1

The role of rain-on-snow in flooding over the conterminous United States 2

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Dongyue Li1,2, Dennis P. Lettenmaier1, Steven A. Margulis2, Konstantinos Andreadis3 4

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1 Department of Geography, University of California Los Angeles 6

2 Department of Civil and Environmental Engineering, University of California Los Angeles 7

3 Department of Civil and Environmental Engineering, University of Massachusetts Amherst 8

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Corresponding author: Dongyue Li (dongyueli@ucla.edu) 10

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Key Points: 12

1. Rain-on-snow relates to a large portion of historical flood events, but its runoff contribution to 13

the total flood runoff is modest. 14

2. Rain-on-snow frequency exerts a first order control on the role of rain-on-snow in hydrologic 15

extremes. 16

3. Future role of rain-on-snow in floods will increase in high-elevation areas and will decrease in 17

areas with moderate elevation. 18

Abstract 19

Based on a process-level characterization of historical and future rain-on-snow (ROS) events, we 20

quantify the runoff contribution from ROS to extreme floods and the source of runoff in large 21

ROS events within the conterminous U.S. (CONUS). We find that the regions impacted most 22

heavily by ROS include the West Coast, the major mountain ranges of the western interior, the 23

Upper Midwest, the Northeast, and the lower Appalachians. While 70% of extreme (upper 0.1%) 24

runoff events in these regions have some contribution from ROS, the runoff generated during 25

these ROS events accounts for less than 10% of the total extreme flood runoff; the much larger 26

fraction of extreme runoff is derived either directly from intense rainfall or from clear-sky 27

snowmelt. Rainfall is the dominant source of runoff in ROS events along the West Coast and 28

over the west-facing slopes of the Cascades and Sierra Nevada, while snowmelt dominates ROS 29

runoff in the other regions in the CONUS. Historically, the role of ROS in streamflow extremes 30

is most significant in mid-elevation areas, but this “significant influence zone” will shift to 31

higher elevations in a warmer future; ROS will account for more of the extreme runoff in the 32

high elevations of the mountainous West and the Upper Midwest, but less in areas with low and 33

moderate elevations in the West and almost the entire East. The future ROS frequency changes 34

exert a first order control on the future change of the runoff contribution from ROS to extreme 35

floods. 36

1. INTRODUCTION 37

Rain-on-snow (ROS) occurs during periods when liquid precipitation falls on a pre-existing 38

snowpack. ROS is common in seasonally snow covered areas and has significant hydrologic and 39

geomorphologic impacts. Intense rainfall and snowmelt that contribute to runoff during ROS 40

events erode soil [Swanston 1974] and redistribute sediment and organic debris [Fredriksen 1965, 41

Sandersen et al., 1997], leading to landslides in areas of high relief [Harr 1981] and contribute to 42

river channel morphology [Bergman 1987]. ROS is also a major trigger of avalanches in 43

maritime climates when rainfall weakens the bond between snow grains and reduces the 44

structural strength of the snowpack [Singh et al. 1997, Conway et al., 1988, Heywood, 1988; 45

Conway and Raymond, 1993]. ROS initiates melting of snowpacks that would otherwise stay 46

frozen, leading to earlier melt onset and longer exposure of soil to the sun and warmer air, which 47

in turn leads to drier soils in the summer that can have broad environmental and ecological 48

implications [Cohen et al., 2015]. Hydrologically, floods associated with ROS events have a 49

long history of causing costly property damage and loss of life [Musselman et al., 2018]. For 50

example, the farmland, cities, and transportation systems of western Oregon have been impacted 51

by ROS flooding numerous times with recorded accounts as early as the mid-1800s when the 52

region was first settled [Harr 1981]. The December 1964 ROS flood in Oregon and Northern 53

California caused over $120 M (1960s dollars) of damage in that region [Waananen et al., 1971]. 54

More recently, the February 2017 ROS events in the Sacramento-San Joaquin Delta caused 55

extensive damage to Oroville Dam’s spillways and led to a massive evacuation of 188,000 56

downstream residents. Kattelmann [1997] and Brunengo [1990] found that most of the largest 57

floods in coastal regions of western North America have been associated to some degree with 58

ROS. 59

Both observation-based (e.g. Sui and Koehler [2001], Garvelmann et al. [2004]) and model-60

based (e.g. Marks et al., 1998, Musselman et al., 2018) studies have explored the mass and 61

energy balance processes associated with ROS events and the mechanisms that produce ROS 62

floods. Snowmelt and rainfall contribute to ROS runoff simultaneously and it is difficult to 63

distinguish the two, although some studies have attempted to quantify the contributions 64

separately. For example, Wayand et al. [2015] studied three mountainous river basins along the 65

U.S. west coast, and found that snowmelt was responsible for only about one-third of the runoff 66

during ROS events. Musselman et al. [2018] found that the portion of ROS runoff attributable to 67

snowmelt generally was higher in the interior of the U.S. West than along the coast, and could be 68

as high as two-thirds in the Rocky Mountains. Studies of other regions around the world have 69

reported that the contribution of snowmelt to runoff in ROS events ranges from 4% to 75% [e.g. 70

Harr, 1981; Singh et al., 1997; Marks et al., 1998, 2001; Sui and Koehler, 2001; Garvelmann et 71

al., 2015] (it should be noted that the definition of what constitutes an ROS event differs among 72

these studies). Other studies have investigated the mechanisms that are responsible for the large 73

runoff during major ROS events. Singh et al. (1997) found that in addition to intense rainfall and 74

snowmelt, large runoff in ROS events also occurs due to the enhanced movement of liquid water 75

through saturated snowpacks (at rates as high as 6 m/hour) as compared with percolation of 76

clear-sky snowmelt (typical rates less than 1.0 m/hour), as a result of snow microstructure 77

metamorphism and the formation of preferential flow pathways in saturated snowpacks. Some 78

studies have also investigated snowpack energy fluxes and their impacts on the snowmelt in ROS, 79

and found that turbulent heat fluxes (latent and sensible) played a more important role in melting 80

snow in ROS than in non-rainy conditions, especially in non-forested areas where snow has large 81

wind exposure that enhances heat transfer [Marks et al. 1998, Garvelman et al., 2014, Wayand et 82

al. 2015, Van Heeswijk et al. 1996]. However, in terms of the dominant energy flux for 83

snowmelt in ROS events, conclusions vary. For example, Marks et al. [1998] studied the 84

February 1996 ROS event in Oregon and found that snowmelt from turbulent fluxes accounted 85

for 60-90 percent of the total snowmelt in the 5-day ROS event, while Mazurkiewicz et al. [2008] 86

studied ROS events from 1996-2003 in the Pacific Northwest (PNW), and found that net 87

radiation (particularly the enhanced longwave radiation in overcast weather [Garvelmann et al. 88

2014]) was the largest contributor to snowmelt during ROS. Wayand et al. [2015] explored other 89

factors that affect ROS, including the specific basin hypsometry, forest cover, and characteristics 90

of individual ROS events such as the elevational distribution of antecedent SWE and the 91

available energy for melt; their work indicates that snowmelt and runoff generation processes 92

can vary substantially among ROS events. 93

Most ROS studies share similar characteristics. First, they are event-based and area-specific. 94

The majority rely on measured hydrological and meteorological data from a specific ROS event 95

or from a specific area that is frequently affected by ROS; large-scale ROS analyses have been 96

limited by a lack of consistent measurements and thus are rare [Cohen et al., 2015]; one 97

exception is the work by Musselman et al. [2018] focusing on the western U.S. Second, 98

compared with studies of the physical processes associated with individual ROS events, there are 99

few studies of ROS in the broader context of hydrologic extremes and predictions of future 100

changes in ROS events and their role in hydrologic extremes. Furthermore; relatively little is 101

known about the relative importance of ROS and non-ROS events to hydrologic extremes, 102

notwithstanding the importance of such information for flood risk prediction. For example, even 103

in areas with frequent ROS-induced floods, possible increases in ROS intensity do not 104

necessarily imply increased flood risk [Sharma et al. 2018]. Therefore, it is critical to 105

characterize both ROS floods and the flood risk from other sources (e.g. intense rainfall) in areas 106

that are susceptible to ROS floods. 107

Here, we examine model-based results that provide a basis for estimating the role of ROS in 108

extreme flood events in space and time over the conterminous United States (CONUS). We also 109

examine, based on model results, how ROS floods are likely to change in the future. The model 110

we use (Variable Infiltration Capacity, or VIC, see Liang et al., 1994 for details) resolves 111

precipitation states, elevational temperature and precipitation gradients, and snowpack 112

persistence and melt that all can affect how ROS events manifest as runoff. We also conducted a 113

systematic basin-wide flood risk analysis over the CONUS to evaluate the connection between 114

ROS and predicted 100-year floods. Our motivation is to answer the following questions: 115

Q1. How much does ROS contribute to flood runoff across the CONUS domain? How do 116

(spatially distributed) ROS runoff contributions relate to basin-scale flooding? 117

Q2. Is rain or snowmelt the dominant source of ROS runoff in a spatially distributed sense? 118

What are their relative contributions to ROS runoff? 119

Q3. What snow processes and associated energy fluxes are primarily responsible for snowmelt 120

during ROS? How much does each process contribute to the snowmelt generated during 121

ROS? 122

Q4. In a warmer climate, how will the contribution of ROS to large runoff events change, and 123

what will be the implications of these changes for flood risk over the CONUS? 124

2. STUDY AREA 125

This study was carried out over the CONUS (Figure 1). High-elevation regions are clustered 126

in the Western U.S., mostly in the Cascades, Sierra Nevada, and Rocky Mountain ranges. In 127

comparison, topographic relief in the eastern part of the domain is less; the Appalachians are the 128

only major mountain range in this part of the domain (Figure 1a). Temperature changes over the 129

period 1991-2012 compared to the 1901-1960 average, based on data from The Third National 130

Climate Assessment [Melillo et al. 2014] (Figure 1b). Warming has occurred in all regions, but is 131

less pronounced in the Southeast. The average temperature increase for 1991-2012 as compared 132

with 1901-1960 was 1.2 , with temperature increases in the major mountain areas (especially 133

the West) that average about 2 . 134

3. METHODS 135

The experiments we report are grouped as follows. First, we report a set of model runs that 136

are intended to provide insight into the physical mass and energy exchange processes in ROS 137

events. Second, we report model runs that are intended to characterize flood risk associated with 138

ROS events. Third, we evaluate the spatial patterns of these two model runs to explore the 139

connection between ROS and floods across the CONUS. 140

3.1 Hydrologic modeling 141

We used the Variable Infiltration Capacity (VIC) hydrologic model (Version 4.2d) to 142

simulate SWE and runoff over the entire CONUS. The VIC model has been described in 143

numerous publications, e.g. Liang et al. [1994], and Andreadis et al. [2009]. In this study we 144

used the VIC snow model to simulate the detailed snow mass and energy balance processes, 145

including mass and energy transfers to and from the atmosphere and the overlying vegetation via 146

snow accumulation on vegetation and the underlying snowpack, drip and mass release of snow 147

intercepted by vegetation, and sublimation from both snow in the vegetation canopy and the 148

underlying pack. In addition, we subdivided each VIC grid-cell into up to five elevation bands 149

and further subdivided each elevation band into up to twelve vegetation tiles to characterize the 150

effects of terrain and vegetation on sub-pixel snow variability; we activated this partial snow 151

coverage function to better capture snow spatial variability. The VIC model as we implemented 152

it requires four primary time-varying forcings: daily precipitation, maximum and minimum 153

temperature, and wind speed. The other time-varying forcing fields required by the model 154

(downward shortwave and longwave radiation, atmospheric pressure and vapor pressure) are 155

calculated internally based on MTCLIM algorithms [Hungerford et al., 1989]. VIC output 156

includes time-series of hydrologic variables (e.g. soil moisture, runoff, and evapotranspiration), 157

snow states (e.g. SWE), and energy fluxes (e.g. reflected shortwave radiation and emitted 158

longwave radiation, latent and sensible heat). 159

We used the Livneh et al. [2015] data set (hereafter referred to as L15) as the VIC forcing 160

data. L15 is available daily at 1/16° (~6 km) resolution over North America (south of 53° N) for 161

the period 1950–2013. We used only the CONUS part of L15, which included ~210,000 grid 162

cells. L15 makes orographic adjustments to precipitation and temperature using PRISM (Daly et 163

al., 1997) climatology from 1961 to 1990. We also adopted the L15 VIC parameterization. The 164

L15 VIC forcing and the model parameterization have been calibrated together over major river 165

basins of the CONUS as a part of L15 study, so that the combined application of the L15 VIC 166

forcing and parameterization have been shown to be able to simulate both snow (discussed in 167

Section 4) and streamflow that agree well with observations, as reported in Livneh et al. (2015). 168

L15 forcings and the associated VIC parameterization have been applied in numerous studies 169

(e.g. Barnhart et al. 2016, Henn et al. 2018). We did not perform additional calibration to the 170

model in this study. The VIC modeling was carried out at an hourly time step so as to better 171

simulate the diurnal characteristics of the energy exchange and the snowpack evolution. While 172

L15 forcings are daily, the MTCLM module automatically adjusted the daily forcing inputs for 173

each hour to reflect the diurnal cycle while maintaining the prescribed daily average for each 174

forcing variable. We conducted the hourly simulations for the 64-year period of 1950 to 2013. In 175

the interest of streamlining data storage and analysis, we aggregated hourly model results to 176

daily for output. 177

We used the Geospatial Attributes of Gages for Evaluating Streamflow version II (GAGES II, 178

Falcone et al., 2010) dataset from USGS to evaluate the VIC streamflow estimates. Of the total 179

9322 GAGE II streamflow gages over the U.S., 2057 are classified as reference gages (generally 180

meaning no upstream regulation or diversions); we only used the data at the 311 reference gages 181

that have over 50 years of data between 1950 and 2009; USGS streamflow measurements were 182

collected for these 311 gages. The published GAGES II data include the boundaries of the 183

upstream drainage areas for each gage. At each selected reference gage, we compared the peak 184

flood each year (i.e. the annual maximum series, or AMS) from the streamflow measurements 185

and from the VIC model, since the AMS is used later as the input for the flood risk analysis. 186

We calculated model output streamflow using the direct aggregation of the runoff and 187

baseflow over the drainage area for each gage, i.e., not routed through the stream network. We 188

made this simplification because most routing models (e.g. the VIC routing model [Lohmann et 189

al., 1998]) suitable for large-scale applications are based on the unit hydrograph and/or the 190

linearized St Venant’s Equation. Therefore, once routing parameters are set, the difference 191

between the routed streamflow and the aggregated streamflow is mostly a timing shift that will 192

minimally affect the magnitude of AMS (because the daily AMS series are dominated by the 193

total runoff and baseflow available within a basin). Note that the T-year flood risk analysis (e.g. 194

the 100-year flood magnitude in this study) needs only the magnitude of AMS and is irrelevant 195

with the its timing. We performed comparisons of routed streamflow and aggregated runoff in 196

several test basins with varying drainage areas (see supplemental material section S1), which 197

showed that runoff routing vs aggregation differences in both streamflow timing and magnitude 198

at the daily time scale are modest. 199

We used the Sierra Nevada SWE reanalysis (SNSR) dataset [Margulis et al., 2016] to 200

evaluate the modeled SWE. The SNSR data were produced by assimilating Landsat snow-201

covered area observations into a snow model via a particle batch smoother [Margulis et al., 202

2016]. SNSR has a high spatial-resolution (90 m) and is available daily for the period 1985 to 203

2015 over the portion of the Sierra Nevada above 1500 m elevation, and the data well reproduce 204

the space-time variations of in-situ observed SWE, with a mean-squared error less than 3 cm and 205

a correlation with 9000 station-years SWE observations greater than 0.95 [Margulis et al. 2016]. 206

3.2 Flood risk estimation 207

We used the Generalized Extreme Value (GEV) distribution to assess flood risk based on 208

VIC-simulated runoff. Specifically, we estimated the GEV distribution with time-varying 209

parameters using the Nonstationary Extreme Value Analysis (NEVA) package [Cheng et al. 210

2014] to characterize the flood risk in a changing climate. NEVA is a generalized framework for 211

estimating flood Intensity-Duration-Frequency curves for both the nonstationary and stationary 212

hydrologic responses to the climate change. It first tests for the presence of trends in the AMS 213

using the Mann-Kendall trend test (Kendall 1975; Mann 1945). Upon detection of a trend at the 214

5% significance level (α=0.05), the GEV distribution is estimated with time-varying parameters. 215

Absent a trend at the 5% significance level, the standard stationary GEV distribution parameters 216

are used. In both the stationary and nonstationary cases, NEVA estimates the GEV parameters 217

with a Bayesian approach implemented using a Differential Evolution Markov Chain (DE-MC, 218

Vrugt et al. [2009]; Ter Braak [2006]) for global optimization over the parameter space [Cheng 219

et al., 2014].We carried out the flood risk analysis for all HUC-6 basins in the CONUS using the 220

AMS derived from the aggregated streamflow. 221

We evaluated the flood risk analysis at the 248 GAGES II reference gages over the CONUS 222

that have over 50-year’s data record from 1950 to 2009 and have drainage areas larger than 100 223

km2. At each of these gages, we calculated the 100-year flood magnitude based on both the VIC 224

modeled streamflow aggregated from the gage’s upstream drainage area and the observed 225

streamflow, using the same NEVA flood risk estimation procedure. 226

3.3 ROS characterization 227

We adopted the criteria in Fruediger et al. [2014] to define ROS days in this study. Fruediger 228

et al. defined a ROS day as one having at least 3 mm of rain falling on a snowpack with at least 229

10 mm SWE, and for which snowmelt makes up at least 20% of the sum of the rainfall and 230

snowmelt for the day. These criteria are designed to identify ROS days that have flood-231

generating potential. Experiments reported in Fruediger et al. [2014] showed that these criteria 232

successfully captured those ROS days that contribute to flood events, and effectively removed 233

spurious ROS days. This ROS definition was also applied with slight adjustments by Musselman 234

et al. [2018] to identify ROS over the Western U.S. In this study the criteria were used to identify 235

every ROS day over the 64-year study period at each grid cell. After identifying the ROS days 236

for all grid cells, we calculated the ROS frequency in days/year, and also calculated the centroid 237

of timing of the ROS days based on the rainfall intensity-weighted average of the ROS timing in 238

days of the water year (i.e., days from October 1). Note that all our analyses are ROS day-based; 239

i.e. there was no attempt to define independent events, where some events could consist of 240

multiple consecutive days. 241

We quantified the relative importance of ROS to both large and extreme runoff over the 242

CONUS. To do so, at each model grid cell, we first selected the 200 days with the largest 243

simulated runoff during the 64-year study period (defined as the large runoff days, or 244

“Day_LARGE_200”), and also selected the 20 days with the largest simulated runoff (defined as the 245

extreme runoff days, or “Day_EXTRM_20”). Note that the two sets are not exclusive of each other 246

(i.e. Day_EXTRM_20 is included in the set of Day_LARGE_200 at each grid cell). The selected 247

Day_LARGE_200 and Day_EXTRM_20 include both ROS days and non-ROS days. Herein we refer to 248

the ROS days among Day_LARGE_200 and Day_EXTRM_20 as “Day_LARGE_ROS” and “Day_EXTRM_ROS”, 249

respectively. We further define the total number of Day_LARGE_200, Day_EXTRM_20, Day_LARGE_ROS, 250

and Day_EXTRM_ROS as ND_LARGE_200, ND_EXTRM_20, ND_LARGE_ROS, and ND_EXTRM_ROS, 251

respectively. Note that ND_LARGE_200 is 200 and ND_EXTRM_20 is 20 by definition, whereas 252

ND_LARGE_ROS and ND_EXTRM_ROS vary among grid cells. We analyzed only the large and extreme 253

runoff days (and the ROS days within them) to focus on days that are likely to contribute to 254

hydrologic extremes; Day_LARGE_200 and Day_EXTRM_20 represent on average about the largest 1% 255

and the largest 0.1% of the daily runoff in the 64-year period, respectively. 256

Hereafter, we refer to the total runoff from Day_LARGE_200 as “Q_LARGE_200”, and the total 257

runoff from Day_LARGE_ROS as “Q_LARGE_ROS”. Similarly, the total runoff from Day_EXTRM_20 is 258

referred to “Q_EXTRM_20”, and the total runoff from Day_EXTRM_ROS is referred to “Q_EXTRM_ROS”. 259

At each model grid cell, we calculated the ratio of ND_LARGE_ROS to ND_LARGE_200, and the ratio 260

of ND_EXTRM_ROS to ND_EXTRM_20 to explore the extent to which Day_LARGE_200 and Day_EXTRM_20 261

are ROS-related. We also calculated the ratio of Q_LARGE_ROS to Q_LARGE_200 and the ratio of 262

Q_EXTRM_ROS to Q_EXTRM_20 at each grid cell to evaluate the overall contribution of the runoff 263

volume from ROS to the large and extreme runoff. 264

We calculated the contribution of rainfall and snowmelt to Q_LARGE_ROS and Q_EXTRM_ROS to 265

determine the dominant hydrologic source of the runoff in the identified ROS days, and to 266

explore the spatial pattern of the dominant source over the CONUS. In the calculation at each 267

grid cell, we summed up the snowmelt and the rainfall in Day_LARGE_ROS and Day_EXTRM_ROS , and 268

divided by Q_LARGE_ROS and Q_EXTRM_ROS, respectively. The snowmelt, rainfall, and runoff 269

required for these calculations are all model output. To better understand the snowmelt processes 270

associated with ROS, we partitioned the snowmelt generated on Day_LARGE_ROS and 271

Day_EXTRM_ROS based on the different energy sources that drive snowmelt. In particular, we 272

investigated the (positive) energy transfer into the snowpack from net radiation, sensible heat, 273

latent heat (condensation), and advection heat transfer from rainfall. These energy fluxes have 274

been identified as the dominant energy sources for ROS snowmelt in previous studies. To 275

quantify the snowmelt associated with each of these energy fluxes, we calculated the ratio of 276

each flux to the total incoming energy to the snowpack that was responsible for the total 277

snowmelt in Day_LARGE_ROS and Day_EXTRM_ROS. The details of the calculation of each energy 278

flux are summarized in S2 in supplemental material. 279

3.4 Characterizing future ROS and floods 280

To explore how ROS is likely to change and how these changes will be reflected in future 281

flood risk, we created a delta-warming by uniformly increasing the air temperature in our VIC 282

forcings from 1950-2013 by 2 while holding the other forcing variables unchanged. Previous 283

studies have found that average 20th century warming over the CONUS has been on the order of 284

1 per century, and the rate of warming in the second half of the century is about double that of 285

the first half century, with much of the observed warming occurring after about 1975 [Melillo, 286

2014]. In contrast to the robust increasing trend in temperature, there is little evidence of large-287

scale precipitation trends in the 20th century, especially for winter season precipitation [Cayan et 288

al., 1998; Mote et al., 2005]. These findings form the basis of our delta-warming set up. The 289

uniform temperature increase over the original L15 temperature data preserves the historical 290

warming trend and thus the non-stationarity of the climate warming contained in the observation-291

based L15 data. Furthermore, insofar is it constitutes a sensitivity test rather than a scenario 292

analysis (as, for instance, would be the case with downscaled climate model projections), it 293

avoids confounding warming effects with, for instance, changes in precipitation and other model 294

forcing variables (such as surface wind) that may well change over time as well. We conducted 295

the same hydrologic modeling and the flood risk modeling as in section 3.1 and 3.2 for the future 296

case with the delta-warming. 297

We compared the spatial pattern of the future change of Q_LARGE_ROS/Q_LARGE_200 with the 298

spatial pattern of the future change of the 100-year flood magnitude to explore the role of ROS in 299

flooding events. We used Q_LARGE_ROS/Q_LARGE_200 in the comparison because the 200 large ROS 300

days roughly correspond to the largest 1% of the runoff steps in the study period. Since the 100-301

year flood is a flood that has 1% chance of occurring in any given year, thus the large runoff and 302

the 100-year flood share a statistical correspondence. We carried out the comparisons at the 303

HUC-6 basin level in the regions that showed significant ROS impact (as revealed from the 304

analysis discussed above). We aggregated the historical and future Q_LARGE_ROS/Q_LARGE_200 at 305

the grid cell level to HUC-6 basins by calculating the weighted average Q_LARGE_ROS/Q_LARGE_200 306

across all the grid cells within each HUC-6 basin, using Q_LARGE_200 at each grid cell as weights. 307

4. RESULTS AND DISCUSSION 308

4.1 Hydrologic and snow model evaluation 309

The VIC modeled SWE captured the details of the snow distribution within the CONUS and 310

agree well with the SNSR SWE in both space and time (Figure 2). Since largest ROS floods are 311

often associated with the rapid melt of anomalous snowpacks [McCabe et al 2007], the spatial 312

pattern of the greater-than-20mm historical mean annual maximum SWE (Figure 2a) provides a 313

general delineation of potentially highly ROS-impacted areas. Our ROS analysis focuses only on 314

these areas with at least 20 mm of mean annual maximum SWE since the low snow 315

accumulation in the other areas is less likely to lead to ROS-related extreme floods. Historically, 316

the western mountains have the largest snow accumulations, where the model grid-averaged 317

SWE can exceed 3 m on mountain peaks and divides. However, the mid-elevation transition 318

zone generally has the largest ROS flood-generating potential [Wayand et al. 2015]. Large snow 319

accumulation elsewhere in CONUS primarily occurs in the Northeast, the Upper Midwest, and 320

the Lower Appalachians. The maximum SWE decreases over the entire CONUS if the air 321

temperature was uniformly increased over the entire 1950-2013 period by (Figure 2b); the 322

largest declines would occur in the mountains, and the snow accumulation in many lower-323

elevation areas almost entirely gone as most snowfall would change to rain. Figure 2b illustrates 324

the areas that are most likely to undergo future ROS changes. 325

The total SWE in the Sierra Nevada from the VIC modeling and from the SNSR data are 326

consistent in the comparison period (Figure 2c). The timing of the Sierra Nevada-wide annual 327

maximum SWE from the VIC modeling highly correlates with that from the SNSR SWE (Figure 328

2d), with R=0.958 (p<0.05) and a root mean square difference (RMSD) of 8 days. The largest 329

timing differences occur in water years (WY) 1990 and 2002; aside from those two years the 330

dates of peak SWE are mostly within 2 days. In the winters of WY1990 and WY2002, there 331

were two major SWE accumulation events, as a result the total SNSR SWE accumulation had 332

double peaks with similar values separated by about one-month. While the VIC SWE also 333

captured both peaks, the larger VIC peak was the one further from the SNSR peak, leading to a 334

relatively large difference in the peak timing in those two years. The domain-wide peak SWE 335

volume comparison between the two datasets (Figure 2e) also show high agreement (R=0.959, 336

p<0.05). The RMSD of the peak annual SWE volume is 2.2 km3, which is about 12 percent of 337

the mean peak annual volume of 19 km3. Comparison of the spatial distribution of the peak 338

annual SWE from VIC modeling and from the SNSR data in the highest (WY1993, Figures 2h 339

and 2i) and lowest (WY1990, Figures 2f and 2g) water years in the comparison period shows 340

that the VIC model SWE captures the SWE variability both spatially (e.g. the SWE difference in 341

low elevation vs. high elevation) and temporally (e.g. inter-annual variability, also in Figure 2c). 342

While we did not perform SWE evaluation in regions other than the Sierra Nevada due to the 343

absence of observations that have similar accuracy and spatiotemporal continuity as the SNSR 344

SWE dataset, the Sierra Nevada has a particularly complex terrain and atmospheric variability 345

and we expect the model accuracy to be comparable elsewhere, which is suggested by more 346

limited pointwise model and observation comparisons in Mote et al. (2018). 347

We evaluated the streamflow and flood risk modeling results with those from the 348

observations (Figure 3). The modeled AMS from VIC is unbiased compared with the 349

observations at the 311 reference gages, especially for the gages and years with large streamflow 350

(Figure 3a). The modeled AMS has average uncertainty of 22.4% and a R-value of 0.79 (p<0.05) 351

in comparison with the observed AMS. The well-agreement between the cumulative density 352

functions of the modeled and observed AMS (Figure 3b) suggests that the two AMS series have 353

consistent statistical characteristics. To evaluate the flood risk modeling, we compared the 100-354

year flood magnitude estimated by NEVA from the VIC modeled AMS and from the observed 355

AMS at the 248 GAGES II reference gages that have over 50-years of data from 1950-2009 and 356

an upper stream drainage area larger than 100 km2 (Figure 3c). The 100-year flood magnitude 357

estimate based on VIC modeled AMS is unbiased in comparison with that based on the observed 358

AMS, with R=0.82 (p<0.05), an overall mean weighted relative uncertainty of 6%, and similar 359

statistical characteristics (Figure 3d). Overall, these comparisons show that the VIC modeling 360

generates plausible streamflow estimates, and the default NEVA setup and parameterization 361

yield unbiased flood magnitude estimates with reasonable accuracy based on the VIC modeled 362

streamflow. 363

4.2 Historical ROS characterization 364

The areas with high historical ROS frequency (based on ROS day selection described in 365

section 3.3) over the CONUS include the Western mountains, the Upper Midwest, the Northeast, 366

and the lower the Appalachians (Figure 4a). As discussed, our ROS analysis focuses on areas 367

with at least 20 mm of mean historical maximum annual SWE. In these ROS-impacted regions, 368

ROS occurs multiple times a year and almost every year; ROS is a part of the local seasonal 369

water cycle and a consistent contributor to the local runoff when normal snow accumulation is 370

available. Within the CONUS, the Pacific Northwest (PNW) is the most ROS-impacted region 371

with the largest ROS frequency, mainly due to the deep seasonal snow on the Cascades and the 372

tremendous rainfall caused by the orographic uplift of moist air in warm/moisture-rich 373

atmospheric river events [Ralph and Dettinger, 2011]. The west-facing slopes of both PNW and 374

the Sierra Nevada have more frequent ROS than the east-facing slopes (Figure 4a), because the 375

west-facing slopes are directly exposed to rainfall, while the east-facing slopes are in the 376

orographic rainfall-shadow. Mid-elevation mountains (1500 m-2500 m) are most sensitive to 377

ROS, while other mountainous areas are less ROS-impacted, due to lower-elevation areas having 378

less snow accumulation and higher-elevation areas (e.g. the southern Sierra Nevada) having 379

snow-dominated winter precipitation; both factors tend to constrain ROS. In the East, ROS 380

occurs mainly in the Northeast, the lower Appalachians, and the Upper Midwest. These areas are 381

mostly adjacent to large water bodies. For instance, the Upper Midwest is affected by the Great 382

Lakes, and at least part of the Northeast is affected by Lake Ontario, the Atlantic Ocean, and the 383

St Lawrence River. Humid air from these water bodies can result in large snow accumulation in 384

the winter and rainfall in the early spring, leading to the potential for large ROS events. 385

Generally though, ROS in the East is much less frequent compared with the West, mainly due to 386

the shallower snow accumulations and the shorter period of snow cover. 387

The spatial distribution of the centroid timing of all ROS days (Figure 4b) reflects the spatial 388

variation in the rainfall seasonality. In the western U.S., the majority of ROS days in PNW and 389

the Sierra Nevada are in the late fall and winter seasons, while ROS days in the Rockies occur 390

mostly in early to mid-spring (on average about one month later than the Western coastal ranges). 391

This temporal difference in ROS timing is mainly because of the timing of the rainfall season in 392

the two regions [Knowles et al. 2006, Gergel et al. 2017]. Orographically, ROS occurs later at 393

higher elevations due to the snowfall to rainfall transition occurring later in high elevation areas. 394

The elevational ROS timing difference is most obvious in the comparison between the northern 395

and southern Cascades, and between the northern and southern Sierra Nevada (Figure 4b). ROS 396

in the Eastern U.S. occurs earlier than in the West; large ROS days tend to occur around mid-397

January in the northern tier of the Northeast and Midwest, and mostly in October in the lower 398

Appalachians and the lower Midwest. 399

Figure 5 shows the fraction of the 200 large runoff days and the 20 extreme runoff days that 400

are ROS-related (ND_LARGE_ROS/ND_LARGE_200 in Figures 5a, ND_EXTRM_ROS/ND_EXTRM_20 in 401

Figures 5b), and the fraction of total large and extreme runoff that is attributable to these ROS-402

related days (Q_LARGE_ROS/Q_LARGE_200 in Figures 5c, Q_EXTRM_ROS/Q_EXTRM_20 in Figures 5d). 403

Generally, the spatial extent and the spatial variation of the impacts of the ROS runoff on the 404

large runoff and extreme runoff are similar over the CONUS. On average, 53% of the 405

ND_LARGE_200 and 77% of the ND_EXTRM_20 are ROS-related in the major ROS-impacted areas 406

(including the major mountain ranges of the West, the Upper Midwest, the Northeast, and the 407

lower Appalachian region. We found that large and extreme runoff days are more likely to be 408

ROS-related in higher elevation areas, but in those areas with very high elevations, such as the 409

southern Sierra Nevada and the ridges of the Cascades (see Figures 5a and 5b). This appears to 410

be attributable to 1) lower temperatures at high elevations, so while rain may be occurring at 411

lower elevations, higher elevations are above the snow line and the local precipitation is mostly 412

snowfall (i.e. less rainfall and thus less ROS), and 2) high runoff production in these high 413

elevation areas (especially on the east slopes of the Cascades) is dominated by clear-sky 414

snowmelt in spring, rather than during fall and early winter storms. It is also clear that a 415

significant portion of floods that occur in basins that drain the west facing slopes of the Cascades 416

and the Sierra Nevada are ROS-related. 417

While a substantial fraction of large and extreme runoff days are ROS-related across much of 418

our domain, the runoff contribution from these ROS days to the total large and extreme runoff is 419

comparatively low in most cases (Figures 5c and 5d vs. Figures 5a and 5b). The reason has to do 420

with several factors, including: 1) in regions with shallow snowpacks (low elevations in the West, 421

and much of the rest of the snow-affected domain, e.g. almost all of the upper Midwest and 422

Northeast), relatively small SWE at the beginning of ROS days leads to lower ROS frequencies 423

and contributions to runoff. Also, Q_LARGE_200 and Q_EXTRM_20 in these areas with relatively low 424

elevation often relate to intense rainfall occurred in non-ROS days. 2) Q_LARGE_ROS/Q_LARGE_200 425

and Q_EXTRM_ROS/Q_EXTRM_20 are also limited at very high elevations in the West, e.g. as 426

discussed, the southern Sierra Nevada and the highest elevations of the Cascades as compared 427

with lower elevations in the same general areas (Figures 5c). 428

The comparison between Figure 5c and Figure 5d shows the role of ROS runoff in large 429

runoff is more significant than that in the extreme runoff. For instance, average 430

Q_LARGE_ROS/Q_LARGE_200 is ~23% (Figure 5c), whereas Q_EXTRM_ROS/Q_EXTRM_20 is only 5% in 431

average (Figure 5d) over the ROS affected areas of the western U.S. Over the most ROS-affected 432

mountains in CONUS (including Cascades, the northern Rockies, and the northern 433

Appalachians), Q_LARGE_ROS/Q_LARGE_200 is ~40% while Q_EXTRM_ROS/Q_EXTRM_20 is only 7%. The 434

large difference between the role of ROS runoff in large runoff as contrasted with extreme runoff 435

could be a result of several factors: (1) heavy rainfall and clear-sky melt that occur in non-ROS 436

conditions are more dominant in the extreme runoff than in the large runoff, and these factors 437

dilute the ROS runoff contribution ratio; (2) Extreme runoff mostly occurs in the late winter and 438

early summer (overall later than large runoff), so the antecedent SWE that is available to melt 439

and contribute to the runoff in extreme runoff days is generally less than in large runoff days, 440

especially at low elevations. The areas with large Q_LARGE_ROS/Q_LARGE_200 and 441

Q_EXTRM_ROS/Q_EXTRM_20 (Figures 5c and 5d) coincide with areas with high ROS frequency (see 442

Figure 4a) and high fractions of ROS-related runoff days (Figures 5a and 5b). 443

Figures 6 shows the source of the runoff generated during ROS days. Rainfall accounts for 444

up to 70% of Q_LARGE_ROS in the PNW and the west-facing slopes of the Sierra Nevada and 445

Cascades (Figure 6a). The coastal areas is impacted by the large moisture transport primarily by 446

atmospheric rivers [Chen et al., 2018]), leading to very high precipitation along the west slopes 447

of the mountain barriers. In this region, intense rainfall outweighs the snowmelt and accounts for 448

most of the ROS runoff. In comparison, snowmelt dominates Q_LARGE_ROS in the Rockies, the 449

Northeast, and the Upper Midwest, where snowmelt in Day_LARGE_ROS accounts for an average of 450

65% of the runoff in these days (Figure 6b). Snowmelt dominates the ROS runoff in these 451

regions for two reasons. First, rainfall magnitude and frequency in these regions are 452

comparatively mild, and thus the role of rainfall in Q_LARGE_ROS is not as strong as it is along the 453

West Coast. Second, Day_LARGE_ROS in the Rockies and the Northeast are mostly coincident with 454

the snowmelt season and hence later in the (water) year than along the West Coast (as in Figure 455

4b); warmer temperatures, increased solar radiation, and longer daylight hours later in this time 456

of a year all favor snowmelt. The reduced effects of rainfall and enhanced snowmelt augment the 457

role of snowmelt in Q_LARGE_ROS in these areas. This finding is consistent with Mazurkiewicz et 458

al. 2007. Furthermore, the quantity and spatial pattern of the contribution of snowmelt and 459

rainfall to Q_LARGE_ROS over the Western U.S. agree well with those in Wayand et al. [2015] and 460

Musselman et al. [2018]. The contribution of rainfall and snowmelt in Day_EXTRM_ROS to 461

Q_EXTRM_ROS (Figure 6c and 6d) are similar with their contributions to Q_LARGE_ROS (Figure 6a 462

and 6b) 463

Figure 7 dissects the snowmelt generated during Day_LARGE_ROS (Figures 7 a-d) and 464

Day_EXTRM_ROS (Figures 7 e-h) into components that are driven by net-radiation, condensation, 465

sensible heat, and rainfall advection. The magnitude and the spatial pattern of the contribution of 466

each of these energy sources to the snowmelt in Day_LARGE_ROS and in Day_EXTRM_ROS are very 467

similar. In both large ROS and extreme ROS cases, net-radiation is the dominant energy source 468

for ROS snowmelt in the mountains of the West (Figure 7a and 7e), explaining an average of 68% 469

of ROS snowmelt in the Cascades, Sierra Nevada and the Rockies. Figure 7b and 7f show that in 470

the coastal west, net-radiation accounts for slightly more ROS snowmelt than do turbulent heat 471

fluxes (sensible heat and the condensation-dominant latent heat). Sensible heat is responsible for 472

over 70% of the snowmelt in ROS days in the Great Basin and the Colorado Plateau (Figure 7c 473

and 7g), where snow cover is shallow and ROS days occur later in a water year when air 474

temperature that drives the sensible heat flux is higher. In the major ROS-impacted regions in the 475

eastern U.S., turbulent heat fluxes are about as important as net-radiation in ROS snowmelt. 476

Rainfall advection makes up less than 5% of ROS melt across the entire CONUS domain (Figure 477

7d and 7h), i.e., rainfall does not directly melt much snow in ROS events. This contradicts a 478

common perception that snowmelt in ROS is caused in large part by energy infusion from the 479

warmer rainfall. In fact, ROS snowmelt directly resulting from rainfall energy (i.e. via advection) 480

is limited by (1) the relatively small temperature difference between the rainfall and the freezing 481

point that controls the maximum amount of advection energy that a unit volume of rainfall can 482

provide to melt snow, and (2) the fact that advection is much less efficient in energy transfer in 483

comparison with processes such as condensation and rainfall water refreeze, because the heat 484

capacity of water, which controls the energy transfer rate via advection, is much less than both 485

the latent heat of vaporization and the latent heat of fusion that control the energy transfer rate in 486

condensation and rainfall water re-freeze, respectively. 487

Our finding that net-radiation is responsible for slightly more ROS snowmelt in the Western 488

U.S. than turbulent heat fluxes is consistent with the conclusion in Mazurkiewicz et al. [2007], 489

but differs with other studies (e.g. Marks et al. [1998], Corripio and López-Moreno, [2017]) that 490

find that turbulent heat fluxes dominate. The difference between our study and those referenced 491

above may be explained by the fact that we investigate ROS with a different perspective. In 492

particular, Marks et al. [1998] and Corripio and López-Moreno [2017] explored the energy 493

balance in single ROS events that lead to unprecedented flooding, with exceptionally high wind 494

and humid air which tremendously enhanced the turbulent heat fluxes and allowed them to 495

dominate snowmelt in the ROS events. In comparison, Mazurkiewicz et al. [2007] and the results 496

presented herein examined all the ROS events across a long period at a larger scale, so (1) not 497

many ROS events have exceptionally high wind (and hence very large turbulent heat transfer) as 498

in the two aforementioned papers; and (2) ROS events occurring late in winter or early spring 499

coincident with high solar radiation for a longer period during daytime than the ROS events in 500

mid-winter (e.g. as in Marks et al. [1998]), which enhance the effects of the radiation on ROS 501

snowmelt. 502

4.3 Future change of ROS and its effects on future hydrologic extremes 503

In a warmer future, more ROS will occur in high-elevation areas due to increased rainfall 504

(transitioned from snowfall), whereas ROS in low-elevation and mid-elevation areas will 505

decrease or diminish due to reduced SWE overall (Figure 8a). The elevation at which ROS 506

frequency transitions from decreasing to increasing mostly is around 1500 m to 2000 m. The 507

elevation-dependent ROS frequency change is most apparent in the Cascades and the Sierra 508

Nevada (Figure 8a), which generally have warmer winter temperatures than the interior of the 509

West. In the eastern U.S., ROS frequency decreases over all ROS-impacted areas, especially in 510

the southern Appalachians. The reduced ROS frequency in these areas is driven by declines in 511

snow accumulation at the onset of ROS. Temporally (Figure 8b), ROS will occur earlier by 512

about a month overall in almost the entire CONUS due to the shift from snowfall to rain earlier 513

in the year. Figure 8 has more white areas than the historical case (Figure 4) because more areas 514

fall below the SWE threshold used for ROS identification in the future and thus the ROS with 515

flood-generating potential diminishes. 516

Figure 9 is indicative of how the role of ROS in future hydrologic extremes will change. In 517

the warmer scenario, large and extreme runoff will be more ROS-related in high elevation areas 518

(where ND_LARGE_ROS/ND_LARGE_200 and ND_EXTRM_ROS/ND_EXTRM_20 increase) and less ROS-519

related in moderate and low elevation areas (where ND_LARGE_ROS/ND_LARGE_200 and 520

ND_EXTRM_ROS/ND_EXTRM_20 decrease), as in Figures 9a and 9b. The largest increases in the 521

Western U.S. occur in the high-elevation mountains that have not been affected by ROS in the 522

past, especially the Upper Cascades in the Pacific Northwest, which is consistent with the finding 523

in Yan et al. (2019). The greatest decreases occur in the coastal Western U.S., especially the 524

middle and low elevation west-facing barriers of the Sierra Nevada and the Cascades, where 525

declines in snow accumulation and increases in rainfall intensity (which dilute ROS runoff 526

contribution ratio) will occur in the future. In most of the eastern U.S., future large and extreme 527

runoff will be less ROS-related, due primarily to reduced snow accumulation, except in the 528

northern part of the upper Midwest, and some high peaks in the Upper Appalachian region. 529

Changes in the ratios of Q_LARGE_ROS/Q_LARGE_200 (Figure 9c) are similar to changes in 530

ND_LARGE_ROS/ND_LARGE_200 (Figure 9a); Q_LARGE_ROS/Q_LARGE_200 shows elevation-dependence 531

in the West; it increases by an average of 11% in high-elevation mountains and decreases by 7% 532

at intermediate and low elevations. In the East, Q_LARGE_ROS/Q_LARGE_200 reduces by 6% 533

compared with the historical case, and the role of ROS increases only at a few mountains in 534

northern Michigan where seasonal snow exists. The spatial pattern of Q_EXTRM_ROS/Q_EXTRM_20 535

changes (Figure 9d) is similar to that of Q_LARGE_ROS/Q_LARGE_200 (Figure 9c), but with a 536

comparatively lower magnitude. While ND_EXTRM_ROS/ND_EXTRM_20 changes more significantly 537

than ND_LARGE_ROS/ND_LARGE_200 does (Figure 9b vs 9a), Q_EXTRM_ROS/Q_EXTRM_200 changes less 538

than Q_LARGE_ROS/Q_LARGE_200 (Figure 9d vs 9c), because of the extreme runoff is more 539

dominated by intense rainfall and clear-sky melt, so the number of ROS day (or ROS frequency) 540

changes have less effects on the ROS runoff contribution change in the extreme runoff case than 541

in the large runoff case. 542

Comparing Figures 9a and 9b with Figures 9c and 9d, it is clear that in a warmer future, ROS 543

will be involved in more flood events in mountainous areas, especially for extreme flood events 544

in many areas that are headwaters of large rivers. Also, the spatial patterns shown in Figure 9a 545

and 9b are highly consistent with those in Figures 9c and 9d, respectively, i.e. in areas with more 546

frequent ROS days, the role of ROS in large and extreme runoff increases, and vice versa. This 547

demonstrates that ROS frequency change is a first order control on the changes in the 548

contribution of ROS runoff to total runoff in large and extreme floods. 549

We calculated changes in Q_LARGE_ROS/Q_LARGE_200 and changes in the 100-year flood 550

magnitude at the HUC-6 level over the entire CONUS (as shown in Figure S4), and compared 551

these changes in the major ROS-impacted regions of the CONUS (Figure 10) to explore the 552

connection between ROS and the hydrologic extremes. Note that the ROS contribution was 553

originally calculated at grid-cell level (e.g. Figures 5c and 5d, Figures 9c and 9d), here we 554

aggregated it to each HUC-6 basin by calculating the runoff-weighted average of 555

Q_LARGE_ROS/Q_LARGE_200 for all the grid-cells within the basin. Figures 10a-d show the spatial 556

patterns of future flood risk changes and changes in Q_LARGE_ROS/Q_LARGE_200; the two changes 557

are largely consistent in the ROS-impacted regions in the eastern U.S. and they both show 558

decreases. Since the large runoff in these regions is usually driven by rainfall, whose intensity is 559

likely to increase in the future as a result of the increased temperature and the resulting increased 560

atmospheric water holding ability (based on Clausius-Claperyon Equation, and increased 561

atmospheric moisture amount is likely to lead to more intense rainfall when saturated), but on the 562

other hand the flood risk in these regions decreases, therefore the indication is the future 563

decreases in snow accumulation and ROS is likely to be a factor that lead to the decreased flood 564

risk in these areas. Indeed, the total water entering the soil column is about the same, but since 565

the snowmelt becomes less (because of reduced snow), so more rainfall water supplies to the soil 566

and reduces the amount of direct rainfall runoff, ultimately resulting in reduced flood risk in 567

areas where local floods are heavy rainfall-dominated. A few basins in the Upper Midwest, 568

where deep snow accumulates and future ROS contributes more runoff to large and extreme 569

runoff events are the exception; in these basins, the flood risk increases. 570

Over the mountains of the West, the Cascades and the northern Rockies have spatially-571

consistent decreases in Q_LARGE_ROS/Q_LARGE_200 and spatially-consistent increases in the flood 572

risk, but Q_LARGE_ROS/Q_LARGE_200 changes and the flood risk changes in some of the basins in the 573

southern Rockies show spatially inconsistent (Figures 10e and 10f). Rainfall is a major part of 574

the floods along the west coast and in the Cascades and the northern Sierra Nevada. The flood 575

risk increases in these regions is primarily due to the more intense rainfall caused by the 576

atmospheric rivers and the increased water amount in the atmosphere; the more intense rainfall 577

directly increases the chance of hydrologic extremes and also dilutes the impacts of ROS runoff 578

to the large floods. The reduced snow accumulations in the future also contributes to the reduced 579

role of ROS in this region. Inconsistency between the change in Q_LARGE_ROS/Q_LARGE_200 and the 580

change in flood risk occurs in a few mid-elevation basins in the southern Rockies, where ROS 581

contribution slightly increases and the flood risk decreases. The peak streamflow in these basins 582

is mostly controlled by clear-sky melt, and floods occur as a result of intense clear-sky snowmelt. 583

Musselman et al (2016) found that in the future, the warmer temperature will shift the snowmelt 584

onset earlier in this area, but the earlier snowmelt will occur in a time of year with lower solar 585

radiation, shorter days, and colder temperatures. As a result, the snowmelt process in these mid-586

elevation areas will become longer and less intense, which will reduce the overall flood risk. 587

Therefore, despite the fact that ROS effects will increase, reduced clear-sky melt will outweigh 588

this, and these areas will have an overall reduced flood risk. 589

Figure 11 compares the flood risk changes and the Q_LARGE_ROS/Q_LARGE_200 changes in the 590

HUC-6 basins shown in Figure 10, with the basins color coded by their median basin elevation. 591

For the basins whose median basin elevation is below 1700 m (Figure 11a), the flood risk and the 592

contribution of large ROS runoff to total large runoff can either increase or decrease, but the two 593

changes are positively correlated, implying that flood risk in these basins is related with ROS. In 594

comparison, for basins higher than 1700m (Figure 11b), Q_LARGE_ROS/Q_LARGE_200 all increase, 595

but the increases in the ROS runoff contribution in these higher basins are not correlated with the 596

flood risk change, likely because floods in these high elevation basins are dominated by clear-597

sky melt, and the ROS effect on local extreme runoff are limited. 598

5. CONCLUSIONS 599

We have quantitatively characterized historical and future ROS conditions across the 600

CONUS, and explored the role of ROS in hydrologic extremes. We find that: 601

1. The main ROS-impacted regions in the CONUS are the major western mountain ranges 602

(including the Cascades, the Sierra Nevada, and the Rockies), the Upper Midwest, the 603

Northeast, and the lower Appalachian region. Historically, the contribution of ROS to 604

extreme runoff in the western U.S. has been greatest in mid-elevation areas (1500 m to 2300 605

m); this “significant influence zone” will shift higher in the future. ROS in the coastal West 606

and in the Eastern U.S. mostly occur in fall and winter, while ROS in the high mountains in 607

the West occurs mostly in early spring. 608

2. While a significant portion of large and extreme runoff days in the historical record are ROS-609

related in the most ROS-affected regions, total runoff from ROS days accounts for a modest 610

part of the runoff from large runoff days (upper 1%), and a small (mostly less than 10 percent) 611

part of the runoff from extreme runoff days (upper 0.1%), indicating that most extreme 612

runoff is a result of either intense rainfall or radiation-driven snowmelt even on ROS-days. 613

3. The runoff generated during ROS days is dominated by rainfall along the west coast and is 614

dominated by snowmelt in the rest of ROS-impacted regions in the CONUS. Net-radiation 615

dominates the snowmelt in ROS days in the high mountains in the West, while net-radiation 616

and turbulent heat flux (including the condensation latent heat and sensible heat) are equally 617

dominant in the rest of the ROS-impacted regions in CONUS. The amount of snow directly 618

melt by rainfall (through heat advection) is negligible. 619

4. In a warmer future, the role of ROS in local hydrologic extremes will increase in high 620

elevation mountains while decreasing at low and moderate elevation areas (especially in the 621

West), and its role will decrease over almost the entire Midwest and the eastern U.S.; the 622

future change of ROS frequency exerts a first order control on the future change of the runoff 623

contribution from ROS to extreme floods. The mean timing of ROS will shift earlier across 624

the entire CONUS by an average about a month in a +2 warmer scenario. 625

Acknowledgements 626

This study was performed under supports from the Strategic Environmental Research and 627

Development Program (SERDP) – Project #RC-2513 granted to the University of California, Los 628

Angeles, and from the U.S.–China Clean Energy Research Center for Water-Energy 629

Technologies/California Energy Commission Grant 300-15-006. The authors declare no real or 630

perceived financial conflicts of interests. All data used in this study are publicly available online 631

at the following URLs: Livneh meteorological forcings: 632

https://data.nodc.noaa.gov/thredds/catalog/nodc/archive/data/0129374/daily/catalog.html, 633

GAGES II data: 634

https://water.usgs.gov/GIS/metadata/usgswrd/XML/gagesII_Sept2011.xml#stdorder, SNSR 635

SWE: https://ucla.app.box.com/v/SWE-REANALYSIS. USGS streamflow observations: 636

https://waterdata.usgs.gov/nwis/uv/?referred_module=sw. Both the VIC hydrologic model and 637

the NEVA flood risk estimation scheme are open source and can be downloaded from 638

https://github.com/UW-Hydro/VIC/releases/tag/VIC.4.2.d and http://amir.eng.uci.edu/neva.php. 639

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771

Figures 772

773

Figure 1. (a) Elevation of the CONUS (the study domain). (b) Observed temperature change in 774

the 20th century (1991-2012 average compared to the 1901-1960 average). The mean temperature 775

increased by about 1.2 on average over the domain (data source: the Third National Climate 776

Assessment, Melillo et al., 2014). 777

(a) (b)

778

(c)

(d) (e)

(f) (h) (g) (i)

(b) (a)

Figure 2. (a) Historical (1950-2013) mean annual maximum SWE over the CONUS from VIC 779

modeling. Regions that have mean annual maximum SWE less than 20 mm are masked out. (b) 780

The change in the maximum SWE that would occur if the air temperature was uniformly 781

increased over the 1950-2013 record by 2.0 . (c) Comparison of the daily time series of total 782

SWE in the Sierra Nevada from the SNSR dataset (blue, Margulis et al, 2016) and from the VIC 783

model (red). The SSNR SWE is available from water year 1985. (d) Comparison of the timing 784

and (e) the total volume of the annual peak SWE over the Sierra Nevada from the two sources. (f) 785

and (g) compare the spatial distribution of the peak SWE from the VIC model and from the 786

SNSR data in water year 1990, which is the lowest water year in the comparison period. 787

Comparison between (h) and (i) are similar with that in (f) and (g), except the comparison is for 788

WY1993, which is the highest water year in the comparison period. 789

790

Figure 3. Evaluation of the VIC modeled streamflow and the 100-year flood magnitude estimates 791

from the flood risk analysis. (a) comparison of the annual maximum streamflow observed at the 792

GAGES II reference gages that have over 50-years of record from 1950 to 2009 with the 793

modeled annual maximum streamflow at these gages. (b) comparison of the cumulative 794

distribution of the annual maximum streamflow from model and observations at the gages from 795

panel (a). (c) comparison of the 100-year flood magnitude calculated from the annual maximum 796

streamflow from the GAGES II reference gages that have over 50-years of record and at least 797

100 km2 drainage area with that calculated using the VIC-modeled annual maximum streamflow 798

at these gages. (d) comparison of the cumulative distribution of the 100-year flood magnitude 799

calculated from the VIC model and observations as shown in panel (c). 800

(a) (b)

(c) (d)

801

Figure 4. (a) The frequency of historical ROS days defined by the criteria in Fruediger et al. 802

(2015). (b) the centroid of timing of all the historical ROS days. Results are shown only for grid 803

cells with average maximum annual SWE > 20 mm (as in Figure 1(b)). 804

(a) (b)

805

Figure 5. (a) the ratio of the number of large ROS days to the number of large runoff days (200), 806

where large runoff days are defined as the 200 days that have the largest runoff during the 64-807

year study period, and the large ROS days are defined as ROS days among the 200 large runoff 808

days at each model grid cell. (b) the ratio of the number of extreme ROS days to the number of 809

extreme runoff days (20), where extreme runoff days are defined as the 20 days that have the 810

largest runoff during the 64-year study period and the extreme ROS days are defined as ROS 811

days among the 20 extreme runoff days at each model grid cell. (c) the ratio of the large ROS 812

runoff (i.e. the runoff from the large ROS days) to the total large runoff (i.e. the total runoff from 813

the 200 large runoff days); (d) the same as (c) except the ratio is extreme ROS runoff to the total 814

(c) (d)

(a) (b)

extreme runoff. The white areas in the maps have mean annual maximum SWE less than 20 mm 815

(see Figure 1(b)) and are excluded in the analysis. 816

817

Figure 6. Fractional contribution to the large and extreme ROS runoff from rainfall and 818

snowmelt. (a) and (b) show the ratio of the rainfall and snowmelt from the large ROS days (i.e. 819

the ROS days in the 200 large runoff days) to the total large ROS runoff (i.e. the total runoff 820

from the large ROS days), respectively. (c) and (d) show the ratio of the rainfall and snowfall 821

from the extreme ROS days (i.e. the ROS days in the 20 extreme runoff days) to the total 822

extreme ROS runoff (i.e. the total runoff from the extreme ROS days), respectively. White areas 823

in the maps have mean annual maximum SWE less than 20 mm and are excluded from the 824

analysis (see Figure 1(b)). 825

(a) (b)

(c) (d)

826

(a) (e)

(b) (f)

(c) (g)

(d) (h)

Figure 7. Fractional contribution to snowmelt on large and extreme ROS days from different 827

energy sources; panels (a) - (d) show the fraction of the total snowmelt on large ROS days (i.e. 828

the ROS days among the 200 largest runoff days) caused by net radiation (dominated by long-829

wave radiation), condensation, sensible heat, and advection; panels (e) - (h) show the fraction of 830

total snowmelt on extreme ROS days (i.e. the ROS days among the 20 largest runoff days) 831

caused by net radiation, condensation, sensible heat, and advection. White areas have mean 832

annual maximum SWE less than 20 mm and are excluded from the analysis (see Figure 1(b)). 833

834

Figure 8: (a) Change in ROS frequency in the +2 warmer scenario in comparison with the 835

historical ROS frequency. (b) change in the centroid of timing of ROS days in the +2 warmer 836

climate in comparison with the historical ROS timing. The white areas either have historical 837

mean annual maximum SWE less than 20 mm (see Figure 1(b)) or no identified ROS days in the 838

warmer clime due to reduced SWE. 839

840

(a) (b)

841

Figure 9. (a) Change in the ratio of the number of large ROS days to the number of large runoff 842

days (200) in a +2 warmer scenario; large runoff days are the 200 days that have the largest 843

runoff during the study period and the large ROS days are the ROS days among the 200 large 844

runoff days. (b) change in the ratio of the number of extreme ROS days to the number of extreme 845

runoff days (20) in a +2 warmer scenario; extreme runoff days are the 20 days that have the 846

largest runoff during the study period and the extreme ROS days are the ROS days among the 20 847

extreme runoff days. (c) change in the ratio of total runoff during large ROS days to total runoff 848

from the 200 large runoff days. (d) same as (c), except the ratio is extreme ROS runoff to total 849

extreme runoff. White areas have historical mean annual maximum SWE less than 20 mm (see 850

Figure 1(b)) and are excluded in the analysis. 851

(a) (b)

(c) (d)

852

Figure 10: Changes in the 100-yr flood magnitude (left column) and in the contribution of large 853

ROS runoff to the total large runoff (right column) in the +2 warmer climate for each HUC-6 854

basin within the three major most ROS-impacted regions within the CONUS, including the 855

Northeast (panel a and b), the upper Midwest (panel c and d), and the western mountains (panel e 856

and f). 857

(a) (b)

(c) (d)

(f) (e)

- 49 -

858

Figure 11: 100-year flood magnitude change and changes in the ratio of large ROS runoff to the 859

total large runoff in a +2 warmer climate at basins in the most ROS-impacted regions in 860

CONUS (from Figure 11). Each dot represents a basin and is color-coded with the median 861

elevation of the basin. (a) compares at basins whose elevation is below 1700m, and (b) compares 862

basins whose elevation is above 1700m. 863