Measuring snow water equivalent (SWE) is important for many
hydrological purposes such as modelling and flood forecasting. Measurements of
SWE are also crucial for agricultural production in areas where snowmelt
runoff dominates spring soil water recharge. Typical methods for measuring
SWE include point measurements (snow tubes) and large-scale measurements
(remote sensing). We explored the potential of using the cosmic-ray soil
moisture probe (CRP) to measure average SWE at a spatial scale between those
provided by snow tubes and remote sensing. The CRP measures above-ground
moderated neutron intensity within a radius of approximately 300 m. Using
snow tubes, surveys were performed over two winters (2013/2014 and 2014/2015)
in an area surrounding a CRP in an agricultural field in Saskatoon,
Saskatchewan, Canada. The raw moderated neutron intensity counts were
corrected for atmospheric pressure, water vapour, and temporal variability of
incoming cosmic-ray flux. The mean SWE from manually measured snow surveys
was adjusted for differences in soil water storage before snowfall between
both winters because the CRP reading appeared to be affected by soil water
below the snowpack. The SWE from the snow surveys was negatively correlated
with the CRP-measured moderated neutron intensity, giving Pearson correlation
coefficients of
Landscape-scale snow water equivalent (SWE) measurements are important for applications such as hydrological modelling, flood prediction, water resource management, and agricultural production (Goodison et al., 1987). Particularly in the Canadian Prairies, snowmelt water is a critical resource for domestic/livestock water supplies and soil water reserves for agriculture purposes (Gray and Landine, 1988). Snow is also a key contributor in recharging Canadian Prairie wetlands, which provide important wildlife habitat (Fang and Pomeroy, 2009).
Common techniques for measuring SWE include snow tubes (gravimetric method),
snow pillows, and remote sensing (Pomeroy and Gray, 1995). Snow tube sampling
is the most common field survey method for determining SWE and, although it
provides a point measurement, can be used to survey a larger area. However,
snow surveys with snow tubes are labour intensive, can be difficult to
perform in remote locations, and are prone to over- and underestimation of
SWE, depending on snowpack conditions (Goodison, 1978). Snow pillows can
provide SWE measurements in remote locations, but they produce merely a point
measurement of roughly 3.5 to 11.5 m
A measurement scale between that of the point measurements and the large-scale remote sensing can be desirable due to the high variability in SWE that can occur even over small distances (Pomeroy and Gray, 1995). Shook and Gray (1996) found high variability in snow depth and water equivalent when performing snow surveys with samples every 1 m along transects in shallow snow covers in the Canadian Prairies. Variability of SWE at this small scale was attributed to differences in wind redistribution and transport, along with variations in surface roughness and micro topography. The high variability of SWE at smaller scales can lead to difficulty when trying to estimate average SWE in a field or catchment from a few point measurements. Instead, labour-intensive snow surveys are generally required. At larger scales, spatial variability of SWE is generally a function of the differences in snowfall and accumulation from varying vegetation and topography (Pomeroy and Goodison, 1997).
The cosmic-ray soil moisture probe (CRP) is a relatively new instrument that
was primarily developed for measuring average soil water content at the
landscape scale (Zreda et al., 2008) but also has the potential to be a
useful tool for measuring SWE (Desilets et al., 2010). The CRP measures
neutrons in the fast to epithermal range, which are emitted from soil and
inversely related to soil water content due to the neutron moderating
characteristic of hydrogen (H). The CRP is an appealing soil water content
measurement tool for several reasons. Firstly, it has a landscape-scale
measurement area with a radius originally thought to be
The possibility of measuring SWE from the moderation of neutrons by snow has been known since the late 1970s (Kodama et al., 1979), but studies have been limited. Kodama et al. (1979) used a cosmic-ray moderated neutron sensor buried beneath the snow to measure SWE. Although their results showed a promising relationship between moderated neutron counts and SWE, the fact that the moderated neutron measuring tube was installed beneath the snowpack resulted in merely a point measurement. Others have successfully used cosmic-ray probes buried under snowpacks to measure SWE, including a network of buried probes in France and the Pyrenees of Spain (Paquet et al., 2008). Desilets et al. (2010) compared SWE values measured with a CRP installed above ground to that of SWE values measured manually with a snow tube at the Mt Lemmon Cosmic Ray Laboratory, Arizona. However, the CRP was installed within a laboratory, and Desilets et al. (2010) provided limited details of their study and did not include the relationship they utilised for deriving SWE from measured moderated neutron counts. Using a CRP to monitor SWE was also tested at the Marshall Field Site, Colorado, USA (Rasmussen et al., 2012). Again, limited details were given on the methods of the study and the empirical relationship used to predict SWE from moderated neutron intensity. Additionally, Rivera Villarreyes et al. (2011) observed the possibility to measure snow with neutron counts from a CRP (model CRS-1000) but only explored the relationship between neutron counting rates and snow cover instead of SWE.
The purpose of this study was to establish a simple empirical relationship between SWE and moderated neutrons measured above a snowpack using a CRP. Average SWE in an agricultural field was predicted from CRP moderated neutron measurements using a relationship developed in this study between SWE and moderated neutrons. Predicted SWE from CRP measurements was compared to manual snow surveys and snow precipitation data from multiple locations around the study site.
(Left) Location of main study site (star), RCS reference site (1), and Saskatoon Airport RCS reference site (2) in Saskatoon, SK, Canada. (right) Location of the CRP (orange dot) at the agriculture study site and the 25, 75, and 200 m SWE sampling radials (red lines). Image from Google Maps.
This work was performed at an agricultural field (52.1326
The altitude and average air pressure of Saskatoon are 482 m and 955 hPa
respectively. According to Desilets and Zreda (2013) the measurement
footprint of the CRP changes slightly based on air pressure of the site. Air
pressure affects the neutron moderation length, which controls the footprint
of the CRP. Using Eq. (21) from Desilets and Zreda (2013) and sea level as a
reference (moderation length
The model of CRP used in this study was a CRS-1000/B (Hydroinnova, NM, USA).
This model consists of two neutron detector tubes and an Iridium modem data
logger for remote data access. One of the detector tubes is shielded (or
moderated) to measure neutrons of slightly higher energy (epithermal to fast
range) and one tube is unshielded to measure lower energy neutrons (slow
neutrons). The neutrons detected by the moderated tube in the epithermal to
fast range are referred to as moderated neutrons. Slow neutrons are affected
by more than just H, including other neutron absorbing elements in soil such
as B, Cl, and K (Desilets et al., 2010). Also, the relationship between the
bare tube counting rate and SWE are thought to be less straightforward than
the moderated neutron and SWE relationship. Thus, only the moderated neutron
count was used in this study following the practice established for soil
moisture observations (Zreda et al., 2012). An in-depth description of how
the CRP measures neutrons can be found in Zreda et al. (2012). The CRP was
installed in the centre of the field site (Fig. 1) from the end of October
2013 until after snowmelt in the spring of 2014 (2013/2014 winter).
Similarly, for the 2014/2015 winter, the CRP was installed in the same
location and again collected data until snowmelt in spring of 2015. After
installation of the CRP and before the first snowfall event of both winters,
average soil water content within the CRP measurement footprint was measured
manually from soil cores of known volume. The soil sampling scheme was as
follows: 18 total sampling locations comprised of 6 locations evenly spaced
along 3 radials spanning outward of the CRP (25, 75, and 200 m).
Each location was sampled in 5 cm increments to a depth of 30 cm. This
sampling scheme follows the typical method for calibrating CRPs for measuring
soil water content (Franz et al., 2012b). Volumetric water content was
measured from the cores via the oven-drying method (Gardner, 1986). The
average bulk density and total porosity from the 0–30 cm soil samples were
1.31 g cm
The soil water storage in the top 10 cm of the soil profile, prior to
snowfall, was estimated for both winters from the measured average soil water
content and precipitation data. Precipitation data were collected from a
Saskatchewan Research Council (SRC) climate station (52.1539
The raw neutron counts must be corrected for differences in air pressure,
atmospheric water vapour, and the temporal variation of incoming cosmic-ray
flux. Corrected neutron counts are attained from multiplying the raw counts
by correction factors:
Correcting for differences in air pressure is important since the incoming
cosmic-ray flux is attenuated with increasing nuclei present in the
atmosphere, i.e. as air pressure increases (Desilets and Zreda, 2003).
Since neutron counts are mainly related to the amount of hydrogen molecules
in an area, raw moderated neutron counts must also be corrected for
differences in atmospheric water vapour. Rosolem et al. (2013) found the
following correction function for atmospheric water vapour:
Correcting for the temporal variation of the cosmic-ray flux is the final
correction for the raw neutron counts. This correction is performed using
counts from neutron monitors along with the following equation:
Snow surveys were performed periodically in the field each winter within the
estimated CRP measurement footprint. During the 2013/2014 winter, seven
surveys consisting of 18 sampling points were completed. Throughout the
2014/2015 winter, 11 surveys composed of 36 sampling points were
performed. The SWE sampling points were evenly spaced along each of the
individual soil sampling radials, 25, 75, and 200 m, away from the CRP. This
sampling scheme is based on a CRP footprint of
Snow depth data from two reference sites were used for a first-order
comparison to the snow surveys and CRP data. These were the SRC site and
Saskatoon Airport Reference Climate Station (RCS) site (52.1736
The snow depth data were converted to SWE values in order to compare to the
snow surveys and CRP data. Shook and Gray (1994) studied shallow snow covers
(less than 60 cm) in the province of Saskatchewan over 6 years and found the
following linear relationship for predicting SWE from snow depth:
Moderated neutron intensity recorded by the CRP and SWE from snow surveys are
shown in Fig. 2. According to the field snow surveys from both winters (2013/2014
and 2014/2015), the measured mean SWE peaked at 64.7 mm in
2013/2014 and 53.7 mm in 2014/2015. The SWE varied significantly throughout
the field between individual sampling locations, despite the study site being
relatively homogeneous. The standard deviation of SWE for the snow
surveys ranged from 5.7 to 18.1 mm in 2013/2014 and 2.5 to 10.7 mm in
2014/2015. It should be noted that the final five mean SWE values for
2014/2015 include the addition of a shallow ice layer that was observed along
the soil surface, below the entire snowpack. The ice layer formed after a
warm period near the end of January 2015 and was present at each SWE sampling
location. The ice layer was too dense for the teeth of the snow tube to cut
through, and thus the depth of ice was recorded. An average ice layer depth of
1 cm was observed during the last five snow surveys. The ice water equivalent was
calculated from an assumed density of 0.916 g cm
Early in both winters (early November), the moderated neutron intensity decreased quite drastically in response to the first snow events of the season. These results are consistent with Desilets et al. (2010) who, although they did not have precipitation data, found that observed snowfall events caused quick decreases in moderated neutron intensity. The first cluster of precipitation events and first significant decrease in moderated neutron intensity in 2014/2015 (Fig. 2) represent rainfall events. The second distinct decrease in moderated neutron intensity, in late November 2014/2015, was caused by snowfall events. In Fig. 2, all of the precipitation events for 2013/2014 were snowfall events.
In general, moderated neutron intensity shows an expected negative
relationship with both precipitation events and SWE, resulting in decreased
moderated neutron intensity and increased mean SWE in response to
precipitation. A relatively strong negative correlation between mean SWE and
the moderated neutron intensity at the time of snow survey can be seen from
the Pearson's correlation coefficients
Moderated neutron intensity and snow survey SWE for 2013/2014 (top) and 2014/2015 (bottom). Precipitation sourced from SRC site and represents daily precipitation.
Simple linear regression was performed on the manually measured SWE values
and the corresponding moderated neutron intensity during the snow survey.
Initial regressions showed that both 2013/2014 and 2014/2015 had similar
slopes but quite different intercepts (Fig. 3). The difference in intercepts
was attributed to the differences in soil water storage in the upper soil
profile prior to snowfall. The previously mentioned calculated difference in
soil water storage in the top 10 cm of the soil profile of 23.8 mm was added
to the SWE values of 2014/2015 and linear regression was repeated. The added
soil water storage caused the intercept of the 2014/2015 regression line to
match more closely with the intercept for 2013/2014 as can be seen in Fig. 3.
This result indicates that the CRP reading is still being affected by water
present in the upper soil profile despite the presence of a snowpack. Thus,
knowledge of the initial or background soil water storage in the top of the
soil profile before each winter is important for predicting SWE from
moderated neutron intensity from year to year. However, the combined
measurement depth of the CRP in the snowpack and underlying soil is not fully
known. With no standing water covering the soil surface, the CRP measurement
depth is thought to range from 70 cm (dry soil) to 12 cm (saturated soil)
(Zreda et al., 2008). In pure water, Franz et al. (2012a) found the effective
measurement depth to be
Linear regression of 2013/2014, 2014/2015 with the soil water storage offset (blue), and 2014/2015 with no offset (grey). The red line is the linear regression for 2013/2014. The blue and grey lines represent the linear regressions for the 2014/2015 data with and without the soil water storage offset respectively. Error bars represent standard deviation of SWE.
Linear regression of 2013/2014 measured SWE and corresponding moderated neutron intensity. Error bars represent standard deviation of SWE.
The individual regression curve for the 2013/2014 data is shown in Fig. 4
with the best-fit linear regression equation for the data producing an
The CRP-estimated SWE from moderated neutron intensity measurements for both
2013/2014 and 2014/2015 winters are shown in Fig. 5. The 2013/2014 regression
equation was used to estimate SWE based on the moderated neutron intensity in
the form of
For both winters, the CRP-estimated SWE match the manually measured SWE well. Of course for 2013/2014 the manually measured SWE corresponds nicely to the CRP-estimated SWE since the regression equation from 2013/2014 was used for SWE prediction. The CRP-estimated SWE for 2014/2015 also agrees with manually measured SWE. The root-mean-square error (RMSE) and mean absolute error for the 2014/2015 CRP-estimated SWE is 8.8 and 7.5 mm respectively. These error results are comparable to Rasmussen et al. (2012), who found an RMSE of 5.1 mm between SWE estimated from snow depth and from a CRP. The 2014/2015 CRP-estimated SWE errors are considerably lower compared to other large-scale SWE measurement methods such as remote sensing. Large-scale (25 km resolution) remotely sensed SWE measurements using microwave radiation for the GlobSnow project (Luojus et al., 2010; Dietz et al., 2012) had RMSE values ranging from 24 to 77 mm when compared to snow courses.
Snowpack melt occurred during both winters, brought about by warmer temperatures and consistent solar radiation, with significant melts occurring in February 2014 and January 2015. The CRP-estimated SWE responded to the melt in February 2014 with a noticeable decrease at the end of January and early February (Fig. 5). However, the CRP overestimated SWE during the melt period in January 2015 (Fig. 5). In January 2015 the manually measured SWE was approximately 20 mm, while the CRP-estimated SWE was generally between 30 and 40 mm. In late January 2015 the CRP-estimated SWE did finally decrease with a corresponding decrease in manually measured SWE. This overestimation of SWE by the CRP during snowpack melt periods is likely caused by a significant portion of snowmelt water that is removed from the snowpack and deposited in or above the upper soil profile. Any snowmelt water that infiltrated or remained on the very top portion of the soil profile would affect the moderated neutron intensity, thus causing the CRP to estimate greater amounts of SWE.
CRP-estimated SWE and manually measured SWE for 2013/2014 (top) and 2014/2015 (bottom).
Desilets et al. (2010) also witnessed an overestimation of SWE by the CRP following a snowmelt period. Nearly all of the snowpacks they studied appeared to have melted close to the end of their winter study season followed by a large snowfall event causing a rapid increase in CRP-predicted SWE. Manual measurements of SWE around the CRP location gave a mean of roughly 25 mm, while the CRP-estimated SWE was around 55 mm (Fig. 2 in Desilets et al., 2010). This CRP overestimation of SWE could also be attributed to snowmelt water remaining in the top of the soil profile and decreasing the moderated neutron intensity.
The CRP-estimated SWE was also compared to estimated SWE from snow depth measurements at two different reference sites near the study site. The linear relationship between SWE and snow depth found by Shook and Gray (1994) was used to estimate SWE from point measurements of snow depth at the reference sites. The average SWE and snow depth from the 2013/2014 and 2014/2015 snow surveys followed the Shook and Gray (1994) relationship quite well (Fig. 6). Figure 7 contains the CRP-estimated SWE along with SWE estimated from the SRC and Saskatoon Airport RCS sites. As mentioned earlier, the SRC site is roughly 2 km away from the study site and the Saskatoon Airport RCS site is approximately 8 km away. The reference sites are similar to the study site in the way that all three are open areas containing few to no trees. The SRC site, located in the middle of an agricultural field (located within the city of Saskatoon) and nearest to the study site, is similar to the CRP location in terms of topography and the surrounding area. It is difficult to quantitatively compare the snow depth results to the CRP-estimated SWE since the two measurement sites are located some distance from the CRP and only a single point measurement was made at each of these reference sites. Thus, the snow depth measurements might not be accurate or spatially representative for SWE, but they do allow the examination of the snowpack dynamics in this region.
The average SWE and snow depth from the 2013/2014 and 2014/2015 snow surveys at the CRP study site. The black line represents the linear relationship between SWE and snow depth found by Shook and Gray (1994) for shallow (< 60 cm) snowpacks in the Canadian Prairies.
CRP-estimated SWE and SWE estimated from snow depth for 2013/2014 (top) and 2014/2015 (bottom).
Looking at Fig. 7, it can be seen that SWE dynamics for both winters at the SRC and Saskatoon Airport RCS sites are quite close to the CRP-estimated SWE. At the beginning of each winter SWE appears at very similar times at all three sites. Increases in SWE also appear at comparable times at all sites. The aforementioned melt periods in January and February of each winter appear more noticeable in the SRC and Saskatoon Airport RCS estimates than in the CRP estimates. In February 2014 it can be seen that the SRC-estimated SWE is consistently lower than the CRP-estimated SWE. Higher SWE at the study site could be attributed to increased accumulation of snow along the irrigation line in the centre of the CRP study site.
It is also interesting to note the late accumulation of snow near the end of March 2015. All three sites show an increase in SWE from the final snowfall event at the end of the winter in 2015. Despite all three sites being over 2 km away from each other and the strong spatial variability of SWE, the general trend is comparable signifying that the CRP is performing well in terms of estimating SWE.
In this study, the footprint of the CRP was assumed to be
A simple empirical equation for estimating SWE with the use of a cosmic-ray soil moisture probe was presented. It was found that the relationship between above-ground moderated neutron intensity and manually measured field SWE was well represented by a negative linear function. CRP-estimated SWE corresponded well with snow surveys performed inside the CRP's measurement footprint. SWE estimates based on snow depth measurements at two sites near the study site were also in accordance with the CRP-estimated SWE. Overall, the presented equation performed favourable with regard to providing an estimate of average field SWE at this agricultural study site.
There are several advantages associated with measuring SWE using a CRP. The
measurement footprint of the CRP (
One apparent limitation with using the CRP to estimate SWE arises from the occurrence of considerable snowmelt during the winter months. Significant snowmelt occurred in both of the studied winter seasons and both situations caused the CRP to overestimate SWE. Hydrogen molecules affect moderated neutron intensity, and thus any melted snow is still recognised by the CRP despite not actually representing snow (SWE) in the field. However, it appears that it requires substantial snowpack melt in order for the CRP to overestimate SWE.
Similar to the way the moderated neutron intensity is affected by snowmelt water, the CRP measurement is also influenced by the soil water storage in the top of the soil profile beneath the snowpack being measured. CRPs may overestimate SWE by measuring water in soil just below the snow cover. However, the overestimation may be advantageous in some cases because soil water in the surface soil is largely similar to SWE and controls snowmelt infiltration and surface runoff (Niu and Yang, 2006). Knowing the soil water storage in the upper soil profile is important when applying the presented empirical function at other sites. Differences in soil water storage in the top 10 cm of the soil profile between the two winter seasons in this study clearly showed the effect that water near the soil surface has on the CRP measurement. Therefore, it is important to have a measurement or estimate of the soil water storage in the upper soil profile before snowfall accumulation occurs. This measurement of soil water storage could be measured by the CRP if installed and calibrated before snowfall or in situ soil moisture probes could be used at the soil surface until freezing. Better understanding the depth to which water within the top of the soil profile affects the CRP reading when a snowpack is present should be looked at in future studies. Other future research should focus on assessing the performance of the empirical relationship at other sites similar to this agricultural study site as well as other forested sites with increased vegetation and snowfall interception.
We would like to thank NSERC, COSIA, the University of Saskatchewan, and
the China 111 project (B12007). We also would like to acknowledge the
Saskatchewan Research Council and Saskatoon Airport RCS for data. We thank
the Plant Science department at the University of Saskatchewan for allowing
the use of their research field. The NMDB database (