Transcript Snow Model Terms

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
Precipitation
and
Air Temperature
Rain
or
Snow
Accumulated
Snow Cover
Rain
on
Bare
Ground
Energy Exchange
at
Snow-Air
Interface
Areal Extent
of the
Snow Cover
Deficit = 0
Snow Cover
Heat Deficit
Ground
Melt
Rain
Plus
Melt
C2
Snow Cover
Outflow
Liquid Water
Storage
Transmission
of
Excess Water
Snow Model Energy Balance


Net Radiation Transfers
Ground Heat Transfer
Latent Heat Transfer
Mass Change
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)]
+
C
80
* Px * Tw
+ Qg
 = Stefan-Boltzmann Constant
 = Psychometric Constant
C = Specific Heat (water or ice)
Normally, To, Q, and Qg are unknown, other terms are
measured or estimated
C2
Snowmelt During Rain-on-snow
Periods
M =
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)
MFMAX  MFMIN
 n * 2
 sin
Mf = 

2
 366
 MFMAX  MFMIN  t
*
*

 6
2

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
C2
Seasonal Melt Factor Variation
MFMAX
Melt Factor
Contiguous
United
States
Alaska
MFMIN
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
C2
Snow Cover Areal Depletion Curve
Mean Areal Water-Equivalent/Ai
1.0
0.8
Snow Cover
Depletion Curve
0.6
Amount
of
New
Snow
0.4
0.2
Effect of Snowfall
on Partially Bare Area
0.0
20
40
60
80
Areal Extent of Snow Cover (percent)
C2
100
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
C2