Calibration of a non-invasive cosmic-ray probe for wide area snow water equivalent measurement

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−0.90 (2013/2014) and −0.87 (2014/2015). A linear regression performed on the manually measured SWE and moderated neutron intensity counts for 2013/2014 yielded an r2 of 0.81. Linear regression lines from the 2013/2014 and 2014/2015 manually measured SWE and moderated neutron counts were similar; thus differences in antecedent soil water storage did not appear to affect the slope of the SWE vs. neutron relationship. The regression equation obtained from 2013/2014 was used to model SWE using the moderated neutron intensity data for 2014/2015. The CRP-estimated SWE for 2014/2015 was similar to that of the snow survey, with an root-mean-square error of 8.8 mm. The CRP-estimated SWE also compared well to estimates made using snow depths at meteorological sites near (< 10 km) the CRP. Overall, the empirical equation presented provides acceptable estimates of average SWE using moderated neutron intensity measurements. Using a CRP to monitor SWE is attractive because it delivers a continuous reading, can be installed in remote locations, requires minimal labour, and provides a landscape-scale measurement footprint.

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 measurement 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 10 and 2014/2015) in an area surrounding a CRP in an agricultural field in Saskatoon, Saskatchewan, CAN. The raw moderated neutron intensity counts were corrected for atmospheric pressure, water vapor, 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 15 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 −0.92 (2013/2014) and −0.94 (2014/2015). A linear regression performed on the manually measured SWE and moderated neutron intensity counts for 2013/2014 yielded an r 2 of 0.84. Linear regression lines from the

Introduction
Landscape-scale snow water equivalent (SWE) measurements are important for ap- 5 plications such as hydrological modeling, 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 impor- 10 tant 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 method for determining SWE and although it provides a point measurement, can be used to survey a larger area. However, snow surveys with snow 15 tubes are labour intensive and can be difficult to perform in remote locations. Snow pillows can provide SWE measurements in remote locations, but produce merely a point measurement of roughly 3.5 to 11.5 m 2 (Goodison et al., 1981). In addition, snow pillows do not accurately measure shallow snowpacks due to snow removal by wind transport and melting (Archer and Stewart, 1995). Remote sensing has the capabil- 20 ity of measuring SWE at large scales based on the attenuation of microwave radiation emitted from Earth's surface by overlying dry snow (Dietz et al., 2012). The applicability of remote sensing techniques for SWE monitoring is limited by their coarse measurement resolutions (∼ 625 km 2 ), their inability to accurately measure wet snow, and their shortcomings in measuring forested landscapes. 25 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  (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.

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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).

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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. 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 15 of hydrogen (H). The CRP is an appealing soil water content measurement tool for several reasons. Firstly, it has a measurement area of ∼ 300 m radius, which helps to fill the gap in scales between that of the point measurements and landscape-scale remote sensing. Secondly, it measures soil water content passively (non-radioactive) and non-invasively (CRP sits above the soil surface). Thirdly, the CRP can be deployed 20 easily in remote areas. Lastly, it provides a continuous measurement of average soil water content, often with a temporal resolution of one hour. The CRP measurement is based on the moderation of neutrons by hydrogen in water, therefore it is also capable of measuring neutrons moderated by the hydrogen in snow, i.e. frozen water.
The possibility of measuring SWE from the moderation of neutrons by snow has 25 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 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 utilized 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. 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 measure-15 ments using 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, providing the ensuing results discussed herein. is mostly free from trees and vegetation except for a small cluster at its south edge and the crop stubble that was left after harvest in the fall of each study year. The same study site was used for both (2013/2014 and 2014/2015) winter field seasons. Wheat stubble (height ∼ 20 cm) was present on the field for the 2013/2014 winter, and canola stubble (height ∼ 25 cm) for the 2014/2015 winter. Also, a set-move wheeled irrigation line was 5 located across the center of the field during the 2013/2014 winter causing increased snow accumulation, but the irrigation line was removed before the 2014/2015 winter.

CRP and background water content
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 re-10 mote data access. One of the detector tubes is shielded (or moderated) to measured 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 H, but also other neutron absorbing elements in soil such as 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 each of 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  (Franz et al., 2012b). Volumetric water content was measured from the cores via the oven-drying method (Gardner, 1986). 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 was collected from a Saskatchewan Research Council (SRC) 5 climate station (52.1539 • N, −106.6075 • W) located near the study site. Rainfall events recorded after soil sampling, but before the appearance of the snowpack, were added to the antecedent soil water storage. It was assumed that all of the water from rain events before snowfall entered the soil and evapotranspiration was negligible due to the low air temperatures. The soil water storage in the top 10 cm of the soil profile was 2.15 cm in 2013 and 4.53 cm in 2014, creating a difference of 2.38 cm in water storage between the beginnings of the 2013 and 2014 winters.

Raw moderated neutron correction
Before further analysis of the hourly neutron count rates from the CRP, the raw neutron counts must be corrected for differences in air pressure, atmospheric water vapor, 15 and the temporal variation of incoming cosmic ray flux. Corrected neutron counts are attained from multiplying the raw counts by correction factors: where N COR is the corrected moderated neutron count, N RAW is the raw moderated neutron count, F p is the air pressure correction factor, F w is the atmospheric water 20 vapor correction factor, and F i is the variation of incoming cosmic-ray flux correction factor. 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). F p is calculated with the following equation: where e is the natural exponential. P is the measured air pressure (hPa) at the site during the moderated neutron count time. Air pressure was measured near the CRP using a WeatherHawk 232 Direct Connect Weather Station (WeatherHawk, UT, USA). P 0 is a reference air pressure chosen to be 1013 hPa (average sea-level air pressure). L represents the mass attenuation length (g cm −2 ), which is a function of latitude and 5 atmospheric depth (Desilets and Zreda, 2003). The mass attenuation length for Saskatoon was found to be 130.24 g cm −2 .
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 vapor. Rosolem et al. (2013) found the following correction function for 10 atmospheric water vapor: where p v0 is the absolute humidity (g m −3 ) at the site during the measurement time. p ref v0 is the reference absolute humidity and was set to that of dry air (0 g m −3 ). Relative humidity and air temperature, which are both used to calculate absolute humidity, were 15 measured at the site using the WeatherHawk weather station. 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: where N avg is the average neutron monitor count rate during the study period and N nm is the specific hourly neutron monitor count rate at the time of interest. Data from the neutron monitor at Fort Smith ( Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | data was scaled relative to high latitude sea level (HLSL). A publically accessible online neutron flux scaling calculator (http://www.seutest.com/cgi-bin/FluxCalculator.cgi) was used to scale the Saskatoon site based on the latitude, longitude, and elevation. The calculated scaling factor for the study location was 1.59. The corrected moderated neutron counts were then multiplied by the scaling factor and averaged over 7 h.

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A seven-hour running average was used for the moderated neutron intensity counts in order to reduce the inherent noise of the hourly moderated neutron data and reduce measurement uncertainty, yet still allow responses to precipitation events to be observed (Zreda et al., 2008). away from the CRP. The sampling radials are unevenly spaced away from the CRP to allow for the calculation of a simple arithmetic mean of SWE based on the non-linear decreasing sensitivity of the CRP with increasing distance away from the probe (Zreda et al., 2008). Snow cores were collected for SWE using a Meteorological Service of Canada (MSC) snow tube with an inner diameter of 7.04 cm. The cores were carefully 20 transferred to plastic bags, sealed, and transported to the lab for processing. The depth of snow was measured in situ at each sampling location during the snow survey.

Snow depth data
Snow depth data from two reference sites were used for comparison to the snow surveys and CRP data. These were the SRC site and Saskatoon Airport Reference Cli- 8.2 km from the CRP. At both reference sites, snow depths were measured using a SR50 Sonic Ranging Sensor (Campbell Scientific, Canada). Manual readings with measuring sticks were also performed occasionally at the SRC site. 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 5 (less than 60 cm) in the province of Saskatchewan over 6 years and found the following linear relationship for predicting SWE from snow depth: where D is snow depth in cm and SWE is in mm. Equation (5) was used to estimate SWE using the snow depth data from the two reference sites. Although the SRC and Saskatoon Airport RCS sites are located a few kilometers away from the study site, comparing estimated SWE from these reference sites to SWE estimated from the CRP is still useful if we look only at the overall trend of snow accumulation.  The ice layer was too dense for the teeth of the snow tube to cut through, thus the depth of ice was recorded. An average ice layer depth of 1 cm was observed during the last 5 snow surveys. The ice water equivalent was calculated from an assumed density of 0.916 g cm −3 , found by Hobbs (1974) to be the average density of ice. A value of 9.2 mm was then added to the mean SWE measured during the final 5 snow surveys 5 of 2014/2015. 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 did not have precipitation data, found that observed snowfall events caused quick decreases in moderated neutron 10 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. 15 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 −0.92 20 and −0.94 for 2013/2014 and 2014/2015, respectively. These correlations show there is potential for predicting SWE from moderated neutron intensity measured above the snowpack. 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 ∼ 58 mm (i.e. the CRP measurement becomes saturated when more than 58 mm of water is above the soil surface. The effective measurement depth is considered the depth at which 86 %

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(two e-folds) of the measured neutrons originate assuming an exponential decrease in neutron intensity with depth. In our case, we observed a CRP response to SWE values of greater than 70 mm, when including antecedent soil water in the upper soil profile, during the 2014/2015 winter. Since snow is substantially more porous and has a lower density than liquid water, neutrons may be able to penetrate deeper in snow 20 packs (> 58 mm) and interact with the water near the soil surface when the snow pack is shallow. After correcting for soil water storage, the 2013/2014 and 2014/2015 manually measured SWE and moderated neutron intensity values were combined to form one dataset and simple linear regression was completed. Figure 3 (1979) found and employed for estimating SWE from moderated neutron intensity. An exponential curve was fit to the 2013/2014 and 2014/2015 combined data, but the r 2 was not improved drastically compared to the linear regression, thus the simpler linear regression was used for modeling SWE from moderated neutrons. The error bars in Fig. 3, representing standard deviation of manually measured SWE, generally over- The root-mean-squared error (RMSE) and mean absolute error for the 2014/2015 CRPestimated SWE is 7.7 and 6.7 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. 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). How-15 ever, 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 pe-20 riods 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 the very top portion of the soil profile would affect the moderated neutron intensity, thus causing the CRP to estimate greater amounts of SWE. Desilets et al. (2010) also witnessed an overestimation of SWE by the CRP following 25 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.

CRP and snow depth estimated SWE
The CRP-estimated SWE was also compared to estimated SWE from snow depth 5 measurements at two different reference sites near the study site. Figure 6 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 little 10 to no trees. The SRC site, located in the middle of an agricultural field and nearest to the study site, is very similar to the CRP location in terms of topography and the surrounding area. It is difficult to fully compare the snow depth results to the CRPmodeled 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. 15 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. Looking at Fig. 6, it can be seen that the overall trend SWE for both winters at the SRC and Saskatoon Airport RCS sites is quite close to the CRP-estimated SWE. At the beginning of each winter SWE appears at very similar times at all three sites. In-20 creases 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 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.

Conclusions
A simple empirical equation for estimating SWE with the use of a cosmic-ray soil mois-5 ture 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 10 with the CRP-estimated SWE. Overall, the presented equation performed favourable with regards 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 (∼ 300 m radius) is appealing since it provides a 15 measurement scale between that of the point scale (snow tubes, snow pillows) and large scale (remote sensing). The CRP can be installed in remote locations where consistent snow surveys are not possible. It is far less laborious to estimate SWE passively using the CRP than to conduct field-scale snow surveys. Also, the CRP can provide a continuous estimate of SWE throughout the winter season. 20 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, thus any melted snow is still recognized 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 5 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 10 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 15 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.