simulating areal snowcover depletion and snowmelt runoff in alpine terrain chris debeer and john...

Simulating Areal Snowcover Depletion and Snowmelt Runoff in Alpine Terrain

Chris DeBeer and John Pomeroy

Centre for Hydrology,Department of Geography and Planning

University of Saskatchewan

Background

• Snowmelt runoff from Rocky Mountains is an important water resource

• High uncertainty in the future hydrological

response to climate and/or landcover change

• Important to be able to better understand and predict likely changes for future water management

– Requires robust and physically based models for simulating snow processes

Variability of Alpine Snow Processes

• Complexities in terrain and vegetation affect snow accumulation, redistribution, and melt

– High spatial variability in snow water

equivalent (SWE)– Large variation in energy for snowmelt during

the spring

• Leads to a patchy snowcover as the spring progresses

• Significantly affects timing, rate, and magnitude of meltwater generation

Areal Snowcover Depletion (SCD)

• Melt rate computations applied to a distribution of SWE yield snowcovered area (SCA) over time (SCD curve)

(SWE)dSWEpSCAaM

0

0.01

0.02

0.03

0.04

0.05

0.06

0 100 200 300 400 500 600

SWE (mm)

p (

SW

E)

Ma

100 mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600

Melt depth (mm)

SC

A

Ma

100 mm

Ma

200 mm

Ma

350 mm

Ma

200 mm

Ma

350 mm

SCA = 0.92

SCA = 0.45

SCA = 0.05

Frequency distribution of SWE Derived SCD curve

Problems with SCD Approach in Alpine Terrain

• The approach assumes uniform melt rate over the SWE distribution– Energy balance melt rate computations depend

on snowpack state (e.g. depth, density, SWE, temperature, etc.)

– Melt rates are not uniform in alpine terrain

• Further problems with new snowfall part way through melt

Study Objectives

• Develop new theoretical framework for areal snowcover depletion (SCD) and meltwater generation

• Test framework using observations in alpine basin

• Determine how variability of SWE and snowmelt energy affect areal SCD and meltwater generation

• Incorporate framework within hydrological model and examine influence of variability on hydrograph

Development of Theoretical Framework

• Framework for areal SCD based on lognormal distribution

0

100

200

300

400

500

600

700

800

-4 -2 0 2 4 6

K

SW

E (

mm

)

2

5

10

15

SWE = 200(1+K(0.4))

days

0

0.25

0.5

0.75

1

0 5 10 15 20

Days

SC

A0

1

2

3

4

-3 -2 -1 0 1 2 3 4 5 6

K

SW

E /

SW

E

CV = 0.0

CV = 0.2

CV = 0.4

CV = 0.6

CV = 0.8

CV = 1.0

0 10 50 80 90 95 99 99.9

P

CV)K(1SWESWE

SCD curve from uniform 30 mm/day applied snowmelt

Development of Theoretical Framework

Frequency factor, K

SW

E (

mm

)

Kmin, i Kmin, ii 0

Initial distribution

50

150

200

100

Following melt

Melt depth for 50 mm initial SWE

Melt depth for 100 mm initial SWE

SW

E

Kmin, 1 Kmin, 2 0

Snowmelt

Subsequent accumulation

Foot

Line representing the distribution can be discretized

New snow added uniformly over remaining distribution

1

32

• Framework handles other important aspects of spatial snowmelt and new snowfall during spring

Field Study Site

• Marmot Creek Research Basin, Kananaskis Country, Alberta

Field Study Site

• Focused data collection at Fisera Ridge and Upper Middle Creek

Fisera Ridge

Mt. Allan

Field Methods and Observations

• Data collection over three years (2007-09) involved:– Meteorological observation– Snow surveys– Daily terrestrial photos– Lidar snowcover mapping– Streamflow measurement

Ridgetop Station

North Facing Station

Southeast Facing Station

Field Methods and Observations

• 100’s of snow surveys over 3 years • Setup and maintenance of many

instruments and met stations• Dozen’s of manual stream discharge

measurements

Terrestrial Oblique Photo Correction1) Viewshed mask created from camera perspective

2) DEM projection in camera coordinate system

3) Correspondence established between DEM cells and image pixels

4) Image reprojection in DEM coordinates

2 & 3

1

4

May 7, 2007May 10, 2007May 14, 2007May 17, 2007May 19, 2007May 22, 2007May 26, 2007May 29, 2007May 31, 2007June 2, 2007June 4, 2007June 7, 2007June 10, 2007June 13, 2007June 18, 2007June 21, 2007June 24, 2007June 27, 2007July 1, 2007July 4, 2007July 9, 2007July 13, 2007

Areal Snowcover Observations

Time lapse digital photography used to monitor areal SCD

Snowmelt Modelling and Validation

• Snowpack evolution simulated using the Snobal energy balance model within Cold Regions Hydrological Model (CRHM) platform

Active layer

Lower layer

LvE H K↑ K↓ L↓ L↑ P E

Soil layer

G R

U

U

Shortwave and longwave radiation inputs corrected for slope, aspect, skyview fraction using algorithms in CRHM (Qm = LVE + H - K↑ + K↓ + L↓ - L↑ + G - dU/dt)

Snowmelt Modelling and Validation

• Model performs well for depth, SWE, internal energy

-25

-15

-5

1-Apr 15-Apr 29-Apr 13-May 27-May 10-Jun 24-Jun

Date (2008)

Snow

tem

p (

°C)

Simulated active layer TMeasured active layer TSimulated lower layer TMeasured lower layer T

0

300

600

900


Date (2008)

Depth

(m

m)

Simulated SWE (mm)Measured SWE (mm)

0

1

2

3


Date (2008)

Depth

(m

)

Measured depth (m)

Simulated depth (m)

0

1

2

3


Date (2009)

Depth

(m

)

Measured depth (m)

Simulated depth (m)

0

300

600

900


Date (2009)

Depth

(m

m)

Simulated SWE (mm)

Measured SWE (mm)

-15

-10

-5

0


Date (2009)

Snow

tem

p (

°C)

Simulated active layer TMeasured active layer TSimulated lower layer TMeasured lower layer T

2008 2009

Effects of Snow Mass and Internal Energy

• Differences in initial state have large influence on computation of snowmelt timing and rate

-8

-6

-4

-2

0

22-Apr 23-Apr 24-Apr 25-Apr 26-Apr 27-Apr 28-Apr 29-Apr 30-Apr 1-May 2-May 3-May 4-May 5-May 6-May

Date (2008)

Co

ld c

on

ten

t (M

J/m

2 )

Sn

ow

pa

ck te

mp

era

ture

(°C

) Shallow CC Intermediate CC Deep CC Shallow T Intermediate T Deep T

0

5

10

15

20

22-Apr 23-Apr 24-Apr 25-Apr 26-Apr 27-Apr 28-Apr 29-Apr 30-Apr 1-May 2-May 3-May 4-May 5-May

Date (2008)

Me

lt ra

te (

mm

/da

y)

Shallow snow

Intermediate snow

Deep snow

Cold Content: Energy required to bring snowpack to 0 °C and satisfy liquid water holding capacity

Spatial – Temporal Snowmelt Variability

0

3

6

9

12

15

0 400 800 1200

SWE (mm)

Me

lt ra

te (

mm

/da

y) a

26-Apr

28-Apr

30-Apr

2-May

4-May

0

10

20

30

40

50

0 400 800 1200

SWE (mm)

Me

lt ra

te (

mm

/da

y) a 14-May 16-May

18-May 16-Jun

21-Jun

0

3

6

9

12

15

0 400 800 1200

SWE (mm)

Me

lt ra

te (

mm

/da

y) a 26-Apr

28-Apr

30-Apr

2-May

4-May

0

10

20

30

40

50

0 400 800 1200

SWE (mm)

Me

lt ra

te (

mm

/da

y) a

14-May 16-May18-May 16-Jun

21-Jun

SE-facing slope

N-facing slope

• Differences in melt energy and SWE lead to large differences in snowmelt that change over time

Landscape Disaggregation for SCD Simulation

• SWE values on different slopes fit theoretical lognormal distribution

SWE = 157.0K + 223.6

R2 = 0.96

0

500

1000

1500

2000

-2.0 0.0 2.0 4.0 6.0 8.0 10.0

K

SW

E (

mm

)

0

0.05

0.1

0.15

0.2

0.25

0.3

015

030

045

060

075

090

010

5012

0013

5015

00

SWE (mm)

f (S

WE

)

SWEmeasurements

Theoreticaldistribution

SWE = 273.5K + 290.9

R2 = 0.97

0

500

1000

1500

2000

2500

-5.0 0.0 5.0 10.0 15.0

K

SW

E (

mm

)

0

0.05

0.1

0.15

0.2

0.25

015

030

045

060

075

090

010

5012

0013

5015

00

SWE (mm)

f (S

WE

)

SWEmeasurements

Theoreticaldistribution

S-facing slope

N-facing slope

Simulation of Areal SCD over Landscape

• Framework applied to predict areal SCD

• Results were improved by considering separate distributions and melt rates on each slope

0

0.5

1

10-May 20-May 30-May 9-Jun 19-Jun 29-Jun 9-JulDate (2008)

SC

A fr

act

ion

Observed overall SCD curve Simulated overall SCD curve

NS = 0.78RMSE = 0.15

0

0.5

1

10-May 20-May 30-May 9-Jun 19-Jun 29-Jun 9-JulDate (2008)

SC

A fr

act

ion

Observed north facing SCD curve Simulated north facing SCD curve

NS = 0.89RMSE = 0.10

0

0.5

1

10-May 20-May 30-May 9-Jun 19-Jun 29-Jun 9-Jul

Date (2008)

SC

A fr

act

ion

Observed south facing SCD curve Simulated south facing SCD curve

NS = 0.84RMSE = 0.16

0

0.5

1


Date (2008)

SC

A fr

act

ion

Observed east facing SCD curve Simulated east facing SCD curve

NS = 0.94RMSE = 0.06

Overall basin

Northfacing

Southfacing

Eastfacing

0

0.5

1


Date (2008)

SC

A fr

act

ion

Simulated overal SCD curve Observed overall SCD curve

NS = 0.92

RMSE = 0.09

Influence of “Inhomogeneous” Snowmelt

• Earlier and more rapid melt of shallow snow on some slopes led to an initial acceleration of SCD

0.25

0.5

0.75

1

24-Apr 27-Apr 30-Apr 3-May 6-May

Date (2008)

SC

A fr

act

ion

Inhomogenous 150 mm initial 300 mm initial

850 mm initial Observed

S facing slope

0.25

0.5

0.75

1


Date (2008)

SC

A fr

act

ion



N facing slope

0.25

0.5

0.75

1


Date (2008)

SC

A fr

act

ion



Overall basin

• Variability in melt over landscape and SWE dist’s. affects location, extent, and timing of meltwater generating area

0 – 5mm/day

5 – 10mm/day

10 – 20mm/day

exposedground

forestedareas

cliffs

April 26 April 29

May 2 May 5

Spatial Variability of Meltwater Generation

• Process-based and conceptual model with spatial structure based on topography, land cover, and SWE distributions

Hydrological Model Development

SWE = 273.5K + 290.9R2 = 0.97

0

100

200

300

400

500

600

700

800

-1.5 0.0 1.5

SW

E (m

m)

K

33% of dist.

34% of distribution

19% of distribution

14% of distribution

• Model is capable of producing reasonable hydrographs with correct volume of runoff

Model Evaluation for Snowmelt Hydrograph

0

0.1

0.2

0.3

01-May 15-May 29-May 12-Jun 26-Jun 10-Jul 24-Jul

Date (2009)

Dis

cha

rge

ra

te (

m3 /s

)

Measured Hydrograph

Simulated Hydrograph

0

0.1

0.2

0.3


Date (2007)

Dis

cha

rge

ra

te (

m3 /s

)

Measured Hydrograph


0

0.025

0.05

0.075


Date (2009)

Dis

char

ge ra

te (m

3 /s)

N-facing slopeS-facing slopeE-facing slopeCirque floorN-facing forestS-facing forest

0

0.025

0.05

0.075


Date (2007)

Dis

char

ge ra

te (m

3 /s)

N-facing slopeS-facing slopeE-facing slopeCirque floorN-facing forestS-facing forest

Total Discharge Component Hydrographs

• Various simulation approaches were used to examine influence on the basin hydrograph

Hydrograph Sensitivity Analysis

0

0.1

0.2

0.3


Date (2009)

Dis

cha

rge

ra

te (

m3 /s

)

Measured Hydrograph


VariableSWE dist.Uniform Energy

0

0.1

0.2

0.3


Date (2009)

Dis

cha

rge

ra

te (

m3 /s

)

Measured Hydrograph


Fixed SWE dist.Uniform Energy

0

0.1

0.2

0.3


Date (2009)

Dis

cha

rge

ra

te (

m3 /s

)

Measured Hydrograph


Fixed SWE dist.Variable Melt

0

0.1

0.2

0.3


Date (2009)

Dis

cha

rge

ra

te (

m3 /s

)

Measured Hydrograph

Simulated HydrographVariable SWE dist.Variable Melt

NS = 0.62

RMSE = 0.03

NS = 0.53

RMSE = 0.03

NS = 0.39

RMSE = 0.04

NS = 0.23

RMSE = 0.04

• Other approaches were used to examine effects of forest canopy and soil depth, and inhomogeneous melt

Hydrograph Sensitivity Analysis

0

0.1

0.2

0.3

0.4


Date (2009)

Dis

cha

rge

ra

te (

m3 /s

)

Measured Hydrograph


Fixed SWE dist. - Uniform Energy; Uniform soil and canopy

0

0.1

0.2

0.3


Date (2009)

Dis

cha

rge

ra

te (

m3 /s

)

Measured Hydrograph

Sim. - Inhomogeneous

Sim. - Homogeneous

NS = -0.28

RMSE = 0.06 NS = 0.47

RMSE = 0.04

NS = 0.62

RMSE = 0.03

Homogeneous Inhomogeneous

• Novel framework that allows for physical, yet spatially simple snowmelt and SCD simulation

– Incorporation of sub-grid distributions of internal energy for melt computation

• Application of the framework, together with a hydrological model showed the influence of the spatial variability of both SWE and snowmelt energy on areal SCD and snowmelt runoff in an alpine environment

Key Conclusions, Significance

• Important to take inhomogeneous melt into account for areal SCD simulations

– Implications for remote sensing, climate models and modelling applications using depletion curves

• Effects are not as important for snowmelt runoff and hydrograph simulation, as other processes tend to overwhelm the response

– Still important to account for spatial variability of snowmelt energy on the slope, and land cover scale

Key Conclusions, Significance

Thank You

• NSERC• CFCAS• Canada Research Chairs Programme• University of Calgary Biogeosciences

Institute• Nakiska Ski Resort• Applied Geomatics Research Group• Students and Staff of Centre for

Hydrology

simulating areal snowcover depletion and snowmelt runoff in alpine terrain chris debeer and john...

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