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\begin{document}

\title{An approach of spatially- and temporally-extensive soil moisture data
combination based on EOF analysis}



\author[1]{Ying Zhao}%
\author[2]{Fei Li}%
\author[3]{Rongjiang Yao}%
\author[3]{Wentao Jiao}%
\author[4]{Robert Hill}%
\affil[1]{Institute of Plant Nutrition and Soil Science}%
\affil[2]{Chinese Academy of Agricultural Sciences}%
\affil[3]{Chinese Academy of Sciences}%
\affil[4]{University of Maryland}%


\vspace{-1em}



  
  \date{May 22, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Modeling and prediction of soil hydrologic processes require the
identification of soil moisture spatial-temporal patterns and effective
methods allowing the data observations to be used across different
spatial and temporal scales. This work presents a methodology for the
combination of spatially- and temporally-extensive soil moisture data
obtained in the Shale Hills Critical Zone Observatory (CZO) from 2004 to
2010. The soil moisture data sets were decomposed into spatial Empirical
Orthogonal Function (EOF) patterns, and their relationship with various
geophysical parameters was examined to determine the dominant factors
contributing to the profiled soil moisture variability. The EOF analyses
indicated that one or two EOFs of soil moisture could explain 76-89\% of
data variation. The primary EOF pattern had high values clustered in the
valley region, and conversely low values located in the sloped hills. We
suggest a novel approach to integrate the spatially-extensive manually
measured datasets with the temporally-extensive automated monitored
datasets based on the EOF analyses. Given the data accessibility, the
current data merging framework has provided the methodology for the
coupling of the mapped and monitored soil moisture datasets, as well as
the conceptual coupling of slow and fast pedologic and hydrologic
functions. This successful coupling implies that a combination of
different extensive moisture data has provided interesting insights into
our understanding of hydrological processes at multiple scales.%
\end{abstract}%



\sloppy


\textbf{An approach of spatially- and temporally-extensive soil moisture
data combination based on EOF analysis}

Ying Zhao\textsuperscript{1,2,*}, Fei Li\textsuperscript{3}, Rongjiang
Yao\textsuperscript{4,*}, Wentao Jiao\textsuperscript{5}, Robert Lee
Hill\textsuperscript{6}

\emph{\textsuperscript{1}College of Resources and Environmental
Engineering, Ludong University, Yantai 264025,
China;\textsuperscript{2}Department of Ecosystem Science and Management,
Pennsylvania State University, University Park,
PA;\textsuperscript{3}Grassland Research Institute, Chinese Academy of
Agricultural Sciences, Huhhot 010010, China; \textsuperscript{4}State
Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil
Science, Chinese Academy of Sciences, Nanjing 210008,
China;\textsuperscript{5}Research center for Eco-environment sciences,
Chinese Academy of Sciences, Beijing, 100085,
China;\textsuperscript{6}Department of Environmental Science and
Technology, University of Maryland, College Park, MD 20742,
USA;}\textsuperscript{*}\emph{Corresponding author: yzhaosoils@gmail.com
(Y. Zhao) and rjyao@issas.ac.cn}

\emph{(R.J. Yao).}

\textbf{Abstract} Modeling and prediction of soil hydrologic processes
require the identification of soil moisture spatial-temporal patterns
and effective methods allowing the data observations to be used across
different spatial and temporal scales. This work presents a methodology
for the combination of spatially- and temporally-extensive soil moisture
data obtained in the Shale Hills Critical Zone Observatory (CZO) from
2004 to 2010. The soil moisture data sets were decomposed into spatial
Empirical Orthogonal Function (EOF) patterns, and their relationship
with various geophysical parameters was examined to determine the
dominant factors contributing to the profiled soil moisture variability.
The EOF analyses indicated that one or two EOFs of soil moisture could
explain 76-89\% of data variation. The primary EOF pattern had high
values clustered in the valley region, and conversely low values located
in the sloped hills. We suggest a novel approach to integrate the
spatially-extensive manually measured datasets with the
temporally-extensive automated monitored datasets based on the EOF
analysis. Given the data accessibility, the current data merging
framework has provided the methodology for the coupling of the mapped
and monitored soil moisture datasets, as well as the conceptual coupling
of slow and fast pedologic and hydrologic functions. This successful
coupling implies that a combination of different extensive moisture data
has provided interesting insights into understanding of hydrological
processes at multiple scales.

\textbf{Keywords:} soil moisture, data merging, Empirical Orthogonal
Function

\textbf{1. Introduction}

Soil moisture is a key variable within earth system dynamics from
regional to pedon scales (Famiglietti et al., 1998; Korres et al.,
2015). Identification and prediction of soil moisture patterns at
different scales are important in a wide range of agronomic,
hydrological, pedological, and environmental studies (e.g., Grayson et
al., 2002; Lin et al., 2006). However, obtaining accurate information on
soil moisture at an appropriate temporal and spatial scales is still
challenging (e.g. Crow et al., 2012; Vereecken et al., 2008). This
shortage of information has impeded the modeling, predication, and
management of water resources (Owe et al., 1982; Grayson et al., 1997;
Zhu and Lin, 2010; Shi et al., 2015). Linking soil moisture mapping with
monitoring can provides a more integrated approach to understanding
soils and water resources (Dunn and Lilly, 2001; Joshi and Mohanty,
2010; Ma et al., 2017), and provides a way of combatting the general
decline of field hydrology relative to modelling (Beven et al., 2020).

Previous studies have indicated that the spatial pattern of soil
moisture is highly dependent on various controlling factors such as
parent material, soil, landuse/vegetation, topography and climate
(Grayson et al., 1997; Famiglietti et al., 1998; Western et al., 1999;
Baldwin et al., 2017). However, separating the relative importance of
individual factors is usually extremely difficult as some of the
influencing factors are interdependent due to the scale-dependence,
dry-wet cycles, and interface exchange from top to deep soil layers
(Zeleke and Si, 2006; Famiglietti et al., 1998; Western et al., 1999).
During wet conditions, subsurface lateral flow may be important, whereas
during dry conditions, the surface vertical flow at the onset of
precipitation has more influence (Grayson et al., 1997; G\selectlanguage{ngerman}ómez-Plaza et
al., 2001). The correlation length of soil moisture ranges from near
zero to a thousand meters. It has been found to be highly dependent on
the scale of the study and on the density of the measurements (Western
and Blöschl, 1999), with a clear direct proportionality of increasing
correlation lengths with increasing scales having been observed. For the
on-site soil moisture monitoring system or networks, the correlation
measurements typically include the several sites, whereas for the
measurements characterizing soil moisture variation within the field,
the area can cover several ha areas, or even much large areas for
satellite-based investigations. It is evident that the potential exists
for more accurate estimations of soil moisture by using synergistic
approaches among a variety of earth observation methodologies.

The procedures for associating the relatively stable spatial patterns of
soil moisture and specific soil hydrologic processes to precipitation
events are sorely lacking. The temporal variations associated with field
measurements of soil moisture have been displayed within numerous
studies that have shown the static, terrain-derived indices rarely
explained more than 50\% of the soil moisture variability (Famiglietti
et al. 1998; Western et al. 1999; Baldwin et al., 2017). Although
climate seasonality and localized vs. non-local hydrological fluxes
exert a strong influence on surface or near-surface soil moisture
distribution (Grayson et al., 1997; Western et al., 1999; D'Odorico and
Porporato, 2010), less is understood regarding how the subsurface soil
moisture spatial patterns change with climate seasonality and seasonal
changes in hydrological fluxes. By integrating spatially-distributed
soil physical properties, topographical variables and meteorological
data, Schwärzel et al. (2009) developed a novel approach in model-based
mapping of soil moisture within forested sites. This approach provided a
more objective description of soil moisture variability than the
traditional mapping by an integrated ecological approach. Other research
using a modification of this approach showed that both the spatial
distribution and temporal evolution of soil moisture may be investigated
at multiple scales (e.g., Deiana et al., 2008). Another potential
improvement was the integration of geophysical scanning with real-time
soil moisture monitoring and dye staining (Guo et al., 2019). Real-time
soil moisture monitoring may provide information concerning actual
hydrologic dynamics and the timing of preferential flow occurrence,
while dye staining patterns may validate the spatial distribution of
preferential flow pathways as revealed by geophysical scans. The
synthesis of these methods may enhance the data accuracy and associated
processes, thus increasing our understanding of hydrological processes
in various soils and landscapes (Ma et al., 2019).

Spatial dependency is commonly characterized and quantified by
geostatistical methods, such as autocorrelation and variogram analysis
(Zhao et al., 2011). An additional way to analyze the spatial patterns
of soil moisture and their connection to regional characteristics is
through an empirical orthogonal function (EOF) analysis (Jawson and
Niemann, 2007; Zhao et al., 2012). The EOF analysis decomposes a dataset
into a series of orthogonal spatial patterns. These patterns may be
correlated with regional characteristics to identify whether the
characteristics have an influence on the most important tendencies of
the soil moisture. Utilizing correlation analyses, these underlying
(stable) patterns of soil moisture variations can be connected to
parameters derived from topography, soil, vegetation, land management
and meteorology. Yoo and Kim (2004) investigated the spatial and
temporal variability of field-scale soil moisture and concluded that
there is no simple and unique mechanism that can be applied to explain
the evolution of the soil moisture field. Wagenet (1998) summarized the
main factors that influence soil moisture from the pore scale to the
global scale, and recognized soil and topography as important local
controls of soil moisture variations. During dry periods, soil moisture
distribution may be conceptualized as being controlled predominantly by
soil properties, whereas during wet periods the topography is the
controlling factor within a landscape. However, the pedon/plot scale
results have not been easily transferable to hillslope and catchment
scales, and both theoretical and empirical approaches have been used to
quantify hydrological dynamics based on such `point-scale' data that
tends to over- or underestimate parameters and fluxes (Sidle et al.,
2017). While the temporal frequency for the manual measurement of soil
moisture has been found to normally be about weekly-or monthly-based,
the automated monitoring data may be hourly-based or daily-based (Korres
et al., 2015).

In this study, part of our soil moisture dataset contains manually
measured data that offers better spatial coverage with many sites, but
with limited temporal frequency as weekly measurements were made.
Another part of our soil moisture dataset contains automatically
monitored data that offers better temporal frequency with repetitive
ten-min to one-hour measurements, but limited spatial coverage with a
limited number of selected sites. It is expected that the product of
this combination captures the temporal variation of soil moisture from
the automatically monitored data and improved spatial resolution using
the information from manual measurements. The objectives of this study
were to: (1) derive the dominant soil moisture spatial-temporal patterns
based on multi-year datasets; (2) determine how these patterns are
controlled by terrain, soil, and vegetation as a function of scale,
wetness, and depth; and (3) provide a possible way to integrate
spatial-extensive datasets with temporal-extensive datasets.

\textbf{2. Materials and Methods}

\textbf{2.1 Study area}

The forested Shale Hills catchment has an area of 7.9-ha, and is located
in Huntingdon County, PA, on the eastern coast of the USA. The catchment
is V-shaped overall, with a first-order stream in the valley and
moderately steep slopes (up to 25\%--48\%) on both sides of the stream
(Fig. 1). Swales are inter-dispersed within the catchment, with five on
the south-facing slope and two on the north-facing slope. Elevation
ranges from 256 m at the outlet of the catchment to 310 m at the highest
ridge. The catchment is underlain by approximately 300-m thick, steeply
bedded, highly fractured Rose Hill Shale. The soils were formed from
shale colluvium or residuum, with many channery shale fragments
throughout most of the soil profiles. Five soil series were identified
in the catchment according to the USDA classification (Takagi et al.,
2011; Fig. 2). The Shale Hills catchment has a typical humid continental
climate, with mean monthly temperatures minimum of \selectlanguage{english}-3degC in January and
maximum of 22degC in July, and an annual precipitation of about 980 mm
(National Weather Service, State College, PA). The precipitation is
roughly evenly distributed throughout the year, during the summer months
typically occurs in convective weather fronts that can produce high
intensity, short duration storm events.

\textbf{2.2 Data collections}

At the Shale Hills Catchment, a total of 106 manual soil moisture
measurement locations were recorded on about a weekly basis over a 6-yr
period (2004 to 2010; Fig. 1). A portable TRIME-FM Time Domain
Reflectomery (TDR) Tube Probe (IMKO, Ettlingen, Germany) was used to
determine soil moisture contents while being placed at specific depth
(i.e., 0.1-, 0.2-, 0.4-, 0.6-, 0.8-, and 1.0-m) intervals using a PVC
access tube installed at each sampling site. The number of locations
measured on each measurement day varied due to the number of actual
locations, personnel availability, and also weather conditions. The
subsequent analysis includes 36 days where at least 65 soil moisture
annual measurement locations were measured, as a trade-off between
having a sufficient number of measuring sites to adequately represent
spatial coverage and sufficient sampling days to have a more complete
temporal coverage. Among these 36 measurement days, it can be classified
as13 wet (\textgreater{}22\%), 14 moist (\textless{}22\%,
\textgreater{}15\%), and 9 dry (\textless{}15\%) times based on the
field averaged wetness condition, respectively.

At each sampling site of soil water content, we also measured other
properties that were anticipated to influence the water transport and
storage. The intact soil cores were collected throughout the catchment
during the installation of soil monitoring tubes. Each soil core was
first described using standard soil survey procedures, including horizon
thickness, color, texture, structure, roots, and amount of redoximorphic
features (Fig. 2). A digital elevation model (DEM) of the catchment was
interpolated from light detecting and ranging (LiDAR) elevation point
clouds collected by an airplane flown over the catchment in 2006 (PAMAP,
PA Department of Conservation and Natural Resources). Approximately
40,000 LiDAR elevation points were converted into a 1x1 m DEM using
ArcGIS 9.2 (ESRI Inc., Redland, CA, USA). The smoothed DEM was then use
to derive the four primary topographic attributes (elevation, slope,
curvature, and upslope contributing area) and one composite topographic
attribute (topographic wetness index). Terrain attributes were then
extracted at all soil moisture monitoring locations using the
coordinates obtained from the total station survey.

In addition to spatially extensive manual measurement, soil moisture has
been monitored in real-time at 5 representative sites, with 4-10 depths
at each site depending on soil thickness and horizonation. These sites
are located from the ridge top (site 74) to the valley bottom (site 61),
and both planar (site 51)/convex (site 53) hillslopes and concave swales
(site 15) (Fig. 1). At each long-term monitoring site, a pit was
excavated, and capacitance-type probes of Decagon Devices, Pullman WA
(EC10 or EC5) were used to monitor the profiled soil moisture at 10 min
intervals. A Pluvio load cell rain gauge (OTT Hydrometry, Kempten,
Germany; precision ) was located in a clearing on the north ridge of the
catchment and automatically recorded precipitation every 10 minutes
automatically. Further details on the soil moisture probe installation
can be found in Lin and Zhou (2008).

\textbf{2.3 EOF analysis}

Empirical orthogonal function (EOF) analysis has been widely applied for
the analysis of the spatial and temporal variability of large
multidimensional datasets (Zhao et al., 2012). The EOF, also known as a
type of principal component analysis, decomposes the observed
variability of a dataset into a set of orthogonal spatial patterns
(EOFs) or a set of time series called expansion coefficients (ECs). This
procedure is accomplished by transforming the original data set into a
new set of uncorrelated variables, and then ordered in a manner so that
the first few of the new variables explain most of the variation
existing in the original data set. For example, it is possible to
construct various second moment statistics linking one point to another
in geophysical data maps. The resulting correlation matrix is real and
symmetric, and therefore possesses a set of orthogonal eigenvectors with
positive eigenvalues. If there are geophysical data maps that are time
series with any \emph{m x n} matrix, \emph{A} , square or rectangular,
there uniquely exists two orthogonal matrices, \emph{U} and \emph{V} and
a diagonal matrix \emph{L} such that,

\emph{A} = \emph{U} x \emph{L} x \emph{V} \textsuperscript{T} (1)

where \emph{V} \textsuperscript{T} is the transpose of a matrix \emph{V}
. Note that \emph{L} is padded with zeros to make the square diagonal
matrix into an \emph{m} x \emph{n} matrix. This assumption also implies
that \emph{L} has at most \emph{M} = min(\emph{m} , \emph{n} ) nonzero
elements. The columns of \emph{U} are called the EOFs of \emph{A} and
the corresponding diagonal elements of \emph{L} are called the
eigenvalues. Each row of \emph{V} serves as a series of time
coefficients that describes the time evolution of the particular EOF.
The map associated with an EOF represents a pattern, which is
statistically independent and spatially orthogonal to the others. The
eigenvalue indicates the amount of variance accounted for by the pattern
(Zhao et al., 2012).

While single soil moisture patterns might be affected by random
processes (e.g., rainfall shortly before measurement), significant EOFs
represent stable patterns of a dataset. The existing degree of
randomness of a single soil moisture pattern is reflected by the
associated EC, since the EC value represents the proportion of the
significant EOF pattern within the soil moisture pattern of each date.
In consequence, single soil moisture patterns (which might be random)
were not used but the EOF patterns used for the subsequent correlation
analysis. That is, the EOF patterns can be further correlated to the
geophysical characteristics of the region to determine the dominant
physical controls. For the EOF analysis, we used the spatial anomalies
of the soil moisture dataset instead of the soil moisture which excludes
the temporal variations from consideration (Perry and Niemann, 2007).
The spatial anomalies are calculated by subtracting the mean soil
moisture for a given sampling day from all the soil moisture
observations collected on that day.

\textbf{2.4 Data combination}

One of the primary benefits of the EOF analysis is a small number of
orthogonal spatial patterns was identified that together explain a large
proportion of the total variability of the soil moisture data. We now
examined how closely these underlying patterns resembled regional
characteristics that might dominate the spatial variability of soil
moisture. For this analysis, we used the correlation coefficient between
the EOFs and the available regional characteristics. Statistical
analyses were conducted using SPSS for Windows (SPSS Inc., Chicago). The
Pearson's correlation was used to investigate the correlation between
soil moisture and soil-terrain attributes. Linear regression was used to
predict soil moisture (as a dependent variable) based on using either
soil properties and/or terrain attributes (as independent variables).

Furthermore, given that the first EOFs exhibited the general patterns of
soil moisture across the whole investigated spatial coverage, if the
EOFs of the manual soil moisture measurements at some sites had the
strong correlations with its automatically recorded values, then it was
possible to apply this relationship to the first EOFs to derive the soil
moisture across the entire area at any automated monitoring time.
Consequently, we considered that this method may have provided an
appropriate way to integrate the spatially-extensive (but
temporally-limited) manual datasets and the temporally-extensive (but
spatially-limited) automated monitoring datasets. The following
narrative describes in detail the four steps involved with the data
merging methods.

First, an EOF decomposition was performed on the soil moisture dataset
to identify the patterns of covariation (the EOFs) and their importance
on each date (the ECs).

Second, statistical tests were used to determine the EOFs between whole
spatially-extensive data and automated monitored data that were
statistically significant and should be retained in the transferring
method.

Third, a multiple linear regression was performed to identify empirical
relationships between automated monitored soil moisture data and its
EOFs.

Fourth, the identified empirical relationships were employed to
calculate soil moisture at each manual measured site within the entire
catchment via its EOFs.

\textbf{3. Results and Discussion}

\textbf{3.1 Spatial-temporal patterns of soil moisture}

The variogram analysis and histogram of soil moisture storage indicated
that interpolated soil moisture maps exhibited seasonal alignments of
soil moisture storage along topographic convergent areas (Fig. 3). We
found the sample variograms with a clear sill and nugget and observed
that the geostatistical structure of soil moisture was seasonally
evolved. During the wet winter period, high sills (15-25
(\%)\textsuperscript{2}) and low correlation lengths (20-30 m) were
observed, whereas during the dry summer periods, sills were smaller
(10-15 (\%)\textsuperscript{2}) and correlation lengths were longer
(30-40 m). Regardless of the wetness conditions, the wettest soil was
always located within the swales and the valley floor (i.e., near-stream
zone). These wet-up and dry-down patterns were consistent with the
overall distribution of the soil types and the topographic wetness index
within the catchment. There was an exponential increase in the
catchment-wide soil moisture variability with increased
averaged-catchment moisture contents (Zhao et al., 2012). These
conditions were obvious due to the well-drained and steep-sloped soils
within the catchment that confined saturated areas to the swales and the
valley floor.

The soil moisture variability was explained by using only the first few
EOF patterns within the Shale Hills (Table 1). At the soil depths, the
first four EOFs together explained approximately 87\% of the total
variability, whereas only the first EOF (or EOF1) explained about 76\%
of the total soil moisture variance, indicating that a single spatial
structure may explain much of the overall soil moisture pattern. With
increased soil depths, the total variations explained by the derived
EOFs also increased. These results indicated that the seemingly complex
patterns of soil moisture within the Shale Hills may largely be
explained by a very small number of the underlying spatial EOFs. In the
EOF analysis of spatial patterns, the impacts of temporally variable
factors, which do not affect the whole area uniformly, also resulted in
noise and would also be expected to have decreased the amount of the
variance explained by the significant EOFs.

A close examination of the EOF patterns associated with soil land units
in Figure 4 reveals that the EOF1 displayed high values within the
valley floor, and low values within the hillslopes, respectively.
Obviously, the high EOF values indicated the clustered site with the
above average soil moistures, and conversely low EOF values is
equivalent to the sites of below average soil moisture values (Fig. 4).
From the weighted EC series (Fig. 5), the variance explained by the EOF1
values closely followed the increased field mean moisture contents,
e.g., the variance is sharply increased with increased moisture contents
following rainfall recharge. Therefore, the EOF analyses seem to
represent a very powerful set of tools that helped explain the patterns
in the variance associated with the general spatial patterns, the
indications of positional characteristics, and the temporal dynamics.
Perry and Niemann (2007) applied an EOF analysis for a 10.5 ha
Tarrawarra grassland catchment, and the first EOF in their study
explained 55\% of the soil moisture spatial variability. The explained
variances found at the Shale Hills are higher than the previously
mentioned studies that were about 55\% to 70\% of surface soil moisture
variability that may be explained by the stable spatial patterns
associated with the soil parameters and topography at their study sites
(Perry and Niemann, 2007; Korres et al., 2010). Because of the strong
combined soil-topographic effects, the observed soil moisture patterns
in the Shale Hills was high, and can largely be explained by only a few
underlying spatial structures or EOF patterns that are obviously
correlated to the various geophysical characteristics.

\textbf{3.2 Controls of primary soil moisture patterns}

The spatial patterns of soil moisture show the higher Pearson
correlation coefficients with soil-topography properties at each
measurement depth (Table 1). The results generally indicated that
terrain features were larger contributors to the variance in soil
moisture than the soil properties. While most of topographical
attributes (e.g., topography wetness index and slope) had strong
correlations with the derived EOFs, only soil texture among the soil
parameter showed significant correlations. Soil organic matter displayed
lower correlations at the surface soil (0-20 cm). Depth to bedrock,
which is related to both soil thickness and topography, seems to have
had a large influence on soil moisture variability at all depths. This
result may be confirmed by examination of the soil moisture values
within the wet locations which are characterized by the soils with
\textgreater{}1 m depth to bedrock. Elevation, slope, and curvature were
negatively related to soil moisture contents, while upslope contributing
area, depth to bedrock, topographic wetness index, and percent silt and
clay were positively correlated to the soil moisture contents. This
result is likely due to the fact that most soils with the deep soil
profiles are generally limited to lower elevations and concave slope
areas (i.e., valley floor and swales) where soil moisture is normally
the highest. Henninger et al. (1976) reported that soil moisture
increased toward the near-stream zone within a predominantly
agricultural watershed, which was a result of both topographic
convergence and moderately to poorly drained soils within the
near-stream zone. Our regression analysis indicated that soil texture
did not exert a strong influence on the soil moisture spatial
distributions at the catchment scale, particularly at soil depth
intervals between 0.4 and 0.6 m. This finding is due to the relatively
small variations in soil textural properties throughout the measured
locations for the different soil-landform units (Takagi and Lin, 2011).
Famiglietti et al. (1998) reported that under wet conditions, the best
correlations existed with porosity and hydraulic conductivity along a
profile of a 200-m length; whereas under dry conditions, the relative
elevation, aspect and clay content provided the best correlations.

The EOF analysis was repeated for the spatial anomaly data in two
categories (depth/wetness), and the degree to which these factors
affected the soil moisture distribution was calculated (Table 1). At the
Shale Hills, the correlation coefficient values generally increased with
soil depth for elevation, slope, and percent silt and clay content,
whereas the highest values were observed at intermediate depths (0.4 m)
for curvature, depth to bedrock, and topographic wetness index. These
results indicate that soil moisture becomes strongly aligned with
convergent topography and suggests that lateral flow processes may be
important driver of soil moisture redistribution at these depths. The
increased influence of the parameters with depth may relate to the
seasonal changes of soil moisture which undergoes more dramatic changes
near the soil surface. As indicated in Takagi and Lin (2012), the
subsurface soil moisture exhibited weak temporal variability in the
correlation coefficient values that suggested the dampened effects of
climate and hydrological fluxes. Thus, the subsurface soil moisture
distribution in this catchment is a function of both topographic
parameters and soil depth. An observation that was reinforced by the
transient hydrological fluxes such as the presence of the ephemeral
shallow water table that seasonally exist within the valley.

\textbf{3.3. Data combining method of spatially- and
temporally-extensive soil moisture}

In this study, we found that the first EOF can predict the general
patterns of soil moisture, for example at the 20-cm soil depth with 85\%
of the variance explained. Although the relative importance of the first
EOF on daily patterns of soil moisture waxes and wanes during cycles of
wetting and drying, the spatial pattern of the EOF is invariant in time.
Therefore, we considered it is an efficient way to integrate the
spatially extensive (but temporally limited) manual measurement sites
with other field long-term automatic monitoring datasets that are
temporally extensive (but spatially limited). Conceivably, based on the
EOFs for all spatially extensive sites, it was possible to predict the
spatially-distributed soil moisture for all those sites based on the
derived regressive equation between the EOFs of the temporally-extensive
sites and its automated monitoring datasets. For instance, the first EOF
of soil moisture at 20-cm soil depth was derived from a manual dataset
with the higher explained variations, but there also was a
strong-correlated regression coefficient between the soil moisture
automated monitoring sites (e.g., five sites 15, 51, 55, 61, and 74) and
their corresponding EOFs values. Based on the derived equations, all
manual measurement values could be predicted by either the manual
measurements or the monitored values at those five monitoring sites. To
validate this assumption, we selected three wetness conditions on the
same dates as used in Figure 3 (i.e. wet: ; moist: ; dry: ). Remarkably,
the predicted values via the manually-measured data (Fig. 6) have a
strong linear correlation to the measurements with high confidence
levels (95\%). These results mean that the suggested method is practical
to combine the manually-measured datasets with the automated- monitored
datasets.

Note that the results showed a relatively large scatter when the
automated- monitored values were used to predicate soil moisture values
at the spatially extensive sites (Fig. 7). Whether this approach is
accurate is also dependent on how well the manually-measured data and
the automated-monitored data closely match for the same soil depths at
the same sites. Due to the differences in the measured thickness and
horizonation, spatial dimensions and scales for the two methods (Gu et
al., 2018), the values between manually-measured and automated-monitored
datasets may not necessarily match well with one another. As indicated
in Figure 8, except for site 55, there were large differences between
manually-measured and automated-monitored soil moisture values. For
instance, the manually-measured moisture contents are consistently
higher than the automated- monitored values for the site 51 during the
entire measurement period. Even worse, the trends between both datasets
for sites 15 and 74 are somewhat irregular. These results challenged the
suitability of this approach when the automated-monitored data, instead
of the manually-measured data were used at the temporally-limited site.
As shown in Figure 9, we found that the fit between manual-measured and
auto-recorded soil moisture datasets were significant, but relatively
weak. Therefore, to apply this method reasonably, it is important for
the predicted data accuracy accounting the manually-measured and
automated monitored data to be somewhat in agreement. It is expected
that the EOF method could be a practical and efficient data merging
method if the primary EOF explains \textgreater{}60\% of the variation.
Nevertheless, taking into account those differences, the EOF method as
applied in this study could be quite valuable, and therefore provide an
essential way to assimilate data from multiple sources.

Furthermore, we explored the EOF method to breakdown a more dynamic time
series of soil moisture in to a lesser number of orthogonal spatial EOF
patterns (that are invariant in time) and the corresponding EC
components (that are invariant in space). This modification greatly
simplifies our task as we can just deal with only a few spatial EOF
structures instead of the whole data set. The higher-order EOFs are
usually taken into account depending on the amount of the total variance
explained by them. The associated EC components show the variation in
the influence of the EOFs during the wetting/drying phases, which could
be reasonably associated with the automated monitoring moisture dynamics
and theoretically provided the basic for the data fusion. To determine
the dominant physical controls, the EOF patterns were correlated to the
geophysical characteristics of the region. From our analyses, we
inferred that some of the variability of the soil moisture EOF patterns
is related to both topography and soil texture. We assessed that, using
the EOF analysis, it is particularly applicable to combine the manual
datasets with the automatic datasets in terms of different resolutions
for different data sources. The soil moisture dataset is currently
providing either better spatial coverage or better temporal coverage.
Our data assimilation approach provides an important way to combine both
datasets together which certainly improved the explanations for the
variation and data use.

\textbf{3.4 Implications}

Existing methods for direct field measurement of soil hydraulic
properties remain complex, time-consuming, costly, and significant
spatial and temporal variability challenges the possibility of extensive
measurements (Ma et al., 2018). However, the spatial patten, as
indicated by the EOF analysis, is the relatively stable. This stability
attribute of the spatial pattern has implied that it is possible to
continuously assess the soil moisture distribution in a catchment. In
addition to the spatial coverage maps, adding in the long-term
monitoring of both surface and subsurface soil moisture provides a
comprehensive picture of the spatial-temporal pattern of soil moisture
dynamics across the whole area and allow the identification of factors
which influence it through time. A unique long-term real time soil
moisture data set was previously used to identify local dominant
hydrological processes and its time dynamics. In this perspective, our
approach becomes more effective given that the long-term monitored site
is characterized as a time-stable location via a time-stability analysis
(Zhao et al., 2010). Our approach also has the capability to assimilate
additional data sources, e.g., remote sensed data at this time-stable
site. Given the high accuracy of the soil moisture monitoring, the
time-resolution soil moisture patterns over an area could be obtained by
selecting a temporally stable monitoring site, which is useful in ground
truthing of a remotely sensed footprint for validation of simulation
modelling results (Zhao et al., 2010). Given the importance of soil
moisture in Earth's land surface interactions and to a large range of
applications, one can appreciate that its accurate estimation is
critical in addressing key practical challenges such as food security,
sustainable planning and management of water resources. The launch of
new, more sophisticated satellites strengthens the development of
innovative research approaches and scientific inventions that will
result in ground-breaking advancements.

One goal of this study was to lay the foundation for the design of
cost-effective real-time soil moisture monitoring networks that fill in
the gap between point sensors and traditional manual measurements or
even remote sensing values. Our study is representative of a novel
approach with the potential benefits for an effective soil moisture
monitoring network design within the study area, determining the
spatiotemporal statistics of the observed soil moisture fields, and the
use of a spatial regression procedure in data merging. It is more
realistic to observe a difference between developed maps as surface
conditions evolve. We believe that this combination reflects more
adequately the basin heterogeneity and complex interactions between soil
moisture and topographic attributes. Although there are the simple
linear data transfer methods that have been applicable to this type of,
our approach may accommodate different data analysis methods, such as a
multi-step regression method based on the EOF analysis (Temimi et al.,
2010). Once the tasks within our approach have been completed, the
EOF-based transfer method may be used as a foundation any region and/or
date under the assumptions that the identified empirical relationships
will be valid for the application conditions.

The present soil-landscape has been shaped through a combination of
long- and short-time processes, and this history can provide some clues
to project future changes. However, linking long-term and slow processes
with shorter-term and fast processes remains one challenge (Ma et al.,
2018). While mapping depicts the spatial distribution of soil-landscape
relationships, as indicated by the dominant EOF patterns; monitoring
captures the temporal dynamics of pedologic and hydrologic properties,
as indicated by the profiled data dynamics (Ma et al., 2018). Given the
spatial-extensive data benefits of traditional mapping, and the
temporal-extensive data benefits of traditional monitoring, the
presented data-integrated method may provide a justifiable basis for the
combination of mapped and monitored data, as well as a conceptual basis
for the coupling of slow and fast processes. Firstly, bridging mapping
with monitoring is very helpful in the dynamic mapping of hydropedologic
functional units (Ma et al., 2018). Secondly, mapping provides
information to aid in optimal site selection for monitoring (Zhao et
al., 2010). Thirdly, mapping and monitoring supplies essential data for
the calibration and validation of modeling, and may help provide
additional information for a more holistic, refined and predictive
management of soil and water resources (Guo et al., 2019). Our approach
provides an essential set of tools to evaluate the improvement of data
use. We assumed that the relationship between different data sources
remains the same over time, but suggest that future studies verify this
behavior.

\textbf{4. Conclusions}

In this study, we developed a data combination approach on the basis of
EOF analysis of space-time soil moisture data at a reference Shale Hills
catchment. We investigated the space-time characterization of soil
moisture and found that the variation of soil moisture could be
explained by using the first few EOFs. Results of the correlation
analysis showed that topography and soil properties have mixed effects
on the variability explained by the dominant soil moisture EOFs.
Benefits based on the derived underlying stable EOF patterns of soil
moisture, the relationships between site characteristics and the EOF
patterns were examined to conduct a spatial-temporal dataset
combination. Based on the long-term spatial extensive sampling campaign
and the specific transect of real-time monitoring, this study
investigated how to integrate the spatially extensive, but temporally
limited manual datasets with the temporally extensive, but spatially
limited automated monitoring datasets. This exercise was helpful for
understanding the soil moisture spatio-temporal patterns and the
hydrological responses at a small landscape scale, and are considered to
be important factors for the effective measurement and the practical
management of soil moisture at multiple scales.

\textbf{Acknowledgments}

This research was supported in part by the U.S. National Science
Foundation through the Shale Hills Critical Zone Observatory grant
(EAR-0725019), the Taishan Scholars Program (201812096) and the National
Natural Science Foundation of China (41977009). Fei Li was supported by
the Agricultural Science and Technology Innovation Program of CAAS
(CAAS-ASTIP-2020-IGR-04). Dr. Hill was partially supported by the USDA
National Institute of Food and Agriculture, Hatch project 1014496.
Assistance in field data collections from the Penn State Hydropedology
Group was gratefully acknowledged.

\textbf{Data Availability Statement}

The data set is available at
http://criticalzone.org/shale-hills/data/datasets/.

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