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)
SCA 


p(SWE)dSWE
Ma
Frequency distribution of SWE
Derived SCD curve
1
0.06
SCA = 0.92
0.9
0.05
0.8
0.7
Ma
100 mm
0.03
0.02
SCA
p (SWE)
0.04
0.5
SCA = 0.45
0.4
Ma
200 mm
0.01
Ma
100 mm
0.6
Ma
200 mm
0.3
0.2
Ma
350 mm
Ma
350 mm
0.1
0
0
0
100
200
300
SWE (mm)
400
500
600
0
100
200
300
SCA = 0.05
400
Melt depth (mm)
500
600
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
800
700
SWE (mm)
SWE  SWE (1 K  CV)
4
SWE = 200(1+K(0.4))
600
500
5
400
10
300
CV = 1.0
15
days
200
100
CV = 0.8
0
3
-4
-2
0
SWE / SWE
CV = 0.6
0.75
SCA
0
-1
0.5
0.25
0
1
2
3
4
5
K
6
0
0
0
10
6
CV = 0.0
1
-2
4
SCD curve from
uniform 30 mm/day
applied snowmelt
1
CV = 0.2
-3
2
K
CV = 0.4
2
2
50
80
90
95
99
99.9
5
10
Days
15
20
Development of Theoretical Framework
• Framework handles other important aspects of spatial
snowmelt and new snowfall during spring
Line representing the distribution
can be discretized
Melt depth
for 50 mm
initial SWE
Melt depth
for 100 mm
initial SWE
200
150
Following
melt
New snow added uniformly
over remaining distribution
100
Snowmelt
Kmin, i
Kmin, ii
0
1
3
2
50
SWE
SWE (mm)
Initial
distribution
Foot
Subsequent
accumulation
Frequency factor, K
Kmin, 1
Kmin, 2
0
Field Study Site
• Marmot Creek
Research Basin,
Kananaskis Country,
Alberta
Field Study Site
• Focused data collection at Fisera
Ridge and Upper Middle Creek
Mt. Allan
Field Methods and Observations
• Data collection over three years (2007-09) involved:
– Meteorological observation
– Snow surveys
– Daily terrestrial photos
– Lidar snowcover mapping
North
Facing
– Streamflow measurement
Station
Ridgetop 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 Correction
1) 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
1
4
2&3
Areal Snowcover Observations
Time lapse digital photography used to
monitor areal SCD
May 13,
June
July
1,
4,
9,
7,
10,
14,
17,
19,
22,
26,
29,
31,
2,2007
4,
7,
10,
13,
18,
21,
24,
27,
2007
2007
2007
2007
2007
Snowmelt Modelling and Validation
• Snowpack evolution simulated using the Snobal energy
balance model within Cold Regions Hydrological Model
(CRHM) platform
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)
Lv E
H
K↑
K↓
L↓
L↑
Soil layer
E
U
Active layer
Lower layer
P
U
G
R
Snowmelt Modelling and Validation
• Model performs well for depth, SWE, internal energy
2
1
0
1-Apr 15-Apr 29-Apr 13-May 27-May 10-Jun 24-Jun
1
0
1-Apr
600
300
0
1-Apr 15-Apr 29-Apr 13-May 27-May 10-Jun 24-Jun
Depth (mm)
Depth (mm)
Simulated SWE (mm)
Measured SWE (mm)
600
300
0
1-Apr 15-Apr 29-Apr 13-May 27-May 10-Jun 24-Jun
-25
1-Apr 15-Apr 29-Apr 13-May 27-May 10-Jun 24-Jun
Date (2008)
Date (2009)
Snow temp (°C)
Simulated active layer T
Measured active layer T
Simulated lower layer T
Measured lower layer T
Simulated SWE (mm)
Measured SWE (mm)
900
Date (2008)
Snow temp (°C)
15-Apr 29-Apr 13-May 27-May 10-Jun 24-Jun
Date (2009)
900
-15
Simulated depth (m)
2
Date (2008)
-5
Measured depth (m)
2009
3
Depth (m)
Depth (m)
Measured depth (m)
Simulated depth (m)
2008
3
0
-5
-10
Simulated active layer T
Measured active layer T
Simulated lower layer T
Measured lower layer T
-15
1-Apr 15-Apr 29-Apr 13-May 27-May 10-Jun 24-Jun
Date (2009)
Effects of Snow Mass and Internal Energy
Shallow CC
Intermediate CC
Deep CC
Shallow T
Intermediate T
Deep T
0
-2
-4
-6
-8
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)
Melt rate (mm/day)
Cold
Content:
Energy
required to
bring
snowpack to
0 °C and
satisfy liquid
water holding
capacity
Cold content (MJ/m 2)
Snowpack temperature (°C)
• Differences in initial state have large influence on
computation of snowmelt timing and rate
20
15
10
Shallow snow
Intermediate snow
Deep snow
5
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
Date (2008)
Spatial – Temporal Snowmelt Variability
SE-facing slope
26-Apr
28-Apr
30-Apr
2-May
4-May
12
9
6
3
Melt rate (mm/day) a
50
0
40
14-May
18-May
21-Jun
30
16-May
16-Jun
20
10
0
0
400
800
1200
0
SWE (mm)
15
50
N-facing slope
26-Apr
28-Apr
30-Apr
2-May
4-May
12
9
6
400
800
1200
SWE (mm)
Melt rate (mm/day) a
Melt rate (mm/day) a
• Differences in
melt energy
and SWE lead
to large
differences in
snowmelt that
change over
time
Melt rate (mm/day) a
15
3
0
14-May
18-May
21-Jun
40
16-May
16-Jun
30
20
10
0
0
400
800
SWE (mm)
1200
0
400
800
SWE (mm)
1200
Landscape Disaggregation for SCD Simulation
S-facing slope
2000
0.3
0.25
1500
SWE
measurements
1000
SWE = 157.0K + 223.6
f (SWE)
SWE (mm)
0.2
2
R = 0.96
Theoretical
distribution
0.15
0.1
500
0.05
00
15
50
00
13
12
50
0
0
0
0
0
K
10
10.0
90
8.0
75
6.0
60
4.0
45
2.0
30
0
0.0
15
-2.0
0
0
0
SWE (mm)
N-facing slope
SWE = 273.5K + 290.9
2500
R2 = 0.97
0.25
2000
SWE (mm)
0.2
1500
f (SWE)
1000
SWE
measurements
Theoretical
distribution
0.15
0.1
0.05
500
K
SWE (mm)
00
15
50
13
00
12
50
0
0
0
0
0
10
90
15.0
75
10.0
60
5.0
45
0
0.0
30
-5.0
0
0
0
15
• SWE values
on different
slopes fit
theoretical
lognormal
distribution
Simulation of Areal SCD over Landscape
Overall
basin
Simulated overall SCD curve
1
NS = 0.78
RMSE = 0.15
0.5
0
10-May
20-May
30-May
9-Jun
Date (2008)
Observed north facing SCD curve
SCA fraction
1
North
0.5
facing
0
10-May
9-Jul
1
NS = 0.89
NS =RMSE
0.92 = 0.10
0.5
0
10-May
20-May
SCA fraction
29-Jun
Observed overall SCD curve
RMSE = 0.09
20-May
30-May
30-May
9-Jun
9-Jun
Date (2008)
19-Jun
(2008)
Observed south facingDate
SCD curve
South
facing
19-Jun
Simulated north facing SCD curve
Simulated overal SCD curve
SCA fraction
19-Jun
29-Jun
29-Jun
9-Jul
9-Jul
Simulated south facing SCD curve
1
NS = 0.84
RMSE = 0.16
0.5
0
10-May
20-May
30-May
9-Jun
19-Jun
29-Jun
9-Jul
Date (2008)
Observed east facing SCD curve
East
facing
SCA fraction
• Framework
applied to
predict areal
SCD
• Results were
improved by
considering
separate
distributions
and melt rates
on each slope
SCA fraction
Observed overall SCD curve
Simulated east facing SCD curve
1
NS = 0.94
RMSE = 0.06
0.5
0
10-May
20-May
30-May
9-Jun
Date (2008)
19-Jun
29-Jun
9-Jul
Influence of “Inhomogeneous” Snowmelt
150 mm initial
Observed
300 mm initial
1
SCA fraction
• Earlier and more rapid melt of
shallow snow on some slopes
led to an initial acceleration of
SCD
Inhomogenous
850 mm initial
0.75
0.5
N facing slope
0.25
24-Apr
27-Apr
30-Apr
3-May
6-May
Date (2008)
Inhomogenous
850 mm initial
150 mm initial
Observed
Inhomogenous
850 mm initial
300 mm initial
SCA fraction
SCA fraction
300 mm initial
1
1
0.75
0.5
150 mm initial
Observed
S facing slope
0.25
24-Apr
27-Apr
30-Apr
3-May
Date (2008)
6-May
0.75
0.5
0.25
24-Apr
Overall basin
27-Apr
30-Apr
Date (2008)
3-May
6-May
Spatial Variability of Meltwater Generation
• Variability in melt over landscape and SWE dist’s. affects
location, extent, and timing of meltwater generating area
April 26
April 29
May 5
May 2
0–5
mm/day
5 – 10
mm/day
10 – 20
mm/day
exposed
ground
forested
areas
cliffs
Hydrological Model Development
• Process-based and conceptual model with spatial structure
based on topography, land cover, and SWE distributions
800
14% of distribution
700
SWE (mm)
600
500
SWE = 273.5K + 290.9
R2 = 0.97
19% of distribution 400
300
34% of distribution
33% of
dist.
-1.5
200
100
0
0.0
1.5
K
Model Evaluation for Snowmelt Hydrograph
• Model is capable of producing reasonable hydrographs with
correct volume of runoff
Total Discharge
Component Hydrographs
Measured Hydrograph
Simulated Hydrograph
0.2
0.1
0
01-May
N-facing slope
S-facing slope
E-facing slope
Cirque floor
N-facing forest
S-facing forest
0.075
15-May
29-May
12-Jun
26-Jun
10-Jul
Discharge rate (m3/s)
Discharge rate (m3/s)
0.3
0.05
0.025
0
01-May
24-Jul
15-May
29-May
Date (2009)
0.2
0.1
15-May
29-May
12-Jun
26-Jun
Date (2007)
10-Jul
24-Jul
10-Jul
24-Jul
N-facing slope
S-facing slope
E-facing slope
Cirque floor
N-facing forest
S-facing forest
0.075
Discharge rate (m3/s)
Discharge rate (m3/s)
Simulated Hydrograph
0
01-May
26-Jun
Date (2009)
Measured Hydrograph
0.3
12-Jun
0.05
0.025
0
01-May
15-May
29-May
12-Jun
26-Jun
Date (2007)
10-Jul
24-Jul
Hydrograph Sensitivity Analysis
• Various simulation approaches were used to examine
influence on the basin hydrograph
Variable SWE dist.
Variable Melt
Measured Hydrograph
Simulated Hydrograph
0.2
NS =
0.62
0.1
RMSE
= 0.03
0
01-May 15-May 29-May 12-Jun 26-Jun
10-Jul
0.3
Discharge rate (m3/s)
Discharge rate (m3/s)
0.3
NS =
0.53
0.1
RMSE
= 0.03
0
01-May 15-May 29-May 12-Jun 26-Jun
24-Jul
Measured Hydrograph
NS =
0.39
0.1
RMSE
= 0.04
Date (2009)
10-Jul
24-Jul
0.3
Discharge rate (m3/s)
Simulated Hydrograph
0.2
0
01-May 15-May 29-May 12-Jun 26-Jun
10-Jul
24-Jul
Date (2009)
3
Discharge rate (m /s)
VariableSWE dist.
Uniform Energy
Simulated Hydrograph
0.2
Date (2009)
0.3
Measured Hydrograph
Fixed SWE dist.
Variable Melt
Measured Hydrograph
Fixed SWE dist.
Uniform Energy
Simulated Hydrograph
0.2
NS =
0.23
0.1
RMSE
= 0.04
0
01-May 15-May 29-May 12-Jun 26-Jun
Date (2009)
10-Jul
24-Jul
Hydrograph Sensitivity Analysis
• Other approaches were used to examine effects of forest
canopy and soil depth, and inhomogeneous melt
Measured Hydrograph
Simulated Hydrograph
Measured Hydrograph
0.3
Sim. - Inhomogeneous
3
Fixed SWE dist. - Uniform
Energy; Uniform soil and
canopy
Discharge rate (m /s)
3
Discharge rate (m /s)
0.4
0.3
0.2
0.1
0
01-May 15-May 29-May 12-Jun 26-Jun
10-Jul
24-Jul
Sim. - Homogeneous
0.2
0.1
0
01-May 15-May 29-May 12-Jun 26-Jun
Date (2009)
NS = -0.28
RMSE = 0.06
10-Jul
24-Jul
Date (2009)
Homogeneous
Inhomogeneous
NS = 0.47
NS = 0.62
RMSE = 0.04
RMSE = 0.03
Key Conclusions, Significance
• 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
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