International Journal of Geosciences, 2010, 1, 87-98
doi:10.4236/ijg.2010.12012 Published Online August 2010 (http://www.SciRP.org/journal/ijg)
Copyright © 2010 SciRes. IJG
Spatial and Te mporal Variability of Soil Moisture
Vanita Pandey1, Pankaj K. Pandey2*
1Department of So il and Water Engineering, CAEPHT, Central Agricultural University, Gangtok, India
2Department of Agricultural Engineering, North Ea stern Regional Institute of Science & Technology,
Nirjuli Itanagar Arunachal Pradesh, India
E-mail: pandeypk@gmail.com
Received February 11, 201 0; revised Marc h 15, 2010; accepted April 20, 2010
Abstract
The characterization of temporal and spatial variability of soil moisture is highly relevant for understanding
the many hydrological processes, to model the processes better and to apply them to conservation planning.
Considerable variability in space and time coupled with inadequate and uneven distribution of irrigation wa-
ter results in uneven yield in an area Spatial and temporal variability highly affect the heterogeneity of soil
water, solute transport and leaching of chemicals to ground water. Spatial variability of soil moisture helps in
mapping soil properties across the field and variability in irrigation requirement. While the temporal vari-
ability of water content and infiltration helps in irrigation management, the temporal correlation structure
helps in forecasting next irrigation. Kriging is a geostatistical technique for interpolation that takes into
account the spatial auto-correlation of a variable to produce the best linear unbiased estimate. The same has
been used for data interpolation for the C. T. A. E. Udaipur India. These interpolated data were plotted
against distance to show variability between the krigged value and observed value. The range of krigged soil
moisture values was smaller than the observed one. The goal of this study was to map layer-wise soil mois-
ture up to 60 cm depth which is useful for irrigation planning.
Keywords: Soil Moisture, Spatial & Temporal Variability, Kriging
1. Introduction
Spatially and temporally varying soil moisture is being
increasingly used as input to hydrological and meteoro-
logical models. Knowledge of spatial and temporal vari-
ability of field soil helps in characterization of the soil.
The use of mathematical model to simulate the water and
solute movement into the field soil has accelerated the
need to understand the variability of soil properties that
affect the interpretation of model output variability.
Soil moisture spatial distribution varies both vertically
and laterally due to evapotranspiration and precipitation,
influenced by topography, soil texture, and vegetation.
While small scale spatial variations are influenced by
soil texture, larger scales are influenced by precipitation
and evaporation [1]. Field soil encompasses considerable
inherent variability in their texture, structure and physi-
cal and chemical properties due to variability in parent
material and other soil forming factors. Variability in
water holding capacity of the soil can adversely affect
yield and would complicate irrigation scheduling. Thus,
variability has been found to have significant affect on
moisture movement, process and the parameters associ-
ated with this process. The characteristics of soil mois-
ture variability is essential for understanding and pre-
dicting land surface processes, that varies based on to-
pography, soil texture, and vegetation at different spatial
and temporal scales [2]. Thus, the spatial characteristics
is a key parameter used in the background statistical er-
ror models as well dynamic propagation of the modeled
state uncertainty in data assimilation modeling systems
[3-7].
Temporal variability of soil water properties are in-
duced by tillage, cropping and other management prac-
tices. Surface seal and compaction of soil are predomi-
nant phen omenon tha t affects wa ter flow.
The geostatistical studies for soil moisture variability
[8-13] are carried out at the scales of small catchments
areas (1-5 km2). S. G. Reynolds [14] found a close relation
between sizes on soil moisture variability, with R2 of 0.7
considered to be best. To reduce uncertainty, O. R. Dani
and R. J. Hanks [15] used state space models for soil water
V. PANDEY ET AL.
Copyright © 2010 SciRes. IJG
88
balance and evapotranspiration in application to spatial
and temporal estimation methods. B. P. Mohanty, et al. [16]
analyzed and mapped field scale soil moisture variability
using high resolution ground based data. J. A. Huisman
[17] studied ground penetrating radar for mapping soil
water content at intermediate scales between point and
remote sensing measurements.
A variogram, a central concept in geostatistics, is used
to analyze the structure of spatial variation of soil mois-
ture. The experimental variogram characterizes the spa-
tial variability in the measured data. This variogram is
used in Kriging to determine soil moisture values at un-
sampled locations. This section first describes the effect
of selection of active separation distance for best model
fitting. The variogram structure consists of the nugget
(the variance at zero lag distance), sill (the variance to
which the variogram asymptotically rises), and decorre-
lation length (range of spatial dependence). The decorre-
lation length varies based on minimum distance between
sampling locations and size of sampled area [13]. In this
study the average grid resolution (40 m × 40 m) of soil
moisture data layer – wise up to 60 cm depths were ana-
lysed. One of the major issues in variographic an alysis is
the selection of total lag distance for variogram fitting to
experimental data. As the separation distance increases,
after half of the total separation distance, the variogram
starts to decompose at larger separation distances due to
the reduced availability of pairs. Thus to obtain robust
estimation of the variogram, we ignored pairs at larger
separation distances that usually have smaller variance.
The separation distance is selected based on the criterion
that 95% pairs should have been used for variogram
model fitting. Kriging is an interpolation techniqu e based
on the theory of regionalized variables developed by G.
Matheron [18]. Kriging offers a wide and flexible variety
of tools that provide estimates for unsampled locations
using weighted average of neighboring field values fal-
ling within a certain distance called the range of influ-
ence. Kriging requires a variogram model to compute
variable values for any possible sampling interval. The
variogram functionality in conjunction with kriging al-
lows us to estimate the accuracy with which a value at an
unsampled location can be predicted given the sample
values at other locations [19-21]. Kriging provides opti-
mal interpolation of so il moisture at grid points in a sp a-
tial domain based on autocorrelation in the variograms.
The theoretical variogram model (Gaussian, spherical,
exponential, or linear) that best fits the experimental
variogram was selected for soil moisture mapping using
the block Kriging technique [22].
We are not aware of any documented study on layer-
wise soil moisture mapping available for study area.
Hence, the study of spatial and temporal distribution of
soil moisture helps in mapping soil properties across the
field and variability in irrigation requirement, which is
helpful in real time management at field scale.
2. Material and Methods
2.1. Measurement of Soil Moisture
The instructional farm of CTAE, Udaipur having an area
of 2.16 hectare was selected for soil sampling. The area
was surrounded by vegetation and the field was bare at
the time of observation. Grid having a si ze of 40 m × 40 m
was formed in that area. Soil samples were taken at each
grid point at the depths of 7.5 cm, 15 cm, 30 cm, 45 cm
and 60 cm. These soil moisture data were then used for
analysis of spatial and temporal variability. One set of
soil moisture was recorded prior to irrigation and the
other, after irrigation.
2.2. Autocovarience and Autocorrelation
Representation of variability of soil properties by fre-
quency distribution does not assume that the values are
random and independent. Physically, it is expected that
the values of any properties of two neighboring points
will be closer to each other then those at two distant
points.
Limiting consideration of spatial relationship only to
the second order, i.e., second moment, the relationship
expressed by the auto covariance as a function of separa-
tion distance ()Ch can be presented mathematically,
thus,
 
()( )()ChEZXZXh

(1)
2
() ()EZXZXh

The computational form of ()Ch is


2
()
1
1() ()
2()
Nh
ii
i
hzxzxh
Nh

(2)
where, γ(h) = Semi-variance for interval distance class
(h), i
z = measured sample value at point i, i
zh
=
measured sample value at point I + h, and ()Nh = total
number of sample couples for the separation interval h.
The least squares best-fit criteria is used to fit a model
to the experimental semi-variance data through which the
nugget (C0), sill (C0 + C), and decorrelation length or
range of spatial dependence (A0). From Equation (1) and
(2), it is clear that C0 is the variance σ2 or its sample es-
timate of the variable. The ratio, C(h)/C0 is auto correla-
tion, γ (h), having values between +1 and –1. It is also
apparent that for C(h) and γ (h) to exist, the mean and
V. PANDEY ET AL.
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89
variance of the population must be finite and constant in
the area of consideration.
2.3. Semivarience and Semivariogram
The Quantification of spatial dependence is called semi
variance. The intrinsic hypothesis states that for any two
locations separated by lag distance, ‘h’, the variance of
the differences of the measured property is finite and
dependent of its (x, y) position. The Variance d epends on
the lag distance (h)

() ()2Varz xz xhh
 (3)
Therefore, the model of soil variance is
Z(x) = μ +ε(x) (4)
where, ()zx = expected value μ = mean, ε(x) = residual
value
Semi variance,

h
is a function of h. This equa-
tion is similar to Equation (1). Expected ε(x) is spatially
dependent random component with zero mean and vari-
ance defined by

h
. The semi variance may be esti-
mated as a function of ‘h’ by Equation (2). The semi-
variogram is a graphical model that indicates the spatial
relationship between measured values. The com- mon
characteristics of semivariogram are that they will in-
crease from some minimum value called the nugget at a
zero separation distance to some finite maximum value
as the separation distance increases. The maximum value
of a variogram is typically an estimate of variance. The
distance at which the variogram first reaches the sill is
termed as the range. The range is an estimate of the dis-
tance over which the measurements are spatially corre-
lated and may reflect the physical extent of similar soil
bodies.
2.4. Selection of Model
Before estimation of soil moisture, a mathematical model
has to be fitted to it. Selection of model is based on sill,
range and nugget of the experimental semivariogram
model. From the various models, i.e., random model,
spherical model, linear model, logarithmic model and
parabolic model, considered for the observations of the
present study, the spherical model was found to be best
suited for the purpose.
Spherical model is probably the most commonly used
model. It has a simple polynomial expression and its
shape matches well with the observed data. The model
ensures almost a linear growth up to a certain distance
before stabilizing. Th e tangent at origin intersects the sill
at a point with an abscissa (2/3*a) and slope of this tan-
gent originates at 3c/2a. This can be useful while fitting
models. It is characterized by two parameters c and a,
and mathematically represented by an equation as:
3
3
3
() <
22
() ()
hh
hC forha
aa
hCforha





After selecting the model, kriging technique was used
for interpolation of values. In the present study, block
kriging is used fo r estimating the krigged valu e. The grid
system was developed to create a common reference
point for all information.
Kriging is the application of geostatistical techniques
for interpolation. The estimation fulfills the following
conditions (Cuenca, and Amegee, 1987).
1) Linearity: Kriging estimate is formed from a linear
combination of measured data at surrounding points. It
can be expressed as:
112 233
()( )()( ).......()
nn
KX KXKX KXKX
 

where, K(X) = value of parameter at (X), λi = weight as-
signed to each measured value of estimation
2) Unbiasedness: The condition of unbiasedness is that
mean of the estimates should be equal to the mean of the
measured value, that is:
'' () ()EK XEKXm


But ''
1
() n
i
i
EK Xm


where, m = mean. The above equation gives the fol-
lowing result
1
n
i
i
= 1, that is, the sum of individual
weight λi , must be equal to unity.
3) Best Criterion: As per the third constraint, the vari-
ance should be minimum, i.e., the error between the
kriging estimates and the true value is minimized. To
fulfill this condition, derivatives of the variance with
respect to weights λ1 should be zero. As there are n
weights, the above procedure will produce n equations
with n unknown weights. Since there is one more Equa-
tion, i.e.,
1
1
n
i
i
hence, there is n + 1 equation with n unknown. To miti-
gate the situation, one new unknown, i.e., Lagrangian
multiplier a constant equal to zero has to be added. For
convenience Lagrangian multiplier has been taken as μ.
Therefore, kriging system of equation in terms of semi
variance function appears as:
111 21231311
121 22232322
112 233
()( )().......( )()
()()() .......()()
.
.
()()() .......()()
nn p
nn p
nnnn nnnp
hhhh h
hhhh h
hhhh h
 
 
 
 

 
V. PANDEY ET AL.
Copyright © 2010 SciRes. IJG
90
By solving the above system all the assigned weights
are determined and value of soil moisture is estimated at
any point p.
2.5. Cross Validation
The estimated krigged values are subjected to cross vali-
dation. For a cross validation at each point, the reduced
estimation error is obtained by dividing the estimation
error by the standard deviation of estimation. The good-
ness of estimation is expressed by two conditions on the
reduced estimation errors: 1) minimum, nearly zero
mean and 2) variance near to unity.
3. Results and Discussion
3.1. Statistical Analysis of Observed Data
This was conducted in two stages
1) The traditional summary of statistics, i.e., mean,
standard deviation, coefficient of variation, skewness and
kurtosis were estimated
2) Semi variance was defined and difference in nugget,
sill and range were examined for each depth.
3.2. Summary Statistics of the Soil Moisture
Data
The different statistical properties for the soil moisture at
different depths and for both observations were calcu-
lated. It was observed that before irrigation the soil was
very dry with mean moisture con tent of 2.89% to 8.68%.
After irrigation, this has been a drastic increase from
10.16% to 11.88%. At lower depths, the variation in
mean is almost constant before and after irrigation.
3.3. Estimation of Geostatistical Parameters
The semi variance was computed using Equation (3) for
different lag distance. Using the data (Table 1) experi-
mental semivariograms for different lags was plotted. A
model was fitted to the plotted experimental semivario-
grams. The parameters of the fitted model are given in
Table 2. The fitted spherical model can be expressed as:


3
12
1
2
3
r
h
r
h
CCh o
Fo r 0 < h < r (5)
10 CCh
For h > r
The experimental semivariogram and fitted model
layer-wise upto 60 cms depth as shown in Figures 1(a)
to 5(b). Nugget indicates error of estimation of parameter
at the smallest sampling interval. If nugget expressed as
a percent of sill, is less than 24 percent, the variable may
be considered showing a strong spatial dependence; if it
is between 25 to 75 percent, it is considered as moder-
ately dependent and if it exceeds 75 percent spatially, it
is said to have poor dependence.
3.4. Contour Maps of Soil Moisture Variability
Contour maps were prepared for all the depths and for
both dry and wet condition, using surfer. Surfer uses the
inverse distance technique for interpolating irregularly
spaced measured data to a specified grid size.
In first set of observations (dry condition), it was ob-
served that for 7.5 cm depth maximum variability is ob-
served at the corner of the field, which is mainly due to
vegetation, which reduce evaporation. In the centre of
Table 1. Lag, average distance and semi variance for soil moisture at different depths (cm).
Semivarince
First Observation Second Observation
Lag Average
Distance (m)
7.5 15 30 45 60 7.5 15 30 45 60
1 40.00 2.8 2.45 3.59 8.46 15.87 16.73 3.62 5.79 9.74 8.04
2 56.57 2.04 2.34 2.72 6.43 11.64 20.32 3.54 6.03 8.05 8.58
3 80.00 3.04 2.33 2.90 5.32 11.35 17.57 4.37 6.08 10.07 7.85
4 89.44 2.41 1.85 2.17 3.81 7.68 14.42 3.95 6.85 8.32 9.86
5 113.14 5.86 5.24 7.21 15.70 30.01 4.92 4.12 5.46 11.82 9.46
6 120.00 4.47 5.17 6.09 10.84 17.54 15.24 6.11 11.69 6.94 9.46
7 126.49 3.63 2.46 3.37 5.95 9.68 26.00 7.05 14.09 7.47 9.05
8 144.22 1.23 5.24 3.51 2.50 3.89 7.37 6.35 9.18 8.51 3.777
9 162.81 4.82 4.39 3.36 2.42 7.41 19.93 11.31 14.74 7.47 7.33
10 178.89 7.14 10.04 8.22 11.57 14.69 8.35 9.24 13.37 44.14 8.62
11 202.26 6.91 4.43 3.06 4.99 5.27 6.09 8.04 7.45 2.39 1.17
12 215.41 9.22 7.95 4.48 0.38 0.56 11.55 13./83 14.83 6.22 4.08
V. PANDEY ET AL.
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91
Table 2. Different parameters of the fitted model of semivariogram.
S.No Depth (cm) Type of Model Range Nugget Sill Nugget as % of Sill Spatial Dependence
First Observation
1 7.5 Spherical 125 0.45 3.05 14.75 Strongly dependent
2 15 Spherical 113.1 0.327 2.947 11.09 Strongly dependent
3 30 Spherical 110 0.46 3.1 14.84 Strongly dependent
4 45 Spherical 113.09 0.638 5.748 11.09 Strongly dependent
5 60 Spherical 113.09 1.1787 10.61 11.10 Strongly dependent
Second Observation
1 7.5 Spherical 125 2.1 14 15 Strongly dependent
2 15 Spherical 113.09 0.548 4.94 11.09 Strongly dependent
3 30 Spherical 113.09 0.836 7.525 11.10 Strongly dependent
4 45 Spherical 113.09 0.848 7.634 11.10 Strongly dependent
5 60 Spherical 113.09 0.804 7.244 11.09 Strongly dependent
the field, soil moisture is almost constant Figure 6(a),
which is due to the bare field, which provides a free
evaporation surface.
As shown in Figure 7(a) for 15 cm depth, variability
is large as compared to 7.5 cm depth, but the same pat-
tern is observed at this depth, i.e., maximum in the cor-
ners and minimum at the centre. Mean moisture content
at 15 cm depth is higher than 7.5 cm depth.
As shown in Figures 8(a), Figure 9(a) and Figure 10
(a) shows a uniform spatial variability with 30 cm depth,
45 cm depth and 60 cm depth respectively. Mean mois-
ture content was found higher at 60 cm depth than other
depths.
In the second set of observations, it was observed that
for 7.5 cm depth, moisture content at the corner of the
fields is almost constant whereas in the middle it is very
high which shows non uniform supp ly of water as shown
in Figure 6(c).
For 15 cm depth, high spatial variability is obtained as
compared to 7.5 cm depth Figure 6(c). In the middle, the
moisture content is very high at 7.5 cm depth due to the
same reason of non uniform supply of water as shown in
Figure 7(c).
For 30 cm depth, 45 cm depth and 60 cm depth the
variability is almost same Figure 8(c), 9(c) and 10(c),
respectively.
From the maps, it was observed that in the first set of
observation high spatial variability was observed as com-
pared to th e second set of obse rvation. This is because of
the reason that the second sets of observation were taken
after irrigation. Soil profile is almost saturated with water.
Some variability was observed, which shows the non
uniform supply of irrigation water. The maximum vari-
ability is observed up to 30 cm depth where as for 45 cm
and 60 cm depths, variability is almost constant in both
sets of observations. In both sets of observations maxi-
mum spatial variability was observed at 30 cm depth
(Figures 8 (a) and 8(c)).
0
1
2
3
4
5
6
7
8
9
10
050100150 200250
Average distance (m)
S emivar ian ce(%)
3
31
( )0.453.050
21252 125
( )0.453.05
hh
hforhr
hforhr

 
 

 
 


 
(a)
0
5
10
15
20
25
30
050100 150200 250
Average distance (m)
Semivariance
3
31
() 2.1140
2 1252125
() 2.114
hh
hforhr
hforhr


 





 
(b)
Figure 1. (a) Experimental semivariogram of first observa-
tion at 7.5 cm depth and fitted model; (b) Experimental
semivariogram of second observation at 7.5 cm depth and
fitted model.
V. PANDEY ET AL.
Copyright © 2010 SciRes. IJG
92
0
2
4
6
8
10
12
050100 150 200250
Average distance (m)
semivar i an ce (% )
3
31
( )0.332.9470
2113.12 113.1
( )0.332.947
hh
hforhr
hforhr


 





 
0
2
4
6
8
10
12
14
16
050100150 200 250
Average distance (m)
Semivarian ce (% )
3
31
( )0.5494.940
2 113.092113.09
( )0.5494.94
hh
hforhr
hforhr


 





 
(a) (b)
Figure 2. (a) Experimental semivariogram of first observation at 15 cm depth and fitted model; (b) Experimental semiva-
riogram of second observation at 15 cm depth and fitted model.
0
2
4
6
8
10
12
14
16
050100150 200 250
Average distance(m)
Semivariance (%)
3
31
( )0.463.10
2110 2110
( )0.463.1
hh
hforhr
hforhr


 





 
0
2
4
6
8
10
12
14
16
050100 150200 250
Average distance(m)
S emivari a n ce (%)
3
31
( )0.8367.5250
2113.092 113.09
( )0.8367.525
hh
hforhr
hforhr


 





 
(a) (b)
Figure 3. (a) Experimental semivariogram of first observation at 30 cm depth and fitted model; (b) Experimental semiva-
riogram of second observation at 30 cm depth and fitted model.
0
2
4
6
8
10
12
14
16
050100150 200 250
Average distance (m)
Semivariance (%)
3
31
( )0.6385.7480
2113.092 113.09
( )0.6385.748
hh
hforhr
hforhr


 





 
0
2
4
6
8
10
12
14
16
050100 150 200 250
Average distance (m)
Semivariance(%)
3
31
( )0.8487.6340
2 113.092113.09
( )0.8487.634
hh
hforhr
hforhr


 





 
(a) (b)
Figure 4. (a) Experimental semivariogram of first observation at 45 cm depth and fitted model; (b) Experimental semiva-
riogram of second observation at 45 cm depth and fitted model.
V. PANDEY ET AL.
Copyright © 2010 SciRes. IJG
93
0
4
8
12
16
20
24
28
32
36
050100 150 200250
Average distan ce (m)
Semivariance (%)
3
31
( )1.17910.610
2113.092 113.09
( )1.17910.61
hh
hforhr
hforhr


 





 
0
2
4
6
8
10
12
14
16
050100150 200 250
Average distance (m)
Semivarience (%)
3
31
( )0.817.240
2 113.092 113.09
( )0.817.24
hh
hforhr
hforhr


 





 
(a) (b)
Figure 5. (a) Experimental semivariogram of first observation at 60 cm depth and fitted model; (b) Experimental semiva-
riogram of second observation at 60 cm depth and fitted model.
Table 3. Statistical parameters of measured and krigged values of soil moisture.
Depth Observation Max. (%) Min (%) Range (%) Mean (%) Var. S.D (%) C.V
First observat i on
Measured 7.89 0.92 6.97 2.93 3.50 1.87 0.64
Krigged 5.29 1.12 4.17 2.87 1.55 1.25 0.43
7.5
Second observation
Measured
18.98 7.16 11.82 10.54 8.11 2.85 0.27
Krigged
14.55 5.89 8.66 10.48 5.90 2.43 0.23
First observat i on
Measured 7.67 1.44 6.23 4.07 3.27 1.81 0.44
Krigged 6.16 2.30 3.86 4.05 1.64 1.28 0.32
15
Second observation
Measured
15.12 7.26 7.86 10.16 4.90 2.21 0.22
Krigged
13.53 7.70 5.83 10.15 2.91 1.71 0.17
First observat i on
Measured 9.30 2.63 6.67 5.38 3.56 1.89 0.35
Krigged 7.68 3.33 4.35 5.33 1.91 1.38 0.26
30
Second observation
Measured
12.84 6.61 6.23 10.21 4.68 2.16 0.21
First observat i on
Measured 12.36 3.28 9.08 7.20 6.39 2.53 0.35
Krigged 11.29 4.37 6.92 7.22 3.60 1.90 0.26
45
Second observation
Measured
16.10 7.45 8.65 11.70 7.63 2.76 0.24
Krigged
14.36 8.59 5.77 11.64 3.33 1.82 0.16
First observat i on
Measured 14.60 3.25 11.35 8.68 11.8 3.43 0.40
Krigged 12.97 5.12 7.85 8.81 6.73 2.59 0.29
60
Second observation
Measured
16.63 7.60 10.30 11.88 5.60 2.37 0.20
Krigged
14.70 9.01 5.69 11.91 3.35 1.83 0.15
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94
3.5. Kriging of Soil Moisture
In order to estimate the soil moisture value at observation
point, the searching radius was determined, which was
based on spatial range observed in the fitted model of
semivariogram. The searching radius indicates that the
measurements within the range are to be considered to
estimate the soil moisture at that point. Range for each
depth as shown in Table 2.
By using Sill, range and nugget as shown in Table 1,
the krigged value of soil moisture were determined at
each depth with the help of Datamine software. Statisti-
cal parameters were calculated for measured and krigged
soil moisture values and the parameters are presented in
Table 3. Mean and measured krigged value is almost
same. By analyzing the statistical parameters, i.e., vari-
ance, standard deviation and coefficient of variation, it
was found that they have always been on the lower side
of the krigged estimate as compared to those obtained
with measured value, the trend is indicative of lesser
variability in the krigged estimates of soil moisture there-
by projecting more consistency and reliability. The lower
value of coefficient of variation of krigged value indi-
cates that there has been consistency in krigged estimates.
3.6. Comparison of Spatial Structure of
Measured and Krigged Soil Moisture
Contour maps of soil moisture variability were plotted
for measurement and krigged values for each depth and
for both observations and their variability and spatial
structure were compared (Figures 6(b), 6(d), 7(b), 7(d),
8(b), and 8(d), 9(b), 9(d), 10(b), 10(d)). Large variabil-
ity is observed in first observation, i.e., before irrigation
compared to second observation, which is spatially less
variable. For first observation large variability is observed
(a) (b)
(c) (d)
Figure 6. (a) and (b) measured and krigged value of soil moisture at 7.5 cm depth for dry condition,
(c) and (d) measured and krigged value of soil moisture at 7.5 cm depth for wet condition.
V. PANDEY ET AL.
Copyright © 2010 SciRes. IJG
95
(a) (b)
(c) (d)
Figure 7. (a) and (b) measured and krigged value of soil moisture at 15 cm depth for dry condition; (c)
and (d) measured and krigged value of soil moisture at 15 cm depth for wet condition.
(a) (b)
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96
(c) (d)
Figure 8. (a) and (b) measured and krigged value of soil moisture at 30 cm depth for dry condition;
(c) and (d) measured and krigged value of so il moisture at 30 cm depth for wet condition.
(a) (b)
(c) (d)
Figure 9. (a) and (b) measured and krigged value of soil moisture at 45 cm depth for dry condition;
(c) and (d) measured and krigged value of so il moisture at 45 cm depth for wet condition.
V. PANDEY ET AL.
Copyright © 2010 SciRes. IJG
97
(a) (b)
(c) (d)
Figure 10. (a) and (b) measured and krigged value of soil moisture at 60 cm depth for dry condition;
(c) and (d) measured and krigged value of so il moisture at 60 cm depth for wet condition.
at 30 cm depth as in Figure 8(a) and comparatively less
variability is observed at 7.5 cm depth as in Figure 6(a)
due to lack of moisture. After kriging, the variability was
reduced as shown in krigged map. Also the range of the
krigged values are less than that of the observed one
(Table 3).
For second observation the largest variability was ob-
served at 15 cm depth as in Figure 7(c), which was re-
duced drastically for krigged estimate whereas least
variability was observed at 7.5 cm depth. The range of
second observation indicates that the water is not uni-
formly distributed in the whole field. For the lower
depths, the variability is almost same for both sets of
observations for measured as well as krigged estimates,
because some time is required for water to percolate
down and during that time sufficient variability is ob-
served at lower depth.
From the maps, it was observed that the spatial vari-
ability is considerably reduced after kriging for each
depth, especially for second observation.
Contour maps of soil moisture for each depth were
plotted. Careful comparison of the contour map of soil
moisture envisaged that there has been considerable re-
duction in spatial variability in case of krigged estimates.
On the basis of the above discussion, it can be said that
the krigged values are more consistent and are true rep-
resentative of soil moisture values. Therefore, contour
maps developed with krigged estimates would be more
precise than those developed with measured value.
4. Conclusions
Based on the findings it can be said that the krigged val-
V. PANDEY ET AL.
Copyright © 2010 SciRes. IJG
98
ues are more consistent and true representative of soil
moisture values. Hence, on the basis of past soil moisture
values the krigged value of soil moisture at particular
time and space may be estimated. Statistical parameters
reflect that the variability of soil moisture reduces sig-
nificantly after kriging. These estimated values help in
proper irrigation scheduling along with necessary infor-
mation on the crops to be grown and expected yield of
the same.
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