Introduction
Field-scale soil moisture is an important variable to drive and evaluate
agricultural, hydrological, and land-surface models . Knowledge about soil moisture states at relevant scales would
have direct implications for flood risk assessment ,
real-time estimation of water deficit in agriculture , or
drought forecasting and analysis .
Consequently, the corresponding models raise a huge
demand for accurate estimations of root-zone soil moisture at scales from
10 to 104 m.
Cosmic-ray neutron sensing (CRNS) is one of the most promising methods for
root-zone soil moisture monitoring at the field scale. These instruments are
able to continuously measure soil water content averaged over several
hectares and up to half a meter in depth . They
are one of the few candidates to close the scale gap between point data and
remote-sensing products .
After the measurement method was first presented by , many
studies were dedicated to calibrating the sensors and to assessing the
performance in comparison to conventional instruments
e.g.,. These studies showed a good agreement between neutron intensity
and independent soil moisture observations. However, outstanding features
were also reported in the CRNS data which did not fit well to the accepted
theory described by . Authors suggested that additional
hydrological processes and hydrogen pools could influence the signal
e.g.,, while others applied
recalibration of semi-physical parameters to better fit individual site
conditions e.g.,.
Despite the unambiguous improvements obtained by corrections and
recalibration approaches, some features in many
datasets could still not be explained using current knowledge and
consequently seemed to be unrelated to hydrological processes.
To address some of these knowledge gaps, investigated
soil hydrological processes with water transport simulations and found that
wetting and drying cycles are non-uniquely represented by the CRNS signal.
Due to the integrative neutron signal, those hysteresis effects can be most
significant when sharp wetting or drying fronts shape the soil water profile.
As a consequence, and recommended
vertical weighting of point measurements in the profile to account for these
effects. Furthermore, also demonstrated that the sensor
could underestimate average soil moisture by up to 10 volumetric percent
depending on the horizontal distribution of water content in the footprint.
They concluded that exact knowledge of the heterogeneity is a prerequisite
for the interpretation of neutron count rates, and distance-weighting
procedures are necessary to obtain sufficient performance during calibration
and validation with point data. In order to average calibration and
validation data horizontally, adopted a sampling scheme
based on initial calculations by to give every sample an
equal weight. The resulting sensor locations at 25, 75, and 200 m correspond
to an almost exponential horizontal weighting function.
were the first who applied this horizontal weighting to an irregularly
distributed point sensor network, albeit indirectly by fitting the cumulative
variant. Nevertheless, many researchers still avoid horizontal weighting by
virtually re-locating their irregularly distributed point sensors to the
nearest radius of 25, 75, or 200 m in post-processing mode
e.g.,. In complex terrain, only a few calibration or
validation locations are accessible and their individual contribution to the
neutron signal has been unknown for a long time.
As the understanding of cosmic-ray neutron physics in the environment has
been more and more elaborated, developed a dedicated
computer model, URANOS, which helped to understand the spatial
sensitivity of the neutron sensor. These authors revealed that the sensor is
extraordinarily sensitive to the nearest few meters, rather than following a
simple exponential decrease in sensitivity as was reported by
and . This revision has since
changed the way CRNS measurements are interpreted. Their findings extensively
describe the footprint volume in which soil water content is measured, and
can now be used to develop new weighting approaches and to revisit previous
data analysis.
The revised footprint and spatial sensitivity of the CRNS probe have since
been confirmed by many observations. were the first
to test the impact of the revised function on the performance of their
calibration data. applied the revised weighting approach
to average complex snow patterns in an alpine terrain. Encouraged by both of
their promising results, the present study has hypothesized that this new
theory could enable an improved performance of CRNS calibration and
validation campaigns for a huge variety of sites and conditions. We further
hypothesize that the initially published relation between neutrons and water
equivalent might be widely applicable without the need
to calibrate all of its parameters on site-specific conditions. Eventually,
an overall improvement of the CRNS data could help to identify hydrological
effects more accurately (such as precipitation, ponding, evapotranspiration,
and infiltration processes).
The paper is structured as follows: firstly, we present the equally weighted, the conventional, and the revised formulations
of the spatial sensitivity function (also called the weighting function). We then provide a procedure to generate a weighted average of
point measurements that can be compared with the CRNS product. The
assumptions and uncertainties of this approach are then discussed, followed
by a short description of measures used to evaluate the calibration
performance, and short descriptions of the studied sites. In the results
section we present and discuss the sensor performance using the
equal, conventional, and revised weighting approaches for calibration
campaigns at two different sites, and for time series data at four sites.
Methods
Stationary cosmic-ray neutron sensors (CRNSs) are particle detectors that
measure the neutron intensity in the well-mixed pool of neutrons above the
land surface . Due to the low interaction probability of
neutrons with air molecules, the measured particles can travel distances of
more than 240 m from the soil to the detector . The
neutron signal is predominantly sensitive to the number of hydrogen atoms in
the soil, but it is also influenced by changes in air pressure, air humidity,
and incoming cosmic radiation. These additional factors can be accounted for
by standard correction approaches , such that
the remaining signal represents only the hydrogen abundance in the soil and
biosphere. To convert the corrected neutron count rate N to gravimetric
soil water equivalent, θ, suggested the following
theoretical relation:
θN,N0=0.0808N/N0-0.372-0.115,
where N0 is a site-specific calibration parameter. It is determined once
for each dataset by comparing the CRNS product, θ(N, N0), with
the actual soil moisture condition in the field. However, neutrons are
sensitive to all kinds of hydrogen in the footprint; hence, the
variable θ denotes the water equivalent of soil moisture,
θsm, and additional hydrogen pools,
θoffset. The latter comprises for example lattice water,
θlw , as well as the water equivalent from
soil organic carbon, θorg , biomass,
θbio, and other dynamic contributors,
θother:
θ=θsm+θoffset,whereθoffset=θlw+θorg+θbio+θother.
Quantities related to absolute water equivalent are either given in units of gravimetric percent (θg in
% ≡ 100 g g-1) or volumetric percent (θv in
% ≡ 100 cm3 cm-3). If no indices “v” or “g” are
indicated and units are not mentioned in the context, this work uses default
units of volumetric percent.
For calibration and validation purposes, the water equivalent in the
footprint volume is typically determined independently by an average of point
measurements, for example from gravimetric samples or data from soil moisture
monitoring networks. However, those locations can contribute differently to
the apparent average of soil moisture as seen by the neutron detector, for
example, depending on their distance r from the CRNS probe and their
depth d below the soil surface. Depending on
their individual contributions, different weights can be assigned to each
data point in the calculation of a so-called weighted average.
Among the variety of weighting concepts in the literature, we have selected
two of the main and most frequently used strategies from recognized
publications, which are based on distinct physical assumptions. On the one
hand, the conventional approach covers the main strategies applied so
far . On the other hand, a revised
weighting approach has been used which is based on recent findings from
and which has been further advanced in the present work by
the following points:
extension of the analytical fit of the radial sensitivity
function Wr to short distances, r ≤ 0.5 m, and
added dependency of the weighting functions on air pressure p and
vegetation height Hveg, by introducing a rescaled distance r*(r, p, Hveg, θ).
The URANOS neutron
transport model has been updated accordingly to provide advanced analytical
functions for the spatial sensitivity (URANOS 0.97, available from
http://www.ufz.de/uranos). These advancements generalize the
applicability of the results from and are recommended for
future applications. Please refer to Appendix for detailed
explanations. There are certainly more factors that influence the shape of
the neutron sensitivity, for example the height of the detector above ground,
different plant species, and large objects. However, those factors are
irrelevant for the investigated sites and are thus of minor importance for
the conclusions in this work.
In addition to the conventional and revised approaches,
this work includes the equal average weighting strategy (weights
equal 1) to compare the performance when the CRNS signal is intuitively
treated as a large-area averaging soil moisture product.
Vertical weighting in the soil profile
Simulations by , , and
have shown that the neutron signal integrated over a
vertical soil column exhibits the highest sensitivity to the uppermost
layers. Therefore, independent soil moisture measurements taken at different
depths, d, need to be weighted differently in order to account for the
underlying physical processes. To show the consequences of neglecting this
step in post-processing, we have compared the equal average of soil
samples with alternative weighting approaches.
The conventional vertical weighting, Wdconv,
is performed using a linear relation from , which was
based on Monte Carlo simulations from and became widely
accepted in most previous studies.
Wdconv=1-d/Dconv,d≤Dconv0,d>Dconv
penetrationdepth:Dconv≡z*(θ)=5.8θ+0.0829,incm;seeFranzetal.(2012b).
The two major shortcomings of this function
are (1) that it assumes similar penetration depths of detected neutrons for
all distances r from the sensor (see Fig. a), and (2) that it
neglects any contribution of soil water below a certain cutoff penetration
depth Dconv (see Fig. b).
In contrast, the revised vertical weighting function, Wd, takes
the full soil profile into account (as neutrons do) and considers the fact
that the effective depth decreases with increasing distance r from the detector:
Wdr,θ,p,Hveg=e-2d/D,
penetrationdepth:D≡D86r*,θ,ϱbulk,incm;seeAppendixA,
where D denotes the effective penetration depth, defined as the depth
within which 86 % of neutrons probed the soil see.
These relations are based on URANOS simulations and follow recent
insights about the physics of neutron transport and detection near the
soil–atmosphere interface. Based on the formulation from
the advancements of the revised penetration depth
D ≡ D86 now add the dependency on air pressure and vegetation
height, expressed in the scaled distance term r* (see
Appendix ).
Horizontal weighting in the footprint area
In this work we make use of three horizontal weighting functions to average
soil moisture measurements at distances r from the CRNS probe. Firstly, the
equal average (weights equal 1), which was usually applied for
validation with soil moisture networks and remote sensing products. It was
also used for calibration datasets if locations were arranged according to
the COSMOS standard sampling scheme (25, 75, 200 m), such that the samples automatically represent areas of
equal contribution to the neutron signal. These calculations were based on a
simple exponential sensitivity function and presented by
and .
(a) A comparison between the revised and the
conventional penetration depths, D(θ, r,
ϱbulk = 1.4 g m-3) and
Dconv(θ), respectively. On average, both approaches follow
an almost similar shape; however, the conventional formulation is independent
of distance r and soil bulk density ϱbulk.
(b) Normalized vertical weighting functions (Eqs.
and ) based on 12 sample points. The conventional, linear approach
overestimates the relative contribution from shallow water when compared to
the revised, exponential function, and neglects contributions from depths
beyond Dconv ≡ z* (= 23 cm in this
example).
Comparison of normalized horizontal weighting functions
(a) from 0 to 5 m, and (b) from 5 to 300 m. Graphs show
the conventional (almost exponential) approach Wrconv
(Eq. ), the revised curves Wr(h, θ) for
three wetness conditions (Eq. ), and an
approximation Wr* based on a simplified equation
(Appendix ). The conventional approach is
insensitive to air and soil water content and highly underestimates the
contribution of nearby areas r < 10 m when compared to the revised
function.
Secondly, the conventional weighting approach uses an (almost)
exponential sensitivity function based on Monte Carlo simulations from
. It is implicitly referred to when using the COSMOS standard sampling scheme . An analytical form of the
conventional horizontal weighting function has never been published. However,
it can be derived from the cumulative function CFoC(r), presented by
Eq. 13, who fitted data from Fig. 3 in
the domain of r ≤ 300 m:
e-r/127≈Wr≤300conv=∂rCFoC(r)∝1-a1r+a2r2-a3r3+a4r4,
where
ai=1.311×10-2,9.423×10-5,3.2×10-7,3.95×10-10.
To account for the remaining contribution
beyond 300 m, the (usually few) data points have been assigned
the weight Wr>300conv = Wr=300conv. One of the major
shortcomings of this exponential approach is the underestimation of the high
sensitivity of the neutron signal to the first few meters around the sensor.
As a third strategy, we use the revised weighting approach based on
URANOS simulations and corresponding analytical fits seefor
details. New technical advancements of this function include the
dependency on air pressure p and humidity h by introducing the rescaled
distance r*, as well as the extension below r ≤ 0.5 m.
Wrh,θ,p,Hveg=F1e-F2r*+F3e-F4r*1-e-F0r*,0m<r≤1mF1e-F2r*+F3e-F4r*,1m<r≤50mF5e-F6r*+F7e-F8r*,50m<r<600m
Parameter functions Fi, their corresponding
parameters, the formulation of the rescaled distance
r*(r, p, Hveg, θ), as well as further explanations are given
in Appendix .
The weighting procedure
The following procedure is recommended to generate a weighted average of
point measurements that can be compared with the CRNS product (see the
illustration in Fig. ). For each experimental site,
consider a number of soil profiles P at distances rP from the
CRNS probe. In each profile, point measurements of volumetric water
equivalent θP,L are given at various layers L of
depth dL. Observations of air pressure p, air humidity h, and
vegetation height Hveg are given at the time of interest, while
estimations of soil bulk density ϱbulk exist for every
profile (or even every sample). The general function to calculate an average
of point measurements i with values θi and weights wi is
given as
wt(θ,w)=∑iwiθi∑iwi.
(a) Schematic of the environment around the cosmic-ray
neutron sensor (CRNS) including point measurements (e.g., soil samples) of
water equivalent θ to calibrate or validate the sensor. The revised
sensitivity functions Wr (teal) and Wd (brown) are
indicated (arb. scale). (b) The measured variables are used in the
weighting procedure (Sect. ), starting with an initial
estimate of field-average water content. Three approaches, using the
equal, the conventional (conv), and the revised
weighting function are compared in this study. The resulting weighted-average
water equivalent 〈θ〉 is then used to calibrate against or
validate with the CRNS product (Eq. ). Calibration of the
parameter N0 is performed towards optimization of four performance
measures (see Sect. ).
The procedure to obtain a weighted average of soil water equivalent,
〈θ〉, is described as follows (see also
Fig. ).
Estimate an initial value 〈θ〉 = wtθP,L,1
by an equally weighted average over all profiles P and layers L.
Calculate the penetration depth DP for each profile P:DPconv=z*(〈θ〉)orDP=D86〈θ〉,rP*.
Vertically average the values θP,L over layers L, to
obtain a weighted average for each profile P:θPconv=wtθP,L,WdLconv,orθP=wtθP,L,WdL.
Horizontally average the profiles θP:〈θ〉conv=wtθPconv,WrPconv,or〈θ〉=wtθP,WrPh,〈θ〉,p,Hveg.
Use the new 〈θ〉 to reiterate through steps 1–5 until
values converge within a user-defined accuracy range (e.g., 1 %).
The final averaged water equivalent 〈θ〉 is then compared
with the CRNS product, θ(N), derived from the neutron count rate N
(Eq. ). It is also possible to calculate gravimetric water
content using local bulk densities before step 3; however, this approach is
not recommended since the revised weighting functions have been determined by
simulations of homogeneous soil and volumetric water content
. While it has been assumed that N0 accounts for
persistent, non-homogeneous features in the footprint , the
influence of this state-of-the-art model assumption is to be investigated in
future studies.
The above procedure weights each data point θP,L according
to its depth d and distance r from the CRNS probe. However, when a finite
number of sample points are chosen, assumptions are involved in the spatial
domain they represent. Depending on knowledge about the individual field
conditions, interpolation between soil layers, for instance, is a good option
to assign each measurement to a certain soil horizon. Let Ω(r,
ϑ) (in m3) be the spatial domain of the footprint volume in
polar coordinates (radius r, solid angle ϑ), ΩP
(in m2) the horizontal representative area of the profile P, and
ΩL (in m) the representative soil horizon of the measurement
at layer L. As each measurement θP,L represents the
volume ΩP ⋅ ΩL, its weighted
contribution to the neutron signal should be integrated over this domain.
HorizontalcontributionofprofileP:wP=∫ΩPWrP=∫ΩP(r)12π∫ΩP(ϑ)Wr⋅dϑdr.VerticalcontributionoflayerL:wL=∫ΩLWdL=∫ΩL(d)Wd⋅dd.
For example, if soil samples were taken at two depths, 10 and 40 cm for
instance, it could be reasonable to integrate their weights from d = 0
to 30 cm and from 30 to 50 cm, respectively. In the horizontal space it
might be sometimes reasonable to integrate a single profile measurement over
the whole area of similar soil and land-use type (as has been done in
Sect. ). If sample locations were arranged in an interpolated,
regular grid (e.g., pixels of size 1 m in Fig. ), then each
pixel should be weighted individually as a point such that the integrals
above can be simplified. While an infinitesimal point at distance r has the
weight Wr/(2πr), a regular pixel of size s at that
distance weighs
Wr/(2πr) ⋅ s ∝ Wr/r. For
all radially symmetric sampling schemes, where each point measurement
represents one of n circular sectors, the sector at distance r has the
size (arc length) of 2πr/n, and thus contributes the weight
Wr/(2πr) ⋅ (2πr)/n ∝ Wr.
The strategy, to take into account estimations of representative volumes,
initially appears to be more realistic. However, the extrapolation of data
points involves assumptions about the site-specific heterogeneity and
therefore about the strategy of interpolation. It further requires expert
knowledge about the individual field conditions. During the preparation of
this work, we found that the usage of weights for distinct measurement points
provided fair approximations of the integrals,
i.e., WrP ≈ wP and
WdL ≈ wL, and eventually
resulted in almost similar averages, 〈θ〉, throughout all
cases investigated (not shown).
Uncertainty due to partial coverage
In addition to the considerations about the representative domain, the
arrangement of the soil samples can play a crucial role for the CRNS
evaluation performance. If the locations of the soil samples (or in
situ monitored soil profiles) do not cover the CRNS footprint
representatively, the corresponding data would not be able to explain parts
of the neutron signal. Many sites exhibit highly irregular configurations
where the soil monitoring network covers only parts of the CRNS footprint.
The corresponding uncertainty in the CRNS evaluation can be estimated as
follows.
Let S be the domain of the representative volume of the sample locations
(e.g., the areal extent of the soil moisture monitoring network), and let
Ω be the spatial domain of the CRNS footprint as defined in the
previous section. Then, the outer region Ω\S denotes the
part of the footprint domain which is not represented by the samples. The
contribution of the “sample area” S to the neutron signal then is
contribution:NS/NΩ=∫SWr/∫ΩWr,
which can range from 0 to 100 % and depicts the fraction of detected
neutrons which carry information from (i.e., had contact with) the sample
area S. Assume that the observed soil moisture in S is on average
〈θ〉, and that the soil moisture in the outer region,
Ω\S, can be estimated as
〈θ〉 ± Δθ. The propagation of this error
through Wr(h, θ) leads to an uncertainty ΔN of the total
neutron signal N,
N±ΔN=∫ΩWr≈∫SWr(h,〈θ〉)+∫Ω\SWr(h,〈θ〉±Δθ),
and eventually adds uncertainty to the CRNS product,
θ(N ± ΔN). In this paper, this estimation is
applied exemplarily to the Schäfertal site
(Sect. ) in order to quantify the errors introduced by
incomplete coverage.
Performance measures
To evaluate the performance of time series and calibration data, we apply
prominent measures used in environmental and hydrological research. The
robustness of this approach is evaluated by applying different performance
measures, which is a common strategy to falsify new methodological approaches
see, e.g.,. Popular efficiency measures are the
Nash–Sutcliffe efficiency (NSE) and the more modern
Kling–Gupta efficiency (KGE) , while the
root mean square error (RMSE) and the Pearson correlation
coefficient (ρ) are well-established standard approaches.
NSE=1-∑(A-B)2∑(B-〈B〉)2,KGE=1-ρ(A,B)-12+σAσB-12+〈A〉〈B〉-1212,RMSE=(A-B)212,ρ=〈(A-〈A〉)(B-〈B〉)〉σAσB,
where A = θ(N, N0) denotes the water equivalent measured by the CRNS
(N0 needs to be calibrated), B denotes the actual field soil water
equivalent, θ, measured by independent instruments, and
〈x〉 = 1n∑1nx denotes the average
(expected value) of a set of data points x. In the ideal case of optimal
agreement between the variables A and B, the measures would reach
NSE = 1, KGE = 1, RMSE = 0, and ρ = 1.
NSE normalizes the mean squared error by the observed variance, where the
mean observed variable 〈B〉 is used as a baseline. Following
this approach, site-specific variations could translate to biased estimation
of model skills among different sites. On the other hand, the KGE measure is
a revised version of NSE that allows one to analyze the relative importance
of the linear correlation ρ, variability σ, and
bias 〈⋅〉 of simulated and observed variables
. RMSE is simply a measure of the differences between two
time series, but is prone to biased datasets and outliers. The
correlation ρ is an accepted approach in experimental geophysics to
identify similar or unknown effects e.g., in two time
series. However, if many factors could explain a single observation, only
using the correlation measure may lead to false recognition of coincidental
effects.
The KGE is the most appropriate performance measure for time series data as
it combines three distinct measures to optimally account for absolute errors
and anomalies compare also. In the following
analysis, we have thus optimized the KGE value between the CRNS and the
independent soil moisture data to find a single calibration parameter N0 per site.
Study sites
In order to provide a robust falsification of a potential benefit when using
the revised weighted-averaging approach, datasets of six distinct sites have
been consulted that offer comparison of the CRNS with independent soil
moisture data under various climatic conditions (Fig. ). At
sites 1–2 the CRNS product is calibrated on datasets from so-called
calibration campaigns. The term typically refers to one or more days
on which soil samples were taken in the field and then analyzed for soil
water content in the lab. Sites 3–6 provide time series data from
soil moisture monitoring networks (e.g., SoilNet; see also
). These datasets are usually applied to validate the
performance of CRNS sensors; however, the present study takes advantage of
the continuous recordings in order to calibrate the CRNS probe.
Table provides an overview of the site characteristics.
Selection of six distinct observation sites, five across Europe, and
one in Utah (US).
The Sheepdrove Organic Farm in Lambourn (UK)
The Sheepdrove Organic Farm is located at 51.528175∘ N,
-1.467311∘ E, 190 m a.s.l. in the Lambourn catchment in southern
England. This region is characterized by a temperate climate with yearly
average precipitation of 815 mm, evenly distributed over the year, and with
a mean daily maximum temperature of 14 ∘C. The CRNS probe is located
at a grass strip which exhibits unmanaged soil and vegetation cover. The
surrounding field is grazed by sheep during several variable periods
throughout the year. During periods of sheep grazing and after harvest the
height of the grass outside the strip is a few decimeters lower than within
the strip. The soil is loamy clay with many flints and pieces of chalk.
Weathered chalk starts at about 25 cm depth. The groundwater is tens of
meters below the surface .
Agricultural site in the lowlands of Braunschweig (GER)
The second calibration site is an irrigated agricultural field in the
northern lowland of Germany near Braunschweig, at an elevation of
60 m a.s.l. Annual precipitation is 620 mm and average temperature
9.2 ∘C. The 12 ha area is irrigated in 50 m wide strips with
pre-treated waste water, as the sandy soils exhibit low water and nutrient
holding capacity. The CRNS probe was located in the center of the field
(52.3587∘ N, 10.4004∘ E) and several FDR devices provided
point measurements of soil moisture. In 2014 the field was cropped with maize
(Zea mays) that was ploughed in mid-April and
harvested on 27 September.
The hillslopes and creek in the Schäfertal (GER)
The Schäfertal intensive monitoring site
(11∘03′ E, 51∘39′ N; 395 m a.s.l.) is an
agriculturally used catchment in the middle-mountain area of the Harz
mountains in central Germany . Parts
of the hillslope grassland transect are equipped with a wireless soil
moisture monitoring network. It has a spatial extent of
ca. 240 × 40 m and comprises a north- and a south-exposed slope as
well as a valley bottom crossed by a creek oriented west to east. Silty-loam
Cambisols occupy the slopes, whilst finer-textured and highly organic soils
evolved in the riparian zone between the footslope and the creek
.
The ponded flood plains at Grosses Bruch (GER)
The Grosses Bruch research site is a mesophilic grassland used as a
meadow, within a nature protection area surrounding the Grosser Graben water
channel (52.029728∘ N, 11.104678∘ E; 78 m a.s.l.)
. The grassland is usually flooded naturally once or
twice a year. Soil type in the grassland is a sandy-loamy fluvisol-Gleysol,
partly covered with a peat layer of up to 1.5 m in depth. Eddy covariance
measurements of energy, water, carbon dioxide, as well as methane are
conducted at the site. Meteorological conditions as well as spatially
distributed soil moisture and soil temperature at several depths are observed
continuously with a wireless soil moisture monitoring network.
Overview of the investigated study sites, their average bulk
densities 〈ϱbulk〉 (in g cm-3), and
average volumetric water equivalent 〈θoffset〉 of
additional hydrogen pools (e.g., soil organic carbon, lattice water, root
biomass; see Eq. ).
Site
Period
Description
〈ϱbulk〉
〈θoffset〉
Calibration on
Sheepdrove Organic Farm, UK
2015–2016
grassland with central strip
1.16
9.0
3 sampling days
Braunschweig, GER
May–Oct 2014
irrigation agriculture
1.49
1.0
3 sampling days
Schäfertal, GER
2012–2013
heterogeneous hillslope
1.15
5.2
time series
Grosses Bruch, GER
Aug–Dec 2012
pasture grassland, floodplain
1.31
10.0
time series
Wüstebach, GER
Apr–Aug 2012
forested river catchment
0.83
6.7
time series
T. W. D. E. Forest, US
Jun–Sep 2012
complex forest, grass, sage
1.10
4.5
time series
The forested Wüstebach catchment (GER)
The Wüstebach test site is located in the German low mountain ranges
within the borders of the Eifel National Park (50∘30′ N,
6∘19′ E) and is part of the TERENO Eifel/Lower Rhine Valley
Observatory . The Wüstebach catchment covers an area
of ≈ 38.5 ha with altitudes ranging from 595 m a.s.l. in the
northern part to 628 m a.s.l. in the southern part. The soil types can be
subdivided into terrestrial soils (i.e., Cambisols, Planosols) and
semi-terrestrial soils (i.e., Gleysols, Histosols) in the riparian zone
. The mean porosity of the soils varied from 20 to
81 % for groundwater influenced soils and from 60 to 78 % for the
terrestrial soils with decreasing values with increasing depth
. In the riparian zone, the water table varied between
0.0 and 1.6 m, while it constantly remained below the soil–bedrock
interface outside of the riparian zone . The mean annual
precipitation was 1220 mm between 1979 and 1999 and the mean monthly
temperature varied from -1.5 to 15 ∘C . Norway
Spruce planted in 1946 is the prevailing vegetation type .
Complex land use in the T. W. Daniel Experimental Forest (US)
The T. W. Daniel Experimental Forest lies in the mountaintops in the
Wasatch Mountains (IMW), which is one of four components of the Intermountain
West of the United States and a transition zone of different climate regimes
in both the seasonal and inter-annual timescales. The landscape of the TWDEF
site is a patchwork of four domain vegetation communities common to the IMW.
Forest communities include aspen and conifer, predominantly Engelmann Spruce,
and subalpine fir. Non-forest communities include grasses, forbs, and
sagebrush. For each dominant vegetation type, three plots and three subplots
within each plot were randomly chosen. Time series data were evaluated from
TDT sensors at 10, 25, and 50 cm and interpolated up to the surface using
hydrophysical simulations .
Results and discussion
The equal, conventional, and revised weighting
approaches have been tested at six distinct research sites. In
Sect. we have analyzed the calibration datasets at the
Sheepdrove Organic Farm and at the Braunschweig site, in order
to test the explanatory power of the theoretical relation, N(θ)
(Eq. ). Section discusses the uncertainty
related to a time series dataset in the Schäfertal catchment, where
the footprint is only partly covered by monitored profiles.
Section analyzes the potential of CRNS and time series datasets
in Grosses Bruch and Wüstebach to identify additional
hydrological processes. At the TWDEF site in Sect. ,
we use monitoring profiles in distinct parts of the footprint, which are
individually weighted based on their areal contribution to the neutron signal.
Recalibration of the CRNS sensor in the Sheepdrove Organic Farm (Lambourn, UK) using different combinations of vertically and
horizontally weighted averages. Sizes of the circles indicate the
corresponding uncertainty range of the measurement. The revised approach
clearly removes the bias by the exceptional strip around the sensor,
improving the calibration performance with regards to the widely accepted
theoretical relation (dashed).
Recalibration of the CRNS sensor in an agricultural maize field
(Braunschweig, Germany). Sizes of the circles indicate the corresponding
uncertainty range of the measurement, while every such measurement
corresponds to a calibration curve θ(N, N0). The
conventional weighting approach is not able to provide a unique
theoretical line through the 3 calibration days. Furthermore, for a given
neutron observation the difference between estimated moisture (lines) and
actual soil moisture (ellipses) indicates unrealistic biomass dynamics
throughout the study period (see explanations in the text). The revised
approach converges the datasets to confirm the accepted neutron theory almost
in a single calibration curve within uncertainties (size of
ellipses).
Improvement of the calibration performance
In the farmlands of Great Britain, managed fields are often divided by
strips of hedges or unmanaged grassland. While unmanaged patches appear to
be ideal positions for environmental-monitoring equipment, the presented
example shows that CRNS measurements can be biased from the intended
information about the field site. Three calibration datasets were collected
at various wetness conditions within 9 months. The sampling design was based
on the COSMOS standard sampling scheme at 25, 75, and 200 m, plus
an additional location at 1 m near the CRNS probe.
Figure demonstrates how the equal (red) and
conventional (orange) weightings of the three calibration datasets
deviate significantly from the unique theoretical relation N(θ)
. By choosing the revised vertical weighting
approach (green), the calibration points become much better in line with each
other and reveal a unique site-specific calibration curve. One of the reasons
is the fact that the conventional approach neglects important parts of the
sub-soil layers (beyond Dconv), as indicated in
Fig. b. Additional revised horizontal weighting (blue)
leads to a precise match with the theoretical line, supporting the hypothesis
that the samples within the strip are most important to the CRNS signal.
As a consequence of the difference between the soil moisture of the grass strip
and the surrounding agricultural fields (wetter in summer and drier in
winter), the application of a non-weighted calibration leads to significant
overestimation or underestimation of the CRNS-apparent soil moisture value,
respectively. Furthermore, the experiment clearly shows the importance of a
proper positioning of the CRNS probe. If a sensor is dedicated to measuring
soil moisture in a certain field, it should be ideally placed in that field.
CRNS stations at the field border can be biased by different local
characteristics, such as land use or soil properties.
Time series of the CRNS soil moisture data at the SoilNet validation
site in Schäfertal (Harz mountains, Germany). The
average soil moisture using the conventional weighting approach
(orange) exhibits poor performance against the CRNS signal (not shown). The
revised approach improves four performance measures of the averaged
soil moisture (blue) and the CRNS signal (light blue), although the SoilNet
probes are unevenly distributed in the CRNS footprint. The uncertainty of
volumetric soil moisture introduced by the insufficient coverage ranges from
1 to 8 % depending on wetness conditions.
Insights from the British grassland have also been confirmed with calibration
datasets from an agricultural site near Braunschweig. During the
agricultural season in 2014, used the COSMOS standard sampling scheme for three calibration campaigns in May (very small
crop, mediocre soil moisture), July (maximum water content in biomass, dry
soil), and October (biomass residues after harvest, mediocre soil moisture).
The general behavior of the soil moisture dynamics could be reproduced well
(Fig. ), independent of the campaign used for calibration
(i.e., determination of N0). In all three cases, the neutron counts
reflect that soil has dried considerably from May to July, to levels below
10 %, followed by a period of high precipitation and irrigation that led to
increased soil wetness in October. However, the performance of the sensor to
reflect exact soil moisture states depends on the calibration dataset. Using
the conventional averaging approach, the corresponding calibration
curves in Fig. (orange lines) indicate a non-unique
relationship between neutrons and soil moisture throughout the study period;
i.e., hydrogen pools other than soil moisture may have changed, where biomass
is the most likely candidate. For example, following the calibration curve
from May (solid orange line), the neutron counts detected in July and October
would correspond to lower soil water content than actually measured in the
field (ellipses); i.e., these neutron observations were higher than expected.
This mismatch could be misinterpreted as a reduced amount of biomass in July
and October, because decreasing biomass water equivalent usually corresponds
to increasing neutron counts . However, the
maize was seeded in May, reached a maximum height in July, and left residues
after harvest in October. Therefore, such a conclusion drawn from the
conventionally weighted calibration data would be unrealistic.
The data weighted with the revised approach (blue in
Fig. ) demonstrate that the calibration curves converge
much closer to a unique theoretical line . Their
deviation is insignificant given the observational uncertainty of the neutron
counter. Although this approach almost removes the unrealistic effect of a
seemingly reducing biomass water equivalent, the assumption of a unique
calibration parameter N0 still does not reflect the expected biomass
dynamics in the investigated period. It remains an open question whether a
revision of the parameters of Eq. () would better catch the
local dynamics and would further contribute to the interpretation of the
signal. Nevertheless, the example shows that the revised weighting strategy
contributes to a more realistic interpretation of the water availability from
CRNS measurements, which is especially important when used in conjunction
with irrigation management.
Time series of soil moisture measured in a pasture/floodplain –
Grosses Bruch. The rain events in mid-October 2014 lead to a rise in
the groundwater level and ponding in regions that are several tens of meters
away from the neutron sensor. In that period, equal and
conventional weighting leads to overestimation of apparent soil
moisture near the CRNS probe, to which the detector has higher sensitivity
than to the remote ponds.
Uncertainty estimation in a partly covered footprint
In the Schäfertal intensive monitoring site, a CRNS
probe is located in the center of a small area that is covered by a soil
moisture monitoring network. The CRNS footprint extends largely beyond this
area and involves patches of agricultural land and a nearby forest
(Fig. ). According to the guideline presented in
Sect. the contribution of the SoilNet area to the neutron
signal ranges from 49 % (dry) to 64 % (wet). As a consequence, 36–51 %
of the neutron variability does not directly respond to the wetness
conditions monitored by the irregularly distributed network. However, in most
cases the soil moisture of the outer area can be assumed to correlate with
the inner area. As an example case, one could assume an absolute variation of
the outer area by Δθv = ±5 %. Then the
uncertainty of the CRNS soil moisture prediction can be further estimated
following Sect. . Under dry conditions
(〈θv〉 ≈ 15 %), the propagated error
is Δθv(N) ≈ 1–4 %, while under wet
conditions (〈θv〉 ≈ 35 %), the
neutron counts are less sensitive to soil moisture changes in the outer area
due to the smaller footprint . This leads to
Δθv(N) ≈ 4–8 %. Therefore, calibration
results that resulted in an RMSEv of ≈ 4 %
(Fig. ) are not meaningful under wet conditions (where
Δθ(N) ≥ 4 %v), and are still uncertain under
dry conditions (where Δθv(N) ≤ 4 %).
Consequently, the partial coverage of the CRNS footprint by the irregularly
distributed SoilNet hampers the proper evaluation of the CRNS data, and
especially of the weighting strategies.
Nevertheless, the Schäfertal data show that the revised
weighting approach is robust enough to improve the overall CRNS performance
(Fig. ), even though the sensor is situated in complex
terrain where the SoilNet sampling locations are not representative of the
CRNS footprint. As the revised approach shows the best accuracy in all four
statistical measures, the RMSEv is still higher than the
measurement error of the daily mean (≈ 2 %). This indicates that
deviations can be attributed (1) to the insufficient coverage of the SoilNet,
and (2) to different processes in different parts of the footprint
(speculative examples are vegetation growth, forest water interception, snow
accumulation, evapotranspiration, plowing, etc.).
Time series of CRNS soil moisture and groundwater at the
Wüstebach forested river catchment. Fitting the CRNS
data to the SoilNet conventional average almost completely hides
effects from excess water storages (which could include water in the litter
layer, interception water, groundwater rise, or ponding close to the stream).
The revised approach emphasizes those additional hydrological
processes while still robustly increasing the sensor
performance.
Identification of additional hydrological processes
The Grosses Bruch pasture site is a good example of how an
inappropriate averaging approach could hinder sufficient interpretation of
time series data. Figure shows the soil moisture
signal predicted from a stationary CRNS probe and the weighted signal of a
soil moisture monitoring network (SoilNet) with sensors installed at depths
from 0.05 up to 0.6 m. Following the precipitation events in the second half
of October, the shallow groundwater and loamy texture allowed large water
ponds to reside permanently in the outer regions of the SoilNet (light blue
indication on the map). As distant areas contribute much less to the CRNS
signal than closer ones, the revised weighting approach has
significantly reduced the influence of the saturated point data on the
apparent CRNS average. Without the revised method, the CRNS product would
have overestimated the absolute volumetric field saturation by more than
5 %. Additionally, beginning in the middle of September, many cows had been
present at this site, which are assumed to have led to large variations of
the neutron signal and thus to a non-meaningful expression of
correlation-related measures.
In the Wüstebach forest site, weighted averaging of the
soil moisture monitoring network is performed based on the data presented in
. The analysis shows three interesting effects on the
resulting soil moisture signal in Fig. . Firstly, the
signal processed with the revised weighting approach (blue) is
wetter than the conventionally weighted signal (orange). This effect
is reasonable due to the higher soil water contents of the
groundwater-influenced riparian zone, where the CRNS is located, compared to
the terrestrial soils at the hillslopes. Secondly, the CRNS signal which was
calibrated to the revised weighted soil moisture (light blue)
outperforms the signal that was calibrated on the conventionally
weighted soil moisture (light orange). This performance gain is robust in
terms of the four measures. In order to avoid incorrect conclusions from
overcalibration of the data during rain events (periods of high interception
water), we repeated the same analysis for dry periods only. In this case the
revised approach again led to the highest performance (not shown) and
confirmed the robustness of this approach. Thirdly, differences between CRNS
and SoilNet appear to be significantly more prominent for the
revised approach (blue) in periods following huge precipitation
events (May, July, and October). Those periods can probably be attributed to
expected canopy water storage, interception storage, groundwater rise, and
nearby accumulation of ponds. Ponded water in local hollows, trenches, and
the litter layer are not visible in the soil profiles of the monitoring
network, which are typically installed in solid and elevated ground. In
contrast, their effect can be visible in stronger oscillations and shifts of
the CRNS signal.
The analysis demonstrates that the revised weighting of calibration
data is essential to identify residual hydrological effects which otherwise
can get lost by overfitting. By comparing CRNS data and point measurements,
residual information could be used to identify additional processes like
biomass dynamics or rainfall interception . The methods
presented here can support efforts to identify those residuals to a much
higher precision. In order to properly quantify the excess water storages in
future studies, we would recommend calibrating the CRNS signal only in
periods when the site had not been exposed to rain events for a few
consecutive days. In the case of the Wüstebach site
(Fig. ), this would lift the deviations of the CRNS
signal (light blue) up from below the averaged soil moisture (blue) and would
thus properly highlight the added water to the system.
Time series of CRNS and TDT soil moisture at the
T. W. Daniel Experimental Forest. The area was split into four
categories (dotted lines), to which the corresponding soil moisture
measurements were assigned. The areal coverage was then averaged (dashed
line) pixel by pixel (1 m resolution) with the revised weighting approach,
leading to the best performance against the CRNS signal.
Areal contribution of distinct land-use classes
analyzed the CRNS performance in the center of a complex
mixture of grass and sage land, surrounded closely by an aspen and conifer
forest located in the north of Utah (US). The authors took continuous TDT
measurements in all four of those land-use types, complemented the dynamics
of the soil moisture profiles with the help of HYDRUS-1D
simulations, and found decent correlation with the CRNS signal (compare also
similar approaches by in a farmland). It is interesting to
note that each of the four land-use compartments actually behaved very
differently in terms of soil water dynamics, depicted as dotted lines in
Fig. .
As each compartment is distributed differently in the CRNS footprint, the
contribution of each area is different and thus cannot be averaged adequately
by a simple weighting approach. However, in contrast to the complex terrain
of the Schäfertal site (Sect. ), here all
land-use and soil types are represented by adequate sample locations. We
therefore grouped the soil moisture information of the four compartments, and
weighted each 1 m2 pixel of the areal contribution map depending on the
pixel's distance r to the CRNS probe (see the last paragraphs of
Sect. ). This strategy again showed improved CRNS
performance for all measures (black dashed line in Fig. )
compared to the simple approach of weighting only the individual monitoring
points (orange and blue solid lines). Although the gained performance is not
significant in the light of the measurement uncertainty, this areal weighting
approach can be suggested as the most realistic representation of the
contribution of heterogeneous soil moisture patterns to the CRNS signal.
Towards a revised sampling scheme
The presented results raise the question whether it could be profitable to
apply a Wr-flavored sampling design to the locations used for
calibration and validation. Based on , the
conventional weighting function Wrconv laid
the basis for the COSMOS standard sampling scheme,
Ri = {25, 75, 200 m} . These radii were
located in the 33 % quantiles of the footprint see
alsoTable 3:
13∫0∞Wrconv≈∫048Wrconv≈∫48142Wrconv≈∫142∞Wrconv.
(a) Illustration of regions of equal contribution (20 %
quantiles) to the neutron signal for three climates, h = {2, 7,
20} g m-3, θv = {2, 20, 50} %.
(b) The COSMOS standard sampling scheme based on
Wrconv, compared to two exemplary three-radii schemes
based on the revised function Wr* for dry
(h = 1 g m-3, θv = 1 %), and wet
(h = 10 g m-3, θv = 40 %) conditions.
Circles represent the borders of the 33 % quantiles, ri (grey,
dashed), and arbitrary sampling distances Ri within these annuluses
(colored, solid).
As introduced the revised weighting function
Wr(h, θ), the standard sampling scheme has become
inappropriate, at least in non-homogeneous terrain, for two reasons: (1) the
revised sensitivity is steeper, particularly at short distances to the probe,
and (2) depends on the total water equivalent of the surrounding hydrogen
pools. In particular, the dynamical horizontal weighting has been applied
here to demonstrate its ability to significantly improve CRNS performance.
While existing data from point sensor networks could be re-weighted in
post-processing mode, the question arises whether positioning schemes for
upcoming soil moisture networks or calibration campaigns could adapt to the
nature of neutron physics to maximize comparability.
Obviously, it is impossible to provide a new general position plan, due to
the temporal variability of Wr and Wd, and the
heterogeneity of local structures and conditions. Instead, selection of
sampling locations should depend on (1) their representativeness for local
features and (2) their distance to the sensor. In general, it can be
recommended to select a significant portion of available sampling points
within the nearest 25 m, since 30–50 % of detected neutrons typically
originated in that area. The conventional sampling scheme from
does not account for this contribution, which is
particularly relevant if local correlation lengths of soil moisture can be
below 20–30 m. The number of samples in an area should also represent its
areal contribution to the neutron signal, in order to reduce measurement
uncertainty in areas where the CRNS probe is most sensitive. This
argumentation justifies a lower amount of samples in regions far afield.
To give further advice on a reasonable distribution of points for homogeneous
terrain, sampling radii Ri of concentric circles could be calculated as
follows. First, select a total number of circles n based on prior
knowledge about the patterns at the individual site. Since the signal
contribution of an area between any radii can be calculated by integrating
Wr compare alsoEq. 1, the n borders of equal
areal contribution, ri, i ∈ (1, …, n), can be calculated by solving
the integral:
∫0riWr*(h,θ)dr*=!i-1n∫0∞Wr*(h,θ)dr*.
Then, the sampling radii Ri can be
selected anywhere between ri and ri+1, as they are assumed to
represent the area of the corresponding homogeneous annulus. A simple
guideline could be to set the sampling radius in the geometrical center:
Rih,θ,p,Hveg=ri+0.5ri+1-ri,i<n,ri+0.5ri,i=n,
where the last sampling distance Rn could be set to any point that is
expected to represent the whole area beyond rn.
As an example for n = 5, Fig. a illustrates five
annuluses of the footprint area which equally contribute to the neutron
signal. Based on this picture, an equal number of sampling locations is
recommended in each annulus. For example, if it is desired to use the
hitherto proposed number of 18 locations for humid conditions, 3 could be
distributed within 2 m distance, another 3 within 17 m, and the remaining
12 locations evenly within 58, 137, and 240 m, respectively. In order to
compare this approach with the conventional sampling scheme by
, a three-annulus scheme can be adapted from
Eq. ():
dry:13∫0∞Wr*≈∫024Wr*≈∫24108Wr*≈∫108∞Wr*,wet:13∫0∞Wr*≈∫04Wr*≈∫461Wr*≈∫61∞Wr*.
Thus, if n = 3 radii are desired for the sampling scheme, a possible (but
arbitrary) suggestion could be Ridry ≈ {10,
65, 160 m} and Riwet ≈ {2,
25, 85 m}, as illustrated in Fig. b compare alsoSect. 4.2.
This arrangement, however, should not relieve scientists of weighting their
data in post-processing mode, because each annulus still exhibits a
sensitivity gradient. But the 20 %-annulus method strongly concentrates
locations within most relevant regions favored by detectable neutrons. It is
also worth noting that locations need not be equally distributed among the
annuluses. The actual partitioning should rather be guided by expert
knowledge about local patterns, ideally including spatial distributions of
soil characteristics and land use. Proper weighting of sampling data in
post-processing can be helpful to compensate for the lack of such
information. Given entirely homogeneous soil, for instance, a single location
would do.
Is this strategy still robust against complex terrain and variable weather?
Field sites differ in terms of spatial heterogeneity and variability due to
terrain features or highly heterogeneous correlation lengths of soil moisture
patterns. Hence, implementing a strict, universal sampling scheme often is
neither feasible nor meaningful with regards to individual conditions in the
field. In this study the application of the revised weighting approach led to
improved CRNS performance at all sites and for regular and irregular sampling
designs. Apparently, the presented weighting procedure is robust across
various sites, sampling configurations, and wetness conditions.
Summary of the CRNS performances achieved by changing from the
conventional to the revised weighting approach.
RMSEv is in units of volumetric %. CRNS data have been
calibrated on 3 sampling days (sites 1–2) or on time series of a soil
moisture monitoring network (sites 3–6). The revised weighting approach
improved the performance at all sites, and helped to identify additional
hydrological features.
Site
KGE
NSE
RMSEv
Correlation
Note
Sheepdrove Organic Farm, UK
5.3 → 1.4
bias from grass strip
Braunschweig, GER
1.2 → 0.6
data became more consistent
Schäfertal, GER
0.88 → 0.93
0.81 → 0.87
4.0 → 3.3
0.92 → 0.94
incomplete SoilNet coverage
Grosses Bruch, GER
0.02 → 0.48
-0.71 → 0.11
3.5 → 2.3
0.80 → 0.78
remote ponding
Wüstebach, GER
0.65 → 0.69
0.41 → 0.65
6.7 → 5.1
0.80 → 0.81
revealed excess water storages
T. W. D. E. Forest, US
0.78 → 0.91
0.72 → 0.82
1.3 → 0.8
0.88 → 0.92
areal weighting of 4 clusters
An advantage of the approach is its straightforward applicability, which
essentially applies a simple distance-weighted average to a set of data
points, and does not require additional, complex analysis or interpolation
strategies. The only assumption made is that each sample point represents an
equal area in the footprint. Apart from sophisticated optimal sampling
designs, three of the most simple sampling strategies are (1) regular grids,
(2) random locations, and (3) locations that represent stable patterns (of
soil moisture or land cover). However, judgment about their performance is
far beyond the scope of this work. In any case, it could be recommended to
reduce the uncertainty of samples close to the detector (e.g., by taking
repeated measurements), because neutron theory has shown that the CRNS signal
is most sensitive to nearby locations.
A simple and pragmatic way to design a reasonable sampling scheme could be to
choose sensor locations based on the approximated horizontal sensitivity
function Wr* (Appendix ). As this function
does not depend on dynamic changes in surrounding hydrogen pools, an equal
average would be sufficient in post-processing mode. However, the dependence
on air humidity h and soil moisture θ will introduce temporal errors
to this approach. In this case it could be recommended to correct the equal
average with its dynamic variability, which can be expressed as the variation
of Wr(h, θ) around its mean, Wr*.
To circumvent a potential bias introduced by arbitrarily distributed
locations, it could be better to apply different zonation approaches or
interpolation methods (e.g., Kriging in polar coordinates) before each cell
of the interpolated grid is weighted. However, this always comes with
additional assumptions. For example, in the sampling strategy presented in
Sect. certain soil moisture patterns in the field were
categorized as four areas of different land uses which were expected to
behave equally in the footprint in terms of soil water dynamics. The
horizontal weighting was then applied to those measurements depending on the
location of the contributing area in the footprint. In our opinion this
method probably provides the highest accuracy in most cases, although it
requires prior knowledge about the distribution of soil type compartments in
the footprint.
This study has focused on the theory and application of the averaging
approach, while the performance of different interpolation strategies might
depend on local soil patterns and deserves a study on its own, for their
performance always depends on the local structures and correlation lengths of
soil moisture.
Conclusions
In this paper a general procedure for horizontal and vertical weighting of
point measurements has been presented in order to calibrate and validate the
CRNS soil moisture product. The method is based on revised spatial
sensitivity functions (or weighting functions) from neutron physics
simulations . Notably, the revised functions have
been further advanced in the present work with an updated version of the
URANOS neutron transport code, by adding dependency on air pressure
and vegetation height, and by extending the analysis to distances below
0.5 m. The performance of the conventional weighting functions has
been compared with the revised functions using datasets from a
variety of distinct sites located in Germany, the UK, and the US. The
improvements of the CRNS performances for each site are summarized in
Table , including a note that highlights specific features
of the analyses.
The study has led to the following conclusions.
The revised averaging of observed point data improved the performance
measures of the CRNS product for all investigated sites when compared with
the equal and conventional approaches. The method is thus
applicable to arbitrarily distributed sampling locations without prior
knowledge of soil and land-use features.
The results show that unrealistic deviations of multiple calibration datasets
from the theoretical line can be removed by applying the revised weighting
functions. Thus they support the original hypothesis by
of a single calibration campaign to capture the local soil moisture dynamics.
The approach can thus substantially reduce the calibration efforts for CRNS
probes, in contrast to recent findings from and .
Although existing data can be weighted in post-processing mode, missing
locations close to the detector as well as insufficient coverage of the CRNS
footprint introduce significant uncertainty. It can be quantified with the
help of the radial sensitivity functions, as has been presented in
Sects. and .
Sampling strategies that are based on concentric rings can only be
recommended for homogeneous terrain (where each sampling location is known to
contribute equally to the signal) and should be adapted on the local site
conditions (air pressure, humidity, soil moisture, vegetation cover). If the
samples are arranged according to Eq. (), their equally
weighted average would provide a value that is comparable to the CRNS
product. On the other hand, if the footprint is covered by heterogeneous soil
and land-use patterns, the sample locations should be adapted to distinct
representative clusters, which in turn should then be weighted based on their
areal contribution to the signal (see Sect. ).
Data points in the first 0 to 10 m radius and 0 to 20 cm
depth around the sensor are most important for calibration and validation
purposes. It is thus recommended to reduce the uncertainty of those
measurements, e.g., by increasing the number of samples in that area.
As previous studies have shown, the CRNS soil moisture signal could be
calibrated to match the simple, equal average of the areal soil moisture in
the footprint. However, important hydrological features could be missed by
doing so and data interpretation might become misleading. When CRNS is
combined with independent soil moisture measurements, the revised weighting
approach has the potential to reveal hydrological features that were
otherwise lost in the signal by overcalibration. The approach improved the
accuracy by which the CRNS probe was able to sense total changes in water
storages other than soil moisture, e.g., from water in the biomass or litter
layer, interception water, groundwater rise, as well as ponding in remote or
local areas.
The revised weighting functions presented here are provided in the
Supplement in R, MATLAB, and Excel
(see Appendix ). Furthermore, an approximated weighting
function Wr* (Appendix ) has been suggested to
simplify quick analysis of the horizontal contributions independently of the
local wetness conditions. However, the latter approach should be taken with
care, for its adequate performance has not been sufficiently confirmed in this work.
Within this study many datasets have been reanalyzed to test the revised
weighting approach. Due to its overall success, it is recommended to also
revisit other studies, especially where the conventional approaches have not
led to the expected results e.g.,. In the light of the discussion provided, we recommend future
studies to improve the sensor performance even further, for example, by
investigating the effect of different sampling designs and interpolation
strategies or by recalibrating the parameters of the theoretical line,
N(θ). Specific URANOS simulations of the neutron distribution
at the individual sites can further help to identify the contribution to the
detector signal of different parts in the footprint.
On the basis of the results gained by this study and in the light of the
conclusions above, it can be deduced that CRNS stations placed in mostly
homogeneous terrain offer the highest interpretability of its field-scale
signal. This is a feature that the CRNS method has in common with many other
hydrometeorological instruments, like weather stations or
eddy covariance towers . However, even in complex terrain
CRNS probes are capable of catching hydrogen pools that otherwise would be
very difficult to monitor (e.g., ponding, interception), while their
sensitivity to specific parts of the footprint can be quantified with the
help of Wr. Thereby, the present study demonstrates a way forward
to a better understanding of the spatial contributions to the neutron signal,
and elaborates the potential of cosmic-ray neutron sensors to quantify
hydrological features that are almost impossible to be caught with
conventional instruments.