Gamma radiation for the estimation of mineral soil water content in a boreal forest

Abstract Continuous monitoring of water quantities in different soil horizons is necessary to understand the behavior of infiltrated water in the soil. Under certain conditions, using measurements of natural ground gamma radiation can help us estimate soil water content measurements over a 100 m2 surface within a 15 cm depth. A CS725 sensor can provide up to four daily estimates of soil water content by detecting the natural emission of gamma radiation. However, in boreal forest environments, gamma radiation mitigated by the water in the thick humus layers (litter, fermented, and humic horizon) can bias the underlying mineral soil water content measurements. The objective of this research was to evaluate the accuracy of methods that incorporate variables describing the surface humus layer into calculations of the underlying mineral soil water content, by measuring the soil’s natural gamma emission with the CS725. Using raw gamma radiation values obtained by CS725 sensors deployed over various boreal soils, we tested two functions. The first one included variables describing the humus layer and the other excluded these variables (manufacturer’s method). The function that included the descriptive humus layer variables showed superior results compared to the function without. The results of this study suggest that the CS725 sensor can adequately estimate mineral soil water content within ±10% absolute of the reference water content when examined with the following humus variables: humus layer thickness, fractioned composition, bulk density, and linear gamma radiation attenuation.


Introduction
The majority of rainfall infiltrates the ground, recharging ground and surface water.The water that transits through soil layers plays an essential role in the water cycle and as such, knowledge about its temporal evolution is essential for various anthropic uses, such as hydro-electricity production.Several direct and indirect methods are used to measure the water content in soils.The manual gravimetric method and automatic time-domain reflectometry (TDR) probes can provide direct information on the water content of a microsite, while remote sensing tools such as microwave sensors and radar can indirectly provide information on the potential capacity of a site to retain water (Quinones et al. 2003;Kemppinen et al. 2018).An alternative technique for measuring certain soil properties, such as water content, is to monitor the gamma radiation that is naturally emitted by the ground.Using either small laboratory samples or large airborne surveys, gamma radiation capture has proven successful for providing soil water content (SWC) measurements (Beamish 2013;Celik et al. 2016).
The estimation of snow water equivalence (SWE) and SWC is possible due to the attenuation of gamma radiation caused by the presence of water between the emitting source and the measurement device.In fact, the radiation emitted by the mineral soil can only be attenuated by the water in the soil or on the surface (snow).Based on this information, the Gamma MONitor was developed and is now commercially available from Campbell Scientific under the name CS725.Mounted 2-3 m above the ground, the CS725 sensor captures continuous gamma radiation from a 100 m 2 area and obviates the need for medium-scale detection devices.Patented by Hydro-Quebec, the device is now deployed over a large network, improving watershed hydrological predictions (Wright 2011).
As Quebec's principal bioclimatic domain, the boreal forest covers more than a third of the landscape (MRNF 2021).The dense coniferous stands that comprise these forests play a key role in the hydrological processes of a variety of Quebec's watersheds.For this reason, the water cycle in this cold, wet biome is particularly important, especially at the watershed level, as many cities and communities depend on the water that comes from these watersheds.
Boreal forest conditions generate heterogenous soil profiles where pedogenetic processes favor the accumulation of a thick humus layer over the podzolized mineral soil (Mcclaugherty and Berg 2020).In this paper, the term humus is used to refer to the organic horizon LFH (litter, fermented, and humic).Humus is composed of organic material and its thickness can vary.This upper layer can consist of up to 90% water, while the mineral material layer can be up to 40% water, at most (Beamish 2013).Because it lies directly between the emission source and the gamma radiation measurement sensor, this wet humus layer attenuates gamma radiation.A failure to consider this additional attenuation of radiation that comes from the underlying mineral soil can result in a significant overestimate of the water content in that layer.This will inevitably lead to a bias in mineral SWC measurements, especially since the humus layer above acts as an absorber of radiation and not an emitter (Reinhardt 2019).Therefore, the objective of this research was to evaluate the likelihood of measuring accurately the mineral SWC over a given area (100 m 2 and within a 15 cm depth) using the CS725 sensor.

CS725 sensor
The CS725 sensor continuously counts gamma radiation and produces a cumulative count every 6 h.Each of these counts cumulates the gamma radiation captured during the previous 24 h.This internal calculation is mostly intended to reduce the temporal variability in the SWE measurements.The device is composed of a cylindrical Nal(Tl) crystal that multiplies the gamma rays naturally emitted by radioactive atoms in the soil.The atoms of interest are potassium-40 ( 40 K) and thallium-208 ( 208 Tl).The peak energy for these elements is 1.46 and 2.62 MeV, respectively.Radiation attenuation that is caused by the water, snow, and air between the source of emission (mineral soil) and the detector allows us to measure SWE in winter or SWC in the absence of snow cover (Ducharme et al. 2015).Figure 1 shows the CS725 as mounted at a typical measurement site.

Humus layer gamma radiation attenuation
The absorption of a monochromatic point radiation source through a homogeneous material is given by the following Beer-Lambert law (Beamish 2013): where I 0 is the initial radiation intensity, β is the effective linear attenuation coefficient (cm −1 ) of the absorber, and x is the thickness (cm) of the absorber.Beamish (2013) suggested that the linear attenuation of a heterogenous material, for instance humus layer, should be taken into account by including the three phases involved: solid, water, and air.Using eq. 1 and the adaptation of β based on the natural composition of the humus layer, gamma radiation absorption of this combination of materials can be given by eq. 2 (Beamish 2013): where I 0m is the radiation intensity at the organic and mineral soil cross section and the linear attenuation coefficient (β) and the fraction (θ ) of the solid (s), water (w), and air (a) are also considered.
To standardize the CS725 radiation count treatment, different theoretical values were used, including both gamma ray  1.The values presented for each of the soil properties (fraction and specific density) are those that were most found at the study sites that were visited during this research.

Device calculations
The CS725 sensor is programed to generate SWE and SWC measurements by using internal calculations that are consistent with the Beer-Lambert law.SWE and SWC equations are given by Choquette et al. (2013) and the device manufacturer (Campbell Scientific Canada 2020).The SWC equation is de- rived from the following SWE equation: where β is the effective linear attenuation coefficient (cm −1 ) of water that varies with snowpack, SWC is soil water content (g/g) set to a constant value under a 20-30 cm snowpack, N is the measured radiation count, and N 0 is the radiation count of dry soil (Choquette et al. 2013).One major challenge associated with this method is that in the field, there are rarely any opportunities to capture the radiation emitted by completely dry soil.This is because most areas are subject to sporadic rainfall events.Conditions are much more likely to reflect the amount of water content that is in the range between field capacity and wilting point (Huang et al. 2016).Choquette et al. (2013) and the CS725 manufacturer suggest that during times when there is no snow cover, β is a constant value and SWE = 0.During these conditions, SWC is calculated using eq.4: As mentioned, N 0 and N represent the 40 K or 208 Tl radiation count over a 24 h period.As separate gamma radiation emitters, 40 K and 208 Tl can each potentially provide SWE and SWC calculations.To date, eq. 4 has only been used for SWC measurements via CS725 gamma radiation capture without considering for the distinction between humus and mineral matter.

Soil water content adjusted for the presence of humus
To achieve our objective, we adjusted eq. 4 for the unique pedological situation associated with boreal forest sites and the humus layers of varied thickness that characterize these forests.This humus layer releases minimal gamma radiation and absorbs much of the radiation coming from the lower soil layers (Reinhardt 2019).Equation 5 considers the attenuation of gamma radiation that is induced by the humus layer.Here, SWC is what we are solving for and SWE is replaced by the humus layer water equivalence (HWE): where HWE is given by In eq. 5, it is clear that the Beer-Lambert law is applied to N 0 .Next, each of the three constituents of the humus layer (soil, water, and air) that affect the radiation attenuation is given by eq.7: The water content of the humus layer was considered constant over time and θ values for the water, air, and solid portions from Table 1 were used.The linear attenuation coefficients (cm −1 ) used in eq.7 were given by the product of the mass attenuation coefficients (cm 2 /g) and the specific densities (g/cm 3 ) listed in Table 1.

Dry soil gamma radiation (N 0 )
To determine the N 0 value, we used eq.8, proposed by Choquette et al. (2013) and the CS725 manufacturer.N 0 was then calculated using the following equation: where N i is the measured radiation count and SWC i is the mineral soil water content (g/g) at the time of measurement i (section 2.10.).
Taking into account the upper humus layer water content, N 0 was calculated using eq.9: where θ s0 , θ w0 , and θ a0 are, respectively, the fraction occupied by solid material, liquid (water), and air in the humus layer at field capacity.Based on the values recorded at one of the study sites that was sampled over several snow-free months, the values were set to the following: θ s0 = 0.07, θ w0 = 0.27, and θ a0 = 0.66, where the void ratio is set to 0.93 (Rawls and Brakensiek 1989).To obtain the SWC i , several manual measurements were made at the time of deployment of the CS725.Also at this time, a manual measurement function on the sensor made it possible to determine N i .Using eq. 9, these measurements allowed calculation of site specific N 0 .

TDR probes
To determine the reference humidity of the mineral soil, we used TDR probes.The CS616 model, manufactured by Campbell Scientific, was used.These probes are composed of two 30 cm long stainless-steel rods that were used to measure the water content in the top 30 cm of mineral soil.To do so, the humus was removed to allow the probes to be inserted vertically into the first 30 cm of mineral soil prior to replacing the humus.This is unlike to the CS725 sensor, which measures the water content in the top 15 cm layer of soil (Ducharme et al. 2015).Measurements from the vertically placed TDR probes could be representative of the CS725 readings that are hypothetically derived from radiation originating from several distinct soil horizons on above and below the 15 cm probe depth.Previous experiments that compared the estimates of SWC from the CS725 sensor and TDR probes demonstrated a higher correlation when the probes were placed vertically (0-30 cm) compared to horizontally at varying depths (10, 20, and 30 cm) (M.Gélinas, unpublished manuscript, 2021).
The volumetric SWC (cm 3 /cm 3 ) (SWC v ), as measured by the TDR probes, is calculated using the time elapsed between the emission of an initial electromagnetic pulse from one rod and the measurement by the second rod.The theory behind the design of this tool is that the emitted signal can be attenuated depending on the number of ions present in the soil solution (Campbell Scientific Canada 2020).The TDR probe manufacturer provides two equations for the conversion of the elapsed time to volumetric water content.The choice of which equation to use was based on the water content range being measured.The texture of the mineral soils that we an-alyzed was typically a sandy loam and the volumetric water content was generally between 10% and 40%.Therefore, according the manufacturer's suggestions, we used the following equation: SWC V = −0.0663− 0.0063 × P + 0.0007 × P 2 (10) where P is the elapsed time (μs) (Campbell Scientific Canada 2020).This equation allows us to estimate the reference water content of a given soil with a certain offset.Vaz et al. (2013) determined the accuracy of this tool to be within ±0.025 cm 3 /cm 3 and discrepancies are attributable to the effects of salinity, soil temperature, and soil texture variations.To measure the reliability of the probes used in our work, TDR probe readings were compared to the reference SWC of the corresponding microsite using the method described below.It was therefore assumed that the arithmetic mean of the TDR values within 100 m 2 best represented the CS725 readings.
To cover an approximate 100 m 2 area below the CS725 sensor, we deployed seven probes in the footprint underneath the device.This allowed us to obtain an estimate for the reference SWC in the mineral soil in that area.Probe dispositions are illustrated in Fig. 2.
As illustrated, four probes were positioned between 2 and 5 m from the CS725 sensor where about 65% of the radiation is received by the sensor when mounted at 2.5 m above the ground (Campbell Scientific Canada 2017) The reference daily mineral SWC was obtained by averaging the readings of the seven probes.This indirectly accounts for the spatial variation of SWC caused by microtopography and other factors.In addition, to capture variations in humidity within a single day, the daily reading was calculated from the average of the previous 24 hourly readings.

Mineral soil water content conversion
Unlike more direct SWC measurement tools, the CS725 sensor measures water content based on raw gamma radiation data by mass (g/g) even though volume-based data from the CS725 sensor are sometimes preferred, especially for easier integration into water supply prediction models.Therefore, we converted the mass output to volumetric SWC to allow for more direct comparison with the TDR probe measurements.To accomplish this, we used eq.11: where SWC v is the volumetric soil water content (cm 3 /cm 3 ), SWC is the mass soil water content (g/g), and ρ is the mineral soil bulk density (g/cm 3 ).For this calculation, we used a theoretical mineral soil bulk density of 1.26 g/cm 3 (Beamish 2013).

Method comparison
To determine the relevance of incorporating variables that describe the humus layer into the mineral SWC measurements, two different methods were compared: one that uses eqs. 4 and 8 (fabricant method) and one that uses eqs.7 and 9.By comparing a method that includes variables describ- ing the humus layer such as thickness, fractioned composition, bulk density, and linear gamma radiation attenuation with a method that does not incorporate these variables, we were able to determine the relevance of these characteristics.

Sites
Six boreal forest study sites with different pedological properties were chosen with specific attention paid to humus layer thickness.The intent was to deploy the device at sites with various humus thicknesses over the mineral soil.All study sites were in the Montmorency Forest, about 100 km northeast of Quebec City.The Montmorency Forest is the teaching forest of Laval University, where several research projects take place.This research area has allowed simplified access to the research sites.In addition, to limit operational constraints, the chosen sites were easily accessible, being close to a forest road and all located within a 10 km radius.The total precipitation (solid and liquid) received annually in the Montmorency Forest is higher than the provincial average.In fact, province-wide, total annual precipitation generally reaches 1000 mm, whereas the Montmorency Forest received an annual average of 1544 mm between 1981 and 2010 (MELCCFP 2023).Table 2 outlines the details of and pedological distinctions between each site.
The Tourbière site stood out from the others as it had the thickest humus layer.At this site, we were able to evaluate the different methods on a totally organic soil that generates poor 40 K and 208 Tl radiation (Reinhardt 2019) by inserting the TDR probes in the top 30 cm of the organic soil.
The Romaine site also had a considerable humus layer thickness (30 cm) above the mineral soil.It had a low N i K and N i Tl compared to the other mineral sites due to the radiation attenuation caused by the low hydraulic conductivity of the thick upper humus layer (Letts et al. 2000).
The pedological characteristics of the four other sites were relatively similar.

Manual measurements
At each site, 12 mineral soil samples (10-20 cm deep) were collected and used to determine the initial SWC via the gravimetric method (Barry et al. 2009).These samples were obtained using copper cylinders about 10 cm high and with known volumes.Recording the original volume of the sample made it possible to calculate the bulk density and the initial SWC (cm 3 /cm 3 ).The manually measured SWC averages were then used to adjust the readings of the TDR probes.The adjustment value is identified as δ (cm 3 /cm 3 ).

Performance evaluation
The performance of mineral SWC measurement methods was assessed using the Kling-Gupta efficiency (KGE) measure.This is often used in hydrological sciences to evaluate the similarity between observed and simulated values (Gupta et al. 2009).In our study, TDR probe data (reference water content) were the observed values and the equation outputs were the simulated values.The KGE measure provides the Euclidean distance between a model of interest and an exact prediction within a three-dimensional space.The three axes bounding this space are the Pearson correlation coefficient I, conditional bias (α), and systematic bias ( x).A perfect model would result in a value of 1 for all three axes and represent a Euclidean distance of 0. Therefore, a KGE measure equal to 1 indicates perfect similarity between the predicted and observed values.According to Gupta et al. (2009), the KGE can be calculated with the following equations: where y i is the ith observed value, y is the simulated value, and ȳ is the mean of the observed values, and

Results and discussion
Gamma ray attenuation within a given soil profile was theoretically evaluated using the Beer-Lambert law (eq.1). Figure 3 illustrates the attenuation of gamma radiation as it exits from different soil column depths and water content levels calculated with eq. 1.The emission from each cm of soil was assumed to be constant.
The use of eq. 1 suggested that a 20% water content mineral soil (thickness = 25 cm) combined with an upper 70% water content humus layer (10 cm) absorbs 90% of the radiation emitted at a depth of 25 cm.Without the humus layer, the same absorption was obtained at 30 and 35 cm of depth for moist mineral soil (SWC = 20%) and for dry mineral soil (SWC = 0%), respectively.These values may explain why the CS725 is mainly able to read the water content of the first few horizons of mineral soils (<30 cm).Radiation produced at depths of more than 40 cm, for any water content condition, is almost completely absorbed by the overlying soil.

TDR probe values
Figure 4 demonstrates mineral SWC readings (0-30 cm depth) from TDR probes at the Bouleau site through summer 2022.Only six probes are presented.The values generated by the seventh probe were below 0 and consequently unreliable.These data have therefore been omitted.
As expected, the parallelism between the different TDR readings indicates similar reactions to SWC variations from one probe to another.We averaged the six probe readings to generate the TDR mean.Similar to the vast majority of hydrological measurement tools, we had to apply a calibration to obtain values closer to the true SWC.Table 3 shows the adjustments for each site that were applied to the TDR mean to obtain Adj.TDR mean.The manual measurements were also used to calculate a 95% confidence interval around the Adj.TDR mean.This interval is represented by the pink shading.With the adjustment applied, the Adj.TDR mean was considered accurate enough for subsequent comparisons with the CS725 data.The Adj. TDR mean was therefore used as the reference SWC for subsequent comparisons.

Dry soil gamma radiation (N 0 )
The potential gamma radiation of a given site varies according to several soil characteristics (texture, water content, and humus thickness).It was therefore necessary to calculate the potential radiation for each site in the absence of water attenuation (N 0 ) using eqs.8 and 9. Table 4 presents the results obtained using the two proposed methods of calculation.
The radiation count detected by the device at the time of manual measurement (N i ) is systematically lower than the dry soil radiation count (N 0 ), for each site.This was expected since N 0 considers the attenuation of the water contained in the mineral soil.It is also interesting to note that the N 0 calculated from eq. 8 is lower than the N 0 from eq. 9.This is likely because eq. 9 considers not only the water contained in the mineral soil, but also in the upper humus layer.

CS725 soil water content estimation
Increases and decreases in SWC following rain/drought events were identified by the 40 K and 208 Tl counts captured by the CS725 sensor.For example, Fig. 5 shows the temporal SWC variations calculated at the Bouleau site during the studied period.
The month of July 2022 was particularly wet compared with the normal recorded between 1981 and 2010.At the Forêt Montmorency provincial station, 185 mm of rain fell during July 2022, compared to the normal 142 mm.The same was true for the months of May to September 2022, where 638 mm of rain fell compared with the normal 560 mm (MELCCFP 2023).
The periods during which the 40 K and 208 Tl curves increase and decrease match the different precipitation events.On the other hand, Adj.TDR mean showed very poor response to precipitation events and was particularly noticeable with the Fig. 3. Attenuation of gamma radiation through mineral soil for different soil water content (SWC).The SWC was calculated with the Beer-Lambert law (eq.1) and the emission from each cm of soil was assumed to be constant.HWE, humus layer water equivalence.Fig. 5. Mineral soil water content variation estimated with the CS725 data at the Bouleau site through summer 2022 precipitation events.These estimations were obtained via potassium (K) and thallium (Tl) gamma radiation.Two methods were compared, one without humus variables consideration (eq.4) and another one with humus variables (eq.7).Adj.time-domain reflectometry (TDR) mean represents the mean of the TDR probe readings inserted vertically under the CS725's effective area.
mid July rainfall.This was observed for both the scenarios with and without the water contained in the humus layer.
The poor response of Adj.TDR mean to precipitation events caused the temporal variation of the SWC calculated with the CS725 data to be greater than the variation obtained from the Adj.TDR mean.This led to a significant difference between the variation of the reference humidity and the results obtained using eqs. 4 and 7.
Although the SWC calculated with eqs. 4 and 7 tended to overshoot the Adj.TDR mean confidence interval (pink shading), the estimated SWC values were not that different from each other.The main difference observed in Fig. 5 between outputs from eqs. 4 and 7 is that when the humus is considered (eq.7), the SWC in the mineral soil from CS725 measurements is lower.These same observations were valid for all study sites.

Performance evaluation of the equation that does not include variables describing the humus layer
To date, the only equation for calculating mineral SWC with the CS725 is eq.4, proposed by Choquette et al. (2013) and the CS725 manufacturer.The performance evaluation for this method for each of the research sites is presented in Table 5.
Using 1 ± 0.2 as an accurate KGE value, results were weak for all study sites.The performance was weak for the KGE values for both 40 K and 206 Tl radiation.These results were mainly due to the large difference between the standard deviation of the Adj.TDR mean and eq. 4 output, which resulted in α values that were significantly higher than 1.However, the Pearson correlation coefficients (r) and the ratios of means ( x) positively affected the KGE values and were approximately within 1 ± 0.2.The performance of eq. 4 for the Tourbière site was not significantly different from the performance at the other sites.To measure SWE correctly, the CS725 manufacturer suggests that the radiation count from potassium and thallium be over 96 000 and 9600, respectively.Unfortunately, the radiation at the Tourbière site did not meet those requirements (Table 4) (Campbell Scientific Canada 2017).The results observed may be due solely to the very low emission at this site.
The Romaine site stood out from the other sites, with the lowest KGE values due to the high α, but also due to the low r and β.As previously mentioned, the CS725 sensor measures the water content in only the top 15 cm of soil (Ducharme et al. 2015).Furthermore, this site is covered by a thick layer of humus (30 cm), which contains water that depletes the gamma radiation.Consequently, very little gamma radiation originating from the lower mineral soil reaches at the surface (N i ,Table 2).These factors may explain why the sensor was unable to measure mineral SWC accurately below the 30 cm thick humus layer present at that site.
The α values obtained for the other four sites (Épais, Roche, Bouleau, and Tour) were better than those for Romaine and Tourbière, as they were closer to 1.However, at these sites, the standard deviation of the measured SWC in the mineral soil using eq. 4 was considerably greater than the Adj.TDR mean standard deviation (α ≥ 2.22).For these four sites, significant Pearson correlation coefficients (r) were obtained (≥0.79), suggesting a strong association between the eq. 4 results and Adj.TDR mean.Furthermore, the ratio of the means for these sites were close to 1, indicating that despite the large standard deviation, eq. 4 generated consistent water content values for the Épais, Roche, Bouleau, and Tour sites.

Performance evaluation of the equation that includes variables describing the humus layer
Equation 7 included the variables that describe the humus layer in the SWC calculation.Its performance evaluation for each of the research sites is presented in Table 6.
The KGE test indicated that the output from eq. 7 produced poor results.The stated eq. 4 observations were valid, meaning that the low KGE values were attributable to differences in standard deviations (α), r and x positively affected the test.The similar patterns of the graph lines in Fig. 5 indicate very strong similarities between the r and α values between the two methods (eqs. 4 and 7).For all sites, the correlation coefficient r remained the same and α was slightly closer to 1.The x values were closer to 1 for all sites compared to those obtained via eq. 4.This indicates that the use of eq.7 reduces the ratio of means and suggests that this approach provides water content readings that are more accurate compared to the Adj.TDR mean.
The performance of this method at the Tourbière site was not evaluated because the TDR probes were installed in the organic soil.These data were therefore irrelevant for use with eq.7 for comparison purposes.Moreover, at such highly organic matter sites, the mineral soil underlying the thick organic soil is likely to be often saturated.The Romaine site generated weak results for the two variables in the KGE test (α and r).However, x improved significantly with the use of eq.7 compared to eq. 4.
The performance of this method (eq.7) at the other sites (Épais, Roche, Bouleau, and Tour) was slightly better than the method proposed by the manufacturer (eq.4).This improvement was illustrated by a reduction in the ratio of standard deviations (α) and means (x).However, similar to the results from eq.4, the overall observations indicate that the standard deviation of the results from eq. 7 is higher than that of the Adj.TDR mean, the correlation coefficients are all higher than 0.79 and the ratio of the means are close to 1.
Measuring the temporal evolution of SWC over a large area (100 m 2 within a 15 cm depth) increases our knowledge of the movement of infiltrated water and improves our ability to manage our water resources.An accurate estimate of the quantity of water in the surface layer of soils and the temporal variability is essential information.However, these estimates inevitably involve uncertainties, both spatially and temporally.As such, SWC estimated using the CS725 sensor could improve water resource management.Whether or not variables describing the humus are considered, it is possible to estimate the water content of the mineral soil by processing the raw gamma radiation captured by the CS725 sensor.This can be done accurately ( x = 1.00 ± 0.10), but with varying degrees of precision (α and r).This varying precision is expected given the high spatial variability of the SWC within the area covered by the CS725 sensor, especially given that Table 6.Performance evaluation for eq.7 against reference soil moisture.this area can be up to 100 m 2 .This spatial scale can be considered an asset for the use of CS725, as the eventual interpolation based on a CS725 network would be more reliable compared to small-scale measurement tools such as TDR probes.

Integration of humus variables
Including variables that describe the humus layer appears to improve the estimation of SWC in the mineral soil.Based on our results, this was true for sites with less than 10 cm of humus.For sites with a high accumulation of organic matter on the surface of the mineral soil (≥30 cm), taking the water content in this thick humus layer into account makes it possible to get consistent SWC in the mineral soil values.However, these estimates are less accurate than sites with under 10 cm of humus.This could be due to the uncertainties in N 0 estimations caused by potentially inaccurate theoretical values (Table 1).Increasing the thickness of the organic matter gives more weight to these values, which may in turn make N 0 less accurate.Therefore, for sites with humus layers that are less than 10 cm thick, the N 0 estimate is more accurate and provides a better estimation of lower mineral SWC.

CS725 data adjustments
SWC can be estimated automatically using a variety of sensors.While the sensors have different spatial and temporal characteristics, they all have something in common: they must first be adjusted according to the specific soil properties of each site (Dong 2014;Campbell Scientific Canada 2020).These pedological and physical properties are obtained by following the manufacturer's instructions and can be used to determine the bulk density, texture, and fraction of each of the three phases of the soil (solid, liquid, and air).The CS725 data require this adjustment procedure to estimate adequately SWC.The methodology used in our study allowed us to obtain this information by analyzing several samples of humus and mineral soils, collected manually at the study sites.This approach is often recommended in the operating manuals for sensors such as the CS725 (Campbell Scientific Canada 2017).The soil properties that are required to estimate SWC with the CS725 sensor are described in Table 7.The humus layer properties are only required for the method that considers these variables, and the mineral soil bulk is optional.
With the exception of the linear attenuation coefficients, the soil properties that describe humus and mineral soil are spatially heterogeneous and consequently must be evaluated individually to provide the best estimate of the soil water SWC in the mineral soil (Brocca et al. 2012).It is important to note that the evaluation of these parameters may represent sources of error in subsequent estimations of SWC in the mineral soil.
In the absence of manual measurements, it may be possible to estimate these different parameters using map information sources such as government soil surveys.These estimates would be less accurate but could potentially provide a basic estimate of SWC.Further research is required to verify the feasibility of this method.

Standard deviation bias
Both methods for estimating SWC using the gamma radiation detected by the CS725 sensor showed a large discrepancy compared to the reference soil moisture.As shown in Tables 6 and 7, these discrepancies are mainly due to the differences in standard deviations (α).The standard deviations of the SWC calculated from the gamma radiation are much higher than those from the TDR probes.
This discrepancy may be due to the very low variance in the Adj.TDR mean due to the vertical positioning of the TDR probes.This vertical orientation can result in very low temporal variation since the hydraulic conductivity of mineral soil is theoretically between 0.0009 and 0.21 m/h, depending on the texture (Rawls and Brakensiek 1989).The probes that were used are made of two 30 cm rods, and in sandy loam, the water draining between these two rods can be present for 5 h.Therefore, the hourly readings exhibited very low variation, resulting in a low standard deviation in the reference humidity.According to the literature, the standard deviation of the reference humidity at the different research sites is low.Based on works conducted by Huang et al. (2016), the temporal standard deviation in the SWC of the top 30 cm is between 6.5% and 10.5%.On the contrary, the reference SWC standard deviations measured at the research sites were actually between 1% and 2%.Therefore, the methods that incorporate gamma radiation generated standard deviations (4%-5%) closer to the values proposed by Huang et al. (2016).The vertical positioning of the probes meant that all soil horizons within the first 30 cm were given equal weight.This was not the case with the CS725 sensor.In fact, as shown in Fig. 3, most of the radiation captured by the device originates from the first few centimeters of soil.The water content of this surface soil, which is largely influenced by sporadic precipitation events, may explain the high temporal variations observed using the CS725 sensor.This may also explain the standard deviation bias.

Volumetric water content
The gamma radiation detected by the CS725 sensor and the calculations that followed provided an estimate of the mass SWC (g/g) of the mineral soil.Thus, as mentioned previously, conversion to volumetric units (cm 3 /cm 3 ) was required to adequately evaluate the performance of the proposed methods against the reference water content (TDR probes).This additional calculation, which relies directly on the bulk density (mg/m 3 ) of the mineral soil, creates additional sources of error.Mineral soil bulk density estimates can come from manual measurements or from the literature (depending on the soil texture).Both sources only provide approximations of the actual values of bulk density.As such, the subsequent use of this bulk density increases the bias of the final calculated value, which in this case, is the volumetric water content (cm 3 /cm 3 ) of the mineral soil.
The unique ability of the CS725 sensor to generate mass SWC readings may be a disadvantage when it comes to subsequent use of the data in water management.Indeed, it is the volumetric water content that allows managers to easily determine the soil water status for a given area.This information is crucial for measuring water variation in a specific area or for making comparisons with other hydrological variables (precipitation, evapotranspiration, etc.) (Hewlett and Nutter 1969).The bulk density of the mineral soil must be known to convert the mass SWC to volumetric SWC.

Temporal adjustment
The humidity calculated from the gamma radiation that was captured by the CS725 sensor covered the 24 h period prior to the reading.Meanwhile, the daily readings from the probes were an average of hourly measurements.The difference between these two measurement periods may have influenced the performance of the two methods and could account for the discrepancies between them.

Large-scale soil water content
Working at the watershed scale allows us to conduct hydrological studies that include different components of the water cycle, such as SWC.The watershed scale is preferred for hydrological modeling and can cover areas ranging from a few ha to thousands of km 2 (Aral and Gunduz 2010).To work at this scale, it is worthwhile to evaluate the effect of the CS725 sensor when estimating SWC over large spatial scales.
The relatively large area covered by the CS725 sensor represents an advantage compared to TDR probes that measure SWC over less than 1 m 2 .However, the area covered by the CS725 sensor is still much smaller than the watershed, necessitating the extrapolation of measurements to larger areas.This could be accomplished using different geostatistical methods, such as interpolation based on a CS725 sensor network.However, due to the high spatial and temporal variability of SWC, the results of any such interpolation would have inevitable biases.This is where the CS725 can play a critical role, since it can estimate mineral SWC accurately, although with some minor precision biases.

Conclusions
Mineral SWC over an area of approximately 100 m 2 (within a 15 cm depth) can be determined using CS725 sensors at sites where the humus layer thickness is ≤10 cm.Including variables that describe the humus improves results for such sites, compared to the method proposed by the manufacturer.The results were also improved for sites with a thick humus layer (30 cm) and therefore a high water equivalence.However, the methods we have presented lead to high variability compared to the reference water content.Incorporating variables that describe the surface humus layer in calculations for lower mineral SWC slightly corrects for the temporal variation bias.Thus, gamma radiation absorption in the humus layer should be considered in calculations for lower SWC in the mineral soil.
To improve upon our findings, the same analyses could de applied to sites with humus thicknesses between 10 and 20 cm.This would help to establish the maximum depth at which the CS725 sensor can adequately estimate the SWC in the mineral soil.
The information provided by this work will allow for the use of CS725 data at sites with compatible soil properties and thus contribute to the development of hydrological models for larger areas.Furthermore, the CS725 sensor has the potential to fill the need for a medium-scale detection tool for SWC.

Fig. 1 .
Fig. 1.The CS725 snow water equivalence and soil water content sensor circled in red mounted 2.5 m over the ground at the Tourbière site.

Fig. 2 .
Fig. 2. (A) Locations of the reflectometric probes around the CS725 sensor.(B) Vertical profile of the position of a probe in the soil under the CS725 sensor.
σ y and μ y are, respectively, the standard deviation and the mean of the simulated values (CS725), and σ− y and μ− y are the standard deviation and the mean of the reference water content.

Fig. 4 .
Fig. 4. Soil water content in the mineral soil readings (0-30 cm depth) from time-domain reflectometry (TDR) probes at the Bouleau site through summer 2022.Probes were inserted vertically in mineral soil under the CS725's effective area.

Table 1 .
Theoretical values used in soil water content calculations.
a Radiation count at time of sampling.

Table 3 .
Adjustments applied to time-domain reflectometry (TDR) probe readings based on manual measurements.
a Radiation count at time of sampling.b Dry soil gamma radiation.

Table 5 .
Performance evaluation for eq. 4 against reference soil moisture.
b Pearson correlation coefficient between simulated values (CS725) and observed values (TDR readings).c Mean ratio between simulated values (CS725) and observed values (TDR readings).d Kling-Gupta efficiency measure.

Table 7 .
Required soil property information for soil water content measurement with the CS725 sensor.Fraction occupied by solid, water, and air at time t a Manual survey Estimation of dry soil gamma emission Average fraction occupied by solid, water, and air b Literature (source) Estimation of soil water content in the mineral soil For this study, average time-domain reflectometry (TDR) probe reading at the Tour site.
a Considered at field capacity.b