What is Hydrological Parameterization?
Masaki Hayashi
Dept. of Geoscience, Univ. of Calgary
Scotty Creek Basin
Abstraction of complex processes into a model.
→ simplification, scaling up, “fitting” (fuzzy!)
p
the ESSENSIAL FEATURE
The model must capture
of physical processes.
How do we identify the Essential Feature?
- Field ”intelligence” gathering
- Knowing what to look for
→ Hydrological process
Equations and models
- Look at big and small picture
This is the best (and most fun) part of
hydrological science!
Hydrologically Distinct Land
Land--Cover Types
flat bog
peat plateau
channel fen
permafrost
Channel Fen Parameterization
2
Quinton et al ((2003. Hydrol.
Q
y
Proces. 17:3665))
2/3 ×level
We can
water
in 1/2
fen,
celerity
= measure
1.7 × (depth)
(slope)
/n
but
not propagation
discharge.
g What to
do??
wave
Manning
n = 0.13-0.17
GS3
GS2
5
hourly
yp
pcp.
p (mm)
(
)
0
46 hr
52
70
1999
50
48
60
GS2
GS3
50
46
40
8/23 8/24 8/25 8/26 8/27 8/28 8/29 8/30
GS3
3 water lev. (cm
m)
GS2
2 water lev. (cm)
10 km
Peat Plateau Runoff Parameterization
- Majority is subsurface,
subsurface above the frost table
- Direction is lateral, not vertical drainage
CLASS 1
CLASS3.1
CLASS3
hydraulic conductivity (m/s)
of saturated peat
10-6 10-5 10-4 10-3 10-2
0
(Verseghy,
1991)
(Soulis
et al.,
2000)
high flow
dep
pth (m )
0.1
0.2
0.3
0.4
0.5
low flow
Lateral Drainage in CLASS 3.1
Drainage flux per area, q
1
Maximum drainage, qmax
→ Complete
C
l t saturation.
t
ti
Depends on slope angle,
hydraulic conductivity.
q
q*
q*
05
0.5
Average water storage, u
Maximum storage
storage, umax
→ Complete saturation.
0
06
0.6
0.8
0
8
u*
u*
1
Normalized drainage
g q
q* = q
q/q
qmax
Normalized storage u* = u/umax
Complex interplay
of many processes
Finite Element Variably Saturated Flow Model
Princeton UNSAT-2D
no flow
1
0.5
eleva
ation (m)
0
-0.5
0
5
10
1
15
20
25
30
observation well
0
0.5
-0.1
-0.2
02
0
-0.3
08/20/2001
-0.5
0
5
10
15
20
distance (m)
25
30
ψ
Finite Element Model (FEM) as a Virtual Slope
- Verify
f the detailed slope model against ffield data.
- Then, use it to parameterize a basin model.
1
CLASS 3.1
Analytically
y
y derived q
q*-u*.
q
q*
FEM
CLASS 3.1
FEM
1. Numerical drainage
experiment.
2 Derive numerical q*-u*.
2.
q* u*
3. Determine equivalent
q*-u* for CLASS 3.1.
q
0.5
0
0.6
0.8
u*
1
Marmot Creek Baseflow Parameterization
Analytical Solution of Brutsaert (2005
(2005. Hydrology)
Boussinesq equation for a hillslope “strip”.
∂ ⎛ ∂h ⎞
∂h K: conductivity
⎜ Kh ⎟ = S y
∂x ⎝ ∂x ⎠
∂t Sy: specific yield
A
B
L
early time solution
h(x)
D
Dc
q
Dc
x=0
late time solution
x=B
x=0
q: flow per shore length (m2 s-1)
q
h(x)
D
x=B
dQ
= −aQb
dt
Time derivative of baseflow discharge
(Q) is proportional to Qb.
→ b = 3 for early time, 1 for late time.
K can be determined from the intercepts
p
of two envelope curves.
dQ/dt (m
d
m3 s-2)
10-5
2004
2005
2006
10-6
K = 3 × 10-3 m/s
Reasonable??
10-7
0.01
0.1
1
Q (m3 s-1)
10
Scale-Dependent Conductivity?
K = 3 × 10-3 m/s
photo
h t by
b J.
J Pomeroy
P
K = 2 × 10-5 m/s
No it is “model
No,
model-dependent
dependent” conductivity!
Lake O’Hara Research Basin
Parameterization? What? How?
MESH
Major Hydrological Land-Cover Types
Example:
Talus slopes
500 m
From Processes to Parameterization
Field observation
physically-based
model (e.g.
(e g FEM)
“virtual”
virtual slope
Q
grid-scale function
simulation and
sensitivity analysis
Q
Storage
Take Home Messages
1. Parameterization by a detailed, “virtual” model.
2 Scale-dependent vs
2.
vs. model-dependent parameter.
parameter
3. Process people need to understand the equations
and models VERY WELL
WELL.
4. Modellers need to make the algorithm transparent
to process people:
→ Consistent with published papers.
No arbitrary “tricks” in the code.