A M ONTE C ARLO M ODEL FOR S IMULATION OF R AIN - ON -S NOW E VENTS IN THE P ACIFIC N ORTHWEST

1. A MONTE CARLO MODELFOR SIMULATIONOF RAIN-ON-SNOW EVENTSINTHE PACIFIC NORTHWEST Matt Brunengo based on presentation at 2007 Western Snow Conference

2. Introduction • What is rain-on-snow? • snowmelt during rainfall • commonly big storms • temps typically warmer than seasonal • rain + melt = can be major water inputs • rain doesn’t cause most of the melt

3. When does ROS occur? • Synoptic scale • SW’ly frontal–cyclonic storms • warm air holds more water • Seasonal storm occurrence • most in fall & winter: rain > melt • some in spring: melt > rain • Climatic variables • circulation patterns, ENSO, PDO

4. Where is ROS most common? • Timing • warm rain + snowpack • requires storm arrival in aut–win–spr • Western North America • intercepts winter storms • snowpacks on mountains, at least • Most other regions: ROS is rare

5. When / where? • McCabe et al., Bull. AMS, March 2007 • spatial & temporal characteristics of ROS • data from 11 western states • WY 1949 – 2003 • 4318 NWS sites, detailed analysis of 477 • “ROS event”  a day on which precip fell and snow depth decreased ( SM)

6. When / where? • McCabe et al., Bull. AMS, March 2007 • spatial: • ROS occurs almost everywhere in the West • more common in the PNW • temporal: • most common Oct – May (Nov – Mar in PNW) • possible in any months (esp at higher elevs)

7. When / where? • McCabe et al., Bull. AMS, March 2007 • correlations of ROS events with • number of rainy days • snow on the ground (temperature, elev) • interannual variability: apparent trends – • ENSO: more common in north during La Nina • declining frequency at lower elevs

8. How does ROS work? • Sequence: shift from • T < 0°C to build a pre-existing snowpack • T > 0°C in warm air and rain • Energy supplied for aut–win melt • long-wave >> short-wave radiation • some heat supplied by rain • minor ground heat

9. How does ROS work? • Energy for melt, cont’d • sensible and latent heat – major • latent heat of condensation »600 cal/g • latent heat of fusion » 80 cal/g • both depend on turbulent transfer – wind • ROS melt function • snowmelt = f [ temp, precip, wind ] simplified

10. Major ROS events in the PNW • Memorial Day 1948 (Vanport flood) • Christmas 1964 • January 1965 • 1975–76 • 1977 • 1980

11. Major ROS events in the PNW • 1983 • 1989–91 • Feb 1996 • 1996–97 (photo by The Oregonian) • (November 2006 – not really ROS)

12. February 1996

13. February 1996

14. Why does ROS matter? • Important water-input process in the PNW • ROS affects people: • floods • landslides, avalanches • roof loads, transportation, etc. • Geomorphic work (long-term) • People affect the process: • effects of land use, climate change

15. Why does ROS matter? • Issue of hydrologic significance • ROS input relative to simple precipitation • magnitude? • frequency? • geography?

16. Background: previous work • Public & scientific recognition (theme of 1983 Western Snow Conf) • Field studies • Pacific NW, Calif, SE Alaska, Alps, … • Use of instrumental records • weather and snow data • Physical/mathematical modeling • accumulation, melt, infiltration

17. Using the record of ROS events • Limited sites and instruments • National Weather Service • usually temp, precip, snow depth (wind) • typically low elevations • Cooperative Snow Survey (NRCS) • snow courses to SNOTEL • depth & SWE, later temp • typically higher elevations • Most sites only 60+ years max • Record is too short and limited to get a large & broad sample of events

18. Probabilistic modeling • Monte Carlo methods • (capital of Monaco/gambling) • use of random sampling techniques (commonly computer simulation) to obtain approximate solutions for mathematical & physical problems

19. M–C modeling • In essence: • distribution function established from data series (mean, std dev, etc.) • random number  probability of occurrence or exceedance • inversion routine returns the value corresponding to that probability for that function • (repeat …..)

20. M–C modeling, cont’d • Use Monte Carlo simulation to • sample frequency distributions • precip, snow, temp, etc.  initial and hourly conditions during storms • combine with deterministic models • snow accumulation and/or melt • infiltration through snowpack

21. M–C modeling, cont’d • for ROS simulation • advantages • simpler than continuous models • sample from many large populations • simulate long “records” of realizations • limitations • still tied to the actual record (distributions) • watch for false assumptions • Running a virtual experiment

22. The problems • Hydrologic significance • amount of water delivered (WAR) w/r/to precip? • frequency of occurrence? • Elevation • peak ROS zone? • Later • effects of climate change? • vegetation and land use: forests vs clearings?

24. Problem statement, cont’d • Hypothesis 1: at individual sites • low elevation: • F-M-D for WAR »F-M-D for gross Pr? • middle elevation: • F-M-D for WAR> F-M-D for Pr? • high elevation: • F-M-D for WAR < F-M-D for Pr? • null hypothesis: no significant differences

25. Problem statement, cont’d • Hypothesis 2: by elevation • if hypotheses 1 not rejected • can find the peak ROS zone • where F-M-D for WAR is max > F-M-D for Pr? • null hypothesis: • no significant differences among elevations

26. Objectives • Create a computer-based model • M–C simulation for probabilistic factors • choose weather & snow conditions • deterministic parts • calculate snow accumulation and melt • track percolation of rain + SM • keep account of hourly values • store conditions and output for analysis

27. Objectives, cont’d • Collect hydrometeorological data • storm: precip, duration, temp, etc. • snow: depth, SWE, etc. • Use these data to generate frequency distributions for the model

28. Objectives, cont’d • Validate the model • deterministic parts: • against actual ROS events • stochastic parts: • against input parameters • against available frequency distributions at sites (especially Stampede Pass)

29. Objectives, cont’d • Run the model: virtual experiments • test hypotheses • hydrologic significance • elevation zones • (later – climate change, forest vegetation)

30. Study region • Data to feed the model • area: west-central Washington Cascades • Tacoma and Seattle watersheds • data-rich environment • National Weather Service • 7 Coop stations: T, P, snow depth • 1 first-order site

33. Stampede Pass • NWS airways obs site • 3958 ft / 1206 m (1065 m eff elev) • T, P, W, snow, etc. • hourly or better • staffed: high-quality observations • almost continuous since mid-1940s • snow course & pillow downhill (3860 ft / 1175 m)

37. Snow measurement • 20 courses • 8 SNOTEL • many co-located • 10 yr record

39. Cascades terrain • Swath 1 (south) • Mitchell & Montgomery, Quaternary Research, 2005

41. Modeling of ROS • Extension to long times and large areas • models + weather records  long series of realizations • Problems • requirements for input data • spatial extrapolations difficult • Not a ROS model, exactly • (Still can’t answer some questions)

42. Model architecture • Parameters, random numbers, codes • Probabilistic section: calculate values • probabilities from random numbers • inversion  values • Deterministic section • snow accum / melt section • infiltration section

47. Model input, cont’d • Initial snow depth and SWE • (1990 Western Snow Conf paper) • mixed distribution • probability of no snow P [0] • log-normal distribution of non–0 values • trend surfaces for parameters • functions of date and elevation