Journal of Hydrology xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Spatial and temporal structure within moisture measurements
of a stormwater control system
Ruben Kertesz ⇑, Lee Rhea, Daniel J. Murray Jr.
U.S. EPA, National Risk Management Research Laboratory, 26 West Martin Luther King Drive, Cincinnati, OH 45268, United States
a r t i c l e
i n f o
Article history:
Available online xxxx
Keywords:
Pervious concrete
Soil
Sensor
Moisture
Stormwater
Infiltration
s u m m a r y
This study develops novel geostatistical methods to investigate the spatial relationship between
individual soil moisture sensors placed within native soil and #57 crushed stone aggregate subbase.
The subbase sensors are beneath a 0.06 ha (0.15 acre) pervious concrete parking lot in Cincinnati, OH,
USA. The parking lot treats runon from a 0.198 ha (0.49 acre) asphalt area. A geostatistical characterization of moisture (measured as permittivity) in the subbase beneath pervious concrete indicates that significant spatial correlation is either not present or only present at very short distances (<2.5 m). A twostage para-statistical model relating antecedent storm moisture to apparent pervious concrete infiltration
was developed to identify temporal trends in the data and to detect the clogging processes with relatively
simple parameterization. The results suggest that either the placement of the sensors is not sufficient to
detect clogging or that clogging is not problematic for the study period. Suggestions are provided to
improve future research installations, based upon the findings here. Subbase moisture analysis results
are compared with native soil moisture results. Seasonal trends are more pronounced in the native soil
than in the subbase. The statistical analyses are applicable to multiple Storm Control Measures (SCM),
Best Management Practices (BMP), agriculture, and soil environments. Other studies can determine the
statistical power of their sensor installation using the methods applied here, which are flexible enough
for multiple applications. Furthermore, data reduction methods presented serve to easily elucidate
short-term moisture responses due to rainfall. A quantile response pattern is provided for sensors
installed in both subbase and soil.
Published by Elsevier B.V.
1. Introduction
Moisture measurement in soils has been an important agricultural pursuit since the early 20th century (Ayers et al., 1943) and
is commonly used in viticulture (Matese et al., 2009; Lunt et al.,
2005). Various sensors have been developed to measure moisture
and sensor accuracy has been consistently improved for better
performance in soils (Seyfried and Murdock, 2001; Kelleners
et al., 2005), but their use in very well drained granular media is
a relatively novel application of the technology and few studies
have examined their performance in such environments (e.g.
Spittlehouse, 2000; Arguedas et al., 2007). This is a nascent issue
in the stormwater field because most previous green infrastructure
studies, where moisture measurements have been made, tended to
focus on bioretention (Houdeshel and Pomeroy, 2010; Brown and
Hunt, 2011; Darner and Dumouchelle, 2011; Aravena and
Dussaillant, 2009). However, recent applications include use in
⇑ Corresponding author. Tel.: +1 513 569 7428.
E-mail address: kertesz.ruben@epa.gov (R. Kertesz).
green roof media (Palla et al., 2011; Sun et al., 2013) and beneath
pervious concrete (Brown and Borst, 2013; Stander et al. 2013).
Previous research in stone aggregate or coarse media has been
performed using largely different sampling network design.
Brown and Borst (2013) observed the down gradient migration of
clogging along a roadway curb of interlocking concrete pavers at
a site in Louisville, KY. The site had a very narrow and long flowpath which was investigated using a geometric transect in the
well-defined flowpath. Research by Palla et al. (2011) and Sun
et al. (2013) focused on the drying and wetting patterns of green
roofs with comparatively thin media depths. Stander et al. (2013)
described the arrangement of water content reflectometers
beneath permeable pavement. The network design involved sensor
placed near the pavement edge for different permeable pavement
types. All of the aforementioned involve a unique spatial arrangement of sensors, but to the knowledge of the authors little if any
information is available regarding optimization of sensor
placement with respect to statistical concerns such as sample
independence or spatial correlation. Studies focused on overall
effects would logically optimize sensor placement by using
http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
0022-1694/Published by Elsevier B.V.
Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
2
R. Kertesz et al. / Journal of Hydrology xxx (2014) xxx–xxx
adequate sensor spacing to ensure spatial independence, and
thereby maximize statistical power. Conversely, studies focused
on aspects such as media uniformity might optimally space sensors
by ensuring they were within the distance over which spatial correlation was expected to extend.
Dobriyal et al. (2012) have documented multiple indirect moisture measurement technologies that suffer from limited spatial
representation in soil. On the scale of most field investigations,
moisture sensors are often thought of as point samples. The present study presents information pertinent to the determination of
the representativeness of individual sensor measurements; if spatial correlation within a system is present, it could be reasonable to
treat the readings from individual sensors as representative of
some volume of soil within the range of spatial correlation, rather
than merely a number of point-wise observations. Among the differing technologies available to measure subsurface moisture, the
technology applied in this study is transmission line oscillation
(TLO) water content reflectometery [Campbell Science CS-650].
TLO technology is based upon the well-described research by
Topp et al. (1980), who formulated an equation to calculate volumetric water content using permittivity. Advancements have been
made in moisture sensing technology since then (Campbell and
Anderson, 1998), and Kelleners et al. (2005) are among the latest
to describe TLO moisture measurement methods. Many other sensor technologies have been developed to measure real-time moisture as well, such as: tensiometry (Coolong et al., 2012); time
domain reflectometry (TDR) (Malicki et al., 1996; Robinson et al.,
2003); time domain transmission (Blonquist et al., 2005); and frequency domain reflectometry (Bandaranayake et al., 2007). TLO
water content reflectometers were selected for the present study
because they are manufactured for the datalogging platform
deployed at the site and were readily available. The authors do
not intend to form comparisons between technologies or make
any claim as to the (dis)advantages of a particular moisture sensing
technology. Rather, the methods presented here are intended to be
cross-applicable.
The promise of gathering data from sensors in a stone aggregate
subbase beneath pervious concrete (PC), is in being able to use the
timing of response to determine patterns in the treatment system.
This may be relatively easier to identify in bioretention systems,
which have a distinct wetting front that may take between minutes and days to migrate through the soil (Hsieh and Davis,
2005; Dussaillant et al., 2005; Shuster et al., 2007; Stander et al.,
2010; Brown and Hunt, 2011), subject to differences in the gradation of the bedding layer and subsurface media (Robinson and
Friedman, 2001). However, the movement of water through the
open-graded subbase (stone aggregate) beneath pervious concrete
is almost instantaneous (Chopra et al., 2010; Stander et al., 2013;
Brown and Borst, 2013). Selective placement of sensors is critical
to answering many research questions. Examples include: determining the spatial progression of clogging; comparing rainfallresponse timing through permeable pavement to the response in
soil; identifying drainage areas that contribute a disproportionate
volume of runoff to one area of the SCM; or identifying localized
flooding in a SCM.
The present study evaluates the utility of moisture sensors to
ascertain spatial and temporal moisture trends in a stone aggregate
subbase beneath a functioning pervious concrete (PC) parking lot
under varying weather conditions. It also evaluates wet weather
responses in native soil. The objectives of this study are to: develop
methods to determine the presence of spatial correlation in sensor
response (as permittivity) monitored in stone aggregate beneath
pervious concrete; determine the utility of these data for monitoring pavement clogging using the established spatial network of
sensors; contrast readings with those made in native soil; and
identify the ramifications for instrumentation and monitoring frequency requirements in future studies.
2. Materials and methods
2.1. Site description
The site is located at latitude 39°80 22.9400 N, longitude
84°250 46.700 W, in the northwest region of the Cincinnati Public
School’s Clark Montessori High School. The subject PC parking lot
is part of a stormwater treatment train to reduce discharge to combined sewers. A 0.198 ha (0.49 acre) asphalt drainage area contributes flow to both the subject 0.061 ha (0.15 acre) PC, and a 0.028 ha
(0.07 acre) bioretention area (BA). The dimensions of stormwater
control system are shown in Fig. 1. Flowpath lines were generated
using a ground-based LIDAR survey and are documented in Fig. 1
as well. Overflow drains through a raised outlet at the far west
end of the BA if ponding occurs in the BA. The site is part of a larger
combined effort by the Metropolitan Sewer District of Greater Cincinnati (MSD) to evaluate green infrastructure (GI) as a tool to
reduce combined sewer overflows.
2.2. Instrumentation and data management
Many sensor technologies on the market calculate dielectric
(electrical) permittivity as a surrogate for volumetric water content. The Campbell Scientific sensors deployed here calculate
dielectric permittivity as a function of Period and electrical conductivity. Stander et al. (2013) recommend the use of permittivity
instead of volumetric water content when installing moisture sensors in stone aggregate because of difficulty calibrating the sensors
in this type of material (Stenger et al., 2005). The permittivity data
recorded in the current investigation are affected by occasional
erratic responses in electrical conductivity readings, perhaps due
to interference from electrical currents in subsurface conduits.
Baselining serves to mitigate the effect of that behavior. Statistical
methods shown in this manuscript are presented for permittivity
but are also applicable to soil moisture.
Sensors are deployed along three east–west transects parallel to
the longitudinal axis of the PC, designated Upstream (U), Downstream (D), and Native (N) (Fig. 1). The U- and D-transects are
located 152 mm (6 in.) and 457 mm (18 in.) from the upgradient
pavement edge, respectively. The N-transect is located along the
centerline of the associated drainage swale. The sensors within
the U- and D-transects are emplaced in a well-drained #57-stone
subbase beneath the pervious concrete (152 mm above the native
soil). The sensors within the N-transect are emplaced in densified
soil (denoted native soil) approximately 150 mm into the native
soil. The native soil type is a stiff to very stiff mixture of brown,
lean clay, with traces of organics, rock, and brick fragments. Table 2
shows physical properties of the pervious concrete. The sensors are
geometrically spaced along the longitudinal axis of transects.
The moisture sensors were installed during the construction
process. The U- and D-transect sensors were installed by first placing them and ancillary communications cabling on the soil surface.
Next, a protective cylinder was placed around them before lifting
sensors, adding media to the inside of the cylinder to a depth of
152 mm (6 in.), and laying sensors on the media bed. The sensors
were then covered with media until flush with the media depth
surrounding the cylinder. Lastly, the cylinder was lifted up and
out, leaving the sensors installed in the matrix before pervious concrete was poured (Fig. 2). The N-transect sensors were installed by
pushing the sensor rods (tines) horizontally into the native soil,
perpendicular to the BA, after the BA was excavated.
Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
R. Kertesz et al. / Journal of Hydrology xxx (2014) xxx–xxx
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Fig. 1. Horizontal (A) and vertical (B) distribution of sensors at the site. Spaces are numbered from 1 to 22 (East to West) along the 60 m (198 ft.) transect. Numerical notes for
part B are as follows. (1) 305 mm (12 in.) open graded #57 stone; (2) filter fabric lapped onto gravel surface; (3) flush concrete curb; (4) subgrade 92% proctor; (5) 152 mm
(6 in.) pervious concrete. Flowlines are superimposed upon (A), colored by drainage location. (For interpretation of the references to color in this figure legend, the reader is
referred to the web version of this article.)
Table 1
Various parameters that were logged at each sensor.
Parameter
Unit
Volumetric water content
Electric conductivity
Temperature
Permittivity
Period
Voltage ratio
m3/m3
dS/m
°C
Unitless
lS
V/V
Table 2
Physical properties of pervious concrete.
Parameter
Density (kg/m3)
Average (n = 8)
Standard deviation
2186
82
Mix design test
Value (various units)
Design strength (psi)
Water/cement ratio
Cementitious (% volume)
Aggregate (% volume)
Design air (% volume)
Slump
Aggregate type
3000
0.31
11
58
20
0
#8 Gravel
All cabling was placed in conduit before installation and
connected to a centralized CR-1000 datalogger (Campbell
Scientific, Inc., Logan, Utah). Six parameters were logged via serial
digital interface protocol (Table 1) and telemetrically uploaded to a
centralized server. Rainfall data measured after October 2011 were
recorded at 1 min intervals using a 152 mm (6 in.) diameter
tipping bucket rain gauge with a 0.1 mm gradation (R.M Young
Company, Traverse City, Michigan). Five minute rainfall data were
provided by MSD’s Rainvieux system for dates before this time, a
service of Vieux Inc. (Norman, OK). The service technology is
discussed by Gourley and Vieux (2005). In order to maintain a
Fig. 2. Illustration of sensor installation in porous media before filling cylinder and
surrounding infiltration gallery.
uniform dataset, the relatively brief record (8/23/11–10/21/11) of
5-min Rainvieux data were linearly apportioned to 1-min increments to match the substantial record of 1-min data collected for
the remainder of the investigation.
Data were uploaded from dataloggers to a remote server using a
wide area network connection and then loaded into a database
with an appropriate format for data reduction and statistical analysis using Base SASÒ v.9.3 (SAS Institute Inc., Cary, NC, USA). Data
reduction and statistical analyses were performed using the 1-min
timestep data recorded at the site. The statistical methods are
timestep agnostic.
2.3. Data reduction
Data reduction for the present study was performed in three
stages. In the first stage, the response data were baselined for each
individual sensor to remove low-frequency effects. Such effects
would obfuscate high-frequency, storm-related responses. In the
Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
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R. Kertesz et al. / Journal of Hydrology xxx (2014) xxx–xxx
second stage, transfer functions were developed for individual sensors that described the time-convolved relationship between precipitation and sensor response. In the third stage, the ensemble
of the adjusted parameters for all sensors was analyzed in a single
model to account for spatiotemporal correlations in the data. The
model was later used to discern whether some effect only ascribable to sensor distance from the upgradient edge of the pavement
(i.e. clogging) was present. This step-wise procedure was intended
to minimize the influences of sensor-specific variations on the
overall analysis for the presence of clogging.
2.3.1. Baselining
Baselining is an important step in rainfall response analysis.
Sensor baseline readings vary considerably, obfuscating stormspecific responses which are often lagged or convolved in time.
Baselining data allows the researcher to remove low frequency
(or long-term, e.g. weeks to months) components in the signal to
elucidate any (relatively) simple high-frequency (short term) relationships between individual rainfall events and sensor response.
Initially, raw permittivity was plotted for each sensor against
timestamps and manually reviewed for anomalies such as inexplicable jumps in baseline (dry weather) values, apparent drifts in
sensor sensitivity (due to factors such as instrument aging), and
confounding effects related to weather (such as air temperature
and potential evaporation). Pronounced variation in the instrument baselines was observed, so all time series were re-baselined
using: quadratic functions of the temperature of the monitored
media; date stamps; and a linear function of a sine-cosine pair with
a period of one year. The error function minimized was the sum of
squared estimation for positive errors (overestimates) and 1/100
this value for negative errors (underestimates). The ratio was
applied because underestimates were not as pronounced as overestimates. Fitting was done using SAS proc model. The calculated
baseline was subtracted from the raw instrument responses to
avail comparison of data between instruments, with respect to
time.
2.3.2. Rainfall-response deconvolution
The baselined rainfall-permittivity response can be deconvolved into components using a transfer function. Differentials in
component timestamps between sensors then provide insight into
changes in sensor response with respect to time as well as space,
such as clogging. Different transfer function methods were evaluated to model the relationship between precipitation and infiltration through pervious concrete into the subbase. There are
parameterizations of such processes that impose restrictions on
the form of the transfer function based on numerous assumptions,
but these methods generally suffer from an inability to accurately
reflect unknown systematic deviations from their underlying
assumptions, such as unanticipated bimodal or trimodal responses.
Another class of transfer function estimation relies on using the
linear covariances or related quantities between the response of
interest and lags of precipitation (such as least squares, linear programming, matrix decompositions, and others). While these methods generally have no problems with ‘‘accurately’’ capturing
atypical behaviors in transfer functions, they do have problems
with stability and over-dispersion.
Using individually calculated covariances between the response
and various lags of precipitation will generally provide a plausible
transfer function. However, it will often be over-dispersed due to
autocorrelation across lags, and therefore indicate responses start
before the precipitation fell. Techniques based on solving a linear
system using statistically-based methods do correct for over-dispersion but suffer from stability problems because of the difficulties with inverting a design matrix with column-wise
collinearity. These problems are generally unavoidable if lags of a
response variable are used because the response is usually highly
autocorrelated. The problem is typically less severe if lags of precipitation are used, but still remains if the observation interval is
shorter than the duration of an individual storm.
These problems were circumvented herein by using a novel
approach to estimate the transfer functions needed for the model
using the primary right eigenvector (v) from singular value decompositions of the matrix direct-products of the baselined moisture
readings (Q), with a Toeplitz matrix comprised of columns of the
precipitation observations offset by increasing lags (Ptoep):
Q Ptoep, where denotes a matrix direct-product. Eigenvectors
were similarly calculated, including those for Date ðd PtoepÞ,
and a sinusoid with a wavelength of one year (sin(y)
Ptoep þ cosðyÞ PtopÞ. The date eigenvector is intended to capture any temporal change in responses attributable to clogging.
The sinusoidal eigenvector is intended to capture seasonal interactions such as temperature-dependence. Initial results showed that
the calculated primary eigenvectors had similar forms to published
rainfall-runoff transfer functions that were developed using more
typical techniques such as ordinary least squares. In comparison
to the aforementioned transfer functions, however, the righthand-side eigenvectors appeared to be insignificantly affected by
either of the over-dispersion or stability issues. This is possibly
due to the matrix rotations inherent in generating the eigenvectors. The primary right hand side eigenvectors were therefore
adopted for the present study as the transfer functions relating
rainfall and sensor response. Precipitation was transformed using
the eigenvectors to remove the temporal offsets between precipitation and instrument responses.
2.3.3. Geospatial modeling
The primary objective of the geostatistical analysis is to discern
whether the data from each sensor can be treated as spatially independent and therefore amenable to classical statistical analyses, or
if, in addition to temporal autocorrelation, spatial correlation exists
that must be accounted for in statistical tests. Overlay plots of precipitation and moisture indicate that the near-saturation population is associated with rainfall, so a rainfall intensity of 0.1 mm
per minute was used to separate the dry-versus wet-weather data
for the geostatistical analysis. Normal probability plots (Fig. 3)
were used to further divide moisture readings from U- and D-subbase sensors into four populations.
Based upon the plot shown in Fig. 3, the sensor responses in the
subbase appear to be from the following four distributions: (1) a
horizontal limb corresponding to instrument baseline or very dry
weather (permittivity less than 1); (2) a gradually rising limb corresponding to dry weather with residual subsurface moisture (permittivity between 1 and 4); (3) a vertical limb corresponding to a
set of readings that bridge the residual subsurface moisture and
subsurface saturation (permittivity between 4 and 30); and (4) a
relatively flat limb corresponding to subsurface measurements
approaching saturation (permittivity >30). Note that some events
do not reach permittivity measurements greater than 5 at either
upstream or downstream locations (e.g. 4/21/2012).
The probability plots indicate that the first two populations
include over 99% of the data. In contrast, a very small proportion
of the data on the probability plot falls on the nearly vertical line
that is the third population and few data are saturated (fourth population). A fraction of the third population could be a transitional
group where water surrounding the stone aggregate drains rapidly
by gravity. However, the authors find that it accurately represents
the immediate short-term response to a storm event. It is the third,
near-vertical, segment between residual moisture and quasi-saturation that is interesting in the context of clogging analysis. Hence,
analyses were based on the data from the population associated
with immediate response to precipitation.
Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
5
R. Kertesz et al. / Journal of Hydrology xxx (2014) xxx–xxx
Fig. 3. Normal quantile plots for base-lined moisture (as permittivity) at typical
stone aggregate (Upgradient = U, Downgradient = D) and soil (Natural Soil = N)
transects. Sensor responses belonging to a normally distributed group should fall
on a straight line. Maximum saturation is typically reached at a permittivity of 40.
date effects such as periodicity or offsets in response times
between sensors.
All of these models have limitations in their ability to fit
semivariograms. They are thus suboptimal for the purpose of
determining whether there is any identifiable semivariance or lack
of independence in the measured data (Isaaks and Srivastava,
1989). Consequently, the authors sought a generalized semivariogram model more flexible than any of the aforementioned models;
the model would thereby provide greater statistical power to
ascertain whether there is lack of independence between moisture
readings from different sensors. We adopted the cumulative
density function of the continuous Weibull distribution as the
semivariogram model. This function includes a shape parameter
as a continuous variable that can be tuned to not only mimic the
aforementioned variogram models, but nearly any intermediate
between them. Expressing this function in terms of semivariance
as a function of lag:
t
The geostatistical analysis is limited by the spatial distribution
of the data. The moisture data for soil are clearly from a different
population than the moisture data for stone aggregate, so an initial
division of the data was made by media type. Consequently the
analysis is limited in spatial dimensions, as the sensors used in
the study were organized into three parallel transects with the
two in the subbase being separated by no more than one foot,
and each having all sensors placed at the same elevation above
the native soil. These transects are spaced in this fashion to capture
the progress of an expected ‘‘clogging front’’, anticipated to move
from the upgradient pavement edge toward the center of the parking lot. The semivariogram calculations for the moisture in the
subbase therefore include: (1) the longitudinal separation between
sensors along the (parallel) axes of the upgradient and downgradient transects; and (2) the transverse separation between the
upgradient and downgradient transects. Calculations do not
include a depth component, but they do allow for anisotropy
between the longitudinal and transverse axes relative to the parallel transects.
This determination was made after assessing whether a
semivariance model could be fit to the semivariogram calculated
from the moisture data, the results of which indicated a significant
relationship between semivariance and lag. The semivariogram
was calculated as one-half the average squared difference between
contemporaneous moisture readings at each possible pairing of
sensors. The spatial distance between each pairing of sensors was
used as the corresponding lag.
Typical semivariogram models include components for
short-range variance unattributable to lag (‘‘nugget’’), and a trend
of increasing semivariance with increasing lag. Common basic
models include linear, spherical, exponential, and Gaussian. Many
models are curvilinear to accommodate a semivariogram that
approaches a maximum semivariance (the ‘‘sill’’) asymptotically;
this is equivalent to the ‘‘true’’ variance of the data in the absence
of cross-correlation between sensors. The linear model, however,
optimally fits only a constant trend in semivariance with lag
(and optionally a nugget). A fit to the semivariogram by this model
generally indicates that either there is a trend in the data that
should be corrected for prior to semivariance calculations, or that
the maximum separation of the data points was insufficient to fully
characterize the spatial structure of the data. In contrast, the spherical model optimally fits only semivariograms that reach independence within a finite lag. It often overestimates the rate of increase
in semivariance at relatively short lags. The exponential model, and
its cousin the gaussian model, differ from the linear and spherical
models in that they both approach the sill asymptotically; the
Gaussian model includes an inflection that allows for persistent
semivariance at short lags. None of these basic models accommo-
DðxÞ ¼ k keð1½xu=sÞ þ nugget
ð1Þ
where x (m) is lag; u (m) is x-offset; s = scale parameter; t = shape
parameter (recall (x u)/s is the standard normal deviate for Gaussian data), and k = scale factor normalizing D(x) to interval [0, 1]. This
is a modification of the more familiar 3-parameter expression for
this function:
YðxÞ ¼ 1 eð½xu=sÞ
t
ð2Þ
Our modifications provide a monotonic function that can
include a nugget and the maximum value of the response variable
(D, or Y in the equations above). The three parameter Weibull was
chosen as a basis because it allows an offset on the x-axis to control
for variation in sensor response due to longitudinal position.
Differential clogging between the upgradient and downgradient
transects could be manifested as very high anisotropy. This model
was therefore fit to the semivariogram data by iteratively recalculating the lags as Euclidean distances with a varying constant
multiplied by the (transverse) distance component.
2.3.4. Clogging
After first baselining and deconcolving the data, then developing a model to account for (auto)correlation with respect to space
and time, data were analyzed to investigate the occurrence of clogging. Time-series plots of moisture sensor permittivity readings
within the subbase indicated that the number of apparent infiltration events, or instances of maximum instrument response, were
less frequent during the latter part of the study relative to the earlier portion of the study. Some instruments might have been
changing in sensitivity as the study progressed. However, precipitation also appeared to accumulate at a slower rate as the study
progressed (Fig. 4), raising the possibility that the decrease in the
frequency of infiltration events could have been merely due to
decreased rainfall. Therefore, a statistical model was employed to
differentiate such nuisance effects on subbase moisture readings.
The clogging model was designed to discern whether sensor
responses were differentiable by some factor that might indicate
clogging rather than by measurable climatic conditions or sensor
aging (drift). We assumed that sensor group was a proxy for proximity to the expected clogging front; the front was assumed to progress from the upgradient pavement edge toward the center of the
pavement. Sensor response and precipitation were related in the
model through the previously calculated transfer functions for
each sensor (time-invariant temporal convolutions). Nuisance
effects included in the model were: a smoothly changing instrument response through time (a quadratic ‘‘main effect’’ of time
and time-squared); the (now convolved) prior 30 min of
precipitation, not changing as a function of time (a ‘‘main effect’’
Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
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R. Kertesz et al. / Journal of Hydrology xxx (2014) xxx–xxx
Fig. 4. Precipitation intensity and accumulation throughout the study. A linear
regression of cumulated precipitation with date accentuates the relatively steady
decrease in measured precipitation as the study progresses. DT is the date and
timestamp of measured precipitation.
of antecedent precipitation); and the prior 30 min of precipitation,
changing as a linear function of time (an ‘‘interaction effect’’
between precipitation and time). Quadratic functions captured
any change in instrument sensitivity through time (instrument
drift). Linear effects were used to model time-invariant and timevariant responses to convolved precipitation.
Our initial concern was that quadratic and linear models are
potentially too constrained to model such effects without biases
if they exhibit behaviors such as logarithmic decays or stepresponses. We found however that, when used in conjunction with
a first-order autoregressive (AR1) term, they were sufficient to contain both nuisance effects and autocorrelation. This finding is supported by the non-significance (P < 0.1) of the slope of the linear
regression of residuals on their first lag. We therefore assumed that
the residuals were not problematically autocorrelated, indicating
that standard errors of the model fixed effects should not be biased
and thereby render invalid statistical tests. The significance of each
term in the model was evaluated using F-tests for overall fixed
effects and random effects, and t-tests for differentiating individual
levels within fixed effects.
3. Results and discussion
3.1. Spatiotemporal description of data
Subsurface permittivity responses differed markedly between
those placed in the stone aggregate subbase and those placed in
soil. In contrast with sensors placed in aggregate, sensors in soil
did not exhibit sharp increases in permittivity immediately after
or during storm events (short term), as evidenced by the differences shown in Fig. 3 as well as between Figs. S1 and S4. Sensors
in soil also exhibited greater seasonality (e.g. Fig. 5, upgradient
stone aggregate sensor V2CU versus soil sensor V2CN). While multiple years of data were not available, seasonality is evidenced by
changes in event frequency that are congruent with seasonal periods (Fig. 4).
Detail plots illustrating short-term sensor responses are not
included in the main text for brevity and because it is extremely
difficult to visually separate additive effects comprising signals.
Supplemental Fig. S1, however, shows upstream and downstream
pairs for selected storm events at sites V2, V5, and V10. Both
upstream and downstream V2 sensors reach saturation more often
than V5, which, itself, reaches saturation more often than V10.
During smaller events (i.e. 4/21/2012), V5 has the highest
response. At V2 and V5, the downstream response is muted, compared to upstream. The opposite is true at V10. Site V10 also shows
a more linear rise to peak and decay compared to other locations.
Fig. 5. Examples of long-term sub-pavement aggregate subbase (A) and sub-trench
soil (B) moisture readings as permittivity. Rainfall (mm) is also plotted on the same
scale.
The same linearity is observed for volumetric water content (not
shown). This indicates that there may be a unique drainage phenomenon at those downstream locations. However, as shown in
Fig. S2 (storm responses for additional upstream locations),
V22CU has a similarly linear signal. Like Fig. S1, Fig. S2 shows
decreasing saturation frequency with increasing location number.
The sensor responses at V1CU are saturated during more events
than at location V18CU and there are no instances of saturation
at site V22 for the time period shown. The apparent lack of consistent difference in response between subbase sites may be simply
due to the difficulty of visually decomposing signals into their constituent parts, or due to a number of factors that are difficult to
control such as non-uniformity of the bedding material, sensor
divergence through long-term drift, non-uniform clogging,
construction irregularities, etc. In fact, observations made during
construction included a distinct difference in gravel bed depth
between locations V1 and locations V5 through V22. There is a
180 mm difference in depth to surface between V1 and V5
(Fig. S3). This would certainly lead to higher magnitude peaks
and a sharper rise to peak at shallow beds because the bed would
get saturated more easily than locations with a deeper bed depth
under storms of the same intensity. Such localized phenomena
may diminish the strength of geospatial trends between sensors.
3.2. Spatial data structure
Semivariograms were constructed from upstream and downstream location data using the responses for events of intensities
greater than 0.1 mm min1. Semivariograms initially constructed
using raw data indicated an unbounded trend in increasing semivariance with increasing lag; when using baselined data and a planar site-wide trend surface, the trend disappeared. Iterative fitting
of our semivariogram model indicated that, if a zero x-intercept is
assumed, the range of spatial correlation would have to be very
short to accommodate the observed data (Fig. 6). Fit characteristics
are tabulated in Table 3. The range is visually estimated to be
between 2.5 m and 6 m but there is no significant support for the
presence of any spatial correlation structure in the data. If the
Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
7
R. Kertesz et al. / Journal of Hydrology xxx (2014) xxx–xxx
generalized semivariogram model is not constrained (not shown),
then it approximates a flat line with no significance (model fit
P > 0.1). Note that many of the high semivariance values are associated with V2 Upstream (V2CU). Even when V2CU is excluded, an
estimated lag of 6 m would be needed for data to be independent
(when forced through x = 0).
As indicated during the discussion of spatiotemporal trends, the
statistical analysis shows that the sensors, as installed, do not provide enough information to show a spatial correlation structure.
There is not enough information to determine if general pavement
response could be determined using a couple of sensors or if there
would need to be multiple sensors, separated by a minimum distance (e.g. 6 m). The pavement performance monitoring method
is dictated by whether or not the researcher thinks that there
should be theoretically zero variation between collocated sensors
or not.
3.2.1. Clogging
Differences in relatively short-term response characteristics
were apparent between subbase sensors; responses were differentiated by sensor group, which could be attributed to differential
clogging along the expected migration of a clogging front (Table 4).
The magnitude of the group-wise difference is small, in part, due to
the varying scales of the constituent variables in the model, which
were not standardized. The practice of non-standardization or normalization is in conformance with the opinions of some statisticians and in nonconformance with the opinions of others.
Regardless of its magnitude, the detection of group-wise difference
supports the concept of using the presented method or variations
of it to detect clogging. While the vast majority of the variation
in the data is attributable to the (random) first-order autoregressive terms associated with lagged permittivity (Estimate > 0.97),
significant amounts of information are also captured by the precipitation effect (Estimate 0.027). Effects of drift or seasonality
through time (Time) are not significant with respect to individual
sensors. Seasonality is likely absorbed by the autoregressive (or
moving average) parameter in the model.
3.2.2. Comparison of native soil response to subbase response
While it is of little use to apply the previously discussed statistical clogging analysis method to the sensors deployed in native
soil, the process of baselining data revealed interesting qualitative
differences between permittivity measurements in native soil and
stone aggregate. Fig. 1 illustrates the locations of native soil
Fig. 6. Variograms for permittivity in stone aggregate subbase during precipitation
intensity at or above 0.1 mm per minute. The variogram function is the 3-parameter
cumulative density function (CDF) for the Weibull distribution. A straight- line-fit
(green, dashed) is provided for visual reference. (For interpretation of the references
to color in this figure legend, the reader is referred to the web version of this
article.)
Table 3
Fit parameters for Weibull-CDF based variogram model and comparison to a linear
model for spatial correlation of permittivity in crushed stone subbase beneath porous
pavement. Neither model is statistically significant (P = 0.48, 0.43). Models were
statistically differentiable from each other (P = 0.02).
Parameter
Value
Weibull CDF fit
x-Offset
Nugget (y-Offset)
Range (correlation length)
Sill (true variance)
Shape
Scale
Anisotropy coefficient
0.0
0.75
20928.0
143.0
0.18
15137.0
2.66 E12
Value
Statistic
Model fit evaluations
SSE
R-sq
R-sq adjusted
P-value
Statistic
Model comparison
F-stat
P-value
Weibull-CDF
Linear
49006
0.017
0.015
0.48
Value
48834
0.02
0.01
0.43
5.56
0.02
sensors along the BA’s east-west transect. Baselines differ between
native soil and aggregate, indicating increased soil moisture retention in the soil (Fig. 5). This is supported by geotechnical analysis of
soil cores which found that the first 2.3 m of soil consists of brown
lean clay, trace organics, and rock and brick fragments. The soil, in
contrast to upstream and downstream sites, has a muted shortterm response (Fig. 3) and much of the change in moisture occurs
over an extended period of time.
As described previously, seasonal trends are more pronounced
in the native soil than in the aggregate beneath the PC (Fig. 5). It
is reasonable to expect a stronger influence of seasonality on sensors in native soil because temperature has a stronger influence on
two factors, permittivity and electrical conductivity, when there is
more water present in the surrounding media. As temperature
decreases, permittivity increases but bulk electrical conductivity
decreases. The temperature dependence of both permittivity and
conductivity are large. In comparing the water content of clay
and gravel after gravitational water drains, there is much more
water held by clay than gravel.
Results also show that the short term response to precipitation
varies by sensor location. Supplemental Fig. S7 shows that the
magnitude of baselined response to rainfall broadly increases from
V2N to V22N. While the trend is affected by aberrations in permittivity, particularly at V22CN, a brief analysis of Period data (which
were largely unaffected by electrical conductivity) supports the
findings and indicates that V22CN maintains a high saturation
level. However, both Period and permittivity data show that site
V5CN maintains a permanently high signal as well. The sensor produced readings during storm events that were higher than even a
saturated clay soil (Bittelli et al., 2008). Perhaps there is persistent
ponding at site V5CN, or perhaps localized soil chemistry has
affected the sensor. Barring site V5CN, the lag effect is congruent
with the physical construction of the facility. Due to the slope of
the bioswale towards the west and due to the purposeful blockage
of the underdrain outflow, upgradient free water is expected to
collect in the underdrain and exfiltrate back out of the underdrain
downgradient.
One major difference between the responses in the native soil
and those in the subbase are that the native soil sensors exhibit
unusual perturbations that are difficult to explain, while upstream
and downstream subbase locations along the same vector do not.
Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
8
R. Kertesz et al. / Journal of Hydrology xxx (2014) xxx–xxx
Table 4
Statistical summary for model of baselined moisture sensor readings (permittivity). P-values less than or equal to 0.01 are considered significant. ‘Group’ is a proxy for proximity
to an expected clogging front. Sensor response and precipitation were related through temporal convolution prior to running the statistical model.
Effect type
Effect-level-specific effects
Group
Fixed effects
Group
Group
Sensor (Group)
Sensor (Group)
Sensor (Group)
Sensor (Group)
Sensor (Group)
Sensor (Group)
Sensor (Group)
Sensor (Group)
Sensor (Group)
Time (Date2)
Time (Date)
Temperature (Celcius2)
Temperature (Celsius)
Precipitation
Intercept
Random effects
Lagged e
Lagged e
Lagged e
Lagged e
Lagged e
Lagged e
Lagged e
Lagged e
Lagged e
D
U
D
D
D
U
U
U
U
U
U
Sensor
V2CD
V5CD
V10CD
V1CU
V2CU
V5CU
V10CU
V18CU
V22CU
V2CD
V5CD
V10CD
V1CU
V2CU
V5CU
V10CU
V18CU
V22CU
Overall effects
Estimate
Std. Err.
t-Value
P-value
F-value
ProbF
0.0013
0
0.0028
0.0054
0
0.0076
0.0004
0.0053
0
0.0005
0.0013
9.30E19
3.10E09
0
0.0003
0.0267
2.5877
0.0003
na
0.0003
0.0003
na
0.0003
0.0003
0.0003
na
0.0003
0.0003
na
na
na
0
0.0009
1.0872
4.13
na
9.91
18.14
na
26.75
1.60
18.43
na
1.72
4.18
na
na
na
13.99
30.75
2.38
<.01
Na
<.01
<.01
Na
<.01
0.11
<.01
Na
0.09
<.01
Na
Na
Na
<.01
<.01
0.02
19.65
<.01
280.15
<.01
10.12
<.01
243.46
<.01
945.78
5.67
<.01
0.02
0.9753
0.9736
0.9893
0.9724
0.9842
0.9727
0.9852
0.9847
0.9890
0.0002
0.0003
0.0004
0.0002
0.0001
0.0003
0.0003
0.0002
0.0003
4821.45
3402.63
2780.93
4985.77
8059.12
3793.06
2884.19
4603.28
2918.41
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
nc
nc
Some effects of very low magnitude are significant because they were not standardized (e.g. Time/Date). High sensor-specific autocorrelation was contained by specifying the
first time-lag of individual sensor responses as the only random effect. na: parameter estimate not available (may be zero-level automatically selected by the software). nc:
not calculated but apparently significant. e: dimensionless permittivity.
These perturbations deviate sharply from the strong seasonal pattern described previously. Supplemental Figs. S5–S7 show longterm data series for a number of upstream, downstream, and
native sites. Site V5CN shows a distinct rise and then sudden drop
in permittivity response in June, 2012. V22CN shows a continuously elevated permittivity response throughout the first part of
2012. It is unknown whether this was a measurement of real
hydrologic phenomenon or not. It is also important to note that
the baselined response is designed to normalize results for better
comparison. However, there is a possibility that it obfuscates real
phenomena (e.g. V22CN). For example, February 2013 readings of
many native soil sites show a sharp drop in permittivity that is
not observed in baselined data. This is a common effect of freezing
water but native soil temperatures at the sample sites were measured to drop to 2–3 °C, just above freezing.
3.2.3. Contribution to future research
The implications of these findings on future research are that,
while it appears that there is no clear geospatial trend in the sensors placed beneath the pavement at the test site, the methods
developed here should be applied to other investigations. The Weibull function is flexible, such that it can be used to analyze other
multi-sensor datasets for geospatial trends without modification.
Particular emphasis should be placed on spacing sensors along
more densely populated transects to determine if it results in better correlation and lower variance between sensors when installed
in coarse media. Improvements to the current study include: placing sensors in a gravel bed of succifient depth; designing the pavement surface with zero transverse slope; placing sensors along a
geometrically increasing distance from the pavement edge using
multiple lag distances; and installing sensors in duplicate. Lastly,
the results suggests that maximum power is achieved by separating treatments from each other by >6 m.
Another very interesting tool that can be applied to other
research methods includes the observations made in Fig. 3, where
the normal quantile plots indicate distinct phases of moisture
response. Researchers can produce such plots to quickly expose
values of interest and to focus on specific components of the drying/wetting cycle. Similarly, the method used for baselining data
may be valuable for application to other datasets to account for
long-term sensor drift and seasonal effects and is a useful first step
in data reduction.
The methods used to detect clogging are a particularly novel
approach to the problem and could be applied to other installations, again with a different spatial arrangement of sensors. In particular, the presented statistical methods are unique in that they
avoid issues of overdispersion while also remaining stable. They
allow modeling of both time-variant and time-invariant responses
to precipitation and can be adjusted to include coupled parameters
not investigated in this project.
All of the methods above can be broadly applied to analyze
other types of moisture sensors and sensor response variables as
well as other applications. Clogging or sealing investigations may
be an interesting component of floodplain analysis in order to
determine if effective infiltration is changing over time.
4. Conclusions
Methods are developed to extract useful spatial and temporal
information from moisture sensors embedded in soil and crushed
stone aggregate. A model removes seasonal trends and offsets. A
simple and intelligent data visualization and reduction technique
is developed. A geostatistical model is used to investigate sensor
(in)dependence. The methods are appropriate for application to
various moisture sensor technologies and soil conditions.
Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011
R. Kertesz et al. / Journal of Hydrology xxx (2014) xxx–xxx
It is apparent that, due to the lack of typical soil properties (capillary action, matric suction, etc), moisture sensors respond
differently in crushed stone aggregate (in subsurface stormwater
retention/detention areas) than in soil. An investigation of the
spatial distribution of sensors installed beneath PC suggests that
sensor independence is achieved within a short lag distance
(6 m). There appears to be more than 1 phase of response in most
sensors buried beneath PC. Statistical analysis suggests that there
is not enough information to identify an upstream-downstream
clogging pattern during the investigation period. A better arrangement of sensors should lead to a more conclusive outcome.
Disclaimer
The US Environmental Protection Agency, through its Office of
Research and Development, funded and managed, or partially
funded and collaborated in, the research described herein. It has
been subjected to the Agency’s administrative review and has been
approved for external publication. Any opinions expressed in this
paper are those of the author (s) and do not necessarily reflect
the views of the Agency, therefore, no official endorsement should
be inferred. Any mention of trade names or commercial products
does not constitute endorsement or recommendation for use.
Acknowledgments
This research was conducted with the support of an appointment to the Research Participation Program at the National Risk
Management Research Laboratory administered by the Oak Ridge
Institute for Science and Education.
Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.jhydrol.2014.02.
011.
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Please cite this article in press as: Kertesz, R., et al. Spatial and temporal structure within moisture measurements of a stormwater control system. J.
Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.02.011