Predictive Contributions of Snowmelt and Rainfall to Streamflow Variations in the Western United States

College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China China Meteorological Administration Training Center (CMA), Beijing 100081, China College of Applied Meteorology, Nanjing University of Information Science and Technology, Nanjing 210044, China School of Atmospheric Physics and Atmospheric Environment, Nanjing University of Information Science and Technology, Nanjing 210044, China


Introduction
e Western United States (WUS) is a semiarid region that covers more than half the land area of the U.S. [1]. is area, which receives little precipitation during summer, relies considerably on the wintertime precipitation phase and snowpack accumulation to sustain a multitude of ecosystem goods and services [2].us, the regional ecology and economy are both vulnerable to water resource anomalies caused by seasonal hydroclimatic variations [3].Recent hydrological disasters in the WUS have been closely related to climate change [4][5][6].
e occurrence probabilities of hydrological anomalies and of hydrological extremes have both increased [7]; these conditions have affected the regional agricultural production, the occurrence of forest fires, and the national socioeconomic development [8,9].erefore, it is of great importance to conduct accurate and effective hydrological forecasting for the WUS within the context of climate change.
Streamflow is a hydroclimatic variable that directly influences drought-and flood-related disasters.It is affected both by natural factors, such as the precipitation system, soil state, and land surface, and by human factors, including land use changes and water use efficiency.Because of the considerable reliance of the WUS on snow as a water resource, snow accumulation represents a factor of first-order importance regarding regional water supply [10].Snowmelt contributes approximately 50%-80% of the total streamflow and is highly seasonal in nature, that is, the majority of streamflow occurs because of snowmelt during the late spring-summer (April-July) [11].In western coastal areas, streamflow is derived mainly from rainfall.erefore, streamflow variation in the WUS has strong correlation with changes in snowpack accumulation and rainfall and has obvious seasonal variation [11][12][13][14].
A considerable amount of research has been undertaken regarding the relationships between runoff and both precipitation systems and snowmelt.In addition, several studies have documented the correlation between oceanic climatic phenomena and streamflow.For example, Hunter et al. [15] reported a strong relationship of streamflow with ENSO and relatively weak correlations with the PDO, AMO, and NAO anomalies.Except for those that researched atmosphericoceanic circulations, most of the studies on the seasonal variation of streamflow focused on the relationship between runoff and snowmelt during the melting season.Snowmelt is related closely to the snowpack amount and temperature in winter and spring.
e spring temperature can affect streamflow by influencing both the time of the onset of snowmelt and the snowmelt slope [16].Recently, spring temperatures have demonstrated a warming tendency coincident with an earlier onset of snowmelt.Many researchers have started to focus on the relationship between early snowmelt and spring and summer runoff [17][18][19][20].Some studies have suggested that warmer spring temperatures would lead to earlier onset of snowmelt and greater associated runoff, thereby resulting in increased spring streamflow and decreased summer streamflow [19,21,22].Jeton et al. [23] derived the same conclusion, believing that early snowmelt occurred when vegetation was less active.
ey claimed that such inactivity disrupts the synchronicity between the water availability and demand, resulting in greater springtime streamflow.Conversely, Bosson et al. [24] thought that earlier snowmelt might contribute more to evapotranspiration (ET) than to streamflow because of the increased vapor pressure deficit due to atmospheric warming, which would result in a lower-than-usual springtime streamflow.Recent findings by Trujillo and Molotch [25] indicated that reduced levels of solar radiation available for driving snowmelt earlier in the year could produce slower rates of snowmelt and decrease the generation of streamflow during the spring.
Based on the relationship between snowmelt and streamflow, snowmelt could be used as a significant predictor of streamflow.However, previous studies simply revealed the possibility of this phenomenon and consequently outlined its potential mechanisms without achieving a uniform conclusion.In addition, earlier work focused primarily on changes in the timing of snowmelt without considering the effects of other snow metrics or of the memory of snowmelt on streamflow.Furthermore, the research cited in this study was based either on the hydrologic situation of the entire WUS or on that of a specific watershed.erefore, this study separated the WUS into six watersheds and selected eight snow metrics to both investigate the relationships among the snow metrics and streamflow and to determine the lead correlation between the snowpack and streamflow in each watershed.e findings of this research demonstrate the potential for the use of snow variations to predict streamflow changes in advance.
In addition to snowpack, rainfall represents another important predictor of streamflow in the WUS.However, because the contributions of rain-derived runoff (also called rainfall contribution, referred to as f rain hereafter) and of snow-derived runoff to the total runoff (also called snowpack contribution, referred to as f snow hereafter) are different in each area; both f rain and f snow have different contributions to streamflow.Previous studies focused primarily on f snow [10].In addition, in most of those studies, f snow was calculated based on metrics such as the total snowfall as a fraction of total precipitation, the total snowfall as a fraction of total runoff, or melt season runoff as a fraction of total annual runoff [26].Partly because of differences among the methods by which f snow was approximated, large variations in the estimates have been reported.For example, most research has reported that snow contribution ratio was 75% [27][28][29][30][31], whereas other studies have produced values in the ranges of 40%-60%, 50%-80%, or 60%-90% [17,[32][33][34].Compared with such ratio metrics, the following methods are considered more reasonable.Li et al. [10] quantified f snow by tracking the fate of snowmelt in modeled hydrologic fluxes and obtained gridded model results.rough calculations of the long-term probability of snowmelt pulse occurrence (i.e., if the snowmelt pulse occurred during the period between the 150th day and the 250th day of the water year), Fritze et al. [35] divided streamflow sites into four categories: clearly rain dominated, mostly rain dominated, mostly snowmelt dominated, and clearly snowmelt dominated.is study used a new method to calculate f rain and f snow at each streamflow site both during an entire year and during the wet season to provide a more accurate basis for a seasonal prediction of streamflow.
To achieve qualitative and quantitative seasonal predictions of streamflow, this study considered three issues based on long-term observational data.First, among the eight snow metrics used widely throughout the literature, those that have significant correlations with the peak streamflow were selected.Second, the lead correlation between the SWE and streamflow at each stream site was calculated.
ird, the relative contributions of rain and snowmelt to streamflow were quantified.ese findings will provide a basis for seasonal streamflow predictions and benefit the evaluation of hydroclimatic models.
e remainder of this paper is organized as follows.Descriptions of the study area and of the observational data are provided in Section 2. e methods adopted for the analysis of the data are presented in Section 3. Section 4 presents the results with respect to the three issues listed above.Finally, the conclusions are summarized in Section 5.

Research Area and Data
is study focused on six hydrologic regions of the WUS which correspond to USGS Regions 13-18 (https://water.usgs.gov/GIS/regions.html):Rio Grande (RG), Upper e distribution of the watersheds and details of their elevations and major rivers are illustrated in Figure 1.

Snow Water Equivalent (SWE).
e primary daily SWE record was obtained from the Natural Resource Conservation Service, which has operated the SNOTEL automated network of snowpack monitoring sites in the WUS since 1978 (http://www.wcc.nrcs.usda.gov/snow/).At each SNOTEL site, the weight of snow on a liquid-lled pillow is measured hourly by a pressure sensor and converted to SWE [16,36,37].e high temporal resolution and long time series of the SNOTEL record (since the late 1970s) make it uniquely suited to the primary goals of this study.Data were selected over a 35-year period (1 October 1981 through 30 September 2016) from SNOTEL sites with continuous daily records during the snow accumulation period (1 September through 30 April the following year).Overall, data from 222 SNOTEL sites located within the 6 watersheds were considered suitable.e numbers of selected SNOTEL sites in the six watersheds are listed in Table 1, and the locations of the stations are marked in Figure 1. e selected stations covered all the mountains of each watershed; thus, the snow metrics could be calculated reliably without undue interference from sampling errors and/or seasonal e ects.

Stream ow.
e stream ow data are available on the Internet from the National Water Information System of the USGS (http://waterdata.usgs.gov/nwis/).e stations were categorized according to the hydrologic drainage basins in the US known as hydrologic unit codes developed by the USGS [12].Because human interventions such as reservoirs and other diversions could potentially alter the routes of river systems, the USGS maintains unimpaired stream ow stations within the Hydro-Climatic Data Network 2009 (HCDN-2009) [38].In the site selection process of this study, these sites were chosen rst.However, the number of HCDN-2009 stations is limited and their spatial distribution is uneven.erefore, other USGS sites (added stations) were incorporated based on the following quality assurance/quality control procedure.First, manual screening was performed to remove those with incomplete daily data.Second, the watershed mean pentad anomaly stream ow of all the HCDN-2009 stations in each watershed was calculated.
en, sites that were obviously inconsistent with the HCDN-2009 stations, based on a comparison of the correlation coe cient of the pentad anomaly stream ow between each added station and the watershed mean, were discarded.is step was performed to remove any station that had been obviously in uenced by anthropogenic activities.e data period was the same as for the SWE sites.e numbers of selected stations in each of the six watersheds is listed in Table 1, and the locations of the stations are marked in Figure 1. e selected stream ow stations covered nearly all the major rivers in each watershed, providing strong support for the subsequent data analysis.the PRISM dataset named AN81d [39,40]. is daily dataset, covering the conterminous US, began on 1 January 1981, and it continues to the present day, and the spatial resolution was 4 km.To derive best estimates, this dataset uses all the station networks ingested by the PRISM Climate Group (13 station networks for temperature and 20 station networks for precipitation).Climatologically aided interpolation (detailed in Descriptions of PRISM Spatial Climate Datasets, 2015 [41]), using 1981-2010 monthly climatologies as predictor grids, was adopted to enhance the accuracy of the climate analysis.Furthermore, the precipitation dataset was created by computing an elevation-precipitation relation for all stations within a subregion, with individual stations weighted di erently, and by applying that relation to a topographic basemap.In this study, the data period was the same as for SWE and stream ow. e precipitation data with 4 km high spatial resolution and correction for elevation were considered suitable for the requirements of precipitation system analysis over high mountain areas and for determining effective rainfall areas.e 2-m temperature data were used to classify precipitation as either rain or snow for analysis of the rainfall contribution.

Snow Metrics.
is study adopted eight snow metrics following the work of Trujillo and Molotch [25].ese metrics comprise the initial snow accumulation day and snow-free days, the peak of snow accumulation and date of the peak, the length of the snow accumulation season and the length of the snowmelt season, and the snow accumulation slope and snowmelt slope.is research focused on the relationship between long-term snow accumulation and stream ow.erefore, the calculations for all of the metrics were based on the longest snow cover period (>20 d) in each water year, and short-term snow periods were neglected.e eight metrics were derived from the daily SWE data at each station.e daily SWE curve (Figure 2) for accumulation and melt seasons shows the basic metrics that can be used to characterize the snowpack dynamics at a particular station.Metrics ( 1) and ( 2) mark the days of initial snow accumulation and snow disappearance, respectively.Metrics (3) and ( 4) mark the peak SWE date and peak SWE value, respectively.Metrics ( 5) and ( 6) indicate the lengths of the accumulation and melt seasons, respectively.e snow accumulation slope and snow snowmelt slope are represented by the peak snow accumulation divided by the length of the snow accumulation season and by the length of the snowmelt season, respectively.
In the correlation analysis with peak stream ow, the snow state in each watershed is considered to have consistent characteristics; thus, the snow metrics are the mean values of all the SWE stations in each individual watershed.

Lead Correlation of Snow Accumulation to Stream ow.
Because stream ow has a long-term snowpack memory, that memory could be calculated as the predictive time of the in uence of snowpack on stream ow.
e lead time (memory) was derived from the lead correlation between the long-term SWE pentad anomaly and the stream ow pentad anomaly.Here, because the study area was divided into six watersheds, it was assumed that the snow characteristics of each individual basin were uniform.e lead correlation was calculated between the basin mean long-term (i.e., 35 years) SWE pentad anomaly and the long-term stream ow pentad anomaly at each stream site in the corresponding basin.As the response time of stream ow to snowpack is di erent at each site, a group of correlation coe cients was calculated with lead times ranging from 0 to 73 pentads for every site.en, the maximum correlation coe cient corresponding to the lead time was considered the predicting period for that site.

Relative Contributions of Rainfall and Snowpack.
In this study, rainfall and snowpack were chosen as the principal stream ow contributors.For snowpack, snow accumulation was adopted rather than snowfall.is is because the inuence of snowpack on stream ow is realized when the snow accumulated in mountainous areas is released during the spring, discounting the negligible amounts of snow that fall directly into rivers.Because it is di cult to obtain observed rainfall data, PRISM precipitation data were classi ed as snowfall or rainfall based on PRISM 2-m-resolution temperature data.To verify the feasibility of this method, the classi ed snowfall data were evaluated against SNOTEL in situ SWE data.Subsequent to data preparation, the contributions of both rainfall and snowpack to stream ow were calculated according to the following procedure.
First, it was necessary to determine the rainfall area with a direct impact on each stream ow station.As rainfall has a direct in uence on stream ow, it was assumed that a change in the stream ow anomaly would have the same pattern as a change in the contributed rainfall anomaly.e rainfall area that a ected each stream ow site was chosen based on the criterion that the pentad rainfall anomaly had a signi cant correlation with the runo anomaly of that site during the wet season.e wet season was chosen instead of the entire year to avoid seasonal variations.e wet season, which di ers among each basin, was selected based upon  2) mark the days of the initial snow accumulation and snow disappearance, respectively.Metrics (3) and ( 4) mark the peak SWE date and peak SWE value, respectively.Metrics ( 5) and ( 6) indicate the length of the accumulation and melt seasons, respectively.4 Advances in Meteorology the long-term averaged seasonal variation in the rainfall (Figure 3, RG: Jul-Sep; UC: Jul-Sep; LC: Jul-Sep; GB: Mar-May; PNW: Oct-Dec; CA: Dec-Mar).e regional mean rainfall anomaly of the selected area was the e ective rainfall anomaly of each station.
Second, the long-term pented rainfall and SWE anomalies at each stream ow site were normalized, and then use (1) to t the two normalized variables into a new variable, which is called comb a .
where SWE a is the normalized basin mean long-term pentad SWE anomaly, Rain a is the normalized long-term pentad rainfall anomaly, lead time is the highest probability of all the lead times in each basin, and a is the relative contribution ratio of rainfall from 0 through 100.e snow accumulation contribution ratio is represented as 100 − a because only these two contributors were considered in this study.ird, using the group of the combined array to perform the correlation with stream ow at each site in each basin, the peak correlation among the group of correlations was selected.e peak correlation corresponding to a and 100 − a represents the contribution ratio to stream ow at each station.

Rain, Snow, and Stream ow in the WUS.
Because stream ow variation depends largely on the precipitation system, the variation and distribution of precipitation should rst be established.Two principal precipitation mechanisms a ect the WUS.
e rst is associated with eastward-moving winter Paci c storms, which bring heavy precipitation to coastal areas and the western highlands, thereby re ecting the considerable orographic e ects generated by upslope motions [42][43][44].
e second precipitation system is associated with subtropical summer monsoon rainfall.e temporal variations and distributions of seasonal rainfall and annual snow amounts over the WUS are illustrated in Figures 3 and 4. It is evident that considerable rainfall occurs during winter, particularly in the Cascade, Klamath, and Sierra Nevada mountains and over coastal areas.Compared with winter, both the amount and the area of rainfall in spring are generally diminished, but the locations of the rainfall centers remain similar.However, in the Rocky Mountains, the rainfall amount increases in spring because snowfall transfers to rainfall with rising temperatures.Summer precipitation is located primarily within the RG and LC watersheds (i.e., summer monsoon rainfall), whereas precipitation is reduced considerably in the PNW because Paci c storm systems are weaker in this season.In the WUS, snowfall generally commences at the end of autumn and it ends in early spring (Figure 4).e area of snow cover is generally concentrated within inland areas of the Cascade, Sierra Nevada, and Rocky Mountains, and the amount of snowfall increases from south to north.
Because of its low latitude, the RG basin receives the least amount of snowfall; however, its large runo in spring suggests that snowmelt in the southern Rocky Mountains is the main source of its stream ow. e summer monsoon constitutes the primary precipitation system a ecting the RG basin throughout the entire year, and it provides a major source of summer runo (Figures 4(a) and 5(a)).Most of the UC basin lies within the southern Rocky Mountains.e considerable accumulation of wintertime snow therein indicates that subsequent snowmelt provides abundant water for spring runo ; thus, the period of high ow, during which time the ow is substantially higher than during the other months, is concentrated during May-July (Figures 4(b) and 5(b)).Stream ow in the LC basin is similar to that in the RG basin.e spring stream ow in both basins is fed primarily by snowmelt from the southern Rocky Mountains.However, because the Rocky Mountains are located further to the south than in the RG basin, the period of snowfall is short and the amount of accumulation is low; therefore, the spring stream ow contributed by snowmelt is less prominent compared with the other seasons.Furthermore, the contributions to runo from both winter and summer rainfall produce a curve of seasonal runo variations with reasonably gentle features (Figures 4(c) and 5(c)).
e GB watershed exhibits a midlatitude desert climate; the amount of rainfall in this basin is the least among all of the studied watersheds.e GB is bordered by the Sierra Nevada range to the west and the Wasatch and Uinta Mountains to the east.
erefore, its stream ow is supplied primarily by snowmelt from these two mountain ranges (Figures 4(d Although the basins of the WUS exhibit a certain degree of consistency in terms of their hydroclimatic situations, the seasonal variations in both precipitation and stream ow reveal that each basin does have its own characteristics.erefore, to enhance an understanding of the hydroclimatic situation of the WUS, the relationships between the precipitation systems and stream ow must be explored for each individual basin.

Correlation between Snow Metrics and Stream ow Peak.
Because stream ow has a short response time to rainfall, only snowfall was considered in this analysis.To obtain meaningful seasonal predictors of runo , the relationships to runo of eight snow metrics (detailed in Section 3) were explored.Based on the work of Trujillo and Molotch [25], the selected metrics have di erent nonlinear relationships in the di erent regions of WUS (i.e., maritime climate, intermountain climate, and continental climate); thus, the relationships between the snow metrics and the runo peak can be discussed independently.e focus of this study was on the relationships between the snow metrics and the runo in each of the six individual watersheds.erefore, the snow metrics were taken as the average values from all of the SWE sites in each watershed.e 95th percentile of the annual stream ow, which is strongly related to the wet season stream ow amount and ood disasters, was used to perform the correlation for the stream ow metric.
Figure 6 shows that each snow metric has di erent characteristics in each region.Except for the initial snow accumulation day, which primarily has a negative correlation with the peak stream ow, all of the other metrics have positive correlations.e negative correlations displayed in Figure 6(a) indicate that an earlier onset of snow accumulation corresponds to a higher peak stream ow. is is intuitively correct because an early occurrence of snow would generally correspond to deeper snowpack, which would cause greater stream ow during the snowmelt season.However, this correlation is not signi cant for all of the six basins, that is, this metric is relevant only in the northern RG, UC, and GB watersheds.Among the remaining metrics,     Advances in Meteorology the peak of snow accumulation, the snow-free days, and the snowmelt slope all demonstrate strong positive correlations with the peak runo (i.e., considerable snow accumulation, late snow disappearance, and rapid snowmelt all correspond to a high peak stream ow), followed by the date of peak accumulation, the length of snow accumulation, and the snow accumulation slope.e distribution of these correlations (Figure 6) shows that most of the metrics are strongest in the UC and GB watersheds. is is because water storage is dominated by snowmelt in these areas; thus, the snow metrics are more informative.In addition, both the RG and the LC basins are located in the lower latitudes of the WUS; therefore, they receive less snow than the other basins (Figures 3 and 4), and their downstream runo is a ected principally by rainfall.ose runo sites that have strong correlations with the snow metrics are concentrated in the upstream areas near the mountains.It is noteworthy that in the coastal areas of the PNW and CA basins, although runo is dependent primarily on winter rainfall, these results do show certain correlations with the snow metrics.
is is because both rainfall and snowfall in these two basins are caused by the same weather systems; thus, they appear almost synchronized, which means that these snow metrics appear to have certain correlations that represent the regional rainfall characteristics.In conclusion, the peak of snowfall accumulation, the snow-free days, and the snow snowmelt slope could be used as the principal metrics for predicting the peak value of the runo throughout the WUS, especially in the inland mountain areas.Among the three most signi cant metrics, the peak of snowfall accumulation demonstrated the strongest correlation with the peak stream ow. is result shows that snow accumulation could be used to quantify the forecast period of runo variations.

Lead Correlation of Snow Accumulation and Stream ow.
is analysis explores the forecasting e ect of snow accumulation on runo based on the long-term pentad anomaly of SWE and runo (detailed in Section 3). Figure 7 shows that almost all runo sites passed the 95% signi cance test and most have strong correlation.e lead correlation between SWE and stream ow was examined from 0 through 14 pentads.Overall, in the inland mountains, the lead time is more than 4 pentads, while in coastal areas, the lead time is 0-1 pentads.
Among the six watersheds, the UC and GB basin show the longest snow memory in terms of the runo , that is, generally 4-10 pentads.Snowfall in the RG basin is concentrated largely over the southern Rocky Mountains, which is where the source of the Rio Grande River (the westernmost of the two main rivers in the RG basin) is located.
erefore, the runo into the river is derived primarily from snowmelt, and the river shows a lead correlation of 5-7 pentads.In contrast, the Pecos River, which is located on the eastern side of the RG basin, originates from the southern edge of the Rocky Mountains.us, summer rain has much greater impact than snowmelt on the runo of this river, and no strong correlation with SWE is observed.In the LC basin, the response time of snow to runo is short, and most runo sites do not have a strong correlation with snowmelt.Because the snow storage in the LC basin is small, the snowmelt period is short compared with those of other watersheds, and most of the water resources in this basin are derived from summer monsoon rainfall.e occurrences of rainfall and snowfall during the winter are highly consistent, indicating that they are both caused by the same weather systems, that is, mountainous areas receive snow while areas at lower elevations receive rain. e response of the runo to rainfall is very short, that is why the lead correlation in the basin is just 0-1 pentads showed in Figure 7. e coastal area of the PNW shows a short lead time and a low correlation coe cient. is is because eastward-moving Paci c storm systems during the winter generate considerable rainfall in front of the mountainous areas and abundant snowfall at high elevations, that is, the rainfall and snowfall in this basin are generated by the same weather systems, as discussed for the LC basin.e amount of precipitation over the eastern area of the PNW is much smaller than that over the coastal areas.Runo in the eastern PNW is caused predominantly by snowmelt; thus, Figure 7 shows that this region has a signi cantly longer lead time correlation than the western part.In the CA basin, except for the eastern Sierra Nevada range, where snow contributes considerably to runo and causes a long lead correlation, most of the regional runo is a ected by rainfall with characteristics similar to the rainfall in the western PNW. is results in a lead correlation of 0-1 pentads with the SWE; however, the short lead correlation simply re ects the relationship between rainfall and runo .
In summary, these ndings provide a reasonably reliable basis for stream ow predictions over the WUS.It is also established that the lead times calculated using the pentad mean data (not show here) are longer than those obtained using the pentad anomaly data. is is because the lead time of the former one represents the period between the snow peak and the runo peak, whereas the pentad anomaly re ects the relationship between changes in snow accumulation during the snowmelt period and the runo anomaly.us, the lead time of the latter is shorter than the former.Furthermore, the above analysis highlights some problems.In some areas where rainfall dominates over runo , the lead correlation re ects the relationship of stream ow with rainfall rather than with snow.erefore, the relative contributions from both rainfall and snow accumulation at each runo site must be combined to perform runo anomaly predictions.

Relative Contributions of Rainfall and Snowmelt.
To obtain predictions with greater accuracy at each stream ow site, the relative contributions from both rainfall and snowpack to each stream ow station were calculated.e 10 Advances in Meteorology rainfall and snowfall areas and their ratio were not used to directly distinguish between f rain and f snow for two reasons.First, the impact of the snowmelt area is greater than that of the snow cover area, that is, a site located in a rainfall area might receive a greater contribution from snowmelt than from rainfall.Second, the response of runo to rainfall is short, while snowmelt has a longer runo memory with a contribution that is mainly in the spring.erefore, for a particular runo site, if the rainfall season and snowmelt seasons occur at di erent times, the site will receive di erent water resources during di erent seasons.Conversely, if the wet and snowmelt seasons occur at the same time, the site will receive contributions from both resources.erefore, this study adopted a new method (detailed in Section 3) to calculate the annual f rain and f snow values and to determine the relative contribution rates for the entire year and the high-ow season (i.e., the wet season).e geographic distribution of the annual relative contributions of rainfall and snowmelt presented in Figure 8 (a) shows that values of f snow > 50% are distributed primarily in the UC, GB, eastern PNW, and northern RG basins.In these areas, the upper streams in the mountains receive greater contributions from snow accumulation, that is, up to 70% or more.Based on the terrain elevation and distribution of precipitation systems (Figures 1 and 3), it is evident that these areas are high mountainous regions that receive large amounts of snowfall.Snowpack provides abundant water storage in these large areas.In the coastal areas of the PNW and CA basins, the value of f rain is >50%.Despite the large amounts of snowfall received by the Cascade Mountains and the Sierra Nevada, the contributions from rainfall still dominate these areas.For the LC basin, monsoon rainfall provides a greater contribution to streamflow than snowmelt; thus, the streamflow situation in the LC basin is dominated by rainfall.
Runoff variations are an important indicator for local hydrological disasters and agricultural irrigation.Of the entire year, the high-flow season is the most crucial period for early hydrological warnings.us, based on Figure 5, three consecutive months with high flow were selected as the wet season for each of the six basins (RG: Apr-Jun, UC: May-Jul, LC: Mar-May, GB: Apr-Jun, PNW: Apr-Jun, and CA: Feb-Apr).Figure 8(b) shows that the distribution of relative contributions in the high-flow season is similar to the annual distribution (Figure 8(a)), that is, rainfall dominates the coastal areas and snowmelt dominates the inner mountain areas.However, some differences between the annual and high-flow season f rain are shown in Figure 8(c).For example, f rain is reduced in the area of the Cascade Mountains in the PNW, while it is increased in the southeastern PNW. is is because the amount of rainfall over the Cascade Mountains is diminished during the high-flow season of this basin (Figure 3); thus, snowmelt becomes comparatively more prominent.e southeastern PNW experiences its heaviest rainfall during the high-flow period (Figure 3); thus, the value of f rain is increased to 5%-25%.For the southern UC and northern RG basins, the contribution from rainfall is increased; alternatively, it could be considered a reduction of the snowmelt contribution.is is because the high-flow period also corresponds to the beginning of the wet season; therefore, the contribution rate of rainfall becomes more prominent.In summary, the relative contributions of rainfall and snowmelt to the runoff could support runoff predictions and could help produce seasonal runoff forecasts that would be more accurate in combination with the lead time results from the previous section.

Conclusions
Runoff is affected by many factors, such as the precipitation, soil state, land surface state, and water use.However, snow accumulation and rainfall both constitute important factors with direct impacts on the regional water supply of the WUS.Based on statistical analyses of long-term hydroclimatic data from each watershed, the predictive contributions from both rainfall and snowmelt to streamflow variations were investigated.First, the hydroclimatic characteristics of each basin were summarized in terms of the seasonal rainfall, snow, and runoff variations.Determining the basin-independent features of runoff that affect the rainfall and snow contributions made it possible to establish numerous runoff forecasting factors.Second, eight snow metrics were selected based on variations in the snow accumulation.Among all of the variables, the peak of snow accumulation, snow-free days, and snow snowmelt slope all have strong correlations with the peak runoff.Over the entire WUS, the correlations among the metrics were stronger in inland regions compared with coastal areas.us, these strong significant factors could be used as primary predictors for the runoff amounts during the wet season since the peak streamflow also represents the state of the high-flow season.Meanwhile, it was found that the variations in the snow accumulation anomaly exhibited a leading correlation with the runoff anomaly. is means that the streamflow prediction time based on the snow accumulation could be quantified in advance.ird, the leading relationship between snow and streamflow was analyzed, the results of which showed a lead time ranging from 0 to 14 pentads.Overall, the lead time exceeded 4 pentads in the inland mountain regions, while it was 0-1 pentads in the coastal areas.Because of the considerable impact of snowmelt on the runoff in the UC, GB, and eastern PNW basins, the snow pentad anomaly in these areas had a 4-10 pentad lead period.In comparison, the LC, western PNW, and CA basins had short lead times largely representative of the rainfall effect.is is because their streamflows were affected primarily by rainfall and because the rainfall and snowfall therein generally occurred simultaneously.Finally, based on the pentad anomaly lead time findings, the relative contributions from both snowmelt and rainfall to the runoff at each site in each basin were analyzed.It was found that the UC and GB basins are snow-dominated areas, in which the f snow was greater than f rain .e f snow was the greatest in the northern RG and eastern PNW watersheds, whereas f rain was the greatest in the other parts of these two basins.e greatest contributions in the LC and CA basins were largely from rainfall.It was found that the contribution rate during the wet period was slightly different from the annual rate, that is, the snowmelt contribution increased in the western PWN while the rainfall contributions increased in the southeastern PWN, southern UC, and northern RG basins.In conclusion, quantitative and qualitative analyses regarding runoff predictions for the studied watersheds of the WUS constitute an important reference for hydrological management and will be useful in the evaluation and improvement of hydrological and climate models.

Discussion
is research explored the predictability of runoff in the WUS; however, scope remains for further study.(1) In this study, for the discussion of the relationship at each runoff station in each basin, the snow state in each basin was based on the average at all snow sites.However, for large watersheds, for example, the PNW, the in situ data were distributed in different mountain areas with different snow factor characteristics; thus, the method of averaging would cause some bias.In future work, subbasins will be defined to reduce this deviation.(2) When considering the contribution rates to runoff, data limitations restricted the discussion 12 Advances in Meteorology to just rainfall and snow.In fact, runoff is affected by many other factors such as evaporation, soil state, and groundwater.In future research, these factors will be taken into consideration.However, the findings of this study have value regarding the seasonal prediction of runoff, and they could serve as a basis for future research and model testing.

2. 3 .
Precipitation and 2-m Temperature.Daily precipitation and daily mean 2-m temperature data were obtained from

Figure 1 :
Figure 1: Research area, station distribution, and the location of the study area in global (gray area in western hemisphere).

Figure 2 :
Figure 2: Sketch of the basic snow metrics based on the daily SWE curve.Metrics (1) and (2) mark the days of the initial snow accumulation and snow disappearance, respectively.Metrics (3) and (4) mark the peak SWE date and peak SWE value, respectively.Metrics (5) and (6) indicate the length of the accumulation and melt seasons, respectively.

Figure 6 :
Figure 6: Distributions of the correlation coe cients between the snow metrics and peak stream ow in each watershed (1981-2016).Panels (a)-(h) represent di erent snow metrics: (a) the initial snow accumulation day, (b) snow-free day, (c) peak SWE value, (d) peak SWE day, (e) length of snow accumulation season, (f) length of snow melting season, (g) snow accumulation slope, and (h) snowmelt slope.Circles represent stations that did not pass the 95% signi cance test.

Figure 7 :
Figure 7: Distribution of the peak lead time and correlation coe cient between the snow anomaly and stream ow anomaly (unit: pentad).Hollow triangles represent stations that did not pass the 95% signi cance test.

Figure 8 :
Figure 8: Distributions of the relative contributions of rainfall and snowfall to each stream ow station (unit: %): (a) annual contribution, (b) high-ow season contribution, and (c) di erence between the high-ow season and annual contributions (i.e., high-ow season-annual).Hollow triangles represent stations that did not pass the 95% signi cance test.

Table 1 :
Numbers of SNOTEL and stream ow stations used in this study.