FE 537
Catchment
Scale
Oregon State University
Outline
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 Soil moisture patterns and watershed scale
response
 Are watersheds the sum of their component
parts?
 How do different catchment units sequence?
 Water tracing at the watershed scale
 Geographic source
 Time source
 Mean residence time
 How can we use this knowledge in watershed
modeling?
 Summary
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We’ll explore each of these separately
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Mean Residence
Time
Process Understanding
Geographic
Source
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Time
Source
Mean
residence
time
Mean residence time
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Mean Residence time
 (aka watershed transit time,
turnover time, age of water
leaving a system, exit age,
mean transit time, travel time,
hydraulic age, flushing time, or
kinematic age)
 tw=Vm/Q
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Tracers and transit times
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Environmental tracers:
added (injected) by natural processes, typically
conservative (no losses, e.g., decay, sorption), or
ideal (behaves exactly like traced material)
We will focus on
this today
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This approach
simplified
Cin (t)
Cout(t)
Figure from Jim Kirchner
Oregon State University
Residence Time Methods
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Model Theory: The Convolution Integral
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t
d (t )   d in ( ) g (t   )d

Predicted or
simulated
output d18O
signature
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Input Function:
Derived from
precipitation d18O signal
Represents d18O in
water that contributes
to recharge
System Response
Function:
Time distribution of
water flow paths
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Father of the field
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Oregon State University
An example: Maimai
Soil water residence time
FE 537
5902100
Annual Data
P 2250 mm
Q 1350 mm
E 850 mm
Average Data
Slope 34o
Relief 100-150m
Ksat
5 m/hr
Pit A
5902050
ln(a/tan)
Pit 5
16.0
5902000
14.0
Raingauge
12.0
5901950
10.0
Near Stream
8.0
5901900
6.0
Tensiometer Network
5901850
2410550
2410600
Precipitation
d18O
‰
-4
-8
-12
Oregon State University
Average -9.4‰
-16
Amplitude 0.1‰
Std Dev. 3.4 ‰
4.0
2.0
2410650
2410700
2410750
2410800
Soil Water
Soil water
Residence
Time
-4
-8
d18O
‰
Soils Data
Depth 1 m
Strong catenary sequence
-12
Average -9.4‰
-16
Amplitude 1.2‰
Std Dev. 0.6 ‰
5902100
Pit A
5902050
ln(a/tan)
Pit 5
16.0
5902000
14.0
Raingauge
5901950
12.0
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10.0
Near Stream
8.0
5901900
6.0
Tensiometer Network
5901850
2410550
If bedrock quite impermeable
MRT and distance from the divide
4.0
2.0
2410600
2410650
2410700
2410750
2410800
Mean Residence time (days)
160
MRT = 1.9(Distance) + 19.0
r^2 = 0.88
120
80
40
0
0
10
20
30
40
50
Distance from divide (m)
Oregon State University
Vache and McD WRR 2005
60
70
80
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Regionalized MRT to the entire basin based on a 2 meter elevation
grid
using a single direction D8 algorithm
Oregon State
University
Comparing sites with different
bedrock permeability
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Fudoji
Maimai
-1 weeks
1-4 weeks
10 m
10 m
1m
1m
4-8 weeks
8-16 weeks
16 weeks -
Divide
Divide
Channel
Channel
Fudoji baseflow MRT = 4x Maimai
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An Oregon example
From hillslopes to the mesoscale
FE 537
MACK (580 ha)
WS08 (21 ha)
WS03 (101 ha)
HI15
WS02 (60 ha)
HJ Andrews
(LOOK – 6200 ha)
PRIMET
WS10
(10 ha)
Photographed by Al Levno Date: 7/91
Oregon State University
WS09
(9 ha)
Some reported mean residence
times
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Small Experimental Watersheds
Dischma Catchment, AU, 33 km2, 4.1 yr
Pukemanga Catchment, NZ, 0.3 km2, 12 yr
Panola, GA, 0.4 km2, 4.5 yr
Rietholzbach, CH; 3.5 km2, 1.1 yr
Few studies have examined how MRT
varies
across
scale
Large River Basins
Colorado R, UT, 75,000 km2, 14 yr
Mississippi R., MN, 253,000 km2, 10 yr
Neuse R., NC, 11,000 km2, 11, yr
2, 10 yr
Sacramento
R,
CA,
277,000
km
Sources: Michel, 1992; Burns et al. 1999; McGlynn et al., 2003; Vitvar et al., in press; Stewart and Mehlhorn, in press
Oregon State University
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Oregon State University
Precipitation Data
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LOOK, 2.0 y
MACK, 2.0 y
WS10, 1.2 y
WS09, 0.8 y
WS08, 3.3 y
WS03, 1.3 y
WS02, 2.2 y
Oregon State University
FE 537
Is stream water residence time related to
the size of the catchment?
Errorbar = 95% confidence limit of
MRT estimate
Catchments ranged from 0.002 to 62.4
km2
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Levno, 1991
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Residence Time and Topography
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How can we use
this knowledge
in modeling?
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What
we’re
striving
What is still beyond our
reach
30+ years
later…for
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Oregon State University
Taka Sayama
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What have we learned so far?
In humid-upland watersheds:
Catchment is a series of cryptic reservoirs
that connect and disconnect
 Activation of hillslopes is very thresholdlike
 Riparian-hillslope sequencing is hysteretic
Pre-event water dominates
 Streamflow is old (usually > 1 yr)
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In our models we have to deal with
this….
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Runoff (l/s)
75
50
25
0
9/30
Q Efficiency
100
0.9
0.7
0.5
10/20
100
11/9
200 Date
11/29
300
12/19
400
K (m/d)
Oregon State University
Vache et al., 2004 GRL
1/8
…and this
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If we want to be right, for the right reasons
(i.e. water-quality-realistic flowpaths)
Q Efficiency
0.9
0.7
0.5
0.3
0.1
30
Oregon State University
50
70
90
110
Mean Residence Time (days)Vache and McDonnell, 2006 WRR
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Our goal
Developing models that are
minimally parameterized and
therefore stand some chance of
failing the tests that they are
subjected to*
Experimentalists delivering
orthogonal measures (but not all
the gory details) that can be
used for model testing
* Kirchner, 2006 WRR
Oregon State University
FE 537
Conceptualization of Runoff Processes
.... following Uhlenbrook et al. (2002) WRR
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Model structure
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Hydrologic Model
Mean Residence
Time
+
Model Evaluation
Tracer Simulation
Break
Curve
NewThrough
Hydrograph
Separation Technique
?
Geographic
Source
Oregon State University
Old / New
Water
Understanding Processes
+
Building New Hypotheses
FE 537
100
Tracers can be used to define the model structure
90
Hillslope
Stream
Rain
Riparian Zone
Soil-Ridge
Soil-Hollow
80
K (mmol/L)
70
60
50
40
30
20
Riparian Zone
Hollow
10
0
0
Oregon State University
50
100
150
Na (mol/L)
200
250
Elsenbeer et al., unpub data
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Example: A simple lumped box model
P E
P E
P E
Hillslope box
Runoff
Hollow box
Riparian box
Umax
U
Umin
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Coupled saturated and
unsaturated storage
Linear outflow equations
Threshold level in hollow box
17 parameters
Flexible box models
FE 537
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The experimentalist influencing the model
structure
Model output evaluation
FE 537
Hydrologic Model
Mean Residence
Time
+
Model Evaluation
Tracer Simulation
Break
Curve
NewThrough
Hydrograph
Separation Technique
?
Geographic
Source
Oregon State University
Old / New
Water
Understanding Processes
+
Building New Hypotheses
FE 537
Tracer data for evaluating model output
Evaluation rules
Experimentalist
Modeller
Values for evaluation rules (ai)
“Degree of acceptability”
1
0
0.06
a2
0.03
a1
0.12
a3
0.15
a4
New water contribution to peak flow [-]
(30/9/87 event, McDonnell et al. 1991)
Oregon State University
Soft data
FE 537
Qualitative knowledge from the experimentalist that cannot be
used directly for model calibration (or validation)
(e.g. new water contribution [%] to peak flow, maximum
groundwater level, mean soil depth, reservoir volume, etc)
Rainfall
Storage
z
Oregon State University
Bypass flow
and mixing
Pipeflow of old
water
Different ways of evaluating model acceptability based on
FE 537
hard (A1) and soft (A2 and A3) data
Acceptability according to:
A1 Fit between simulated and
observed data
A2 Agreement with perceptual
(qualitative) knowledge
A3 Reasonability of parameter
values
Example
Measure
Runoff
Efficiency
New water
contribution
Spatial extension
of riparian zone
Percentage of
peak flow
Fraction of
catchment area
Combined objective function:
A A A A
n
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n1
1
n2
2
n3
3
with n  n1  n2  n3
e.g. Model performance
FE 537
Goodness measure
1
0.8
Runoff efficiency
GW hard
GW soft
Parameter values
New water
0.6
0.4
0.2
0
r
3
2
e
W
t
A
A
a
G
d
d
w
ft
n
n
o
a
a
w
s
2
1
e
n
A
A
nd
,
d
a
1
A
an
Q
Q
Oregon State University
A1
Q
Increasing amount
of soft data
Model efficiency
FE 537
 Model performance is usually assessed using the Nash Sutcliffe
(Nash and Sutcliffe 1970) efficiency factor (E).
E is a measure of model fit:
(Q

E  1
 (Q
o
 Qm 
o
 Qo

where Qo is observed discharge and Qm is modeled discharge.
 An E value greater than 0 indicates the modeled results fit
measured discharge better than the mean discharge.
 An E of 1.0 is a perfect fit.
Oregon State University
Model efficiency : 0.93
Q [mm/h]
Groundwater level [m]
FE 537
Hillslope
Hollow
Riparian
3
2
1
0
6
Observed Q
Simulated Q
4
2
0
28-Sep
Oregon State University
8-Oct
18-Oct
28-Oct
7-Nov
17-Nov
27-Nov
Model efficiency : 0.92
Q [mm/h]
Groundwater level [m]
FE 537
Hillslope
Hollow
Riparian
3
2
1
0
6
Observed Q
Simulated Q
4
2
0
28-Sep
Oregon State University
8-Oct
18-Oct
28-Oct
7-Nov
17-Nov
27-Nov
Model efficiency : 0.93
Q [mm/h]
Groundwater level [m]
FE 537
Hillslope
Hollow
Riparian
2
1
0
6
Observed Q
Simulated Q
4
2
0
28-Sep
Oregon State University
8-Oct
18-Oct
28-Oct
7-Nov
17-Nov
27-Nov
Model performance
FE 537
Goodness measure
1
0.8
Runoff efficiency
GW hard
GW soft
Parameter values
New water
0.6
0.4
0.2
0
r
3
2
e
W
t
A
A
a
G
d
d
w
ft
n
n
o
a
a
w
s
2
1
e
n
A
A
nd
,
d
a
1
A
an
Q
Q
Oregon State University
A1
Q
Increasing amount
of soft data
Best overall performance
Q [mm/h]
Groundwater level [m]
FE 537
Hillslope
Hollow
Riparian
2
1
0
6
Observed Q
Simulated Q
4
2
0
28-Sep
Oregon State University
8-Oct
18-Oct
28-Oct
7-Nov
17-Nov
27-Nov
Model rejection
FE 537
Hydrologic Model
Mean Residence
Time
+
Model Evaluation
Tracer Simulation
Break
Curve
NewThrough
Hydrograph
Separation Technique
?
Geographic
Source
Oregon State University
Old / New
Water
Understanding Processes
+
Building New Hypotheses
FE 537
Residence time as a process-based model
rejection tool
Model 1
Model 3
Precipitation
Precipitation
Saturated
Zone
Effective
Porosity
Yes
No
No
Model 2
Yes
Yes
No
4
Model Model
2 3
Yes
No
Model Yes
4
5
Yes
Yes
Yes
Evapotranspiration
Model 1
Model
4
Precipitation
Lateral Subsurface Stormflow
Evapotranspiration
3
Lateral Subsurface Stormflow
6
Precipitation
Evapotranspiration
Lateral Subsurface Stormflow
Oregon State University
Explicit
# Tuned
Evapotranspiration
Unsaturated Parameters
Zone
Lateral Subsurface Stormflow
FE 537
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Runs with NS > 0.7
Breakthroughs
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Note early time and late time differences between Models 1-4
Oregon State University
Model 1
FE 537
Q Efficiency
0.9
0.7
0.5
0.3
0.1
30
50
70
90
110
Mean Residence Time (days)
Oregon State University
Vache and McDonnell, 2005 WRR
100
Model output from before
75
Runoff (l/s)
FE 537
Measured
Run1426
Run1836
50
25
0
9/30
10/20
11/9
11/29
12/19
1/8
Date
…we would reject
this model…recall
that our
measured range
was 0-120 days
Oregon State University
How much detail is warranted?
FE 537
Complementary measures for evaluation and rejection
Oregon State University
Vache and McDonnell, 2005 WRR
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Course
Summary
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What we have addressed
FE 537
A
B
C
Oregon State University
 Where does water
go when it rains?
 How long does it
reside in the
catchment?
 What flowpath
does the water take
to the stream?
FE 537
Oregon State University
New problems that catchment
hydrologists are tackling and where this
knowledge is essential….
http://www.mdbc.gov.au/education/basinkids/kidsencyclopaedia/salinity.htm
Approaches we have discussed
FE 537
Field site
Intercomparisons
Field
experiments
Oregon State University
Process
understanding
Conceptual
& PB models
First-order
controls
Virtual
experiments
FE 537
Hillslope and Watershed Hydrology
Physical
Chemical
Isotopic
Photo: Kevin McGuire
Explicit solution of water and tracer mass balance
Oregon State University
FE 537
Some benchmark paper era
words of wisdom to remember
“Accurate prediction of the
headwater hydrograph implies
adequate modeling of sources,
flowpaths and residence
time of water and solutes.
Hewlett and Troendle, 1975
Oregon State University
FE 537
…and
“Runoff concepts need to be refined,
developed and formalized through
more vigorous combination of
rigorously defined field
experiments and realistic
physically-based mathematical
models”
Dunne (1983, p.25) Journal of Hydrology
Oregon State University
Markus Weiler, UBC
Kurt Roth, University Heidelberg, Germany
FE 537
1m
0.01 m
Multi-scale processes in hydrology
Network behavior at all scales10,000 m
100 m
Jim Kirchner, UC Berkeley
Oregon
State
University
Weiler
and
McDonnell,
WRR in review
Markus Weiler, UBC
FE 537
IAHS Prediction in Ungauged Basins
Approach
Improve existing models
Diagnostic Analysis
and Interactive Learning
Innovative developments leading to new models
M agnitude
Understanding
Predictive
uncertainty
Oregon State University
PUB initiative timeline
Wagener et al., 2004 EOS
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PUB science themes
Theme 1. Basin inter-comparison and
classification
Theme 2. Conceptualization of process
heterogeneity
Theme 3. Uncertainty analyses and model
diagnostics
Theme 4. Develop and use of new data
collection approaches
Theme 5. New hydrological theory
Theme 6. New model approaches
Oregon State University
FE 537
Oregon State University
Our future grand challenge
Sivapalan, 2006 Encyclopedia of Hydrological Sci.