) 4 ( . . . . . . . 0
2
2
=
∂
∂
−
∂
∂
z
k
t
θ θ
) 1 ( . . . . . . 0 2
2
=
Ζ ∂
∂
−
∂
∂ T
k
t
T6
The steady state solution of (4), which satisfies (5) and (6), can be found in many texts
[5,6] and is
θ (z, t)  = A0 e 
- ∝z  cos (ωt - ∝z - ε )        .  .  .  .  (7)
where
In terms of original variable  T (z, t),
T (z, t)    =    Ta  + A0 e 
-∝z  cos (ωt - ∝z - ε)  . . .  (8)
Equation (8)  represents a temperature wave of wave number,  ∝.    Amplitude of
fluctuations reduce as the wave penetrates into the medium, by a factor
Thus,  the waves are very strongly attenuated,  especially the higher harmonics. In other
words, diurnal waves will dampen more rapidly than the annual. Lower the thermal
diffusivity, more rapid the attenuation.  This formulation is widely used to study the soil
temperature regime.  Yet, it is appropriate to bear in mind that it is a simplified view of
otherwise more complex situation. Soil temperature is dependent on convective, latent and
radiative heat exchange between soil and atmosphere. All this is not accounted for. Effect
of occasional rains is ignored.  Soil is assumed to be homogeneous,  which often is  not
the case. Moisture regime varies in soil with depth, which will change the thermophysical
2 / 1
2  


 


=
k
w ω
−
2 / 1
2  


 


=
k
ω
α
k 2
ω
α =
z
k
z
e or e
2
ω α − −7
properties assumed constant here.  Nevertheless, as we will see presently the main effects
are well captured by the above formulation.
Soil Temperature  Regime at Ahmedabad
In order to make equation (8) specific to Ahmedabad, we need to determine   Ta ,  A0,  and
∈  from empirical data.  Although an approximate magnitude of average soil temperature
could be derived from our data,  it would not be satisfactory, being based on only one-year
data. Average soil temperature is expected to be equal to the (long-term) annual mean air
temperature.  Mean air temperature for Ahmedabad based on ten-year data, is published in
Handbook of Solar Radiation Data of India [7].  The mean is  27
oC.   We will use this as
an approximation of the average soil temperature (Ta).
Amplitude  A0   of the annual temperature wave at the soil surface is 10
oC (table-2,
column-3).    Value of  ∈   can be determined by noting (figure-3) that the peak of the
wave at the surface occurs at about the day  105 (April 15).  Using these values soil
temperature regime at Ahmedabad can be described by,
Parameter,  ∝  relates to the thermophysical property of soil.  Probe is installed on a lawn,
which has some shrubbery nearby. Soil samples were drawn from three locations as the pit
was dug and tested at Soil Mechanics Laboratory of L.D. Engineering College,
Ahmedabad. Test results given below indicated that the soil is silt loam.
Soil Sample depth : 1.5 m
      Field moisture content:  15.74  (% d.b)
      Grain size analysis :    Sand - 48%,  Silt - 41%,   Clay - 11%,
() ) 9 ( ..........
365
2
cos 10 27 ) , (
105
 

 
 − + =
− − z e z t T
t z α
π α8
The Lab is not equipped to measure thermal diffusivity.  Values for a set of materials
including soils of various types (both wet and dry) are tabulated in  [5, 6].  We will use the
values for wet and dry loam drawn from these sources.
Amplitude Attenuation and Phase Lag : Measured and Predicted
Attenuation
Figure-4  shows the waves at the surface,  1-m,  2-m  and  3-m  depth using equation (9)
with thermal diffusivity of wet loam.  Note the amplitude of the wave at surface is  10
oC.
We, of course, have set this.  The amplitudes get attenuated with depth.  At  1-m depth it is
reduced to 6.7
oC,  at 2-m  to  4.4
oC  and at  3-m,  2.9
oC.  Normalized magnitudes of these
are listed in  table-3  for comparison with the ones resulting from our measurements.
Table also lists the computed values for dry loam.  Note that the measured values lie
between the wet and dry loam values.  Accordingly, these can be considered reasonable.
Phase Lag
Figure-4  clearly shows the increase in phase lag with depth.  Occurrence of peaks is
delayed at deeper layers.  The peak of the wave at  1-m  depth for instance occurs about 24
days later than that of the wave at surface, which occurs near about  April 15.  At  2-m
depth the delay increases to  48 days and at  3-m depth to 72 days.  Delay in occurrence of
peaks is evident in the measured values as well  (figure-3), though it is difficult to tell
clearly the magnitude of delay.  Occurrence of rains in late June, July and August cools
the surface tending to flatten  the peaks.  Presently  we will conclude only that the
attenuation and phase lags predicted by equation (9) are broadly supported by the
empirical results.9
Conclusion
1.  Measurement of temperature upto the depth of 3-m at Ahmedabad displays the
pattern known to exist elsewhere.  Diurnal fluctuations diminish rapidly with
depth, such that the temperatures at  1-m  and beyond  become constant except for
seasonal changes.  Amplitudes of annual wave too diminish with depth, but less
rapidly than the diurnal.
2.  Temperature at 1-m depth varies from a low of 21
oC in January to a high of 30
oC
in June.  At  2-m depth the variation in between 22
oC - 28.4
oC.  At  3-m depth it is
between  24
oC and 29.8
oC.  The strata between   2-m  to  3-m  appears well suited
for siting of earth tube heat exchanger.   Amplitudes will of course diminish further
if one went deeper.  But then,  the cost of  trenching will increase without
significant reduction in amplitude.10
Table-1
Amplitudes of Diurnal Temperature Fluctuation ( 
oC )
Day +1 m
(ambient)
0
(soil surface)
-1 m -2 m -3 m
January  15 8.7 5.45 0 0 0
February  15 8.5 7.8 0 0 0
March  15 10.5 12.5 0 0 0
April  15 10.1 14.85 0 0 0
May  15 6.9 11.95 0 0 0
June  20 6.4 8.65 0.1 0 0
July  20 6.95 8.2 0 0 0
August  20 4.4 5.5 0.35 0.15 0.3
September 15 3.4 2.3 0 0 0.05
October  11 5.5 3.1 0 0.05 0.05
November 16 5.9 3.9 0 0.05 0
December 13 65 5.6 0 0.05 011
Table-2
Ambient and Soil Temperature on a typical day of each  month at the
Campus of  Indian Institute of Management, Ahmedabad
Month Ambient ( 
0C) Soil  Temperature ( 
0C) at Depth
Date
1 m 0 m
(Soil Surface)
-1 m -2 m -3 m
January 15 20.0 15.5 20.9 22.5 24.2
February 15 23.1 17.1 20.9 22.0 25.2
March  15 27.4 26.4 22.5 22.3 25.8
April   15 31.6 35.6 25.8 23.8 26.6
May   15 33.8 34.8 28.8 26.4 26.6
June  20 31.8 34.8 30.2 28.1 29.8
July   20 28.7 31.9 30 28.4 28.5
August  20 28.0 26.3 25.6 26.3 28.9
September   15 28.0 27.5 26.5 26.6 25.6
October  11 27.7 27.6 26.0 26.7 26.1
November  16 24.3 24.5 23.9 25.2 24.3
December   13 21.0 20.1 22.2 24.0 24.4
Amplitude 6.9 10.0 4.6 3.2 2.8
Note :  Values are mean of 24 hours.12
Table-3
Amplitude Attenuation
Depth
( m )
Amplitude
Measured
(normalised)
Normalised
Amplitude
Computed
(wet loam)
Normalised
Amplitude
Computed
(dry loam)
01 1 1
1 0.45 0.67 0.48
2 0.31 0.44 0.23
3 0.27 0.29 0.11
Note :   Thermal diffusivity (k) for wet loam was taken to be
             0.0518 m
2/day,  for dry loam  0.0155 m
2/day)13
Digital Indicator
Sensor   +1 m
Sensor   3 m
Sensor   2 m
Sensor   1 m
Sensor    0 m
GL
Leads
Figure-1:   Temperature  Probe at IIM Ahmedabad Campus14
Figure-2:  Soil Temperature at various depth and ambient air 
           at IIM campus Ahmedabad 20 - 21 August 1999
20
22
24
26
28
30
32
34
18:30 20:30 22:30 0:30 2:30 4:30 6:30 8:30 10:30 12:30 14:30 16:30 18:30
Hour of Day
T
e
m
p
e
r
a
t
u
r
e
(
0
C
)
3m
2m
1m
Amb15
 Figure-3:  Ambient and Soil temperature at the Campus of  IIM Ahmedabad 
10
15
20
25
30
35
40
February April June August October December
Month
T
e
m
p
e
r
a
t
u
r
e
 
(
0
C
)
1
0
-1
-2
-316
Figure-4:   Simulated  Soil  Temperature  Regime  at  Ahmedabad
0
5
10
15
20
25
30
35
40
0 50 100 150 200 250 300 350 400 450
Day
T
e
m
p
e
r
a
t
u
r
e
 
(
o
C
)
z=0
z=1
z=2
z=317
References
1.  Krishnan A. and GGSN Rao (1979).  Soil temperature regime in arid zone of India.
Arch. Met. Geoph. Ser. B, 27,   15-22.
2.  Tripathi R.P. and B.P. Ghildyal (1979). Thermal regime of Mollisols under high water
table conditions.   Agricultural Meteorology, 20-493.
3.  Chaudhary T.N. and B.S. Sandhu (1982).  Soil temperature and plant growth. In:
Review of Soil Science Research in India Part 1,  International Convention of Soil
Science, New Delhi.
4.  Singh Baldev and Sandhu (1979). Effect of irrigation, mulch, and crop canopy in
forage maize.   Journal of Soil Science, 27-225.
5.  Hewitt G.F., G.S. Shires and T.R. Bott (1994).  Process heat transfer.  CRS Press, New
York.
6.  Carslaw H.S. and J.C. Jaeger (1959). Conduction of heat in soils.  Clarendon Press,
Oxford.
7.  Mani A. (1984).  Handbook of solar radiation data for India.  Department of science
and technology.  Government of India.  Indian Institute of Tropical Meteorology.
Allied Publishers Private Limited, New Delhi.

Conduction of heat in soils.

Effect of irrigation, mulch, and crop canopy in forage maize.

Handbook of solar radiation data for India. Department of science and technology. Government of India. Indian Institute of Tropical Meteorology. Allied Publishers Private Limited,

Process heat transfer.

Soil temperature and plant growth. In:

Soil temperature regime in arid zone of India.

Thermal regime of Mollisols under high water table conditions. Agricultural Meteorology,

Soil Temperatures Regime at Ahmedabad

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Soil Temperatures Regime at Ahmedabad

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