The tap-o-meter was created to measure the force from hand taps. A total of three devices were built to enable data collection in different parts of the world in a similar time frame (Fig. ). Each tap-o-meter has the following components:

a shovel blade which acts as the loaded surface

Data collection was conducted at events in Norway, Switzerland, Austria, the US, and Canada. In Norway, data were collected from avalanche forecasters and mountain guides. In Switzerland, data were collected at the European Avalanche Warning Services (EAWS) general assembly. Canadian and Austrian events only included avalanche forecasters. Events in the US contained a mix of avalanche workshop participants and avalanche forecasters. A total of 286 individuals (232 males and 54 females) contributed to the study. A detailed table of the number of samples, event, and date can be found in Table A1. We did not provide any specific instructions on how to conduct the ECT other than asking participants to tap as they would in the field. We provided a wide range of gloves with different thicknesses, but it was up to the participants themselves to select which glove or whether to use a glove at all.

We made the setup as similar as possible by using three identical tap-o-meter devices. All tap-o-meters were firmly attached to a wooden CT (30 cm × 30 cm × 85 cm) or ECT (30 cm × 90 cm × 85 cm) column (Fig. ). By using a fixed height, we acquired data with a consistent sampling method but were not able to adjust for changes in simulated snowpack thickness. Furthermore, participants were given the choice to use different types of gloves depending on their preferences. The intent was that all participants should be able to conduct the test like they would do in the field. However, we left the shovel handle off as early tests during the development showed that even gentle touches are picked up with our sensitive load cell.

The raw voltage data are processed using Python to identify the individual taps. After the taps are identified, two metrics are pulled from each one: maximum force (newtons, N) and loading rate (Ns-1). Other quantities, such as impact duration, rise time, and stress, were considered but not chosen. Impact duration was not used because the measurements frequently contained long, oscillatory tails that are artifacts of the load cell rebounding and vibrating – a phenomenon expected to be less present during an actual field test. Rise time is calculated as an intermediary step to loading rate. However, loading rate was chosen because snow response has been shown to depend on its rate of deformation (Shapiro et al., 1997, Reiweger et al., 2015; Verplanck and Adams, 2024). Lastly, our measurements are presented as forces (N) rather than stresses (kPa) because presenting them as a stress would rely on an assumption of a cross-sectional area.

The recorded time and voltage are imported as NumPy arrays (Harris et al., 2020). The voltage values are zeroed by subtracting the entire array's mean from each data point. Then, voltage is converted to newtons by scaling according to the calibration. SciPy's (Virtanen et al., 2020) peak-finding algorithm, scipy.signal.find_peaks, is implemented to determine when the taps occur by comparing neighboring values. The peak-finding algorithm is driven with two parameters: a 25 N minimum peak magnitude and 0.4 s minimum time between peaks. These criteria are chosen by iteratively trying different values and viewing the results. This peak-finding method is used as a first pass through the data and is later refined with a more manual process. See Fig.  for an example of tap data with the peaks algorithmically identified.

After the peaks are found the individual taps are defined as 70 ms prior to and 40 ms after the peak. These values are chosen to allow for enough time surrounding the peak to determine tap metrics. Each tap array is then re-zeroed by subtracting the mean of the first 0.2 ms of that specific tap. This re-zeroing process is implemented because subtle shifts in the baseline recording are occasionally apparent, particularly during the taps hinging from the wrist if the tapper kept contact with the shovel blade throughout these taps. The two metrics, maximum force and loading rate, are ascertained from each tap array. Maximum force, Fpeak, is simply the maximum value in the re-zeroed array. The loading rate, r, is defined as a linear interpolation (Eq. refeq2) between the maximum force, Fpeak, and a threshold value greater than typical noise, λ. In our measurements, a λ of 15 N was deemed appropriate. The difference in force is divided by the rise time, Δt, to determine the loading rate. The rise time is the difference in time between the peak force and the initial threshold crossing. 2r=(Fpeak-λ)Δt

After this automated process is applied to all 286 tap recordings, a manual quality control process is done. This process entails viewing the taps for each recording (Fig. ), flagging misidentified taps, and classifying which taps are hinging from the wrist, elbow, and shoulder. This manual process determined that 262 out of 286 recordings were correctly processed with the first-pass algorithm. The remaining 24 recordings were reprocessed by changing the parameters for SciPy's peak-finding algorithm. The changes to peak-finding parameters involved reducing the time between peaks or minimum magnitude until all the clear taps are identified. In some cases, the metrics were not calculated accurately because there was a spike in noise that was close enough in time to the tap signal. In these cases, the individual taps were not included in the analyzed data set.

We tested height, weight, sex, and geographic region to understand the underlying factors influencing hand-tap loading using ordinary least squares (OLS) regression models. The peak force was the dependent variable in these models. To compare hand-tap loading at different loading steps, we conducted a one-way ANOVA. This analysis assessed whether the mean impact forces were statistically different during wrist, elbow, and shoulder taps. ANOVA, or analysis of variance, compares the means of three or more groups to determine if at least one group's mean is significantly different from the others (Fisher, 1970). All analyses were considered statistically significant at p values below 0.05.

Both the peak force, Fpeak, and the loading rate, r, are used to idealize the impact curves. First, we consider the equation describing a Gaussian function of force, F, as a function of time, t: 3F(t)=Fpeake-12t-tpeakσ2, where Fpeak is the peak force, and tpeak is the time at which the peak force occurs. The duration of the force curve is governed by σ, the standard deviation if the Gaussian function described a normal distribution. Since 99.7 % of the curve's magnitude occurs during 6σ, the duration of impact is defined as 6σ in our study. Thus, the rise to peak force occurs over approximately 3σ, leading to the following relationship used to calculate the loading rate, r: 4r≈Fpeak3σ.

This is an approximation rather than equality because it assumes a linear rise rather than the non-linear Gaussian shape. However, since loading rate and peak force are the two metrics ascertained from the measured data, this approximation provides a convenient way to idealize the measured force curves. Rearranging the approximation yields 5σ≈Fpeak3r.

And substituting this relationship for σ in Eq. () yields the Gaussian approximation used to idealize the measured force-time curves: 6F(t)≈Fpeake-123r(t-tpeak)Fpeak2.

The data set consists of 2837 wrist taps, 2839 elbow taps, and 2846 shoulder taps across 286 individuals. Outliers are excluded using 1.5 times the interquartile range (IQR) method, which is a widely recognized and accepted standard in statistical analysis (Tukey, 1977). Saturation occurred in rare instances due to a limitation with the amplifier in the tap-o-meter. See Table  for more information.

In Table , we provide some descriptive statistics of peak force and loading rate. The median peak force approximately doubles from one loading step to the next at 79 N, 185 N, and 373 N. The standard deviation is also roughly half of the mean peak force for each loading step, showing that the variability in loading increases proportionally with increasing peak force. The loading rate, and its standard deviation, increases with each load step. The loading rate is positively correlated with peak force (R2 = 0.70).

We observed different mean and median values for each loading step, and if we consider the interquartile range, which represents the data between the 25th and 75th percentiles, there is nearly no overlap between loading steps. Doing a one-way ANOVA, we get a p value lower than 0.01, indicating that the three loading steps are statistically different from each other, mirroring the findings of Sedon (2021) and Griesser et al. (2023).

In Fig. , the distribution of peak forces across different tap numbers is graphically represented for three tapping levels. While the median forces across each loading step remain relatively consistent, there is a large spread across all loading steps. Collectively, this figure emphasizes the inherent differences in peak forces across the three tapping levels and underscores the variability present within each level across different tap numbers.

To showcase the overlap between loading steps, we made a confusion matrix based on a tapping norm. The IQR for wrist, elbow, and shoulder is 50–101, 123–237, and 239–481 N, respectively. We selected the value between the highest IQR value in one loading step and lowest IQR in the next to define the tapping norms between loading steps. For example, the upper-bound wrist norm is 112 N, which lies halfway between 101 and 123 N. The lower bound for the wrist norm is the 25th percentile threshold, and the upper bound for the shoulder norm is the 75th percentile threshold. Using these values, we can make a confusion matrix to highlight how many hand taps are within each interval (Table ). From this, we can see, for example, that 17.79 % of elbow taps are within the wrist tapping norm, and 25.75 % are within the shoulder norm.

The three columns in Table  contain the results for the different loading steps. Column 1 shows the result for taps from the wrist, column 2 for taps from the elbow, and column 3 for taps from the shoulder. We estimated five models for each type of tap to evaluate the role of weight (model I), height (model II), and sex (model III), respectively. Models IV and V add a control for sex to the height and weight variables.

Overall, the models explain very little of the variance in peak tap force (between 3.1 % and 7.2 %). In other words, over 90 % of peak tap force variance is explained by factors other than height, weight, sex, and geographical region. While we do find a significant positive correlation between peak tap force and both height and weight, the effects are very small. An increase in weight by 1 kg is associated with an increase in peak force by 0.6 % to 0.8 % in our sample. The effect of height is slightly larger but still very small. An increase by 1 cm is associated with an increase in peak force by about 1 %. In addition, in the models for taps from the elbow and shoulder, the effects of height and weight drop below 10 % significance when we control for sex. The models for elbow and shoulder taps further suggest that sex is a more important explanatory factor than height and weight, as can be seen by the relatively larger R2-adjusted values for models where sex is included. This result does not hold for wrist taps, where sex is an equally poor (if not poorer) predictor of peak tap force compared to weight and height. In general, our results suggest that females' peak force is about 20 % less than males' peak force.

Using the median metrics along with their 25th and 75th percentiles (Table ), the force curves idealized as Gaussians are shown in Fig. .

By idealizing these tap curves as Gaussians, their respective linear impulses can be compared by calculating the area under the curve (Hibbeler, 2010). Using NumPy's implementation of the trapezoidal rule (Harris et al., 2020), the median wrist, elbow, and shoulder tap impulses are 0.65, 1.00, and 1.60 Ns, respectively. We estimate the median loading duration (6σ, Sect. ) of the impact curve to be 21 ms for the wrist, 14 ms for the elbow, and 11 ms for the shoulder.

If we compare the results from our study with the ones from Sedon (2021) and Griesser et al. (2023), we find surprisingly large discrepancies when comparing the measured mean values (Table ). It is unlikely that participants from New Zealand (Sedon, 2021) tap half as hard as Griesser et al. (2023) observed or one-third of what we observe in our sample from Scandinavia, Europe, and North America. Griesser et al. (2023) recognize that they are not able to accurately measure peak force values due to their lower sampling rate but that the relative differences are systematic when comparing the mean values from wrist, elbow, and shoulder with data from our study. We measured the 62 participants from Griesser et al. (2023) in parallel with our own measurement device, and the measurements are very similar to the rest of our samples. This comparison suggests that the differences are likely due to the difference in sampling rate.

At a sampling rate of 100 Hz, we would only measure the impact force every 10 ms, making it unlikely to capture the peak force value accurately. The discrepancies in sampling rates make for an invalid comparison of peak force values between the studies. However, the relative difference between wrist, elbow, and shoulder is almost identical for all studies. All three studies have an approximately doubling in peak impact force from wrist to elbow to shoulder.

Sedon (2021) did not investigate whether there were differences due to weight, height, sex, or geographical region. Griesser et al. (2023) investigated shoulder height and found that participants with greater shoulder height had higher impact forces. They also mention that they found statistically significant correlations when comparing against height and weight, but no p values are provided. Our main finding from the survey data is that only sex has a statistically significant relationship with peak force. Body features (weight and height) are also correlated with peak tap force, but when included in a multivariate analysis with sex, they disappear. We believe the correlation found by Griesser et al. (2023) for body features is likely due to males generally being taller and heavier.

Given the variations in observational guidelines for the ECT, we hypothesized that measuring differences among participants from the Alps, Scandinavia, and North America would be feasible. Despite this expectation, we observed no regional variations in peak tapping force. The lack of significant findings might be attributed to our limited predictive capability from the small sample size in a statistical context (n=286) or because there are no differences to be found.

It is widely agreed that whether a crack propagates across the entire column or not is the key discriminator between unstable and stable slopes (Techel et al., 2020). However, both Winkler and Schweizer (2009) and Techel et al. (2020) show that the number of taps provides additional information, allowing for a more refined distinction between results related to stable and unstable conditions. Techel et al. (2020) found the optimal threshold between ECTP20 and ECTP22, which aligns with the ECTP21 threshold suggested by Winkler and Schweizer (2009). Moving away from a binary classification came at the cost of introducing intermediate stability classes (Techel et al., 2020).

These new intermediate stability class definitions rely heavily on the tap number when failure occurs. Variability in the applied force-time curves likely leads to variability in test results, particularly regarding the number of taps required to induce weak-layer failure. It is important to emphasize that no tests offer a definitive go or no-go result. With accuracies of around 80 %, these tests are not reliable enough to be the main factor in our slope-scale decision-making (Birkeland et al., 2023).

We found the three loading steps to have statistically different IQRs; this aligns with the results from Griesser et al. (2023), which highlight this as a positive outcome, indicating that the CT and ECT hand-tap procedure is somewhat reliable. Despite the statistical differences in each loading step, we question the application of average results to individual cases. The main difference in our argument lies in relying solely on mean statistics to develop tapping norms used by individuals. For example, from Table , we can see that 17.79 % and 25.75 % of elbow taps have a peak force value that falls within the tapping norms for wrist and shoulder taps, respectively. This implies that 43.54 % (17.79 % + 25.75 %) of elbow taps would be misclassified as taps hinging from the wrist or shoulder. Assuming peak applied force influences test results, this misclassification of loading steps will then lead to a misclassification of test results. Because stability test results aid in an individual's decision-making process, a misclassification of test results could lead to dangerous consequences for real-world applications.

The Gaussian function is often used in wave propagation problems because it represents a smooth, continuous pulse of disturbance (Langtangen and Linge, 2017). The measured shape of force-time curves is not a perfect Gaussian (Fig. ), particularly after the peak force has been reached. The noisy, oscillatory decay following the peak is attributed, in part, to the instrumentation. Despite these imperfections, we intend to use this idealization as a steppingstone towards mathematical modeling efforts. In addition to providing this steppingstone, the idealization shown in Fig.  provides a visualization of peak force, loading rate, impact duration, and variability associated with these quantities. The taps from the shoulder generally have a sharper pulse (i.e., shorter duration, higher peak force) than a wrist tap. Despite the impact duration decreasing with increasing load step, there is an increase in linear impulse. The linear impulse is equated to the change in linear momentum of the system (Hibbeler, 2010). Thus, the increase in snow momentum from a hand tap is expected to be larger for higher load steps despite the shorter duration of impacts. The Gaussian idealization provided a convenient method of comparing linear impulses from the tap data, whereas direct numeric integration of the load cell data would be inaccurate due to the long, oscillatory tails.

Given the variability in tapping demonstrated in this study, we propose two considerations to improve the ECT standards. The two ideas outlined below are intended to be a foundation for further discussion in the broader avalanche community.

During data collection, we asked participants if they regularly conduct CTs or ECTs for work, recreation, or both. Participants were also asked to self-evaluate their avalanche assessment level on a scale from 1 to 6, following the definitions from the Center for Avalanche Research and Education Panel study (Hetland and Mannberg, 2023). Our hypothesis was that more experienced participants, particularly those frequently performing stability tests, would be more consistent within each loading step. However, the study's shift in focus towards more experienced individuals meant that we lacked a suitable reference group for comparison. For future studies, a more effective approach might involve quantifying the frequency of CTs or ECTs performed by each participant per season. This method could provide a more nuanced understanding of the relationship between the quantitative experience and tapping consistency.

Snow response to impact forces remains an active research topic and is out of the scope of this study. However, variability in the magnitude and duration of applied force will result in variability in the stress state within the snow, which may lead to variability in test results. For more on this topic, we refer the reader to studies by Napadensky (1964), Wakahama and Sato (1977), Johnson et al. (1993), Schweizer et al. (1995), van Herwijnen and Birkeland (2014), Thumlert and Jamieson (2015), Griesser et al. (2023), and Verplanck and Adams (2024). Quantifying how variability in the applied force may lead to different ECT results would be a useful extension of our work presented here.