Measuring soil moisture with cosmic-ray neutrons is a promising technique
for intermediate spatial scales. To convert neutron counts to average
volumetric soil water content a simple calibration function can be used (the
Determining average soil moisture content over larger areas is difficult, mainly for two reasons. First, soil moisture can be highly variable even at small spatial scales, especially under intermediate wetness conditions (e.g., Western et al., 2004). Second, most common in situ measurement techniques only yield point measurements. To obtain a valid estimate of area-average soil moisture one needs to collect data from numerous locations within a given area. This can be time-consuming and expensive. More recently, remote sensing of soil moisture at larger scales has become a research focus (e.g., see Ochsner et al. (2013) for a recent review); however, the measurement depth of many of these methods is still limited to the upper 5 cm of the soil. Also, both spatial and temporal resolution is rather coarse. A technique that intends to bridge the scale gap between point measurements of soil moisture and remote sensing is the use of cosmic-ray neutrons as indicators of soil moisture. A detailed description of the cosmic-ray neutron sensor (CRS) can be found in Zreda et al. (2008, 2012); here we will only describe the basic measurement principle. Cosmic-ray neutrons on Earth are formed when high-energy protons derived from galactic sources (such as supernovae) enter the Earth's atmosphere. Once in the atmosphere, the protons interact with atomic nuclei (mainly nitrogen and oxygen) producing cascades of secondary neutrons (also called high-energy neutrons) that travel towards the Earth's surface and into the soils. When secondary neutrons interact with air or soil nuclei they trigger the release (evaporation) of fast neutrons. The number of fast neutrons above the soil surface depends strongly on the number of hydrogen atoms in the surroundings because hydrogen atoms have a very high capacity to moderate fast cosmic-ray neutrons (that means to slow them down and turn them into thermal neutrons with even less energy – effectively removing the fast neutrons from the system). The number of hydrogen atoms increases with increasing soil water content and hence soils with high water contents re-emit fewer fast neutrons than soils with low water content. That leads to fewer fast neutrons being detected aboveground by the CRS, which is generally installed 1–2 m above the soil surface.
Previously, Hendrick and Edge (1966) reported that the intensity of fast
(low-energy) neutrons (
The original measurement method uses a relationship between neutron flux and
volumetric soil water content with the shape of the relationship being known
from neutron transport simulations. For this relationship, Desilets et al. (2010)
presented an equation with three constant shape parameters
(
Other external factors influencing the neutron count that need to be corrected for are (a) atmospheric pressure (Bachelet et al., 1965), (b) incoming neutron flux (see e.g., Zreda et al., 2012, Bogena et al., 2013) and (c) specific humidity (Rosolem et al., 2013). More recently, the effects of biomass on the neutron signal have been discussed. Bogena et al. (2013) noted that aboveground biomass reduced the neutron count rate and thus decreased the sensitivity of the sensor. To counter this loss of sensitivity they recommended a 24 h integration time for their forested catchment as a compromise between decreased uncertainty and decreased time resolution. Hawdon et al. (2014) and Baatz et al. (2015) compared neutron counts for locations with different amounts of biomass. Hawdon et al. (2014) reported that the variation in biomass could explain 80 % of the variation in neutron counts when assuming a nonlinear relationship between biomass and neutron counts; Baatz et al. (2015) explained 87 % of the variation proposing a linear relationship between the two variables. Baroni and Oswald (2015) suggested that the influence of aboveground biomass between the sensor and the ground, which decreases the effective measurement depth of the CRS, can be incorporated into the weighting approach of Franz et al. (2012a). This is especially important in locations where frequent large biomass changes occur, for example in agricultural fields. Coopersmith et al. (2014) found that soil moisture in a corn crop is often overestimated when the leaf area index (LAI) is relatively high while it is underestimated when LAI is relatively low – circumstances which could cause differences in the calibration and resulting soil moisture measurements. The influence of the litter layer in forested environments was investigated by Bogena et al. (2013). Water content in the litter layer changes rapidly and adds additional temporal variability to the CRS time series complicating the extraction of the soil moisture signal. Therefore, Bogena et al. (2013) recommended considering the water dynamics in the litter layer explicitly in the calibration approach. Franz et al. (2013) introduced a new approach (the universal calibration function) that takes into account all sources of hydrogen thereby requiring estimates of lattice water, soil organic carbon and vegetation biomass, as well as a regression factor that can be derived from calibration or may directly be retrieved from neutron count measurements over a large water body (500 m on all sides and deeper than 1 m).
Soil sampling locations for calibration (white dots) and forest vegetation around the CRS (red dot in the center). The TDT soil moisture sensors are located in close vicinity to the sampling locations. The larger yellow circle approximates the footprint of the CRS as it was assumed when sampling took place (diameter approximately 300 m). The smaller yellow circle approximates the footprint of the CRS according to newer modeling results by Köhli et al. (2015) (diameter approximately 200 m). Inset: field site location in Müritz National Park in north-eastern Germany.
Since the launch of the cosmic-ray neutron method many changes and corrections have been brought forward that altered the way the method is applied. These changes and corrections can be divided into two groups. On the one hand, there are corrections that are applied to the raw neutron count in order to remove the influence of other variables (such as air pressure and humidity variations or fluctuations in incoming neutron counts). On the other hand, changes have been made to the way we average the soil moisture measurements during the calibration campaigns in order to get a representative soil moisture value that corresponds to what the sensor actually “sees” at the time of calibration (changing effective measurement depth, changing footprint diameter, inclusion of lattice water and soil organic matter water equivalent). All this has led to improvements in the method's accuracy for many environments. Most of these studies were performed in medium- to high-count environments with neutron count rates above 1000 counts per hour, in generally dry environments, at higher elevations and with little vegetation. Only a few studies were performed in low-count environments with count rates below 1000 counts per hour (e.g., Rivera Villareyes et al., 2011; Bogena et al., 2013). In the present study, we evaluated whether the CRS also provides reliable and consistent soil moisture measurements in a low-count environment, i.e., in a temperate mixed forest close to sea level. We tested several weighting approaches to convert gravimetrically determined soil water content of the top 30 cm into an average soil water content that can be used for the calibration of the CRS. Additionally, we analyzed whether the annual forest cycle of foliation and defoliation is important to consider for instrument calibration. We furthermore compiled a best-practice for the calibration of a CRS in forested, low-count environments, which is provided in Appendix A.
The CRS (CRS-1000 by Hydroinnova) was installed in late 2013 in the
Müritz National Park in north-eastern Germany (53
Fractions of different tree stands in percent within the footprint of the CRS. The total represents a distance-weighted average with an exponential decay towards more distant areas (approximating the exponential distance weighting from Zreda et al., 2008).
For validation of the CRS soil water content measurements, in May of 2014 we
installed 18 soil moisture sensors (TMS dataloggers from TOMST) close to the soil
sampling/calibration locations. They are based on the principle of time
domain transmission (TDT) and each sensor comes with its own logger and
power supply (more information under:
We conducted a total of 10 calibration campaigns throughout one calendar
year (2014). The first one (WI) took place in February during winterly
conditions with very wet soils. The next four calibrations (S1–4) followed
in spring (April–May) and covered the entire period of tree foliation. The
sixth calibration (SU) was done under very dry conditions in July and the
last four calibrations (F1–4) in fall (October–November) covering the trees'
defoliation. For all the calibration campaigns, we followed the recommended
sampling pattern for the calibration of CRS, which was developed by Zreda et
al. (2012) and slightly modified and detailed in Franz et al. (2012b). The
sampling pattern prescribes three concentric circles around the CRS with radii
of 25, 75 and 200 m (Fig. 1). The three circles are intersected by
six straight lines that point from the sensor towards north (0
The neutron counts from the sensor were smoothed with a 12 h moving window
to reduce measurement noise (see Bogena et al., 2013). The next step was to
correct the neutron counts for variations in (a) pressure, (b) incoming
neutron flux and (c) water vapor in the air. This was done by applying the
following corrections:
Pressure correction, Incoming flux correction (Zreda et al., 2012), As the time series of the closest neutron monitor, located in Kiel, Germany,
contains several data gaps, we selected the continuous time series of the
Jungfraujoch, Switzerland, for this study. We scaled this time series by
adjusting its mean (309 counts h Water vapor correction (Rosolem et al., 2013),
Finally, to convert corrected neutron counts (
Simplified representation of factors influencing the raw neutron
count and the measurement support volume of the CRS in terms of effective
measurement depth and footprint. Temporally variable factors are shown on
the left: barometric pressure (
Overview of the four weighting approaches for other than soil moisture effects on the CRS signal.
Example of depth weighting (DSW) for an effective measurement depth
of
We tested four soil moisture weighting approaches (Table 2), described in
detail below, to determine which information is necessary for an accurate calibration.
In the first approach (simple depth weighting, SDW) a linear
depth-weighting function was used (Franz et al., 2012b), where wt( and The second approach (depth-specific weighting, DSW) was identical to the
first one (SDW) except for using depth-specific measurements of For the third approach (distance–depth weighting, DDW), we adopted the
weighting approach described in Köhli et al. (2015). This approach
introduces the distance-dependent variable depth weighting where the effective
measurement depth decreases with distance from the sensor. The effective
measurement depth The fourth approach (distance–depth weighting, nonlinear, DDWnl) was
identical to the third one (DDW) except for using the nonlinear
depth-weighting function recommend by Köhli et al. (2015) instead of the
linear one (from Eq. 5):
Biomass influences neutron counts due to its hydrogen content. In order to
test (and potentially exclude) the influence of seasonal changes in
aboveground forest biomass, we estimated living tree biomass and tree
biomass changes throughout the year by applying the aboveground dry biomass
functions for beech forest (
To apply these functions, we conducted a survey of tree diameters and tree
density in the beech forest that surrounds the CRS. This allowed us to
determine both the total biomass of the beech forest, as well as the
seasonally variable fraction of biomass (leaf biomass divided by total
biomass). We first calculated the water mass (
As an objective performance measure to compare the soil moisture time series
derived from the CRS with the soil moisture time series from the TDT sensors
we used the modified Kling–Gupta efficiency KGE
Soil water content in the sandy soils ranged between 0.03 and 0.37 m
Gravimetrically determined volumetric soil water content patterns in the footprint of the CRS for the 10 calibration dates. The colored dots indicate the unweighted average value from 0 to 30 cm at the 18 calibration locations. Background colors represent the unweighted average value of all 108 soil samples. Different forest stands (pine, beech, oak, spruce) are indicated by the patterned background.
Atmospheric and soil parameters as well as neutron counts for the
10 calibrations. Atmospheric pressure
The average bulk density (
The footprint diameters calculated according to Köhli et al. (2015) and
used in approaches 3 and 4 ranged from 185 m for the wettest to 200 m for
the driest conditions. This resulted in distance weights of
The average reference atmospheric pressure (
The values in Table 3 result in a depth-weighted average volumetric water
content
Table 4 lists the parameters relevant for calibration for all 10 calibration
dates (again following approach 2, DSW, with depth-specific values of
Following the standard
In fact, none of the four weighting approaches were able to solve the problem
of determining a unique calibration parameter for our field site. All
weighting approaches resulted in largely deviating
Means (
Upper panel: volumetric water content derived from CRS data for
each of the 10 calibration dates separately (vertical lines indicate
calibration dates, colors correspond to time series colors). Filled circles
represent the weighted volumetric water content at the time of calibration
(according to DDW). Lower panel: differences in water content between
calibration S1 and all other calibrations expressed as a percentage of the
total possible range of average soil water content – ranging from
0.04 to 0.34 m
Modified calibration functions (solid lines) for the four different weighting approaches (simple depth weighting SDW, depth-specific weighting DSW, distance–depth weighting DDW, distance–depth weighting, nonlinear DDWnl), each one derived from 10 calibration points (circles). Calibration points are better captured by flatter calibration functions (solid lines) with modified calibration parameters than by any of the standard calibration functions (dotted lines) based on a single calibration data set only (days S2 and F1 as an example). Black lines illustrate that differences in soil moisture between the results of individual calibrations are larger when soil moisture is high. The inset magnifies the area around the calibration points.
To include all information of our 10 calibration campaigns into our
analysis, we fitted modified calibration functions to four sets of 10
calibration points derived from the four different weighting approaches (see
Sect. 3.1). This was done by using the Microsoft Excel Solver software to
optimize the three shape parameters (
The optimized parameters for the four approaches are shown in Table 6. The resulting soil moisture time series are shown in Fig. 6.
Modified calibration parameters for the four weighting approaches.
We tested whether the modified calibration functions improved the
performance of the CRS measurements relative to in situ measurements and, if
so, which of the weighting approaches performed best. In order to do that we
compared the soil moisture time series from the CRS (using the standard
Time series of volumetric water content derived from modified calibration functions using parameters based on the four calibration approaches: simple depth weighting (SDW), depth-specific weighting (DSW), distance–depth weighting (DDW) and distance–depth weighting, nonlinear (DDWnl). Filled circles represent the weighted average of volumetric water content obtained from soil cores at the time of calibration (weighting according to DDW).
Performance measures for the four weighting approaches – comparison
of modified calibration (mdf) with standard calibration (stan).
KGE
Average volumetric water content derived from TDT point
measurements (black line) and CRS measurements (orange line) using different
calibration functions. Upper panel: the orange line is an average of the
volumetric water content derived from the 10 calibration campaigns of the
CRS, using the standard
We further tested whether two or more individual calibration campaigns are required to determine a comprehensive calibration function shape, and under which soil moisture conditions these calibrations should be conducted. We paired each individual calibration point (derived from the best-performing weighting approach, DDW) with all the other calibration points (WI and S1, WI and S2, WI and S3, etc.) and computed best-fit calibration functions for all of these pairings (Fig. 8).
Best-fit
Then we used the resulting calibration functions to convert the measured
neutron counts into time series of volumetric soil water content and
compared these to the in situ TDT measurements (again using the KGE
The tree survey revealed a median diameter of 23.9 cm (min: 3.2 cm,
Hydrogen pools (in kg hydrogen per m
Performance of CRS soil water content data derived from two-point
calibrations in relation to difference between soil moisture states (
Mass of hydrogen in individual beech trees in stem and branches (red diamonds) and leaves (green triangles) in relation to diameter at breast height (DBH). Fraction of leaf hydrogen mass to total aboveground tree hydrogen mass (orange line).
Varying hydrogen pools in the beech forest surrounding the CRS for three different site conditions. AGB (aboveground biomass) wet variable represents hydrogen contained in deciduous leaves (both in the biomass and in the leaf water). AGB wet static comprises hydrogen contained in biomass and water of tree stems and branches as well as in biomass of the litter layer.
The 10
With regard to other varying hydrogen pools, we noticed that the influence of
interception storage both in the canopy and in the litter layer can
potentially have an impact. When both the canopy and the litter layer are
wet, the combined hydrogen amount within these two stores can sum up to
almost 5 % of the total hydrogen pool equaling a change in volumetric
soil water content of 0.067 m
The fact that the DSW approach performed better than the SDW is an indication that the depth variations in lattice water, soil organic matter and root biomass content should be explicitly accounted for during the calibration of the CRS. The best performance was achieved with a weighting approach (DDW) that explicitly takes into account both depth weighting as well as distance weighting of the soil water content (Table 7). This suggests that the variation in the footprint diameter needs to be considered during individual calibration campaigns. Linear depth weighting resulted in a better CRS performance than nonlinear depth weighting since the nonlinear depth weighting basically underestimated soil water contents during wet periods (because higher weights of deeper (drier) soil layers were included). This caused both a decrease in the mean soil water content as well as a decrease in the variability of the soil water content time series and hence reduced the performance of the CRS. In soils where water content increases with depth, the difference between linear and nonlinear depth weighting could be smaller (even negligible). At our field site, however, the decrease of water content with depth apparently favors the use of a linear depth-weighting function.
The differences in calibration results are likely caused by the fact that
the shape of the
We can only speculate about the reasons behind this shape inconsistency of
the calibration function for our site since we did not do any theoretical
neutron modeling. To our knowledge we are dealing with the lowest number of
counts of all published studies (average
If it was possible to fully correct for all factors that influence footprint size, depth weighting and neutron count, a one-time calibration of the CRS would be sufficient. However, the abundance of different hydrogen pools and the uncertainties in the sensing depth estimation will always lead to uncertainties in the calibration process. Therefore, we argue that for the use of the CRS as a simple tool to measure soil water content at intermediate scales, the efforts of measuring all necessary parameters are not justified. As shown by Iwema et al. (2015) and by the results of this study, this issue can be dealt with by using site-specific calibration parameters estimated from in situ samples taken during dry and wet conditions. Hence, we recommend a two-point calibration that – although being empirical in nature – inherently incorporates many of the required corrections.
Our results suggest that a one-time calibration of the CRS using the
available neutron count corrections and weighting approaches is not
sufficient at our field site. This is mainly due to the fact that the shape
of the standard
When measuring soil water content with a CRS, it is important to note that over time the measurements are hardly ever representative of the exact same soil segment around and below the sensor (Köhli et al., 2015). With the footprint shrinking and expanding and the effective measurement depth in the soil decreasing and increasing, we have to be careful when interpreting and using our results. If we keep that in mind, however, this new technology will indeed be able to bridge the gap between point in situ and areal remote sensing soil moisture measurements and thus provide a valuable tool for the advancement of hydrologic understanding.
We provide an Excel file as a Supplement to perform the calculations
described in the following step-by-step instructions.
Set up (or use) a weather station that monitors air temperature and relative
humidity close to the CRS. Set up the CRS in a location where the conditions within a radius of at
least 30 m around the sensor are relatively homogeneous (similar soils, tree
species, expected soil moisture conditions). Switch on the CRS and come back later for calibration (or set it up before
06:00 LT (local time) and start calibrating on the same day). You should at least have
12 h of CRS data for one calibration. Do not switch it off after the
calibration, let it record continuously. Choose a day with very dry or very wet soil moisture conditions for the
first calibration campaign and wait for the opposite conditions for your
second calibration (this might take a full year to achieve, but you will not
lose any data, you will just not be able to accurately convert the data immediately). Choose days without rain or snow for your calibrations, litter and canopy
should be dry. Take 108 soil samples from 18 locations (six directions, three distances)
and six depths (0–30 cm). For equal distance weights choose distances
according to Köhli et al. (2015) ( Weigh the samples the same day you take them, let them oven-dry for 24 h at
105 Create six bulk samples from the six different soil depths (2 g from each of
the 18 locations suffices for each soil depth). Determine the combined soil organic matter (SOM) and root biomass ( Caution: in clay-rich soils this method tends to overestimate soil organic
matter content because some of the lattice water is removed already at
temperatures around 400 Determine the lattice water ( Caution: Carbonate-rich soils experience thermal breakdown of carbonates at
temperatures above 430 Determine the water equivalent of the average hydrogen content of
belowground hydrogen pools ( Apply a linear weighting function to your gravimetrically determined
Apply an additional distance weight to the depth-weighted volumetric water
contents from the different locations in order to account for variations in
the footprint size. Also do this iteratively adjusting Equations are conveniently provided as a Supplement by Köhli et al. (2015)
in the form of an Excel file. Use the depth–distance weights to compute weighted values of soil water
content ( Average raw neutron counts ( Retrieve data from the neutron monitor close to your location in order to
correct for the varying intensity of incoming neutrons (you may have to
correct this data and fill gaps). Using the entire time series for the period where cosmic-ray data are
available determine average atmospheric pressure ( Correct raw neutron counts for atmospheric pressure variations ( Correct raw neutron counts for incoming neutron intensity variations ( Correct raw neutron counts for absolute humidity variations ( Fit a function through the two calibration points altering Plot the Use best-fit parameters to convert time series of
Funding was provided by the Terrestrial Environmental Observatories (TERENO) and the Virtual Institute for Integrated Climate and Landscape Evolution (ICLEA). We would like to thank the Müritz National Park for allowing us to conduct our research in their forest. Marvin Reich, Iris Heine, Lisei Köhn, Janek Dreibrodt, Stephan Schröder, Erik Reinholz, Christian Rippich, Christopher Gravesen and Jörg Wummel all helped out in the field while Philip Müller and Hans-Peter Nabein assisted in the lab. Gabriele Baroni, Lena Scheiffele and Katja Mroos lent us their field equipment and Martin Schrön provided us with scripts for depth–distance weighting. We thank Heye Bogena and two anonymous referees for their constructive feedback, which helped us a lot to improve the manuscript. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: H.-J. Hendricks Franssen