An Automatic Snow Depth Probe for Field Validation Campaigns

Abstract

An automatic snow depth probe (magnaprobe) patented in 1999 (United States Patent 5,864,059, 1999) and produced commercially by Snow-Hydro LLC has now been used to obtain more than a million simultaneous snow depths (up to 140 cm) and GPS measurements during a wide range of field validation campaigns. The magnaprobe consists of a ski pole-like rod housing a magnetostrictive device along which a basket and magnet assembly slides. The rod is inserted to the base of the snow, the basket floats on the snow, and when a button is pushed, the distance between rod tip and basket is measured while a position is acquired. The nature of the substrate beneath the snow controls the snow depth accuracy with errors ranging from near zero for hard bases to +5 cm in soft vegetation. The Wide Area Augmentation System-enabled GPS provides a position accurate to ±2.5 m. The probe increases the speed with which a depth and position measurement can be obtained by a factor of 10 compared to measuring with a traditional ruler probe and writing down the results. The highest boost in snow depth measurement efficiency occurs when the distance between measuring locations is kept relatively small (<10 m). Magnaprobes have materially improved our ability to evaluate airborne and satellite-based snow depth products and are likely to see continued heavy use over the next decade as efforts to develop satellite systems for monitoring snow remotely are tested in various field settings.

Key Points

• Since 1999 a magnetostrictive device called a magnaprobe has been used to measure simultaneous snow depths and positions (GPS) during dozens of snow research field campaigns worldwide, with more than a million data points collected in this manner
• Depths measured in this manner are accurate to better than 5 cm, with the ease penetration of the substrate below the snow determining the over-probe error; position errors are ±2.5 m
• The device, or something similar, is likely to see continued use until airborne and satellite products reach a stand-alone level of accuracy and reliability

Plain Language Summary

We developed an automatic snow depth probe that can measure both depth and position simultaneously. These probes have been used extensively in snow field campaigns. They are accurate to better than 5 cm in measuring depth, with the poorer accuracy coming when soft ground under the snow is encountered; they are accurate to about ±5 m in measuring position. We expect probes like these will continue to be used in field validation campaigns for the foreseeable future.

1 Introduction

In 1992 the authors began conducting long traverses on the North Slope of Alaska as part of our snow research. On these traverses, we would travel, stop, and make snow depth measurements, then move again. We needed to measure a large number of depths as rapidly as possible at each stop. Writing down the measurements in a field book was slow and difficult with gloved hands when it was extremely cold. We tried voice recorders to bypass the need to write, but a number of failures led to data losses and dissuaded us from this approach. By 1994 we had begun investigating the use of a magnetostrictive device as part of a system that could record snow depth automatically and rapidly. We soon had a robust and portable system (Figure 1) that worked well. Initially, we used the probe at fixed distances along a 100-m tape stretched out along the snow surface, but as GPS units became more affordable and portable in the late 1990s, a GPS and antenna were integrated into the magnaprobe system, resulting in a device that could record both snow depth and position simultaneously.

Figure 1

A magnaprobe in use. The probe has two main components: (1) a backpack containing a data logger, batteries, electronics, speaker, switches, and a GPS and (2) a heavy steel rod with a plastic handle, thumb switch, and a sliding basket similar to (but larger than) a ski pole basket. Snow depth (h_s) is measured vertically from the floating basket to the tip of the probe. The two main sources for error are that (1) the basket may settle into soft snow (cratering) and/or (2) the tip of the rod may penetrate into the ground beneath the snow (over-probe). The inset in the lower left shows the contents of the backpack.

We did not intend to become a commercial producer of the device, but as other researchers saw the probes in use (and the high number of depths that could be collected by a single individual), they began to request that we build instruments for them. Eventually, in 1998 we formed a company (Snow-Hydro LLC: http://www.snowhydro.com/) and today have shipped more than 50 such units. These have been used extensively in snow depth validation and snow monitoring research campaigns all over the world.

The magnaprobes have worked well, though there has always been some confusion over the name. The magna is not for magnificent but rather refers to the magnet that rides on the floating basket and triggers the depth measurement in the magnetostrictive device, as explained below. After 24 years of use, and numerous studies published in which the probes have been pivotal to the success of these studies, we were asked by members of the snow research community to produce a reference document that describes the device, how it works, and its depth and position accuracy. Here we satisfy that request.

2 Principle of Operation

Figure 1 shows a magnaprobe in use and how the measurement is computed. The probe has two main components: (1) a backpack containing a data logger, batteries, electronics, speaker, switches, and a GPS and (2) a heavy steel rod (153 cm long) with a plastic handle, thumb switch, and a sliding basket (25-cm diameter) similar to but larger than a ski pole basket. On the magnaprobe rod an axial ring magnet is attached to a hollow plastic cylinder that slides up and down the rod. The plastic cylinder has coarse threads that allow for the sliding basket to be threaded on/off when the unit is in use/storage. When the operator inserts the rod downward through the snow to the ground or ice below, the basket floats on the surface of the snow, allowing the rod to slide through the plastic cylinder. Once the operator feels the bottom, he or she presses a switch on the handle that triggers the measurement.

The heart of the probe lies in the rod, where a magnetostrictive device (MTS, 2018) is installed. It utilizes the Wiedemann effect (cf. Williams, 1911) to measure the travel time of a sonic pulse. A 153-cm-long tightly stretched ferromagnetic wire runs down the center of the rod. When a current is sent down this wire, it induces a physical twist where the wire passes through the magnetic field induced by the axial ring magnet on the sliding basket. The twist will then propagate back up the wire at the speed of sound through the wire (2.8 × 10³ m/s), which is more easily timed than the initial electronic pulse traveling at the speed of light (~3 × 10⁸ m/s). The time it takes for the twist to travel up to the head of the rod is converted to a distance by the solid-state electronics integrated into the probe. That distance, subtracted from the full length of the rod, is used to measure the distance from the steel tip of the rod to the sliding basket at the snow surface, that is, the snow depth. The rod is connected by a cable to a data logger (Campbell Scientific CR800) that records the depth and GPS position. The GPS is a GARMIN™ receiver and integrated antenna modified and sold by Campbell Scientific (GPS16X-HVS) and is a 12-channel Wide Area Augmentation System-enabled device (Federal Aviation Administration, 2013; Garmin, 2017). The data logger software code for the magnaprobe tests whether a GPS position has been obtained before it allows the data logger to record a depth. The initiation of a measurement cycle and its completion are indicated to the operator by a series of beeps, allowing an experienced operator to move very quickly: a full measurement can be taken in less than 2 s. At the end of the field day (or several days) the probe is downloaded to a computer using a memory stick and a spreadsheet of time, depth, position, and other metrics is produced.

In developing the probe, the chief difficulties that had to be overcome were related to (a) cold weather operation and (b) hard snow. The hard snow required that we house the magnetostrictive device in a strong outer rod and design a tip that would prevent the rod from sticking when pushed deep into the snow. Cold weather caused many cabling failures early in the development stage (breakage and cold cracking) and led eventually to the use of specialty cables produced by PQ Systems (http://www.pqsystemsltd.com/) with sheaths that were flexible down to −40 °C and robust connectors. All system components also had to be robust enough to withstand the extreme vibration and abuse that occurs while traveling via snowmobile over hard wind-packed Arctic snow.

3 Accuracy

3.1 Depth

The magnetostrictive device has a precision of better than 0.1 mm, so the real limitations on snow depth accuracy are (a) the degree to which the probe penetrates the substrate under the snow (over-probe), (b) the depth of cratering by the basket (Figure 1), and (c) how far off vertical the operator holds the probe. Most operators can visually hold the probe within 5° of vertical producing an error of less than 0.4%, or 0.2 cm for 50-cm-deep snow. Basket cratering (which produces a low bias) is easily ascertained visually, and in our experience, rarely much over 1 cm. Most of the time this can be ignored. In unusual conditions (fluffy new snow) where the cratering is deeper, one can estimate the amount and then apply a mean correction to the recorded values when analyzing the data.

The degree of penetration below the snow base is highly dependent on the nature of ground. For snow over sea, lake, or river ice, penetration is virtually zero and recorded depths are accurate to better than +0.1 cm. Over hard soils, rocks, and vegetation wetted in the fall and then frozen, the depth accuracy is nearly as high. However, over soft tundra it is possible to push the probe into the matte a considerable distance. The average during the Alaskan CLPX campaign was 5 cm. Berezovskaya and Kane (2007) using a hand probe (probably a ski pole) had average over-probe values between 5 and 9 cm. Similar over-probe values were found in tests done in soft Canadian tundra. Unfortunately, correcting for this over-probe error, whether it happens with a magnaprobe or a hand probe, is difficult because the error is random, determined by the nature of the soil and vegetation at horizontal scales of just a few centimeters. This precludes a systemic correction. The error can be minimized, however. Operators can learn to push a magnaprobe through hard snow yet not impale it too deeply it into underlying vegetation by developing a feel for the base of the snow pack.

The standard device is built on a 153-cm-long transducer resulting in an instrument that can measure up to 140 cm depth (allowing for the handle). Probes capable of measuring up to 180 cm have been built, but with increasing length, ease and speed of use are reduced, reducing the basic advantage of the device.

3.2 Position

Each magnaprobe that is built is tested on a fixed course. In Figure 2, six different probes, each with the same model of GPS, were used over this course during a 9-month manufacturing period. In four cases, a counterclockwise circuit was measured, and in two cases (purple and red), a snowdrift prevented a full circuit, so the operator doubled back on the track. These repeat measurements show that there was about a ± 3-m error in position over the course (black double-headed arrow) during the 9-month period of measuring the same transect, a value that is slightly greater but consistent with Wide Area Augmentation System standards (typically ±3 m; Federal Aviation Administration, 2013). The inset in the figure shows the start and end of each test transect, which normally take less than 30 minutes to complete, minimizing the change in GPS satellite constellation. These endpoints would overlap exactly if there was no positional error associated with the GPS units. The mean closure offset for these six cases was 4.47 m (see figure key), suggesting a GPS error of about ±2.5 m over the course of a snow survey, again consistent with the stated error of this type of GPS.

Figure 2

GPS tests of six probes over a fixed course, with the tests done over a period of 9 months. Each device was used to take about 100 measurements in random locations along a fixed course with the line of travel marked with fixed markers and accurate to better than 0.2 m. The inset indicates the position difference (in meters) between the start (squares) and end (circles) of a particular course measurement, which typically took 10 to 30 min. The closure error is an indicator of the accuracy of the GPS. The key provides the distance (in meters) between the start and end (closure error) for each run.

4 Field Application

The time-saving achieved using a magnaprobe accrues chiefly from the greater speed with which a measurement can be made. If we assume one is interested in obtaining N snow depths from a study area, then two factors will determine the total work time (t) needed to collect these data: the time to take each measurement, t_m, and the speed an operator moves from one measurement to the next, w_s:

(1)

where the physical spacing between measurements is denoted by P. The first term in the parenthesis is the travel time of the operator between measurements.

We are interested in the improvement in overall efficiency obtained by using a magnaprobe, so replacing t_m with Δt_m, the difference in measurement time with versus without a magnaprobe, we can compute the time saving (Δt) as

(2)

Equation 2 is linear with the number of measurements. In our experience, given the need to record both depth and position when using a hand probe, Δt_m varies from about 10 to 30 s. Typically, with a simple hand probe, a worker takes two or three measurements in a row, remembering the values, then writes them down, requiring 10 to 15 seconds. If recording GPS position as well, the recording process takes considerably longer, perhaps 30 seconds, and the operator risks the problem of data loss due to a momentary distraction. In a campaign where 1,000 depth measurements might be taken, the magnaprobe can reduce the work time by 3 to 9 hr, significant amounts.

We can extend this work effort analysis with the results applying equally well to magnaprobe and hand-probe surveys. Blöschl and Sivapalan (1995) and Sturm (2015) have discussed the three parameters of a snow measurement campaign: support (S), extent (E), and spacing (P). Support is the area sampled by the measurement, which for a magnaprobe is technically the circular cross-sectional area of the tip of the steel rod, about 0.001 m². More realistically, we would hope that the measurement is representative of a somewhat larger area, S*, where S* is S times r, with r (called here the r-factor) being a value greater than 1. The extent (E) is the size of the domain to be sampled, which could be a one-hectare basin or all of Rocky Mountain National Park. E is typically given as a lineal dimension, so the implied domain area is E². For a square domain, P is given by , which can be substituted into equation 1 to produce a formula for total work time as a function of number of measurements, speed of travel, and speed of measuring:

(3)

There is one other metric of interest, γ, the ratio of the actual sampled area to the area of the total domain, which is a measure of how representative the sampling campaign has been. For a domain area of A_d, assumed to be a square for ease of computation, γ is given by

(4)

To illustrate these relationships, we have compared the results from a hand-probe survey to a survey done for the same domain using magnaprobes. The data are for a 1-by-1-km grid at Imnavait Creek just north of the Brooks Range in Alaska. The hand-probe survey was done in 1997 (Figure 3a), locating each depth from a survey grid delineated with fiberglas markers. The magnaprobe survey in 2014 (Figure 3b) used the same markers for orientation, but operators probed about every stride, producing an along-track spacing on the order of 1 to 2 m. Assuming an r-factor of 50, the gamma value for 1997 with N = 231 was 0.00095, while in 2014 with 10,079 measurements it was 0.04165, an improvement of 44 times. The mean point spacing (P) dropped from 72 (1997) to 11 m (2014) between the two surveys. The payment for this improvement, of course, is that the work effort increased from 5 to 45 hr, but as this is only an increase in effort of a factor of 8, it is clear that using the magnaprobe has produced more than 5 times as many depth values per unit time as in 1997. Not surprisingly, the resulting snow depth map is far more detailed. While the values listed above are theoretical, being based on equations 3 and 4, they in fact fall quite close to the actual realized times that were needed to conduct the surveys, which was about 4 hr in 1997 and 40 hr in 2014 (five people using snowshoes during one 8-hr day).

Figure 3

Snow depth maps for Imnavait Creek in Arctic Alaska from April 1997 (a: Hand probing, mean depth 62 cm) and 2014 (b: Magnaprobing, mean depth 58 cm). The color scale ranges from 20 cm (red) to 100 cm (purple). The black dots indicate the locations where depth was measured. These are so close together for 2014 they appear as lines. The mean depths for both years being so close, the depth patterns would change little even if normalized depth values were used.

We have summarized the combined effects of P, w_s, and t_m on work time in Figure 4. Holding E constant at 1,000 m, we have varied the other factors, including increasing the travel speed (w_s) up to a value that would require a snowmobile to be achieved. Being able to move faster between measurement points (compare lines of similar color in Figure 4) greatly reduces the work time for a given value of N. This is true whether a magnaprobe is used or not. However, the faster one can move between points, the greater the leveraging effect of the magnaprobe on reducing the overall work time needed to conduct a survey. This effect is clear in Figure 4 where the larger spread between the dot-dash lines (i.e., all done at the same travel speed) is driven by the measurement speed. For the three fast scenarios the decrease in total survey time due to being able to measure rapidly (i.e., a magnaprobe is used) is substantial. The take-away lesson in reducing the total time to conduct a snow survey seems to be move fast; measure fast. The latter can be achieved by using a magnaprobe compared to traditional methods.

Figure 4

The effect of variations in travel (w_s) and measurement speed (t_m) on total work time for a snow depth survey consisting of N measurements. The computations are for a domain (E²) of 1 km² and would scale in a relative way for larger or smaller domains. In the key, ws1_tm20 indicates a travel speed of 1 m/s, with a 20-s measurement time, and so forth.

5 Field Campaigns Using Magnaprobes

Magnaprobes have been used in many snow depth validation and snow monitoring research campaigns. Table 1 lists the number of depth measurements made during a few of these. Given their diverse nature and varied sampling schemes, the increase in efficiency due the use of the device is variable, but those involved in the campaigns have suggested that a magnaporbe produces a nearly 10-fold increase in the number of depth data collected versus hand probing. Moreover, since it is unlikely a field group would actually commit to producing 81,210 measurements by hand in a single campaign (see Table 1), the device clearly changes the way field campaigns are designed.

Table 1. Selected Field Validation Campaigns Using Magnaprobes

Location	Date	N value	Group	Source
Inuvik, NT, Canada	1 March 2018	13263	Environment Canada	P. Toose
Eureka, NU, Canada	1 March 2016	54125	Environment Canada	P. Toose
Saskatoon, ALT, Canada	2014 to 2015	6946	Environment Canada	P. Toose
Eureka, NT, Canada	1 March 2014	81210	Environment Canada	P. Toose
Inuvik, NT, Canada	2012 to 2013	41817	Environment Canada	P. Toose
Eureka, NU, Canada	1 April 2011	15325	Environment Canada	P. Toose
Churchill, MN, Canada	2009 to 2010	28800	Environment Canada	P. Toose
James Bay, Canada	1 March 2009	1307	Environment Canada	P. Toose
Inuvik, NT, Canada	1 April 2008	5545	Environment Canada	P. Toose
Daring Lake, NT, Canada	1 April 2008	4401	Environment Canada	P. Toose
Puvirnituq, QC, Canada	1 February 2008	12228	Environment Canada	P. Toose
		264,967
Imnavait Grid, North Slope, AK	1 April 2009	16985	CRREL and U. of Alaska	C. Parr
Imnavait Grid, North Slope, AK	1 April 2010	26090	CRREL and U. of Alaska	C. Parr
Imnavait Grid, North Slope, AK	1 April 2011	27436	CRREL and U. of Alaska	C. Parr
Kuparuk Basin, North Slope, AK	1 April 2012	92073	CRREL and U. of Alaska	C. Parr
Imnavait and CLPX squares, AK	1 April 2013	29958	CRREL and U. of Alaska	C. Parr
		192,542
AMSRIce 2006, Barrow, AK	1 March 2006	4000	CRREL, U. of Alaska, Dartmouth	C. Polashenski
SIZONET	1999 to 2012	55000	CRREL, U. of Alaska, Dartmouth	C. Polashenski
NRL Airborne Radar Validation	2005 to 2015	50000	CRREL, U. of Alaska, Dartmouth	C. Polashenski
Sub-ICE	??	7000	CRREL, U. of Alaska, Dartmouth	C. Polashenski
N-Ice Campaign	2015	150000	CRREL, U. of Alaska, Dartmouth	C. Polashenski
Snow, Wind & Time	1 March 2017	87000	CRREL, U. of Alaska, Dartmouth	C. Polashenski
IceX	2018	8000	CRREL, U. of Alaska, Dartmouth	C. Polashenski
		361,000

6 The Future

There are multiple ongoing efforts to develop satellite remote sensing products for snow depth in the United States, Canada, China, and the European Union. Hopefully, these will prove successful, but an operational satellite appears to still be decades off. In the interim, airborne lidar and structure from motion photogrammetry (SfM) are increasingly being used to map smaller areas of snow depth (Deems et al., 2013; Nolan et al., 2015; Painter et al., 2016) and are seen as a bridge between on-the-ground measurements and satellite products during validation campaigns (Kim, 2018). But there are inherent difficulties in the bridging process between these three types of products due to large differences in support (S), extent (E), and the spacing (P) of the measurements. Satellites products typically have a support that is hundreds of square meters, if not square kilometers or more, and are space filling. Over these large areas, significant subpixel snow depth variation is present, but at scales that the space products cannot resolve. For example, in Figure 3 there is a highly structured variation in snow depth with the depths varying by up to a factor of 5, yet for many satellite sensors the entire domain would be a single pixel. For an ecological study, and even for a detailed snow runoff study, that subpixel structure might matter. Moreover, it remains an area of active research whether space sensors produce unbiased areal depth averages, or, in fact, due to sensor characteristics, respond with to low- or high-snow conditions in a nonlinear way. That question that can only be answered convincingly by comparison of depths (or SWE) measured in various ways and at various scales.

But ground-based measurements, like those taken with a magnaprobe, face the unsolvable problem of area filling. These measurements have supports that are thousands of times smaller than those of sensors in space and can never be used to create areal products or maps without employing either statistical or physics-based interpolation models (Fassnacht et al., 2018). Even with considerable work effort (Figure 4), they cannot produce γ values (ratio of the actual sampled area to the area of the domain) higher than 0.1. Moreover, ground sampling in steep and avalanche-prone terrain is dangerous, so hydrologically important areas go unsampled (Hood & Hayashi, 2010). Nonetheless, the very directness of the measurement, and the fairly clear nature of the inherent errors (in contrast to the more complex uncertainties associated with sensors in space), makes such measurements an essential reality check.

Over the past few years, the hope in the snow community has been that airborne lidar or SfM photogrammetric techniques might bridge the ground-space measurement gap (e.g., Painter et al., 2016), but airborne methods have proven to have their own set of difficulties. For example, in steep and rugged terrain aircraft GPS position uncertainty can produce large depth errors (> 1 m vertically) when pixels are differenced. Furthermore, our experience, based on 7 years of annual SfM mapping of thousands of square kilometers of snow in Arctic Alaska is that in the absence of ground-based measurements, the airborne results tend to have an undetermined float, or translation error, that can exceed 50 cm or more, and which must be removed either using snow-free ground control points (often difficult to find) or ground-based depth measurements like those collected with a magnaprobe (cf. King et al., 2018).

It is our view, then, that for the foreseeable future we will need to use all three types of products as we move toward space-borne sensors. We therefore expect that magnaprobes, or some similar high efficiency snow depth measuring device, will continue to be needed for field studies of snow.

Acknowledgments

We wish to thank all of the many magnaprobe users who have provided constructive feedback that has helped improve the device. The initial developmental work was done with funding from the U.S. Army Cold Regions Research and Engineering Laboratory, and the device was patented by us through the U.S. Army Corps of Engineers. Production has been done under a license agreement. Mike O'Gorman of MTS Inc. and Robert deRot of PQ Systems have been helpful in developing a more robust probe and cabling. Peter Toose, Josh King, and Arvids Silas provided data in Table 1 and many helpful comments on the paper. We also thank Steven Fassnacht and two anonymous reviewers for helpful comments and editorial suggestions. Data are available in the tables and figures presented in the text.