## 1. Introduction

### a. Manual snow depth measurements

In Canada, for all meteorological stations prior to the 1960s, and for most nonsynoptic stations over their entire history, snowboards were used to measure new snow within a specified time period (Potter 1965). The depth of snow on the board was measured with a ruler that, since 1978, has been 1 m long and graduated every 0.2 cm. The board was then reset on the surface of the snow cover to prepare for the next snowfall (SF) event. A limitation of this approach is that a change in snow depth (SD) does not provide information on the bulk density of the freshly fallen SF. Traditionally, the snow on the board was assumed to have a density of 100 kg m^{−3}, even though the density of new snow can commonly vary from 50 to 120 kg m^{−3} (Pomeroy and Gray 1995).

To improve the presumed density, Groisman (1998) and Mekis and Hogg (1999), adjusted monthly estimated accumulated SF amounts using a mean density calculated from the ratio of manual Nipher gauge measurements (Goodison 1978), which measures fresh snowfall water equivalent (SWE) to snow ruler measurements (thus creating an adjusted precipitation archive for Canada). A limitation of this approach is that SF amounts are corrected over daily to monthly time scales and may not accurately account for other meteorological processes that affect the height of the snow cover.

Other efforts have concentrated on data assimilation techniques of snow-settling rates to reconstruct the snow that must have fallen to produce the observed SD (Jordan 1991; Bartelt and Lehning 2002; Cherry et al. 2005, 2007; Ryan et al. 2008a). A limitation with this approach is that the SF amounts are derived in part numerically and are not directly measured, which introduces an unknown error.

### b. Automation of snow depth measurements

Human observations at Environment Canada’s (EC) Surface Weather (SWX) and Reference Climate Station (RCS) networks have decreased since the 1980s and are being replaced by automated stations (presently there are about 630 SWX and 300 RCS stations, respectively). Currently, the Campbell Scientific, Inc., SR50 (Campbell Scientific 2009) Ultrasonic Snow Depth Sensor (USDS) is used to provide direct measurements of the depth of the snow cover (Gubler 1981; Goodison et al. 1984) in Canada. An advantage of using USDS is that random disturbances in ultrasonic measurements related to the vertical gradients of temperature and wind speed taken above snow, where the surface boundary layer is typically stable, are only on the order of 1 mm for a SD measurement of 1 m (Goodison et al. 1988). Additionally, recent work has shown that SD observations recorded from many SR50s compared well with manual SD observations taken adjacent to the sensor (Ryan et al. 2008b).

On the other hand, the underlying snow surface can result in SD measurement errors if the ultrasonic pulse penetrates the freshly fallen snow and is reflected by a denser layer beneath the snow cover surface (Goodison et al. 1988). Another point of concern is that USDS readings of SD are point-oriented, distance-to-target measurements. Neumann et al. (2006) showed that a single, fixed-point measurement of SD often did not represent the average SD at a site. At times, up to 44-point measurements were needed to be within 25% of the landscape mean.

In comparison to other measurements taken by atmospheric observation networks (e.g., air temperature), the variability in SD is almost always greater than can be obtained by measured observations (Blöschl 1999; Sturm and Liston 2003; Liston 2004). Atmospheric dynamics determining storm tracks and the formation of solid precipitation influence the spatial distribution of the snow cover on a regional scale (Stewart et al. 1998; Linkin and Nigam 2008). At local scales, the elevation, topography of terrain, and forest–canopy interactions with SF influence the distribution of the snow cover (McKay 1964; McKay and Gray 1981; Bonan 1991; Spreitzhofer 1999; Hiemstra et al. 2002; Liston et al. 2007).

### c. Overview

Owing to increased surface weather station automation in the last few years, EC has employed a crude SF derivation algorithm using the SR50 for its SWX and RCS networks. In view of this, the primary aim of this study is to identify and describe some of the sources of error that impact on the ability of a USDS to derive SF measurements from the evolution of the snow cover. The secondary aim is to discover whether a SF value can be obtained with a reasonable accuracy over very short (minute–hour) time scales using a USDS. The third goal is to determine the potential benefits of using multiple USDS to observe changes in the snow cover depth. The fourth goal is to illustrate the importance the snow depth spatial variability has on the SF measurement process.

To accomplish these tasks, this study introduces a complex algorithm to derive SF values from changes in SD measurements using three collocated snow depth sensors and other in situ observations. What differentiates this algorithm from other approaches is that a SF measurement is indicated only if positive changes in SD are observed by multiple sensors. The use of multiple collocated sensors helps in the identification of other processes that affect the depth of the snow cover. These processes—other than SF such as settling/compaction (snow density), drifting–blowing snow, and melt–sublimation (wet versus dry snow)—will be hereinafter referred to in this paper as the snow cover dynamic measurement error (SCDME).

This study will also show that the derived SF value is highly dependent on the frequency and number of observations used to produce a SF value (similar to an observation in Doesken and McKee 1999; Doesken and Leffler 2000) and the choice of “noise” filter used on the SD time series. The main reason for this is the SCDME, though other studies such as Ryan et al. (2008a) have stressed the importance of instrument siting and data assessment procedures to deal with occurrences of blowing snow, heavy snow, and dendrites, which can degrade USDS data quality. The use of multiple USDS measuring changes in SD over short time intervals should reduce errors associated with signal noise from the acoustic sensors, which can indicate large amounts of false precipitation. This study will also introduce case studies that suggest the characteristics of the snowdrift signal in the SD time series. From these results, analysts should be able to identify this SF measurement error in the future.

## 2. Data sources, measuring devices, and observations

### a. Site locations and time periods

The locations of three Canadian test sites from the Observing Systems and Engineering Section (OSE) of EC are as follows: St. John’s International Airport, Newfoundland (CYYT); Iqaluit International Airport, Nunavut (CYFB); and the Centre for Atmospheric Research Experiments in Egbert, Ontario (CARE)—they are presented in Fig. 1. These sites represent a broad spectrum of climate zones (Phillips 1990), with differing mean monthly and seasonal SF accumulations (Brown and Braaten 1998) and seasonal snow cover differentiated by physical properties such as depth, density, and type of snow layers (Sturm et al. 1995). Table 1 presents precipitation climate statistics for these locations (Éva Mekis 2010, personal communication). Table 2 presents the direction of the observed prevailing wind by quadrant during the SF events used in this study.

Owing to either missing data or sensor malfunction, the following time periods are collected for each of these locations, respectively. For St. John’s the period runs from 0600 UTC 29 January 2006 to 0600 UTC 1 April 2006. For Iqaluit it runs from 0600 UTC 12 October 2007 to 0600 UTC 13 April 2008. For CARE, the first period runs from 0600 UTC 1 November 2007 to 0600 UTC 12 November 2007, while the second runs from 0600 UTC 16 November 2007 to 0600 UTC 9 March 2008.

### b. Ultrasonic snow depth sensors

*V*

_{sound}) in meters per second for the ambient air temperature (

*T*

_{air}) in kelvin, the following equation is used:With (1), the distance from the sensor to a target is typically obtained in 1 s. The error of measurements is ±1 cm or 0.4% of the distance to the target, whichever is greater (hereinafter referred to as the sampling error). The sampling error grows with the increase of the distance from the reflecting surface.

High-frequency, small-amplitude noise can be an impediment to accurate snow accumulation measurements (Ryan et al. 2008a). To reduce this occurrence, the SR50 sensors were polled once a minute with SD measurements recorded. Any missing measurement was replaced by the recorded value 1 min earlier. The SR50 also outputs indicators of measurement quality. These data, named quality numbers, have no units of measurement but can vary from 152 to 600 (Campbell Scientific 2009). Numbers greater than 300 indicate a degree of uncertainty in the measurement. Any measurement of poor quality was replaced by the value measured by that SR50 1 min earlier.

Additionally, a 4-min weighted moving average for each individual SR50 is produced every 5 min as follows. If all four SD measurements, or three of the four measurements, are found to be within 2.5 cm of each other, then either three or four of the minute SD measurements are averaged to produce the weighted SD value at 5 min. When at least three of the SD measurements are found not to be within 2.5 cm of each other, the measurements taken over the last 2 min of each 4-min window were checked to see if they were within 2.5 cm of each other. If they are, then these last 2 min of the four minute values are averaged to produce the weighted SD value at 5 min. Otherwise, the weighted SD value recorded 5 min earlier was placed into that location in the time series.

At all test locations, three SR50s were installed between 1 and 2 m above the surface onto a trestle 3 m high and 15 m long. At CARE (see Fig. 2a), the trestle was oriented in the north–south direction. The first sensor (referred as SR50_{1}) was placed 9 m to the north of the other two and faced north. The remaining SR50s (SR50_{2} and SR50_{3}) were oriented 180° apart and faced west and east, respectively. All sensors were installed over closely mowed grass.

At CYFB (Fig. 2b), the trestle was oriented in the northeast–southwest direction. All three sensors faced to the northwest, with the SR50_{1} (the one farthest to the northeast) and SR50_{2} spaced 5 m apart; and the SR50_{1} and SR50_{3} spaced 10 m apart. All sensors were installed over bare earth.

At CYYT (Fig. 2c), the trestle was oriented in the northeast–southwest direction. The SR50_{1} faced northwest and was placed 7 m to the northeast of the other two. The SR50_{2} and SR50_{3} were oriented 180° apart at the southwest end of the trestle and faced southeast and northwest, respectively. All sensors were installed over bare earth.

The test sites infrastructure reflected the World Meteorological Organization (WMO; WMO 2008) siting and exposure criteria. Out of the three test sites, CYYT experienced the largest observed snowdrifts. While the concrete posts at the bases of the trestles at CYYT did result in some additional localized snow accumulation/melting, these influences on the derived SF measurements were lessened because the SR50s were placed on metal posts 1.5 m away from the bases of the trestles (same for all sites). At the other two locations, the effects of the concrete used at the base of the trestles had much less impact on the evolution of the snow cover surface.

Finally, an important point to address is the nonuniform installation of the three SR50s at the three test sites. While this fact introduces limitations in intercomparison (such as the effects of snowdrift on each of the test sites will be different if one uses different sensor orientations and therefore the derived SF values can be significantly different for individual snow events), numerical data analysis presented later in this paper will show that the influence of the SCDME and changes in data assessment procedures produced similar results, irrespective of the aforementioned nonuniform installation.

### c. Snowdrift acoustic sensors

Snow particles are transported by the wind in three different processes: creep, saltation, and suspension (subcategorized as drifting or blowing snow). Creeping particles roll along the snow surface. Saltation is defined as snow particles that bounce along the snow surface and whose height rarely exceeds 0.1 m. Creep or saltation is not seen in snowdrift flux measurements but can be measured by a trap buried in the snow (Jaedicke 2001). Suspension occurs when the snow particles become mobile as the shear stress exerted by the wind becomes large enough to overcome gravity and cohesion (Pomeroy and Gray 1990; Gordon et al. 2009).

This study presents results from an instrument that records the snowdrift flux acoustically. The Swiss designed sensor FlowCapt (FC), built by IAV Engineering (Chritin et al. 1999), consists of Teflon-coated tubes with a microphone in it. When snow particles hit the tube during snowdrift events, they induce acoustical pressure inside. By Fourier transformation, the signal can be divided into the high frequencies of the impacting snow particles and the low frequencies resulting from the wake eddies behind the tube. Since the mass flux of snow [denoted as *Q* (g m^{−2} s^{−1})] usually decays exponentially with height, the FlowCapt measurements serve as an estimate rather than a precise flux measurement (Clifton et al. 2006).

*P*denotes the acoustic pressure (Pa),

*F*is the mass flux of particles (g m

^{−2}s

^{−1}),

*U*is the particle speed (m s

^{−1}),

*N*is the particle concentration (m

^{−3}), and

*α*is a proportionality constant.

At first approximation, the (*UN*^{−1})* ^{α}* term is regarded as a constant, so (2) becomes linear in

*F*. It is beyond the scope of this paper to discuss more recent results using this sensor. For additional information, see Jaedicke (2001), Lehning et al. (2002a), Cierco et al. (2007), and Lehning and Fierz (2008).

FlowCapt sensors are used to delineate the characteristics of the snowdrift signal in the SD time series. Measurements of the mass flux of snow taken every 15 s are averaged to produce a snowdrift flux value every 15 min. At CARE, one FlowCapt is placed just outside the 22° field of view of each of the three SR50s. Therefore, concurrent measurements of SD and snowdrift essentially represent the same sampling point.

### d. Defining the daily snowfall reference

One of the goals of this study is to show that small changes in data assessment procedures can produce relatively large differences in derived SF. Unfortunately, only at the CYYT site did a NAV CANADA contract weather observer record daily 0600 UTC SF using a ruler and an EC Weaver Snow Board as per the EC Manual of Service Weather Observations (Environment Canada 2009) standards (a measurement with which we can compare the daily SF values derived from changes in the snow cover).

*i*is denoted by

*X̃*,

_{i}*X*is the current output value of the precipitation gauge, and

_{i}*W*is a weighting constant, which in this case is 10% (0.1).

Additionally, at both sites OSE constructed a WMO Octagonal Vertical Double Fence Intercomparison Reference (DFIR) and placed within it a GEONOR. An adaptation of the one-wire GEONOR algorithm currently used by EC (Lamb and Durocher 2004) is used to filter this data. Furthermore at CARE, various present weather sensors [Meteorological Service of Canada Precipitation Occurrence System Sensor (POSS), Ott Parsivel, and Vaisala Present Weather Detector (PWD)] were used to delineate periods of solid, mixed, and liquid precipitation. Data analysis at CYFB determined that only solid precipitation fell during the test period.

Snowfall is defined as the total accumulation of new snow since the last observation, while SWE is conventionally measured with a precipitation gauge (manual or automated) by weight or by volume. If the snow density is known or estimated, SWE can be converted to SD and vice versa. Many factors can affect the density of snow and can be estimated with careful diagnosis of in-cloud and surface air temperatures and humidity, surface wind speeds, and vertical motion using carefully collected measurements and model forecast fields (Roebber et al. 2003, 2007; Cobb and Waldstreicher 2005; Dubé 2006; Ware et al. 2006). An alternative approach is through the use of a disdrometer, where the density can be parameterized by a power law based on the snow size distribution (e.g., Pruppacher and Klett 1997).

Even though the aforementioned studies have exhibited some successes, since there are inherent uncertainties in the use of these approaches, this study employed a 10-to-1 snow-to-liquid ratio (SLR) on all the aforementioned GMs during periods of known SF. These recorded amounts, plus the SF measurements provided by the Vaisala PWD at CARE, are averaged over every 15-min interval and summed to produce a daily 0600 UTC SF reference value. The total recorded precipitation accumulations for the defined test period at CARE is 326.1 mm (230.6 mm of SWE) and at CYFB 125.2 mm.

*S*

_{amount}, as a function of liquid equivalent precipitation

*P*

_{rate}, the temperature in kelvin

*T*

_{air}, and the 10-m wind in meters per second

*U*

_{10}, is given byIn (4),

*ρ*

_{water}is the density of water (1000 kg m

^{−3}), and

*ρ*

_{snow}is the density of snow (kg m

^{−3}) given by

With (5), the *S*_{amount} values were calculated for every 15-min time interval during periods of known SF and summed for the entire test period. In comparison, the 10-to-1 liquid equivalent SF reference values (summed over the entire test period) gave 17.11% and 31.62% less SF for CARE and CYFB, respectively. This comparison suggests that the 10-to-1 SLR approach underestimates the true SF amounts.

## 3. Snow depth time series algorithms

### a. Telescoping series

A telescoping series is a series whose sum can be found by exploiting the fact that nearly every term cancels with either the succeeding or preceding term. In this study, a modified telescoping series is used to show that the SF measurements exhibit a sensitive dependence on the frequency of observations (we will only sum the positive differences in SD since SF is defined as the accumulation of new snow). This is accomplished by sampling the same SD time series over and over again using different time steps and different threshold values similar to the selection criteria to be described in section 3b. If the derived SF measurement was expected to have little sensitivity with regards to the chosen sampling time period, or the way the SD time series is filtered, one would expect to derive SF measurements very close to each other. In this study, we show that, in general, this is not the case.

*T*,

_{s}*T*

_{s+1}), the quantityis calculated, where LSF(

*T*,

_{s}*T*

_{s+1}) represents the local snowfall value over (

*T*,

_{s}*T*

_{s+1}), and

*H*(

*T*) denotes the height of the snow cover at time

*T*. We approximate the total SF during the period in question by the following formula:where

*H*(

*T*

_{0}) represents the height of the snow cover at the start.

### b. S3–1 snowfall algorithm

Next, a more complex algorithm is introduced. This SF derivation algorithm, denoted as S3–1, works on the principle that three SR50s are used to find correlations of positive changes in SD between collocated SD time series. These collocated measurements are then combined to obtain the “first-order estimate” of SF, while a GM is used as a verification to ensure that changes observed in the SD levels by the SR50s occurred during a period of precipitation. In S3–1, the number 3 refers to the number of SR50s used, while the number 1 refers to the use of a GM. Variations of the algorithm are to run it without using the GM verification check or to use only one or two SR50s.

At the beginning of the measurement process, the SD values for the three SR50s, and the measured weight of water collected by the GM, are put into placeholders. For each subsequent measurement (taken every 5, 10, 15, 20, or 30 min; 1, 2, 3, or 6 h), new SD and GM values are recorded and from these, the placeholders are subtracted. The minimum time period used is the length of the time step, while the maximum time period allowed is 6 h as per the Environment Canada (2009) standards (i.e., this measurement should be taken minimally daily, but it can be taken 4 times per day).

*if*

_{i}Note that the S3–1 algorithm is an adaptation of the GEONOR weighing precipitation gauge algorithm (Baker et al. 2005) developed by the National Oceanic and Atmospheric Administration (NOAA)’s National Climatic Data Center. The SD measurements taken by the three SR50s are analogous to the measurements of the change in weight of liquid water measured by three transducers.

### c. S3–1 normalization parameter

*i*≤ 3; 2 ≤

*j*≤ 3, and

*i*<

*j*.

The right side of (10) represents the “difference of newly recorded SF” between two SR50 sensors in the numerator divided by the “total magnitude of new SF” recorded by both SR50 instruments. If the difference in SF between any two sensors is less than 35% (i.e., NP* _{ij}* ≤ 0.35) of the total SF measured by summing the SF recorded by these sensors, then the measurements corroborate.

*h*and the change in SD recorded beneath the second sensor as (

*h*+

*d*). Inserting these values into the inequality NP

*≤ 0.35 yields the relationshipFrom which by rearrangement we obtainThe selection criteria in inequality (12) states that SF is said to have occurred if the change in the second sensor is the same as the change in the first sensor*

_{ij}*h*, plus some small difference

*d*.

### d. S3–1 estimated value of snowfall

Denote the measurement of SR* _{i}* by

*M*for 1 ≤

_{i}*i*≤ 3. Define empirically their probabilities and denote them as

*P*for 1 ≤

_{i}*i*≤ 3.

#### 1) Outcome 1

If NP12, NP13, and NP23 are all less than or equal to 0.35, then *P*_{1} = *P*_{2} = *P*_{3} = ⅓ and SF = *P*_{1}*M*_{1} + *P*_{2}*M*_{2} + *P*_{3}*M*_{3} = (⅓)(*M*_{1} + *M*_{2} + *M*_{3}).

#### 2) Outcome 2

If two of three NPs are less than or equal to 0.35 (e.g., NP12 and NP13), then *P*_{1} = 1 and SF = *P*_{1}*M*_{1} = *M*_{1}.

#### 3) Outcome 3

If only one of the three NPs has a value less than or equal to 0.35 (for example NP12), then *P*_{1} = *P*_{2} = ½ and SF = *P*_{1}*M*_{1} + *P*_{2}*M*_{2} = (½)(*M*_{1} + *M*_{2}).

#### 4) Outcome 4

All three NP have values greater than 0.35. This means that the change in SD observed by each of the three SR50s is not of the same relative order of magnitude. Therefore, a SF value of 0 cm is generated (actual SF may be missed in this case).

## 4. Results and discussion

### a. Snow cover evolution at CARE and Iqaluit

Figure 3 illustrates a sequence of ultrasonic measurements taken by the three SR50s at CARE and Iqaluit once daily at 0600 UTC. Since precipitation and other processes that affect the height of the snow cover may take place simultaneously, the height changes observed represent either a net accumulation or net ablation.

At CARE (Fig. 3a) from late November 2007 to early March 2008, several periods of heavy SF and significant melting were observed by all three SR50s. One can differentiate between the periods of melting and snowpack settling/compaction by observing that SD levels decrease more rapidly during melting. Furthermore, it is noticeable that the snow cover evolution derived from the three SR50s represent three essentially pairwise different time series. First, note that the north facing SR50_{1} sensor tended to observe more snow on the ground throughout the winter season than the other two. Second, note the high degree of spatial variability exhibited by the three sensors, which were sited very close to each other. Third, note the number of times the three curves crossed each other throughout the time series. All these factors reaffirm the point that the snow cover is spatially variable at several scales (Schweizer et al. 2008). It also reaffirms the difficulty of taking accurate SF measurements from changes in the height of the snow cover over time.

Examining the evolution of the ultrasonic measurements taken over the winter of 2007/08 at Iqaluit (Fig. 3b), one does not observe evidence of major snowmelt since temperatures at this test site remained well below or close to 0°C throughout the time period investigated. Note, as observed in Neumann et al. (2006), the differences in SD between collocated SD depth sensors became greater as the winter season progressed because more snow accumulated on the ground and the effects of snowdrift became more pronounced.

### b. Derived snowfall amounts are dependent on the frequency of observations

We now introduce a modified telescoping series to show that the derived SF measurements exhibit a dependence on the frequency of observations (Fig. 4). By repeatedly measuring the changes in snow cover while moving forward in time, and then summing all the terms in the series using Eq. (7), it is obvious that changing the frequency of observations results in profoundly differing SF accumulations (for all six sensors at two different locations with different test site configurations). The spread between the neighboring “trajectories” increases in time, with the smallest frequency of sampling used by Eq. (7) resulting in the most SF.

It is important to emphasize that the modified telescoping series used in this subsection looks only at positive changes in snow cover and does not remove the SCDME or the sampling error. Thus, the measurement process itself introduces another type of uncertainty in the sense that if the sampling has a smaller time period, there is a possibility of accumulating a larger sampling error (observe Figs. 4a, 4b, and 4c where the spread between the 15- and 30-min accumulations are noticeably greater than in Figs. 4d, 4e, and 4f). Additionally, observe that the SF accumulations progressively diminish as the frequency of SD difference measurements increases over the chosen sampling time period. This result is in agreement with the work done by Doesken and McKee (1999) who showed that on average SF measurements taken manually every 6 h and summed for daily totals measure 19% more SF than those taken once daily (owing to the processes of snow settling/compaction and snow cover redistribution due to the wind).

In Fig. 5, Eq. (7) is rerun using a 15-min measurement window and employing the MISDT filter to remove some of the aforementioned sampling errors. Every 15 min the observed change in SD must be greater than or equal to the MISDT (0.5, 0.8, 1.0, 1.2, 1.5, and 2.0 cm are used) for that term in the series to be summed to produce a SF measurement. These figures show that filtering the SD time series can affect the value of the derived SF measurements. The total SF obtained progressively diminishes as the value of the MISDT increases over the chosen 15-min-sampling time period. This effect is much less pronounced using a 3- or 6-h frequency of sampling (figures not shown).

Finally, Pearson correlation coefficient statistics and their associated *p* values are presented for CARE (see Table 3) to illustrate the changes in SD measurements (both increasing and decreasing) between collocated sensors as a function of the frequency of sampling. There is a high degree of correlation between all three pairs of SR50s using a 6-h sampling interval (all nearly 70%). These correlation values decrease quite significantly for the 1-h sampling (21% through 47%) and are negligible at 15 min (note that the *p* values are significant for these). These results show that the derivation of SF for very time short time scales (minutes to hours) by a single SR50 sensor may be problematic, and the application of a more complex algorithm with multiple sensors and/or multiple types of sensors is more than likely needed.

### c. Diagnosing snowfall measurement errors owing to snowdrift

Hanesiak et al. (2003) observed between 500 and 600 h of blowing snow (6%–7% of the year) in the Canadian arctic. Li and Pomeroy (1997) showed that between 3.5% and 12% of the year, drifting and blowing snow was observed at sites located in the Canadian Prairie Provinces. Any attempt to measure the true SF value from changes in SD over time must take into account the effects of snowdrift and snowpack creep. This subsection presents four case studies at CARE to diagnose the snowdrift signal from the SR50 SD measurements and to show that the effects of snowdrift can result in an underestimation of true SF amounts.

There are important observations to note from Fig. 6a. First, observe that after 1.5 cm of snow was indicated by the S3–1 time series near 1300 UTC, the SD levels began to fall while the SWE time series was rising. This shows that the effects of snowpack settling can be an important subcomponent of the SCDME. Second, after 1.2 cm of SF was produced by the S3–1 time series at 0800 UTC, no further SF value was indicated until 1300 UTC. Note the large values of the observed snowdrift flux and the SR50_{2} and SR50_{3} time series become parallel to the *x* axis while the SWE time series remained increasing (which suggests that mass was removed here from the snow cover surface by wind erosion).

Snow on the ground has a complex microstructure that changes with the environmental conditions. Using data collected from the National Aeronautics and Space Administration (NASA) Cold Land Processes Field Experiment in Colorado during February and March of 2002 and 2003, Azar et al. (2008) showed again that the density of snow increases toward the bottom of the snowpack. Snow density was found to be about 0.1 kg m^{−3} for the recently fallen snow, increasing to 0.4 kg m^{−3} for the older snow found on the bottom layers. This result implies that lighter density, recently fallen snow should often represent a larger component of the snow that is transported by the wind than the higher density, older snow.

Figures 6b, 6c, and 6d present three additional case studies, which suggest that the snow drift signal is represented when the SD time series becomes parallel to the *x* axis (though the possibility that the accumulation and compaction rates are equal needs to be considered). Compare the behaviors of the SD time series versus the SWE time series during observed periods of snowdrift (as in Fig. 6c from 0800 through 1100 UTC, where 3.8 mm of SWE was recorded while no SF could possibly be derived from the SR50_{2} and SR50_{3} time series). Additionally, in Fig. 6c after 1300 UTC, note that the effects of snowpack settling and snowpack creep introduce a SF measurement error. In fact, owing to the combined effects of snowdrift and snow settling/compaction in Fig. 6c, 13.0 mm of liquid equivalent precipitation was recorded by the reference versus 7.5 cm derived by the S3–1 algorithm over the entire day. In Fig. 6b, note the 2 mm of SWE recorded from 0600 through 1400 UTC. Contrast this with the negligible changes in SD and observations of snowdrift. In Fig. 6d, the occurrence of snowpack creep results in the S3–1 algorithm giving a 17.5 cm value at 0130 UTC 9 March 2008.

To further investigate the behavior of the snow cover surface during periods of observed snowdrift and SF, Table 4 is presented for each SR50 sensor and its associated snowdrift sensor at the CARE test site. The range between the maximum and minimum observed 15-min changes in SD is provided during periods of measured snowdrift and SF. Observe that, as we isolate the stronger measurements of snowdrift, the 15-min changes in snow cover depth become close to 0 (specifically note the differences in the range between the maximum and minimum changes of SD for the first and last columns for the SR50_{1} and SR50_{3} sensors). Notice as well that the range of SR50 SD changes for the SR50_{2} are similar until all occurrences of snowdrift flux are greater than or equal to 10 g m^{−2} s^{−1}. This shows that the prevailing wind direction and test site infrastructure can affect the measurements. Furthermore, these statistics provide corroborating evidence of the characteristics of the snowdrift signal in the SD time series (i.e., the SD time series becomes parallel to the *x* axis).

### d. Validation results for the S3–1 snowfall algorithm

We propose to identify the combined magnitude of the SCDME and sampling error by comparing the average of the absolute value of differences between 24-h recorded GM and S3–1 SF. In addition, we will take the percent difference between GM and S3–1 SF summed over the entire dataset. By comparing the results generated from both statistical approaches, we can obtain a better understanding of the combined magnitude of the SCDME and sampling error generated by the snowpack on a case-by-case basis versus the entire winter season. It is also important to note that the recorded variations of the absolute value of difference statistics are small owing to the fact that lighter precipitation events are also included in the data analysis.

Our investigation begins with a series of statistics generated at the CARE test site (see Table 5). These results confirm the benefits of using multiple sensors and multiple types of sensors to derive a SF value. First, compare the two numbers in the average of the absolute value of difference column between the 1.0S3–1 and 1.0S3–0 algorithms. Note that the use of a GM as a precipitation verification check can diminish the occurrence of false precipitation being recorded as SF. Second, in the same column, compare the 1.0S3–1 algorithm results with all the algorithms using only one instrument (1.0S1–1 SR50_{1}, 1.0S1–1 SR50_{2}, and 1.0S1–1 SR50_{3}). This shows that the consensus of three USDS sensors yields an improved derived SF value (i.e., the SCDME is reduced).

Next, note that the average of absolute value of difference statistics produced different values corresponding to different MISDT values, and they increased with larger threshold values. This result suggests that the use of a smaller MISDT is better in a statistical sense. However, in an event-to-event analysis (case studies are not shown) no preferred MISDT value was found to systematically reduce the SF measurement errors from the underlying snowpack.

A comparison of the numbers for 1.0S3–1 and 1.0S3–0 algorithms in the percent difference column suggests that, statistically, one obtains a better answer over the entire winter season if a GM is not used as a precipitation verification check. The reason for this discrepancy (in comparison to the statistics in the average of the absolute value of difference column) is complicated. First, there is a tendency during heavy SF events for both the S3–1 and S3–0 algorithms to be unable to measure new SF when the snow cover heights fall because of snow settling/compaction (as observed in Figs. 6a and 6c). Second, while the 1.0S3–1 algorithm that uses a GM eliminates some false SF being recorded due to snowpack creep on a case-by-case basis, the extra SF gained from these same occurrences using the 1.0S3–0 algorithm falsely reduces the SCDME for the percent difference statistic generated for the entire winter season.

Next, compare the percent differences in column 3 of Table 5 given by the 1.0S1–1 SR50_{1}, 1.0S1–1 SR50_{2}, and 1.0S1–1 SR50_{3} algorithms. Note how small the percent difference value for the SR50_{3} is relative to the other two. This result provides corroborating evidence that sensor installation location and orientation influenced by prevailing wind direction and snowpack depth spatial variability can have a profound effect on the magnitude of the derived SF measurement.

Additionally, we provide evidence that the use of three sensors to derive a SF measurement is better in a statistical sense than two sensors (see Table 6). Compare the numbers in the absolute value of difference column between the 1.0S3–1 algorithm and all its variations using two sensors [GM = 1 (on)] and the 1.0S3–0 algorithm and all its variations using two sensors [GM = 0 (off)]. Note that three sensors have a smaller combined SCDME and sampling error than two sensors, and that in all instances the use of a GM as a precipitation verification check improves the results (e.g., 1.0S2–1; 23 versus 1.0S2–0; 23). Furthermore, by examining both Tables 5 and 6, we can see that two sensors have a smaller combined SCDME and sampling error than one.

Table 7 is presented to provide additional statistical evidence that the SF measurement has a sensitive dependence on the frequency of observations used to derive it. Compare the numbers in the average of the absolute value of difference column for 15 and 30 min (higher values) versus 5, 10, and 20 min (lower values). Then, in the same column compare the numbers for 15 and 30 min (higher values) versus 1 and 2 h (lower values) and then 1 and 2 h (lower values) versus 3 and 6 h (higher values). Using time steps of 15 and 30 min and 3 and 6 h statistically results in a worse answer than using time steps of 5, 10, and 20 min and 1 and 2 h. These statistics demonstrate that the SCDME plays a significant role in influencing the ability to derive a SF measurement from changes in the snow cover height over time, and that its effects are random.

Finally, SF verification statistics are provided for the other two test sites (CYFB and CYYT) to show that the results presented for CARE are not an artifact of the test site setup or geographic location (see Tables 8 and 9). Note that the derived SF measurements once again exhibit sensitivity on the frequency of observations used to derive it. Additionally, the combined SCDME and sampling error are reduced yet again by the usage of multiple USDS and using a GM as an SF verification check.

## 5. Concluding remarks

The findings of this study demonstrate the difficulty in obtaining a reasonably accurate snowfall value from the changes in snow cover levels over time using an ultrasonic ranging sensor over very short (minute–hour) time scales. The interplays of numerous essential factors that influence these levels result in the measurement exhibiting a strong sensitivity on the time interval between consecutive measurements used to generate the snowfall value. Pearson correlation statistics at CARE showed that the degree of linear association between collocated snow depth time series diminishes as one sample’s change in the snow cover depth over shorter time intervals. These results brings into question the reasonable accuracy of snowfall measurements derived in the past using ultrasonic ranging sensors, especially in locations not well shielded from the wind and where snow depth spatial variability is prominent.

Another important finding of this study was to propose possible characteristics of the snowdrift signal in the snow depth time series obtained from measurements using an ultrasonic snow depth ranging sensor (identified when the snow depth levels remain essentially constant over a time interval even when snowfall is occurring). Case studies of snowdrift reinforced the complexity and difficulty of extracting a snowfall measurement from changes in snow depth levels over time. They also provide proof of the characteristics of the snowpack creep signature, where one sees an increase or decrease in observed snow depth levels from one sensor where the others have not observed a change of similar magnitude.

The S3–1 algorithm introduced in this study was shown to successfully reduce some of the errors in the measurement (in many cases a reasonably accurate measurement was produced). This fact was verified through statistics presented, which show that using a triple configuration of SR50s gives a better answer than using just one SR50. Additionally, the use of three sensors was found to be statistically better than two, and two sensors were statistically better than one. Also, using a total precipitation gauge to verify periods of snowfall was shown to reduce the occurrence of false snowfall reports.

To improve upon the accuracy of derived snowfall measurements in many more cases, the use of more sophisticated formulas should be taken into consideration in the development of a second-generation S3–1 algorithm. Measurements of snowfall derived from sonic measurements could be corrected for the effects of snow settling/compaction using relationships described in the SNTHERM (Jordan 1991) or SNOWPACK (Bartelt and Lehning 2002; Lehning et al. 2002b) models. Since the characteristics of the snowdrift signal in the snow depth time series obtained from measurements using an SR50 were identified in this study, the next version of the algorithm should be able to improve the result. Finally, the possibilities of doing weighted, weather-dependent combinations of multiple sensors, and/or developing site specific “snow depth correction factors” analogous to those developed to correct for snow gauge undercatch, should be explored.

## Acknowledgments

Thanks are given to my colleagues Rodica Nitu, Sorin Pinzariu, Tomasz Stapf, Kai Wong, Chris Hampel, Julie Michaud, Emelia Vaserbakh, George Davies, Kenneth Wu, Julie Narayan, and Bill Sukloff for their technical assistance; Yves Durocher for his guidance developing the S3-1 snowfall derivation algorithm; and Dr. Éva Mekis for providing the climate precipitation statistics. Thanks are given also to Dr. Paul Joe, Dr. Chris Fogarty, and three anonymous reviewers for their suggestions to improve this paper.

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Climate precipitation statistics for Egbert, Iqaluit, and St. John’s.

Prevailing 3-m wind direction (averaged over 15 min for minute wind speeds greater than or equal to 1 m s^{−1}) measured while snowfall was occurring for all events used in this study at Egbert, Iqaluit, and St. John’s. The numbers denote the percentage of time the wind direction was observed by quadrant.

Pearson product moment coefficients of correlation (*r*) and associated *p* values for observed changes in snow depth (excluding the value 0) between the three SR50s over 15-min and 1- and 6-h intervals at the CARE test site. The period of sampling for these statistics runs from 0600 UTC 16 Nov 2007 to 0600 UTC 9 Mar 2008. Pearson correlation statistics measure the degree of linear association between two variables (range between −1 and 1). A value close to 0 indicates there is no linear association between the two variables. A *p* value measures the probability of observing a value as extreme as or more extreme than the one observed. A *p* value ≤ 0.05 indicates that the Pearson correlation value is significant.

Observing the maximum and minimum 15-min changes in snow cover depth for each SR50 (cm) when snowdrift is indicated by its collocated FC sensor (*Q*; g m^{−2} s^{−1}) at CARE. Each column in this table changes the lower bound of the snowdrift flux value to observe how the range of changes in snow cover depth are affected by progressively reducing the sample size *N* to isolate stronger occurrences of snowdrift. Note that all measurements of snowdrift and 15-min changes in snow cover depth occurred during known occurrences of snowfall indicated by Present Weather Sensors. The period of sampling for these statistics is the same as in Table 3.

Average of the absolute value of difference statistics (first column) between 0600 UTC GM SF and various variations of the S3–1 algorithm at CARE. The algorithm time step used for each algorithm variation is 15 min and the number of days in the dataset is 125. The numbers before the letter *S* represent the value of the MISDT in cm. The number immediately after the letter S represents the number of ultrasonic sensors used to generate the statistics (3 or 1). The number after the dash indicates whether or not the 0.2-mm GM verification check is used (1 = on; 0 = off). For the last three rows, the algorithm variations use only one SR50 sensor. Each of these employs a 1.0-cm MISDT and uses 0.2 mm as the GM verification check. Note the numbers immediately after the semicolon to identify the sensor used. The percent difference statistics (second column) are taken as the difference in the total GM SF for the entire dataset (125 days) vs the total S3–1 SF summed over the entire dataset. The false-alarm ratio for the 1.0S3–1 algorithm is 0.8%.

As in Table 5, but varying the number of ultrasonic sensors used (2 or 3). To identify the sensors used for each algorithm variation, note the numbers immediately after the semicolon. All algorithm variations use 1.0 cm as the MISDT, and 15 min as the algorithm time step.

As in Table 5, but varying the length of the algorithm time step. To differentiate between the lengths of time steps, note the numbers immediately after the semicolon. All algorithm variations use 1.0 cm as the MISDT.