C2

NWS Snow Model

C2

Snow Model Terms SWE - Snow water equivalent

AESC - Areal extent of snow cover

Heat Deficit - Energy required to bring the snowpack to isothermal 0º C

Lapse Rate - Change in temperature with elevation

Snow Course - Regular location where snow measurements are taken

Energy - 8 cal/cm2 = Energy required to melt 1 mm of ice

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

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)

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

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)

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

C2

NWS Snow Accumulation and Ablation Model

Precipitationand

Air Temperature

Rainor

Snow

AccumulatedSnow Cover

Energy Exchangeat

Snow-AirInterface

Snow CoverHeat Deficit

GroundMelt

Snow CoverOutflow

RainPlusMelt

Rainon

BareGround

Areal Extentof the

Snow Cover

Liquid WaterStorage

Transmissionof

Excess Water

Deficit = 0

C2

Snow Model Energy Balance

Ground Heat Transfer

Mass Change

Net Radiation Transfers

Latent Heat Transfer

Sensible Heat Transfer

C2

Snow Cover Energy Balance Equation

Qn + Qe + Qh + Qg + Qm = Q

Qn = net radiation transfer

Qe = latent heat transfer

Qh = sensible heat transfer

Qg = heat transfer across snow-soil interface

Qm = heat transfer by mass changes (advected heat)

Q = change in the heat storage of the snow cover

C2

Qn + Qe + Qh + Qg + Qm = Q

Qn = net radiation transfer = (Qi, Qa, A, To)

Qi = incoming solar radiation

Qa = incoming long-wave radiation

A = Albedo

To = snow surface temperature

C2

Qn + Qe + Qh + Qg + Qm = Q

Qe = latent heat transfer = (ea, eo, a)

eo:ea = vapor pressure gradient

a = wind speed

C2

Qn + Qe + Qh + Qg + Qm = Q

Qh = sensible heat transfer = (Ta, To, a)

Ta = air temperature

To = snow surface temperature

a = wind speed

C2

Qn + Qe + Qh + Qg + Qm = Q

Qg = heat transfer at snow-soil boundary = (Tg, Ts)

Tg = ground temperature

Ts = bottom of snowpack temperature

C2

Qn + Qe + Qh + Qg + Qm = Q

Qm = mass change heat transfer (advected heat) = (Px, Tw)

Px = water equivalent of rain

Tw = wet bulb temperature

C2

Qn + Qe + Qh + Qg + Qm = Q

Q = Qi * (1.0 - A) + Qa - t * 1.0 * * (To + 273)4

+ 8.5 * (a) * [(ea - eo) + * (Ta - To)]

+ * Px * Tw

+ Qg

= Stefan-Boltzmann Constant = Psychometric ConstantC = Specific Heat (water or ice)

Normally, To, Q, and Qg are unknown, other terms are measured or estimated

80C

C2

Snowmelt During Rain-on-snow PeriodsM = 6.12 *10-10 * t * [(Ta + 273)4 - 2734]

+ (0.0125 * Px * Ta)

+ 8.5 * UADJ * t/6 * [(0.9 * esat - 6.11) + 0.00057 * Pa * Ta]

M = snowmelt (mm)

t = Computational time interval (hours)

UADJ = average wind function during rain-on-snow periods (mm * mb-1 * 6hr-1)

Ta = temperature of the air (ºC)

Px = water-equivalent of precipitation (mm)

esat = saturation vapor pressure at the sir temperature (mb)

Pa = atmosphere pressure (mb)

C2

Snowmelt During Non-rain Periods

M = Mf * (Ta - MBASE)

Mf = melt factor (mm * ºC-1 * t -1)

MBASE = base temperature where melt begins (ºC)

Mf =

MFMAX = maximum melt factor, assumed to occur on June 21 (mm * ºC-1 * 6hr -1)

MFMIN = minimum melt factor, assumed to occur on December 21 (mm * ºC-1 * 6hr -1)

n = day number beginning with March 21

6t*

2MFMINMFMAX*

3662*nsin

2MFMINMFMAX

C2

Seasonal Melt Factor Variation

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

MFMAX

MFMIN

Alaska

Contiguous United States

Mel

t F

acto

r

C2

Snow Cover Areal Depletion Curve1.0

0.8

0.6

0.4

0.2

0.020 40 60 80 100

Mea

n A

real

Wat

er-E

quiv

alen

t/A

i

Areal Extent of Snow Cover (percent)

Effect of Snowfallon Partially Bare Area

Snow CoverDepletion Curve

Amountof

NewSnow

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 * ºC-1 * 6hr -1)

MFMIN

– Minimum melt factor during non-rain periods, assumed to occur on December 21 (mm * ºC-1 * 6hr -1)

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