What is Hydrological Parameterization?

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.