fe 537 catchment modeling · 0.2 0.4 0.6 0.8 1 goodness measu r e a 1 , a 2 s a n d a 3 a 1 a d a 2...

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Oregon State University

CatchmentCatchmentModelingModeling

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This sectionThis section

An experimentalistAn experimentalist’’s view of models and s view of models and their development in their development in catchmentcatchment hydrology hydrology Example of a model that captures Example of a model that captures

dominant runoff processesdominant runoff processesUsing our new process knowledge to build Using our new process knowledge to build

the model and calibrate the modelthe model and calibrate the modelHow to judge the worth of a model with our How to judge the worth of a model with our

process knowledgeprocess knowledgeBringing detailed processes (that we Bringing detailed processes (that we

cannot observe!) into the modelcannot observe!) into the model

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The PrehistoryThe PrehistoryThe need for a design discharge

Examples:• the Rational Method and the Time Area Curve• the Unit Hydrograph, the Effective Rain and Separation of Hydrographs• the Linear Models: the linear channel, the linear reservoir, the Nash cascade• …

only for small and impervious catchmentsvery strong assumptions (e.g. linearity)

Mario Martina

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The Middle AgesThe Middle AgesThe conceptual models

Examples (WMO Intercomparison, 1976):• the STANFORD model IV• the SACRAMENTO model• the continuous API model• the CLS

the parameters are physically meaninglessMario Martina

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The RenaissanceThe RenaissanceThe physically based models

Examples:• the R.A. Freeze Model• the Systeme Hydrologique Europeen• the Institute of Hydrology Model• the SHETRANbreakthrough in hydrological modelling physical processes are now represented

too many parameters, too many information needed for the calibrationMario Martina

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The RomanticismThe RomanticismThe Variable Contributing Area models

Examples:• the Probability Distributed Soil Capacity model• the Xinanjiang Model• the VIC model• …

few parameters, but they are not directly related to measurable quantities

A probabilistic representation of spatially distributed variables

Mario Martina

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The Modern AgeThe Modern AgeThe derived from topography models

Examples:• the Soil Conservation Number model• the Geomorphologic Unit Hydrograph• the TOPMODEL• …

few parameters and they can be related to measurable quantities

but are they really physically based ?

TOPMODELTopographicIndex

Mario Martina

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The Contemporary AgeThe Contemporary AgeNew physically based / process oriented models

Examples:• the Representative Elementary Watershed (REW) model• the Tracer Aided Catchment Distributed (TACD) model• the TIN-based Real-time Integrated Basin Simulator (tRIBS)• the TOPographic KInematic wave APproximation and Integration (TOPKAPI)• …

Physically-based distributed representation of the dominant processes (synthesis)

sometimes a coupled conceptual/physically based approach Mario Martina

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Complexity / PredictabilityComplexity / Predictability

Grayson & Bloschl(Advances in Water Resources, 2002)

More complex does not always mean better !

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Different scalesDifferent scales

Measures Phenomena(and theory)

Models

Mario Martina

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Process assumptions that we have reviewed Process assumptions that we have reviewed (and rejected!)(and rejected!)

Z

T0(a) Topography

(b) Index

(c) Depth to WT

SaturatedArea

ln(a/tanβ)

Depth

T T eZZ= −

0

PreferentialflowBedrock topography

Not steady state

Threshold connections

Bloody Hell!

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Remember this slide from the Introduction?Remember this slide from the Introduction?

0

25

50

75

100

9/30 10/20 11/9 11/29 12/19 1/8

Date

Run

off (

l/s)

0.5

0.7

0.9

100 200 300 400

K (m/d)

Q E

ffici

ency

Vache et al., 2004 GRL

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This is what such uncertainty can mean for This is what such uncertainty can mean for something we (now) know aboutsomething we (now) know about

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If an experimentalist was to build a If an experimentalist was to build a catchmentcatchment modelmodel

““After much whittling down, After much whittling down, this is my most parsimonious this is my most parsimonious

catchmentcatchment model structuremodel structure……..””

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If an experimentalist were to build a model If an experimentalist were to build a model for realfor real

Hillslope box

Riparian box

P E

Runoff

Umax

UUmin

Hollow box

P EP E

Coupled saturated and unsaturated storage

Linear outflow equationsThreshold level in hollow box

Seibert and McDonnell, 2002 WRR

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ExampleExample

hollo

w

Plan

ar

slope

3 ha catchment

Stream and riparian zones

17 ha catchment

Downstream

Hillslope throughflow trench

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The sat and The sat and unsatunsat zone need to be coupled zone need to be coupled from what we have examined todayfrom what we have examined today

nd

n

Saturated zone

Unsaturated zone

Soil

dept

h D

nAWV sat =)()( dunsat nnAWDV −−=

Wat

er ta

ble

dept

h W

Volume:

Saturated zone

Unsaturated zone

ΔW output

Falling water table

Saturated zone

Unsaturated zone

ΔW

Rising water table

intput

)( dsat

sat nnAwVm

m −Δ=Δ

Mass exchange:

)( dunsat

unsat nnAwVm

m −Δ=Δ

Mass exchange:

Initial condition

Weiler and McDonnell, 2003 Weiler and McDonnell, 2003 JoHJoH

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Hillslope

Riparian Zone

Hollow

Why three boxes in this application?

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Na (mol/L)

010

2030405060

7080

90100

K (μ

mol

/L)

StreamRainRiparian ZoneSoil-RidgeSoil-Hollow

0 50 100 150 200 250

Riparian Zone Hollow

Hillslope

Geochemical End Members

Elsenbeer et al., unpub data

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McDonnell et al.,1991 WRR

Hillslope

Hollow

Riparian

Cluster Analysis of Deuterium Concentration in Subsurface Water

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A nonA non--linear reservoir in the linear reservoir in the hollowhollowboxbox

Hillslope box

Riparian box

P E

Runoff

Umax

UUmin

Hollow box

P EP E

Hillslope typediscussed earlier…

Seibert and McDonnell, 2002 WRR

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Effect of drainable porosity decline on Effect of drainable porosity decline on hillslopehillslope response to rainfall (and mixing)response to rainfall (and mixing)

⎟⎠⎞

⎜⎝⎛−=

mznznd exp)( 0 ψψ<0

ψψ<0

δδ1818Ο = Ο = −−55οο//οοοο

Storm Rainfall ΣδΣδ1818Ο = Ο = −−1010οο//οοοο

δδ1818Ο = Ο = −−4.54.5οο//οοοο

⎟⎠⎞

⎜⎝⎛−=

mznznd exp)( 0

McD, 1990 WRR; McD et al 1996 EOS; Freer et al. 2002 WRR

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Model efficiency : 0.93Model efficiency : 0.93

28-Sep 8-Oct 18-Oct 28-Oct 7-Nov 17-Nov 27-Nov

0

2

4

6

Q [m

m/h

]

0

1

2

Gro

undw

ater

leve

l [m

]

Observed QSimulated Q

HillslopeHollowRiparian

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It works, eh?It works, eh?

0

0.2

0.4

0.6

0.8

1

Goo

dnes

s m

easu

re

A1, A2 and A3

A1 and A2

Q and new water

Q and soft GW A1 Q

Runoff efficiencyGW hardGW softParameter valuesNew water

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0

2

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6

Q [m

m/h

]

0

1

2

3

Gro

undw

ater

leve

l [m

]



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6

Q [m

m/h

]

0

1

2

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undw

ater

leve

l [m

]



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The internal tugThe internal tug--ofof--warwar…what about fieldexperience?!

… we need real datafor model calibration!

reviewers

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What is What is ““soft datasoft data””??

Qualitative knowledge from the geoscientist 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))

Bypass flowand mixing

Pipeflow of oldwater

z

StorageRainfall

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Dialog between the experimentalist and Dialog between the experimentalist and modelermodeler

Hillslope box

Riparian box

P E

Runoff

Umax

UUmin

Hollow box

P EP E

Experimentalist ModelerEvaluation rules

Values for evaluation rules

Seibert and McDonnell, 2002 AGU Monograph

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Dialog between experimentalist and Dialog between experimentalist and modelermodeler

Experimentalist ModelerEvaluation rules

Values for evaluation rules (ai)

a1

a2 a3

a4

0.03

0.06 0.12

0.15

(30/9/87 event, McDonnell et al. 1991 WRR)

0

1

New water contribution to peak flow [-]

“Degree of acceptability”

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Soft data and degree of acceptabilitySoft data and degree of acceptability

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

>

<≤−−

<≤

<≤−−

≤

=

4

4334

4

32

2112

1

1

0

1

0

)(

axif

axaifaaxa

axaif

axaifaaax

axif

xμ

a1

a2 a3

a4

Fuzzy Rules- new water at peak- reservoir volumes, Ksat etc- range of gw levels- hollow threshold level

0

1“Degree of acceptability”

Seibert and McDonnell, 2002 AGU Monograph

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Different ways of evaluating model acceptability based on Different ways of evaluating model acceptability based on hard (A1) and soft (A2 and A3) datahard (A1) and soft (A2 and A3) data

Acceptability according to: Example MeasureA1 Fit between simulated and Runoff Efficiency

observed dataA2 Agreement with perceptual New water Percentage of

(qualitative) knowledge contribution peak flowA3 Reasonability of parameter Spatial extension Fraction of

values of riparian zone catchment area

321321321 nnnnwithAAAA n nnn ++==

Combined objective function:

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Model performanceModel performance

0

0.2

0.4

0.6

0.8

1

Goo

dnes

s m

easu

re

A1, A2 and A3

A1 and A2

Q and new water

Q and soft GW A1 Q

Runoff efficiencyGW hardGW softParameter valuesNew water

Increasing amount of soft data

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Best overall performanceBest overall performance——a little a little ““less less rightright”” but for the correct process reasons but for the correct process reasons


0

2

4

6

Q [m

m/h

]

0

1

2

Gro

undw

ater

leve

l [m

]



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Other reservoir assemblages Other reservoir assemblages (it(it’’s a soft model approach that you can use in your area)s a soft model approach that you can use in your area)

It is physically-based

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Other modeling Other modeling examples at the examples at the hillslopehillslope scale (where scale (where we can use our new we can use our new process knowledge)process knowledge)

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PipeflowPipeflow

Pipeflow is mostly pre-event water but, applied line sources of tracer often show rapid lateral breakthrough through the pipe/hillslope system.

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Our simple modelOur simple model

⎟⎠⎞

⎜⎝⎛−=

bznznd exp)( 0

1

1)(−

⎟⎠⎞

⎜⎝⎛ −=

m

o DzKzK

wtTtqSSF β)()( =

Lateral subsurface flowLateral subsurface flowDupuitDupuit--ForchheimerForchheimerassumptionassumption (slope of (slope of water table)water table)22--D explicit grid by grid D explicit grid by grid cell approach cell approach (Wigmosta, 1994 WRR)(Wigmosta, 1994 WRR)

Water and mass balance Water and mass balance within the saturated and within the saturated and unsaturated zone unsaturated zone in each in each grid cellgrid cellSimple infiltration (soil Simple infiltration (soil water content, power law) water content, power law) and evapotranspirationand evapotranspiration

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Combining this with the process Combining this with the process understandingunderstanding

Experimental commonality**:Experimental commonality**:PPipeipe diameter within a narrow range. diameter within a narrow range.

Uchida et al. 2002 WRRUchida et al. 2002 WRRPPipeipe length and connectivity mapping length and connectivity mapping shows discontinuous pipe sectionsshows discontinuous pipe sections ((mamax.x.length length << somesome mmeters)eters)

KitiharaKitihara 1994 Bull. FFPRI1994 Bull. FFPRIPipe Pipe location within the soil profiles is location within the soil profiles is mostly within a narrow band above the mostly within a narrow band above the soilsoil--bedrock interfacebedrock interface..

Uchida et al. 2002 HP; Uchida et al. 2002 HP; WWaterater flow in the pipe flow in the pipe

Sidle et al. 1995 Sidle et al. 1995 JoHJoH::

( ) 4.0hkq p =**from review by Uchida et al 2001 HP

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Pipe height within starting cell

z

How to model the unknown pipe How to model the unknown pipe system?system?

slop

e

Spatial pipe geometry

Despite the limited length of preferential flow structures (e.g.Despite the limited length of preferential flow structures (e.g. pipes), pipes), they can connect by water flow from microthey can connect by water flow from micro--mesomeso--macro porosity.macro porosity.

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Visualizations Visualizations -- MaimaiMaimai

RunoffRunoff

ConcentrationConcentration

00 maxmax

Relative concentration in soil columnRelative concentration in soil column

Pipe FlowPipe Flow

Matrix FlowMatrix Flow

00 maxmax

Relative flow in soil pipesRelative flow in soil pipes

Pipe Flow Line tracer movement

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MaimaiMaimai

0.0

1.0

2.0

3.0

0.0

0.5

1.0

1.5

2.0

20 30 40 50 600.0

0.5

1.0

1.5

2.0

Run

off (

mm

/h)

Average with Pipes Ensembles with Pipes W ithout Pipes Measurements

Run

off (

mm

/h)

Total Pre-event runoff Average with Pipes Ensembles with Pipes W ithout Pipes

Trac

er R

ecov

ery

(%)

T ime (h)

Average with Pipes Ensembles with Pipes W ithout Pipes

Evaluation Criteria*

Flow

Event TracerWater % Recovery

*Consistency more important than optimality

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More QuestionsMore Questions………………

HHowow does soil depth does soil depth variation affect flow?variation affect flow?How can placeHow can place--based based experimental knowledge experimental knowledge be coupled with the model be coupled with the model approach? approach?

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Remember this site from beforeRemember this site from before……..

Soil depth mapped Soil depth mapped at 2 m gridat 2 m gridAverage: 0.63 mAverage: 0.63 mStd: 0.3 mStd: 0.3 mCorrelation length: Correlation length: 12 m12 m

Subsurface flow Subsurface flow measured at 10 2measured at 10 2--m m wide trench sectionswide trench sections

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

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Time2/1/02 2/15/02 3/1/02 3/15/02 3/29/02 4/12/02

Sub

surfa

ce fl

ow (m

m/h

r)

0.00.10.20.30.40.50.60.7

ObservedModel: mapped soil depthModel: uniform soil depth

Pre

cipi

tatio

n (m

m/h

r)0

25

50

75

100

Model results: total subsurface flowModel results: total subsurface flow

Time2/6/02 2/7/02 2/8/02 2/9/02 2/10/02 2/11/02 2/12/02

Sub

surfa

ce fl

ow (m

m/h

r)

0.0

0.1

0.2

0.3

0.4

ObservedModel: mapped soil depthModel: uniform soil depth

Pre

cipi

tatio

n (m

m/h

r)0

5

10

Soil depth variability has a very large influence on modeled subsurface storm flow volume

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Model results: statistical representationModel results: statistical representation

Time2/6/02 2/7/02 2/8/02 2/9/02 2/10/02 2/11/02

Sub

surfa

ce fl

ow (m

m/h

r)

0.0

0.1

0.2

0.3

0.4Model: statistical representationsObservedModel: mapped soil depth - 20 m long trenchModel: mapped soil depth - 28 m long trenchModel: uniform soil depth

Pre

cipi

tatio

n (m

m/h

r)0

5

10

Multiple realizations of a model with statistical representations of soil depth represent observed subsurface storm flow better than a model with average soil depth

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Time2/6/02 2/7/02 2/8/02 2/9/02 2/10/02 2/11/02

Sub

surfa

ce fl

ow (m

m/h

r)

0.0

0.1

0.2

0.3Model: statistical representationsAverage of statistical representationsModel: uniform soil depth

Pre

cipi

tatio

n (m

m/h

r)0

5

10

Moving to larger segments of the landscapeMoving to larger segments of the landscape

70 x 100 m wide hillslopeFor larger hillslopes the effect of soil depth variability on total subsurface flow is less than for the smaller hillslope but the effect on timing of subsurface flow is large

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Other modeling Other modeling examples where we examples where we can use our new can use our new process knowledgeprocess knowledge

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m n

Init. Sat. Keff

Use this Use this expert knowledgeexpert knowledge to constrain to constrain our models alsoour models also

Vache et al GRL 2005

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Red dotsRed dots = % new = % new water < 50water < 50Black dots = % new Black dots = % new water > 50water > 50

Identifies parameter Identifies parameter sets that produce sets that produce the the ““efficientefficient””results for the wrong results for the wrong reasonsreasons

m n

Init. Sat. Keff

Rejecting nonsense dotsRejecting nonsense dots

Vache et al GRL 2005

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Other modeling Other modeling examples where we can examples where we can use our new process use our new process knowledge to determine knowledge to determine how much complexity is how much complexity is warranted in the modelwarranted in the model

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Discharge

Soil Water MRT

Stream Water MRT

Discharge

Soil Water MRT

Stream Water MRT

A Multi-Criteria Evaluative Strategy

Towards more orthogonal measures for model structural improvement and uncertainty

reduction

Gordon Grant’s Blob

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Captures flow path Captures flow path heterogeneityheterogeneity

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MaimaiMaimai: The simplest of our various : The simplest of our various experimental watershedsexperimental watersheds

hollo

w

Plan

ar

slope

3 ha catchment

Stream and riparian zones

17 ha catchment

Downstream

Hillslope throughflow trench

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Grid-based, highly simplified with 3 tunable parameters

The simplest of models to start

Vache et al., 2004 GRL inoutout SSSOFSSETPdtdV

+−−−=

The volume of water within each reservoir is accounted for using the familiar continuity equation:

Precipitation

Evapotranspiration

Lateral Subsurface Stormflow

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StreamwaterStreamwater residence time (120 days)residence time (120 days)but also soil water residence timebut also soil water residence time

2410550 2410600 2410650 2410700 2410750 2410800

5901850

5901900

5901950

5902000

5902050

5902100

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Near Stream

Pit 5

Pit A

Tensiometer Network

ln(a/tanβ)

Raingauge

Annual DataP 2250 mmQ 1350 mmE 850 mm

Average DataSlope 34o

Relief 100-150mKsat 5 m/hr

Soils DataDepth 1 mStrong catenary sequence

Soil water Residence

Time

-4

-8

-12

δ18O

‰

-4

-8

-12

δ18O

‰

Soil WaterPrecipitation

Average 9 4‰ ‰

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MRT and distance from the divideMRT and distance from the divide2410550 2410600 2410650 2410700 2410750 2410800

5901850

5901900

5901950

5902000

5902050

5902100

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Near Stream

Pit 5

Pit A

Tensiometer Network

ln(a/tanβ)

Raingauge

0

40

80

120

160

0 10 20 30 40 50 60 70 80

Distance from divide (m)

Mea

n R

esid

ence

tim

e (d

ays

MRT = 1.9(Distance) + 19.0r 2̂ = 0.88

Based on data from Stewart and McDonnell, 1991 WRR

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Regionalized MRT to the entire basin based on a 2 meter elevation grid using a single direction D8 algorithm

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Model outputModel output

0.1

1

10

100

9/30 10/20 11/9 11/29 12/19 1/8

Date

Run

off (

l/s)

Measured Run1426 Run1836

0

25

50

75

100

9/30 10/20 11/9 11/29 12/19 1/8

Date

Run

off (

l/s)


1750 runs, cutoff NS > 0.75

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Tracer in the modelTracer in the model

outinpt qCqCpC

dtdM

−+=

∫

∫∞

∞

=

0

0

Cdt

tCdtMRT

Then defined as a mass balance of some arbitrary conserved tracer:

The mean residence time is derived by the concentration breakthrough:

i.e. time averaged C normalized by total mass of the tracer

Precipitation

Evapotranspiration


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Simulated tracer breakthroughSimulated tracer breakthrough

0

5

10

15

20

9/2 10/12 11/21 12/31 2/9 3/20 4/29

Time

Bre

akth

roug

h (m

g/l)

Directly simulated MRT over the prior parameter range varied from 30 to 95 days.

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0.1

0.3

0.5

0.7

0.9

30 50 70 90 110Mean Residence Time (days)

Q E

ffici

ency

…the slide you saw earlier

Vache and McDonnell, 2005 WRR

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Model output from before

0

25

50

75

100

9/30 10/20 11/9 11/29 12/19 1/8

Date

Run

off (

l/s)


…we would rejectthis model…recall that ourmeasured rangewas 0-120 days

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Precipitation

Evapotranspiration


Residence time as a process-based model rejection tool

Model 1

Model 4

Model 3

Model 2

Precipitation

Evapotranspiration


Precipitation

Evapotranspiration


Precipitation

Evapotranspiration


66YesYesYesYesYesYesModel 4Model 4

55YesYesNoNoYesYesModel 3Model 3

44NoNoYesYesYesYesModel 2Model 2

33NoNoNoNoYesYesModel 1Model 1

# Tuned # Tuned ParametersParameters

Explicit Explicit Unsaturated Unsaturated

ZoneZone

Effective Effective PorosityPorosity

Saturated Saturated ZoneZone

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Runs with NS > 0.7Runs with NS > 0.7

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BreakthroughsBreakthroughs

Note early time and late time differences between Models 1-4

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How much detail is warranted?How much detail is warranted?Complementary measures for evaluationComplementary measures for evaluation

Vache and McDonnell, 2005 WRR

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Take a virtual field trip that deals Take a virtual field trip that deals with with catchmentcatchment scale hydrology atscale hydrology at

http://www.cof.orst.edu/cof/fe/watershd/fe537/FE605http://www.cof.orst.edu/cof/fe/watershd/fe537/FE605--VFT_oak.htmVFT_oak.htm

fe 537 catchment modeling · 0.2 0.4 0.6 0.8 1 goodness measu r e a 1 , a 2 s a n d a 3 a 1 a d a 2...

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