This is a faily detailed description of how soil moisture is derived using the cosmic-ray neutron counter; the references at the end of page provide greater detail.

Primary cosmic-rays are high-energy sub-atomic particles that originate from outer space and continuously bombard the Earth. The intensity of cosmic-rays arriving at the top of the Earth’s atmosphere varies with the events that generate them (distant astronomical events) and factors such as variations in the solar magnetosphere. The particles are mostly (90%) protons with a typical energy of around 1 GeV.

When these particles enter the Earth’s atmosphere they collide with atoms in the air and create a shower of secondary cosmic-ray particles (including neutrons), which may or may not interact with other particles before reaching the Earth’s surface. Each collision causes the particle (neutron) to lose energy. The energy spectrum of these neutrons at the Earth’s surface contains a number of peaks. At around 100 MeV are high energy neutrons, which interact with air and soil to produce a second peak, at around 1 MeV, of fast neutrons, also known as evaporated neutrons (that is not evaporation as understood by hydrologists but the “release” of neutrons following the collision of a high energy particle, e.g. a proton or neutron, with the nucleus of an atom).

Further collisions cause a further reduction in the energy of the neutrons until they become ‘thermalised’ i.e. in thermal equilibrium with the environment; that is they can neither lose more energy nor regain lost energy. These thermalized, or thermal, neutrons, have typical energies of around 0.1 eV. Neutrons with energies greater than thermal neutrons may be referred to as epi-thermal, generally meaning greater than 0.5 eV; fast neutrons are therefore within the epi-thermal range. Kohli et al. (2015) provide an illustration of this energy spectrum.

The themalisation of neutrons (also known as moderation) is highly dependent on the properties of the particles (elements) the cosmic rays hit. Hydrogen is the most efficient element in terms of its stopping power of fast neutrons; 18 collisions with hydrogen will thermalize a fast neutron whereas this takes 149 collisions with oxygen. This is explained by the fact that the light hydrogen nucleus, comprising just one proton, can absorb a lot of the energy from the neutron in a collision (much like when two billiard balls collide) whereas when a neutron hits a large nucleus it bounces off retaining most of its energy (like a billiard ball hitting the cushion on the snooker table, this nice analogy from Zreda et al., 2012). This stopping power combined with the abundance of hydrogen in air and soil means that the process of thermalisation is largely determined by the presence of hydrogen.

These collisions result in neutrons being scattered in all directions, i.e. between and within the air and soil, and the process of thermalisation is effectively instantaneous because of the high energy/velocity of the fast neutrons. The concentration of fast neutrons therefore very quickly reaches an equilibrium in both the soil and the air, and a key factor in determining the concentration is the amount of hydrogen that is present.

This is the basis of the cosmic-ray soil moisture method. A sensor at the land surface will count more fast neutrons when there is little hydrogen (water) present and fewer fast neutrons when there is more hydrogen to remove energy from the neutrons leading to their themalisation.

The neutron counter is basically a tube containing a gas that can convert thermal neutrons into detectable electrons by ionisation; higher energy neutrons pass through the tube without interacting with the gas. In its “bare” format the sensor therefore counts themalised rather than fast neutrons, although there is not a sharp cut-off in its detection limit.

A “moderated” tube contains the same sensor embedded in a material that causes the themalisation of neutrons and therefore counts neutrons in a higher energy range, although some lower energy neutrons are also likely to be counted. Andreasen et al., 2015 presents figures showing part of the neutron energy spectrum sampled by bare and moderated detectors.

Zreda et al (2012) suggest that the moderated tube is used to measure soil moisture and that the bare tube is potentially useful water that is present above the land surface in snow, vegetation etc. COSMOS-UK prototype sites were equipped with both types of tubes; sites installed subsequently only have moderated tubes.

From the above there is an understanding, in principle at least, of how the intensity of cosmic ray derived neutrons measured at the Earth’s surface is influenced by water contained within in soil. The processing of neutron counts to derive volumetric water content has been described in, for example, Evans et al. (2016) and what follows is a brief overview.

Firstly, correction factors are applied to the recorded neutron counts to account for variations in background cosmic ray intensity (as measured by a high altitude reference site at Junfraujoch, Switzerland), altitude, atmospheric pressure and atmospheric water vapour. This adjusted number of counts is known as the ‘corrected counts’.

There are currently three methods that can be used to derive water content from the corrected counts: (1) Site specific N0 method, (2) universal calibration method (also known as hydrogen molar fraction, hmf, method), and (3) neutron transport modelling (e.g. MCNP, COSMIC, URANOS). These methods are described in Baatz et al. (2014) and Bogena et al. (2015). The first of these methods is the most straightforward to apply and as a consequence the most widely used. Baatz et al. (2014) conclude that all three methods estimate soil water content with acceptable errors when compared to estimates determined using soil sampling and laboratory analysis.

COSMOS-UK uses the first of these methods in which a reference soil water content is obtained from field calibration, see Franz (2012) and Zreda et al. (2012). This reference value is then used in combination with an equation relating corrected counts to soil water content (with parameters applicable for a generic silica soil matrix; see Desilets et al. (2010)), to calculate a site specific N0 calibration coefficient. The COSMOS-UK procedure also follows the procedures in Zreda et al. (2012) and Franz et al. (2013) to account for the effects of lattice and bound water (structural water associated with clay minerals in the soil) and soil organic carbon (a minor constituent of mineral soils, but the major constituent of peat soils).

As noted in Evans et al. (2016), although the counts are recorded by COSMOS-UK on an hourly basis “the noise associated with the cosmic-ray technique … (in) UK conditions” means that averaging at 6 hours or 24 hours is recommended. The UK conditions referred to here are the general wetness of the UK soils, low altitude and high soil organic carbon at particular sites, which reduce the number of neutron counts; from the background above it will be noted that this is the basis of the measurement technique but the wetness of the UK soils was outside the range observed in the USA where the method originated. In practice processing on an hourly basis using standard equations as referenced above can lead to values of soil moisture of greater than 100% or less than 0%, hence the necessity to censor or average values at some stage in the processing. In fact some 1.2% of all hourly VWC values were greater than 100%, whereas less than 0.01% of values were less than 0%. Note that hourly VWC data could also be unavailable because of missing data, i.e. the numbers of counts or those variables needed to derive the corrected counts.

COSMOS-UK has employed several variations in methods of data processing and by late 2016 had generally adopted a method that censored (filtered) hourly values with >100% or <0% water content and then averaged as appropriate, e.g. to give a daily mean. An arbitrary decision had to be made about how many hourly values could be missing for a daily mean to be considered acceptable (generally one missing value was allowed). The COSMOS-UK recommendation was that generally the hourly data were too noisy to be useful and that the daily mean data should be used. Because of the filtering, the daily VWC could not be outside the range 0-100%, but could approach these limits and therefore not be considered sensible measurements of soil moisture. Data supplied to users alerted then to these issues and advised caution in their use.

Across all sites the changes to the averaging and VWC calculation methods have improved the number of daily VWC values calculated from 84% to 92%. However, the degree of improvement varies between sites with the biggest improvement being at the sites with high soil organic carbon content such as Redmere where the changes have led to a 60% improvement on the number of daily days of data generated.

ote that the problems associated with high VWC generally relate to sites with peat soils in which higher VWC values are expected. VWC data from mineral soils with lower water content are more reliable; problems are rare in the daily data from mineral soils, although the hourly data are still noisy.

The characteristics of the sensor footprint were understood to vary relatively little with distance from the sensor as soil wetness changes, but the sensor penetration depth below the ground surface decreases markedly with soil water content. This variation has been characterised by the soil depth from which 86%[1] of the measured neutron counts have originated (effective depth). Franz et al. (2013) provide a way of calculating an average effective depth which was initially used by COSMOS-UK. In the wettest conditions this depth can be as little as 0.08m, very much less than the 0.76m given by Zreda et al. (2008) for dry soils in the USA. At this time the sensor footprint was considered to be roughly 300m in radius (i.e. 86% of measured neutrons were generated from within this footprint).

These footprint characteristics informed the field soil sampling protocol used to obtain the reference soil water content mentioned above.

Kohli et al. (2015) published a re-evaluation of the sensor footprint and changes to way in which calibration data are used to calculate the reference soil water content. A key finding was that 50% of the neutrons counted came from within 50m of the sensor, and that the sensor showed “extraordinary sensitivity” to the closest few meters to the sensor.

While this result led to a change in the field sampling protocol used by COSMOS-UK (i.e. the protocol was changed to take samples closer to the sensor), this in itself has little impact as the COSMOS-UK sites have been selected to have similar characteristics over the larger footprint. There is no reason to suspect that soil moisture varies significantly with distance from the sensor.

Kohli et al. (2015) also suggested other changes which relate to the way averaging of soil moisture and bulk density is performed both for calibration of the sensor and the derivation of water content. Of these changes the biggest impact comes from using the bulk density averaged across all samples rather than using just those samples corresponding to the effective depth at the time of the field sampling. This has a particular impact in peat soils in which bulk density increases considerably with depth.

Introducing this new method of deriving VWC further reduced the number of hourly VWC values that were below zero, or greater than 100%, by about 30%. It has been decided to set negative values to zero but to leave values greater than 100% in the data set, so that the user should determine how to handle data considered unreliable.

However, whilst making these changes it was decided to change the way in which daily averages were derived. The “old” method was to filter counts to avoid out of range values of VWC and then average to daily. The new method is to derive an average number of hourly counts for the day and use this to derive the daily VWC; this method resulted in only a tiny percentage of values greater than 100% and no negative values. These >100% values are left in the data set with the user advised to check all high VWC values. Again it was decided that the daily mean number of counts could be used even with some hourly counts missing. After inspecting the data for missing values, which could arise from any of the required variables being missing, it was decided to allow up to two missing hourly values in deriving daily mean VWC.

As mentioned above, a feature of the CRS is that since the neutrons resulting from cosmic rays penetrate the soil, the derived VWC represents a depth averaged value. Franz et al. (2012) provide a method of estimating an effective depth for the sensor. This depth is dependent on VWC and has an approximate range from 10 cm in wet soils to 80 cm in dry soils. This effective depth was calculated for COSMOS-UK sites and made available with the VWC.

The same study that proposed a reduction to the spatial footprint of the sensor, also reviewed depth penetration of the sensor (Kohli et al., 2015; termed D86). They conclude that the source of neutrons sampled by the sensor is dependent on both water content and distance from the sensor, and provide a means to estimate the decreasing penetration depth with distance from the sensor.

It will be appreciated that various alternative methods can be adopted to derive the VWC from the counts recorded in the cosmic ray neutron sensor. It is possible that there will be further changes to the processing of these data.

References

Andreasen, M., K. H. Jensen, M. Zreda, D. Desilets, H. Bogena, and M. C. Looms (2016), Modeling cosmic ray neutron field measurements, Water Resour. Res., 52, 6451–6471, doi:10.1002/2015WR018236.

Baatz, R., H. R. Bogena, H.-J. Hendricks Franssen, J. A. Huisman, W. Qu, C. Montzka, and H. Vereecken (2014), Calibration of a catchment scale cosmic-ray probe network: A comparison of three parameterization methods, J. Hydrol., 516, 231–244, doi:10.1016/ j.jhydrol.2014.02.026.

Bogena, H. R., Huisman, J. A., Güntner, A., Hübner, C., Kusche, J., Jonard, F., Vey, S. and Vereecken, H. (2015), Emerging methods for noninvasive sensing of soil moisture dynamics from field to catchment scale: a review. WIREs Water, 2: 635–647. doi:10.1002/wat2.1097

Desilets D, Zreda M, Ferré TPA. 2010. Nature’s neutron probe: land surface hydrology at an elusive scale with cosmic rays. Water Resources Research 46: W11505. DOI:10.1029/2009WR008726

Evans J. G., Ward H. C., Blake J. R., Hewitt E. J., Morrison R., Fry M., Ball L. A., Doughty L. C., Libre J. W., Hitt O. E., Rylett D., Ellis R. J., Warwick A. C., Brooks M., Parkes M. A., Wright G. M. H., Singer A. C., Boorman D. B., and Jenkins A. (2016) Soil water content in southern England derived from a cosmic-ray soil moisture observing system – COSMOS-UK, Hydrol. Process., 30: 4987–4999. doi: 10.1002/hyp.10929.

Franz TE. 2012. Installation and calibration of the cosmic-ray solar moisture probe. pp: 12.

Franz TE, Zreda M, Rosolem R, Ferre TPA. 2013. A universal calibration function for determination of soil moisture with cosmic-ray neutrons. Hydrology and Earth System Sciences 17: 453–460. DOI:10.5194/hess- 17-453-2013

Kohli, M., M. Schron, M. Zreda, U. Schmidt, P. Dietrich, and S. Zacharias (2015), Footprint characteristics revised for field-scale soil moisture monitoring with cosmic-ray neutrons, Water Resour. Res., 51(7), 5772–5790, doi:10.1002/2015WR017169.

Zreda, M., D. Desilets, T. P. A. Ferr_e, and R. L. Scott (2008), Measuring soil moisture content non-invasively at intermediate spatial scale using cosmic-ray neutrons, Geophys. Res. Lett., 35, L21402, doi:10.1029/2008GL035655.

Zreda M, Shuttleworth W, Zeng X, Zweck C, Desilets D, Franz T, Rosolem R. 2012. COSMOS: the cosmic-ray soil moisture observing system. Hydrology and Earth System Sciences 16: 4079–4099.