Preliminary Uncertainty Analysis of Selected Hydrodynamic ... · Preliminary Uncertainty Analysis of Selected Hydrodynamic and Ecological Models in the Louisiana Coastal Area Ecosystem

Preliminary Uncertainty Analysis of Selected Hydrodynamic and Ecological Models in the Louisiana Coastal Area

Ecosystem Restoration Plan

Emad Habib

University of Louisiana at LafayetteUniversity of Louisiana at Lafayette

Victor H. Rivera-Monroy, Jenneke M. Visser, Kenneth A. Rose

Louisiana State University

Bill Nuttle

Eco-hydrology, Canada

Acknowledgements

•• Louisiana Department of Natural ResourcesLouisiana Department of Natural Resources

•• CLEAR Facility CLEAR Facility

•• CLEAR CLEAR Uncertainty Analysis TaskEmad Habib

Victor H. Rivera-Monroy

Emily Hyfield

Dubravko Justic

William Nuttle

Kenneth A. Rose

Erick Swenson

Jenneke Visser

Background• Louisiana is experiencing nationally critical coastal wetland

erosion and land loss

• Key causes are reduction in freshwater and sediment inputs

• Louisiana Coastal Area (LCA) study was developed to establish framework for solving Louisiana coastal problems.

• The Coastal Louisiana Ecosystem Assessment and • The Coastal Louisiana Ecosystem Assessment and Restoration (CLEAR) effort was initiated to develop a modeling tool for evaluation of restoration alternatives and their environmental benefits.

• CLEAR model combines a set of linked modules as an ecosystem forecasting tool for geophysical processes, geomorphic features, and ecological succession.

Linkage of CLEAR Modules

Organic

MatterElevation

Land

Water

Ratio

Land

Water

Ratio

Salinity & Water Level

Land Building Module

Habitat Use Module

Water Level

Salinity

Nutrient

Availability

Water Quality Module

Nutrient

Sinks

Ratio

Hydro-dynamics Module

Habitat Switching

Module

For the purpose of the CLEAR modeling effort,model uncertainty can be defined as:

Models are not perfect

The unpredictable deviation of model

predictions from the actual response of

the ecosystem

Sources of Uncertainty

Can be reduced Not reducible

understanding processes

Knowledge Uncertainty

spatial variability

Inherent Natural variability

objectives

Decision Uncertainty

Sources of Uncertainty

model structure

parameters

data

temporal variability Evaluation criteria

Performance measures

(values and targets)

Sources:Baecher et al., 2000Loucks et al., 2002LCA draft report, Chapter 13

Propagation of Uncertainties

uncertainty

uncertainty

uncertainty

uncertainty

uncertainty

uncertainty

Hydro-

dynamics

Habitat Switching

Land

Building

Module

Habitat

Use

Module

Water

Quality

Module

uncertainty

uncertainty

uncertaintyuncertainty

dynamics Module

Switching Module

Benefits

Combined Uncertainty

Why quantify uncertainty?

� Users might wrongly attribute too much accuracy to model predictions and infer unrealistic differences between restoration scenarios when no differences actually exist!

� Information about uncertainties of model predictions is essential to guide the selection among alternative

� Users might digest all sources of uncertainties and wrongly conclude that model predictions are useless!

� Quantifying uncertainties associated with model predictions is critical to ensure that predictions are properly interpreted.

is essential to guide the selection among alternative restoration projects.

A complete model uncertainty analysis involves:

• Identification of all sources of uncertainty that contribute to probability distributions of each input or output variable

• Specification of marginal and joint probability

• Constructing probability distributions of model outputs and their performance measures

• Specification of marginal and joint probability distributions of input variables and parameters

• Propagating these uncertainties through the different modules

Instead, we will focus on one module and its interactions with other modules

Organic

MatterElevation

Land

Water

Ratio

Land

Water

Ratio

Salinity & Water Level

Land Building Module

Habitat Use Module

Water Level

Salinity

Nutrient

Availability

Water Quality Module

Nutrient

Sinks

Ratio

Hydro-dynamics Module

Habitat Switching

Module

Inundation

Salinity

Bottomland Hardwood

Swamp Forest

Fresh

Marsh

Conceptual Model Habitat Switching

Inundation

Salinity

Salinity

Intermediate Marsh

Brackish Marsh

Saline Wetlands

Open

Water

Barrier

Islands

Inundation

Inundation

Salinity

Tools: Monte Carlo Simulations

pdfGenerate random

Module

pdf

Prob. density

function of

uncertain

parameter

random realizations of uncertain parameters

ModuleModule Output

Repeat many times

Prob. density

function of module

predictions

Selected Uncertainty Analysis Examples

Objective:

Investigate the Effect of the following Uncertainties on the Predictions of the Habitat Switching Module:

1. Effect of Hydro-climatic Variability

– Dry versus wet years

– Global climate change

3. Effect of Parameter Uncertainty

– Salinity switching thresholds

– Global climate change

4. Effect of Data Uncertainty

– Salinity input data as predicted by the Hydrodynamic (HD) modules

2. Effect of Natural Variability

- Annual Salinity

Effect of Natural Variability of Salinity

Observed Monthly Salinities

Lognormal Fitted Monthly Salinities

GeneratedAnnual Salinities

Effect of Temporal Natural Variability of Salinity

GeneratedAnnual Salinities

#o

fcells

inB

ox

3B

0

5

10

15

20

25

30

35

40

45

50

UPLSWF FFM INM BRM SAW BAI WATFAM

year 5

Habitat Switching

Module

Effect of Uncertainty in Model Parameter:switcher thresholds of habitat switching module

Time 1 habitat

Time 0 habitat

UPL

SWF

FAM

INM

BRM

SAW

WAT

UPL always

Based on average annual salinities of each habitat:

UPL always

SWF always

FAM <2.5 2.5-9 >9

INM <1 1-6 6-15 >15

BRM <6 6-15 >15

SAW =15 >15

WAT

UPL: UplandSWF: Swamp forestFAM: Fresh marshINM: Intermediate marsh

BRM: Brackish marshSAW: Saline wetlandWAT: Water

Pdf of salinity switching threshold

Mean=2.5 ppt

Standard deviation=10%

Standard deviation=25% Standard deviation= 50%

Mean=2.5 pptMean=2.5 ppt

Effect of Uncertainty in Salinity Switching Thresholds

%o

fB

ox

Are

a

10

20

30

40

50

60

Error Standard Deviation = 25%

%o

fB

ox

Are

a

10

20

30

40

50

60


Base Scenario B01

Box 3B; Province 2

0UPLSWF FFM INM BRM SAW BAI WATFAM


%ofB

ox

Are

a

0

10

20

30

40

50

60



• Inputs to many of the CLEAR modules are mostly based on predictions from

Data Uncertainty

mostly based on predictions from hydrodynamic (HD) models; these HD predictions can be associated with:

– Random errors

– Systematic errors

Effect of Uncertainty in HD Salinity Predictions: Random Error

%ofB

ox

Are

a

0

10

20

30

40

50


Standard Error in salinity input: 50%

%o

fB

ox

Are

a

0

10

20

30

40

50



Base Scenario B01

Box 3B; Province 2


%o

fB

ox

Are

a

0

10

20

30

40

50




Effect of Uncertainty in HD Salinity Predictions: Extreme conditions

#o

fcells

inB

ox

3B

100

200

300

400

500

Standard Error of salinity input: 30%

Wet Year

#o

fcells

inB

ox

3B

100

200

300

400

500

Standard Error of salinity input: 30%

Dry Year

#o

fcells

inB

ox

3B

0

100

200

300

400

500



#o

fcells

inB

ox

3B

0

100

200

300

400

500





Uncertainty in HD Salinity Predictions: Bias%

ofB

ox

Are

a

0

10

20

30

40

50

Bias in salinity input: 0 ppm

%o

fB

ox

Are

a

10

20

30

40

50

Bias in salinity input: +1 ppm+0 ppm +1 ppm

Base Scenario B01, Box 3B; Province 2

0UPLSWF FFM INM BRM SAW BAI WATFAM 0


%o

fB

ox

Are

a

0

10

20

30

40

50


Bias in salinity input: +3 ppm

%o

fB

ox

Are

a

0

10

20

30

40

50


Bias in salinity input: +6 ppm+3 ppm +6 ppm

Summary: Natural variability and climate change effects

• Systematic, persistent long-term changes in salinity levels have more impact on model predictions than local temporal variability in the salinitythe salinity

• Effect of uncertainties in parameters of habitat switching module (e.g., switching thresholds) can be significant

– More research and data are required to improve

Summary: Effect of Uncertainty in Model Parameter

– More research and data are required to improve the selection of these parameters

Summary: Uncertainty in Hydrodynamic Salinity Predictions

• Effects of random errors in salinity predictions of hydrodynamic models are not significant (except in extreme conditions)

• Effects of systematic errors (bias) in salinity predictions of hydrodynamic models can be very significant

– Make sure hydrodynamic models are CALIBRATED

What did we learn from these examples?

• Describe range of possible model outputs

• Estimate statistical characteristics of model outputs (mean, variance)

• Assign confidence intervals on model outputs or on

uncertainty analysis can help us to:

• Assign confidence intervals on model outputs or on functions of model outputs

• Describe model performance under different forcing conditions

• Estimate probability that performance measure will exceed a specified threshold

• Identify research needs and future data and model improvements

A complete uncertainty analysis of the CLEAR model faces the following challenges:

• The CLEAR modules are not conducive to complete uncertainty analysis.

• Lack of necessary information (e.g., marginal and joint probability distributions, parameter joint probability distributions, parameter covariance functions)

• Large number of uncertain variables and parameters

• Data (and computational) requirements

• Lack of validation in some modules

What can be done?

• We need to have a feasible strategy to conduct incomplete, yet informative, uncertainty analysis

• This practical strategy should provide us with probability distributions of the uncertain model predictions

Recommended Steps to Conduct Uncertainty Analysis for the CLEAR Model: Short Term

1. Identify the significant sources of uncertainty that impact the outcome of the proposed restoration projects.

2. Use sensitivity analysis to identify a narrower set of

3. Construct probability density functions for the selected uncertain variables and parameters.

2. Use sensitivity analysis to identify a narrower set of independent input variables and parameters that are most significant.

Recommended Steps to Conduct Uncertainty Analysis for the CLEAR Model: Short Term

4. Use Monte-Carlo random sampling simulations (or other methods) to propagate the uncertainties of the identified parameters and variables using a probability distribution formulation.

5. Use the derived probability distributions to make

6. Use the derived probability distributions and their confidence intervals to compare and select amongst the alternative proposed restoration projects.

5. Use the derived probability distributions to make quantitative assessment about the likelihood that a certain restoration project will meet a pre-specified performance target.

Long Term Strategy:

• Model calibration and validation

• Model restructuring

• Acquisition of reference baseline data sets• Acquisition of reference baseline data sets

• …….

• …….

EndThank You!

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Examples of Probability Distributions of Habitat Switching Output

Effect of uncertainty in salinity input(Dry year, 50% error in salinity input)

Effect of uncertainty in switching thresholds(Dry year, 50% error in salinity thresholds)

Effect of Uncertainty in Switching Thresholds

Wet Year(25% error)

10

20

30

40

50

60

% o

f B

ox A

rea

year 0 year 1 year 5

Dry Year(25 % error)

0

SWF FAM FFM INM BRM SAW BAI WAT UPL

0

10

20

30

40

50

60

SWF FAM FFM INM BRM SAW BAI WAT UPL

% o

f B

ox A

rea

year 0 year 1 year 5

Effect of Uncertainty in Salinity Switching ThresholdsOn Habitat Switching Output

%o

fB

ox

Are

a

10

20

30

40

50

60Wet yearError in switching thresholds: 25%

%o

fB

ox

Are

a

10

20

30

40

50

60Dry yearError in switching thresholds: 25%


%ofB

ox

Are

a

0

10

20

30

40

50

60


Dry yearError in switching thresholds: 50%

%o

fB

ox

Are

a

0

10

20

30

40

50

60


Wet yearError in switching thresholds: 50%


How to quantify uncertainty?

�Model validation is a key factor for

performing uncertainty analysis!

�Problem: Lack of validation (for some modules)

�Problem: some models are difficult to validate

(e.g., habitat use)

Effect of Hydro-climatic Variability

Little Lake Monthly Mean Salinity: 1993

8.0

12.0

16.0

20.0

Sa

linity (

pp

t)

Wet (1993)

Little Lake Monthly Mean Salinity: 2000

8.0

12.0

16.0

20.0

Sa

linity (

pp

t)

Dry (2000)

Little Lake Monthly Mean Salinity: 1981-2001

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12

Month

Sa

linity (

pp

t)

Data source LDWF, anlayzed by E. M. Swenson, LSU-CEI

Average (1981-2001)

0.0

4.0

1 2 3 4 5 6 7 8 9 10 11 12

Month

Data source LDWF, anlayzed by E. M. Swenson, LSU-CEI

0.0

4.0

1 2 3 4 5 6 7 8 9 10 11 12

MonthData source LDWF, anlayzed by E. M. Swenson, LSU-CEI

Effect of Hydro-climatic Variability%

ofB

ox

Are

a

10

20

30

40

50

60

Wet Year

%o

fB

ox

Are

a

10

20

30

40

50

60

Dry year5 Wet years 5 dry years

Box 3B; Province 2

%o

fB

ox

Are

a

0

10

20

30

40

50

60


Sequence of wet and dry years (1989-1992)



Effect of Global Climate Change:Long-term increase in salinity

0

2

4

6

8

8

Baseline

+30% MR

-30% MR

LDWF S326: Little Lake

A

Mean = 4 ppt

Ning, et al, 2003

0

2

4

6

Salinity (ppt)

0

2

4

6

8

1 2 3 4 5 6 7 8 9 10 11 12

Month

-10% P

+10% PBaseline

Baseline

-30% MR, -10% P, +30 cm

+30% MR, +10% P, +30 cm

B

C

Mean = 7 ppt

Effect of Global Climate Change:Increase in salinity levels

#ofcells

inB

ox

3B

5

10

15

20

25

30

35

40

45

50

baseline

#o

fcells

inB

ox

3B

5

10

15

20

25

30

35

40

45

50

+ 1 ppt

0

5

UPLSWF FFM INM BRM SAW BAI WATFAM0

5


#o

fcells

inB

ox

3B

0

5

10

15

20

25

30

35

40

45

50


+ 2 ppt

#ofcells

inB

ox

3B

0

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+ 3 ppt

Documents

Preliminary Uncertainty Analysis of Selected Hydrodynamic ... · Preliminary Uncertainty Analysis of Selected Hydrodynamic and Ecological Models in the Louisiana Coastal Area Ecosystem