Exploring
p
g Hydrologic
y
g Similarity
y
in the Marmot Creek Basin
By:
Ken Snelgrove and Yanhzen Ou
Memorial University of Newfoundland
For:
IP3 Third Annual Workshop
Whitehorse, Yukon
November 12-15, 2008
http//www.geography.ryerson.ca/wayne/thesis.htm
Outline
Marmot Creek
Review of Last Years Presentation
New Data Sources and the need for Hydrologic Similarity
Topographic Index Calculation
Evaporative Resistance Simulations using CLASS
Potential Evapotranspiration Estimation using Penman-Monteith
TOPMODEL Simulation and Genetic Algorithm Calibration
Relations between Static Similarity Measures
land cover vs. topographic index
Future Work
Marmot Creek Basin
Located at latitude 50°57’N and longitude 115°10’W
About 110km southwest of Calgary
Marmot Creek Basin
Total area : 9.5km2
Elevation: 1585-2805m, the
mean value is 2112m, the
difference of elevation is
1220m
Marmot Creek Basin
Three sub-basins:
Twin Creek
Middle Creek
C bi C
Cabin
Creek
k
Marmot Creek Basin
F
Forest
t Cover:
C
60%
Soil types: Brunisolic Grey Wooded Soils, podzolic soils,
regosolic soils, alpine black soils, local gleysolic and
organic soils (Stevenson
(Stevenson, 1967(thesis))
Climate Characteristic:
Mean annual precipitation—1080mm
Average July temperature— 2 to 18°C
Average January temperature — -6 to -18°C
Streamflow Characteristic:
Groundwater is the main source
In midsummer,
midsummer 70% derived from snow melting
Mean Annual Runoff = 425 mm
Data Collection
Topographic Data
Shuttle Radar Topography
Mission (SRTM) data– 90m
Light Detection and Ranging
(LiDAR) data – 1m
Meteorological Data
Hay Meadow Station
Vista View Station
1437
Last Year in Re
Review
ie
TOPMODEL
P
y
Continuity:
dS
= 0 ((Steadyy Assumption)
p
)
d
dt
AR − Q = 0
I−O=
Q = AR
R
c
Q
β
Darcy’s Law:
dh
dx
q(Dc) = K(Dc)tan(β )
Q = Tc tan(β )
q=K
Transmissivity vs Depth
To
Problems:
Precipitation Uniform
I t t
Instantaneous
Redistribution
R di t ib ti
T = Toe−(s / m )
D
s - soil moisture deficit
T
Last Year in Re
Review
ie
AR = Q = Tc tan(β )
AR
= Toe−( s / m )
c tan(β )
Ra
= e−(s / m )
To tan(β )
a=
⎡ ⎛ R⎞
⎛ a ⎞⎤
s = −m⎢ln⎜ ⎟ + ln⎜
⎟⎥
T
(
β
)
tan(
⎝
⎠⎦
⎝
⎠
⎣
o
⎡ ⎛ R⎞ ⎤
s = −m⎢ln⎜ ⎟ + λ⎥
⎣ ⎝ To ⎠ ⎦
A
c
flow accumulation
⎛ a ⎞
ln⎜
⎟ - Topographic Index
⎝ tan((β ) ⎠
Simple
Algebra
λ - Average Topographic Index
⎡ ⎛ a ⎞
⎤
si − s = −m⎢ln⎜
⎟ − λ⎥
β
)
tan(
⎝
⎠i
⎣
⎦
known from DEM
TOPMODEL
Linear Redistribution Equation ☺
Last Year in Re
Review
ie
Topographic Index Distribution
0.14
Hydrologic Similarity via Slope Position
0.12
0.1
Moisture Distribution via Average Storage
0.08
0.06
Measurable Parameters [To, m, ln(a/tan(β))]
0.04
0.02
0
Group 1
Group 2
Group 3
Group 4
Topographic Index
Topographic Index
Marmot Creek
Need For Hydrologic
H drologic Similarity
Similarit
How will we summarize and
utilize all the spatial data?
4 m Land Cover
1 m Topography
Topographic Index
What is topographic index?
ln(a/tanβ)
a is specific contributing area
D8
tanβis ground surface slope
Flo routing
Flow
ro ting algorithms
Single flow direction algorithm(D8)
Biflow direction algorithm
g
((D∞))
D∞
Topographic Index Results
1-m DEM
90-m DEM
D8
D∞
Topographic Index Results
D8
The discrepancy of
1-meter resolution
is obvious
90-meter
0.25
Relative freq
quency
No big difference
between 90-meter
resolution DEM
1-meter
0.03
0.02
0.01
0.15
0.10
0.05
0.00
-3 -1
1
3
5
Variable
SFD
BFD
0.20
0.00
8 10 12 14 17 19 21 23
4
6
8
10
12
14
Topographic Index
Topographic
p g p
Index
1.2
1 .0
1
V a r ia b le
SFD
BFD
0 .8
0.8
1m/SFD
0.6
1m/BFD
04
0.4
0.2
CDF
Frequency
Distributions of
ln(a/tanβ)
D∞
0 .6
0 .4
0 .2
0
-3
-1
1
3
5
8
10 12 14 17 19 21 23
Topographic Index
0 .0
2
4
6
8
10
12
T o p o g ra p h ic In d e x
14
16
Topographic Index Results
Grid Size
Algorithm
g
Variable
Mean
90-meter
D8
ln(a/tan β)
6.77
D
D∞
l ( /t β)
ln(a/tan
6 95
6.95
D8
ln(a/tan β)
3.05
D∞
ln(a/tan β)
4.50
1-meter
D8
1-meter
D∞
ln(a/tanβ)
90-meter DEM
ln(a/tanβ)
CLASS & Resistance Calcs
What is CLASS?
Canadian Land Surface Scheme is
first developed in 1987 at the
Meteorological Service
What is the aim of CLASS
To simulate the energy and water
balances of vegetation, snow and
soil
Whatt is
Wh
i the
th objective
bj ti off CLASS
simulation in this study?
To simulate stomatal resistance
and
d aerodynamic
d
i resistance
i t
Schematic diagram of CLASS (from Verseghy, 2000)
Stomatal Resistance
Stomatal resistance is estimated as:
r c,i = f 1(T air ) f 2(Δe) f 3(ψ s )r c,u ,i
r c,u = r s,minκ e / ln[( K ↓ + K ↓1/ 2 / κ e) /( K ↓ exp(−κ eΛ) + K ↓1/ 2 / κ e)]
= 250.0
T air ≥ 50°C , or , T air ≤ −5°C
− 5°C < T air < 5°C
= 1.0 /[1.0 − (5.0 − T air ) × 0.1]
= 1.0
1 0 /[1.0
/[1 0 − (T air
40 0) × 0.1]
0 1]
i − 40.0)
f 2(Δe) = (Δe /10.0)cv 2 / cv1
40°C < T air
i < 50°C
cv1=cv2=1
Air Temperature, Tair (oC)
Vapor pressure deficit, Δe (mb)
cv 2 > 0
f(Δ
Δe)
cv 2 ≤ 0
f(ψ
ψs)
= 1/ exp(−cv1 Δe /10.0)
f(Δe)
5°C ≤ T air ≤ 40°C
f(Tair)
f 1(T air ) = 1.0
f 3(ψ s ) = 1 + (ψ s / cψ 1)cψ 2
=1
For PET Calculation
cψ1 =0.5, cψ2=0.5
Soil moisture suction,
suction ψs (mb)
cv1=1 cv2=-1
Vapor pressure deficit,
deficit Δe (mb)
Res lts
Stomatal Resistance Results
The estimate of stomatal resistance
rc(s m
m-1)
1600
1200
800
400
0
28-Oct
Mean value is 267 s m-1
8-Oct
Low in May-September, High in October
18-Sep
Period from 9:00 a.m. to 5:30 p.m.
29-Aug
9-Aug
20-Jul
30-Jun
10-Jun
21-May
1-May
2007 (5.1-10.31)
Aerodynamic Resistance
What is aerodynamic resistance (ra)?
The resistance encountered by fluxes of water vapor or heat or
momentum along the path of transfer, which is from the source to a
given reference air level above
How does CLASS determine aerodynamic resistance?
ra =
1
C Dva
Where CD is the surface drag coefficient, and va is the wind speed
Aerod namic Resistance (cont’d)
Aerodynamic
How to determine drag coefficient for heat and water vapour
fluxes CD,E?
C D ,E
⎡
⎤⎡
⎤
⎢
⎥⎢
⎥
k
k
⎥⎢
⎥ Φ EΦ M
=⎢
−
−
z
z
z
z
d ⎥⎢
d ⎥
⎢ ln(( m
) ln(( m
)
⎢⎣
⎥
⎢
z 0, E ⎦ ⎣
z 0, M ⎥⎦
Where zm (m) is the reference height; zd (m) is the zero-plane
displacement; k=0.04
k=0 04 is von Karman’s
Karman s constant; z0,M
0 M (m) is the
roughness length for momentum transfer; z0,E (m) is the roughness
length for heat or vapor pressure transfer; ФM andФE are stability
correction factors.
Aerodynamic Resistance (cont’d)
Is there another method to determine aerodynamic resistance?
⎡ z m− z d ⎤
)⎥
⎢ ln(
z0 ⎦
⎣
r ah 0 =
k 2v a
2
Is this method available under all the conditions?
It is onlyy available under neutral condition.
ФM = ФE =1 and z0,E = z0,M , these two methods are the same
Aerodynamic Resistance Results
The estimate of aerodynamic resistance
100
rah
rah0
80
60
40
20
0
Period from 9:00 a.m. to 5:30 p.m.
Mean valuMean value of rah is 20.52 s m-1
e of rah0 is 19.83 s m-1
Note: rc values average 270 s m-1
29/Oct
9/Oct
19/Sep
30/Aug
10/Aug
21/Jul
1/Jul
11/Jun
22/May
2/May
2007(5.1-10.31
Potential Evapotranspiration
What is p
potential evapotranspiration
p
p
(PET)?
(
)
PET expresses as the amount of water that could evaporate and
transpire from a vegetated landscape without restrictions other than the
atmospheric demand.
How can we estimate PET?
Lysimeters
Eddy correlation
Theoretical or empirical equation
Multiplying standard pan evaporation data by a coefficient
Which method do we use in this study?
Penman-Monteith Equation
Potential Evapotranspiration
What is the Penman-Monteith Method?
*
e a = 0.611 ⋅ exp(
17.3 ⋅ T
)
37.3
T + 237.3
Δ ⋅ ( K + L ) + ρ a ⋅ c a ⋅ C at ⋅ e *a ⋅ (1 − W a )
PET =
ρ w ⋅ λ v ⋅ [ Δ + γ ⋅ (1 + C a t / C can ) ]
Δ=
2508.3
17.3 ⋅ T
p(
)
⋅ exp(
2
T + 237.3
(T + 237.3)
−3
λ v = 2.50 − 2.36 ×10 ⋅ T
γ ≡
ca⋅P
0 .6 2 2 ⋅ λ
C can = f s ⋅ LAI ⋅ C leaf
v
PET Results
PET seasonal trends in 2007
PETe(mm day
P
y-1 )
16
14
12
10
8
6
4
2
0
Oct
Highest
g
in July,
y, lowest in October
Sept
Mean value is 10.52 mm day-1
Aug
Jul
Jun
May
2007 ( 55 10)
PET Res
lts (cont’d)
Results
Aerodynamic resistance effect on PET
20
PET (mm da
ay-1)
PETe
PETn
16
12
8
4
0
Sign test shows that PETe and PETn is not significant different
PET is insensitive to aerodynamic resistance
Mean value of rah is 20.52 s m-1 , the mean value of rc is 267s m-1
28-Oct
8-Oct
18-Sep
29-Aug
9-Aug
20-Jul
30-Jun
10-Jun
21-May
1-May
2007 (5
(5.1-10.31)
1 10 31)
TOPMODEL
What is TOPMODEL?
A physically-based model based on the concept of variable
source area
Why we used TOPMODEL in this study?
It can be used to predict streamflow, overland and
subsurface flow, and soil moisture deficit with less
parameters
What is the objective for this study?
To simulate runoff in the Marmot Creek catchment using
TOPMODEL
TOPMODEL (cont’d)
How does TOPMODEL determine streamflow?
∑ ai p + ∑ ai si
q streamflow=
A
A
A
−λ −
+ T 0e e
s
m
where ai is specific area, p is precipitation, si is local soil moisture
deficit, A is watershed area, T0 is saturated transmissivity, λ is the
mean ln(a/tanβ) for the catchment, s is catchment-average
saturation deficit, and m is parameter
How does TOPMODEL determine soil moisture deficit (si)?
s i = s + m[λ − ln(
a
)]
tan β x
TOPMODEL (cont’d)
How many parameters involved in TOPMODEL?
Parameter
Name in theory
Description
Range
SZM[m]
m
Transmissivity decay parameter
0.005-0.06
T0 [m2h-1]
ln(T0)
Effective lateral saturated transmissivity
0.1-8
TD [m h-1]
td
Unsaturated zone time delay
0.1-500
Channel velocity
100-10000
CHV [m h-1] CHV
RV [m-2 h-1]
RV
Routing velocity
100-10000
SRMAX [m]
SRmax
Maximum allowable root zone storage
0.005-0.3
SR0[m]
SR0
Initial root zone deficit
0.0-0.3
TOPMODEL (cont’d)
How to calibrate the parameters?
Genetic Algorithm
How to evaluate the model efficiency?
) − ∑ (QOBS
−Q
QOBS i −QOBS
Q
Q
QSIM i )
∑ (Q
m
i
EFF =
2
∑ (QOBS i −QOBS m)
2
2
Where QOBSi is the observed streamflow
streamflow, QSIMi is the simulated
streamflow, and QOBSm is the mean of the observed streamflow.
TOPMODEL Results
The result of calibration
Marmot Creek Basin (2007)
5.00E-05
Strreamflow (m/h)
QSIM
4.00E-05
QOBS
3.00E-05
2.00E-05
1.00E-05
0.00E+00
The model efficiency value is 0.611
29-Octt
Period of 20th August to 31st October in 2007
19-Octt
9-Oct
29-Sep
p
p
19-Sep
9-Sep
30-Aug
g
20-Aug
g
2007 (08.20-10.31)
TOPMODEL Results (cont’d)
Calibration results for 1-meter and 90-meter resolution DEM,
DEM
using D8 and D∞.
1
90
Flow
SZM
(m)
T0
(m2h-1)
SR0
(m)
SRMAX
(m)
CHV
(m h-1)
RV
(m-2h-1)
Td
(mh-1)
EFF
QSUB
(%)
D8
0.046
0.29
0.0015
0.0059
371.53
449.81
382.24
0.611
84.91
D∞
0.046
0.29
0.0015
0.0059
371.53
449.81
382.24
0.583
86.4
D8
0 060
0.060
1 18
1.18
0 00006
0.00006
0 0060
0.0060
1725 00
1725.00
114 84
114.84
261 85
261.85
0 656
0.656
52 55
52.55
D∞
0.060
1.18
0.00006
0.0060
1725.00
114.84
261.85
0.565
53.96
TOPMODEL Results (cont’d)
The relation between soil
moisture deficit(si) and
t
topographic
hi index
i d [ln(a/tanβ)]
[l ( /t β)]
on August 28th in 2007.
Large value of ln(a/tanβ)
indicates the locations within a
watershed most likely to be
saturated and produce overland
flow
Co er Classes Vs Topographic Inde
Land Cover
Index
What are the procedures off land cover classification?
f
Images processing
Calculation of vegetation index
Land cover classification
Which Normalized Difference Vegetation Index (NDVI) is
used in this study?
ρ nir − ρ red
NDVI =
ρ nir + ρ red
−1.0 ≤ NDVI ≤ 1.0
Where ρnir and ρred represent reflectance at the red and
near infrared (NIR) wavelengths
near-infrared
wavelengths, respectively
respectively.
Land Cover Classes Vs Topographic Index
How can we classify
f the land cover?
Using Decision tree approach
Land
d Cover
C
Classes
Cl
NDVI Rang
R
Snow or Water
NDVI<0.1
Bare Ground
0.1≤ NDVI < 0.2
Grass
0.2≤ NDVI<0.3
Tree
0.3≤ NDVI <0.8
NDVI Calculation Results
The results off NDVI calculation
NDVI in this study area varies from -0.67 to 0.77, mean
value is 0.29, in October 18th, 2003.
0.014
F requenc y
0.012
0.01
0.008
0.006
0.004
0.002
0
0.68
0.57
0.46
0.34
0.23
0.12
0.00
-0.11
-0.22
-0.33
-0.45
-0.56
-0.67
NDVI
Co er Classification Res
lts
Land Cover
Results
The results off land cover classification
f
0.6
52.7%
F re q u e n c y
0.5
0.4
0.3
19.97%
0.2
11.21%
16.12%
0.1
0
1
2
3
Land Cover Classes
4
De eloping New
Developing
Ne Measures
Meas res of Similarity
Similarit
NDVI - Land Cover
Topographic Index - Terrain
Future work
Future Work
Theme II - Parameterization
Potential evapotranspiration estimates
Topographic Index Calculation - scaling behavior
Develop Similarity Estimates - terrain, topo, elevation, aspect
Th
Theme
III - Prediction
P di ti
Implement TOPMODEL redistribution within CLASS
Prediction of finer scale topography
p g p y