Snow Models and Snowmelt Runoff

1. C2 NWS Snow Model

2. C2 Snow Model Terms SWE - Snow water equivalent AESC - Areal extent of snow cover Heat Deficit - Energy required to bring the snowpack to isothermal 0 C Lapse Rate - Change in temperature with elevation Snow Course - Regular location where snow measurements are taken Energy - 8 cal/cm 2 = Energy required to melt 1 mm of ice

3. C2 Various Snowmelt Models Available WMO Intercomparison of Models of Snowmelt Runoff (WMO Operational Hydrology Report No. 23, WMO - No. 646, 1986) All operational models use air temperature to compute snowmelt

4. C2 NWSRFS Snow Model Can be applied at a point (need observed water-equivalent) Can be used with a rainfall/runoff model to simulate streamflow (apply model to each elevation zone)

5. C2 Updating Model State Variables Need snow course data and/or areal extent of snow cover Use historical data to develop relationships between simulated and observed values Use relationship to update operationally Water-equivalent prior to start of melt Areal extent during melt season

6. C2 Data Requirements Air Temperature Used to compute snowmelt and determine the form of precipitation (rain or snow) Precipitation Used to determine amount of snowfall and amount of rain-on-snow Daily total adequate (short interval better if basin shows a fast response during rain-on-snow events) Other Data (when available) Snow course (water-equivalent) Areal extent of snow cover (satellite)

7. C2 Basin Subdivision by Elevation Number of Elevation Zones If not modeling areal extent Approximately one zone for every 300 meters for portion of basin with significant snow Larger zones for portions with infrequent snow If modeling areal extent Two to three zones normally sufficient Zones should not exceed about 1,000 to 1,2000 meters Selecting Zones (modeling areal extent) Snow always contributes to runoff Snow contributes to runoff only during big snow years Little or no snow occurs

8. C2 NWS Snow Accumulation and Ablation Model Precipitation and Air Temperature Rain or Snow Accumulated Snow Cover Energy Exchange at Snow-Air Interface Snow Cover Heat Deficit Ground Melt Snow Cover Outflow Rain Plus Melt Rain on Bare Ground Areal Extent of the Snow Cover Liquid Water Storage Transmission of Excess Water Deficit = 0

9. C2 Snow Model Energy Balance Ground Heat Transfer Mass Change Net Radiation Transfers Latent Heat Transfer Sensible Heat Transfer

10. C2 Snow Cover Energy Balance Equation Q n + Q e + Q h + Q g + Q m = Q Q n = net radiation transfer Q e = latent heat transfer Q h = sensible heat transfer Q g = heat transfer across snow-soil interface Q m = heat transfer by mass changes (advected heat) Q = change in the heat storage of the snow cover

11. C2 Q n + Q e + Q h + Q g + Q m = Q Q n = net radiation transfer = ( Q i , Q a , A, T o ) Q i = incoming solar radiation Q a = incoming long-wave radiation A = Albedo T o = snow surface temperature

12. C2 Q n + Q e + Q h + Q g + Q m = Q Q e = latent heat transfer = (e a , e o , a ) e o :e a = vapor pressure gradient a = wind speed

13. C2 Q n + Q e + Q h + Q g + Q m = Q Q h = sensible heat transfer = (T a , T o , a ) T a = air temperature T o = snow surface temperature a = wind speed

14. C2 Q n + Q e + Q h + Q g + Q m = Q Q g = heat transfer at snow-soil boundary = (T g , T s ) T g = ground temperature T s = bottom of snowpack temperature

15. C2 Q n + Q e + Q h + Q g + Q m = Q Q m = mass change heat transfer (advected heat) = (P x , T w ) P x = water equivalent of rain T w = wet bulb temperature

16. C2 Q n + Q e + Q h + Q g + Q m = Q Q = Q i * (1.0 - A) + Q a - t * 1.0 * * (T o + 273) 4 + 8.5 * ( a ) * [(e a - e o ) + * (T a - T o )] + * P x * T w + Q g = Stefan-Boltzmann Constant = Psychometric Constant C = Specific Heat (water or ice) Normally, T o , Q, and Q g are unknown, other terms are measured or estimated

17. C2 Snowmelt During Rain-on-snow Periods M = 6.12 *10 -10 * t * [(T a + 273) 4 - 273 4 ] + (0.0125 * P x * T a ) + 8.5 * UADJ * t/6 * [(0.9 * e sat - 6.11) + 0.00057 * P a * T a ] M = snowmelt (mm) t = Computational time interval (hours) UADJ = average wind function during rain-on-snow periods (mm * mb -1 * 6hr -1 ) T a = temperature of the air (C) P x = water-equivalent of precipitation (mm) e sat = saturation vapor pressure at the sir temperature (mb) P a = atmosphere pressure (mb)

18. C2 Snowmelt During Non-rain Periods M = M f * (T a - MBASE) M f = melt factor (mm * C -1 * t -1 ) MBASE = base temperature where melt begins ( C) M f = MFMAX = maximum melt factor, assumed to occur on June 21 (mm * C -1 * 6hr -1 ) MFMIN = minimum melt factor, assumed to occur on December 21 (mm * C -1 * 6hr -1 ) n = day number beginning with March 21

19. C2 Seasonal Melt Factor Variation Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep MFMAX MFMIN Alaska Contiguous United States Melt Factor

20. C2 Snow Cover Areal Depletion Curve 1.0 0.8 0.6 0.4 0.2 0.0 20 40 60 80 100 Mean Areal Water-Equivalent/A i Areal Extent of Snow Cover (percent) Effect of Snowfall on Partially Bare Area Snow Cover Depletion Curve Amount of New Snow

21. C2 Snow Model - Major Parameters SCF Multiplying factor that adjusts precipitation data for gage catch deficiencies during periods of snowfall and implicitly accounts for net vapor transfer and interception losses At a point, SCF also implicitly accounts for gains or losses due to drifting MFMAX Maximum melt factor during non-rain periods, assumed to occur on June 21 (mm * C -1 * 6hr -1 ) MFMIN Minimum melt factor during non-rain periods, assumed to occur on December 21 (mm * C -1 * 6hr -1 )

22. C2 Snow Model - Major Parameters (continued) UADJ The average wind function during rain-on-snow periods (mm * mb -1 * 6hr -1 ) SI The mean areal water-equivalent above which there is always 100 percent areal snow cover (mm) Areal Depletion Curve Curve that defines the areal extent of the snow cover as a function of how much of the original snow cover remains Implicitly accounts for the reduction in the melt rate that occurs with a decrease in the areal extent of the snow cover