Recent advances in radar remote sensing popularized the mapping of surface soil moisture at different spatial scales. Surface soil moisture measurements are used in combination with hydrological models to determine subsurface soil moisture values. However, variability of soil moisture across the soil column is important for estimating depth-integrated values, as decoupling between surface and subsurface can occur. In this study, we employ new methods to investigate the occurrence of (de)coupling between surface and subsurface soil moisture. Using time series datasets, lagged dependence was incorporated in assessing (de)coupling with the idea that surface soil moisture conditions will be reflected at the subsurface after a certain delay. The main approach involves the application of a distributed-lag nonlinear model (DLNM) to simultaneously represent both the functional relation and the lag structure in the time series. The results of an exploratory analysis using residuals from a fitted loess function serve as a posteriori information to determine (de)coupled values. Both methods allow for a range of (de)coupled soil moisture values to be quantified. Results provide new insights into the decoupled range as its occurrence among the sites investigated is not limited to dry conditions.

Although recent decades have seen great advances in remote sensing
applications for mapping surface soil moisture

The amount of soil moisture at any given time is controlled by factors
operating at different timescales. While prevailing atmospheric conditions
directly affect surface layers and control the temporal dynamics of soil
moisture

Given the variability along a soil column, during which conditions does surface
soil moisture reflect subsurface soil moisture? Several studies have
investigated this relation to address the correspondence between surface and
subsurface soil moisture. One of the earliest studies is by

Based on previous studies, the term decoupling refers to a weak dependence
between soil moisture contents at the surface and subsurface. Recognition of
decoupling is important; however, most studies have been limited to providing
qualitative characterization of conditions when decoupling occurs (e.g., dry
period). Only

We utilized in situ time series datasets at depths of 5 and 40 cm to
represent surface and subsurface, respectively. Values outside the decoupled
range are considered coupled since soil moisture is inherently bounded up to a
maximum value equal to soil's porosity. The investigation of (de)coupling is
based on the idea that surface conditions will be reflected at the subsurface
after a certain delay, indicating strong coupling between the two zones, and
vice versa. More focus is given to the decoupled soil moisture range since it
has greater implications for extrapolation of surface soil moisture values to
deeper soil layers. We applied statistical methods to identify conditions of
decoupling with no prior assumptions on the type of functional relation
between surface and subsurface. As an exploratory step, we first assessed the
dependence without considering lags using regression and residual analysis.
The main approach for assessing decoupling was application of distributed-lag
nonlinear models

Four time series datasets from the Twente soil moisture and temperature
monitoring network

Land cover in the area varies from corn in one field (SM05), to grass in two
fields (SM05 and SM13), to a forest area (SM20). Values at 40 cm capture the
root zone of vegetation for each site. In reality, rooting depths vary and
depend on species composition, climate, and plant growth rate. However, the
depth considered would still allow for approximation of root zone conditions.
The landscape is characterized by flat to slightly sloping terrain. It is
important to note that SM20 is located at the eastern foot of a small hilly
terrain. Throughout the study period, either land cover remained unchanged or
the same crop was planted. The soil types for the stations range from coarse
sandy soils to weakly silty soils

Location of study site in the eastern part of the Netherlands (inset).
Triangles represent stations used within the Twente soil moisture and temperature
monitoring network

Summary of land cover descriptions at each station covering the period
of 2014–2016. Soil descriptions and codes are based on BOFEK 2012

Soil moisture values were averaged into daily values to match the available
daily rainfall data from the Dutch national weather service (KNMI). For SM13
and SM20, there are some missing data from the beginning of 2014. The
datasets from SM13 begins on 25 April 2014 while SM20 begins on 2 May 2015 (Fig.

As an exploratory step, the dependence between surface and subsurface soil
moisture was initially visualized using scatter plots. Conditional means for
every 0.01 cm

Time series plots of surface (5 cm in light blue) and subsurface (40 cm in dark blue) soil moisture. Vertical black bars at the top show daily precipitation data from the nearest KNMI station.

Schematic diagram using hypothetical soil moisture values to show
vertical variability.

A flexible nonparametric locally weighted regression function (commonly
called a loess function,

Results of the exploratory methods were considered a posteriori knowledge for analysis of lagged dependence and interpretation of results.

Since decoupling is based on the strength of lagged dependence, the existence
of lag between surface and subsurface soil moisture values was first
determined. Cross-correlation is known to be a quick and easy method to apply
for this objective. Lagged values of surface soil moisture were correlated
with instantaneous values at the subsurface. A maximum cross-correlation at
negative lags indicated that surface soil moisture is leading subsurface soil
moisture, and vice versa

Scatter plots of 5 cm vs. 40 cm soil moisture values at lag

We incorporated delayed or lagged effects in evaluating the relation between surface and subsurface values, and eventually in determining the (de)coupled values. It should be emphasized that the analysis was primarily focused on examining the trends and relation between surface and subsurface soil moisture. Moreover, it was not intended to replace other existing models for estimating soil moisture or examining its patterns.

A distributed-lag nonlinear model developed by

In assessing lagged dependence, event-scale patterns were of interest rather
than large-scale trends within the time series

For consistency in modeling, the range of surface soil moisture values used
was from 0–0.50 cm

The following section concisely describes the mathematical formulation of a
DLNM. However, the reader may choose to skip this section as the general
description of the methods applied has already been given in the text above.
For a more detailed explanation, readers are referred to

To more formally describe a DLNM, let us first consider a general time series
model, where outcomes

Within the DLNM framework, a response

The cross basis function

A further extension to DLNM is the application of penalties for smoothness of
the lag structure and shrinkage of lag coefficients to null at very high
lags. These penalties were applied in the analysis using a second-order
difference

Application of a DLNM resulted in the estimation of parameter

Residual variance plots from the fitted loess function. Vertical bars
at the bottom of each plot represent the variance for every 0.1 cm

The overall dependence between surface and subsurface given by the Spearman's
rank coefficient (

Assessment of the regression fit quality was performed by comparison using
residual standard errors (RSEs). The results for both linear and loess
functions show highly similar values (Fig.

Figure

The correlation between normalized variance and sample size yielded a value
of

Scatter plot of sample size vs. normalized residual variance calculated
for each 0.01 cm

Figure

Figure

Based on

List of surface soil moisture values (SSM in cm

Cross-correlation plots of soil moisture values. The lagged surface
soil moisture values at 5 cm are correlated with subsurface values at 40 cm.
A 1–2 day lead of surface soil moisture is observed, except for SM20. This is
indicated by maximum correlation values at lags of

The relative influence of surface soil moisture on subsurface values
obtained by summing the predicted

Regression and residual analyses show that there is an inherent vertical
variability between surface and subsurface soil moisture values based on the
lack of 1 : 1 correspondence between the two (Fig.

Both residual analysis and DLNM were successful in identifying a decoupled
soil moisture range, and there is good agreement between the results from
both. Three out of four sites show decoupled values in the dry to
intermediate soil moisture range (Fig.

The vegetation type at each site exerts some influence on the soil moisture
variability and the resulting (de)coupled values. First, the vegetation type
affects how much ground surface is directly exposed to atmospheric
conditions. Forested areas and grass fields are almost fully covered by
vegetation compared to a corn field where the crops are organized in
equidistant rows. Vegetation or canopy cover will determine how atmospheric
conditions affect the soil moisture values. For instance, the amount of
intercepted precipitation and evaporation are both dependent on vegetation
cover. This in turn will have direct impacts to the surface soil moisture
dynamics at each of the sites. For comparison, the variability given by the
standard deviation bars in Fig.

Among the four sites, the subsurface trends observed for the 40 cm values at
SM13 show consistently high values, which can be more pronounced during
winter months. This resulted in decoupling during wet soil moisture
conditions (Fig.

Site-specific characteristics at each station control the magnitude of variability as well as the range at which decoupling is observed. However, the occurrence of decoupling is independent of the magnitude of variability since it was observed from SM05, where variability is least up to that of SM13 where it is greatest. The methods applied in this study only identify conditions when decoupling occurs but do not explicitly determine its controls. Identification of controls for decoupling requires a separate analysis where mechanistic models or statistical approaches can be applied.

To assess the applicability of the methods applied, we further discuss their strengths and weaknesses. We also present opportunities for further studies as well as foreseen limitations for other sites.

The residual analysis and DLNM methods allow quantification of a range of
soil moisture values where decoupling occurs. This provides further extension
to previous studies where decoupling is only described qualitatively. As seen
from the results at the four sites, decoupling can occur at any soil moisture
value, and is not confined to dry periods or ranges. Furthermore, by making
no initial assumptions on data distributions and the type of functional
relation and lag structure, the methods applied were considered robust.
Nonlinear functions were applied as they conform to the nonlinearity of
water flow in the unsaturated zone. They can also handle a variety of
bivariate dependence, even in cases where the relation is linear, as shown by
the highly similar fit of the loess and linear functions in Sect.

The first aspect that needs to be further investigated is the selected

Another aspect to further examine is the use of cross-correlation for
confirming the presence of leading surface soil moisture values. Results from
SM20 show maximum correlation at positive lags which indicate leading
subsurface values (Fig.

Subsurface soil moisture dynamics for vertically discrete (40 cm) and depth-average value. Left panels: time series of soil moisture at 40 cm and depth-averaged values. The dynamics observed for depth-average values are highly similar to those at 40 cm. Right panels: scatter plot showing that these two sets of values are highly correlated.

In relation to utilizing remote sensing techniques, our results imply that the accuracy of estimating subsurface values from surface soil moisture can be greatly affected by vertical coupling. Lower variability and hence lower uncertainties are expected in the coupled soil moisture range. Assessment of decoupling can be used in combination with modeling studies as a preliminary method to determine the range where variability is expected to be higher. Furthermore, it can be helpful in assessing whether simulation results capture the variabilities observed in both the coupled and decoupled ranges. Taking decoupling into account can also assist in evaluating the necessity of complex models for simulating vertical soil moisture content.

For data assimilation applications, (de)coupling methods can be used for
cross-comparison of the vertical coupling derived from DA model outputs with
those observed from long term in situ measurements. This can aid in examining
the adequacy of the assumed inherent connection between surface and
subsurface values. As

Although the study focused on vertically discrete values, the results are
also applicable for depth-average values commonly used in remote sensing and
DA applications. This requires that the vertically discrete values adequately
capture the overall dynamics within zone being investigated. In such a case,
we infer that the translation to depth-averaged values would result in
(de)coupled values that are close, but not identical, to the values obtained
when only comparing two discrete depths. As an illustration, we calculated
the depth-average values using all the available measurements at each site
(i.e., 5, 10, 20, and 40 cm depth) following the formula from

In this study, only meteorological factors were incorporated into the DLNM
analysis since vertical movement was assumed to be the dominant flow
mechanism. However, the subsurface can also be influenced by lateral movement
or groundwater by capillary rise. In such scenarios, decoupling will not be
limited to changes in surface conditions. For this, SM20 provides an
excellent example. This station is located at the foot of a small hill
(Fig.

The methods applied in this study allow for investigation of vertical soil moisture variability. More importantly, application of DLNM allowed for a decoupled soil moisture range to be quantitatively identified. The results also reveal that decoupling is not confined to dry soil moisture range as implied by previous studies. The reasons for decoupling are manifold, and controls for the dry soil moisture range may differ from those for the wet range. The results of this study have implications for remote sensing and data assimilation methods, especially for uncertainties related to the use of surface soil moisture to obtain integrated soil moisture values.

The datasets for soil moisture were obtained from the Water Resource Department of ITC-Twente University. At the moment, the datasets are not publicly available. Access to the datasets may be granted upon request from the institute through Rogier van der Velde, PhD (r.vandervelde@utwente.nl).

CDUC and MPvdP initially conceptualized the idea for investigating the relation between surface and subsurface soil moisture values. PJJFT provided significant contributions to the statistical analysis applied. All three authors contributed to writing and editing of the paper.

The authors declare that they have no conflict of interest.

The authors are grateful for the Water Resources Department of ITC-Twente University, the Netherlands, for sharing the datasets from their network. We thank the three anonymous reviewers for providing critical insights that improved the paper. This work is part of the research programme Optimizing Water Availability through Sentinel-1 Satellites (OWAS1S) with project number 13871 which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). We also thank colleagues in the lab meeting group for insightful discussions as well as Demi Moore for proofreading earlier versions of the text. Edited by: Nunzio Romano Reviewed by: three anonymous referees