Snow Processes and ModellingSnow Processes and Modelling

John PomeroyJohn PomeroyCentre for HydrologyCentre for Hydrology

University of Saskatchewan, SaskatoonUniversity of Saskatchewan, Saskatoonand collaboratorsand collaborators

Richard Essery (U Wales), Kevin Shook (U Saskatchewan)Richard Essery (U Wales), Kevin Shook (U Saskatchewan)and studentsand students

Dan Bewley, Pablo Dan Bewley, Pablo DornesDornes, Xing Fang, Rick Janowicz, , Xing Fang, Rick Janowicz, Warren Helgason, Nicholas Warren Helgason, Nicholas KinarKinar

Hydrological Science Contributions Hydrological Science Contributions to IPYto IPY

Improved predictionImproved prediction of terrestrial snow and soil of terrestrial snow and soil frost, freshwater flux to the ocean, surface frost, freshwater flux to the ocean, surface hydrometeorologyhydrometeorologyHow might we better predict? By improving theHow might we better predict? By improving the

understanding of polar snow and hydrological understanding of polar snow and hydrological processes, andprocesses, andparameterization of these processes so that they can parameterization of these processes so that they can be better included in hydrological, land surface and be better included in hydrological, land surface and climate numerical models of the earth systemclimate numerical models of the earth systemobservation of key physical variables that drive the observation of key physical variables that drive the polar hydrological cycle: e.g. snowfall polar hydrological cycle: e.g. snowfall

Snow Hydrology Prediction in Snow Hydrology Prediction in Polar RegionsPolar Regions

Want to know: Want to know: rate, durationrate, duration and and timingtiming of of arealareal snowmeltsnowmeltSnow accumulation and Spatial DistributionSnow accumulation and Spatial Distribution

SnowfallSnowfallSnow redistribution by wind and vegetationSnow redistribution by wind and vegetation

Blowing snowBlowing snowIntercepted SnowIntercepted Snow

Snowmelt energeticsSnowmelt energeticsEnergy for snowmelt: radiation, turbulent transfer, advectionEnergy for snowmelt: radiation, turbulent transfer, advectionInfluence of vegetation on radiation and air movementInfluence of vegetation on radiation and air movement

Snow Covered Area DepletionSnow Covered Area DepletionControlled by spatial frequency distributions of SWE and Melt EnControlled by spatial frequency distributions of SWE and Melt Energyergy

Climate changeClimate change is rapidly altering polar snow and is rapidly altering polar snow and increasing vegetation cover and so a physically based increasing vegetation cover and so a physically based approach is necessary for prediction approach is necessary for prediction SnowSnow--Vegetation InteractionsVegetation Interactions are exceedingly complex and are exceedingly complex and not always well represented in modelsnot always well represented in models

IP3 Cold Regions IP3 Cold Regions Research BasinsResearch Basins

Trail Valley Creek, arctic tundra

Havikpak Creek, taiga woodland

Baker Creek, Subarctic shield lakes

Wolf Creek, subarctic tundra cordillera

Scotty Creek, permafrost wetlands

Lake O’Hara, wet alpine

Marmot Creek, Dry subalpine

Peyto Creek, glacierized alpine

Polar Snow Research Basins: IP3, Arctic HydraPolar Snow Research Basins: IP3, Arctic Hydra

Trail Valley Creek, NWT

Wolf Creek, Yukon

Havikpak Creek, NWT

IP3 = Improved Processes & Parameterisationfor Prediction in Cold Regions Network

Arctic Hydra = Canadian IPY Hydrology

Surface Snow ObservationsSurface Snow Observations

Complex terrain Simple Terrain Complex terrain Simple Terrain

Granger Basin Grid ElevationGranger Basin Grid ElevationNorth Face

Valley Bottom

South Face

Spring SWE from Spring SWE from GriddedGriddedObservations (5 m spacing)Observations (5 m spacing)

0 50 100 150 200 250 300 350 4000

50

100

0

100

300

500

Snow Water Equivalent mm

North Face Valley Bottom South Face

Janowicz & Pomeroy, in preparation

Snow Patches, Granger Basin, Wolf Snow Patches, Granger Basin, Wolf Creek, 2001Creek, 2001

Perimeter = 3.9043 Area0.7014

R2 = 0.99Dp=1.4

1

10

100

1000

0.1 1 10 100 1000Area (m)

Per

imet

er (m

)

Granger, Pomeroy, Parviainen, 2002

SelfSelf--similar Snow Depthsimilar Snow Depth

0.1

1

10

0.1 1 10 100 1000 10000Sampling Distance (m)

0.1 m (Stubble SE-NW)1 m (Stubble NW-SE)1 m (Stubble NE-SW)

FractalSection

Random SectionCutoff Length

sD(Depth

StandardDeviation)

(cm)

Shook and Gray, 1996

Acoustic Determination of SWE

1

2

3

•Application of digital signal processing adapted from Frequency-Modulated Continuous-Wave (FMCW) Radar

•continuous sound pulse in the audible frequency range (20 Hz to 20 kHz)

Kinar and Pomeroy, 2007

Original and Reflected Waves

Distance to Each Layer of Distance to Each Layer of SnowpackSnowpack

Calculated in a fashion similar to FMCW radar:Calculated in a fashion similar to FMCW radar:

⇒

• Using Biot’s Theory can estimate density of each layer of the snowpack.

•Using Berryman’s Relationship can estimate tortuosity.

Interface Number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Tortu

osity

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Depth (cm)

0 20 40 60 80

SW

E (m

m)

0

5

10

15

20

25

Total Depth-Integrated SWE: 92.62 mm

Interface Number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Den

sity

(kg

m-3

)

0

100

200

300

400

500

Tortuosity Density

SWE

Saskatchewan Sites

86.02 =r

Lake O’Hara Sites

81.02 =r

Saskatchewan

British Columbia

Kinar and Pomeroy Hydrological Processes 2007

Blowing Snow Blowing Snow

Blowing Snow: Transport, Blowing Snow: Transport, Redistribution and Sublimation of SnowRedistribution and Sublimation of Snow

Saltation of SnowSaltation of Snow

Pomeroy and Gray, Water Resources Research, 1990

Turbulent Suspension of SnowTurbulent Suspension of Snow

Pomeroy and Male, J Hydrol, 1992

Probability of Blowing Snow Occurrence Probability of Blowing Snow Occurrence Depends on Wind Speed and Air TemperatureDepends on Wind Speed and Air Temperature

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Wind Speed (m/s)

Blo

win

g S

now

O

ccur

renc

e P

roba

bilit

y

T = -25T = -15T = -5T = -25T = -15T= -5

I = 2

Total Snow Transport Total Snow Transport (saltation + suspension)(saltation + suspension)

0.0001

0.001

0.01

0.1

1

10

100

1000

0 5 10 15 20

Wind Speed (m/s)

Tra

nspo

rt R

ate

(g/m

s)

-1 °C-15 °C-30 °C

Fresh snow

0.0001

0.001

0.01

0.1

1

10

100

1000

0 5 10 15 20

Wind Speed (m/s)T

rans

port

Rat

e (g

/m s

)

1 Hour30 Hours100 Hours

T = -10 oC

Pomeroy and Li, J Geophys Res, 2000

Sublimation of Blowing SnowSublimation of Blowing Snow

Rapid turbulent Rapid turbulent transfer to transfer to snow particles, snow particles, high surface area to high surface area to mass ratiomass ratioRadiation is Radiation is unimportantunimportantVery sensitive to Very sensitive to temperature and water vapour deficittemperature and water vapour deficitWhere large scale entrainment Where large scale entrainment andand large large fetches then high sublimation rates can fetches then high sublimation rates can develop develop

Pomeroy, Gray & Male J Hydrol 1993

Sublimation of Blowing SnowSublimation of Blowing Snow

0.0001

0.001

0.01

0.1

1

10

0 5 10 15 20Wind Speed (m/s)

Subl

imat

ion

Rat

e (g

/m2 s

)

-1 °C-15 °C-30 °C

Fresh snowRH = 80%

0.0001

0.001

0.01

0.1

1

10

0 5 10 15 20Wind Speed (m/s)

Subl

imat

ion

Rat

e (g

/m2 s)

70% RH80% RH90% RH

Fresh snowT = -10 oC

Pomeroy and Li, J Geophys Res, 2000

Can ablate several mm per day of SWE

Macroscale Simulated Annual Sublimation Macroscale Simulated Annual Sublimation from Blowing Snow: from Blowing Snow: Sensitivity to fetch Sensitivity to fetch -- AlaskaAlaska

Bowling, Pomeroy & Lettenmaier, J Hydrometeorol 2004

Wind Redistribution of Snow over Wind Redistribution of Snow over Complex LandscapesComplex Landscapes

Blowing snow Blowing snow transport, and transport, and sublimation sublimation relocate snow relocate snow across the across the landscape from landscape from sourcessources to to sinkssinksdepending on depending on fetch, orientation fetch, orientation and area.and area.

Source SinkSnowfall Sublimation Snowfall

Deposition Erosion/ Deposition

Transport Transport

Snowpack

Ground

Source

SinkPomeroy & Li Proc WSC 1997

How to Model Blowing Snow over How to Model Blowing Snow over Complex Landscapes?Complex Landscapes?

Dual Scale Approach Dual Scale Approach

~250,000 grid cells 7 HRU

Spatially Distributed Snow RedistributionSpatially Distributed Snow Redistribution

Snow mass balance equation

St Denis, Saskatchewan

Results Results –– Spatially distributed SWESpatially distributed SWE

Fang and Pomeroy, Hydrol Proc, in preparation

Spatially distributed SWE contSpatially distributed SWE cont’’

Spatially distributed SWE contSpatially distributed SWE cont’’

Spatially distributed SWE contSpatially distributed SWE cont’’

Spatially distributed SWE contSpatially distributed SWE cont’’

Spatially distributed SWE contSpatially distributed SWE cont’’

Spatially distributed SWE contSpatially distributed SWE cont’’

Spatially distributed SWE contSpatially distributed SWE cont’’

Spatially distributed SWE contSpatially distributed SWE cont’’

Spatial Pattern of Blowing Snow SublimationSpatial Pattern of Blowing Snow Sublimation

Comparison of Model to ObservationsComparison of Model to Observations

Blowing snow in the ArcticBlowing snow in the Arctic

Havikpak Creek, Inuvik, Havikpak Creek, Inuvik, NWT sparse woodland, NWT sparse woodland, some shrub and open some shrub and open tundratundraTrail Valley Creek, 50 km Trail Valley Creek, 50 km north of Inuvik, shrub and north of Inuvik, shrub and open tundra, some open tundra, some sparse woodlandsparse woodlandSnow surveys, blowing Snow surveys, blowing snow modellingsnow modelling

Pomeroy, Marsh, Gray Hydrol Proc 1997

Topography Vegetation

2 km

Blowing Snow Redistributes Blowing Snow Redistributes Snow over Complex LandscapesSnow over Complex Landscapes

Landscape Contribution to Annual Snow Accumulation

0

20

40

60

80

100

120

140

160

180

Havikpak Trail Valley

mm

SW

E/m

² of b

asin

Forest

Drift

Taiga

Shrub Tundra

Lowland Tundra

Upland Tundra

Variable Wind Speed over Complex Variable Wind Speed over Complex TerrainTerrain

MS3DJH/3R Windflow MS3DJH/3R Windflow model applied to model applied to Trail Valley Creek, Trail Valley Creek, NWTNWT

Normalised Wind speed from North

Essery, Li & Pomeroy, 1999

Distributed Distributed Blowing Snow Blowing Snow

Model Model Seasonal Seasonal

Snow Snow Accumulation Accumulation Trail Valley Trail Valley Creek, NWTCreek, NWT

light tones are light tones are deeper snowdeeper snow

0

200

400

600

800

Open tundra Shrub tundra Taiga

SW

E (m

m)

Survey

Model

No sublimation

Distributed Blowing Snow Model Distributed Blowing Snow Model ––seasonal evaluation over complex terrain for areal seasonal evaluation over complex terrain for areal

snow accumulation estimatessnow accumulation estimates

Distribution of snow accumulation from Blowing Distribution of snow accumulation from Blowing Snow Model Snow Model –– realistic frequency distributionsrealistic frequency distributions

05

1015202530

0 50 100 150 200 250 300

SWE (mm)

% a

rea

Open tundra and lakes

Shrub tundra and taiga

snowfall

Calculated Snow AccumulationCalculated Snow Accumulation

05

1015202530

0 50 100 150 200 250 300

SWE (mm)

% a

rea

Open tundra and lakes

Shrub tundra and taigaTrail Valley Creek, NWT

0

200

400

600

800

Open tundra Shrub tundra TaigaS

WE

(mm

)

Survey

Model

No sublimation

Essery, Li, PomeroyHydrol Proc 1999

0

100

200

300

0 0.5 1 1.5 2

Shrub height (m)

SW

E (m

m)

Shrubs

Snowfall

Open

0

100

200

300

0 0.2 0.4 0.6 0.8 1

Shrub fraction

SW

E (m

m)

Effect of Changing Tundra Shrub Cover and Height on Snow Accumulation using a Blowing Snow Model

Simulation over Trail Valley Creek

Essery & Pomeroy, J Hydrometeorol 2004

Blowing Snow in Arctic MountainsBlowing Snow in Arctic Mountains

Inter-basin water transfer

Transport of snowto drifts

Supports glaciers,late lying snowfields

Alpine Tundra Ridgetop Alpine Tundra Ridgetop –– most most snowfall eroded by blowing snowsnowfall eroded by blowing snow

0

20

40

60

80

100

120

140

160

180

23-Sep 23-Oct 22-Nov 22-Dec 21-Jan 20-Feb 22-Mar 21-Apr 21-May

Snow

Wat

er E

quiv

alen

t (m

m)

Snow Accumulation

Snowfall

Source

0 500 1000 1500 2000 2500 30000

500

1000

1500

2000

2500

3000

0 500 1000 1500 2000 2500 30000

500

1000

1500

2000

2500

3000

Linear simulation of westerly flow over Wolf Creek, Yukon

Windspeed Direction

3 km

Essery and Pomeroy, in preparation

3 km

Simulation of Hillslope Snowdrift

Distributed Blowing Snow Model

Mountain Drift Simulation Mountain Drift Simulation -- YukonYukon

1340

1360

1380

1400

1420

0 50 100 150 200 250 300 350 400

Horizontal distance (m)

Ele

vatio

n (m

) AltimeterDEM

Wind

0

50

100

150

200

0 100 200 300 400

Horizontal distance (m)

SW

E (m

m)

ObservedSimulated

Snowmelt RateSnowmelt RateAt a point controlled by At a point controlled by energy inputs, snow energy inputs, snow internal energy and internal energy and available snow massavailable snow massOver some area controlled Over some area controlled by the spatial distribution by the spatial distribution of snow mass (including of snow mass (including snow covered area) and snow covered area) and energy inputs energy inputs Strong influence of Strong influence of topography and vegetationtopography and vegetation

Turbulence generation Turbulence generation mechanisms in mountainsmechanisms in mountains

upper level winds

valley winds

surface winds (internal B-L)tributary valley

winds

flux tower in clearing

strong shear zone

transported turbulence

Roughness Length (zRoughness Length (z0m0m))

0 10 20 30 4010

-6

10-5

10-4

10-3

10-2

10-1

100

U u* -1

z0m

(m)

Prairie

0 10 20 30 4010

-6

10-5

10-4

10-3

10-2

10-1

100

U u* -1

z0m

(m)

Alpine Ridge

0 10 20 30 4010

-6

10-5

10-4

10-3

10-2

10-1

100

U u* -1

z0m

(m)

Lake

0 10 20 30 4010

-6

10-5

10-4

10-3

10-2

10-1

100

U u* -1

z0m

(m)

Meadow

( )⎥⎦

⎤⎢⎣

⎡−⎟⎠⎞

⎜⎝⎛= ζψmmz

zku

U0

ln1*

0 < ζ < 0.1

expected range for snow

Helgason and Pomeroy, in preparation

Typical Estimation ResultsTypical Estimation Results

-60 -50 -40 -30 -20 -10 0-60

-50

-40

-30

-20

-10

0

Modeled Flux (W m-2)

Mea

sure

d Fl

ux (W

m-2

)Sensible heat flux in meadow site (mountain valley)

Incoming Longwave in MountainsIncoming Longwave in Mountains

0.5 0.6 0.7 0.8 0.9 1Vf

0

5

10

15

20

25

30

Ts (°

C)

Percent increase in longwave irradiance due to terrain emission due to sky view factor (Vf) and surface temperature (Ts).

Air temperature is 0°C and the clear sky emissivity is 0.65

Sicart et al. 2006 Hydrological Processes Thermal IR Image

Sky View Factor

Psychrometric Outgoing Longwave Psychrometric Outgoing Longwave Formulation for SnowFormulation for Snow

-40-35

-30-25

-20-15

-10-5

05

1017-Feb 22-Feb 27-Feb 03-Mar 08-Mar 13-Mar 18-Mar

SST

C

irtcmodel

( ) ( )[ ]apa

asaaaas rLcT

rPTQQLTLWTT/)(

/,3

sat4

ρεσρσε

Δ++−+−↓

+=

Pomeroy et al., in preparation

0

100

200

300

400

74 75 76

Day (2005)

SW

(W/m

2 )

0

200

400

600

800

1000

123 124 125

Day (2003)

SW (W

/m2 )

Solar radiation to snow beneath shrubs and trees

Wol

f Cre

ek s

hrub

s

Mar

mot

Cre

ek le

vel f

ores

t

Pomeroy et al., J Hydrometeorol, submitted

Modelling solar radiation to snow beneath shrubs

Aerial photograph fromModel Helicopter

Shadow simulation

Bewley, Pomeroy, Essery, Arctic, Antarctic and Alpine Research, 2007

-200

-100

0

100

200

300

400

105 110 115 120 125 130 135

Day

Sens

ible

Hea

t (W

/m2 )

105 110 115 120 125 130 135

Day

0

0.2

0.4

0.6

0.8

Snow

dep

th (m

)

Granger Basin plateau Granger Basin valley

Bewley PhD Thesis 2006

1

15

29

43

57

71

85

99

0 1 2 3Total Melt/ mean SWE

CVSWE = 0.2CVSWE = 0.3CVSWE = 0.4CVSWE = 0.5CVSWE = 0.7

Snow-cover(%)

Hypothetical Snow Covered Area Hypothetical Snow Covered Area Depletion CurvesDepletion Curves

Spatial Covariance between SWE (S) and Melt Spatial Covariance between SWE (S) and Melt Energy (M) Biases SWE Estimates during AblationEnergy (M) Biases SWE Estimates during Ablation

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8Melt Period

Snow

Wat

er E

quiv

alen

t (m

m)

A Uniform S, M

B Variable S

C Variable M

D Positive Covariance

E Negative Covariance

Complex Terrain SnowmeltComplex Terrain Snowmelt

-20

0

20

40

60

80

100

120

Mean Energy (W/m2)

ValleyBottom

South Face North Face

Melt + InternalNet RadiationGround HeatSensible HeatLatent Heat

20o slopesSouth Face

North FaceValley Bottom

Solution: landscape units

Cold Regions Hydrological Model Cold Regions Hydrological Model Water Balance Wolf Creek-Alpine 1998/99

-100

-50

0

50

100

150

200

250

22-Sep 11-Nov 31-Dec 19-Feb 10-Apr 30-May

mm

CRHM RunoffCRHM SnowfallCRHM InfiltrationCRHM M eltCRHM Ground SWEM easured M eltM easured SWE

Pomeroy et al., Hydrol Proc, in press

snowfall, blowing snow, snowmelt, infiltration to frozen soils, runoff

Modelling ApproachModelling ApproachAggregated vs. Distributed

Distributed models can capture snowmelt synchronicity effects

Basin Areal SWEBasin Areal SWENorth Face, South Face, and North Face, South Face, and

Valley BottomValley Bottom2002

Time [days]

4/17/02 4/24/02 5/1/02 5/8/02 5/15/02 5/22/02 5/29/02 6/5/02

SWE

[mm

]

0

20

40

60

80

100

120

140

160

180

Obs SWEAggregatedDistributed

2003

Time [days]

4/17/03 4/26/03 5/05/03 5/14/03 5/23/03 6/01/03

SWE

[mm

]

0

50

100

150

200

250

Obs SWEAggregatedDistributed

We cannot model average snowmelt with aggregated approaches in complex terrain

Dornes, Pomeroy & Pietroniro, Hydrol Sci J, submitted

Granger Creek DischargeGranger Creek Discharge2002

Time [days]

5/01/02 5/09/02 5/17/02 5/25/02 6/02/02 6/10/02

Q [m

3 /s]

0.0

0.2

0.4

0.6

0.8

1.0ObsAggregatedDistributed

2003

Time [days]

4/17/03 4/26/03 5/05/03 5/14/03 5/23/03 6/01/03 Q

[m3 /

s]0.0

0.1

0.2

0.3

0.4

0.5ObsAggregatedDistributed

We can more reliably model spring streamflow using distributed snowmelt calculations in complex terrain

Dornes, Pomeroy & Pietroniro, Hydrol Sci J, submitted

Process Implications for Polar Process Implications for Polar Hydrological ModellingHydrological Modelling

Slope, aspect and altitude based landscape Slope, aspect and altitude based landscape units for modelsunits for modelsSnow transport between landscape unitsSnow transport between landscape unitsAccurate sublimation parameterisations Accurate sublimation parameterisations ‘‘PerfectPerfect’’ process physics will fail without process physics will fail without reference to appropriate scales, variability and reference to appropriate scales, variability and covariabilitycovariability of processes, inputs, outputs.of processes, inputs, outputs.Appropriate level of complexity derived from Appropriate level of complexity derived from understanding both process sensitivity and understanding both process sensitivity and realistic expectations of upscaled grid behaviourrealistic expectations of upscaled grid behaviour

Implications for Polar Snow Implications for Polar Snow Hydrology MissionHydrology Mission

Spatial variability of SWE and melt is extremely Spatial variability of SWE and melt is extremely high and would require satellite resolution of <10 high and would require satellite resolution of <10 m and ability to detect extremely high SWE (~ m and ability to detect extremely high SWE (~ 2000 mm SWE) and mixed wet and cold snow.2000 mm SWE) and mixed wet and cold snow.Blowing snow parameterisation for land surface Blowing snow parameterisation for land surface hydrology models hydrology models –– need snowfall inputneed snowfall inputWith a DEM, snowfall and meteorological fields it With a DEM, snowfall and meteorological fields it is possible to calculate at the process scaleis possible to calculate at the process scale

SWE distributionSWE distributionMelt distributionMelt distribution

Aggregated results useful for LSS, polar Aggregated results useful for LSS, polar hydrologyhydrology