3.1.1 Air temperature, relative humidity, ground temperature, and air pressure measurements

Air temperature and relative humidity are measured at CUES and Sesame simultaneously using radiation-shielded Campbell HMP 45C sensors (Table 1 and Table 2). Ground temperature is measured at CUES using a buried thermistor string. The highest depth, labeled “0 cm”, was used, which corresponds to the soil layer just beneath the surface. Atmospheric pressure is measured at CUES using a Met One 092 barometer pressure sensor.

3.1.2 Wind speed and direction measurements

Wind speed and direction are measured at CUES using three anemometers: an RM Young 81000 Ultrasonic Anemometer, a Lufft WS600 UMB, and an RM Young 5103. The RM Young 81000 measures the 3-D wind vectors at a high sampling rate (10 Hz) for application of the eddy covariance method (e.g., Reba et al., 2009) to estimate sensible and latent heat fluxes. Because of the high sampling rate, the time series of the 3-D wind components is large, 52 GB. Processing this massive time series over the entire study period is impractical and therefore beyond the scope of this study. Because of the size of those data, unlike almost all the other raw measurements from CUES, they are not available at http://www.snow.ucsb.edu, but are available upon request.

Table 2List of measurements and instruments used in this dataset at CUES.

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Table 3List of measurements and instruments used in this dataset at Mammoth Pass.

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3.1.3 Radiation measurements

At CUES, uplooking broadband solar radiation, both diffuse and direct, is provided in this dataset by the Sunshine Pyranometer SPN-1. Incoming longwave radiation is measured via an Eppley Precision Infrared Radiometer (PIR). The broadband and near-infrared (nIR) snow albedos are measured using uplooking and downlooking radiometer pairs, with the downlooking radiometers on a fixed boom prior to September 2016 and on an adjustable boom thereafter.

3.2.1 Air temperature, relative humidity, ground temperature, and air pressure filtering

Air temperature, relative humidity, ground temperature, and air pressure were the simplest variables to process. Hourly averages were queried from the database containing measurements at 1 min temporal resolution. Visual examination of plots of these data revealed a few out-of-bounds measurements that were set to missing values. As with all the measurements, there were gaps of an hour to a few weeks, mostly in the summer, when instruments were removed for calibration or had failed. We arbitrarily chose a gap threshold of 12 h, and then used three approaches for gap-filling. For gaps below the gap threshold, a spline interpolation was performed. For gaps at or above the threshold, measurements were preferentially filled using a regression from two nearby sites with long-term measurements. All of the gaps in the air temperature, relative humidity, and air pressure were filled using these two methods. For air temperature and relative humidity, a site in the town of Mammoth Lakes was used as the other sensors on Mammoth Mountain suffered data losses during the same time periods at CUES/Sesame and MHP does not have a relative humidity sensor. The site is C2998, its station ID on Mesowest (http://mesowest.utah.edu, Horel et al., 2002). A regression for the matching times at each site was developed for both air temperature and relative humidity, with r² values ranging from 0.53 to 0.91 (Table 4). The C2998 station did not have reliable pressure readings, so a regression from the local airport, called KMMH on Mesowest, was used (Table 4). Air temperature and relative humidity from KMMH were not used to gap fill as the airport is located in a rain shadow and in a flat valley with cold air pooling. These characteristics did not affect the air pressure as much, as the r² value for the air pressure regression was 0.91. Because of the operational nature of the Sesame site, there were many more gaps that needed to be filled (N=6758–6868) compared to gaps at CUES (N=418–652). For ground temperature, the longer gaps had to be filled with climatology, given no other nearby measurements, while the gaps < 12 h were interpolated.

3.2.2 Wind speed and direction filtering

Wind speed and direction were queried from the database as average hourly values from 1 min samples. The Yamartino (1984) approach was used to average wind directions, consistent with the 1 min averaging that takes places on the data loggers with the raw measurements. CUES has three different wind sensors, but only the RM Young 5103 and the Lufft WS600-UMB provide reliable 1 min averages (Table 2). The RM Young 5103 and the WS600 are about 2 m apart in height, with the 5103 being at the platform height of about 6 m above the bare ground. The WS600 is mounted higher, about 3 m above the platform surface. Both of the wind sensors had periods of missing data or high readings, e.g., > 60 m s⁻¹ for an hourly average. Thus, the RM Young 5103 values were preferentially used, with the WS600 measurements used to fill gaps using simple replacement. After this step, there were some small remaining gaps that were interpolated with a spline or filled with climatology using the same 12 h gap threshold. The measurement instrument and type of processing (i.e., measured, interpolated, or climatology) are recorded in the data table.

3.2.3 Uplooking radiation filtering

The direct B_↓ and diffuse D_↓ broadband radiations were queried from the database as average hourly values from 1 min samples. Direct broadband radiation values where transmittance T was above 0.95 were adjusted such that T=0.95 on the assumption that the absolute measurement errors for direct radiation are greater than for diffuse radiation.

where θ₀ is the solar zenith angle, S=1367 W m⁻² is the solar constant and R_v is the radius vector. These values can all be determined using location, date/time, and Ephemeris estimates, e.g., from the National Oceanic and Atmospheric Administration's Solar Calculator (https://www.esrl.noaa.gov/gmd/grad/solcalc/).

Periods of time with missing uplooking radiation were filled in with radiation from the nearby Dana Meadows, California Data Exchange Center (California Department of Water Resources, 2018), code DAN, at 37.897^∘ N, 119.257^∘ W at 2987 m. Comparisons of total solar radiation from CUES and DAN show decent though not excellent agreement, r²=0.85, RMSE = 133 W m⁻². When DAN was the incoming solar radiation source, direct and diffuse components were estimated using an empirical method (Erbs et al., 1982) with a high-altitude modification (Olyphant, 1984). The uplooking SPN-1 is heated, so snow covering the radiometer was not observed, but the DAN radiometer is not heated. Without reliable co-incident downlooking measurements, it is difficult to flag these snow-covered periods, but we suggest that any snow cover on the radiometer is a minor issue given that DAN measurements during snowfall only comprise 0.26 % of the hourly uplooking measurements. Finally, there were a few periods left when neither CUES nor DAN had working uplooking broadband radiometers. These periods were multiple days in length, so climatology was used to estimate the incoming solar radiation. After plotting the gap-free dataset, there were some obvious spikes at night or around sunrise/sunset; therefore, all uplooking solar measurements are set to zero when cos θ₀≤0; that is when the Sun was below the horizon. This will zero out some of the low-energy diffuse radiation at these times, but they are so small as to be insignificant to the energy balance.

The uplooking longwave radiation was relatively error free and required almost no filtering. There were gaps in the measurement record however that were filled using an empirical approach (Marks and Dozier, 1979) based on air temperature, and relative humidity when these ancillary measurements were available. We note that this approach is optimal for clear skies and produces low biased values, but it was only used for < 1 % of the uplooking longwave measurements. If these ancillary measurements were not available, climatology was used.

Table 4Gap-filling regression statistics. Shown are the stations with each of their measurements (“Stations”); measurements; the station that supplied the independent variable for the regression (“Regression station”); the r² value of the regression; and the number of missing measurements filled using the regression (N).

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3.2.4 Snow albedo filtering

The snow albedo estimates were by far the most complicated to process. In summary, snow albedo was calculated by (1) measuring the snow surface slope and aspect with a lidar; (2) using those slope and aspect measurements along with uplooking and downlooking radiometer measurements to create terrain-corrected direct broadband and near-infrared albedo measurements on clear days around solar noon; (3) bias correcting those observed albedos using theoretical maximums by season to account for different sensor configurations and other biases; (4) inverting the broadband and near-infrared albedos to estimate grain size and impurity content using a radiative transfer model; (5) interpolating the grain size and impurity content across non-clear days; and (6) creating an hourly direct broadband albedo, accounting for the solar geometry using the same radiative transfer model, run as a forward model.

For snow albedo measurement at CUES, there are four downlooking radiometers: a clear and nIR Eppley PSP on a fixed boom, and a clear and nIR Eppley PSP on an adjustable boom. In theory, these measurements can be used in conjunction with the uplooking radiometers to measure snow albedo. In practice, there are many biases and steps that need to be taken to obtain accurate measurements. Potential sources of error include a sloped snow surface such that the level uplooking radiometers do not receive the same amount of solar radiation as the snow; shadows cast by trees or other objects that can affect the uplooking and downlooking radiometers at different times; non-snow objects in the radiometers' field of view; an inability of the downlooking radiometers to distinguish diffuse radiation from the sky from that from the snow; direct solar radiation reaching the downlooking radiometers at high solar zenith angles; and imperfect cosine response and other instrument biases in the radiometers (Wilcox and Myers, 2008), especially at the higher solar zenith angles. To address the issue of non-snow objects in the downlooking radiometers' field of view, an adjustable boom was installed in September 2015. The boom is kept about 1 m above the snow surface to eliminate non-snow objects from the radiometers' field of view. Thus, for water years 2016 and 2017, the adjustable downlooking boom measurements were used, while for all other years, only the fixed boom downlooking measurements could be used. We could not find a good relationship between the fixed boom and downlooking boom radiation values to correct the prior years. Instead, we used a bias correction based on the maximum observed annual albedo, explained below.

Because of the issue of not being able to discriminate diffuse radiation from the sky versus diffusion radiation from the snow and problems with measurements at high solar zenith angles, albedo measurements were only used 1 time a day during clear-sky conditions, $D_{\downarrow }/\left(B_{\downarrow }+D_{\downarrow }\right)\le \mathrm{0.2}$, around solar noon. In addition, to eliminate problems with shadows, only the maximum downlooking daily values were retrieved. Thus, the database was queried to find the maximum daily downlooking broadband radiation values during clear-sky conditions and to return the associated time, uplooking broadband/nIR measurement, and downlooking nIR measurement. Queries were further restricted to times when at least 30 cm of snow was measured on the ground and direct solar radiation was > 400 W m⁻² to ensure that only sunny days with broad snow cover were selected. The uplooking direct and nIR measurements were then corrected to the snow surface using a correction factor c (Bair et al., 2015; Painter et al., 2012):

with θ as the local solar illumination angle such that the albedo α is the ratio of the reflected solar radiation D_↑ and the terrain-corrected direct and diffuse solar radiation, with the diffuse being uncorrected assuming a negligible terrain effect on it:

For the uplooking near-infrared measurements, the diffuse fraction was not known, so we assumed that all of the radiation was direct based on atmospheric scattering being small at these wavelengths.

To compute θ, the slope and aspect of the snow surface must be measured. To do this we used a Reigl Z390i laser scanner that operates automatically on a schedule at CUES that has varied over the study period from every 15 min to every hour. A point cloud from the scan nearest the albedo acquisition was selected. Then, a 2 m² bounding box within both the fixed and adjustable downlooking radiometers' fields of view was used to filter this point cloud. This filtered point cloud was then fit with a plane to determine the local slope and aspect. There were periods when the laser scanner was not working properly or times prior to its installation in February 2011. For these times, the modal aspect (north) and slope (4^∘) were used for the terrain correction. Because the albedos were measured near solar noon and the slope of the terrain is low, c is significantly less than 1 only during times when θ₀ is high; those are times around solar noon during the accumulation season. From mid-April through melt-out, c is close to 1, making the terrain correction negligible.

From the corrected albedos, for each season, the maximum value for that season was compared with a theoretical maximum of 0.89 for a broadband albedo and 0.74 for an nIR albedo (Dozier et al., 2009). Values were then adjusted up or down by the difference between the observed and theoretical maxima on an annual basis. The average annual correction was +5.1 % for the broadband albedo and −3.9 % for the nIR albedo. These values suggest that trees, which are darker in the visible spectrum but brighter than coarse grained dirty snow in the nIR, were often in the downlooking radiometers' field of view, especially later in the season. A minimum theoretical albedo was not used for correction as this will vary from season to season (e.g., Painter et al., 2012) depending on the concentration of impurities on the surface of the snowpack.

The assumption behind our maximum albedo correction is that the annual calibration or swapping of some of the instruments that occurs at CUES each fall could explain the bias, and that this bias is scalar in nature. The latter assumption is unlikely to be true, but we decided it was the best correction given the documented radiometer biases (Wilcox and Myers, 2008). We note that WY 2017 required a negligible correction since the adjustable downlooking boom was used. Curiously, albedos from WY2016 required a negative correction even though this was the first year that the adjustable downlooking boom was installed. Our explanation is that between WY 2016 and WY 2017 the downlooking boom design changed such that aluminum from the downlooking boom was visible to the radiometers on the downlooking boom in 2016 but not in 2017. Reflected light from the aluminum boom caused the downlooking radiometers to have high biased measurements. Also, we note that the spectral range of the SPN-1 and the PSP are different, 0.400 to 2.700 vs. 0.285 to 2.800 µm (Table 2); however, because of different documented biases (Wilcox and Myers, 2008), especially at higher solar zenith angles, the SPN-1 shows 2.5 % more broadband radiation on average than the PSP. This sort of unanticipated bias further supports our approach of using a theoretical maximum albedo to bias correct our measurements.

For the times when the uplooking radiometers at CUES were not working, albedos were estimated using a multivariate regression based on time since last snowfall (of at least 2.54 cm/1 inch) and θ. This approach showed similar accuracy to what was expected from a simple statistical model based only on snowfall and solar geometry, r²=0.62, RMSE = 7.0 %. Other variables such as new snow density and total snow depth were added to the regression but did not improve its accuracy. We note that this RSME value is only slightly larger than the average annual bias correction of 5.1 %, illustrating the uncertainties associated with in situ snow albedo measurement.

From these broadband and near-infrared albedos, the grain size and impurity content of the snowpack were estimated using a two-stream radiative transfer model where grain size and impurity content are solved simultaneously using nonlinear optimization (Meador and Weaver, 1980; Moré, 1977). The grain sizes and impurity content were then interpolated from the daily to hourly times across the study period. This grain size interpolation likely overestimates grain sizes on days with new snowfall that were cloudy, as no albedo measurements were taken on these days. One approach would be to use a constant value for new snow albedo, which is done for age-based models (e.g., Dickinson et al., 1993; U.S. Army Corps of Engineers, 1956); however, on the days with new snowfall of greater than 2.54 cm/1 in. that were sunny and therefore had albedo measurements around solar noon, there was substantial scatter in the new snow albedo, ranging from 0.60 to 0.89, illustrating the pitfalls of using a constant new snow albedo.

The interpolated grain sizes and impurity content were then fed back into the model varying by θ₀ with each hour as the solar zenith changed. The assumptions of this approach are that (1) the grain size changes relatively less than the albedo throughout the diurnal cycle; and (2) the daily albedo cycle is more accurately modeled than measured, which is based on our experience at CUES. Assumption (1) is the weaker assumption as grain size decay or growth can be rapid in the first day or two after snowfall (Flanner and Zender, 2006), but for snow that is older than a day or two, which is most melting snow, the assumption is reasonable.

3.3.1 Automated snow depth/SWE and manual precipitation measurements

The mass balance measurements come from all three sites. We provide snow depth from ultrasonic sensors at each site over the entire period of record. We also provide snow pillow measurements for all three sites, but only over the entire period of record at MHP. At CUES, the snow pillow measurements start with the installation of the pillow in September 2012 and are provided continuously through September 2017. At Sesame, snow pillow measurements start in October 2013 and are provided continuously up until February 2017, when the pressure transducer failed. At CUES and Sesame, the ultrasonic depth sensors are located directly above the snow pillows. At MHP, the depth sensor is mounted on a boom adjacent to the pillow. Heated tipping bucket measurements were taken at Sesame and MHP over the entire period of record; however, only the MHP tipping bucket measurements are provided because of gaps and quality problems with the Sesame gauges discussed in Sect. 2.1. The MHP tipping bucket measurements were not without problems, including undercatch, data gaps, and spurious precipitation during times when it was not precipitating. These problems are discussed below.

3.3.2 Automated snow depth/SWE and manual precipitation measurement filtering

The snow depth measurements from the ultrasonic depth sensors at all three sites required extensive filtering and interpolation, which is common. For the Sesame site, the raw depth measurements were taken every minute. At CUES, the depth measurements were taken every 15 min from October 2010 until September 2012. From September 2012 onwards, the depth measurements were taken every 5 min. All of these depth readings are actually averages, as each depth pinger samples at once a minute or more frequently. At MHP, depth measurements are only available hourly, also presumably as averages rather than instantaneous measurements.

Ultrasonic snow depth measurements suffer from both drops and spikes, but spikes are more prevalent, especially at CUES, where blowing snow can reflect the sound, thereby causing the snowpack to appear to be at or near the sensor height. Thus, the aggregation used the minimum depth at CUES and Sesame over each hour to limit spikes. The aggregated data were then plotted and inspected visually. First, snow-free periods were identified manually based on visual inspection of the measurements and ancillary knowledge of the snow accumulation season, e.g., Sesame manual measurements. These manually identified periods were set to zero depth. Likewise, a snow-covered period was created as the opposite of the snow-free period. Values of zero during snow cover were set to a missing value. Other large spikes over extended periods of time, such as during sensor maintenance, were set to a missing value. An outlier filter (Hampel, 1974) was used to reduce spikes and drops further. Missing values were then interpolated using a shape-preserving piecewise cubic spline. The interpolated data were then smoothed using a smoothing spline to reduce high-frequency noise. This method tended to produce very small values (≪ 0.1 cm) rather than zeros at times. These small values were set to zero.

The snow pillow measurements at all three sites were quite clean in comparison to the snow depth measurements. The same snow-free periods used for the depth sensors were used to set the pillows to zero, usually to eliminate high-frequency noise during the snow-free season. Likewise, values of zero during snow cover were set to a missing value. Missing values were interpolated also using cubic splines. High-frequency noise was smoothed with a spline and values < 0.6 cm were set to zero.

Measurements from the heated tipping bucket at MHP showed many problems. They were given as accumulated precipitation over the water year and converted to hourly precipitation intensity values using a forward-looking difference. There were many time gaps with missing measurements, possibly because the modem could not transmit or because of power losses to the sensor or its heater. In the case of a gap, any increase in precipitation since the last measurement time was interpolated linearly across the length of the gap. This approach assumes a data transmission failure where the logger provides the correct accumulated precipitation value after the gap. Then, there were five measurements with rates above the maximum rate P_max, assumed to be 1 in./2.54 cm per hour, based on our experience with measuring precipitation at Sesame. We assumed these were due to clogging of the orifice or a heater failure; thus, we spread the high values P_hi out over N hours such that the precipitation rate P_t at time t is

Comparison of the hourly Sesame heated tipping bucket precipitation during times when the tipping bucket was working (approx. November–May, 2013–2017) and the hourly MHP heated tipping bucket measurements shows a low r²=0.08, although accumulated precipitation was closer, with Sesame showing 92 % of the accumulated precipitation of MHP. Further analysis shows many times when the Met One tipping bucket was not recording precipitation but the MHP precipitation bucket was recording small values (0.1 cm). Given that we are more confident in the limited tipping bucket measurements from Sesame based on our experience with the site, we suggest that there was a heater problem at MHP that caused the tipping bucket there to accumulate snow during storms and melt it afterwards. Because of the above problems, we caution against using the MHP tipping bucket measurements for hourly precipitation, as they are more accurate for accumulated sums over longer time periods.

The manual Sesame measurements were checked visually for errors and edited to be consistent from year to year and adjusted to conform to operational standards (American Avalanche Association, 2016), but no major adjustments were made. We have kept the measurements in Imperial units to preserve how they were taken and how the notes refer to the measurements. Minor adjustments included altering the table to show “Trace” amounts of new snow in a consistent way and some formatting changes. For example, null or blank values that were not applicable such as new snow density on days with rain only were converted to “NaN” (not a number). Also, we note that the reported “density” is not sampled from the snowpack, but is simply a measure of the weighed SWE/height of new snow. Given mixed precipitation, the SWE measurements sometimes contain liquid water leading to high densities, e.g., 90 % on 19 October 2015. Also, snow is only recorded to the nearest 0.5 in., which for small snowfall events can also led to unrealistic densities due to the lack of measurement precision.

5.1.1 Snow depth

Overall, the snow depth at both sites agrees well (Fig. 5), with CUES having a later melt-out date, explained by its higher elevation and slightly north-facing terrain, while Sesame had slightly greater snow depths in the wet years, i.e., 2011 and 2017, possibly because the snow under the depth sensor at CUES was removed by wind transport during the big storms.

The 2011 to 2017 water years show a tremendous diversity in snow accumulation. At Sesame, where precipitation records go back to the 1983 water year, 2017 was the wettest year on record, with 255 cm of precipitation, while 2015, with 55 cm of precipitation, was the driest. We stress that the measurements from Sesame do not cover the entire water year and do not always cover consistent time periods from year to year, depending on when the ski resort opened and closed. An examination of the nearby MHP snow course, with records back to 1928, shows 2 years with greater maximum SWE on the ground: 220 cm of SWE on 27 March 1969 and 216 cm on 25 April 1983. Water year 2017 was third, with 208 cm of SWE on the ground on 31 March 2017. There are no reliable precipitation gauges with record lengths > 40 years in the area around Mammoth Mountain. The closest is Huntington Lake, lower at 2134 m elevation, where 2017 ranks fifth among water years going back to 1912.

Figure 5Snow depth at Sesame and at CUES during the study period. Note the similar depths with slightly later melt-out at CUES, especially in the drier years.

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In terms of maximum snow depth, 2015 was the lowest on record, with 75 cm at Sesame and 112 cm at CUES. Despite having the most precipitation, water year 2017, with peak snow depths of 526 cm at Sesame and 543 cm at CUES, did not have the deepest snow depths recorded at either site. At Sesame, 2006, with a 610 cm peak snow depth, and 1995 with a 561 cm peak snow depth, both had more snow on the ground than 2017. At CUES, reliable snow depths only go back to 2001, but snow depth was over 600 cm in 2006 when the downlooking boom was buried. Subsequently, it was raised up to the top of the railing from the platform floor.

5.1.2 Air temperature

The Sesame site is slightly warmer than CUES, with an average annual temperature of 4.88 ^∘C vs. 4.50 ^∘C, although the November through May temperatures, which correspond to the average period when snow is on the ground, are equivalent to within the instrument uncertainty with both sites at −0.11 ^∘C. Comparing midwinter temperatures at both sites (Fig. 6), we see that above-freezing temperatures are common and that the diurnal range is considerably narrower at CUES, which follows given its mid-mountain and exposed location in comparison to Sesame's location near a valley, with Seame subject to longwave heating from the trees and cold air pooling at night.

Figure 6Air temperature at Sesame and at CUES during a selected midwinter period. Note the greater diurnal range for Sesame.

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5.1.3 Albedo

The broadband snow albedo at CUES is usually above 0.80 for much of the accumulation season, with values reaching above 0.90 for the highest solar zenith angles. When the albedo stops being refreshed by new snow and the old snow is covered with pumice, the albedo drops dramatically. In every season, minimum albedo values were < 0.60. A large diurnal variation in albedo of > 20 % is evident for days late in the melt season due to the range of solar zenith angles (Fig. 7). Although there is little energy reaching the snowpack in the early morning and late afternoon, when the solar zenith angles and albedo are highest, the illumination angle effect on albedo is significant and should be included in all snowmelt models nonetheless.

Figure 7Diurnal variation in albedo for a day in June 2017. Note the large range, although the solar energy reaches the snowpack at the times when the highest albedo is low.

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5.1.4 Wind

A wind rose for CUES (Fig. 8) shows wind speeds in the range of previously published measurements from an anemometer mounted on top of Main Lodge (Bair, 2013). As with all mountain areas, there is substantial variability in the wind speed. For example, the average ridge top wind speeds are at least 50 % greater than these (Bair, 2011) and the highest reliably recorded wind gust from the top of Mammoth Mountain was measured at 82.3 m s⁻¹.

Figure 8Wind rose for CUES, a windy site. Hourly values are plotted. Note the predominant southwest wind direction.

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5.1.5 Uplooking longwave radiation

To illustrate the importance of measuring incoming longwave radiation rather than modeling it using the more commonly available temperature and relative humidity measurements, we have plotted modeled values against measured values for clear-sky conditions during the day (Fig. 9). The model (Marks and Dozier, 1979) is optimal for clear-sky conditions, with clear conditions defined the same as for direct albedo measurement: $D_{\downarrow }/\left(B_{\downarrow }+D_{\downarrow }\right)\le \mathrm{0.2}$. There is a strong negative bias of −40 W m⁻² or −17 % of the mean measured value. The RMSE of 43 W m⁻² is within the ranges reported in Marks and Dozier (1979), and they also report a similar negative bias.

Figure 9Density plot of modeled vs. measured uplooking longwave radiation for clear-sky measurements. The number of measurements N is represented by the color scale. Note the clear negative model bias.

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