Available online at www.sciencedirect.com

Catena 73 (2008) 125 – 133
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Temporal stability in soil water content patterns across agricultural fields
A.K. Guber a,b , T.J. Gish b , Y.A. Pachepsky c,⁎, M.T. van Genuchten d , C.S.T. Daughtry b ,T.J. Nicholson e , R.E. Cady eaDepartment of Environmental Sciences, University of California, Riverside, United States
Hydrology and Remote Sensing Laboratory, USDA, ARS, Beltsville, MD, United StatescEnvironmental Microbial Safety Laboratory, USDA, ARS, Beltsville, MD, United StatesdU.S. Salinity Laboratory, USDA, ARS, Riverside, CA, United StateseU.S. Nuclear Regulatory Commission, US NRC-ORR, Rockville, MD, United Statesb

Received 3 February 2007; received in revised form 20 August 2007; accepted 18 September 2007

Abstract
When a field or a small watershed is repeatedly surveyed for soil water content, locations can often be identified where soil water contents areeither consistently larger or consistently less than the study area average. This phenomenon has been called temporal stability, time stability, temporalpersistence, or rank stability in spatial patterns of soil water contents. Temporal stability is of considerable interest in terms of facilitating upscaling ofobserved soil water contents to obtain average values across the observation area, improving soil water monitoring strategies, and correcting themonitoring results for missing data. The objective of this work was to contribute to the existing knowledge base on temporal stability in soil water
patterns using frequent multi-depth measurements with Multisensor Capacitance Probes (MCPs) installed in a coarse-texture soil under multi-year
corn production. Water contents at 10, 30, 50, and 80 cm depths were measured every 10 min for 20 months of continuous observation from May 2001
to December 2002. The MCPs revealed temporal stability in soil water content patterns. Temporal stability was found to increase with depth. The
statistical hypothesis could not be rejected (P b 0.0001) that data collected each 10 min, each 2 h, each day, and each week had the same temporalstability. The locations that were best for estimating the average water contents were different for different depths. The best three locations for thewhole observation period were the same as the best locations for a month of observations in about 60% of the cases. Temporal stability for a specificlocation and depth could serve as a good predictor of the utility of this location for estimating the area-average soil water content for that depth.
Temporal stability could be efficiently used to correct area-average water contents for missing data. Soil water contents can be upscaled and efficiently
monitored using the temporal stability of soil water content patterns.
Published by Elsevier B.V.
Keywords: Temporal stability; Multisensor capacitance probe; Soil water content; Spatial pattern; Upscaling; Measurement frequency

1. Introduction
When a field or a small watershed is repeatedly surveyed forsoil water content, locations can be often identified where soil
water contents are either consistently larger or consistently lessthan the study area average. This phenomenon has been calledtime stability or temporal stability (Vachaud et al., 1985), temporal persistence (Kachanoski and de Jong, 1988), or rank

⁎ Corresponding author. USDA-ARS-BA-ANRI-EMSL, 173 Powder MillRd, BARC-EAST, Beltsville, MD, 20705, United States. Tel.: +1 301 504 7468.
E-mail address: ypachepsky@anri.barc.usda.gov (Y.A. Pachepsky).
0341-8162/$ - see front matter. Published by Elsevier B.V.
doi:10.1016/j.catena.2007.09.010

stability (Tallon and Si, 2003) in soil moisture spatial patterns.
Soil water content temporal stability has been demonstrated forthree different time-dependent characteristics of soil water
dynamics, namely: (a) water contents at specific depths; (b) soil
water storage usually interpreted as the total amount of soil water
within a range of depths; and (c) soil water fluxes estimated at
specific depths. Temporal stability causes time series of soil watercontents or fluxes at different locations to have similar shapes
while being offset from each other. Although a mechanistic
explanation of temporal stability in spatial soil water patterns has
never been given, its presence has been routinely observed inwidely different environments, provided measurement locations
did not change in time.

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A.K. Guber et al. / Catena 73 (2008) 125–133

Several consequences of temporal stability in soil water patterns (TSSWP) have caused more interest recently in thisfeature. One consequence is that one or more locations can often
be found that have a time series of the soil water content (or of
the soil water storage or the estimated soil water flux) very
similar to the time series of the average value of the soil watercontent (or soil water storage or soil water flux) across the study
area. Once such locations are found, only a small number of soil
moisture sensors at those locations are needed to monitor the
average soil water content across relatively large areas. This
aspect of TSSWP has been actively used in remote sensing ofsoil moisture because of the possibility to upscale water contents from several or even single point measurements to theaverage soil water content across a footprint area (Mohanty and
Skaggs, 2001; Cosh et al., 2003; Jacobs et al., 2004). Other
applications include establishing field- or catchment-wide antecedent moisture conditions for runoff simulations (Western
et al., 2003), relating spatio-temporal variations in soil water tothe onset of subsurface flow as measured with a network of
piezometers (Penna et al., 2006 ), and upscaling soil moisturedata in irrigated and dryland crops (Rolston et al., 1991; Rocha
et al., 2005).
Another consequence of TSSWP is that relative differences
between average soil water contents across the study area andwater contents at specific points within this area, may remain
relatively constant. In other words, the pattern of variation acrossthe study area remains more or less the same, even though theaverage soil water content changes. This aspect of TSSWP has
been used to estimate time series of the soil moisture content at
locations for which only a few data are available, but with
continuous records available from nearby locations (Pachepsky etal., 2005; Fernández-Gálvez et al., 2006). Downscaling of remotesensing data of soil moisture based on the stability of patterns has
also been suggested (Narayan and Lakshmi, 2005). Spatial
patterns of moisture-affected soil properties have similarly
demonstrated temporal stability (Goovaerts and Chiang, 1993;
Douaik et al., 2006), a feature that was further used to explain
spatial variability in crop yield (Cassel et al., 2000; King et al.,2005; Starr, 2005).
Although information on TSSWP has been steadily accumulating, several contentious questions require more insight. The useof TSSWP to decrease the number of monitoring devices requires
the selection of a time period to identify locations that can be used
to estimate time series of the average soil water content, soil water
storage, or flux measurements. Grayson and Western (1998),
among others, recognized that the observation time span has to be
split into a training period during which the best locations forrepresenting the averaged soil water patterns are identified, and avalidation period for testing the “best” locations. MartínezFernández and Ceballos (2005) recommended using one year as a
training period. Soil water contents in their study were measured
every two weeks. Unfortunately, currently it is not known how thefrequency of soil moisture measurements affects the selection of
the training period.
No conclusive results have been obtained on how andwhere to identify the “best” locations for the purpose of demonstrating and using TSSWP. Da Silva et al. (2001) found thatclay content and organic matter can serve as good explanatory
variables, whereas topographic variables cannot. On the contrary, topography and vegetation rather than soil properties
appeared to be leadings factors of TSSWP in a study ofGomez-Plaza et al. (2000), while Jacobs et al. (2004) indicatedthat locations with mild slopes consistently exhibited timestable features. Grayson and Western (1998) found that the“best” sites to represent catchment average soil moisture werelocated in areas that were neither strongly convergent nor
divergent, and tended to be near the mid-slopes or in areas that
had topographic aspects close to the average. Jacobs et al.
(2004) observed that sampling sites with the highest sandcontent tended to generate the least time stability, whereas
Mohanty and Skaggs (2001) found better time stability on a
sandy loam soil than a silt loam. Tallon and Si (2003) observedthat time stable sites showed poor relationships to soil andtopographic properties, thus suggesting the absence of a single
dominant control.
Several studies indicate that TSSWP may be affected by thetype of soil water sensor used. Kirda and Reichardt (1992) foundthat spatial patterns in soil water demonstrated temporal stability
when measured with neutron probes, but not when tensiometers
or gypsum blocks had been used. These authors hypothesized thatthe soil water sensor has to average over a sufficient soil volume
to uncover temporal stability. Van Pelt and Wierenga (2001)
demonstrated temporal stability in pressure heads measured withtensiometers. Mohanty et al. (2000) found little or no temporalstability in measurements of surface soil water contents in the
Little Washita watershed with theta probes that were inserted
anew at each location for each sampling. However, they demonstrated excellent temporal stability using the same measurement technique in the Walnut Creek watershed (Jacobs et al.,2004). Although multisensor capacitance probes (MCPs) haverecently become more popular for measuring soil moisture
contents (Starr and Paltineanu, 2002), little is known about
TSSWP assessment using MCPs. We were aware only of one
study, by Tallon and Si (2003), in which MCPs had been used
to investigate temporal stability in the soil water contents ofChernozem and Regosol.
Whereas temporal stability in soil water contents has been
amply demonstrated, the presence of temporal stability in estimated soil water fluxes is less obvious. Reichardt et al. (1993)
concluded that it was not feasible to estimate mean field behavior
with respect to soil water fluxes due to soil variability, if fieldmeasured hydraulic conductivities and pressure heads are used toestimate water fluxes and pressure gradients. It is not known
if temporal stability in estimated soil water fluxes can bedemonstrated, and whether the same locations can be used toestimate time series of average soil water contents and averagesoil water fluxes.
The objective of this study was to contribute to existingknowledge on temporal stability in soil water patterns using
extremely frequent multi-depth measurements with Multisensor
Capacitance Probes installed in a soil profile under multi-year
corn production. In this paper we investigate: (a) the effect ofmonitoring frequency on temporal stability and selection of thebest locations to estimate the area-average soil water content; andA.K. Guber et al. / Catena 73 (2008) 125–133

127

Fig. 1. Layout of fields, elevation map, and soil water probe locations; A, B — the field code, H, M, and L — range of distances (high, medium, low) to theimpermeable layer, 1 to 4 — replication number.

(b) using temporal stability to correct the average soil watercontents for missing data from individual locations.
2. Materials and methods
2.1. Soil water monitoring
The research site is part of the Optimizing Production inputs
for Economic and Environmental Enhancement (OPE3)
research site located at the USDA-ARS Beltsville Agricultural
Research Center, in Beltsville, Maryland (39° 01′ 00″ N, 76°
52′ 00″ W). The site is part of a 25-ha watershed formed fromfluvial deposits with slopes ranging from 1 to 4% (Gish, 2002).
Data from two fields at the site with a total area of 6 ha wereused in this study (Fig. 1). The fields were under continuous
corn production. Each year the tillage practices were the same,with fields being disked about one month prior to a second
disking operation, followed by planting. Soils at these fields
have been classified as a coarse loamy, siliceous, mesic Typic
Hapludults, and the fine–loamy, siliceous, semiactive, mesic
Aquic Hapludults with either well or excessively well drainage.
On average, the soil has a coarse loamy sand surface horizon(0–25 cm, organic matter 1.2–5.1%), followed by a sandy loam
horizon (25–80 cm), and a loam horizon (80 –120 cm), withloamy sand and fine-textured clay loam lenses between 120 and
250 cm. The lenses in the latter form a nearly impermeable layer
in this soil (Gish et al., 2002) that prevents deep leaching andcauses lateral movement of water and solutes. This subsurface

layer furthermore has numerous localized depressions that form
braided flow pathways throughout the field causing drainage
toward a riparian wetland and a first-order stream.
The capacitance probes (EnviroSCAN, SENTEK Pty Ltd.,South Australia) were installed in the spring of 1998 to better
understand surface and subsurface soil water dynamics. For
details on sensor location and installation, see Gish et al. (2002).
Each sensor was calibrated before installation (Paltineanu andStarr, 1997). In this study we used data from 24 soil moisturemultisensor capacitance probes (Fig. 1) that were installed at
depths of 10, 30, 50, 80, 120, 150, and 180 cm, with watercontents recorded each 10 min for 610 days from May 1, 2001
to December 31, 2002. Depths of sensor installation at different
locations are shown in Table 1.
Table 1
Depths of sensor installation by locations, “+” — sensors are installed, “−” nosensors at this depth
k

1
2
3
4
5
6
7

Depth,
cm

Location
AH1, AH2, AH3,
AH4, BH1, BH2,
BH3, BH4

AM1, AM2, AM3,
AM4, BM1, BM2,
BM3, BM4

AL1, AL2, AL3,
AL4, BL1, BL2,
BL3, BL4

10
30
50
80
120
150
180

+
+
−
+
−
−
−

+
+
+
−
+
+
+

+
+
+
+
+
+
+

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A.K. Guber et al. / Catena 73 (2008) 125–133

Fig. 2. Example of monthly soil water dynamics measured with the MCP probes at a depth of 10 cm. Combine the letters on a panel with the curve number in the legend
to obtain the MCP ID of for the individual curve (e.g., red curve of top left panel shows data from the AH2 MCP).

2.2. Evaluating temporal stability in soil water patterns

where θikj is the water content measured at location i at the jthmeasurement time at the kth depth, and θ̄ kj is the average watercontent at the jth measurement time at the kth depth:P
1 X Nkhkj ¼hð2Þ
i¼1 ikjNkseparately for each observation depth k and each location i by using
empirical probability distribution functions, βikj. The temporalstability index Tik , computed as the width of the 90% empiricaltolerance interval, i.e., βik(P=0.95)−βik(P=0.05), was used as ameasure of the temporal stability in soil water content of sampling
location i at depth k. Larger values of Tik correspond to lower
temporal stability. The two-sample Kolmogorov–Smirnov goodnessof fit test as implemented in the S-PLUS200 software (Mathsoft,
1999) was used to test whether values of βik obtained with different
observation frequencies could have come from the same distribution.
Locations were ranked by their utility to estimate average soil
water contents using the χ2 statistic:P
P !2
X hjk hikj = bik
2
vik ¼
ð3Þ
rjk
j

in which Nk is the total number of probes at depth k (Table 1).
Temporal stability in the water content patterns was characterized

where summation runs over all observation times, σjk is the standard
deviation of the average soil water content θ̄ jk for observation time j

Temporal stability was quantified using the approach of
Pachepsky et al. (2005), which is similar to one proposed earlier
by Vachaud et al. (1985). The relative water contents βikj for eachsampling location i at depth k for measurement time j werecomputed as:
hikj
bikj ¼ P
h kj

ð1Þ

A.K. Guber et al. / Catena 73 (2008) 125–133

at depth k (i.e., the standard error of observed water contents at thistime and depth), and β̄ ik is the average value of the relative watercontent at location i and depth k. Root-mean-squared differences
vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

uP  Pu Nik h h = bP 2
ikj
t j
jk
ik
Dik ¼
ð4Þ
Nik  1
were also computed, with Nik being the total number of observationsat depth k and location i in the field. We note that Eqs. (3) and (4)both use measurements at a particular location, corrected by theaverage relative water content rather than uncorrected measurements that are invoked to represent the average water content(Gomez-Plaza et al., 2000; Kaleita et al., 2004).
The use of temporal stability in soil water contents to correct
the average soil water content for missing data was studied byapplying the equation (Pachepsky et al., 2005)
X
XP
P
hjk c
hikj =
bik
ð7Þ
i

i

where β−ik is the average relative water content at depth k at
location i. Eq. (7) is summed over all locations for whichmeasurements are available at observation time j.
3. Results and discussion
3.1. Temporal stability in soil water contents
The MCPs revealed considerable temporal stability in thesoil water contents. Fig. 2 shows an example of monthly soil

129

water dynamics measured with MCPs at the 10-cm depth.
Temporal changes in soil water contents at different locations
were very similar in that the graphs of the water contents at
different locations were mostly only shifted relative to eachother. These similarities translated into water content profiles
characterized in Fig. 3 by the average and the 5% and 95%
quantiles of the distribution individual soil water contents whichwere significantly (P b 0.05) different from the average soil
water content in 9 of 24 locations at the 10 cm depth, in 17 of 24
locations at 30 cm, in 12 of 16 locations at 50 cm, and in 11 of
16 locations at the 80 cm depth. The number of locations withwater contents significantly different from the average wasmuch larger than, for example, in the study of Comegna andBasile (1994) where soil homogeneity prevented large differences between water contents at different locations. Also, we
did not observe a dependency of temporal stability on the
average water content at a particular location, as was reported inearlier studies. For example, Martínez-Fernández and Ceballos(2003) and Jacobs et al. (2004) found that relative watercontents of drier locations tended to have less variability than
the wetter locations.
The temporal stability index Tik is shown in Fig. 3 as thewidth of the interval between the error bars. The index
decreased with depth between 0 and 60 cm, which reflects
increased stability with depth. Average values of Tik over 24
locations were 0.42, 0.23, and 0.24 at depths of 10 cm, 30 cm,
and 50 cm, respectively. A similar increase in temporal stability
with depth was observed by Cassel et al. (2000) for cropland
and by Lin (2006) for forest watersheds. A similar result wasalso reported by Kamgar et al. (1992) who suggested that

Fig. 3. Variations in relative soil water contents at four depths during the observation period from May 1, 2001 to Dec 31, 2002. Symbols show the median value, error
bars show values at the 5% and 95% probability levels.

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A.K. Guber et al. / Catena 73 (2008) 125–133

temporal stability in soil water storage was less pronounced inshallow soil layers owing to the impact of crop root water
uptake, whereas pedogenetically derived variations at deeper
layers conserved a relatively stable pattern in spatial variation
through time. Another possible reason for the increased
temporal stability with depth may be the dynamics in soil
structure and its ability to retain water, which is much more
pronounced at lower depths (Korsunskaya et al., 1995). The
water table at some locations in our study was less than 80 cm,
which explains the considerable variability in relative watercontents as seen in Fig. 2. The temporal stability index for thesereasons varied widely at this depth.
Sensors at different locations in the field often showed
consistently lower or higher water contents than the average watercontent at a particular depth. The AL2 location presents an
example (Fig. 2) for which water contents at 10 cm (30 cm) depth
were significantly less than (greater than) the average watercontent. This may be the result of considerable soil heterogeneitythat was demonstrated for this site with data from a ground
penetration radar survey (Gish et al., 2002).
To evaluate the effect of the sampling frequency on temporalstability characteristics, the data were sequentially reduced. Dataobtained at time intervals of 2 h, 1 day and 7 days were selected byretaining each 12th, 144th and 1008th measurement, respectively.
We next compared probability distribution functions, βik, of therelative water contents. The statistical hypothesis that values ofβikj at four different measurement time intervals (10 min, 2 h,
1 day, 7 days) for the same depth and location belonged to thesame distribution could not be rejected (P b 0.0001). An important
implication of this result is that temporal stability in soil watercontents can be revealed equally well with a low frequency ofobservations as with high frequency.
3.2. Selection of soil water monitoring locations
Locations BM1, AH3, and BM3 appeared to be the best for
estimating the average water contents at depths of 10 cm, 30 cm,
and 50 cm, respectively, having root-mean-squared differences
Dik of 1.16, 0.77 and 0.98%, respectively. Given that the observed
average soil water contents at these depths ranged from 2 to 31%,from 7 to 25%, and from 5 to 20%, respectively, the accuracy ofthe estimated average may well be sufficient for many applications. Location AH1 was the worst estimator of the average at
depths of 10 cm and 30 cm, having errors of 3.7 vol.% and 1.8 vol.
%, respectively. Our results concur with the observation by Tallon
and Si (2003) that within the same field, time stable sites can bedifferent at different depths. This observation does not seem to beuniversal. For example, Cassel et al. (2000) found that the rankingof the various locations was similar at different depths. The small
errors in estimated average water contents indicate that a two-stage
monitoring method as suggested by Rolston et al. (1991) and later
by Gomez-Plaza et al. (2000) is very much feasible at our study
site. The method consists of initial intensive sampling in order to
identify locations giving mean soil water storage. Only theselocations could subsequently be sampled for changes in soil water.
Several best locations can be selected if no statistically significant
differences exist between the root-mean-squared differences Dik.

Table 2
Utility of locations to estimate the average soil water contents at the depth of
10 cm across the field B over the whole observation period and over the calendar
month observation periods
Location, sortedby the χ2 statistic
for the 19-monthobservation period

The χ2statistic forthe 19-monthobservation
periodThe root-meansquared difference
D for the wholeobservation period,
vol.%The number ofmonthlyobservation periods
over which thelocation had thelowest χ2 statistic

BL3
BL1
BL4
BL2
BH3
BH1
BM4
BM1
BH2
BM3
BM2
BH4

139
146
155
167
171
175
199
207
210
232
236
270

1.34
1.42
1.18
1.77
1.84
2.04
1.79
1.91
2.00
2.12
2.58
2.52

4
5
3
1
2
1
3
0
0
0
0
0

A change in the duration of the observation period was found
to affect the selection of the best monitoring locations. An
example of data for monthly observations periods is presented inTable 2 for the 10 cm depth across field B. Only data from field B
were used since some locations of field A had a large number ofmissing data. The best three locations to estimate the average soil
water content over the whole observation period were the best
locations over a month-long period of observations in about 60%
of cases. The worst six locations over the entire observation
period never were the best over a month of observations. The
lowest values of χ2 for May, June and July were about two times
larger than the lowest χ2 for other months. These results are
consistent with the observation by Da Silva et al. (2001) that therelative importance of different factors affecting temporalstability varies during the growing season and between seasons.
The May–June period was a period of active vegetative growthof corn for both years of observations. Zhang and Berndtsson(1988) and Hupet and Vanclooster (2002) also observed weakertemporal stability during dry periods compared with wet periods.
The sequential data reduction technique was used to evaluate
the effect of sampling frequency on the utility of locations toestimate the field average soil water content. Table 3 shows theeffect of sampling frequency across Field B at three depths. We
encountered only slight changes in the root-mean-squared
differences Di1 when the sampling frequency was changed from10 min to 2 h, 1 day, and 7 days. No changes in location ranking
by the χ2 statistic were found. The implication of this result is thatthe utility of a location to estimate the field average soil watercontent can be evaluated with the same accuracy using a low
frequency of observations as compared to a high frequency.
3.3. Correction for missing data using temporal stability
To evaluate the efficiency of correcting the average soil watercontent for missing data at some locations, we first performed asimulation experiment. All hourly measurements were used over

A.K. Guber et al. / Catena 73 (2008) 125–133

131

Table 3Root-mean-squared deviations (cm3 cm− 3) of corrected location water contentsfrom the average soil water content across the field B
Location

Time interval between measurements
10 min2h

1 day

7 daysDepth 10 cm
BM1
BL3
BL1
BL2
BM4
BL4
BH3
BH2
BH1
BM3
BH4
BM2

1.18
1.34
1.42
1.77
1.79
1.91
1.84
2.00
2.04
2.12
2.52
2.58

1.17
1.35
1.43
1.78
1.79
1.92
1.84
1.99
2.06
2.13
2.51
2.59

1.15
1.35
1.49
1.86
1.79
1.95
1.82
1.94
2.13
2.20
2.52
2.64

1.06
1.27
1.30
1.56
1.69
1.90
1.71
1.88
2.01
2.19
2.58
2.65

Depth 30 cm
BM1
BH4
BH3
BH2
BL4
BM3
BM4
BL3
BM2
BH1
BL2
BL1

0.89
0.97
1.09
1.17
1.24
1.37
1.37
1.50
1.55
1.64
1.66
2.31

0.90
0.98
1.10
1.17
1.23
1.38
1.39
1.49
1.58
1.66
1.70
2.32

0.91
1.00
1.14
1.20
1.22
1.38
1.44
1.49
1.69
1.73
1.84
2.40

0.88
0.94
0.94
1.13
1.18
1.39
1.42
1.36
1.63
1.79
1.76
2.16

Depth 50 cm
BM4
BM1
BL4
BM3
BL2
BM2
BL3
BL1

0.95
1.03
1.03
1.05
1.09
1.33
1.44
2.83

0.96
1.02
1.02
1.05
1.11
1.34
1.45
2.88

0.98
1.09
1.09
1.06
1.16
1.39
1.45
3.01

0.85
0.68
0.68
0.96
1.15
1.30
1.39
2.88

the period when all 24 probes worked at the 10-cm depth. Data
from 1 to 22 probes were removed for each sampling time, and theaverage water content was estimated in two ways: (a) as theaverage water content over remaining probes (assumed to beworking); and (b) as the corrected value of the average watercontent according to Eq. (7). The efficiency of the correction was
evaluated by computing the root-mean-squared difference,
RMSD, between the actual and estimated average soil watercontent. The probability distribution of RMSD from thissimulation is shown in the Fig. 4. The improvement depended
on the total number of working probes. The fewer the number ofworking probes, the more efficient was the correction.
Fernández-Gálvez et al. (2006) investigated how to use
temporal stability in soil water patterns to estimate soil watercontents at rarely sampled locations from soil water contents at
densely monitored locations. This problem is closely related tothe problem of estimating missing data. Fernández-Gálvez et al.
(2006) found that their interpolation procedure appeared to beleast successful during infiltration events. We did not find such

Fig. 4. Probability distributions of the root-mean-squared difference RMSD
between actual and estimated average soil water contents.

an effect when estimating the average water content. This may
be related to the fact that we used average values of the relative
water contents, rather than relative water contents at specifictimes.
Substantial corrections for the missing data were obtained atsome observation times within the entire observation period of
610 days when the missing data log was used (Fig. 5). The watercontent corrections generally decreased with an increase in thenumber of working probes (Fig. 6). The maximum correction
was equal to 2.5 vol.% at an average water content of 19.2 vol.
%, corresponding to a time interval when 10 probes functioned
properly. The advantage of correcting for missing data may beeven more substantial if the effect of the number of probes on
the accuracy of the average is considered (Teuling et al., 2006).
The MCPs were installed at temporally unchanged sampling
locations at the OPE3 site. Since small-scale variability can besubstantial, we concur with Kirda and Reichardt (1992) and
Hupet and Vanclooster (2002) that temporally unchanged
locations are preferable to establishing and using temporalstability relationships. In spite of the stable location of probes,

Fig. 5. Temporal stability-based corrections for missing data to the average soil
water content at the 10 cm depth. The number of working probes is shown by thedotted line.

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A.K. Guber et al. / Catena 73 (2008) 125–133

with the soil moisture observation network. Lin (2006) found that
temporal stability in soil moisture spatial patterns varied overspace and between seasons in complex terrains with heterogeneous soils and landforms. The one-month observation duration
used here is probably specific for the location and spatial scale ofour study site, and should not be generalized.
4. Concluding remarks

Fig. 6. Relationship between the temporal stability-based correction and theaverage soil water content at the 10 cm depth and the number of working probes.

considerable variability existed between sites in terms of thetemporal stability index (Fig. 3). This implies that the overall
spatial pattern in moisture changed dynamically but that somelocations within that overall pattern remained at a consistent
proportion of the mean.
Several methods have been suggested to characterize consistency in temporal patterns of the soil water contents. In particular,
temporal persistence in soil water series can be quantified alongwith temporal stability. Whereas temporal stability analysis uses
statistics of relative water contents as defined by Eq. (1) or
statistics of relative differences in water contents as defined by
Vachaud et al. (1985), the temporal persistence is characterizedusing autoregression of the soil water content time series assuggested by Kachanoski and de Jong (1988). Lin (2006)
developed four conditions of temporal persistence based on theslope and intercept of this autoregression. Several otherparameters have been suggested, such as rank stability (Vachaud
et al., 1985), spatial coherency (Kachanoski and de Jong, 1988),
variance in relative differences (Martínez-Fernández and Ceballos, 2003; Jacobs et al., 2004), and parameters of the soil moisture
semivariogram (Kaleita et al., 2004). An interesting avenue for
future research would be to somehow combine these alternative
characteristics of consistency in temporal patterns for the purposeof selecting monitoring locations or estimating missing data.
Obtaining the average water content across the observation
area from point-scale MCP measurements can be interpreted as amethod of upscaling. Upscaling in this sense is valuable in many
applications, such as for estimating groundwater recharge,
modeling contaminant transport in the vadose zone, watershed
modeling, and remote sensing of soil moisture. Upscaling of watercontents in our study could be accomplished using relatively low
temporal resolution. Good locations for upscaling could be foundwith reasonable probability using only one month of data. Several
have suggested a need for longer periods of observations in order
to find representative locations for the soil water sensors.
Martínez-Fernández and Ceballos (2005) found that one year
was needed to identify representative mean soil moisturemeasuring stations for both a small catchment of 0.62 km2 witha complex vegetation cover and a large area of 1285 km2 covered

Multisensor capacitance probes can provide soil watercontent data with high temporal frequency. Using such data,
we demonstrated considerable temporal stability in soil water
patterns across field in a coarse textured soil for the observation
period of 610 days.
By sequentially reducing data, we found that high-frequency
data collection did not provide advantages for establishingtemporal stability in the soil water contents. Sampling
frequencies in the range from 10 min to one week resulted invery similar parameters of temporal stability and in the selectionof the same locations as the best for estimating the averagewater content across the observation area for a single depth.
Temporal stability in soil water contents was found beneficial
for correcting measured average soil water contents when some
sensors malfunctioned. However, overall, the error resulting
from malfunctioning of some sensors was relatively modest in
our work.
Although the mechanisms behind temporal stability in soil
water patterns need further research, empirical evidence indicatesthat this phenomenon is widespread and pervasive. We conclude
that soil water contents can be monitored and upscaled more
efficiently when taking advantage of the temporal stability in soil
water patterns.
Acknowledgement
The work has been partially supported by Interagency
Agreement RES-02-008 “Model Abstraction Techniques forSoil Water Flow and Transport,” and by the SAHRA Scienceand Technology Center through NSF grant EAR-9876800.
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