# Soil moisture sensor calibration for organic soil surface layers

Simone Bircher, Mie Andreasen, Johanna Vuollet, Juho Vehviläinen, Kimmo Rautiainen, François Jonard, Lutz Weihermüller, Elena Zakharova, Jean-Pierre Wigneron, Yann H. Kerr

► To cite this version:

Simone Bircher, Mie Andreasen, Johanna Vuollet, Juho Vehviläinen, Kimmo Rautiainen, et al. Soil moisture sensor calibration for organic soil surface layers. Geoscientific Instrumentation, Methods and Data Systems Discussions, 2016, 5, pp.109-125. 10.5194/gi-5-109-2016. hal-02638461

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# Soil moisture sensor calibration for organic soil surface layers

Simone Bircher<fnref n="1" />, Mie Andreasen<fnref n="2" />, Johanna Vuollet<fnref n="3" />, Juho Vehviläinen<fnref n="3" />, Kimmo Rautiainen<fnref n="3" />, François Jonard<fnref n="4" />,<fnref n="5" />,
Lutz Weihermüller<fnref n="4" />, Elena Zakharova<fnref n="6" />, Jean-Pierre Wigneron<fnref n="7" />, and Yann H. Kerr<fnref n="1" />

*Correspondence to:* Simone Bircher (simone.bircher@cesbio.cnes.fr)

Received: 30 November 2015 – Published in Geosci. Instrum. Method. Data Syst. Discuss.: 11 December 2015

Revised: 17 March 2016 – Accepted: 18 March 2016 – Published: 29 April 2016

**Abstract.** This paper's objective is to present generic calibration functions for organic surface layers derived for the soil moisture sensors Decagon ECH2O 5TE and Delta-T ThetaProbe ML2x, using material from northern regions, mainly from the Finnish Meteorological Institute's Arctic Research Center in Sodankylä and the study area of the Danish Center for Hydrology (HOBE). For the Decagon 5TE sensor such a function is currently not reported in the literature. Data were compared with measurements from underlying mineral soils including laboratory and field measurements. Shrinkage and charring during drying were considered. For both sensors all field and lab data showed consistent trends. For mineral layers with low soil organic matter (SOM) content the validity of the manufacturer's calibrations was demonstrated. Deviating sensor outputs in organic and mineral horizons were identified. For the Decagon 5TE, apparent relative permittivities at a given moisture content decreased for increased SOM content, which was attributed to an increase of bound water in organic materials with large specific surface areas compared to the studied mineral soils. ThetaProbe measurements from organic horizons showed stronger nonlinearity in the sensor response and signal saturation in the high-level data. The derived calibration fit functions between sensor response and volumetric water content hold for samples spanning a wide range of humus types with differing SOM characteristics. This strengthens confidence in their validity under various conditions, rendering them

highly suitable for large-scale applications in remote sensing and land surface modeling studies. Agreement between independent Decagon 5TE and ThetaProbe time series from an organic surface layer at the Sodankylä site was significantly improved when the here-proposed fit functions were used. Decagon 5TE data also well-reflected precipitation events. Thus, Decagon 5TE network data from organic surface layers at the Sodankylä and HOBE sites are based on the here-proposed natural log fit. The newly derived ThetaProbe fit functions should be used for hand-held applications only, but prove to be of value for the acquisition of instantaneous large-scale soil moisture estimates.

## 1 Introduction

The circumpolar northern colder climate zone (boreal forest and tundra) contributes with a substantial fraction to the total global land mass. Because of slower decomposition rates in these regions pronounced organic layers have been accumulating on top of the mineral soils. Particularly when frozen, organic-rich soils store a significant amount of carbon acting as important sinks. However, the higher northern latitudes are especially sensitive to climate change (IPCC, 2007) due to above-average rising temperatures (e.g., Hansen et al., 2006). Thus, a considerable positive feedback on global warming is likely once additional carbon is respired from thawing

<footnote n="1">¹Centre d'Etudes Spatiales de la Biosphère, Toulouse, France</footnote>

<footnote n="2">²Department of Geosciences and Natural Resource Management, University of Copenhagen, Copenhagen, Denmark</footnote>

<footnote n="3">³Finnish Meteorological Institute, Arctic Research, Helsinki, Finland</footnote>

<footnote n="4">⁴Agrosphere (IBG-3), Institute of Bio- and Geosciences, Forschungszentrum Jülich GmbH, Jülich, Germany</footnote>

<footnote n="5">⁵Earth and Life Institute, Université catholique de Louvain, Louvain-la-Neuve, Belgium</footnote>

<footnote n="6">⁶Laboratoire d'Etudes en Géophysique et Océanographie Spatiales, Toulouse, France</footnote>

<footnote n="7">⁷Division Ecologie fonctionelle et Physique de l'Environnement, Institut National de la Recherche Agronomique,
Bordeaux-Aquitaine, France</footnote>
grounds (Stokstad, 2004). The prediction of the overall re-
sponse of these ecosystems to global warming is currently
highly uncertain. In this context, hydrological processes play
a key role and soil moisture is one of the main factors to
be assessed to understand and quantify the processes and
feedback mechanisms controlling water, energy, and carbon
fluxes at the land surface–atmosphere interface.

Given the particular hostility and remoteness of high lat-
itude environments, spaceborne remote sensing techniques
together with land surface modeling constitute essential tools
for soil moisture observations at high temporal resolution and
with complete spatial coverage (e.g., Reichle et al., 2007;
Albergel et al., 2012). Nevertheless, spatially distributed in
situ soil moisture measurements are indispensable for the
calibration/validation (cal/cal) activities of these global soil
moisture products as well as in order to increase process-
understanding at local scale.

Electromagnetic-based sensors belong to the most popu-
lar in situ soil moisture measuring techniques, as they can be
used for automated continuous measurements at high tempo-
ral resolution in most soil types and plant growth substrates,
including shallow recordings close to the surface. Differ-
ent sensor types have been developed using capacitance and
impedance as well as time- or frequency-domain reflectome-
try and transmissometry (TDR, FDR, TDT, and FDT) meth-
ods. The shape and design of the sensors as well as the mea-
surement and/or raw data “interpretation” is highly variable
(Robinson et al., 2008). Nevertheless, they all take advantage
of the large difference between the relative permittivity (ε;
relative to free space, also referred to as dielectric constant)
of dry soil and water in order to estimate the volumetric frac-
tion of the latter (e.g., Topp, 2003; Robinson et al., 2003). ε is
a complex number whose real part ε' expresses energy stor-
age based on the ability of a particle to align with the electric
field. The imaginary part ε'' describes energy losses due to
absorption and electrical conductivity. In the frequency range
where most electromagnetic sensors operate the measured
relative permittivities mainly correspond to ε'. However, as
ε'' contributes to a certain degree to the signal and because
the observed relative permittivity is the bulk value of com-
pound solid, gaseous, and liquid constituents, it is usually
termed apparent relative permittivity ε_a (e.g., Blonquist et al.,
2005).

In the case of all electromagnetic sensors, the measured
raw signal of a substrate is closely related to εₐ, from which
the soil moisture can be derived using either dielectric mix-
ing models or empirical calibration equations (e.g., Jones et
al., 2002; Mätzler, 2006; Nagare et al., 2011). These rela-
tions are affected by the sensor design, and thus, are sensor
type specific. Manufacturers generally provide default cali-
brations, often including both raw signal to soil moisture as
well as εₐ to soil moisture relationships. Though calibrated
and validated over a wide range of soil types, there is general
consensus that these functions cannot hold for all conditions,
and therefore, soil- and site-specific calibration is often re-

quired to improve the measurement accuracy (e.g., Walker
et al., 2004; Czarnomski et al., 2005; Blonquist et al., 2005;
Evett et al., 2006; Dorigo et al., 2011; Mittelbach et al., 2012;
Vaz et al., 2013).

Currently available impedance and capacitance sensors
operate at frequencies between 20 and 300 MHz, while
TDR/FDR and TDT/FDT mainly function in the GHz range
(Vaz et al., 2013). The latter are generally considered more
accurate with less signal contribution of ε'' and hence, re-
duced sensitivity to salinity (electrical conductivity), temper-
ature, and soil type effects (e.g., Blonquist et al., 2005; Kel-
leners et al., 2005; Saito et al., 2009). However, the former
are often cheaper and power consumption is lower. Given the
high spatial and temporal soil moisture variability throughout
scales (e.g., Western et al., 2002; Famiglietti et al., 2008),
there is broad agreement concerning the benefit of increas-
ing soil moisture network density using cheaper sensors at
the cost of accuracy, in order to better represent large-scale
satellite footprints and model grid cells (e.g., Czarnomski et
al., 2005; Bogena et al., 2007; Kizito et al., 2008; Dorigo et
al., 2011; Mittelbach et al., 2012).

While a lot of authors find manufacturers’ default cali-
brations sufficiently accurate for various mineral soil types
(apart from very clayey soils), many studies conclude that
calibrations specific to organic-rich soils and humus hori-
zons are crucial (e.g., Topp et al., 1980; Herkelrath et al.,
1991; Roth et al., 1992; Paquet et al., 1993; Jones et al., 2002;
Pumpanen and Ilvesniemi, 2005; Kizito et al., 2008; Sakaki
et al., 2011; Vaz et al., 2013). Organic material differs from
mineral by its complex structures and small bulk densities.
The resulting high porosities and large specific surface areas
cause the following two effects: (1) substantial water holding
capacities up to 0.8–0.9 cm³ cm⁻³ compared to around 0.4–
0.6 cm³ cm⁻³ in the case of mineral soils (e.g., Kellner and
Lundin, 2001; Li et al., 2004), and (2) a higher amount of
bound water altering εₐ (Jones et al., 2002). Water molecules
in the vicinity of solid surfaces are subjected to interfacial
forces hindering their rotation. Consequently, their ability
to align with the applied electric field (and thus, ε) is re-
duced. Therefore, the water layer in close proximity (several
angstroms) to the solid particles exhibits a relative permittiv-
ity similar to water fixed in ice structures with ε' ≈ 3 (Wang
and Schmugge, 1980), while in subsequent layers the value
gradually approaches the one of free liquid water (Or and
Wraith, 1999). Hence, the use of a calibration function for
mineral soil leads to a significant underestimation of the ac-
tual moisture content in substrates like organic material with
large specific surface area and thus, increased bound water
fraction (e.g., Topp et al., 1980; Roth et al., 1992; Paquet et
al., 1993). The relative permittivity of the dry solid particles
are reported to range between 2 and 5 without a clear differ-
ence between organic and mineral substrates (e.g., Topp et
al., 1980; Roth et al., 1990; Malicki et al., 1996). This lead
to the assumption that εsolid has only little effect on εₐ (Yu et
al., 1999).
The influence of organic matter on the TDR response has been studied by many authors (e.g., Topp et al., 1980; Roth et al., 1990, 1992; Herkelrath et al., 1991; Pepin et al., 1992; Paquet et al., 1993; Malicki et al., 1996; Börner et al., 1996; Myllys and Simojoki, 1996; Schaap et al., 1996; Kellner and Lundin, 2001; Jones et al., 2002; Pumpanen and Ilvesniemi, 2005; Shibchurn et al., 2005; Nagare et al., 2011; Vasquez, 2013). However, for other electromagnetic sensors, such analyses are more scarce in the literature. Recently, Vaz et al. (2013) evaluated standard calibrations for eight electromagnetic sensors. They pointed to the rarity, and thus, necessity of further investigations on the capacitance and impedance sensor response in substrates of varying organic matter content.

At the Finnish Meteorological Institute's Arctic Research Center (FMI-ARC) in Sodankylä, northern Finland, the exploration of hydrological processes is one of the multidisciplinary key research topics. On this site there are several projects dealing with the characterization of moisture content in organic-rich soil surfaces as well as freeze-thaw characteristics using different remote sensing techniques as well as land surface modeling (e.g., Rautiainen et al., 2012, 2014; European Space Agency: ESA SMOS + Innovation Permafrost, ESA CCI Soil Moisture, ESA SMOSHiLat; National Aeronautics and Space Administration: NASA SMAP cal/val). In the Skjern River catchment in western Denmark related actions are ongoing coordinated by the Danish Center for Hydrology (HOBE). Therefore, a joined effort aimed at calibrating the used soil moisture sensors, namely, the capacitance Decagon ECH2O 5TE sensor (Decagon 5TE)<fnref n="1" /> and the impedance Delta-T ThetaProbe ML2X (ThetaProbe)<fnref n="1" />, for organic substrate. At both sites, the Decagon 5TE sensors are installed at permanent network stations (Bircher et al., 2012a; Ikonen et al., 2016) providing data to the International Soil Moisture Network (ISMN, Dorigo et al., 2011) – a global in situ soil moisture database to support validation and improvement of satellite observations and land surface models. Meanwhile, ThetaProbes are used for hand-held measurement campaigns (e.g., Bircher et al., 2012b), a current method for spatial variation studies of soil water content at different scales (e.g., Baggaley et al., 2009; Lopez-Vicente et al., 2009) and thus, frequently applied in the scope of satellite validation (e.g., Cosh et al., 2005; Kurum et al., 2012).

With the purpose of serving coarse-resolution satellite remote sensing and land surface modeling studies, the objective was to provide generic calibration functions holding for different types of organic material as encountered within the large areas under consideration. Necessarily, these functions hold a decreased degree of detail and might lack high accuracy, but will clearly outperform default calibration functions provided by the sensor manufacturers. Additionally, they should be applicable without requiring auxiliary information

for the large area of interest, such as bulk density/porosity or specific surface area/bound water fraction, as integrated in more sophisticated calibration methods (e.g., Malicki et al., 1996; Dirksen and Dasberg, 1993).

This article presents the Decagon 5TE and ThetaProbe sensor calibrations for organic soil surface layers, derived from field and laboratory measurements using soils from different locations in northern regions, mainly including the Sodankylä and HOBE network areas. While some ThetaProbe calibration efforts are present in the literature for organic material from natural soils (see Sect. 3.2), to the knowledge of the authors so far no equivalent studies have been reported in the case of the Decagon 5TE sensors. It seems that only Vaz et al. (2013) had looked into the issue for this sensor type, however, using artificial organic material in a limited water content range. Thus, the goal here was to extend the range of validity of the 5TE calibration function for a variety of natural organic substrates and create something more widely applicable.

To avoid inconsistencies, the same measurement and calibration protocol was followed at all sites. The developed fit functions were evaluated against the manufacturers' calibrations as well as earlier published fitting functions. Furthermore, soil moisture time series from both sensors collected at two Sodankylä network sites were compared, using both manufacturer's default and our own derived calibrations. Measurements from the underlying mineral soil layers with variable soil organic matter content were also considered in order to demonstrate the validity of the manufacturer calibrations within those layers.

## 2 Description of study sites and data

Figure 1 gives an overview of the soil sample locations used in this study. At the two main sites in Finland and Denmark, the Decagon 5TE and ThetaProbe responses were studied in detail. Additionally, some samples used for ThetaProbe analysis were collected in Scotland and Siberia. The soil samples used for calibration and their characteristics are listed in Table 1. It is also indicated which samples were used for laboratory and field calibrations, respectively. According to humus form classifications (Broll et al., 2006; Zanella et al., 2011), a layer is considered organic if the soil organic matter (SOM) content is greater than ~30–35 %. Classification of the organic samples was undertaken according to the European Humus Forms Reference Base (Zanella et al., 2011) applying a simplified three-level scheme (water regime, form, and biotype). An overview of the classified samples is shown in Table 2, which indicates that the substrates used cover a wide range of different humus types typically encountered in the higher northern latitudes.

Soil dry bulk densities range 0.05–0.4 and 1.0–1.5 g cm⁻³ for the organic and mineral samples, respectively, and sand is the largest textural fraction (exceeding 80%) in the stud-

<footnote n="1">¹Mention of manufacturers is for the convenience of the reader only and implies no endorsement on the part of the authors.</footnote>
<table><caption>**Table 1.** Overview of the samples used for calibration. The sample name starts with the study site, followed by land cover type, soil material and indication whether used in laboratory or field calibration. O, M, F, and L denote organic, mineral, field, and lab, respectively. The letter specifying the soil material is complemented by a number if more than one sample of the same soil material is available at a given study site. *N* is the number of sensor measurements.</caption><thead><tr><th>Soil material</th><th>Sample name</th><th>Location</th><th>Land cover</th><th>Method</th><th>Layer depth (cm)</th><th>SOM (%)</th><th>Sand/silt/clay (%)</th><th>N Decagon 5TE</th><th>N ThetaProbe</th></tr></thead><tbody><tr><td rowspan="8">Organic</td><td>HOBE_Forest_O_F</td><td>Gludsted, DK</td><td>Forest</td><td>Field</td><td>0-5</td><td>69-93.0</td><td>NaN</td><td>19</td><td>13</td></tr><tr><td>HOBE_Forest_O1_L</td><td>Gludsted, DK</td><td>Forest</td><td>Lab</td><td>0-5</td><td>69.0</td><td>23.1/7.8/0.1</td><td>11</td><td>11</td></tr><tr><td>HOBE_Forest_O2_L</td><td>Gludsted, DK</td><td>Forest</td><td>Lab</td><td>0-5</td><td>31.0</td><td>66.1/3.3/0.0</td><td>11</td><td>11</td></tr><tr><td>HOBE_Heath_O_F</td><td>Gludsted, DK</td><td>Heath</td><td>Field</td><td>0-5</td><td>NaN</td><td>NaN</td><td>2</td><td>8</td></tr><tr><td>FMI_Forest_O_L</td><td>Sodankylä, FI</td><td>Forest</td><td>Lab</td><td>0-5</td><td>36.6</td><td>61.7/1.4/0.3</td><td>7</td><td>7</td></tr><tr><td>SIB_O_L</td><td>Siberia, RU</td><td>Tundra/bog</td><td>Lab</td><td>0-5</td><td>NaN</td><td>NaN</td><td>0</td><td>3</td></tr><tr><td>ISL_O_L</td><td>Islay, GB</td><td>Bog</td><td>Lab</td><td>0-5</td><td>NaN</td><td>NaN</td><td>0</td><td>17</td></tr><tr><td>Mineral</td><td>HOBE_Forest_M_L</td><td>Gludsted, DK</td><td>Forest</td><td>Lab</td><td>10-15</td><td>8.0</td><td>83.9/7.6/0.3</td><td>11</td><td>11</td></tr><tr><td></td><td>HOBE_Heath_M_F</td><td>Gludsted, DK</td><td>Heath</td><td>Field</td><td>10-15</td><td>15.8</td><td>84.7/13.9/1.4</td><td>4</td><td>7</td></tr><tr><td></td><td>FMI_Forest_M_L</td><td>Sodankylä, FI</td><td>Forest</td><td>Lab</td><td>10-15</td><td>15.1</td><td>84.8/0.2/0.0</td><td>6</td><td>6</td></tr><tr><td></td><td>FMI_Heath_M1_L</td><td>Sodankylä, FI</td><td>Heath</td><td>Lab</td><td>0-5</td><td>6.9</td><td>91.5/1.4/0.3</td><td>5</td><td>5</td></tr><tr><td></td><td>FMI_Heath_M2_L</td><td>Sodankylä, FI</td><td>Heath</td><td>Lab</td><td>10-15</td><td>5.0</td><td>92.4/2.6/0.0</td><td>4</td><td>4</td></tr></tbody></table>

<table><caption>**Table 2.** Overview over organic samples, classified according to the European Humus Forms Reference Base (Zanella et al., 2011).</caption><thead><tr><th>Location</th><th>Land cover</th><th>Water regime</th><th>Form</th><th>Biotype</th><th>Horizons</th><th>Decagon 5TE</th><th>ThetaProbe</th></tr></thead><tbody><tr><td rowspan="2">Gludsted, Denmark</td><td>Coniferous forest</td><td>Terrestrial</td><td>Terro</td><td>Mor</td><td>OL-OF-OH</td><td>x</td><td>x</td></tr><tr><td>Heathland</td><td>Terrestrial</td><td>Terro</td><td>Moder</td><td>OL-OH</td><td>x</td><td>x</td></tr><tr><td rowspan="2">Sodankylä, Finland</td><td>Coniferous forest</td><td>Terrestrial</td><td>Terro</td><td>Mor</td><td>OL-OF-OH</td><td>x</td><td>x</td></tr><tr><td>Heathland</td><td>Terrestrial</td><td>Enti</td><td>Mor</td><td>OL-OF-OH</td><td>x</td><td>x</td></tr><tr><td rowspan="2">West Siberia, Russia</td><td>Tundra</td><td>Semi-terrestrial</td><td>Hydro</td><td>Hydromor</td><td>(OLg)-OFg-(OHg)</td><td>-</td><td>x</td></tr><tr><td>Bog</td><td>Semi-terrestrial</td><td>Histo</td><td>Histomor</td><td>hf</td><td>-</td><td>x</td></tr><tr><td>Islay, Scotland, GB</td><td>Bog</td><td>Semi-terrestrial</td><td>Histo</td><td>Histomor</td><td>hf-hm</td><td>-</td><td>x</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Overview over all sampling locations (main study sites are in bolt).</figcaption></figure>

ied mineral soils. Decagon 5TE electrical conductivity measurements of all sites remain low with values in the range between 0.00 and 0.13 d Sm⁻¹.

In the following, the different sites, including the collected samples and data, are described in detail.

## 2.1 Arctic Research Center, Sodankylä, Finland (FMI)

The FMI-ARC is situated in Sodankylä (67.368° N, 26.633° E) in the boreal forest of northern Finland intermixed

with heathland, bogs, and open water (e.g., Rautiainen et al., 2012; Ikonen et al., 2016). The prevailing soil type in aerated zones is podsol of mainly very sandy texture and overlying organic surface layers. A soil moisture and soil temperature network (Ikonen et al., 2016) is distributed in different land cover and soil types around the Sodankylä Research Center Decagon 5TE Sensors were placed at 5, 10, 20, 40, and 80 cm depths, whereby the top layers (5 and 10 cm depth) hold three sensors each. Calibration samples were collected from two stations. At the station within a coniferous forest ("UG Forest 1") one sample was taken from the organic surface layer along with one sample from the underlying sandy A horizon. At the station in heathland located within a forest clearing ("HA Open 1"), a pronounced organic surface layer is absent and samples were excavated from the sandy A horizon.

Around the same two stations spatial soil moisture variability had been assessed during summer 2012 by means of ThetaProbe measurements. For 20 days within a 3-month period (June–August 2012), these measurements were taken from the surface in a hand-held fashion. As they were not
<table><caption>**Table 3.** Soil moisture sensor characteristics from manufacturer manuals as well as findings of Vaz et al. (2013).</caption><thead><tr><th rowspan="2">Sensor</th><th rowspan="2">Type</th><th rowspan="2">Frequency (MHz)</th><th rowspan="2">Output type</th><th rowspan="2">Length of prongs (cm)</th><th colspan="2">Sampling diameter (of influence) (cm)</th><th colspan="2">Soil moisture accuracy (factory calibration mineral) (cm<sup>3</sup> cm<sup>-3</sup>)</th></tr><tr><th>Manufacturer</th><th>Vaz et al. (2013)</th><th>Manufacturer</th><th>Vaz et al. (2013)</th></tr></thead><tbody><tr><td>Decagon ECH2O 5TE</td><td>Capacitance</td><td>70</td><td>Raw (= 50ε<sub>a</sub>)</td><td>5.2</td><td>8.6</td><td>4.4</td><td>0.030 (Topp et al., 1980)</td><td>0.040</td></tr><tr><td>Delta-T ThetaProbe ML2x</td><td>Impedance</td><td>100</td><td>Voltage</td><td>6.0</td><td>4.0</td><td>2.0</td><td>0.050</td><td>0.029</td></tr></tbody></table>

involved in the calibration process these data served for validation in this study.

## 2.2 Gludsted plantation, Denmark (HOBE)

The Danish site is situated in the Skjern River catchment in western Denmark and has been intensely investigated in the framework of HOBE (Jensen and Illangasekare, 2011). Soil samples were collected within the Gludsted spruce plantation (56.074° N, 9.334° E) in forested parts as well as heathland. The naturally occurring soil type is a podsol of coarse sandy texture with pronounced organic surface layers. Soil moisture and soil temperature measurement stations, part of a spatially distributed network (Bircher et al., 2012a; Andreasen et al., 2016), are installed in the forest with Decagon 5TE sensors at 5, 25, and 55 cm depths of the mineral soil as well as in the overlying organic layer. The samples used for laboratory calibration were taken from organic surface layers in the vicinity of two forest network stations. Additionally, at one of the two stations a sample from the underlying mineral horizon was collected. At this location a field calibration experiment (Sect. 4.2) took place. The resulting series of field data measured in organic horizons also include some Decagon 5TE-ThetaProbe-gravimetric sample couples collected around other Decagon forest stations, taken in the scope of cosmic-ray neutron detector calibration (Andreasen et al., 2016). In order to further increase the number of field calibration points some measurements acquired during a remote sensing cal/val campaign in 2013 (Jonard et al., 2014) were added to the database. This includes samples from the organic surface layer as well as the underlying sandy A horizon of a heathland soil (Gludsted Plantation, Denmark) measured by means of Decagon 5TE sensors, ThetaProbes, and gravimetric samples.

## 2.3 Additional organic samples

In fall 2013, the Centre d'Etudes Spatiales de la Biosphère (CESBIO), Toulouse, collected peat samples in two neighboring bogs on the Island Islay in western Scotland (55.743° N, 6.178° W). Additionally, the Laboratoire

d'Etudes en Géophysique et Océanographie Spatiales (LE-GOS), Toulouse, provided organic samples taken on the West Siberian Plain during their field campaigns from a tundra area in summer 2012 (65.910° N, 74.659° E) and a bog in summer 2013 (56.941° N, 82.607° E).

# 3 Soil moisture sensors

## 3.1 Decagon ECH2O 5TE

The Decagon ECH2O 5TE sensor is based on the capacitance method to measure the medium around three 5.2 cm-long prongs at 70 MHz frequency (Decagon Devices Inc., 2014). The plastic-coated sensor head is sensitive to the surrounding permittivity and thus, should be completely covered by the medium. When using a Decagon Em50 digital/analog data logger, εₐ can be estimated dividing the raw sensor output by 50. By default, the Topp equation for mineral soils (Topp et al., 1980) is used to calculate soil moisture. In addition, the probe also provides temperature and electrical conductivity measurements. The Decagon 5TE sensor as well as its predecessor TE have been tested in several studies (e.g., Kizito et al., 2008; Saito et al., 2009; Assouline et al., 2010; Rosenbaum et al., 2010, 2011; Sakaki et al., 2011; Varble and Chavez, 2011; Ganjegunte et al., 2012; Vaz et al., 2013). To our knowledge, only one calibration curve for organic material has previously been reported. However, this function developed by Vaz et al. (2013) is based on a sample from an artificial organic plant potting mix and was never tested in organic material from a natural soil horizon. It was only calibrated up to a water content of ~0.35 m³ m⁻³ and without burying the sensor head in the material.

Some of the probe's characteristics are listed in Table 3, including information from the manufacturer manual as well as findings by Vaz et al. (2013). Soil moisture accuracy in mineral soils is around 0.03–0.04 cm³ cm⁻³ (applying the Topp equation), and the diameter of the probe's sensitivity lies in the range of approximately 4–8 cm. In the framework of HOBE, the Decagon 5TE sensor has been previously evaluated for near-surface sandy soil layers in the Skjern River
catchment. Using Topp's equation, both Vasquez and Thom-
sen (2010) and Bircher et al. (2012a) independently found
the sensor to be accurate within ±0.02–0.03 cm³ cm⁻³ under
coniferous forest, heathland, as well as in agricultural fields.

## 3.2 Delta-T ThetaProbe ML2x

The Delta-T ThetaProbe ML2x is a soil moisture sensor with four 6 cm-long steel rods building an array whose impedance varies with the moisture content of the measured medium (Delta-T Devices Ltd., 1999). The corresponding voltage output V at 100 MHz can be converted into the soil's apparent relative permittivity, using $\sqrt{\varepsilon_a} = 1.07 + 6.4V - 6.4V^2 + 4.7V^3$ (Gaskin and Miller, 1996). $\varepsilon_a$ can then be related to moisture content using the manufacturer's calibrations for mineral and organic substrates. The probe has been evaluated in different studies and calibration functions are already reported for a range of natural organic substrates (e.g., Kurum et al., 2012; Overduin et al., 2005; Yoshikawa et al., 2004), and artificial potting/compost substrates (e.g., Nemali et al., 2007; Kargas and Kerkides, 2008; Kang et al., 2010; Vaz et al., 2013). Major probe characteristics are listed in Table 3. Soil moisture accuracy in mineral soils is around 0.03–0.05 cm³ cm⁻³ (applying factory-supplied calibration), and the diameter of the probe’s sensitivity lies in the range of approximately 2–4 cm.

# 4 Method

## 4.1 Laboratory calibration measurements

Laboratory sensor calibrations for the organic and mineral substrates collected in Finland and Denmark (Sects. 2.1 and 2.2) were carried out at the respective institutions, following the same protocol. As organic material can be strongly affected by shrinkage during drying (e.g., Schaap et al., 1996; Pumpanen and Ilvesniemi, 2005), a significant error might occur when assuming a constant bulk density over the entire water content range. To avoid this issue the material was initially saturated and the changing volume and bulk density during the subsequent dry down were automatically accounted for. The saturated bulk densities of the respective soils were previously estimated from field samples and the collected saturated material was packed accordingly into large buckets. In the center of each bucket one Decagon 5TE sensor was installed permanently at the surface. The sensors were always placed in horizontal position with the blades in a vertical direction in order to avoid ponding of water. Distances to the bucket borders were clearly larger than the maximum diameter of the probe's sensitivity (Table 3). The Decagon 5TE readings were logged continuously, while ThetaProbe measurements and gravimetric samples were taken from the surface at defined times. A lot of attention was paid to proper application of the ThetaProbes: the four rods of the instrument were inserted vertically and

pushed firmly into the substrate in order to assure good con-
tact and avoid air gaps, and yet careful not to compress the
material too much. This is common practice with this sensor
type, in the case of organic material, for example, applied by
Nemali et al. (2007), Kargas and Kerkdis (2008), and Vaz et
al. (2013) in the laboratory as well as by Kurum et al. (2012)
in the field. In our case, three readings were taken at a given
time step in order to check the repeatability of the measure-
ments, while the mean was recorded each time. Addition-
ally, one reference sample was extracted per time step using
steel rings of known volume. As buckets were of large sizes,
enough material for all the gravimetric samples was available
without disturbing the sensor measurements and no backfill-
ing of material was necessary. The samples were oven dried
at 105°C for 24 h for the mineral soils and at 85°C for 48 h
for the organic material as, for example, practiced by Nagare
et al. (2011). O'Kelly (2004) had found that around this tem-
perature, mass loss due to charring balanced the effects of
residual water caused by the strong water-binding capacities
of organic matter. Subsequently, the estimated gravimetric
moisture contents were converted into volumetric moisture
contents by the knowledge of the bulk density. Soil texture
and organic carbon were determined using standard proce-
dures (sieving as well as using a Malvern Mastersizer 2000
and loss on ignition).

The samples from organic surface horizons in Siberia
and Scotland (Sect. 2.3) were handled at CESBIO, France.
They were not large enough to place Decagon 5TE sensors.
Thus, only ThetaProbe readings (in triplicates) and respec-
tive gravimetric samples were taken.

## 4.2 Field calibration measurements

During the field calibration experiment in the vicinity of
one Danish forest network station (see Sect. 2.2), a Decagon
5TE sensor was installed in the organic horizon and logged
continuously. After the first measurements of extremely dry
conditions in summer 2013, the soil was saturated. During
the drying period, three ThetaProbe readings and gravimet-
ric samples were acquired and averaged for each measure-
ment in time. In the case of these data and all additional field
observations used in this study (Decagon 5TE–ThetaProbe–
gravimetric sample couples described in Sect. 2.2), sensor in-
stallation, measurement, and drying protocols were identical
to the ones described above for the laboratory calibration.

## 4.3 Fitting of calibration functions and validation

All field and laboratory data were gathered and sen-
sor output was plotted against volumetric moisture con-
tent for Decagon 5TE–ThetaProbe and organic–mineral
samples, respectively. In the case of continuously logged
Decagon 5TE data, the two measurements closest to each
ThetaProbe/sample timestamp were extracted and averaged.
The resulting number of available data points per site and
sensor type is indicated in Table 1. Sensor calibrations based on our measurements were carried out for the ensemble of data measured in the organic horizons of all studied sites, while for the data from underlying mineral soil layers the validity of the manufacturer calibrations was tested. Calibration curves were fitted through the data using mathematical descriptions already reported in the literature on soil moisture sensor calibration. The fitted functions were compared with corresponding manufacturer calibration curves as well as calibrations reported in the literature (specified in Sect. 5.3, Table 6, Fig. 4).

To further validate the proposed fit functions, Decagon 5TE and ThetaProbe soil moisture time series from the forest ("UG Forest 1") and heathland ("HA Open 1") network stations in Sodankylä recorded during summer 2012 (see Sect. 2.1) and not used in the calibration process were compared to test whether the soil moisture from the two sensor types agreed. At both sites, one of the three Decagon 5TE sensors at 5 cm depth was chosen for this study together with the ThetaProbe surface data sampled in the immediate vicinity. The five ThetaProbe values available per day were averaged for our purpose. In the case of the Decagon 5TE data the two time steps closest to the mean ThetaProbe acquisition time were averaged, resulting in maximum time shift between the two measurements of less than 30 min. For the organic surface layer at the "UG Forest 1" site soil moisture estimates using manufacturer default calibrations as well as newly derived fit functions were compared. Thereby, the ThetaProbe "organic" default function was chosen, while for the Decagon 5TE sensor the only available Topp et al. (1980) equation for mineral soils was applied. For the low organic mineral surface soil at the "HA Open 1" site default functions for mineral soils provided by the manufacturers were considered. To get a better insight into the temporal evolution of the soil moisture pattern over time, hourly rainfall intensities (R_1H) measured at Tähtelä at the center of the Sodankylä research area (~0.5 and 2.5 km distance from the "HA Open 1" and "UG Forest 1" network stations) were plotted.

For the statistical analysis throughout our study the Pearson's correlation coefficient (R), bias (mean difference between excepted and measured values), and bias-corrected root mean square deviation (RMSD) were computed.

# 5 Results and discussion

## 5.1 Sensor output – volumetric moisture content response

Figure 2 depicts the Decagon 5TE and ThetaProbe output ($\epsilon_a$ and voltage, respectively) separately plotted against the volumetric moisture content for the studied organic (> 30% SOM, top row panels) and mineral soil horizons (< 30% SOM, bottom row panels). The corresponding manufacturer

<figure><img src="image_5.png" /></figure>

**Figure 2.** Decagon 5TE apparent relative permittivity $\epsilon_a$ (left panels) and ThetaProbe voltage (mV) (right column panels) against volumetric moisture content $\theta$ for organic (SOM > 30%, top row panels) and mineral soil horizons (SOM < 30%, bottom row panels), laboratory ● and field ▼ data, with color codes from highest to lowest SOM content (yellow–dark red and purple–dark blue, respectively). For mineral horizons, blue and purple signatures mean SOM < 10 and > 10%, respectively. Manufacturer's default calibration curves (black dashed and continuous lines) are also included. Regarding the specifications of sample names and respective SOM fractions, please see Table 1.

calibrations are depicted as well (continuous and dashed black lines for organic and mineral, respectively). Additionally, points were color coded to distinguish between SOM contents (yellow–red and blue–purple for organic and mineral, respectively; see Table 1 for SOM contents of the respective samples), while data obtained from laboratory and field measurements are discriminated by different symbol types (dots and triangles, respectively).

For both sensor types, the field measurements (triangles) are in good agreement with the laboratory data (dots). For the mineral soils with a SOM content below 10% (blue colors) both Decagon 5TE and ThetaProbe data scatter around the respective manufacturer calibration curves, and thus, demonstrate the validity of the latter. In the case of the Decagon 5TE sensor this underlines earlier results by Vasquez and Thomsen (2010) and Bircher et al. (2012a) who also found the sensor to be accurate within $\pm 0.02–0.03 \text{ cm}^3 \text{ cm}^{-3}$ in sandy A horizons with low organic matter contents using the default Topp's equation.

In contrast, for the mineral samples with a SOM exceeding 10% (purple colors) the trends in the data differ for both sensor types. While for the ThetaProbe (right column) the
data of increased SOM content show a behavior comparable to the measurements in mineral soils with SOM < 10%, in the respective Decagon 5TE data (left column) a clear tendency towards a decrease in apparent relative permittivities at given moisture contents can be observed. For the measurements in the organic horizons (> 30% SOM, yellow-red colors), this trend of decreasing εₐ for a given moisture content with increasing SOM content is even more distinct, and despite the scatter, consistent in the data measured throughout a range of humus types from different locations. Especially at higher moisture contents a more or less constant offset is detectable, while below ~0.4 cm³ cm⁻³ an increase in curvature is observable, indicating only a small change in εₐ for a relatively large change in soil moisture. This behavior is in good agreement with observations from TDR readings (e.g., Topp et al., 1980; Roth et al., 1992; Paquet et al., 1993; Kellner and Lundin, 2001; Jones et al., 2002), and can be explained by the substantial fraction of bound water on the large specific surface area of the organic material. Considerable amounts of rotationally hindered water molecules result in the recording of lower apparent relative permittivities for organic-rich materials compared to low organic mineral soils for the same water content. Adsorption forces decrease exponentially with increasing distance to the solid surface. At low water contents where first layers affected by binding forces closest to solid surfaces are filled, an increase in moisture content barely increases εₐ. Once these layers are filled, a further increase in moisture level results in a more rapid rise of εₐ. Hence, the offset compared to the sensor response in mineral soils of low SOM content becomes constant. The value of 10% SOM (blue colors < 10% SOM > purple colors) as threshold for the appearance of bound water effects is in accordance with findings reported by Paquet et al. (1993), Vaz et al. (2013), and Vasquez (2013). Hence, these data suggest that if more such Decagon 5TE readings were collected in the future, an attempt could be made to derive a calibration law for mineral horizons as a function of intermediate SOM content (10–30%). In purely organic horizons, bound water effects are most pronounced, whereby, above 30% SOM content (yellow-red colors) the dependency of the magnitude of bound water effects on the SOM content seems to level off, meaning that no further decrease of εₐ with augmenting soil organic matter is clearly detectable.

The ThetaProbe data (right column panels) for the organic soil layers (top row panels) again show scatter but with a clear trend irrespectively of the sample location or humus type. However, in contrast to the Decagon 5TE data (left column, top row panels), there is a closer match between our soil moisture measurements and soil moisture computed based on the default calibrations for mineral and organic substrates. It is worth noting that there is only a small difference in the soil moisture estimation between the two default calibration curves whilst their shape remains consistent. Nevertheless, in the medium to high range of the sensor outputs (600–1000 mV) for the organic samples the default curves are not

able to reproduce our measurements due to more pronounced curvature in our data. This results in (1) a tendency towards increased sensor output at a given moisture content compared to both default curves in the middle range, and (2) saturation in the sensor's response around 1000 mV.

In conclusion, one can state that for both sensor types deviating sensor outputs in the case of measurements conducted in organic horizons (yellow-red colors) compared to mineral layers with low SOM content (blue colors) are clearly demonstrated. The scatter in the data from organic horizons is in comparable range as reported for similar calibration studies using TDR sensors (e.g., Schaap et al., 1996; Kellner and Lundin, 2001; Pumpanen and Ilvesniemi, 2005; Nagare et al., 2011). Thereby, the spread is always higher for organic substrates compared to mineral soils due to the complex nature (i.e., very high porosities and large specific surface areas) of the former. However, no distinct differences in measurements' behavior from samples ranging a variety of humus types and acquired by different users are noticeable. Based on this first analysis it can be hypothesized that for each sensor type one calibration function should hold for reliable estimates of the moisture content in organic surface horizons (> 30% SOM) of different characteristics and variable SOM. In the following, the presented results and discussion will concentrate on this subject.

## 5.2 Curve fits for organic material

Figure 3 illustrates the calibration curves fitted through the data measured in the different organic soil layers (black circles). For the Decagon 5TE sensor data pairs of apparent relative permittivity readings and corresponding volumetric moisture contents (left column panels) different functions were tested: third-order polynomial (dark blue), power (light blue), natural logarithm (red), and square root (orange). With respect to the ThetaProbe (right column panels), fit functions (red) were derived for both output voltage-volumetric moisture and apparent relative permittivity-volumetric moisture pairs, (third- and first-order polynomial in top and bottom row, respectively), as they are equally used in many studies. For comparison, manufacturer calibration curves are also included in the plots (continuous and dashed black lines in the case of curves for organic and mineral materials, respectively). All functions shown in Fig. 3 are listed in Table 4 and the corresponding fitting statistics are presented in Table 5.

For the Decagon 5TE sensor, the statistics show no clear difference between the different tested fit functions. Compared to the manufacturer calibration all of them result in a significantly decreased bias and an improved RMSD while *R* remains unchanged. Based on a visual inspection in Fig. 3 (left column panels) the natural logarithmic fit seems to most closely follow the measured data with a more pronounced curvature at low moisture contents up to about 0.2 cm³ cm⁻³, and a similar curvature as the mineral default function for higher moisture contents.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Fitting functions for the Decagon 5TE apparent relative permittivity $ε_a$ (left panels), and ThetaProbe voltage (mV) (upper right panel) as well as $ε_a$ (lower right panel) against volumetric moisture content $θ$ including manufacturer's default calibration curves for the organic soil layers (SOM > 30%).</figcaption></figure>

For the ThetaProbe the third-order polynomial fit between the sensors millivolt (mV) output and the measured soil moisture (right column, top row panels) shows a similar curve shape as the default functions for mineral and organic substrates, but with the aforementioned increased curvature. Meanwhile, a steeper slope compared to the quasi-linear default curves becomes apparent in the case of the first-order polynomial fit through the $ε_a$-moisture content couples (right column, bottom row panels). For both new functions (mV-moisture content and $ε_a$-moisture content), the *R* and RMSD improved slightly, whereas the bias stayed in the order of the default function for mineral soils, which is clearly lower than for the default function for organic materials.

## 5.3 Comparison of fitted versus the literature calibrations for organic materials

Figure 4 displays the functions fitted (red curves) to the measurements performed on our organic samples (only the selected logarithmic function for Decagon 5TE) together with petrophysical or empirical relationships for organic samples taken from the literature. In the case of the Decagon 5TE sensor (left column) this includes the calibration for an organic plant potting mix reported by Vaz et al. (2013) for the same sensor type (orange line) as well as the following calibration laws for organic samples obtained from TDR measurements (blue and green lines): Pepin et al. (1992), Roth et al. (1992), Paquet et al. (1993), Malicki et al. (1996) using a bulk density of 0.1 g cm⁻³, Schaap et al. (1996), Kellner and Lundin (2001), Yoshikawa et al. (2004) for living sphagnum, and Pumpanen and Ilvesniemi (2005). Concern-

ing the ThetaProbe (right column panels), only functions derived for organic soil layers with the same sensor type were selected, namely those of Nemali et al. (2007), Kurum et al. (2012) for an OL layer using a bulk density of 0.1 g cm⁻³, and Vaz et al. (2013) for the relationship between mV output and moisture content (wine red, dark red, and orange lines in top row panels), and Yoshikawa et al. (2004, living sphagnum) as well as Kargas and Kerkides (2008) for the relationship between $ε_a$ and moisture content (beige and yellow lines in bottom row panels), respectively. Manufacturer calibration curves are also included in the plots (continuous and dashed black lines in the case of curves for organic and mineral materials, respectively). Corresponding statistics are listed in Table 6.

The natural log fit through the Decagon 5TE data (left column panels, red line) and the calibration proposed by Vaz et al. (2013) applied to the respective data (left column, orange line) exhibit a similar *R* value, while both RMSD and bias increased for the latter. The two curves follow each other closely within the calibration range of Vaz et al. (2013), while they deviate beyond a water content of ~0.5 cm³ cm⁻³ due to a more pronounced curvature of our natural log fit. Good agreement within the calibrated range of two curves derived from different natural organic horizons and a plant potting mix further strengthens confidence that the type and structure of organic material does not drastically affect the measurements themselves. And the same seems to account for the application with or without burying the sensor head in the materials, as practiced in this work and by Vaz et al. (2013), respectively. This adds a further point of validity, making the here-derived function even more generally applicable.
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Comparison between reported petrophysical and empirical relationships applied to our data measured in organic soil layers for the Decagon 5TE apparent relative permittivity $ε_a$ (left panel), and ThetaProbe voltage (mV) (upper right panel) as well as $ε_a$ (lower right panel) against volumetric moisture content $θ$ including respective manufacturer's default calibration curves and best fits.</figcaption></figure>

For the functions derived from TDR measurements in organic soil layers R values also stayed in the same order as for our functions fitted through the Decagon 5TE data (left column panels). Compared to our best suited function (natural log fit, red line) the ones proposed by Paquet et al. (1993), Schaap et al. (1996), Kellner and Lundin (2001), and Malicki et al. (1996) using a bulk density of 0.1 cm³ cm⁻³ (curves in blue colors), lie in the same range with very similar RMSD, and small (though some order of magnitudes larger) bias of around ±0.01 cm³ cm⁻³. Furthermore, the curvatures of these functions are slightly less pronounced either in the dry or wet range. Other functions (curves in green colors) are clearly offset with mostly larger RMSD, significantly larger bias (above 0.03 cm³ cm⁻³) and less curvature (Pepin et al., 1992; Roth et al., 1992; Yoshikawa et al., 2004; Pumpanen and Ilvesniemi, 2005). While the absolute match between the calibration curves for organic material of the Decagon 5TE sensor and the TDR-based ones is not always good, it is still worth noting that they all show the same general curve shape. The discrepancies between these different calibration laws presumably arise from the different sensor designs, measurement principles, and measurement frequencies used as also pointed out by Vaz et al. (2013).

For the ThetaProbe mV versus moisture content relationship (right column, top row) all considered calibrations show very similar behavior as the default calibrations (black lines) up to ~0.2 cm³ cm⁻³. However, at higher moisture contents the curves start deviating significantly without a clear pattern. Like our third-order polynomial fit (red line) the function reported by Vaz et al. (2013, orange line) exhibits the same type of shape as the default functions though with weaker cur-

vature. Meanwhile, the Nemali et al. (2007, wine red line) and Kurum et al. (2012, dark red line) functions show differing characteristics. In any case, the statistics in terms of all measures clearly deteriorate when applying other calibration laws to our data. The Nemali et al. (2007) curve and our fit function were calibrated even for high moisture contents (0.8–0.9 cm³ cm⁻³), while the Vaz et al. (2013) and Kurum et al. (2012) fits were derived only for low to moderate moisture contents up to 0.3–0.35 cm³ cm⁻³.

In the case of the ThetaProbe $ε_a$ versus moisture content calibration (right column, bottom row panels), all included calibration laws perform similarly well in terms of R, while those of Kargas and Kerkides (2008, yellow line) and Yoshikawa et al. (2004, beige line) showed increased RMSDs and biases (with opposite signs for the two specified functions). The Kargas and Kerkides (2008) curve (calibrated up to 0.75 cm³ cm⁻³) exhibit a shape similar to the default curves though with lower $ε_a$ at a given moisture content. Yoshikawa et al. (2004) show a more analog trend to our data with larger $ε_a$ for a given moisture content compared to the mineral default curve and deviation starts above 0.3 cm³ cm⁻³ beyond the Yoshikawa et al. (2004) calibration range.

The presented results indicate that for the ThetaProbe data a clear consistency between measurements, fitted functions, theory, and the literature calibrations is lacking. As practiced in our experimental setup, Nemali et al. (2007), Kurum et al. (2012), and Vaz et al. (2013) also removed and reinserted the ThetaProbe after each measurement, while in the studies by Yoshikawa et al. (2004) and Kargas and Kerkidis (2008) probes remained installed throughout the entire experiments.
<table><caption>**Table 4.** Manufacturer's default calibration functions and functions fitted through the data measured in organic layers (SOM > 30%) as shown in Fig. 3 for Decagon 5TE ($\theta$ = fct. ($\varepsilon_a$)) and Delta-T ThetaProbe ($\theta$ = fct. ($\varepsilon_a$) and $\theta$ = fct. (voltage)), respectively. $\theta$ is volumetric moisture content, $\varepsilon_a$ is apparent relative permittivity.</caption><thead><tr><th>Sensor type</th><th>θ = fct. (x)</th><th>Function type</th><th>Function</th></tr></thead><tbody><tr><td rowspan="5">Decagon ECH2O 5TE</td><td rowspan="5">ε<sub>a</sub></td><td>Default mineral</td><td>θ = 4.3 × 10<sup>-6</sup> × ε<sub>a</sub><sup>3</sup> - 5.5 × 10<sup>-4</sup> × ε<sub>a</sub><sup>2</sup> + 2.92 × 10<sup>-2</sup> × ε<sub>a</sub> - 5.3 × 10<sup>-2</sup></td></tr><tr><td>Fit (third-order polynomial)</td><td>θ = 6.9593 × 10<sup>6</sup> × ε<sub>a</sub><sup>3</sup> - 9.8511 × 10<sup>-4</sup> × ε<sub>a</sub><sup>2</sup> + 4.5834 × 10<sup>-2</sup> × ε<sub>a</sub> - 5.0595 × 10<sup>-2</sup></td></tr><tr><td>Fit (power)</td><td>θ = 0.831074 × ε<sub>a</sub><sup>0.192743</sup> - 0.978084</td></tr><tr><td>Fit (natural logarithm)</td><td>θ = 0.262621 × ln(ε<sub>a</sub>) - 0.279003</td></tr><tr><td>Fit (square root)</td><td>θ = 0.140543 - 0.139004 × √ε<sub>a</sub></td></tr><tr><td rowspan="5">Delta-T ThetaProbe ML2x</td><td rowspan="5">ε<sub>a</sub></td><td>Default mineral</td><td>θ = -0.190 + 0.119 × √ε<sub>a</sub></td></tr><tr><td>Default organic</td><td>θ = -0.168 + 0.130 × √ε<sub>a</sub></td></tr><tr><td>Fit (first-order polynomial)</td><td>θ = 1.4894 × 10<sup>-2</sup> × ε<sub>a</sub> - 3.2685 × 10<sup>-3</sup></td></tr><tr><td>Default mineral</td><td>θ = 0.56 × V<sup>3</sup> - 0.762 × V<sup>2</sup> + 0.762 × V - 0.063</td></tr><tr><td>Default organic</td><td>θ = 0.61 × V<sup>3</sup> - 0.831 × V<sup>2</sup> + 0.831 × V - 0.030</td></tr><tr><td colspan="2">Voltage</td><td>Fit (third-order polynomial)</td><td>θ = 1.4964 × 10<sup>-9</sup> × mV<sup>3</sup> - 2.0401 × 10<sup>-6</sup> × mV<sup>2</sup> + 1.0516 × 10<sup>-3</sup> × mV - 1.9707 × 10<sup>-2</sup></td></tr></tbody></table>

Certainly, a hand-held application with slightly changed sampling location each time results in increased data variability compared to permanently installed probes, the effect being more pronounced in organic substrate of complex structure compared to more homogeneously distributed mineral soils. However, irrespectively of the two approaches used, no clear difference is detectable in the functions' curve shapes. Another plausible explanation for the nonuniform behavior could be the ThetaProbe's rod configuration that significantly concentrates the electromagnetic field around the central electrode, resulting in a small sampling volume (Table 3). This drawback was already raised by Robinson et al. (1999) and Vaz et al. (2013) who stated that this possibly renders the measurements more sensitive to compaction during the insertion of the instrument, as the effect is most distinct around the probe's center. Additionally, this problem becomes more important as moisture content increases. This would explain why the agreement between different calibration curves is best at very small water contents and deteriorates more and more towards high soil moisture values.

## 5.4 Comparison of soil moisture time series at two Sodankylä network sites

Figure 5 shows the comparison of average ThetaProbe and Decagon 5TE soil moisture estimates collected in Sodankylä during summer 2012. Time series (left column panels) and scatter plots (right column panels) of soil moisture measured in 0–5 cm depth from the “HA Open 1” network station with low organic mineral soil (top row panels) as well as at the “UG Forest 1” network station with a pronounced organic surface layer (bottom row panels) are depicted. In the case of “UG Forest 1”, soil moisture data sets using both default calibrations (black) and newly derived fits (red) are presented. For the ThetaProbe average of five readings, respective standard deviations are displayed as error bars in the time series (left column), and hourly rainfall intensities (R_1H) are also plotted along (black bars). Details on the applied calibration functions as well as corresponding statistics are given in Table 7.

The measurements of the two sensor types at the “HA Open 1” site (top row panels) are in very good agreement using the default calibrations (black signatures) for mineral soils. In contrast, applying the most appropriate default calibrations available for the two sensors at the “UG Forest 1” site (bottom row), a pronounced difference in soil moisture content is observed. Thereby the ThetaProbe soil moisture estimates are much wetter and their dynamic range much larger compared to the Decagon 5TE sensor. When using our fit functions derived for organic material (third-order polynomial for ThetaProbe and natural logarithm for Decagon 5TE, red signatures), the agreement becomes much better with significantly decreased RMSD and bias. Also, it now nicely stands out that the mean soil moisture level of the sandy mineral soil (top row panels) is lower but with larger temporal
<table><caption>**Table 5.** Statistics for manufacturer's default calibration curves and functions fitted through the data measured in organic layers (SOM > 30 %) as listed in Table 4 for Decagon 5TE ($\theta$ = fct. ($\varepsilon_a$)) and Delta-T ThetaProbe ($\theta$ = fct. ($\varepsilon_a$) and $\theta$ = fct. (voltage)), respectively: N is the number of sampling points, R is Pearson's correlation coefficient, RMSD is bias-corrected root mean square deviation, BIAS is bias, $\theta$ is volumetric moisture content, $\varepsilon_a$ is apparent relative permittivity.</caption><thead><tr><th>Sensor type</th><th>θ = fct. (x)</th><th>Function type</th><th>N</th><th>R</th><th>RMSD</th><th>BIAS</th></tr></thead><tbody><tr><td rowspan="5">Decagon ECH2O 5TE</td><td rowspan="5">ε<sub>a</sub></td><td>Default mineral</td><td>50</td><td>0.92</td><td>0.077</td><td>0.127</td></tr><tr><td>Fit (third-order polynomial)</td><td>50</td><td>0.92</td><td>0.068</td><td>1.17 × 10<sup>-17</sup></td></tr><tr><td>Fit (power)</td><td>50</td><td>0.92</td><td>0.070</td><td>-4.82 × 10<sup>-16</sup></td></tr><tr><td>Fit (natural logarithm)</td><td>50</td><td>0.92</td><td>0.070</td><td>3.68 × 10<sup>-9</sup></td></tr><tr><td>Fit (square root)</td><td>50</td><td>0.91</td><td>0.071</td><td>-2.42 × 10<sup>-12</sup></td></tr><tr><td rowspan="6">Delta-T ThetaProbe ML2x</td><td rowspan="3">ε<sub>a</sub></td><td>Default mineral</td><td>70</td><td>0.84</td><td>0.110</td><td>-0.004</td></tr><tr><td>Default organic</td><td>70</td><td>0.84</td><td>0.110</td><td>-0.080</td></tr><tr><td>Fit (first-order polynomial)</td><td>70</td><td>0.87</td><td>0.102</td><td>0.004</td></tr><tr><td rowspan="3">Voltage</td><td>Default mineral</td><td>70</td><td>0.84</td><td>0.110</td><td>-0.004</td></tr><tr><td>Default organic</td><td>70</td><td>0.84</td><td>0.110</td><td>-0.078</td></tr><tr><td>Fit (third-order polynomial)</td><td>70</td><td>0.87</td><td>0.100</td><td>0.001</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Time series (left column panels) and scatter plots (right panels) for the soil moisture ($\theta$) measured at 0–5 cm depth by ThetaProbe (average of five readings with standard deviations as error bars) and Decagon 5TE sensors at the Sodankylä “HA Open 1” (upper row panels: low organic mineral soil, SOM = 6.89 %) and “UG Forest 1” (lower row panels: organic substrate, SOM = 36.59 %) network stations during summer 2012. Hourly rainfall intensities (R_1H) from Tähtelä are plotted along. Details on the applied calibration functions (default in black and newly derived in red) as well as corresponding statistics are given in Table 7.</figcaption></figure>

dynamics compared to the organic surface layer (bottom row panels). This behavior is expected due to low and high water retention capacities of the two materials, respectively.

Only the correlation between the two sensors remains still low in the case of the organic layer, especially caused by the observed scatter in the ThetaProbe data obtained by a handheld application with constantly changed sensor locations. This scatter is in similar range with the data variability pre-

sented by Kurum et al. (2012), and significantly larger than observed in the mineral soil, both in terms of daily standard deviations of the five probe readings (error bars) and day-to-day variations. As already discussed in Sect. 5.3, the more pronounced small-scale variabilities in the organic substrate are a consequence of more complex structure compared to the more homogeneously distributed sandy soil encountered at the “HA Open 1” site, possibly intensified by compaction
<table><caption>**Table 6.** Statistics for the applied petrophysical and empirical relationships for organic soil layers extracted from the literature as well as for manufacturer's default calibration curves and our best fits (as presented in Fig. 4). *N* is the number of sampling points, *R* is Pearson's correlation coefficient, RMSD is bias-corrected root mean square deviation, BIAS is bias, *θ* is volumetric moisture content, *ε*<sub>a</sub> is apparent relative permittivity.</caption><thead><tr><th>Sensor type</th><th>θ = fct. (x)</th><th>Sensor type original study</th><th>Source</th><th>N</th><th>R</th><th>RMSD</th><th>BIAS</th></tr></thead><tbody><tr><td rowspan="12">Decagon ECH2O 5TE</td><td rowspan="12">ε<sub>a</sub></td><td rowspan="12">–<br>Decagon ECH2O 5TE<br>TDR</td><td>Fit (Natural logarithm)</td><td>50</td><td>0.92</td><td>0.070</td><td>3.68 × 10<sup>-9</sup></td></tr><tr><td>Vaz et al. (2013)</td><td>50</td><td>0.91</td><td>0.075</td><td>0.003</td></tr><tr><td>Roth et al. (1992)</td><td>50</td><td>0.91</td><td>0.072</td><td>0.084</td></tr><tr><td>Yoshikawa et al. (2004) (living org.)</td><td>50</td><td>0.91</td><td>0.077</td><td>0.133</td></tr><tr><td>Pepin et al. (1992)</td><td>50</td><td>0.90</td><td>0.077</td><td>0.032</td></tr><tr><td>Pumpanen and Ilvesniemi (2005)</td><td>50</td><td>0.91</td><td>0.086</td><td>0.077</td></tr><tr><td>Malicki et al. (1996) (bulk density = 0.1)</td><td>50</td><td>0.91</td><td>0.071</td><td>-0.013</td></tr><tr><td>Kellner and Lundin (2001)</td><td>50</td><td>0.91</td><td>0.071</td><td>-0.012</td></tr><tr><td>Schaap et al. (1996)</td><td>50</td><td>0.92</td><td>0.071</td><td>-0.008</td></tr><tr><td>Paquet et al. (1993)</td><td>50</td><td>0.92</td><td>0.069</td><td>-0.018</td></tr><tr><td rowspan="10">Delta-T ThetaProbe<br>ML2x</td><td rowspan="10">ε<sub>a</sub></td><td rowspan="10">–<br>Delta-T ThetaProbe ML2x</td><td>Fit (first-order polynomial)</td><td>70</td><td>0.87</td><td>0.102</td><td>0.004</td></tr><tr><td>Yoshikawa et al. (2004) (living org.)</td><td>70</td><td>0.87</td><td>0.111</td><td>0.063</td></tr><tr><td>Kargas and Kerkides (2008)</td><td>70</td><td>0.84</td><td>0.123</td><td>-0.169</td></tr><tr><td>Fit (third-order polynomial)</td><td>70</td><td>0.87</td><td>0.100</td><td>0.001</td></tr><tr><td>Vaz et al. (2013)</td><td>70</td><td>0.81</td><td>0.124</td><td>-0.008</td></tr><tr><td>Nemali et al. (2007)</td><td>70</td><td>0.70</td><td>0.154</td><td>0.045</td></tr><tr><td>Kurum et al. (2012) (OL layer,<br>bulk density = 0.1)</td><td>70</td><td>0.80</td><td>0.124</td><td>-0.129</td></tr><tr><td rowspan="3">Voltage</td><td rowspan="3">–<br>Delta-T ThetaProbe ML2x</td><td>Fit (first-order polynomial)</td><td>70</td><td>0.87</td><td>0.102</td><td>0.004</td></tr><tr><td>Yoshikawa et al. (2004) (living org.)</td><td>70</td><td>0.87</td><td>0.111</td><td>0.063</td></tr><tr><td>Kargas and Kerkides (2008)</td><td>70</td><td>0.84</td><td>0.123</td><td>-0.169</td></tr></tbody></table>

<table><caption>**Table 7.** Statistics for comparison of 0–5 cm volumetric moisture content (*θ*) estimates by means of Delta-T ThetaProbe and Decagon 5TE sensors at the Sodankylä “HA Open 1” (low organic mineral soil, SOM = 6.89 %) and “UG Forest 1” (organic substrate, SOM = 36.59 %) network stations during summer 2012, using calibration functions as indicated below. *N* is the number of sampling points, *R* is Pearson's correlation coefficient, RMSD is bias-corrected root mean square deviation, and BIAS is bias.</caption><thead><tr><th rowspan="2">Site</th><th colspan="2">Calibration function type</th><th rowspan="2">N</th><th rowspan="2">R</th><th rowspan="2">RMSD</th><th rowspan="2">BIAS</th></tr><tr><th>Delta-T ThetaProbe ML2x</th><th>Decagon ECH2O 5TE</th></tr></thead><tbody><tr><td>Sodankylä “HA Open 1”</td><td>Default mineral</td><td>Default mineral</td><td>17</td><td>0.82</td><td>0.0142</td><td>-0.0097</td></tr><tr><td rowspan="2">Sodankylä “UG Forest 1”</td><td>Default organic</td><td>Default mineral</td><td>18</td><td>0.12</td><td>0.0663</td><td>0.1566</td></tr><tr><td>Fit third-order polyorganic</td><td>Fit natural log organic</td><td>18</td><td>0.06</td><td>0.0355</td><td>-0.0238</td></tr></tbody></table>

effects originating from the susceptible sensor. However, in- respectively the cause, the newly derived fit functions clearly outperform the default calibration functions at the “UG Forest 1” site.

We suggest that these new ThetaProbe calibrations for organic substrates should only be used for the probe application method they were derived from, i.e., handheld. In that case, even if soil moisture data acquired using the ThetaProbe in organic-rich soils should be interpreted carefully, the sensor used together with the here-proposed calibration functions proves robust and of value for the acquisition of quick and instantaneous information about the moisture content for large areas as, for example, practiced in airborne campaigns for satellite cal/val purposes (e.g., Cosh et al., 2005; Bircher et al., 2012b). There, averaging over larger sets of readings will further balance out differing compaction and heterogeneity effects in individual readings – compared to our example where the mean of only five ThetaProbe readings was taken for comparison with point station data.

Finally, comparison with hourly rainfall intensities shows that the Decagon 5TE soil moisture time series estimated using the newly developed calibration function also well reflect the precipitation pattern, demonstrating the sensor's ability to yield reliable soil moisture time series in both mineral and organic substrates. Based on the very satisfying overall performance of the derived natural log fit function, it was applied in the calculation of the Decagon 5TE network soil moisture from organic surface layers at the Sodankylä and HOBE study sites to improve the quality in the data gathered so far.

## 6 Summary and conclusions

At both the Finnish Meteorological Institute's Arctic Research Center (FMI-ARC) in Sodankylä and the study site of the Danish Center for Hydrology (HOBE), soil moisture is a key research topic. With the purpose of serving coarse-resolution satellite remote sensing and land surface modeling studies, Decagon 5TE sensors are applied in permanent soil
moisture networks while ThetaProbes are used for hand-held
soil moisture measurement campaigns. Because both loca-
tions are characterized by organic-rich soils, a joined effort
aimed at calibrating these two electromagnetic sensor types
for organic surface layers with SOM contents above 30%.
While some ThetaProbe calibration efforts for organic soil
horizons are present in the literature, for the Decagon 5TE
sensor such a calibration function has only been reported
for an artificial organic material measured throughout a lim-
ited water content range (Vaz et al., 2013). The objective of
the here-presented study was to provide generic and widely
applicable calibrations for both studied sensor types hold-
ing for a variety of natural organic substrates as encountered
within the large areas under consideration. Necessarily, these
functions hold a decreased degree of detail and might lack
high accuracy, but will clearly outperform standard calibra-
tion functions reported by the manufacturers. The used soil
samples originated from different locations in northern re-
gions, mainly including the Sodankylä and HOBE network
areas, spanning a wide range of different humus types. We
believe that a reliable calibration approach has been worked
out with (1) the same measurement and calibration proto-
col followed at all sites, (2) comparison of data from organic
and mineral horizons including laboratory and field measure-
ments, and (3) consideration of material-specific characteris-
tics such as shrinkage and charring during drying.

For both the Decagon 5TE sensor and the ThetaProbe,
the variety of organic samples showed a consistent sensor
output-moisture content response. Likewise, this was the
case when the laboratory experiment was repeated in the field
under less disturbed conditions, demonstrating independence
of the acquired data from the chosen experimental setup. De-
viating sensor outputs for measurements conducted in or-
ganic horizons (> 30% SOM) compared to mineral layers
were clearly identified (see Table 1 for SOM contents). For
the mineral soil layers with a soil organic matter content be-
low 10%, the validity of the respective manufacturer calibra-
tions could be demonstrated in the case of both Decagon 5TE
and ThetaProbe. For the mineral samples with a SOM con-
tent exceeding 10%, the ThetaProbe data showed a behavior
comparable to the measurements in mineral soils with SOM
fraction < 10%, while in the respective Decagon 5TE data
a clear tendency towards decreased ε<sub>a</sub> at a given moisture
content could be observed. This effect became even more
pronounced for the measurements in the organic horizons
though it seemed to level off, meaning that beyond a SOM
content of 30% no further ε<sub>a</sub> decrease with augmenting soil
organic matter was clearly visible. This behavior is in ac-
cordance with previous TDR studies (e.g., Topp et al., 1980;
Roth et al., 1992; Paquet et al., 1993; Kellner and Lundin,
2001; Jones et al., 2002), and explicable by an increased
bound water fraction in porous organic matter with larger
specific surface area compared to the underlying sandy min-
eral soils. In contrast, the ThetaProbe data acquired from the
organic soil layers showed a closer match with the manufac-

turer's functions derived for mineral and organic substrates,
though with more pronounced curvature.

Based on the above results, for all data measured in the organic horizons, one calibration function was derived per sensor type. A natural logarithm and first-order polynomial were fitted through the ε<sub>a</sub> and soil moisture couples for the Decagon 5TE and ThetaProbe sensors, respectively. In the case of the ThetaProbe, a third-order polynomial was selected for the corresponding pairs of voltage and soil moisture.

The fact that there was no clear difference in the data ob-
tained from the different sampling sites spanning a variety of
humus types and acquired by different users strengthens con-
fidence that the derived calibration functions are not only site
specific but can be applied over a wide range of locations and
organic materials of differing characteristics and SOM con-
tents. This renders them highly suitable to support large-scale
remote sensing and land surface modeling studies.

In the case of the Decagon 5TE sensor, the reliability of
the proposed calibration function is further underlined by the
fact that it obeys basic physical principles (i.e., increased
bound water fraction in the case of organic material), the
good agreement with the Decagon 5TE calibration law for
a plant potting mix reported by Vaz et al. (2013), as well as
by comparable curve shapes as presented in respective TDR
calibration studies. Meanwhile, for the ThetaProbe data, such
a clear consistency between measurements, fitted functions,
and theory is lacking, which is further reflected in the nonuni-
form behavior of earlier derived calibration laws for organic
material reported by other authors.

Comparison of independent Decagon 5TE and ThetaProbe
soil moisture time series using default calibrations (not used
for the calibration) yield good agreement for the Sodankylä
"HA Open 1" network stations' mineral surface layer. In the
case of the "UG Forest 1" network stations' organic surface
horizon reasonable accordance could only be achieved when
using our fit functions derived for organic material (natu-
ral logarithm for Decagon 5TE and third-order polynomial
for ThetaProbe). The latter significantly improved RMSD
and bias so that average soil moisture levels coincided. Only
the correlation between the two sensors in the organic layer
stayed low, especially caused by the observed scatter in the
ThetaProbe data. This is mostly a consequence of the hand-
held application with constantly changed sensor locations,
leading to more pronounced short range variabilities in the
data from a highly heterogeneous material, possibly intensi-
fied by compaction effects originating from the susceptible
sensor. However, irrespectively the cause, the newly derived
calibration fit functions clearly outperform the default func-
tions at the "UG Forest 1" site.

We suggest that the newly derived ThetaProbe calibration
fit functions for organic substrates should only be used to-
gether with the probe application it was derived from, i.e.,
handheld. In that case, the functions prove robust and of
value for the acquisition of quick and instantaneous infor-
mation about the moisture content for large areas, where averaging over larger sets of readings will balance out differing compaction and heterogeneity effects in individual readings.

Finally, field data from Sodankylä demonstrate the ability of the Decagon 5TE sensor to reflect precipitation patterns in mineral soils as well as organic horizons. Based on the very satisfying overall performance of the derived natural log fit function it was applied in the calculation of soil moisture from organic surface layers at the Sodankylä and HOBE network sites to improve the quality in the so far gathered data.

Though the here-proposed calibration functions are derived based on samples collected in the higher northern latitudes, they should also be applicable to soil moisture measurements in similar media encountered in other regions of the world. If more data were collected in the future, a Decagon 5TE calibration law for mineral horizons as a function of SOM content could possibly be derived.

*Acknowledgements.* Financial support for conducting this research by the following institutions is gratefully acknowledged: European Space Agency (Support to Science Element – Changing Earth Science Network and Expert Support Laboratory); Centre National d'Etudes Spatiales (Terre, Océans, Surfaces Continentales, Atmosphère Programme, TOSCA), France; Villum Foundation (Hydrological Observatory, HOBE), Denmark; University of Copenhagen (Department of Geosciences and Resource Management), Denmark; Finnish Meteorological Institute; German Federal Ministry of Education and Research (Terrestrial Environmental Observatories, TERENO); Transnational Access to Research Infrastructures activity in the 7th Framework Programme of the EC under the ExpeER project.

Edited by: C. Ménard

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