1. Introduction
Winter precipitation forecasting typically involves three steps: 1) production of a quantitative precipitation forecast (QPF), 2) determination of precipitation type, and 3) application of a snow-to-liquid ratio (SLR) if snow is expected to be the dominant precipitation type. The resulting snowfall amount forecast is the product of QPF and SLR. In addition to QPF uncertainties, large inter- and intrastorm SLR variabilities are major contributors to snowfall forecast error. For example, the 6-h SLR observed at National Weather Service (NWS) offices ranges from 1.9 to 46.8 (Roebber et al. 2003), whereas the daily SLR in the central Rocky Mountains ranges from 3.9 to 100 (Judson and Doesken 2000). Given these wide ranges, even a perfect QPF is often of limited value if an incorrect SLR is applied. The continued use of unproven empirical techniques to predict SLR led Roebber et al. (2003) to describe this portion of the winter precipitation forecast process as “largely a nonscientific endeavor.”
Defined as the ratio of the depth of new snowfall to the depth of melted liquid equivalent, SLR was chosen over several other methods of quantifying snow character (e.g., density, percent water content, specific gravity) due to its relevance in operational forecasting. An SLR of 12.5 corresponds to a snow density of 80 kg m−3, 8% water content, and a specific gravity of 0.08. SLR depends on the fraction of void space within a sample of snow, a property controlled by ice crystal size and shape (habit), riming, aggregation, sublimation or melting of exterior crystal branches at the surface and aloft, mechanical fragmentation by strong winds, rain falling on snow, and snow metamorphism on the ground (Roebber et al. 2003; Baxter et al. 2005). These processes can be viewed in a top-down manner following an ice crystal from formation in a cloud to settlement on the ground. Crystal habit can serve as a first guess for SLR and is determined primarily by temperature, except between −14° and −17°C where supersaturation with respect to ice controls a shift from plates to dendrites (Nakaya 1954). Power et al. (1964) found the highest SLR values (19–25) for dendrites and the lowest (10–11) for columns, although Nakaya (1954) found SLR values as high as 100 for dendritic snowfalls in low-wind conditions immediately after accumulation.
During or after depositional crystal growth, riming can fill pore space and decrease SLR by 50% or more (Power et al. 1964). Aggregation of multiple crystals can lead to higher SLR values (Roebber et al. 2003). Regions of above-freezing temperatures or subsaturation with respect to ice can further decrease the SLR by melting or sublimating falling crystals (Roebber et al. 2003). Once near or at the ground, surface wind speeds above 9 m s−1 transport snow and reduce SLR by mechanically removing outer crystal branches (Li and Pomeroy 1997; Roebber et al. 2003). Sublimation or melting on the ground can further decrease SLR, as can rain on snow, which adds mass while maintaining or decreasing depth. Snow metamorphism, often beginning while snow is still accumulating, can result in more rounded forms with a lower SLR (Doesken and Judson 1997; Judson and Doesken 2000; Baxter et al. 2005).
The complexity of the snow formation process has prompted forecasters to take a variety of approaches to predicting SLR, including climatologically, statistically, and physically based methods. The commonly accepted “10-to-1 rule” for SLR is thought to have originated from a climatology in the mid–nineteenth century (Roebber et al. 2003), and problems with this approach were noted well over a century ago (Abbe 1888). Based on SLR observations from Cooperative Observer (COOP) stations across the United States, Baxter et al. (2005) found that SLR varies regionally and suggest that 13 is more appropriate if a fixed ratio is desired.
Various empirical prediction methods relate SLR to temperatures at the surface or aloft. Bossolasco (1954), Diamond and Lowry (1954), Judson and Doesken (2000), Wetzel et al. (2004), and Simeral (2005) produced least squares fits between snow density (inversely related to SLR) and surface or 700-hPa air temperature, with linear correlation coefficients of 0.52–0.74. Loosely based on this relationship, the NWS New Snowfall to Estimated Meltwater Conversion Table (U.S. Department of Commerce 1996; hereafter, NWS table) relates SLR to surface temperature. Initially created for hydrological applications, the NWS table has since been applied directly by human forecasters (Roebber et al. 2003) and within the Global Forecast System and Eta Model output statistics (MOS) text products (Cosgrove and Sfanos 2004) to predict snowfall amounts from QPFs. Roebber et al. (2003) and Byun et al. (2008) show, however, that the NWS table has limited predictive ability because SLR is more closely related to temperatures at the level of snow formation than at the surface (Kyle and Wesley 1997).
Using surface and radiosonde observations as input, Roebber et al. (2003) used an ensemble of 10 artificial neural networks to predict SLR in one of three classes: heavy (1 < SLR < 9), average (9 ≤ SLR ≤ 15), and light (SLR > 15). When tested using operational model guidance, the ensemble offered a large enough improvement over the use of a fixed number of 10 SLRs or the NWS table to be economically beneficial to municipal snow-clearing operations (Roebber et al. 2007).
Alternatively, Cobb and Waldstreicher (2005) propose a more physically based method for SLR prediction. In numerical model forecasts, Cobb and Waldstreicher (2005) apply a Gaussian relationship between SLR and temperature in regions of inferred snow growth. SLR values in each region are then weighted based on the relative magnitude of the upward vertical velocity to yield a single SLR value. The Cobb and Waldstreicher (2005) method is used widely at NWS offices (R. Graham, NWS Salt Lake City, 2009, personal communication), but does not explicitly account for riming or processes occurring below cloud base. The method also relies upon vertical velocities from the North American Mesoscale (NAM) or Global Forecast System (GFS) models, which fail to predict the distribution and intensity of terrain-induced vertical motions in regions where the topography is poorly resolved.
The aforementioned studies use data from numerous sites to construct their SLR algorithms. While studying more than one site increases the sample size, it does not account for the possibility that the atmospheric factors affecting SLR might differ from one site to another, particularly in regions of complex topography. Here, we take a different approach by concentrating on a single high-mountain site with frequent winter storms and a record of consistent and accurate snow and precipitation measurements to 1) develop an SLR climatology, 2) determine relationships between SLR and atmospheric conditions, and 3) evaluate the use of stepwise multiple linear regression (SMLR) for SLR forecasting. This approach seeks to remove contributions from geographic variability and minimize (but unfortunately not eliminate) the influence of measurement error, while maintaining a large sample size. In many respects, this represents a “best case scenario” for daily SLR observations and predictions. The results, while specific to the study site, provide insight into the limits of statistical SLR prediction.
The study site is the Collins Snow Study Plot (CLN) at the Alta ski resort in the Wasatch Mountains of northern Utah, which rise abruptly up to 2000 m from the eastern bench of the Salt Lake Valley (Figs. 1a and 1b). Alta, located at the upper terminus of Little Cottonwood Canyon (LCC in Fig. 1a), averages 1300 cm of snowfall annually and 17.4 days with at least 25 cm of snow per winter [November–April; Steenburgh and Alcott (2008)].
Accurate QPF, SLR, and snowfall forecasts are critical for protecting lives and property at Alta and within Little Cottonwood Canyon, where thirty-six avalanche paths cross State Highway 210 (UDOT-District Two 1987). When a major storm creates high avalanche danger, residents and visitors can be legally required to remain in reinforced buildings in the upper canyon (Steenburgh 2003). QPF is considered one of the most important atmospheric variables in avalanche forecasting (LaChapelle 1980), but knowledge of the SLR can provide additional information regarding snow stability (Casson et al. 2008). The skill of Cottonwood Canyons probabilistic snowfall forecasts issued by the NWS in Salt Lake City has shown no improvement over the past decade (L. Dunn, NWS Salt Lake City, 2009, personal communication), despite increases in the resolution of the operational model guidance, a factor shown to increase QPF skill in the Intermountain West region (Hart et al. 2005). Refinements in SLR prediction are needed for the potential of these QPF forecast advances to be fully realized.
2. Data and methods
The SLR climatology uses eight seasons (November–April 1999–2007) of 24-h snow observations collected at CLN. Although the full record from CLN spans 27 yr (January 1980–April 2007), the most recent eight seasons include a complete record of automated hourly precipitation observations, which enables the identification of periods when precipitation is falling. CLN is a midmountain (2945 m) site that provides a high frequency of winter storms sampled with reliable measurement techniques (Fig. 1b). Snow depth is measured by Alta snow safety professionals twice daily on a white snow board, although only the 24-h sum of these measurements is archived. The snow board is placed in a packed and level area atop the existing snowpack (e.g., Fig. 1c), which has average depths of 86 cm in November and 325 cm in April, greatly reducing the possibility of warm ground temperatures causing a decrease in SLR through snowmelt. Since we take steps to ensure that the precipitation observed at CLN is almost entirely snow for the events under study, we assume that CLN precipitation amounts are equal to the depth of water from melted snow (i.e., the snow water equivalent, SWE). SWE observations are taken using a shielded 8-inch antifreeze-based weighing rain gauge designed to minimize snow buildup on gauge walls. When the accuracy of the measurement is questionable, cores are taken from the snowboard and weighed to determine SWE. Snowfall depth observations are rounded to the nearest 0.5 in., and SWE to the nearest 0.01 in., but converted to metric units for this study.
CLN is sited in a small clearing surrounded by evergreen trees and away from ridgelines (Fig. 1c), which greatly reduces the speed of wind moving over the gauge opening. However, Yang et al. (1998) found an undercatch of 15%–20% by a similarly shielded 8-in. rain gauge in winds of 4 m s−1 at 1-m height. We do not attempt to adjust for the effects of wind on observation accuracy due to the complex topography around CLN and the lack of wind observations at the site. It should therefore be assumed that the distributions of SLR presented for CLN are erroneously shifted toward higher values.
To remove most rain-on-snow events from the dataset, we further restrict events to where 650-hPa temperatures remain below 0°C. Using the Bourgouin (2000) precipitation-type method and accounting for localized depression of the freezing level over sloping terrain (Marwitz 1987), this places the snow level at or below the elevation of CLN for saturated conditions and a moist-adiabatic lapse rate. Freezing rain and sleet are rare at CLN, and although freezing drizzle is not uncommon, the water equivalent received in these events is small and therefore not expected to have an appreciable effect on SLR.
Here an “event” is defined as 1200 UTC–1200 UTC snowfall, regardless of where that 24-h period falls with respect to a complete storm cycle. Events are also restricted to days with at least 2.8 mm (0.11 in.) of SWE and 5.1 cm (2 in.) of snow, representing 457 events. These criteria, used by Judson and Doesken (2000), Roebber et al. (2003, 2007), and Baxter et al. (2005), are intended to reduce the relative errors in SLR due to rounding and measurement inaccuracies.
Upper-air data used to diagnose relationships between SLR and atmospheric conditions comes from the North American Regional Reanalysis (NARR; Mesinger et al. 2006), which was obtained from the National Climactic Data Center and chosen over radiosonde observations (raob) due to its availability at 3-h, rather than 12-h, intervals. Vertical profiles were extracted from the NARR using the Grid Analysis and Display System. Some linear spline interpolation occurs as the software opens raw 32-km horizontal-resolution gridded-binary NARR files and displays fields on a 0.375° latitude–longitude grid. Following this interpolation, temperature, wind speed, and relative humidity were obtained for the grid point nearest to CLN, located approximately 11 km to the northwest of the study site at an elevation of 1900 m. The true elevation at this location is higher, but the topography of the Wasatch Mountains is not fully resolved by the NARR. Additional variables obtained or derived from the NARR include stability (lapse rate and moist and dry Brunt–Väisälä frequencies), moist and dry Froude numbers, a month index (following Roebber et al. 2003), and a wind direction index equal to the number of degrees deviation from 310°, the direction shown to be most favorable to orographic precipitation enhancement at CLN (Dunn 1983). For comparison to 24-h SLR values, the aforementioned NARR variables are averaged during only the 3-h periods of each event (e.g., 1200–1500 UTC) where at least 0.25 mm (0.01 in.) of precipitation fell at CLN. Grid interpolation and the use of reanalysis are potential sources of error. Table 1 shows root-mean-square (RMS) deviations between 0000 and 1200 UTC NARR and Salt Lake City raob profiles for Alta storms.
3. Results
a. General SLR characteristics at Alta
The mean SLR for the 457 snowfall events is 14.4, and the median 13.3, with the former close to the 14.8 obtained by Roebber et al. (2003) for the NWS office in Salt Lake City (KSLC). Grouping the data in bins of width 2 yields a mode between 10 and 12 (Fig. 2). SLR values of exactly 10 occur in only 3% of the events, much lower than reported by many cooperative weather observing sites, where the erroneous use of an SLR of 10 to determine SWE without melting a snow core is common (Baxter et al. 2005). The 25th and 75th percentile SLR values are 10 and 18, respectively, nearly identical to the Baxter et al. (2005) results for lower-elevation sites in northern Utah. This contrasts with the increase in SLR with increasing elevation found by Grant and Rhea (1974), a result that could be due to undercatch by primarily low-elevation cooperative precipitation gauges producing a high SLR bias. SLR at CLN varies from 3.6 to 35.7, the latter much smaller than was found by Judson and Doesken (2000) and Roebber et al. (2003) for multiple sites in the Rocky Mountains and the contiguous United States, respectively. The lack of extremely high SLR events at CLN might reflect snow settlement during the 1–12-h intervals between snow ending and the measurement time.
Day-to-day SLR variability can be large. During a series of snowfall events totaling 233 mm SWE from 3 to 12 January 2005, the daily SLR ranged from 5.2 to 35.7. Similarly, another storm cycle from 21 to 27 November 2001 (described in depth by Steenburgh 2003) produced 210-mm SWE, with daily SLR values ranging from 7.1 to 23. Subday SLR variability certainly exists, but is not captured by our dataset. Higher-frequency measurements are needed to examine this variability.
SLR varies considerably in all months, with the widest range of 3.6 to 35.1 occurring in February (Fig. 3). Mean and median monthly SLRs are lowest in April (12.3 and 11.6, respectively) and highest in March (15.6 and 14.1), although the medians for the months of December–March are not significantly different at the 5% level. There is a marked midwinter peak in the number of extremely high SLR events. Twenty-four of these 26 wild snow events [where SLR is 25 or more; Judson and Doesken (2000)] occur during December–February, with none observed in April.
The 26 wild snow events represent only 5.7% of the total, less than the 8% found in the Park Range of Colorado (Judson and Doesken 2000). Nonetheless, wild snow events at CLN include a 52-cm snowfall with an SLR of 27 on 5 March 2004. While the data here are restricted to 1998–2007, the full CLN snowfall dataset includes a 66-cm event with an SLR of 41 on 7 February 1990. Wild snow events have the potential to yield large forecast errors when a fixed SLR value is applied and, although our sample size is small in this regard, we will later examine the atmospheric conditions characteristic of these events.
On the low end of the SLR distribution, an SLR of less than 7 is observed in 28 events (6.1% of the total). Applying a fixed 10 or climatological SLR in these events can lead to false alarms for NWS Winter Storm Warning issuance. Although none of these events exceeded the 12- or 24-h Winter Storm Warning criteria for the Wasatch Mountains, predicted snowfall in half of these events would exceed the 12-h warning criteria if the climatological mean SLR of 14.4 were applied to the observed SWE. These events include 10 January 2005, when a 52-mm SWE yielded only 26.7 cm of snowfall, corresponding to an SLR of 5.2. The full 1980–2007 CLN snowfall dataset contains additional very low SLR events, notably 11 April 1982, when a 43.4-mm SWE and only 10.1 cm of snow were recorded (an SLR of 2.3). Large SLR variability is clearly present at CLN, and the remainder of this study is concerned with understanding and predicting this variability.
b. Relationship between SLR and local atmospheric conditions
1) Vertical profiles
NARR thermal, moisture, and wind profiles offer insights into relationships between atmospheric conditions and SLR during CLN storm events. Figure 4 shows profiles of the linear correlation coefficient (R) between SLR and NARR temperature, wind speed, and relative humidity at all available levels from 850 to 400 hPa. The strongest relationship is found between temperature and SLR, with R between −0.59 and −0.64 from 850 to 400 hPa (Fig. 4a). For a subset of 80 high (>25 mm) SWE events, the correlation is stronger (−0.62 to −0.76; Fig. 4b). The near-constant correlation coefficient magnitudes for all events contrast with Diamond and Lowry (1954), who observed no relationship between snow density at the Central Sierra Snow Laboratory and 500-hPa radiosonde temperatures, despite finding R = 0.64 at 700 hPa. We attribute our findings at CLN to the thermal structure of Alta snowfall events, during which the lapse rate in the 700–500-hPa layer is consistently near moist adiabatic, and thus temperatures at 700 and 500 hPa are closely related (R = 0.86).
The correlation between wind speed and SLR peaks at 650 hPa for all events (R = −0.39) and at 600 hPa for the high SWE subset (R = −0.64). The value of R between relative humidity and SLR varies considerably with respect to pressure, but the magnitude never exceeds 0.28 for all events. However, for the high SWE subset, the R between relative humidity and SLR is greater in magnitude above 700 hPa and peaks at −0.46 at 600 hPa, indicating that at least in larger storms, higher mid- and upper-level relative humidities are associated with lower SLR values. The SLR in high-SWE events appears to be entirely independent of the low-level moisture profile, evidenced by the near-zero correlations between relative humidity and SLR found below 700 hPa. Based on these results, our examination of the relationships between SLR and the atmospheric conditions at CLN now focuses on temperature and wind speed at 650 hPa, a level typically near the higher ridges surrounding the study region (i.e., crest level), where correlation coefficients are at a local maximum.
2) Near-crest-level temperature
SLR increases with temperature from −23° to −17°C, and decreases with temperature above −13°C (Fig. 5a). The relationship is weak near −15°C, where the highest SLR values occur and large scatter is present. We attribute the reversal in trend and variability near −15°C to the influence of temperature on crystal type, crystal size, and riming. Wetzel et al. (2004) suggest that temperatures near crest level are likely to be close to the temperatures of primary snow growth, since orographic upward vertical motions are generally strong at this level and thus high supersaturations are maintained. Therefore, the crystal types in falling snow should be generally characteristic of the 650-hPa temperature. Operational forecasters typically define the “dendritic growth zone” as the −12° to −18°C temperature range [e.g., Buffalo Toolkit for Lake Effect Snow (BUFKIT); Mahoney and Niziol (1997)], where crystal growth rates are at a local maximum (Nakaya 1954). Thus, when 650-hPa temperatures are between −12° and −18°C, atmospheric conditions can favor the growth of large dendritic crystals having a high SLR [25 or more; Power et al. (1964)]. Accordingly, we find that 24 of the 26 wild snow events occur in these conditions. The large range in SLR at these temperatures probably reflects a range in snow crystals both from large dendrites to small plates and from unaltered, mechanically aggregated snowflakes falling through a glaciated cloud in light winds to rimed and heavily fragmented crystals falling through a mixed-phase cloud in high winds. The dataset also likely contains events where snow growth takes place in higher, colder clouds that produce columns or other crystal habits when near-crest-level temperatures are within the dendritic growth zone but supersaturations are lower.
Temperatures colder than −18°C or warmer than −12°C produce crystal types associated with lower SLR and yield slower crystal growth rates. In addition, supercooled water is more likely to be present in clouds at warmer temperatures (above −10°C), increasing the probability of a reduction in SLR due to riming (Pruppacher and Klett 1978). The increase in SLR with temperature noted below −17°C was observed by Grant and Rhea (1974), but most studies find a homologous increase in SLR with temperature, although it is nonlinear and with substantial scatter (e.g., LaChapelle 1962; Judson and Doesken 2000; Wetzel et al. 2004). The trend observed here, which we attribute to a shift from dendritic to columnar crystals near −18°C (Nakaya 1954) and reduced growth rates, might be missing from some studies because of a small sample size at cold temperatures [e.g., Simeral (2005), where there are no events included with temperatures below −15°C].
Following Ware et al. (2006), the 457 snowfall events were divided at quintiles of near-crest-level temperature (Fig. 5b). The distribution for the lowest fifth of the temperatures (<−15.1°C, the 20th percentile) has a mode near 17, and a long tail toward higher SLR values. Fewer than 20% of these events have SLR values less than 15. For the highest fifth of the temperatures (>−8.2°C, the 80th percentile), no SLR values exceeding 20 are observed, and 59% of these events have SLR values below 10. Thus, near-crest-level temperatures provide a rough approximation for SLR and can be used in a probabilistic sense to restrict the distribution of possible SLR values when temperatures are very warm or cold.
3) Near-crest-level wind speed
SLR generally decreases with increasing 650-hPa wind speed, with R = −0.37 and considerable scatter present at low speeds (Fig. 5c). The trend is most pronounced above 10 m s−1, suggesting that 650-hPa free-air wind speeds of this magnitude are associated with surface winds near CLN reaching a threshold for transport (Li and Pomeroy 1997; Roebber et al. 2003). The greatest variability and highest values of SLR occur when wind speeds are between 8 and 12 m s−1, with no wild snow events noted outside of this range. Applying the Ware et al. (2006) approach here yields a clear shift in the SLR distribution from the lowest to highest 650-hPa wind speeds (Fig. 5d). For the lowest quintile of the 650-hPa wind speed (<8.1 m s−1), the SLR values are distributed over a wide range, with 27% of the values exceeding 20. However, in the highest fifth (>14.8 m s−1), 43% of the events had an observed SLR below 10 (versus only 3% for the lowest fifth of the wind speeds), and only 3% of the values were above 20. High wind speeds therefore suggest a low probability of high SLR, while wind speed has limited predictive ability at low speeds.
4) SWE
Although the correlation between SWE and SLR is weak (R = −0.33) and shows considerable scatter at low SWE values, this relationship has received attention in past studies (Judson and Doesken 2000; Roebber et al. 2003; Ware et al. 2006). At CLN, SLR generally decreases with increasing SWE (Fig. 5e; some grouping of points along hyperbolas is an artifact of rounding snowfall amounts to the nearest half inch, with the hyperbolas representing lines of constant snowfall). SLR variability is greatest for SWE < 10 mm, which is partly a function of measurement and rounding errors, and is smaller at high SWE, although the sample size is small above 50 mm. Wild snow occurs only for SWE < 20 mm. Application of the Ware et al. (2006) approach adds some further insight through comparison of SLR distributions for exceptionally high or low SWE values (Fig. 5f). The mean SLR for the lowest fifth of the SWE (<6.1 mm) is 16.1, versus 10.1 for the highest fifth (>22.9 mm). SLR above 15 occurs in 55% of the lowest fifth of the SWE values, but only in 13% of the highest fifth. Thus, a rough probabilistic approach to SLR forecasting can be applied based on the SLR–SWE relationship, provided that the forecaster is using an accurate QPF.
Past studies have offered several explanations for the decrease in SLR with increasing SWE, including accelerated settlement due to the weight of overlying snow, and an association between high SWE events and warmer temperatures, which favor more riming and lower SLR crystal habits (Judson and Doesken 2000, Roebber et al. 2003). The relationship between SWE and 650-hPa temperature at CLN is very weak (R = 0.16; Fig. 6a), but the highest SWE values tend to occur at temperatures above −12°C, where riming is more likely and growth of lower-SLR plates and needles is favored. The correlation between SWE and 650-hPa wind speed is stronger (R = 0.40; Fig. 6b) and indicates that high SWE events are also characterized by higher wind speeds. High wind speeds lead to snow transport and hence mechanical fragmentation, which decreases SLR. Thus, a portion of the SLR–SWE relationship likely comes about indirectly, due to high-SWE events being both warmer and windier.
5) Surface temperature and problems with the NWS table at CLN
The relationship between SLR and surface temperature (i.e., event mean temperature at the CLN observing site when precipitation was occurring; R = −0.63) is very similar to that with NARR 650-hPa temperature, which contrasts with Kyle and Wesley (1997), who note the limitations of applying a relationship between SLR and the surface rather than the free-air temperature aloft in the central United States. This similarity is likely due to a strong correlation (R = 0.93) between free-air 650-hPa temperatures and surface temperatures at CLN, a mountain site less prone to nocturnal or persistent temperature inversions. The highest SLR values are observed with surface temperatures between about −9° and −15°C, which, for a moist-adiabatic lapse rate, corresponds to −13° to −19°C at 650 hPa. Nevertheless, the relationship between surface temperature and SLR at CLN is quite different from that implied by the NWS table (Fig. 7). At nearly all temperatures, the NWS table assigns an SLR that is higher than the majority of the CLN observations. It also does not assign an SLR less than 10 to any temperature range, while these events represent 27% of the total. The NWS table thus has limited forecast value at CLN.
6) Other variables
The wind direction and month indices, Froude numbers, and stability parameters individually explain less than 5% of the variance in SLR (R < 0.23; not shown) for all events. For the high-SWE subset, higher values of the wind direction index at 700 hPa (i.e., greater deviation in flow direction from northwesterly) are weakly related to lower SLR (R = −0.28; not shown). Although our primary focus is on the atmospheric factors affecting SLR, there are other processes that must be considered. Snow metamorphism can reduce SLR in the hours between snowfall and measurement (Doesken and Judson 1997). Judson and Doesken (2000) find snow density differences of 15% between cases where snowfall occurs during the last part of a measurement period and snowfalls that occur throughout the measurement period. A similar effect is observed at CLN, where the mean SLR is 14.2 when snow has been falling within 2 h of both the evening and morning measurement times, versus 13.8 when there has been no precipitation during the 4 h prior to either measurement time. Shortwave radiation effects are likely minimized at CLN due to its northerly aspect and the timing of the observations. Further, snow that falls during the day is typically exposed to limited solar radiation due to associated cloud cover during the storm, while snow that falls at night is measured before the sun rises (0400 LST). Nonetheless, snow that falls in the hours immediately following morning measurement, followed by afternoon clearing, could receive enough shortwave input to melt and decrease its depth, yielding an erroneously low SLR. In December, the mean SLR is 15.4 when snow falls within 3 h of evening measurement, versus 14.9 when snow falls during the day and ceases more than 3 h prior to evening measurement. In April, the decrease is greater, from 12.7 to 10.2, suggesting that solar radiation does play a role.
c. Diagnosis and prediction of SLR
1) Stepwise multiple linear regression (SMLR) using reanalysis
The previous sections have discussed relationships between SLR and temperature, moisture, and wind near CLN. Two types of tests are now performed using the NARR to evaluate 1) the utility of SMLR for explaining the SLR variability for all and high SWE events and 2) the sensitivity to the use of only those predictors with smaller observational and forecast uncertainties. Results of these tests are shown in Table 3, with selected comparisons of modeled and observed SLRs shown graphically in Fig. 8.
Test 1 seeks to determine the ability of SMLR to diagnose SLR. For all events, the SMLR selects 17 predictors (Table 4) and produces a regression equation that yields R = 0.82 and R2 = 0.68 between the estimated and observed SLRs (Table 3; Fig. 8a). The fit produces a MARE (defined in section 2) of 19%, which corresponds to a range in estimated SLR of 12.2–17.9 for an observed SLR of 15.0, and places 73% of the events, which is within the correct Roebber et al. (2003) SLR class, compared to 60% for their neural network ensemble for multiple sites. The fit is much better for high-SWE events (Table 3; Fig. 8b), with nine predictors (Table 5) producing R = 0.94, R2 = 0.88, and an MARE of 13%. This MARE corresponds, for example, to an estimated SLR range of 13.1–17.0 for an observed SLR of 15.0. The SMLR approach also places 83% of the high-SWE events in the correct Roebber et al. (2003) SLR class. The final values of R2 are much higher than those achieved using any single variable in this study or in past studies by Diamond and Lowry (1954), Judson and Doesken (2000), Wetzel et al. (2004), and Simeral (2005).
In test 2, we investigate whether reducing the field of potential predictors to only those more accurately resolved by the NARR has a significant negative effect on our results. Including only temperature and wind speed and direction as potential predictors yields a fit with R2 = 0.63 for all events (Fig. 8c) and R2 = 0.83 for high-SWE events (Fig. 8d). In both tests, MARE only increases by a few percent. Thus, there is not a large reduction in fit quality when limiting predictors to those that are better known. In a further test (not shown), a fit using temperature predictors alone explains 53% of the variance in SLR for all events and 63% for high-SWE events.
2) Application to Eta forecasts
The tests above involve the use of reanalysis data and are, therefore, not a true assessment of forecast skill, which requires the use of forecast variables to predict SLR. To test the use of operational model forecasts for SLR prediction, we ran SMLR on archived forecasts produced by the Eta/NAM model, which were obtained from the National Center for Atmospheric Research’s Mass Storage System on a grid with 40-km horizontal spacing. For this test, the total number of events was reduced to 356 (78% of the original dataset), due to gaps in the Eta/NAM archive. These events were randomly split into a dependent set of 180 events and an independent set of 176 events. The SMLR selected six predictors: temperatures at 750, 700, 650, and 600 hPa; 550-hPa meridional wind speed; and maximum 650-hPa wind speed, which fit the dependent set with R2 = 0.58 (not shown). When applied to the independent set, R2 between the observed SLR and the SMLR predictions was 0.51 (Fig. 9). The MARE was 25%, equivalent to a forecast range of 11.3 to 18.8 for an observed SLR value of 15, and the ARE exceeded 50% in less than 12% of the events. SMLR also placed 63% of the events in the correct Roebber et al. (2003) SLR class. Testing 1000 unique selections of independent and dependent sets yielded median and standard deviation R2 values of 0.48 and 0.04, respectively, indicating that the performance of SMLR in the aforementioned test reflects typical results, and that the process is not overly sensitive to the specific choice of events included in the two sets.
The SMLR approach offers considerable improvement over some existing techniques. Applying a climatological SLR value to the independent set yields a MARE of 0.45, nearly double that of the SMLR results. ARE (defined in section 2) for the climatological SLR exceeds 50% in 28% of the forecast cases. Testing of the predictive ability of the NWS table is somewhat difficult due to the lack of an accurate Eta/NAM 2-m surface temperature for CLN (since the nearest grid point is at a much lower elevation). The NWS table was instead tested using 700-hPa temperature as an approximation for CLN surface temperature, noting that RMSE = 1.0°C between the NARR 700-hPa temperature and the observed surface temperature. The NWS table consistently overpredicts SLR, with an MARE of 99% and ARE values exceeding 50% in more than half of the forecast events.
A test of the Byun et al. (2008) algorithm, which calculates SLR as a function of surface temperature and precipitation rate, was also conducted using the 700-hPa temperature in place of the surface temperature. Forecasts of QPF, and hence precipitation rate, by the 40-km Eta/NAM show very low skill at Alta, so a second test was conducted using observed, rather than forecast, precipitation rates. The Byun et al. (2008) algorithm produced an MARE greater than 60%, with R2 values between the forecast and observed SLRs of 0.25 and 0.34 when using forecast and observed precipitation rates, respectively. While low QPF skill contributes to SLR errors with this approach, the Byun et al. (2008) equations were developed for the Korean Peninsula, and, thus, likely also at issue is an apparent lack of portability of SLR regression equations from one site or region to another.
A caveat to improving SLR prediction is that snowfall forecasting remains a three-step process. An accurate forecast of snowfall amount, and hence improved skill in warning issuance, relies on accurate prediction of both QPF and SLR. The assessment of any potential benefit of the SMLR approach to point-specific snowfall forecasting requires knowledge of QPF skill in LCC. At the time of writing, the NWS in Salt Lake City maintained a record of gridded precipitation forecasts dating back to September 2008. Figure 10 compares the NWS QPF at the Alta grid point to the observed precipitation at CLN for the period from September 2008 to March 2009. On the 63 days when at least 2.8 mm of precipitation was observed at CLN, the MARE between that forecast and observed was 70%, corresponding, for example, to a forecast of 17 mm when 10 mm was observed. The largest errors were from underforecasts, including a forecast of 13 mm when 47 mm was observed, and two forecasts of 3 mm when 19 mm was observed. In these cases and others where large QPF errors occur, it is unlikely that any refinement of the SLR forecast technique will lead to improved predictions of snowfall amounts. However, ARE values for the three highest QPF amounts were all less than 20%, and in these cases and others where QPF is skillful, improving the final step of the snowfall forecast process beyond using a fixed climatological SLR or an incorrect empirical relationship is a worthwhile endeavor.
4. Conclusions
We have investigated the variability of SLR at Alta, Utah, a high-mountain site where winter storms are frequent; the effects of sun, wind transport, and ground temperature are reduced; and measurement practices are reliable and consistent. The mean SLR of 14.4 is similar to that found for nearby lowland sites and large daily SLR variability is present during all months. Our analysis provides information regarding the relationship between SLR and the atmospheric conditions at CLN:
SLR is most strongly correlated with near-crest-level temperature and wind speed, particularly for high-SWE events, and weakly correlated with SWE, relative humidity, Froude number, stability, wind direction, and time of year.
SLR decreases (increases) with increasing near-crest-level temperature above −13°C (below −17°C), and variability in SLR is at a maximum near −15°C. We attribute the reversal in trend and peak in variability to changes in crystal type and growth rate, and increased riming potential at warmer temperatures.
SLR decreases with increasing near-crest-level wind speed above 10 m s−1, an approximate threshold for snow transport.
Although the relationship between SLR and SWE at CLN is weak, higher SWE is associated with lower SLR as in some past studies (e.g., Roebber et al. 2003), which might be due to warmer crest-level temperatures and higher wind speeds during high-SWE events.
Wild snow events (where SLR > 25) compose only 5.7% of the events in this study, but can be associated with large snowfall amount errors. Most wild snow events occur within three ranges of conditions: (i) 650-hPa temperatures between −18° and −12°C, (ii) 650-hPa winds between 8 and 12 m s−1, and (iii) SWE less than 20 mm.
When applied using NARR and observed surface variables, the SMLR approach explains 68% of the variance in SLR for all 457 snowfall events. While we are able to diagnose to a great extent the conditions affecting SLR at CLN, we are still unable to explain a sizable portion of the variance. This portion of the variability could stem from a variety of sources, from our failure to entirely capture the nonlinear relationships between selected predictors and SLR to unresolved physical processes, observational errors, the low temporal resolution of the measurements, and the high temporal variability in the atmospheric conditions. Although our results could be affected by a small sample size (n = 80), the skill of the stepwise approach is greater for larger events, explaining 88% of the variance in SLR for a high-SWE (>25 mm) subset. The ability of SMLR to diagnose SLR is not greatly reduced by restricting potential predictors to only temperature and wind speed and direction.
When developed from and applied to Eta–NAM forecasts, an SMLR equation is able to predict SLR for an independent set of events better than a modified Byun et al. (2008) approach and with much greater skill than using a fixed ratio or the NWS table, which produced large errors in SLR. Forecasters should be reminded that the NWS table and its associated temperature–SLR relationship were intended for use in checking hydrological observations for errors, rather than operational forecasting of snowfall (Roebber et al. 2003). The Eta–NAM SMLR equation correctly predicts the Roebber et al. (2003) SLR class for 63% of the events. Although a direct comparison is not made [e.g., testing of the Roebber et al. (2003) neural network at CLN using model forecasts], the performance of the SMLR at CLN slightly exceeds that achieved by Roebber et al. (2003) at NWS forecast office sites, primarily in the eastern United States.
The fundamental problem with improving SLR forecasts is that any resulting improvement in snowfall forecasting is dependent upon accurate model- or human-generated QPF. A small relative error in SLR is of little consequence when QPF errors are large. It is possible that the portion of the snowfall amount error due to incorrect SLR is much smaller in magnitude than the portion due to QPF errors. Byun et al. (2008) showed this to be the case in some of their snowfall forecast scenarios. Full evaluation of the potential for snowfall forecast improvements will require a long period of consistent verification of both snowfall and QPF forecasts at a site where accurate measurements are taken.
Other limitations of this work include the use of 24-h SLR observations, a problem that is particularly relevant in frontal events where atmospheric conditions change rapidly and SLR, which might evolve considerably during an event, is represented by a single value. Snow crystal studies by Casson et al. (2008) show wide variations in crystal type and degree of riming (and hence changes in SLR) between observations conducted at 15-min intervals. Baxter et al. (2005) note that the effects of wind on snow metamorphism can be highly nonuniform due to gustiness. Thus, also at issue is the absence of wind observations at the study site, which if available could allow for better diagnoses of the surface processes affecting the daily SLR. While in this study snow crystal structures are inferred, rather than observed, future work on this subject might benefit from a snow crystal imaging system, such as the one recently installed near CLN by the University of Utah’s Atmospheric Sciences Department.
Variations in orography and local storm climatology between CLN and other sites suggest that the specific relationships between SLR and atmospheric conditions and the SMLR results presented in this manuscript might not be directly applicable to other sites across the United States or even in the Intermountain West region. However, the approach described herein serves as proof of concept for the use of a straightforward regression method that could be incorporated into existing guidance products, with the goal of improving the snowfall amount forecast process. In addition, while skill in snowfall amount forecasts ultimately relies on accurate QPF, the forecasts of SLR alone are useful for avalanche forecasting and hydrological applications.
Acknowledgments
We thank Alta Ski Area, the Alta Snow Safety Patrol, General Manager Onno Wieringa, Snow Safety Director Titus Case, and Assistant Snow Safety Director Daniel “Howie” Howlett for collecting and providing the Alta snow data, as well as Randy Graham of NWS Salt Lake City for his input and assistance in obtaining archived NWS forecasts. As this research was conducted in pursuit of a master of science degree, we also thank thesis committee members John Horel and Larry Dunn. This research is based in part on work supported by a series of grants provided by the NOAA/National Weather Service CSTAR program and Grant ATM-0627397 from the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation.
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(a) Topography of the study region, with elevation shaded according to scale at upper left and geographic features annotated. (b) Google Earth view of Alta and CLN, looking south. (c) View of the CLN snow study site, looking northeast.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
Histogram of observed SLRs for all events.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
Box-and-whisker plot of SLRs for all events. Box top and bottom represent the 75th and 25th percentiles, monthly median is indicated by a horizontal line, whiskers extend to the last outlier within 1.5 times the interquartile range, and additional outliers are indicated by a plus sign (+). Notches express statistical significance. Specifically, where medians of two months are different at the 5% level, the notches do not overlap.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
Vertical profiles of the linear correlation coefficient between SLR and temperature, relative humidity, and wind speed for (a) all events and (b) high-SWE events.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
(a) SLR vs 650-hPa temperature (dashed line represents an SLR of 25). (b) Probability density functions of the lowest and highest fifths of the 650-hPa temperature, from fitting to a normal distribution. (c),(d) As in (a),(b), but for 650-hPa wind speed. (e),(f) As in (a),(b), but for SWE.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
SWE vs (a) 650-hPa temperature and (b) 650-hPa wind speed for all events.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
Observed SLRs (circles) and SLRs indicated by the NWS table (solid line) vs surface temperature for all events.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
Observed vs SMLR-estimated SLRs for (a) all events and (b) high-SWE events when run using all potential predictors, and for (c) all events and (d) high-SWE events when run with only temperature and wind speed and direction predictors. Diagonal solid lines are one-to-one lines representing a perfect estimate.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
Observed vs forecast SLRs for the independent set of Eta/NAM forecast events. Diagonal solid line is a one-to-one line representing a perfect forecast.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
Observed precipitation vs NWS Alta grid point QPF. Diagonal solid line is a one-to-one line representing a perfect forecast.
Citation: Weather and Forecasting 25, 1; 10.1175/2009WAF2222311.1
RMS deviations between NARR and raob profiles during Alta storms.
Potential predictors used as input for the SMLR.
Results of the SMLR for test 1 (all potential predictors) and test 2 (only temperature, wind speed, and direction), where n denotes the number of events in the subset, np is the number of predictors selected, R is the linear correlation coefficient, R2 is the variance explained, and MARE is the mean absolute relative error.
Predictors included in the reanalysis-based SMLR equation for all events.
Predictors included in the reanalysis-based SMLR equation for high-SWE events.
