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Hypothesis-Testing Model-Complexity

Hypothesis-Testing Model-Complexity. Hypothesis Testing …

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Page 1: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Hypothesis-Testing

Model-Complexity

Page 2: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Hypothesis Testing …..

Page 3: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Domain of groundwater model ...

Page 4: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

…topographic contours ...

Page 5: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

… a dam ...

Page 6: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

… irrigated area ...

Page 7: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

… channel system ...

Page 8: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

… extraction bores ...

Page 9: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

… native woodland ...

Page 10: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

… observation bores

Page 11: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Inflow from uphill

Supplied “from outside”

Page 12: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Inflow from uphill

Groundwater interaction with rivers

Supplied “from outside”

Page 13: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Inflow from uphillGroundwater interaction with dam

Groundwater interaction with rivers

Supplied “from outside”

Page 14: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Inflow from uphillGroundwater interaction with dam

Groundwater interaction with rivers

Leakage from channels

Supplied “from outside”

Page 15: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Inflow from uphillGroundwater interaction with dam

Groundwater interaction with rivers

Leackage from channels

Aquifer extraction

Supplied “from outside”

Page 16: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Inflow from uphillGroundwater interaction with dam

Groundwater interaction with rivers

Leackage from channels

Groundwater recharge

Aquifer extraction

Supplied “from outside”

Page 17: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

More often than not, a definitive model cannot be built.

Recognize this, focus on the question that is being asked and, if necessary, use the model for hypothesis testing.

Page 18: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Remember that model calibration is a form of data interpretation. The whole modelling process is simply advanced data processing.

Page 19: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Cattle Ck.

Page 20: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Cattle Creek Catchment

Page 21: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Soils and current land use

Page 22: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Model grid; fixed head and drainage cells shown coloured

Page 23: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Groundwater levels in June 1996

Page 24: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Groundwater levels in January 1991

Page 25: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Modelled and observed water levels after model calibration.

Page 26: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

264

279

4

1000

1000 10001000 253

77

10

171000

56

9

1000

2

2

2 3

7

18

3

27

24

Calibrated transmissivities

Page 27: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Cattle Creek Catchment

Page 28: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

CANE EXPANSION

New Development CURRENT

Page 29: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

2.5 mm/d at calibration2.5 mm/d for prediction

46R10P8

Page 30: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

2.5 mm/d at calibration2.5 mm/d for prediction

46R15P8

Page 31: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

2.5 mm/d at calibration2.5 mm/d for prediction

Zone 17 absent

48R14P8

Page 32: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

0.0 mm/d at calibration0.0 mm/d for prediction

46R3P7

Page 33: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

0.0 mm/d at calibration0.0 mm/d for prediction

46R4P7

Page 34: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

0.0 mm/d at calibration0.0 mm/d for prediction

Zone 17 absent

48R8P7

Page 35: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

2.5 mm/d at calibration2.5 mm/d for prediction

46R10P10

Page 36: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

2.5 mm/d at calibration2.5 mm/d for prediction

46R11P10

Page 37: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increased cane productionLeakage from balancing storage:

2.5 mm/d at calibration2.5 mm/d for prediction

Zone 17 absent

48R14P10

Page 38: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

P E

d

M

Ks

Simple ModelRunoff

Page 39: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

P E

d

M

Ks

Runoff

Simple Model

•M Soil Moisture Capacity (mm/m depth)•d Effective Rooting Depth•Ki Initital loss•fcap Field Capacity•Ks Saturated Hydraulic Conductivity

Page 40: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

MP E

d

M

Ks

Simple ModelRunoff

•M Soil Moisture Capacity (mm/m depth)•d Effective Rooting Depth•Ki Initital loss•fcap Field Capacity•Ks Saturated Hydraulic Conductivity

Page 41: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

A probability contour:-

“Fixing” a parameter

Page 42: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

This has the potential to introduce bias into key model predictions.

A probability contour:-

Page 43: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

Also, what if this parameter is partly a surrogate for an unrepresented process?

A probability contour:-

Page 44: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

“Fixing” a parameter

A probability contour:-

Page 45: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

“Fixing” a parameter

A probability contour:-

Page 46: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

• Not only does uncertainty arise from parameter nonuniqueness; it also arises from lack of certainty in model inputs/outputs and model boundary conditions.

• The model can be used as an instrument for data interpretation, allowing various hypotheses concerning inputs/outputs and boundary conditions to be tested.

• Where did the idea ever come from that there should be one calibrated model?

Page 47: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

modeller

construction calibration prediction

“the deliverable”

Page 48: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

prediction

“the deliverable”

Page 49: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

prediction

“the deliverable”

Page 50: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

modeller

construction calibration prediction

Page 51: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

“Dual calibration”

Page 52: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Observation bore

Pumped bore

K = 5Sy = 0.1

K = 5Sy = 0.1

K = 25Sy = 0.3In

flow

= 2

750

Fix

ed h

ead

= 5

0

A River Valley

Page 53: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Recharge × 10-3

0 100 200 300

0

1

2

Recharge rate

Page 54: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0 100 200 300

0

1000

2000 Discharge

Discharge

0 100 200 300

0

1000

2000

Pumping rate

Page 55: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Water level

Water level

0 100 200 300

48

52

56

0 100 200 300

48

52

56

Borehole hydrographs

Page 56: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

The finite-difference grid

Page 57: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

The finite-difference grid

and parameter zonation

Page 58: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0 100 200 300

48

52

56

K=5; Sy=0.1

K=5; Sy=0.1

K=25; Sy=0.3

Calibrated parameters

Field dataModel-calculated

Field andmodel-generatedboreholehydrographs

Page 59: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0 100 200 300

48

52

56

K=10.2; Sy=0.21

K=10.2; Sy=0.21

K=18.8; Sy=0.21

Field dataModel-calculated

Calibrated parameters

Field andmodel-generatedboreholehydrographs

Page 60: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Simulation of Drought Conditions

• Decrease inflow from left from 2750 to 2200 m3/day.

• Increase pumping from left bore from (1500, 1000, 0, 1500)

to 2000 m3/day.

• Increase pumping from right bore from

(2000,1000,500,1500) to 3000 m3/day.

• Run model for 91 days.

• Same initial heads, ie. 54 m.

For “true parameters”, water level in right bore after this run is 43.9m.

Page 61: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Is it possible that the water level in the left bore will be as low as 42m?

Page 62: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Use PEST with “model” comprised of two MODFLOW runs, one under calibration conditions and one under predictive conditions.

In the latter case there is only one “observation”, viz water level in right pumped cell is 42m at end of run (weight is the sum of the weights used for all water levels over calibration period).

Methodology

Page 63: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Model

Input files

Output files

PEST

writes model input files

reads model output files

Page 64: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Modelcalibration conditions

Input files

Output files

PEST

Input files

Modelpredictive conditions

Output files

Page 65: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0 100 200 300

48

52

56

K=22; Sy=0.14

K=16; Sy=0.16

K=9.8; Sy=0.28

Field dataModel-calculated

Field andmodel-generatedboreholehydrographs overcalibration period.

Water level in right pumped bore at end ofdrought = 42m.

Calibrated parameters

Page 66: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Is it possible that the water level in the left bore will be as low as 40m?

Page 67: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0 100 200 300

48

52

56

K=22; Sy=0.14

K=16; Sy=0.16

K=9.8; Sy=0.28

Field dataModel-calculated

Water level in right pumped bore at end ofdrought = 40m.

Field andmodel-generatedboreholehydrographs overcalibration period.

Calibrated parameters

Page 68: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0 100 200 300

48

52

56

K=5; Sy=0.099

K=14; Sy=0.11

K=20; Sy=0.32

Field dataModel-calculated

Water level in right pumped bore at end ofdrought = 40m.

K=4.6; Sy=0.090

Calibrated parameters

Field andmodel-generatedboreholehydrographs overcalibration period.

Page 69: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Is it possible that the water level in the left bore will be as low as 36m?

Page 70: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0 100 200 300

48

52

56

K=8.8; Sy=0.13

K=15; Sy=0.14

K=18; Sy=0.29

Field dataModel-calculated

Water level in right pumped bore at end ofdrought = 36m.

K=2.7; Sy=0.19

Calibrated parameters

Field andmodel-generatedboreholehydrographs overcalibration period.

Page 71: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

We are not calibrating a groundwater model.

We are calibrating our regularisation

methodology.

Page 72: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Some Lessons

• if possible, include in the calibration dataset measurements of the type that you need to predict

• intuition and knowledge of an area plays just an important part in modelling as does the model itself

• focus on what the model needs to predict when building the model…..

Page 73: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

There should be no such thing as a model for an area, only for a specific problem.

Page 74: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

So how should we model?

Page 75: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

open cut mine

open cut mine

underground mine

underground mine

waterholes

A model area

extraction bores

Page 76: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

open cut mine

open cut mine

underground mine

underground mine

waterholes

A model area

extraction bores

monitoring bores

guaging stations

Page 77: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 78: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 79: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 80: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 81: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 82: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 83: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 84: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 85: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 86: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 87: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Sources of Uncertainty Close to Waterholes

• conductance of bed (and heterogeneity thereof)

• change in bed conductance with wetted perimeter

• change in bed conductance with inflow/outflow and season

• relationship between area and level

• relationship between level and flow

• rate of evaporation

• hydraulic properties of rocks close to ponds

• behaviour during flood events

• change in hydraulic characteristics after flood events

• uncertainty in future flows

• inflow to ponds from neighbouring surface catchment

• lack of borehole data to define groundwater mounds

• uncertainties in streamflow

Page 88: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Let’s start again…..

Page 89: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Complexity leads to parameter uncertainty.

Parameter correlation can be enormous due to inadequate data.

Page 90: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Parameter uncertainty may lead to predictive uncertainty.

The more that the prediction depends on system “fine detail”, the more this is likely to occur.

Page 91: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Predictive uncertainty must be analysed.

Page 92: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Complexity must be “focussed” - dispense with non-essential complexity.

No model should be built independently of the prediction which it has to make.

Page 93: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 94: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 95: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 96: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 97: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 98: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model area

Page 99: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

open cut mine

open cut mine

underground mine

underground mine

waterholes

Sensitive area

Page 100: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

open cut mine

open cut mine

underground mine

underground mine

waterholes

Sensitive area

Page 101: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

open cut mine

open cut mine

underground mine

underground mine

waterholes

Sensitive area

Page 102: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

A model is not a database! A model is a data processor.

Page 103: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Ubiquitous complexity in a “do-everything model”

Page 104: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Ubiquitous complexity in a “do-everything model”

Page 105: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Focussed complexity in a prediction-specific model

Page 106: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Focussed complexity in a prediction-specific model

Page 107: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Model Complexity

Page 108: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

For reasons which we have already discussed, a complex model is really a simply model in disguise.

Page 109: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Complex models:-

More parameters Longer run times Greater likelihood of numerical

instability More costly Destroys user’s intuition

Page 110: Hypothesis-Testing Model-Complexity. Hypothesis Testing …
Page 111: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

The level of complexity is set by system properties to which the prediction is most sensitive.

Page 112: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

Objective functionminimum

Objective function contourslinear model

Page 113: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

A probability contour:-

Page 114: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

11

A probability contour:-

Page 115: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

11

2

2

A probability contour:-

Page 116: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

A probability contour:-

Page 117: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

p1+p2

A probability contour:-

Page 118: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

p1+p2 p1-p2

Ideally, simplification of a model should be done in such a way that only the parameters that “don’t matter” are dispensed with.

Page 119: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

There are many cases where a specific prediction depends on at least one of the values of the individual parameters - the parameters that cannot be resolved by the parameter estimation process.

In fact, that is often why we are using a physically based model; if calibration alone sufficed for full parameterisation, then a black box would be all we need.

Page 120: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

Over-simplified model design introduces bias, for we are effectively assuming values for unrepresented parameters.

Page 121: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

A probability contour:-

“Fixing” a parameter

Page 122: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

A probability contour:-

“Fixing” a parameter

Page 123: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

p1

p2

A probability contour:-

“Fixing” a parameter

Page 124: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increasing model complexity

pote

ntia

l er r

o r in

pre

dict

ion

complexity

bias

But we don’t know how much bias we are introducing.

?

Page 125: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increasing model complexity

complexity

bias

predictive uncertainty

These levels are equalpo

tent

ial e

r ro r

in p

redi

ctio

n

Page 126: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Increasing model complexity

complexity

bias

predictive uncertainty

These levels are equalpo

tent

ial e

r ro r

in p

redi

ctio

n

Page 127: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

The point where no further complexity is warranted, is the point where the uncertainty of a specific model prediction no longer rises.

Page 128: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Essential and non-essential complexity are prediction-dependent.

Page 129: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Complexity does not guarantee the “right answer” - it guarantees that the right answer will lie within the limits of predictive uncertainty.

Page 130: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Complexity without uncertainty analysis is a waste of time. A complex model can be just as biased as a simple model.

Use a simple model and add the “predictive noise” – far cheaper.

A complex model allows you to replace “predictive noise” with science. But if you don’t do it, what is the point of a complex model.

Page 131: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

An Example….

Page 132: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

NO RTH C AR O LINA

Neuse R iver basin

Contentnea C reekwatershed

N C County BoundariesSandy RunM iddle Sw am pLittle C ontentneaC ontentneaN euse

(77 km 2)

(140 km 2)

(470 km 2)

(2600 km 2)

(14500km 2)

Page 133: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

1

10

100

1000

10000

1-Jan-83 1-Mar-83 1-May-83 1-Jul-83 1-Sep-83 1-Nov-83 1-Jan-84

Observed and modelled flows

Page 134: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0.E+00

1.E+09

2.E+09

3.E+09

4.E+09

5.E+09

6.E+09

7.E+09

8.E+09

1970 1972 1974 1976 1978 1980 1982 1984 1986

Observed and modelled monthly volumes

Page 135: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0

0.2

0.4

0.6

0.8

1

10 100 1000 10000

Flow (cu ft /sec)

Exc

ee

de

nce

fra

ctio

n

Observed and modelled exceedence fractions

Page 136: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

ParameterLZSN 2.0UZSN 2.0INFILT 0.0526BASETP 0.200AGWETP 0.00108LZETP 0.50INTFW 10.0IRC 0.677AGWRC 0.983

Page 137: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

1

10

100

1000

10000

1-Jan-83 1-Mar-83 1-May-83 1-Jul-83 1-Sep-83 1-Nov-83 1-Jan-84

Observed and modelled flows

Page 138: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0.E+00

1.E+09

2.E+09

3.E+09

4.E+09

5.E+09

6.E+09

7.E+09

8.E+09

1970 1972 1974 1976 1978 1980 1982 1984 1986

Observed and modelled monthly volumes

Page 139: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0

0.2

0.4

0.6

0.8

1

10 100 1000 10000

Flow (cu ft/sec)

Exc

eede

nce

frac

tion

Observed and modelled exceedence fractions

Page 140: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Parameter Set 1 Set 2 Set 3 Set 4 Set 5 Set 6LZSN 2.0 2.0 2.0 2.0 2.0 2.0UZSN 2.0 1.79 2.0 2.0 1.76 2.0INFILT 0.0526 0.0615 0.0783 0.0340 0.0678 0.0687BASETP 0.200 0.182 0.199 0.115 0.179 0.200AGWETP 0.00108 0.0186 0.0023 0.0124 0.0247 0.0407LZETP 0.50 0.50 0.20 0.72 0.50 0.50INTFW 10.0 3.076 1.00 4.48 4.78 2.73IRC 0.677 0.571 0.729 0.738 0.759 0.320AGWRC 0.983 0.981 0.972 0.986 0.981 0.966

Page 141: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

1

10

100

1000

10000

1-Jan-93 1-Mar-93 1-May-93 1-Jul-93 1-Sep-93 1-Nov-93 1-Jan-94

Observed and modelled flows over validation period

Page 142: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0.E+00

1.E+09

2.E+09

3.E+09

4.E+09

5.E+09

6.E+09

7.E+09

8.E+09

9.E+09

1.E+10

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995

Observed and modelled monthly volumes over validation period

Page 143: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

0

0.2

0.4

0.6

0.8

1

10 100 1000 10000

Flow (cu ft/sec)

Exc

ee

de

nce

fra

ctio

n

Observed and modelled exceedence fractions over validation period

Page 144: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

1

10

100

1000

10000

1-Jan-93 1-Mar-93 1-May-93 1-Jul-93 1-Sep-93 1-Nov-93 1-Jan-94

Observed and modelled flows over validation period

Page 145: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

1

10

100

1000

10000

1-Jan-93 1-Mar-93 1-May-93 1-Jul-93 1-Sep-93 1-Nov-93 1-Jan-94

Observed and modelled flows over validation period

Parameterisation using PEST’s predictive analyser

Page 146: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

1

10

100

1000

10000

1-Jan-83 1-Mar-83 1-May-83 1-Jul-83 1-Sep-83 1-Nov-83 1-Jan-84

Observed and modelled flows over calibration period

Page 147: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

ParameterLZSNUZSNINFILTBASETPAGWETPLZETPINTFWIRCAGWRC

Page 148: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

ParameterLZSNUZSNINFILTBASETPAGWETPLZETPINTFWIRCAGWRCDEEPFR

Page 149: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

Observed and modelled flows over validation period

Parameterisation using PEST’s predictive analyser

1

10

100

1000

10000

1-Jan-93 1-Mar-93 1-May-93 1-Jul-93 1-Sep-93 1-Nov-93 1-Jan-94

Page 150: Hypothesis-Testing Model-Complexity. Hypothesis Testing …

1

10

100

1000

10000

1-Jan-83 1-Mar-83 1-May-83 1-Jul-83 1-Sep-83 1-Nov-83 1-Jan-84

Observed and modelled flows over calibration period