シンポジウム特集

J. Jpn. Soc. Soil Phys.

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土壌の物理性LecturesNo. 132, p.25 ∼ 30 (2016)

Land-surface hydrology with cosmic-ray neutrons:
principles and applications
Marek Zreda1

Abstract: Soil moisture plays the critical role in landsurface processes. But it is not well understood, in part
because of its strong spatial variability that makes difficult obtaining representative measurements. The recently
developed cosmic-ray soil moisture probe provides themeans for such representative measurements and therefore
has the potential to provide useful area-average data forland-surface hydrology.
Key Words : cosmic-ray neutrons, soil moisture, land surface hydrology, measurement method

1. Introduction
Soil moisture is the most important part of the water andenergy cycle (Fig. 1). It plays a critical role in weather andseasonal climate forecasting and in linking water, energy
and biogeochemical cycles over land. But our understanding of water at the land surface is poor, in part because of
the mismatch between the scales at which processes aboveand below the land surface are observed, parameterized
and modeled. In the well-mixed atmospheric boundary
layer that scale is from hectometers to tens of kilometers.
Below the surface, states and fluxes are usually measured
at a point. To remove the mismatch, the subsurface must
be characterized at the scale comparable to that above theland surface. I call it the useful scale and define it as arange 100 m – 1000 m that broadly matches the needs offuture high-resolution land-surface and hydrological models (Wood et al., 2011; Maxwell et al., 2015).
Area-average water states and fluxes are difficult to measure at the useful scale. Point measurements are not representative because of strong spatial heterogeneity (e.g., Fig.
1 in Zreda et al., 2012) and must be upscaled, which isimpractical. Scale-integrating methods for soil moisture,such as satellite microwave methods, usually measure overlarge areas (10 km – 50 km), integrate meteorological,
Department of Hydrology and Water Resources, University of Arizona,1133 E James E Rogers Way J W Harshbarger Bldg, Tucson, AZ, USA.
2016 年 1 月 27 日受稿 2016 年 3 月 1 日受理

topographic and other factors, and must be downscaled,
which is uncertain.
The cosmic-ray method (Zreda et al., 2008, 2012; Desilets et al., 2010), with the hectometer footprint (Desilets
and Zreda, 2013; Köhli et al., 2015), integrates out smallscale variations, but is not affected by large-scale variability. It is, therefore a good scale integrator of soil moisture
for land-surface and hydrological studies. In this review,
I discuss the principles of the cosmic-ray method, the instruments for measuring cosmic-ray neutrons, the methodology for converting neutron data to moisture and some
applications to land-surface hydrology.

2. The principle of the cosmic-ray
methodThe cosmic-ray method (Zreda et al., 2008, 2012; Desilets et al., 2010) takes advantage of the extraordinary sensitivity of cosmogenic low-energy, moderated neutrons ofenergy between 1 eV and 1000 eV to hydrogen present
in materials at the land surface. Most neutrons on earth
are cosmogenic (Fig. 1). Primary cosmic-ray protons collide with atmospheric nuclei and unleash cascades of energetic secondary neutrons that interact with terrestrial nuclei
and produce fast (evaporation) neutrons at the land surface.
The fast neutrons that are produced in air and soil travelin all directions within the air-soil-vegetation continuum
and in this way an equilibrium concentration of neutrons
is established. The equilibrium is shifted in response tochanges in the water present above and below the land surface, for example in soil. Adding water to soil results inmore efficient moderation of neutrons by the soil, causing
a decrease of fast neutron intensity above the soil surface,where the measurement is made. Removing water fromthe soil has the opposite effect. The resultant neutron intensity above the land surface is inversely proportional tosoil water content (Zreda et al., 2008, 2012).
The measurement volume is a quasi-cylinder with the diameter of a few hectometers (also called the footprint) and26

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Fig. 1 Left: Water mass balance at the land surface; red labels indicate pools and fluxes measurable using
cosmic rays. Right: Cosmic-ray neutron interactions with air and soil. Tracks of two neutrons are shown in
the lower panel. Neutron n1 was absorbed in soil and removed from the pool of neutrons measurable bycosmic-ray probe above the surface; neutron n2 went back to the atmosphere and is measurable there.
These tracks are copied onto the left panel (red lines). Background image — European Space Agency (ESA).

a depth of a few decimeters (Desilets et al., 2013; Köhli etal., 2015). The footprint increases with increasing altitude(decreasing pressure), and decreases with increases of eachof the following: air pressure, absolute humidity of air, soil
moisture and vegetation density. The measurement depth
decreases strongly with increasing soil moisture.
Because of the large size of the footprint, it usually contains many sources of water, in addition to soil water. Fig.
2 shows an estimated footprint for the cosmic-ray probe at
the Rietholzbach site in Switzerland. The visible sourcesof water include soil (including water in pore spaces, inminerals and in organic matter), vegetation (grass, crops,
trees), small creeks and man-made infrastructure (buildings, roads). The largest source of water is soil, but theother reservoirs, especially vegetation, may be importantand they should be assessed independently.

Fig. 2 Footprint of the COSMOS probe located at the Rietholzbach site, Switzerland (cosmos.hwr.arizona.edu/Probes/StationDat/018/index.php). The white dashed line with theradius of 300 m is the footprint estimated using Desilets
and Zreda (2013); the footprint estimated by Köhli et al.
(2015) would be smaller. Red dots located on three smaller,
yellow circles at radii of 30 m, 80 m and 200 m show thelocations of calibration samples.

Neutron measurements can be made using stationary or
roving probes. The former provide time series of moisture
over the hectometer footprint, the latter gives moisture forswaths of land along driving routes.

3. Instruments
Low-energy cosmogenic neutrons are measured using
proportional counters (Knoll, 2000), which are sensitive
to thermal neutrons (median energy of 0.025 eV), shieldedby a layer ofplastic that shifts the energy sensitivity of the解説：Land-surface hydrology with cosmic-ray neutrons: principles and applications

counter to neutrons of the desired energy (>1 eV). The
cosmic-ray probe (Fig. 3) is powered using a solar panel
paired with a rechargeable battery and is equipped with an
Iridium satellite modem or a cellular modem for real-time27

telemetry. It can be operated almost anywhere in the world,
except areas with insufficient day light. A stationary neutron probe of this type is implemented in the Cosmic-ray
Soil Moisture Observing System (Fig. 4), or COSMOS(Zreda et al., 2012; cosmos.hwr.arizona.edu); therefore, it
is sometimes called “COSMOS probe”. The instrument is
described in Zreda et al. (2012). A mobile COSMOS detector is a bigger version of the stationary probe, additionally equipped with a GPS system for real-time positioning(Chrisman and Zreda, 2013).

4. Conversion of neutron data
to soil moisture
The measured neutron intensity ϕ (in the equation below), normalized for variations in pressure, humidity andsolar activity (Zreda et al., 2012), is converted to soil moisture SM using the response function, such as that developed by Desilets et al. (2010):
SM =Fig. 3 Cosmic-ray soil moisture probe installed at Marshall
Lake, Colorado, USA. For description of the components,
see Fig. 9 in Zreda et al. (2012).

a0− a2
ϕ /ϕ0 − a1(1)where SM is in weigh fraction (g of water per g of dry soil),
ϕ0 is the neutron intensity in air above dry soil (obtained bycalibration) and a0 , a1 and a2 are fitted constants that define the shape of the calibration function. Modeling conducted by Desilets et al. (2010) gave the following fitting
constants for bare soil composed of SiO2 : a0 = 0.0808,
a1 = 0.372 and a2 = 0.115. For water content measured involumetric units (cm3 of water per cm3 of soil) both sidesof the equation should be multiplied by the dry bulk den-Fig. 4 The COsmic-ray Soil Moisture Observing System (COSMOS). The network consists ofapproximately 100 probes of the type shown in Fig. 2 or similar. The Australian probes displayed
here belong to the CosmOz network. Not shown here are other networks that either already exist
or that are under construction, most notably the TERENO network in Germany and the COSMOSUK network in the United Kingdom.

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Fig. 5 Collecting soil samples for calibration. Soil samples are collected using a split corer that is pushed into soil,
dug out, opened lengthwise, the core is divided into 5-cm long samples and each sample is sealed in a soil tin forshipment to the laboratory. Soil samples are obtained at each of the 18 coring sites shown in Fig. 2.

sity of soil. Other measurements needed for the conversion are atmospheric pressure, atmospheric water vapor,incoming high-energy neutron intensity and temperature.
They are used to compute various corrections necessary
for the computation of soil moisture from neutron data, as
described by Zreda et al. (2012) and other sources.

5. Calibration
Cosmic-ray soil moisture probes have to be calibrated on
independently measured area-average soil moisture. Thisis accomplished by collecting a large number (typically108) of soil samples (Fig. 5) within the cosmic-ray footprint (Fig. 2), measuring soil water content by independent methods such as oven drying, and computing the areaaverage soil moisture. Neutron intensity is measured overthe duration of sampling. The average soil moisture is thenused with the response function, such as the equation given
in section 4 above, to obtain a calibration parameter. One
calibration data set is sufficient for soils with sparse vegetation, but multiple data sets, obtained at different soil watercontents, provide a more accurate calibration and can account for the effects of other pools of water on the response
function, such as biomass (Heidbüchel et al., 2015).

解説：Land-surface hydrology with cosmic-ray neutrons: principles and applications

29

site nearby (Franz et al., 2013a). The difference in neutron
intensities between the sites was converted to biomass water equivalent, and then to dry biomass. The dry biomass
was found consistent with allometric measurements at theforested site, showing that the cosmic-ray method is feasible.

Fig. 6 COSMOS-derived time series of soil moisture fromthe Tonzi site, California (data from http://cosmos.hwr.arizona.
edu/Probes/StationDat/032/index.php). Gray dots show hourly
soil moisture; the black line shows 12-hour moving average.
Data inside the light gray box in 2012 show a single drying
curve that would be used for analysis of infiltration andevapotranspiration (see text for details).

Vegetation has a significant effect on neutron intensity(Franz et al., 2013a; Bogena et al., 2013) and on the shape(slope) of the calibration function. Thus, measuring soil
moisture in the presence of vegetation requires a correction factor (Baatz et al., 2015) or more than one calibration
point to define that slope. Heidbüchel et al. (2015) foundthat two calibration data points are sufficient if the two soil
moisture states are very different. (If they are similar, theslope cannot be defined accurately.)
Snow-water equivalent can be measured with cosmicray probe (Desilets et al., 2010). Calibration for snow isconducted in a similar way to that for soil moisture, by
making independent measurements of snow-water equivalent over the cosmic-ray footprint. But the effect of snow
on neutron intensity is not well known and details still haveto be worked out.

6. Applications
The cosmic-ray method was originally designed formeasuring soil moisture at a fixed location (Fig. 6). Much
progress has been made in the past five years. Recent work
has shown that the probe can be used for measuring otherpools of water, such as snow on the ground and on canopy,
water in vegetation, and possibly water on canopy; thatit can be used in a moving vehicle to map moisture overlarge areas; and that it can be used to measure infiltration
rates, and possibly hydraulic conductivities, of variablysaturated soils at hectometer scale. These applications are
discussed briefly below.
Biomass can be measured with cosmic rays because
plants contain significant amounts of water whose presencenear the land surface affect the moderation of neutrons andtherefore their intensity. The proof-of-concept study involved measurements in a forest and a recently-deforested

Spatial mapping of soil moisture using a mobile probe,
or rover, is possible with two recent advances: the development of a larger probe that has high count rate andis equipped with GPS to monitor position as the probemoves; and the development of a universal calibration
function (Franz et al., 2013b) that permits conversion ofneutron intensity to soil moisture without local calibration.
Several rover surveys have been conducted in the past,
including a year-long project in Tucson, Arizona, USA,
which generated maps of soil moisture for a 1000-km2
area at 22 different times, permitting mass balance calculations for the entire basin and the entire duration of theexperiment (Chrisman and Zreda, 2013). In a recent paper,
Franz et al. (2015) combined roving surveys with stationary probes to improve the accuracy of soil moisture determination over a large area.
Infiltration or recharge rate can be inferred from measured soil moisture and mass balance of water in soil.
Following a precipitation event, soil moisture slowly decreases over many days (Fig. 6). The drying curve provides information on changes of moisture with time and its
temporal derivative gives change of storage. That change
is then used in a mass balance equation, which can be converted to infiltration rate. Furthermore, if the hydraulicgradient is known or can reasonably be assumed, that infiltration rate can be converted to unsaturated hydraulicconductivity. Our first study (Karczynski, 2014) showedthat cosmic-ray derived effective hydraulic conductivity is
consistent with an (upscaled) average of 36 point measurements near the saturation, but that it is much larger than the
average at lower levels of saturation. The reasons for that
discrepancy have not been elucidated.
In a similar way, area-average precipitation rates can bemeasured using cosmic-ray probes. The underlying assumption is that all rain water enters the soil where it stays
long enough to be measured using neutrons. The difference between neutron-derived soil moisture before and after the rain event equals precipitation amount. Potential
problems include surface runoff and fast infiltration; however, both appear to be insignificant at two locations where
we conducted proof-of-the-concept experiments.
These and many other results show the utility of thecosmic-ray probe to land-surface studies. The large footprint of the probe averages the small-scale variabilities instates (for example, moisture), fluxes (for example, infiltration rate) and properties (for example, hydraulic conductiv-

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ities), eliminates the needs for upscaling and permits treatment of processes that occur below and above land surfaces
at the same useful spatial scale.

第 132 号

(2016)

Franz, T.E., Wang, T., Avery, W., Finkenbiner, C. and Brocca,
L. (2015): Combined analysis of soil moisture measurementsfrom roving and fixed cosmic ray neutron probes for multiscale real-time monitoring. Geophys. Res. Lett., 42: 3389–
3396.

Acknowledgements

Heidbüchel, I., Güntner, A. and Blume, T. (2015): Use of cos-This work was supported by the US National Science
Foundation under grant number 0838491. I thank Dr.
Ieyasu Tokumoto (Saga University) for his help in the
preparation of this manuscript.

mic ray neutron sensors for soil moisture monitoring in forests.
Hydrol. Earth Syst. Sci. Disc., 12: 9813–9864.
Karczynski, A.M. (2014): Measuring unsaturated hydraulic conductivity of variably-saturated soils at the hectometer scaleusing cosmic-ray neutrons. MS thesis, University of Arizona,
Tucson.

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Bogena, H.R., Huisman, J.A., Baatz, R., Franssen, H.-J. andVereecken, H. (2013): Accuracy of the cosmic-ray soil water content probe in humid forest ecosystems: The worst casescenario. Water Resour. Res., 49: 5778–5791.

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要旨

土壌水分は，表層土壌のプロセスにおいて重要な役割を果たす．しかし，土壌水分の空間変動が大きく代表的な測定値の決定が困難であるために，幾分か土壌水分量の把握は難しい．近年に開発された宇宙線による土壌水分計測は，そのような代表的な土壌水分量の平均値を与えるので，表層土壌の水文学において有益な面的平均値の提供を可能にする．
キーワード：宇宙線中性子，土壌水分量，表層土壌水文学，測定方法