How Do We Deﬁne Climate Change? Considering the Temporal Resolution of Niveo-Meteorological Data

: Historically, snowpack trends have been assessed using one ﬁxed date to represent peak snow accumulation prior to the onset of melt. Subsequent trend analyses have considered the peak snow water equivalent (SWE), but the date of peak SWE can vary by several months due to inter-annual variability in snow accumulation and melt patterns. A 2018 assessment evaluated monthly SWE trends. However, since the month is a societal construct, this current work examines daily trends in SWE, cumulative precipitation, and temperature. The method was applied to 13 snow telemetry stations in Northern Colorado, USA for the period from 1981 to 2018. Temperature trends were consistent among all the stations; warming trends occurred 63% of the time from 1 October through 24 May, with the trends oscillating from warming to cooling over about a 10-day period. From 25 May to 30 September, a similar oscillation was observed, but warming trends occurred 86% of the time. SWE and precipitation trends illustrate temporal patterns that are scaled based on location. Speciﬁcally, lower elevations stations are tending to record more snowfall while higher elevation stations are recording less. The largest SWE, cumulative precipitation, and temperature trends were + 30 to − 70 mm / decade, + 30 to − 30 mm / decade, and + 4 to − 2.8 ◦ C / decade, respectively. Trends were statistically signiﬁcance an average of 25.8, 4.5, and 29.4% of the days for SWE, cumulative precipitation, and temperature, respectively. The trend in precipitation as snow ranged from +/ − 2% / decade, but was not signiﬁcant at any station.


Introduction
Seasonal snow, i.e., snow that accumulates and persists all winter [1], covers about 42% of the land surface of the Northern Hemisphere [2]. This snow is an important water resource [3] and the presence of snow cover alters the local energy balance [4] due to the increase in albedo [5,6]. However, the snowpack has been changing in regions where a seasonal snow cover is present [2,7]. For such regions that have extended periods of snow cover, one common date is used to represent peak snow water equivalent (SWE). In the Western United States, April 1st is often used as SWE data have been collected on or about this date at over 2000 locations since as early as 1936 [8]. Trend analyses have shown a decrease in April 1st SWE across much of this domain [9][10][11][12][13][14]. However, this surrogate date under-represents peak SWE [15] and when snow course data are used, measurements are often taken 3-4 days prior to the first of the month [16,17]. Further, non-stationarity [18] may result in a change in the timing of peak SWE [19].
Combined investigations of SWE, precipitation, and temperature data illustrate that snowpack changes are complex [6,11,12,14,17,20,21]. For example, in Northern Colorado there was little net change in winter precipitation with some warming in the winter, yet there were monthly variations: November and March were warmer and drier, December and January were warmer and wetter, while February and May were cooler and wetter [17]. While the monthly analysis is at a finer temporal resolution, a month is still an arbitrary human-defined time step. To determine snowpack climatology, Fassnacht and Derry [22] showed that using daily data was more appropriate [19][20][21]23].
Most of the snowpack analyses have used a single date in time to identify change [9][10][11][12][13][14], and even monthly analyses [17] may be too coarse of a temporal resolution to fully identify the patterns of snowpack change, thus, this work evaluates trends in SWE at a daily time-step. We also examine trends in the precipitation and temperature data related to SWE trends [6,11,12,14,17,20,21], but on a daily time step. We investigate the correlation of trends in these three niveo-meteorological variables. Since many studies have examined trends over large regions [2,7,[9][10][11][12][13][14]24] or group stations [20] or trends [19] together, we investigate what the patterns of daily trends for individual stations [6,17]. We pose the following research questions: (1) what are the daily trends in SWE, cumulative precipitation and temperature? (2) what are the fluctuations in daily trends, and are there patterns over the year? (3) if temporal trend patterns exist, are there correlations between the three variables?

Study Domain and Data
We used 13 longer-term snow measurement stations (Figure 1a) located across the Northern Front Range of Colorado (NFRCo), as per Fassnacht et al. [17] (Figure 1b). This regional domain is located in the state of Colorado within the Western United Stated (Figure 1c). These SNOTEL stations [8,25] were divided into those on the west side of Rocky Mountain National Park (RMNP), denoted as orange stations, and those on the east side of RMNP, denoted as purple (Figure 1a), as per Clow [20]. The SNOTEL stations range in elevation from 2612 to 3265 m.a.sl. (Copeland Lake and Willow Park, respectively) ( Figure 1a). The area around each of the stations is moderately sloped and nine of the stations are somewhat south-facing, i.e., the northness (sine slope x cosine aspect) [26] is negative (Table 1). From the 30-m resolution U.S. Geological Survey National Land Cover Database, all stations are in evergreen forest except Phantom Valley that is in considered to be in developed, open space (Table 1). Their characteristics are also described in Fassnacht et al. [17].
The SNOTEL data were retrieved from the Natural Resources Conservation Service (NRCS) National Water and Climate Center at <https://www.wcc.nrcs.usda.gov/> [8,25]. Most of these stations have been monitoring snow and precipitation since the late 1970s. We used the water year (WY; 1 October to 30 September) for the period from 1981 to 2018 for all stations except Stillwater Creek that began recording in WY 1986 (1 October 1985). The Copeland Lake station was missing data for WY 1983. The quality-controlled data [27] from Fassnacht et al. [17] were used in the current study, with the addition of the WY 2016 to 2018 data. Figure 1. Location of (a) the 13 SNOTEL data collection stations (b) within the Northern Front Range of the state of Colorado (c) in the Western United States. The median niveograph and the daily SWE trend of each station over the period of record is presented in (a), scaled according to the legend. The SNOTEL orange and purple stations refer to those on the western and eastern side of Rocky Mountain National Park, as used by Clow [20] and Fassnacht et al. [17]. The median niveograph and the daily SWE trend of each station over the period of record is presented in (a), scaled according to the legend. The SNOTEL orange and purple stations refer to those on the western and eastern side of Rocky Mountain National Park, as used by Clow [20] and Fassnacht et al. [17].
The mean peak SWE varied from 147 mm at Copeland Lake, the lowest elevation station with the warmest annual temperature of 5.26 • C, to 700 mm at Lake Irene, the second highest station with the coldest mean temperature at 0.48 • C (Table 1). Mean annual precipitation varied from 482 mm at Stillwater Creek to 1132 mm at Joe Wright ( Table 1). Example of SWE, temperature and precipitation conditions are presented for the Lake Irene station ( Figure 2). Since this paper focuses on snow, the entire SWE time series is shown in Figure 2a; averages are shown for the other variables.  Figure 1a) including station number (#), and location: latitude (lat), longitude (long), and elevation (elev). The slope and northness (sine slope x cosine aspect) are derived from the U.S. Geological Survey National Elevation Dataset. The canopy density is from the U.S. Geological Survey National Land Cover Database (NLCD). The NLCD land cover is evergreen forest for all stations, except * Phantom Valley that is denoted as developed, open space. The mean peak snow water equivalent (SWE), mean annual temperature (temp), and mean annual precipitation (precip) are from the SNOTEL station data. The mean peak SWE varied from 147 mm at Copeland Lake, the lowest elevation station with the warmest annual temperature of 5.26 °C, to 700 mm at Lake Irene, the second highest station with the coldest mean temperature at 0.48 °C (Table 1). Mean annual precipitation varied from 482 mm at Stillwater Creek to 1132 mm at Joe Wright ( Table 1). Example of SWE, temperature and precipitation conditions are presented for the Lake Irene station ( Figure 2). Since this paper focuses on snow, the entire SWE time series is shown in Figure 2a; averages are shown for the other variables.

Methodology
SWE is a memory of snowpack processes that is initially dominated by accumulation which is driven by precipitation, but also a function of temperature conditions. The SWE time period for each station differed ( Figure 1); the start date began once at least 17 of the total years of record had snow accumulation (ranging from 11 October at Joe Wright to 27 November at Copeland Lake), and ended once fewer than 18 years had complete melt (ranging from 29 March at Copeland Lake to 20 June at University Camp). We use cumulative precipitation rather than daily precipitation data due to interannual inconsistency in daily precipitation [28] and the numerical instability of analyzing a daily time series with many zeros. The cumulative precipitation trend analysis began on 8 October through 30 September; the first week was ignored to remove statistical problems due to an abundance of zero

Methodology
SWE is a memory of snowpack processes that is initially dominated by accumulation which is driven by precipitation, but also a function of temperature conditions. The SWE time period for each station differed ( Figure 1); the start date began once at least 17 of the total years of record had snow accumulation (ranging from 11 October at Joe Wright to 27 November at Copeland Lake), and ended once fewer than 18 years had complete melt (ranging from 29 March at Copeland Lake to 20 June at University Camp). We use cumulative precipitation rather than daily precipitation data due to inter-annual inconsistency in daily precipitation [28] and the numerical instability of analyzing a daily time series with many zeros. The cumulative precipitation trend analysis began on 8 October through 30 September; the first week was ignored to remove statistical problems due to an abundance of zero data. The temperature time series is shorter (starting in the late 1980s) and, due to changes in location and the sensor itself, there is a problem with discontinuity [29][30][31]. A co-located adjustment was presented in Oyler et al. [30] and used by Ma et al. [31]. The data from Ma et al. [31] were used in this analysis.
We evaluated the annual fraction of the precipitation that fell as snow. Since no specific observations of snow versus rain were available, we used the probability of snow versus air temperature linear function developed for Colorado [32]. This has been applied to other areas where no snow observations were available [33].
There is autocorrelation in the time series of daily values, but for the trend analysis the inter-annual autocorrelation could influence analysis results. We examined the autocorrelation for each day over the 38 years of record. Statistically, the autocorrelation is only relevant for a particular day when the trends are significant, as per the Mann-Kendall test [34][35][36]. The autocorrelation coefficient was computed at a lag of one timestep (lag-1), i.e., one year [37].
The significance of each daily trend was computed using the non-parametric Mann-Kendall test [34][35][36]. Two levels of significance levels were computed for each day, per variables and station: confidence levels of p < 0.05 (called significant) and p < 0.10 (called moderately significant). While we computed all trends regardless of significance level, we focused on the Lake Irene station to illustrate the significance of the trends in the three niveo-meteorological variables (plotted in Figure 2b-d).
Each time series trend was computed using the Theil-Sen median slope of the all pairs of linear trends [36,38,39]. This is a non-parametric approach that determines a monotonic trend across all time steps, regardless of missing years [36]. While the length of record influences the trend [40], outliers have a limited impact on the computation of the Theil-Sen slope [41].
To reduce visual clutter, the time series of daily trends for the west/orange stations were plotted separately from the east/purple stations, and there are individual plots for SWE and cumulative precipitation yielding four figures. Due to the nature of the temperature trends, all station trends are presented in one plot; the period with the greatest warming and cooling trends were highlighted. To reduce the "noise" that was apparent in the daily trends, a seven-day running average applied to the SWE and cumulative precipitation daily trends for seven of the stations that represented the extent of the variability in trends. The plots were visually evaluated to identify temporal trend periods, i.e., periods of increasing, no change or decreasing trends.
Finally, the daily temperature trends and daily SWE trends were plotted against the daily cumulative precipitation trends; the daily temperature trends were also plotted against the daily SWE trends for a subset of four stations. Each of the three plots was visually examined to evaluate any potential correlation between the variable trends per station. Where a potential correlation existed, the daily points were divided into the temporal trend periods identified above.

Results
On average, accumulation begins in October at most stations (e.g., Figure 2a,b), and November at the lower elevation stations (e.g., Copeland Lake) ( Figure 1a). Complete melt-out of the snowpack occurs between late April and early July, depending on the characteristics of the station, including elevation and land cover type (Table 1, [42]), temperature patterns (e.g., Figure 2c), and the amount of snowfall in the year (e.g., Figure 2d). Similarly, there is inter-annual variability in the date and quantity of peak SWE (e.g., Figure 2a). At some stations, such as the highest elevation Lake Irene station, the first decade of the period of record had a 12.5% lower peak SWE than the last decade ( Figure 2b). The decadal differences in temperature and precipitation were less obvious (Figures 2c and 2d, respectively). These specific temporal differences were an impetus to evaluate trends on a daily basis.
On average, 70% of the annual precipitation fell as snow, ranging from 58% at Copeland Lake to 78% at Lake Irene and Deadman Hill. There is a strong correlation between amount of precipitation as snow and elevation (Figure 3a). However, there is mix of trends from the largest decrease of 1.9% per decade at Copeland Lake to an increase of 1.5% and 1.7% per decade at Willow Park and Willow Creek Pass, respectively (Figure 3b).
For the Lake Irene station, the inter-annual autocorrelation (AC) of SWE is largest early in the accumulation period, i.e., in mid-October (~0.40), and once there is consistent snow on the ground from mid-November through mid-December (~0.21 to 0.31) (Figure 4a). There is a negative AC from mid-January through mid-May (maximum of −0.26) and then a small AC at the end of the melt season in early June. For Copeland Lake, SWE AC was smaller and mostly negative (Figure 4b).
The AC for cumulative precipitation is similar to SWE at Lake Irene, except it begins negative and then remains negative (and small) into the summer (Figure 4a). At Copeland Lake, the precipitation AC is mostly positive with a 20-day period (12 to 31 December) with AC > 0.4 (Figure 4b). The temperature inter-annual AC fluctuates with a period of about 5.5 days (66 cycles in a year) for both stations (Figure 4a,b). The temperature AC is more than 0.4 on 9 (and 2) days at Lake Irene (Copeland Lake), For the Lake Irene station, the inter-annual autocorrelation (AC) of SWE is largest early in the accumulation period, i.e., in mid-October (~0. 40), and once there is consistent snow on the ground from mid-November through mid-December (~0.21 to 0.31) (Figure 4a). There is a negative AC from mid-January through mid-May (maximum of −0.26) and then a small AC at the end of the melt season in early June. For Copeland Lake, SWE AC was smaller and mostly negative (Figure 4b). The AC for cumulative precipitation is similar to SWE at Lake Irene, except it begins negative and then remains negative (and small) into the summer (Figure 4a). At Copeland Lake, the precipitation AC is mostly positive with a 20-day period (12 to 31 December) with AC > 0.4 (Figure 4b). The temperature interannual AC fluctuates with a period of about 5.5 days (66 cycles in a year) for both stations ( Figure  4a,b). The temperature AC is more than 0.4 on 9 (and 2) days at Lake Irene (Copeland Lake), respectively, and less than −0.4 on 13 (and 8) days (Figure 4a (4b)). The same patterns of low AC values were observed for all the other stations. On average, SWE, cumulative precipitation, and temperature trends were statistically significant at a value p-value < 0.1 for 25.8, 4.5, and 29.4% of the total days, respectively ( Figure 5). SWE trends were statistically significant at all stations except the two most northerly stations, Roach and Deadman Hill (Figure 1a); only Bear Lake illustrated both increasing and decreasing trends that were significant (Figure 5a). When significant SWE trends were observed, they often occurred at or about peak SWE. For some stations, such as Lake Irene (Figure 2b) or Copeland Lake (Figure 5a), significant SWE trends occurred throughout the year. Cumulative precipitation trends were only significant at  For the Lake Irene station, the inter-annual autocorrelation (AC) of SWE is largest early in the accumulation period, i.e., in mid-October (~0. 40), and once there is consistent snow on the ground from mid-November through mid-December (~0.21 to 0.31) (Figure 4a). There is a negative AC from mid-January through mid-May (maximum of −0.26) and then a small AC at the end of the melt season in early June. For Copeland Lake, SWE AC was smaller and mostly negative (Figure 4b). The AC for cumulative precipitation is similar to SWE at Lake Irene, except it begins negative and then remains negative (and small) into the summer (Figure 4a). At Copeland Lake, the precipitation AC is mostly positive with a 20-day period (12 to 31 December) with AC > 0.4 (Figure 4b). The temperature interannual AC fluctuates with a period of about 5.5 days (66 cycles in a year) for both stations ( Figure  4a,b). The temperature AC is more than 0.4 on 9 (and 2) days at Lake Irene (Copeland Lake), respectively, and less than −0.4 on 13 (and 8) days (Figure 4a (4b)). The same patterns of low AC values were observed for all the other stations. On average, SWE, cumulative precipitation, and temperature trends were statistically significant at a value p-value < 0.1 for 25.8, 4.5, and 29.4% of the total days, respectively ( Figure 5). SWE trends were statistically significant at all stations except the two most northerly stations, Roach and Deadman Hill (Figure 1a); only Bear Lake illustrated both increasing and decreasing trends that were significant (Figure 5a). When significant SWE trends were observed, they often occurred at or about peak SWE. For some stations, such as Lake Irene (Figure 2b) or Copeland Lake (Figure 5a), significant SWE trends occurred throughout the year. Cumulative precipitation trends were only significant at On average, SWE, cumulative precipitation, and temperature trends were statistically significant at a value p-value < 0.1 for 25.8, 4.5, and 29.4% of the total days, respectively ( Figure 5). SWE trends were statistically significant at all stations except the two most northerly stations, Roach and Deadman Hill ( Figure 1a); only Bear Lake illustrated both increasing and decreasing trends that were significant (Figure 5a). When significant SWE trends were observed, they often occurred at or about peak SWE. For some stations, such as Lake Irene (Figure 2b) or Copeland Lake (Figure 5a), significant SWE trends occurred throughout the year. Cumulative precipitation trends were only significant at a p-value < 0.05 for 0.9% of the station days (Figure 5b). Using the same significance level, 17.1 (0.9)% of the station days had positive (negative) trends (Figure 5c).
Hydrology 2020, 7, x FOR PEER REVIEW 8 of 17 a p-value <0.05 for 0.9% of the station days (Figure 5b). Using the same significance level, 17.1 (0.9)% of the station days had positive (negative) trends (Figure 5c). There are large fluctuations in the temperature trends over the water year, with an average periodicity of about 10 days (35 local maxima per year in the trends of Figure 6a). These include some pronounced periods, such as the greatest warming from 29 October to 11 November, with a maximum of 3.4 to 4 °C/decade (Phantom Valley and Copeland Lake, respectively) occurring on 1 or 2 November (Figure 6b). There is also a mid-December warming for 13 days with a maximum of 2.3 to 3.4 °C/decade occurring on 19 December (Lake Irene and Niwot, respectively). The longest sustained cooling period was 20 to 26 February with the coolest trend of 1.6 to 2.7 °C/decade (Willow Creek Park and University Camp, respectively) on 24 February (Figure 6c). Starting on 25 May, the magnitude of the fluctuations is less (56%) than the previous period, and most of the daily trends are warming (Figure 6a). For the earlier, winter period (1 October to 24 May), warming occurs 63% of the time with a mean warming of 0.37 °C/decade, while warming occurs 82% of the time for the springsummer period (25 May to 30 September) with a mean warming of 0.63 °C/decade. There are large fluctuations in the temperature trends over the water year, with an average periodicity of about 10 days (35 local maxima per year in the trends of Figure 6a). These include some pronounced periods, such as the greatest warming from 29 October to 11 November, with a maximum of 3.4 to 4 • C/decade (Phantom Valley and Copeland Lake, respectively) occurring on 1 or 2 November (Figure 6b). There is also a mid-December warming for 13 days with a maximum of 2.3 to 3.4 • C/decade occurring on 19 December (Lake Irene and Niwot, respectively). The longest sustained cooling period was 20 to 26 February with the coolest trend of 1.6 to 2.7 • C/decade (Willow Creek Park and University Camp, respectively) on 24 February (Figure 6c). Starting on 25 May, the magnitude of the fluctuations is less (56%) than the previous period, and most of the daily trends are warming (Figure 6a). For the earlier, winter period (1 October to 24 May), warming occurs 63% of the time with a mean warming of 0.37 • C/decade, while warming occurs 82% of the time for the spring-summer period (25 May to 30 September) with a mean warming of 0.63 • C/decade.
There are also fluctuations in the daily SWE and cumulative precipitation trends (Figures 7a and  7b, respectively). However, while there is daily noise, there are more distinct longer period patterns present, especially for the purple east-side stations (Figure 7(aii,bii)). The temporal trend patterns for the orange west-side stations are mostly consistent across all the stations for both SWE and cumulative precipitation (Figure 7(ai,bi)). The SWE trends outliers are Willow Creek Pass (Figure 7(ai)) on the west side that is always positive and Willow Park on the east side that is almost always negative (Figure 7(aii)). There are also fluctuations in the daily SWE and cumulative precipitation trends (Figure 7a and 7b, respectively). However, while there is daily noise, there are more distinct longer period patterns present, especially for the purple east-side stations (Figure 7aii,bii). The temporal trend patterns for the orange west-side stations are mostly consistent across all the stations for both SWE and cumulative precipitation (Figure 7ai,bi). The SWE trends outliers are Willow Creek Pass (Figure 7ai) on the west side that is always positive and Willow Park on the east side that is almost always negative (Figure 7aii).   There are also fluctuations in the daily SWE and cumulative precipitation trends (Figure 7a and 7b, respectively). However, while there is daily noise, there are more distinct longer period patterns present, especially for the purple east-side stations (Figure 7aii,bii). The temporal trend patterns for the orange west-side stations are mostly consistent across all the stations for both SWE and cumulative precipitation (Figure 7ai,bi). The SWE trends outliers are Willow Creek Pass (Figure 7ai) on the west side that is always positive and Willow Park on the east side that is almost always negative (Figure 7aii).  The seven-day running average for SWE and cumulative precipitation (sumP) trends for seven representative stations (Figure 8), subset from Figure 7, show the beginning of the accumulation season through early December sees either no change or a slight decrease (yellow background). From December through the end of February, SWE and sumP is either not changing or increasing (green background). Next, there is about 1.5 months (through mid-April) of decreasing SWE trends, except at Willow Creek Pass that has a slight increase. Cumulative precipitation only decreases for about two weeks in early March, followed by no change for about a month. The 10-day increase in SWE and sumP in mid to late April is followed by a little change through early May. For SWE, mid-May through early June and for sumP through the end of July, there is a decrease. The exception is the end of the snow period at Lake Irene where there is an increase (Figure 8a). August and September sumP trends are a mix of increasing and decreasing (Figure 8c).
The seven-day running average for SWE and cumulative precipitation (sumP) trends for seven representative stations (Figure 8), subset from Figure 7, show the beginning of the accumulation season through early December sees either no change or a slight decrease (yellow background). From December through the end of February, SWE and sumP is either not changing or increasing (green background). Next, there is about 1.5 months (through mid-April) of decreasing SWE trends, except at Willow Creek Pass that has a slight increase. Cumulative precipitation only decreases for about two weeks in early March, followed by no change for about a month. The 10-day increase in SWE and sumP in mid to late April is followed by a little change through early May. For SWE, mid-May through early June and for sumP through the end of July, there is a decrease. The exception is the end of the snow period at Lake Irene where there is an increase (Figure 8a). August and September sumP trends are a mix of increasing and decreasing (Figure 8c). From the four of 13 stations shown in Figure 9, the remaining stations show the same patterns, there is no correlation between sumP and temperature trends (Figure 9a). However, increasing (decreasing) sumP trends do correspond with increasing (decreasing) SWE trends (Figure 9b). There is no correlation between SWE and temperature trends (Figure 9c). From the four of 13 stations shown in Figure 9, the remaining stations show the same patterns, there is no correlation between sumP and temperature trends (Figure 9a). However, increasing (decreasing) sumP trends do correspond with increasing (decreasing) SWE trends (Figure 9b). There is no correlation between SWE and temperature trends (Figure 9c).
Using the temporal trend periods identified in Figure 8a,c, the correlation between sumP and SWE is similar (Figure 10). Most of the time periods illustrate a similar slope, i.e., correlation in the trend of cumulative precipitation with SWE trend changed at a similar rate, for the four stations (Figure 10a-d). This includes the first five periods from 14 October through 24 April. Most noticeable are the declines from 28 February to 14 March. The increasing SWE trend versus a decreasing precipitation trend at the end of the winter (20 May to 17 June) at Lake Irene presents itself as perpendicular to the firs, third and fifth time periods (Figure 10a). Since snow accumulates later and melts earlier at Copeland Lake (Figure 10d), only four of the eight time periods are available. Using the temporal trend periods identified in Figures 8a and Figure 8c, the correlation between sumP and SWE is similar ( Figure 10). Most of the time periods illustrate a similar slope, i.e., correlation in the trend of cumulative precipitation with SWE trend changed at a similar rate, for the four stations (Figure 10a to 10d). This includes the first five periods from 14 October through 24 April. Most noticeable are the declines from 28 February to 14 March. The increasing SWE trend versus a decreasing precipitation trend at the end of the winter (20 May to 17 June) at Lake Irene presents itself as perpendicular to the firs, third and fifth time periods (Figure 10a). Since snow accumulates later and melts earlier at Copeland Lake (Figure 10d), only four of the eight time periods are available.   Using the temporal trend periods identified in Figures 8a and Figure 8c, the correlation between sumP and SWE is similar ( Figure 10). Most of the time periods illustrate a similar slope, i.e., correlation in the trend of cumulative precipitation with SWE trend changed at a similar rate, for the four stations (Figure 10a to 10d). This includes the first five periods from 14 October through 24 April. Most noticeable are the declines from 28 February to 14 March. The increasing SWE trend versus a decreasing precipitation trend at the end of the winter (20 May to 17 June) at Lake Irene presents itself as perpendicular to the firs, third and fifth time periods (Figure 10a). Since snow accumulates later and melts earlier at Copeland Lake (Figure 10d), only four of the eight time periods are available.

Discussion
While the daily time step trends in SWE and cumulative precipitation are complicated (Figure 8), there are distinct time periods with temporal patterns (Figure 9), such as the winter season beginning with less SWE at most stations then increasing through the end of February. By 1 March, there is a mean increase in SWE at 11 of 13 stations, but by 1 April, SWE is decreasing at all but two stations (Figure 7(ai,aii)). The 1 April decreases match previously research in many areas across the Western U.S. [9][10][11][12][13][14], with SWE decreasing at all stations from 1 March to 1 April [17]. This decrease in SWE continues through mid-April (Figure 8a), and corresponds to a decrease in precipitation at all stations ( Figure 10) for the first two weeks of March, and at most stations through mid-April (Figure 8c). Later in April, all stations with snow (thus not Copeland Lake) saw an increase in SWE. This late season increase is not captured when using 1 April as the date of peak SWE [15]. This current analysis (Figures 6 and 7) illustrates that even a monthly assessment of SWE trends [17], while more informative than a 1 April evaluation, does not fully establish the actual patterns ( Figure 8). Further, the temporal trend periods do not align with monthly periods [22]. Unfortunately, daily (automated) snow data are available at fewer locations than monthly (usually manual) snow data [17], and the manual measurements extend over a longer time period of record that is twice as long across the Western U.S. [40]. Thus, where daily data are available, it is recommended that snowpack and meteorological trends be examined on a daily (Figures 6 and 7), or at least weekly ( Figure 8) time step [22].
The day to day noise is more pronounced for temperature than SWE or precipitation ( Figure 6 versus Figure 7). Warming and cooling trends have short periodicities that do not match the typically used longer time periods, such as months [17], seasons [43], or the annual trends [44]. Overall temperatures are warming at all stations [30,31] with a weak inverse correlation between mean temperature trends and elevation. Specifically, higher elevation stations are tending to warm less than lower elevation stations with Willow Park, University Camp, and Lake Irene warming the least in the winter and summer. Bear Lake, located only 15 km southeast and 370 m lower than Willow Park, is warming the most over the entire year, especially in the summer. The Bear Lake area is a very popular destination for tourists [45], and Willow Park is much less accessible in the summer and is not accessible in the winter [46]. While differences in temperature trends among stations are possibly due to sensor issues [29][30][31], the trends are consistent among the stations (Figures 6 and 8b) [31].
The warmest period of temperature increases, 13 days from 29 October to 10 November (Figure 5b), had a mean warming of 2.1 • C/decade with a maximum daily warming from 3.4 to 4 • C/decade on 2 November. With the exception of Roach, Phantom Valley, and Willow Creek Pass (Figure 7(ai)), this period is seeing a decrease in SWE (Figure 7(ai,aii)). The highest elevations (Joe Wright, Lake Irene, Willow Park) accumulate snow the earliest, and see the largest decrease in SWE. This is illustrated at Lake Irene (Figure 2b) where there is about twice as much SWE for the first decade compared to the last decade. During this warming period, there may be a lower net albedo due to decreasing precipitation ( Figure 8c) meaning less fresh snow and thus fewer increases in albedo. Further, less snow could mean that there is more of an influence on albedo from the underlying vegetation or even vegetation protruding from the snowpack due to a lower snow depth. Dormant vegetation has a higher albedo than actively growing vegetation [47]. With a reduced net albedo, and thus more absorbed solar radiation [48], this could yield a more positive energy balance [5] that could influence or warm the near surface air temperature. Snow begins to accumulate during this time at the lowest elevation stations (Stillwater Creek and Copeland Lake), so it is possible that, combined with summer warming (Figure 6), a longer growing period for vegetation may occur in these locations. A longer growing season may result in more transpiration and loss of water that may otherwise become soil moisture recharge, groundwater, or streamflow [49,50].
The changing of the timing of precipitation (Figure 7b) alters snow accumulation patterns (Figures 7a, 8a, 9 and 10). Combined with warmer temperatures (Figure 6), this may cause earlier snowmelt [20,21], which can cause earlier runoff [51][52][53]. This has been observed at most locations across Colorado [54]. Warming may also cause a change in the phase of the precipitation, specifically less snowfall [6,55]. In this study, precipitation phase is correlated with elevation ( Figure 3a) due to the computation method [33] and the correlation of temperature with elevation at the SNOTEL scale in this area [56]. However, the change in the fraction of precipitation that falls as snow is not a function of elevation (Figure 3b) due to the combined changed in timing of precipitation ( Figure 7b) and periodicity of the temperature trends (Figure 6a). These fractions of precipitation as snow (Figure 3a) and their trends could be different if observations of fresh snow were available [6,57], or a different method was used, such as the dewpoint temperature to distinguish snow from rain [58].
This paper analyzes daily trends in SWE and illustrates a correlation to cumulative precipitation ( Figure 10) that is more difficult to illustrate using manual snow course data that only have a monthly time step [17,40] but do not have measured precipitation. This could be addressed using interpolation of station data [24] or modeling [59,60]. The SNOTEL stations used in this current analysis represent a point in space and over-represent the surrounding area [61], which could make interpolation of the station data [30] or trend results [24] difficult. Modeling [59,60] can ameliorate the point to area dilemma [62], but modeling is often at a resolution too coarse to adequately represent snowpack spatial variability in complex terrain [26,63]. An opportunity may be the combination of remote sensing, in situ data, and modeling [64,65].

Conclusions
Changes in temperature, precipitation, and SWE are variable in both time and space. Typically, the evaluation of trends in SWE use 1 April data, but these do not capture the nuance of a changing snowpack shown by evaluating trends in the daily data. These show temporal patterns that vary from 10 days to three months, and do not align with first of the month data. Noise was found in the daily trends, but a seven-day moving average removed much of this noise for SWE and precipitation. There were larger fluctuations from positive to negative in the temperature trends, with a five to 10-day period. After late May, temperatures were almost exclusively warming. Temperature trends were very similar among all stations, different that precipitation and SWE trends that varied less from week to week and more from location to location. The trends in SWE were partially correlated to cumulative precipitation over eight temporal periods. There was no correlation between temperature and precipitation or SWE. The limitations of using daily (automated) time-step data are their shorter records compared to monthly or annual (manual) data. Understanding temperature and SWE trends on a fine temporal scale is important for climatological, ecological, and hydrological studies, water resources management, as well as for recreation and tourism.