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  • View in gallery

    (a) Location of 447 SNOTEL sites (black dots) and 49 R sites used for water balance model verification, and (b) probability density functions illustrating the distributions of correlations between measured and water-balance model estimated 1 April SWE (black line) and water year R (red line).

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    Location of eight-digit HUs used for analyses.

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    Trends (expressed as values of Kendall’s tau) in Sfrac and Reff for the period 1951–2014 (a),(d) for all HUs and (b),(e) for HUs with trends that are statistically significant at p = 0.05; (c),(f) probability density functions illustrating the distribution of trends slopes for all HUs.

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    Number of HUs with significant linear trends (at a 95% confidence level) in Sfrac and Reff for periods beginning in 1951 and ending in 1980–2014. Trends were computed using Kendall’s tau.

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    (a) Time series of Sfrac PC1 and Twin for 175 HUs, (b) time series of Reff PC1 and Pwy for 175 HUs, (c) loadings of Sfrac PC1 on Sfrac for 175 HUs, (d) loadings of Reff PC1 on Reff for 175 HUs, (e) correlations of Sfrac PC1 with mean November–March 500-hPa heights, and (f) correlations of Reff PC1 with mean water year 500-hPa heights. For the maps illustrating correlations with 500-hPa heights, the solid isolines indicate positive correlations, and the dashed lines indicate negative correlations. The contour interval is 0.1, and the first solid isoline is the zero correlation isoline.

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    Comparison of (a) trends in Twin with trends in Sfrac, and (b) trends in Pwy and Reff for 175 HUs across the western United States. Trends are expressed as values of Kendall’s tau for the 1951–2014 period.

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    Percentiles [i.e., 25th (p25), 50th (p50), and 75th (p75)] of differences in mean monthly P, AET, S, RAIN, MELT, and R (mm) for 175 HUs in the western United States for the period 2001–14 minus the period 1951–65.

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Warming is Driving Decreases in Snow Fractions While Runoff Efficiency Remains Mostly Unchanged in Snow-Covered Areas of the Western United States

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  • 1 U.S. Geological Survey, Denver, Colorado
  • | 2 U.S. Geological Survey, Lawrence, Kansas
  • | 3 U.S. Geological Survey, Denver, Colorado
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Abstract

Winter snowfall and accumulation is an important component of the surface water supply in the western United States. In these areas, increasing winter temperatures T associated with global warming can influence the amount of winter precipitation P that falls as snow S. In this study we examine long-term trends in the fraction of winter P that falls as S (Sfrac) for 175 hydrologic units (HUs) in snow-covered areas of the western United States for the period 1951–2014. Because S is a substantial contributor to runoff R across most of the western United States, we also examine long-term trends in water-year runoff efficiency [computed as water-year R/water-year P (Reff)] for the same 175 HUs. In that most S records are short in length, we use model-simulated S and R from a monthly water balance model. Results for Sfrac indicate long-term negative trends for most of the 175 HUs, with negative trends for 139 (~79%) of the HUs being statistically significant at a 95% confidence level (p = 0.05). Additionally, results indicate that the long-term negative trends in Sfrac have been largely driven by increases in T. In contrast, time series of Reff for the 175 HUs indicate a mix of positive and negative long-term trends, with few trends being statistically significant (at p = 0.05). Although there has been a notable shift in the timing of R to earlier in the year for most HUs, there have not been substantial decreases in water-year R for the 175 HUs.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Gregory J. McCabe, gmccabe@usgs.gov

Abstract

Winter snowfall and accumulation is an important component of the surface water supply in the western United States. In these areas, increasing winter temperatures T associated with global warming can influence the amount of winter precipitation P that falls as snow S. In this study we examine long-term trends in the fraction of winter P that falls as S (Sfrac) for 175 hydrologic units (HUs) in snow-covered areas of the western United States for the period 1951–2014. Because S is a substantial contributor to runoff R across most of the western United States, we also examine long-term trends in water-year runoff efficiency [computed as water-year R/water-year P (Reff)] for the same 175 HUs. In that most S records are short in length, we use model-simulated S and R from a monthly water balance model. Results for Sfrac indicate long-term negative trends for most of the 175 HUs, with negative trends for 139 (~79%) of the HUs being statistically significant at a 95% confidence level (p = 0.05). Additionally, results indicate that the long-term negative trends in Sfrac have been largely driven by increases in T. In contrast, time series of Reff for the 175 HUs indicate a mix of positive and negative long-term trends, with few trends being statistically significant (at p = 0.05). Although there has been a notable shift in the timing of R to earlier in the year for most HUs, there have not been substantial decreases in water-year R for the 175 HUs.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Gregory J. McCabe, gmccabe@usgs.gov

1. Introduction

Snow S is an important surface-water resource and a hydrologic variable that is a useful index of climatic variability and change (Frei and Robinson 1999; Frei et al. 1999; Brown 2000; McCabe and Wolock 2010). Because S is climatically sensitive and global temperatures have been increasing, there have been numerous studies that examined changes and trends in snow cover (Brown 2000; Bamzai 2003; Déry and Brown 2007; McCabe and Wolock 2010), rain-on-snow events (McCabe et al. 2007), trends in snowpack accumulations (Dettinger and Cayan 1995; Hamlet et al. 2005; Mote et al. 2005; McCabe and Wolock 2009; Abatzoglou 2011; Clow 2010), and the timing of snowmelt runoff (Stewart et al. 2004; McCabe and Clark 2005; Mote et al. 2005; Regonda et al. 2005; Clow 2010). Also, several studies have indicated declining S across the western United States (Dettinger and Cayan 1995; Hamlet et al. 2005; Mote et al. 2005; McCabe and Wolock 2009; Abatzoglou 2011; Clow 2010), which has primarily been attributed to increases in winter temperatures T.

Changes in the fraction of precipitation P that falls as S (Sfrac) have substantial effects on the magnitude and timing of hydrologic variables such as runoff R and soil-moisture storage (Huntington et al. 2004; Knowles et al. 2006), but there have been few studies of trends in Sfrac (Huntington et al. 2004; Knowles et al. 2006; Feng and Hu 2007). Huntington et al. (2004) performed an analysis of Sfrac values for 21 sites in the northeastern United States for the period 1949–2000 and found that 11 of the 21 sites had statistically significant negative trends in annual Sfrac values. They also concluded that the negative trends in Sfrac were primarily due to decreases in snowfall, rather than to increases in P, indicating that the decreases in Sfrac were related to increases in temperature T. Huntington et al. (2004) also reported a correlation between the timing of spring (snowmelt) runoff and Sfrac, such that as Sfrac has decreased, the timing of snowmelt runoff has occurred earlier in the year. Additionally, Berghuijs et al. (2014) examined the effects of warming on R for 420 basins in the conterminous United States (CONUS) for the period 1948–2001 and concluded that a shift from snow to rain results in a decrease in R.

Knowles et al. (2006) examined variability and trends in Sfrac for the western United States for the 1949–2004 period. This study, based on sites in the western United States, complemented the research by Huntington et al. (2004) for sites in the eastern United States. Knowles et al. (2006) reported decreases in Sfrac across the western United States and related these declines to warming across the region. The results presented by Knowles et al. (2006), although for a different region of the CONUS, are consistent with those presented by Huntington et al. (2004).

In a study of the factors controlling the decline of S in the western United States, Abatzoglou (2011) indicated that changes in atmospheric circulation [quantified by changes in the Pacific North American (PNA) index] accelerated the decline of S projected because of anthropogenic warming. Abatzoglou (2011) reported that a tendency for PNA values to be above average during recent decades resulted in decreased fractions of winter P that falls as S and increases in snowmelt (MELT).

Another useful index of the hydrologic effects of climate change is runoff efficiency (Reff; which also is referred to as runoff ratio or runoff coefficient). Reff is defined as the quantity of R produced per unit precipitation and is computed here as the ratio of water-year R to water-year P. A water year is the period from 1 October through 30 September and is identified by the calendar year in which it ends. Reff is known to vary geographically and temporally (e.g., Garbrecht et al. 2004; Gupta et al. 2015). In a study of the hydroclimatic variability of the upper Colorado River basin (UCRB), Nowak et al. (2012) reported that low-frequency variability of UCRB flow is related to T variability (through effects on Reff), whereas decadal UCRB variability is strongly controlled by precipitation. Nowak et al. (2012) also reported that a 1°C increase in UCRB T resulted in a 2% decrease in Reff. In a recent study, Frans et al. (2013) examined the drivers of increases in R for the upper Mississippi River basin (UMRB). Frans et al. (2013) used a hydrologic model to examine the effects of climatic variability and other factors (e.g., land use changes) on R and showed that climatic variability was the principal cause of changes in UMRB R during the 1918–2007 period. Frans et al. (2013) also reported decreases in modeled annual R magnitude by as much as 9% when cropland replaced grasslands. Frans et al. (2013) also found increases in annual R of as much as 5% when cropland replaced forests. In a study of the Corn Belt region of the United States, Schilling et al. (2008) showed that when a perennial cropping system is replaced by an annual cropping system, evapotranspiration decreases and R and Reff increase.

Studies of the effects of land use on R also suggest the installation of drainage tiles has increased R and Reff (e.g., Schilling et al. 2008; Xu et al. 2013; Schottler et al. 2014). The magnitude of anthropogenic factors such as cropping and drainage practices on R is still in question. For example, Gupta et al. (2015) suggest that increases in Reff observed in the UMRB are largely due to increases in P. Such increases in P lead to increases in soil moisture that are associated with increases in Reff. The results from Tomer and Schilling (2009) also indicate that increases in R in the midwestern United States are principally caused by changes in climate rather than to changes in cropping practices.

In an analysis of variability of water-year Reff across the CONUS during 1951–2012, McCabe and Wolock (2016) reported increases in Reff for some parts of the north-central United States and large decreases in Reff for the south-central United States. The increases in Reff in the north-central United States were attributed to trends in climate, whereas the large decreases in Reff in the south-central United States appear to be related to groundwater withdrawals from the Ogallala aquifer.

In a more recent study of Reff in the Rio Grande River in the southwestern United States, Lehner et al. (2017) suggest that negative trends in Reff since the 1980s are unprecedented in the context of paleo reconstructions of Reff for the last 445 years. Lehner et al. (2017) also reported that Reff is primarily driven by variability in P, and they also showed that T has a secondary influence on Reff such that during years with low P, low Reff becomes more likely due to increased T. Lehner et al. (2017) suggest that the Reff sensitivity to T has strengthened during recent decades and that water supplies of the Rio Grande are likely to become more vulnerable as warming continues.

An anticipated hydrologic effect of global warming is a change in the timing of snowmelt R such that it occurs earlier in the year (Gleick 1987; Gleick and Adams 2000; Mote et al. 2005; Regonda et al. 2005). Consistent with this expectation, several previous studies have identified a change to earlier snowmelt R for numerous rivers across the western United States (Aguado et al. 1992; Dettinger and Cayan 1995; Rajagopalan and Lall 1995; Cayan et al. 2001; Regonda et al. 2005; Stewart et al. 2004). These previous studies also showed that the principal driving force of the change in snowmelt R timing has been an increase in spring and early summer T, related to global warming (Aguado et al. 1992; Dettinger and Cayan 1995; Regonda et al. 2005; Stewart et al. 2004).

Although previous studies have identified decreases in S across the western United States, as well as a change in the timing of snowmelt R to earlier in the year, thus far it has not been shown if decreases in S and the shift in R timing also resulted in changes in total water-year R in the western United States. In this study we examine variability and trends in both Sfrac and Reff in basins with snowmelt R to 1) identify and compare long-term trends in Sfrac and Reff, 2) determine the climatic factors driving interannual variability and significant long-term trends in Sfrac and Reff, and 3) determine if long-term trends in Sfrac have affected long-term trends in Reff.

2. Data and methods

a. Data and model

The analyses in this study focused on variability and trends in late fall and winter months (November–March) Sfrac and water-year Reff. Monthly P and T data were obtained from the Parameter-Elevation Regressions on Independent Slopes Model (PRISM; PRISM Climate Group, Oregon State University, http://www.prism.oregonstate.edu). These data are available as 4 km × 4 km grid cells for the CONUS for the period from January 1895 until present. Only data for the period 1951–2014, however, were used in the analyses because previous work has indicated that PRISM data before about 1950 are not reliable for trend analyses, due in a large part to the sparseness of meteorological stations prior to 1950 (Gibson et al. 2002; McCabe and Wolock 2011). These data then were spatially aggregated to provide monthly total P and mean monthly T for the 2109 U.S. Geological Survey eight-digit hydrologic units (HUs). The monthly T and P aggregated to the HUs were used as input to a monthly water balance model to compute monthly S and R for sites across the western United States (west of 105°W longitude; McCabe and Wolock 2011). Model-simulated S and R estimates were used in the analyses because they provide long and complete records. The monthly T and P data, and monthly water balance estimates of S and R for the PRISM 4-km grid cells for the CONUS, are available online (https://doi.org/10.5066/F71V5CWN; Wolock and McCabe 2018).

The water balance model computes the distribution of water among various components of the hydrologic system [the discussion of the water balance model provided here follows the discussion presented in McCabe and Wolock (2011)]. For example, the water balance model accounts for the climatic water supply and demand, seasonality in climatic water supply and demand, S accumulation and melt, and soil-moisture storage (McCabe and Wolock 2011).

The water balance model parameters used for this study were taken from parameter sets used in previous studies (McCabe and Wolock 1999, 2010, 2011). The parameter set includes 1) a parameter that specifies the fraction of monthly P that becomes direct R, 2) T thresholds that determine the proportions of monthly P that are rain and/or S, 3) a snowmelt factor that controls the melt rate of the snowpack, and 4) a parameter that specifies how much surplus in a month becomes R. Each of the aforementioned parameters is assumed not to vary across space; that is, only a single value for each parameter is specified everywhere. Only soil-moisture storage capacity varied spatially, and this parameter was computed using the available water-capacity values from the State Soil Geographic Data Base (STATSGO) dataset and by assuming a 1-m rooting depth (available at https://www.nrcs.usda.gov/wps/portal/nrcs/detail/soils/survey/geo/?cid=nrcs142p2_053629).

The specific values of water balance model parameters were selected to provide reliable estimates of monthly runoff across a large number of sites (McCabe and Wolock 2011). There is concern that some of the parameters may influence simulated trends in runoff. However, McCabe and Wolock (2011) showed that trends in runoff simulated using the selected water balance parameters were similar to trends in measured runoff for 18 sites located across the CONUS for the 1951–2008 period. Additionally, a sensitivity analysis of the effects of the parameter used to estimate the fraction of monthly P that becomes direct R (not shown) indicated that simulated trends in runoff (and runoff efficiency) are insensitive to this parameter.

b. Verification of water balance model estimates

Although water balance model estimates of S and R have been verified in previous studies, we performed an additional verification of water balance estimated S and R for this study (McCabe and Wolock 2009, 2010, 2011). For this verification we compared water balance model estimates with 1) 1 April snow water equivalent (SWE) measurements from 447 Snowpack Telemetry (SNOTEL) sites across the western United States for the period 1991–2015, and 2) total water-year R for 49 sites for the period 1955–2014 (Fig. 1a).

Fig. 1.
Fig. 1.

(a) Location of 447 SNOTEL sites (black dots) and 49 R sites used for water balance model verification, and (b) probability density functions illustrating the distributions of correlations between measured and water-balance model estimated 1 April SWE (black line) and water year R (red line).

Citation: Journal of Hydrometeorology 19, 5; 10.1175/JHM-D-17-0227.1

The 447 SNOTEL sites were selected because these sites have complete monthly T, P, and SWE data during years 1991–2015 and indicated at least 30 mm of 1 April SWE for 50% of the years during this period (SNOTEL data were obtained from the National Resources Conservation Service, United States Department of Agriculture, https://www.wcc.nrcs.usda.gov/snow/). The 49 sites used for verification of water balance model estimated R were selected from a set of sites with minimal anthropogenic influences (Falcone et al. 2010) and had complete monthly T, P, and R data for water years 1951–2014. The monthly R values were converted from measured monthly streamflow data (computed as flow per unit area) for comparison with R estimated by the water balance model. The 49 sites selected to verify water balance model estimates of runoff cover a range of climatic and physiographic regions.

Because the water balance model requires several years of simulations to equilibrate to arbitrarily set initial conditions, the first few years of SWE and R simulations were not used for verification of the water balance model. Thus, water balance model SWE verification was performed using data for 1995–2015, and water balance model R verification was performed using data for 1955–2014.

Since this analysis is focused on interannual variability and long-term trends of Sfrac and Reff, we evaluated how well the water balance model could estimate the temporal variability of measured April 1 SWE and water-year R across the western United States. This model evaluation was performed by computing Pearson correlations between 1) time series of measured 1 April SWE and time series of water balance estimated March SWE for the 447 SNOTEL sites (1995–2015) and 2) between time series of measured water-year R and time series of water balance estimated water-year R for the 49 sites (1955–2014).

Comparisons of model-estimated and measured 1 April SWE at the 447 SNOTEL sites indicated relatively high positive and statistically significant correlation values, with a 25th percentile of 0.69, a median of 0.82, and a 75th percentile of 0.90 (Fig. 1b). The correlation values for 415 (93%) of the sites are statistically significant at p = 0.05, and the correlation values for 396 (89%) of the sites are statistically significant at p = 0.01.

The distribution of correlation values between model-estimated and measured water-year R for the 49 sites had a 25th percentile value of 0.80, a median of 0.91, and a 75th percentile of 0.95 (Fig. 1b). For 48 (98%) of the 49 sites, the correlations are statistically significant at p = 0.05, and the correlations for 47 (96%) of the sites are statistically significant at p = 0.01.

Results of previous water balance model verifications, in combination with the aforementioned correlation analyses, show that the water balance model appropriately simulates the temporal variability in 1 April SWE and water-year R for sites across the western United States.

The water balance model simulations used in these analyses represent hydroclimatic variability driven solely by climate (i.e., T and P). Other influences such as vegetation and land-use changes, groundwater pumping, reservoirs, and water diversions can have significant effects on individual watersheds, but these factors are not included in the simulations examined. The water balance simulations we use isolate the effects of variability and changes in T and P on S and R.

c. Selection of eight-digit hydrologic units for analysis

Because many HUs in the CONUS do not experience S, we selected HUs for analysis where water balance model simulated March SWE was greater than 30 mm (SWE, not snow depth) for at least 50% of the years during 1951–2014 and are located west of 105°W longitude. Water balance estimated March SWE was used for this selection process because March SWE best represents measured 1 April SWE, which is the date of maximum SWE for many sites in the western United States (McCabe and Legates 1995; Serreze et al. 1999; Bohr and Aguado 2001; Clark et al. 2001). This process resulted in the selection of 175 HUs in the western United States for analysis (Fig. 2).

Fig. 2.
Fig. 2.

Location of eight-digit HUs used for analyses.

Citation: Journal of Hydrometeorology 19, 5; 10.1175/JHM-D-17-0227.1

d. Analyses

Sfrac is computed as total water balance estimated winter S divided by measured total winter P. The months of November–March were used to define winter because over the 1951–2014 period, mean November–March water balance estimated S accounts for 91% of mean water-year S. In addition, mean monthly S for each of the months during November–March accounts for at least 10% of water-year mean S. Reff is computed as water balance estimated total water-year (October–September) R divided by measured total water-year P.

Monotonic trends in Sfrac and Reff were estimated using Kendall’s tau (Hirsch et al. 1982; Press et al. 1986). The rationale for using Kendall’s tau is that it is 1) a nonparametric trend statistic that does not assume a specific underlying distribution and 2) less sensitive to data outliers compared to parametric statistical tests (such as the Pearson correlation coefficient).

We also used S-mode principal component analyses of the Sfrac and Reff data for the 175 HUs to identify primary modes of variability in Sfrac and Reff. The time series of component scores for the primary modes of Sfrac and Reff variability were subsequently correlated (using Pearson correlation) with 500-hPa height anomalies to identify atmospheric pressure patterns associated with variability in Sfrac and Reff. Atmospheric pressures for the 500-hPa level are used because this atmospheric pressure surface affords a reasonable representation of midtropospheric atmospheric circulation that influences seasonal surface weather variations. Monthly 500-hPa height anomaly data were obtained from the Twentieth Century Reanalysis version 2 dataset (https://www.esrl.noaa.gov/psd/data/gridded/data.20thC_ReanV2.html) for 1951–2012 for the domain 10°–70°N and 180°–0° [support for the Twentieth Century Reanalysis Project dataset is provided by the U.S. Department of Energy, Office of Science Innovative and Novel Computational Impact on Theory and Experiment (DOE INCITE) program, and Office of Biological and Environmental Research (BER), and by the National Oceanic and Atmospheric Administration Climate Program Office]. The monthly 500-hPa anomaly data were averaged to compute mean winter atmospheric pressure anomalies for comparison with the Sfrac data and mean water-year anomalies for comparison with the Reff data.

3. Results and discussion

a. Variability and trends

The Sfrac time series primarily indicate long-term negative trends (Figs. 3a–c). Only 2 HUs indicate long-term positive trends in Sfrac (Fig. 3a), and none of these positive trends in Sfrac are statistically significant at p = 0.05 (Fig. 3b), whereas 172 HUs indicate long-term negative trends in Sfrac (Fig. 3a) with 139 of these trends being statistically significant at p = 0.05 (Fig. 3b).

Fig. 3.
Fig. 3.

Trends (expressed as values of Kendall’s tau) in Sfrac and Reff for the period 1951–2014 (a),(d) for all HUs and (b),(e) for HUs with trends that are statistically significant at p = 0.05; (c),(f) probability density functions illustrating the distribution of trends slopes for all HUs.

Citation: Journal of Hydrometeorology 19, 5; 10.1175/JHM-D-17-0227.1

There is a mix of long-term positive and negative trends in Reff for the 1951–2014 period (Figs. 3d,f; 59 HUs with positive trends in Reff and 116 HUs with negative trends in Reff); however, positive trends in Reff at only two HUs are statistically significant (at p = 0.05), and negative trends at only 12 HUs are statistically significant (at p = 0.05; Fig. 3e). Thus, there have been few statistically significant long-term trends in Reff for the 175 HUs across the western United States. A comparison of the monotonic trends in Sfrac with the monotonic trends in Reff for all 175 HUs indicates a statistically significant, yet small, correlation (Pearson r = 0.26, p < 0.01).

To examine the monotonic trends in Sfrac and Reff in greater detail, and to determine when the trends began to emerge in the time series, we computed trends in Sfrac and Reff at each site for periods beginning in 1951 but ending in 1980–2014. Thus, trends were computed for progressively longer periods of time. For each time period, the number of HUs with statistically significant (at p = 0.05) trends was calculated.

Few HUs indicate statistically significant positive trends in Sfrac for any of the periods examined (Fig. 4). However, the number of HUs with statistically significant negative trends in Sfrac increased dramatically for periods ending with years after about the year 2000. For periods ending in 2015 most HUs indicate statistically significant negative trends in Sfrac (Fig. 4). After about the year 2000, mean winter T (Twin) for the 175 HUs became consistently warmer than long-term Twin for the western United States (Fig. 5a).

Fig. 4.
Fig. 4.

Number of HUs with significant linear trends (at a 95% confidence level) in Sfrac and Reff for periods beginning in 1951 and ending in 1980–2014. Trends were computed using Kendall’s tau.

Citation: Journal of Hydrometeorology 19, 5; 10.1175/JHM-D-17-0227.1

Fig. 5.
Fig. 5.

(a) Time series of Sfrac PC1 and Twin for 175 HUs, (b) time series of Reff PC1 and Pwy for 175 HUs, (c) loadings of Sfrac PC1 on Sfrac for 175 HUs, (d) loadings of Reff PC1 on Reff for 175 HUs, (e) correlations of Sfrac PC1 with mean November–March 500-hPa heights, and (f) correlations of Reff PC1 with mean water year 500-hPa heights. For the maps illustrating correlations with 500-hPa heights, the solid isolines indicate positive correlations, and the dashed lines indicate negative correlations. The contour interval is 0.1, and the first solid isoline is the zero correlation isoline.

Citation: Journal of Hydrometeorology 19, 5; 10.1175/JHM-D-17-0227.1

The number of HUs with statistically significant positive or negative trends in Reff is relatively low for all periods examined (Fig. 4). This lack of significant trends in Reff is inconsistent with a recent analysis of changes in Reff for the Lee’s Ferry stream gauge, which is located at the outlet of the UCRB (McCabe et al. 2017). McCabe et al. (2017) reported a statistically significant decrease in Reff for this site since the late 1980s, whereas results from this analysis indicate only one HU within or near the UCRB with a statistically significant negative trend in Reff (Fig. 3d). Differences in these results can be explained, in part, by differences in the spatial representation of the data used to compute the trends in Reff. In this study, trends in Reff are computed for individual HUs, whereas the trend in Reff for the UCRB reported by McCabe et al. (2017) is for an aggregate of 62 HUs in the UCRB. Aggregation of data for several HUs can reduce overall variability and increase the likelihood of detecting a trend (Helsel and Frans 2006; Clow 2010). The 175 HUs used in this analysis only include 21 of the HUs that are among the 62 HUs for the UCRB used by McCabe et al. (2017), and these 21 HUs are located at high elevations (over 3800 m) where T may not have warmed enough to cause substantial changes in Reff.

Overall, the overwhelming number of HUs that do not indicate significant trends in Reff (as estimated by the water balance model) strongly suggests that Reff has changed little for HUs in the western United States with snow accumulations during 1951–2014.

To examine the primary modes of variability of Sfrac and Reff across the western United States, we performed an S-mode principal component analysis (PCA) of Sfrac and Reff for all 175 HUs. Results of the PCA for Sfrac indicated that the first principal component (PC) explained 61% of the variance in Sfrac across all 175 HUs. All other PCs explained less than 10% of the variance in Sfrac. For the Reff data, the first PC explained 39% of the variance in Reff for the 175 HUs. The second PC explained 14% of the variance in Reff, and all other PCs explained less than 7% of the variance in Reff. Because the first PCs resulting from the PCAs of Sfrac and Reff explain so much more variance than other PCs, we examined the variability in these PCs in more detail.

Figure 5a illustrates the time series of PC1 for the Sfrac data (Sfrac PC1), and Fig. 5c shows the loadings of Sfrac PC1 on the Sfrac data for each HU. Sfrac PC1 indicates interannual variability as well as a long term negative trend (Kendall’s tau = −0.313, p < 0.001). The loadings for Sfrac PC1 are positive for all the 175 HUs (Fig. 5c).

Sfrac PC1 is highly negatively correlated with Twin (Fig. 5a), which indicates that interannual variability in Sfrac is strongly related to variability in Twin [the Pearson correlation between Sfrac PC1 and Twin is −0.85 (p < 0.01)]. Additionally, the median Pearson correlation between Sfrac and Twin at each of the 175 HUs is −0.77 (p < 0.01), with a 25th percentile of −0.82 (p < 0.01) and a 75th percentile of −0.69 (p < 0.01). In contrast, the median correlation between Sfrac and mean winter P (Pwin) at each of the 175 HUs is 0.19 (nonsignificant), with a 25th percentile of 0.12 (nonsignificant) and a 75th percentile of 0.26 (p < 0.05). These correlations indicate that Sfrac at only about 25% of the HUs is significantly correlated with Pwin, whereas Sfrac at all the 175 HUs is highly significantly negatively correlated (p < 0.01) with Twin.

The strong negative correlation between Sfrac PC1 and Twin, and the positive loadings of Sfrac PC1 for all 175 HUs, indicates that Sfrac decreases as Twin increases. Thus, there is a strong negative relation between Sfrac and Twin, and Twin appears to be the most significant climatic driver of temporal variability in Sfrac.

An examination of the Sfrac PC1 score time series (and the time series of Twin × −1) indicates a substantial decrease after about 2000 (Fig. 5a). This period coincides with the period during which relatively large numbers of HUs indicated statistically significant negative trends in Sfrac appear (i.e., periods with ending years after 2000; Fig. 4).

To characterize atmospheric circulation patterns associated with variability of Sfrac PC1 scores, we also computed correlations between the Sfrac PC1 score time series and mean winter 500-hPa height anomalies (Fig. 5e). The correlations of Sfrac PC1 and winter 500-hPa heights indicate negative correlations across the entire western United States (Fig. 5e). This spatial pattern of correlations indicates that when Sfrac PC1 is positive (negative), atmospheric pressures over the western United States are generally below (above) average. Below-average atmospheric pressures over the western United States indicate a breakdown of the atmospheric ridge that often occurs over the western United States and a weakening of the Aleutian low, which suggests anomalous zonal atmospheric flow. Zonal atmospheric flow brings moisture from the Pacific Ocean into the western United States as well as cooler temperatures that result in above-average Sfrac. In contrast, above-average atmospheric pressures result in atmospheric subsidence and a warming of the atmosphere, thus resulting in above-average temperatures and lower-than-average Sfrac. These results are consistent with the positive loadings on Sfrac PC1 on Sfrac for all 175 HUs (Fig. 5c).

The score time series for the first PC for Reff (Reff PC1) is highly correlated with mean water-year precipitation (Pwy; Fig. 5b). The correlation between Reff PC1 and Pwy is 0.71 (p < 0.01). The loadings of Reff PC1 on Reff are positive for all 175 HUs (Fig. 5d). Additionally, the median Pearson correlation between Pwy and Reff at each of the 175 HUs is 0.62 (p < 0.01), with a 25th percentile of 0.53 (p < 0.01) and a 75th percentile of 0.71 (p < 0.01). These correlations indicate that Reff at all the 175 HUs is significantly positively correlated with Pwy at p < 0.01. In contrast, the median correlation between Reff and mean water-year T (Twy) at each of the 175 HUs is −0.27 (p < 0.05), with a 25th percentile of −0.37 (p < 0.01) and a 75th percentile of −0.13 (nonsignificant). Although there are at least half of the HUs with statistically significant negative correlations between Reff and Twy, the correlations between Reff and Twy are smaller in absolute magnitude than are the correlations between Reff and Pwy. These results suggest that Reff for the 175 HUs is largely driven by variability in Pwy, rather than by Twy.

Correlations between the Reff PC1 score time series and water-year 500-hPa height anomalies indicate negative correlations (i.e., negative atmospheric pressure anomalies) over the northwestern United States and positive correlations (i.e., positive atmospheric pressure anomalies) over the southwestern United States and northern Mexico (Fig. 5f). This juxtaposition of atmospheric pressure anomalies produces an anomalous flow of moist air from the Pacific Ocean into the western United States, thus increasing Pwy and subsequently increasing Reff.

For dry years (negative Pwy anomalies) the pressure pattern is reversed, with positive atmospheric pressure anomalies over the northwestern United States and negative atmospheric pressure anomalies over the southwestern United States and northern Mexico. Such a pattern of atmospheric pressure anomalies results in an anomalous flow of air from the central western United States toward the Pacific Ocean, thus cutting off the supply of moist Pacific Ocean air that can result in precipitation. This pattern is often referred to as a Rex Block (Rex 1950).

Given the strong correlations between Sfrac and Twin, and between Reff and Pwy, we also compared long-term (1951–2014) trends in Sfrac and Twin and long-term trends in Pwy and Reff at each HU (Fig. 6). The correlation between the trends in Twin and trends in Sfrac is −0.85 (Fig. 6a). Additionally, the long-term trends in Twin for almost all 175 HUs are positive and the long-term trends in Sfrac for almost all HUs are negative. Thus, the long-term positive trends in Twin are strongly associated with the long-term negative trends in Sfrac. These results are consistent with results of previous studies that indicated a substantial effect of increases in Twin on declines in S and SWE in the western United States (Dettinger and Cayan 1995; Hamlet et al. 2005; Mote et al. 2005; McCabe and Wolock 2009; Abatzoglou 2011).

Fig. 6.
Fig. 6.

Comparison of (a) trends in Twin with trends in Sfrac, and (b) trends in Pwy and Reff for 175 HUs across the western United States. Trends are expressed as values of Kendall’s tau for the 1951–2014 period.

Citation: Journal of Hydrometeorology 19, 5; 10.1175/JHM-D-17-0227.1

The correlation between long-term trends in Pwy and long-term trends in Reff is 0.70 (Fig. 6b). There are both positive and negative trends in Pwy and Reff, but the high positive correlation between long-term trends in Pwy and Reff indicates that Pwy has likely been the primary climatic driver of trends in Reff.

b. Changes in mean monthly water balance components

To better understand the large number of statistically significant (p < 0.05) trends in Sfrac and the lack of significant trends in Reff, we examined changes in mean monthly water balance components [i.e., P, actual evapotranspiration (AET), S, liquid P (RAIN), MELT, and R] computed for 1951–65 and 2000–14. The period 2000–14 was selected for this analysis because it represents a time frame when a relatively large number of HUs indicate statistically significant changes (p < 0.05) in Sfrac. The period 1951–65 was chosen because it spans the same number of years as the 2000–14 period but for an earlier period of time. Figure 7 illustrates changes in mean monthly water balance values for 1983–2014 minus mean monthly values for 1951–82.

Fig. 7.
Fig. 7.

Percentiles [i.e., 25th (p25), 50th (p50), and 75th (p75)] of differences in mean monthly P, AET, S, RAIN, MELT, and R (mm) for 175 HUs in the western United States for the period 2001–14 minus the period 1951–65.

Citation: Journal of Hydrometeorology 19, 5; 10.1175/JHM-D-17-0227.1

Changes in AET are small and likely have little effect on changes in R or Reff (Fig. 7b). Changes in P were negative for December–February (Fig. 7a), and these decreases in P account for some of the decreases in S during the winter months (Fig. 7c). While S decreased during the fall and winter months (Fig. 7c), RAIN increased during the winter and spring months (Fig. 7d), consistent with a decline in Sfrac. Additionally, even though S decreased during the winter months, MELT increased during January–March and decreased substantially during May–August (Fig. 7e), indicating a shift to earlier snowmelt timing. Thus, during the winter months there has been a decrease in Sfrac (and thus an increase in RAIN/P), as well as an increase in MELT. These changes correspond to increases in R during the winter months. Additionally, decreases in MELT during the summer months correspond to a decrease in R during the summer months. Together, these changes in water balance variables indicate a shift of R to earlier in the year, due to a decrease in S and earlier MELT related to increases in T (Stewart et al. 2004; McCabe and Clark 2005; Regonda et al. 2005). Although, there has been a shift to earlier snowmelt R timing across the western United States, there has not been a significant decrease in total water-year R for the HUs examined in this study. The change in mean water-year R from 1951–82 to 1983–2014 for all 175 HUs is only −5 mm, which is only about −1% of mean water year R for the 175 HUs. The decrease in R is somewhat consistent with the results reported by Berghuijs et al. (2014), who indicated that a shift from S to rain leads to a decrease in R. Although our results indicate a small decrease in R, concomitant with a decrease in Sfrac, the decrease in R is minor and not physically meaningful for most of the HUs examined.

4. Conclusions

A water balance model was used to estimate time series of Sfrac and Reff for 175 HUs across the western United States for the period 1951–2014. Results indicate that there have been statistically significant long-term declines in Sfrac across the western United States. The number of HUs indicating statistically significant negative trends in Sfrac increases dramatically when time series of Sfrac (beginning in 1951) have end points after 2000 (Fig. 4). The period after about 2000 also coincides with when Twin became consistently above the long-term Twin mean (Fig. 5a). It appears that after about 2000, Twin became warm enough for S and Sfrac at most of the 175 HUs to decline.

Although there have been decreases in Sfrac, there has been a mix of positive and negative long-term trends in Reff that are mostly nonstatistically significant (long-term trends in Reff are statistically significant for only 14 of the 175 HUs). The interannual variability in Reff is highly correlated with Pwy. However, decreases in S, increases in RAIN, and increases in MELT during winter months suggest a shift to earlier R, resulting in increases in R during the winter months for much of the western United States, but not an overall decrease in water-year R for the 175 HUs examined.

Because Sfrac appears to be highly sensitive to increases in Twin, Sfrac is likely a useful indicator to monitor the effects of future warming in snowmelt runoff basins. Additionally, decreased Sfrac may have some implications for an increased risk of winter flooding for some areas (Knowles et al. 2006) as more winter precipitation in the western United States is occurring as rain rather than as snow. Another effect of decreases in Sfrac and a shift to earlier R is decreased R during summer months (Fig. 7f) when the climatic demand for water is highest (Stewart et al. 2004; McCabe and Clark 2005). Furthermore, decreased MELT and earlier snowmelt R can result in increased stream temperatures, especially during the warm season, and affect aquatic ecosystems (Ficklin et al. 2013).

Research by Lehner et al. (2017) indicates Reff for the Rio Grande River (and other locations in the southwestern United States) has decreased, especially since the 1980s. Lehner et al. (2017) also show that although T has a secondary influence on Reff variability and trends, when compared with P, the T sensitivity of Reff in the Rio Grande River basin has strengthened in recent decades. This result suggests that as warming continues T may become a more significant control of both Sfrac and Reff for sites across the western United States. Additional research is needed to better understand the effects of changing T on R and Reff for sites across the western United States with varying elevations, climates, and physiography. Supplementary research also is needed to understand how model parameterizations and model structure can influence (i.e., constrain or enhance) simulated runoff sensitivities and trends to climate drivers.

The results from this study characterize changes in Sfrac and Reff for HUs with snow accumulations. Changes and trends in Sfrac and Reff for other HUs across the western United States, such as those without snow accumulations, may be different from those reported here.

Acknowledgments

The authors thank Andy Bock (U.S. Geological Survey, Denver, Colorado), Paul Barlow (U.S. Geological Survey, Massachusetts), and three anonymous reviewers for comments that helped improve this manuscript. This work was completed as part of the research supported by the Water Mission Area of the U.S. Geological Survey.

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