Int. Agrophysics, 2008, 22, 209-214

INTERNATIONAL

Agrophysics
www.international-agrophysics.org

Temporal stability of estimated soil water flux patterns across agricultural fields**
A.K. Guber1, T.J. Gish2, Y.A. Pachepsky1*, M.T. van Genuchten3, C.S.T. Daughtry2, T.J. Nicholson4,
and R.E. Cady4
1

USDA-ARS Environmental Microbial Safety Laboratory, 173 Powder Mill Rd, BARC-EAST, Beltsville, MD, 20705, USA
2
USDA-ARS Hydrology and Remote Sensing Laboratory, Beltsville, MD, USA
3
USDA-ARS George E. Brown Jr. Salinity Laboratory, Riverside, CA, USA
4
US NRC-ORR, Rockville, MD, USA
Received April 11, 2008; accepted June 23, 2008

A b s t r a c t. When a field or a small watershed is repeatedly
surveyed for soil water content, sites often can be spotted where
soil is consistently wetter or consistently dryer than average acrossthe study area. This phenomenon has been called time stability,
temporal stability, temporal persistence, or rank stability in spatial
patterns of soil water content or in soil water contents. The
temporal stability presents significant interest for upscaling
observed soil water contents to obtain average values across theobservation area, improving soil water monitoring strategies, andcorrecting the monitoring results for missing data. The objective of
this work was to research the temporal stability in estimated soil
water fluxes using extremely frequent multi-depth measurementsof soil water content with multisensor capacitance probes installed
in soil in multi-year corn production. Data on water contents at 10,30, 50, and 80 cm depths were collected every 10 min for 20 monthsof continuous observations from May 2001 to December 2002.
Temporal stability was well pronounced for soil water fluxes
estimated from soil water balance for the depth of 60 m. Soil water
fluxes can be upscaled and efficiently monitored using the
temporal stability of soil water patterns.
K e y w o r d s: soil water flux, temporal stability, agricultural
fieldsINTRODUCTION

When a field or a small watershed is repeatedly surveyed for soil water content, sites often can be spotted where
soil is consistently wetter or consistently dryer than average
across the study area. This phenomenon has been called timestability or temporal stability (Vachaud et al., 1985), tempo*Corresponding author’s e-mail: Yakov.Pachepsky@ars.usda.gov**The work has been partially supported through the Interagency
Agreement RES-02-008 ‘Model Abstraction Techniques for Soil
Water Flow and Transport’.

ral persistence (Kachanoski and de Jong, 1988), or rank
stability (Tallon and Si, 2003) in spatial patterns of soil
water content or in soil water contents. The temporal stability has been demonstrated for three different time-dependent
characteristics of soil water dynamics, namely for (a) watercontents at specific depths, (b) soil water storage usuallyinterpreted as the total soil water amount within a range of
depths, and (c) soil water fluxes estimated at specific depths.
The temporal stability causes time series of soil watercontents or fluxes in different locations to have similar
shapes while being offset from each other. Although themechanistic explanation of the temporal stability in spatial
soil water patterns has never been given, the presence of thisstability has been routinely observed in various very different environments provided measurement locations did
not change in time.
Several consequences of temporal stability in soil water
patterns (TSSWP) caused recent growing interest to thisphenomenon. One consequence is that one or more locations
can be found that have the time series of soil water content(soil water storage or estimated soil water flux) very similar
to the time series of the average value of soil water content(soil water storage or soil water flux) across the study area.
After such location(s) are found, only small number of soil
moisture sensors in such locations is needed to monitor the
average soil water content across large areas. This aspect of
the TSSWP has been actively used in remote sensing of soil
moisture because of the opportunity to upscale soil watercontent from several or even single point measurements tothe average soil water content across a footprint area (Mohanty© 2008 Institute of Agrophysics, Polish Academy of Sciences

210

A.K. GUBER et al.

and Skaggs, 2001; Cosh et al., 2003; Jacobs et al., 2004).
Other applications included establishing field- or catchment-wide antecedent moisture conditions for runoff simulations (Western et al., 2003), relating spatio-temporal variation of soil water to triggering of subsurface flow, as measured by a network of piezometers (Penna et al., 2006 ), andupscaling soil moisture monitoring data in irrigated anddryland crops (Rocha et al., 2005; Rolston et al., 1991).
Whereas the temporal stability for soil water contents
was amply demonstrated, the temporal stability of estimatedsoil water fluxes was questioned. Reichardt et al. (1993)
concluded that it was not feasible to estimate mean field
behavior with respect to soil water fluxes due to the soil variability, if field-measured hydraulic conductivity and soil
water potential are used to estimate the fluxes and gradients.
It is not known if the temporal stability of estimated soil
water fluxes can be demonstrated, and whether the same
locations can be used to estimate time series of average soil
water contents and average soil water fluxes.
The objective of this work was to research the temporalstability in estimated soil water fluxes using extremely frequent multi-depth measurements with multisensor capacitance probes installed in soil in multi-year corn production.
MATERIALS AND METHODS

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). Data form two fields of the OPE3
site with the total area of 6 ha are used in this work (Fig. 1).
The fields are under continuous corn. Each year the tillage
practice is the same, fields are being disked about a monthprior to a second disking operation that was followed withplanting. Soil at these fields has been classified as a coarseloamy, siliceous, mesic Typic Hapludult with either well orexcessively 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), with loamy sand and finetextured clay loam lenses between 120 and 250 cm. The
latter form a nearly impermeable layer in this soil (Gish etal., 2002) that prevents deep leaching and causes lateral
movement of water and solutes. This subsurface layer has
numerous localized depressions that form braided flow
pathways throughout the field that drain toward a riparian
wetland and first-order stream.
The multisensor capacitance probes, or MCP(EnviroSCAN, SENTEK Pty Ltd., South Australia) were
installed in spring of 1998 to better understand surface andsubsurface soil water dynamics. For details on sensor location and installation, see Gish et al. (2002). Each sensor wascalibrated before installation (Paltineanu and Starr, 1997).
This work uses the data from 24 soil moisture multisensor
capacitance probes (Fig. 1) that have been installed at depthsof 10, 30, 50, 80, 120, 150, and 180 cm and water content
was 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.

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

TEMPORAL STABILITY OF ESTIMATED SOIL WATER FLUX PATTERNSj

Evaluating temporal stability of soil water fluxes
Soil water fluxes Qij (cm h-1), were estimated at thedepth of 60 cm at locations of MCP installations where thedata were available (Table 1) as:j

3(

Qi =- åk=1

j+1
jq ik - q ik

)Dz / Dt + R - ET ,
j

j

211

The flux deviations B i were defined as differences
between the estimated hourly fluxes at each location fromaverage estimated hourly fluxes across the field for the sameobservation interval:j(1)

where: è is the volumetric water content, Äz = 20 cm is the
thickness of a soil layer where soil water contents is assumed
equal to the MCP reading for a single depth, Rj and ETj are
rainfall and evapotranspiration rates, respectively, cm h-1,
between observation times j and j+1, Dt =1 h is the timeinterval between observations at times j and j+1, subscripts‘i’ and ‘k’ refer to locations and depths, respectively; k=1,2,
and 3 refer to depths of 10, 30 and 50 cm.

j

1

N j3

j

å Q ,
(2)
N j 3 i=1 iwhere: Nj3 is the total number of locations having working
probes at depths 10, 30, and 50 cm. Values of hourly
precipitation and evapotranspiration were assumed the samefor all locations within the field, and therefore the value ofj
B i was actually the difference between the hourly change inwater storage in 0-60 cm layer in location i and averagehourly change in water storage in 0-60 cm layer across thefield between the observation times j and j+1. The temporalstability of the estimated soil water fluxes was characterized
for each location by the empirical probability distributionjfunction of the values of B i .
B i = Qi -T a b l e 1. Depths of sensor installation by locations
Location
k

Depth
(cm)

1
2
3

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

-

+

+

4

80

+

-

+

5

120

-

+

+

6

150

-

+

+

7

180

-

+

+

Fig. 2. Cumulative estimated soil water fluxes. Locations are shown in Fig. 1

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A.K. GUBER et al.

RESULTS AND DISCUSSION

The cumulative soil water fluxes are shown in Fig. 2. All
locations show a similar trend of cumulative fluxes following cumulative rainfall. This reflects the low and infrequent
runoff and predominantly strong and short rainfall at the site.
Nevertheless, as Fig. 2 shows, the differences between
locations can be substantial. This is further illustrated in Fig.
3 where the statistical distributions of the flux deviation
jvalues B i are shown. Some locations, eg AM2 or BM2 havefluxes larger than the average, and other locations, eg BL1 or
Al1, have fluxes smaller than the average most of the time.
This demonstrates and illustrates the temporal persistence insoil water fluxes. The data on flux deviation are further

condensed in Fig. 4 where average and standard deviation ofjflux deviation values B i flux are shown. Locations withsmall average and large variability in flux deviations, eg
BL4, along with locations with relatively large absolutevalue of the average and small standard deviations, eg BL1
and BL2, can be found. The temporal stability-based
estimates of the average soil water flux at 60 cm depth were
found from data in each location by subtracting the average
deviation in this location from the deviations at eachobservation time. The smallest root- mean-squared error ofsuch estimates was found in locations AM1 and BM4 at
fields A and B, respectively (Fig. 5). These were locations
that corresponded to the smallest variability in flux
deviations as shown in Fig. 4.

Fig. 3. Probability distributions of flux deviations computed over two-hour intervals across fields A and B. Locations are shown in Fig. 1

Fig. 4. Statistics of soil water flux deviations from the average flux deviation across fields A and B. Locations of soil water probes areshown in Fig. 1.

TEMPORAL STABILITY OF ESTIMATED SOIL WATER FLUX PATTERNS

213

Fig. 5. Root-mean-squared errors of the estimates of the average soil water flux at 60 cm depth based on the temporal persistence.
Locations of soil water probes are shown in Fig. 1.

Grayson and Western (1998) have hypothesized that thelocations representative for the ‘mean’ landscape response
in terms of soil water contents should be ‘mean’ with respect
to main influences on spatial soil water distribution. At the
Tarrawarra catchment, these authors found such locations inareas that are neither strongly convergent nor divergent,tend to be near the mid-slopes, and are in areas that have
topographic aspect close to average. Our data demonstratethat similar assumptions can be made regarding locations
representing mean soil water fluxes. Indeed, at the field A,
the midslopes are the areas where the average deviations
from the average flux and the standard deviations of fluxes
are relatively low (see AM1, AM2, and AL2 in Figs 4 andFig. 1). Similarly, in the field B, locations with low average
deviations from the average flux and the standard deviationsof fluxes are in midslopes (BL3, BM3, BM4 in Fig. 4 andFig. 1). Locations with the largest deviations of average
fluxes from the average flux over the field B are in thedivergence area of highest elevations (BL1, BL2, and BM2
in Figs 1 and 4).
Multisensor capacitance probes provide soil watercontent data with high temporal frequency. From such data,soil water fluxes can be estimated that appear to exhibit
temporal stability. We stress that soil water fluxes are
estimated rather than measured in this work. The flux
estimations with Eq. (1) have unaccountable errors because
rainfall and evapotranspiration rate values used in thisequation are measured or computed from measurements inlocations different from locations of MCP, the accuracy of
evapotranspiration estimates is essentially unknown, etc.
Uncertain as they are, such soil water balance-based flux estimates are needed and used in the multitude of applications ofsoil moisture data for groundwater recharge and contaminant hydrology modeling. Limitations and necessary precautions of using Eq. (1) and its analogs are thoroughly
discussed ie Gee and Hillel, 1988; Zhang et al., 2002.

Although the mechanisms behind the temporal stability
in soil water patterns need further research, the empiricalevidence indicates that this phenomenon is widespread andpervasive. It remains to be seen whether the temporal stability of soil water fluxes is affected by the interannual variations in weather conditions. We have not observed a seasonal effect of the persistence (data not shown).
The similarity in temporal stability of estimated soil
water fluxes and soil water contents should not be expected.
Flux estimation with Eq. (1) uses the approximation of thetemporal derivative in soil water storage. The rainfall andevapotranspiration are set the same for all locations, andtherefore spatial variations in estimated flux values are infact spatial variations of temporal derivatives of soil water
storage. There are no reasons to expect similarities in spatial
variability of soil water contents and spatial variability of thetemporal derivative of soil water storage which is the weighted
sum of soil water contents at several depths. Therefore, thetemporal stability of soil water contents established for our
research site (Guber et al., 2008) does not necessarily imply
the temporal stability of soil water fluxes.
The temporal persistence in soil water fluxes series canbe quantified along with temporal stability. Whereas
temporal stability analysis uses statistics of relative watercontents or statistics of relative differences in water contents
as defined by Vachaud et al. (1985), the temporal persistence is characterized using the autoregression of the soil
water content time series as suggested by Kachanoski and deJong (1988). Lin (2006) has developed four conditions of
temporal persistence based on the slope and intercept of thisautoregression. There have been suggested other characteristics of consistency in temporal patterns of soil watercontents, such as rank stability (Vachaud et al., 1985), spatial coherency (Kachanoski and de Jong, 1988), variance ofrelative differences (Martínez-Fernández and Ceballos,
2003; Jacobs et al., 2004), and parameters of soil moisture214

A.K. GUBER et al.

semivariogram (Kaleita et al., 2004). Combining characteristics of consistency in temporal patterns of soil watercontents to select monitoring locations and fill in missing
data presents an interesting avenue of research.
Values of soil water fluxes are of interest for both groundwater recharge estimations and estimations of shallow
groundwater input in crop water uptake. The near-real-timemonitoring of soil water storage with MCP provides thesufficient information for point estimates of soil water
fluxes. Using a large number of MCPs to upscale fluxes tothe field scale by averaging is prohibitively costly.
However, the short term monitoring to establish a location
which is representative for the field-average soil water flux
is feasible, since the set of MCP can be reused many times indifferent locations. Therefore, the temporal persistence insoil water fluxes, if proven, opens the possibility of theefficient monitoring and upscaling soil water fluxes.
CONCLUSIONS

1. This work demonstrates the temporal persistence insoil water fluxes estimated from near-real-time monitoringof soil water contents with multisensor capacitance probes.
2. The efficient upscaling and monitoring of soil water
fluxes can be achieved thus providing essential information
for both groundwater recharge estimation and estimation ofshallow groundwater input in crop water uptake.
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