GROWING COMPLEXITY: THE MODELING TRILEMMA

GROWING COMPLEXITY: THE MODELING TRILEMMA

Rafael Muñoz-Carpena, Ph.D., ProfessorUF/IFAS Agricultural and Biological Engineering

OUTLINE

• Take-home messages

• Complex systems, models and evaluation

• Concept 1: complexity –uncertainty-relevance

• Concept 2: uncertainty-resilience

• Case studies: biological migration

TAKE-HOME MESSAGES!

An iterative global sensitivity and uncertainty analysis (GSUA) framework integrated with migration model incremental building:

• Identification of optimized model relevance

• systematic evaluation of sources of uncertainties in complex coupled natural-human systems models

• quantification of alternative states and resilience of complex systems

• informing management decisions by MC filtering of important factors.

• transdisciplinary integration through complex system analysis!

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• After Robert Rosen, 1991, ”World” (the natural system) and “Model” (the formal system) are internally entailed - driven by a causal structure.

• Nothing entails with one another, “World” and “Model”; the association is hence the result of a craftsmanship.

[after A. Saltelli. 2008. SAMO’08. Venice, Italy]

Robert Rosen

A WORD ABOUT MODELS…

(Gong et al., 2013; WRR) [provided by Grey Nearing, NASA]

Real Complex

system

Observed

data

Model

George Box, the

industrial statistician, is

credited with the quote,

although probably the

first to say that was W.

Edwards Deming.

G. BoxW.E. Deming

[after A. Saltelli. 2008. SAMO’08. Venice, Italy]

‘…all models are wrong, some are useful’

HUMANSBIOLOGICAL

PHYSIC0-CHEMICAL

COMPLEX NATURAL-HUMAN SYSTEMS ANALYSIS

Transdisciplinary research!

• Internal Structure

• Emergent Behavior

• Resilience

• Adaptation and Evolution

• Uncertainty

COMPLEX SYSTEMS-CS

[Peterson- NSF Directorate for Engineering]

Issues in CS Modeling

• Predicting Emergent Behavior

• Understanding Evolution and Adaptation

• Calibrating predictive and forecasted complex

systems"Modeling to understand, reproduce, forecast and

control (management and planning) the system

behavior"

• What processes should be added?

• How does this impact uncertainty?

• Can the real system behavior (resilience, alternative states) be modeled?

• Will the model be usable based on available knowledge of the system (input factors)?

HOW TO MODEL MIGRATION CS?9

Multiple lines of evidence needed to develop and

test CS model validity, and only for particular settings:

• Non-linear dynamics data diagnostics to match

model specification (Type III error - misspecification)

• Conceptual model matching: Global sensitivity and

uncertainty analysis (Type II error- fail to detect an

effect)

• Goodness-of-fit against measured/benchmark

dataset (Type I error- detecting effects not present)

COMPLEX MODEL DEVELOPMENT/EVALUATION

MIGRATIONMODEL OUTPUTS

INPUT

FACTORS

A

B

C

GLOBAL SENSITIVITY/UNCERTAINTY ANALYSIS

Boundary conditions

(forcings, source/sinks)

Initial conditions on

state variables

Physical and numerical

parameters

GLOBAL SENSITIVITY ANALYSIS

A

B

C

A

BC

Apportions output variance into input factors

0

75

150

225

300

0.00

0.03

0.06

0.09

0.13

0.16

0.19

0.22

0.25

0.28

0.31

0.34

0.38

Freq

uen

cy

Bin

UNCERTAINTY ANALYSIS

Propagates input factor variability into output Output indicator

Uncertainty

HOW MUCH?

WHY/WHEN?

(Model independent – assumption free framework)

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Concept 1:

Model Complexity-Uncertainty-Relevance

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[Muller, Muñoz-Carpena, G.Kiker. 2011. In: I. Linkov and T.S.S. Bridges (eds.). NATO Science for

Peace and Security Series C: Environmental Security. Springer:Boston doi:10.1007/978-94-007-1770-1_4.]

MODEL “LIFE CYCLE”13

MIGRATION: SELECTION OF MODEL COMPLEXITY

2010 NSF-CHN [Perz, Muñoz-Carpena and Kiker]

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Lofti Zadeh

(father of “Fuzzy logic”)

…as the COMPLEXITY of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which PRECISION and RELEVANCE become almost mutually exclusive characteristics..."

“Principle of Incompatibility” (Zadeh, 1973)

COMPLEXITY VS. RELEVANCE CONUNDRUM

As model COMPLEXITY increases it leads to:

• Over-parameterization

• Hard/impossible to parameterize

• Equifinality, non-uniqueness

• …

• Loss of RELEVANCE –

“ability to answer the problem it was designed for”

COMPLEXITY VS. RELEVANCE CONUNDRUM 16

Relevance

UNCERTAINTY, SENSITIVITY, AND COMPLEXITY

complexity

Un

ce

rta

inty

Se

nsi

tiv

ity

Input uncertainty

Total uncertainty

(Hanna, 1993)

(Snowling and Kramer,1991)

[Muller, Muñoz-Carpena, G.Kiker. 2011. In: I. Linkov and T.S.S. Bridges (eds.). NATO Science for Peace

and Security Series C: Environmental Security. Springer:Boston doi:10.1007/978-94-007-1770-1_4.]

17

?

UncertaintyComplexity

Relevance

THE MODELING TRILEMMA

[Muller, Muñoz-Carpena, G.Kiker. 2011. In: I. Linkov and T.S.S. Bridges (eds.). NATO Science for Peace

and Security Series C: Environmental Security. Springer:Boston doi:10.1007/978-94-007-1770-1_4.]

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A NEW HOPE?

A step-wise model-building approach integrated with global uncertainty and sensitivity analysis (GSUA) to evaluate sources of uncertainty can be used to guide model development across increasing levels of model complexity (and relevance)

– Avoid unintended model prediction artifacts

– Achieve precision and capacity of the model to reproduce real and complex system responses (alternative states, etc.)

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…. IN SEARCH OF OPTIMAL MODEL RELEVANCE Rmax = optimal relevance? (a.k.a. the “Modeling Holy Grail”)

[Muller, Muñoz-Carpena, G.Kiker. 2011. In: I. Linkov and T.S.S. Bridges (eds.). NATO Science for Peace

and Security Series C: Environmental Security. Springer:Boston doi:10.1007/978-94-007-1770-1_4.]

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Concept 2:

Uncertainty Basis for System Resilience

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RESILIENCE DEFINITIONS

• Engineering resilience: speed with which a system returns to its initial state after a disturbance (Holling 1996; Rodriguez-Iturbe et al. 1991a; Scheffer 2009:101-103)

• Ecological resilience: the degree of disturbance a system can incur and still remain in its pre-existing state (Gunderson and Pritchard 2002:5-7; Scheffer 2009:101-103).

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Resilience: Ball-and-cup analogy

SYSTEM

MODEL

OUTPUT PDF1st alt. state

2nd alt. state

[Perz, Muñoz-Carpena, Kiker, Holt. 2013. Ecological Modelling Volume 263:174-186]

Output PDF multimodality: alternative system states and basins of attraction

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Rodriguez-Iturbe, I., D. Entekhabi, R.L. Bras. 1991. Non-linear dynamics of soil

moisture at climate scales. 1. Stochastic analysis. WRR 27(8)

σ2=0.1

σ2=0.5

σ2=1.0

Resilience also depends on stress intensity

Same model

structure with

different input

variability

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[Perz, Muñoz-Carpena, Kiker, Holt. 2013. Ecological Modelling Volume 263:174-186]

Model Complexity Window: Low complexity limits representation of

potential alternative system states (when plausible)

Resilience and model complexity: Ball-and-cup analogy

MO

DEL

O

UTP

UT

S

YSTE

M25

Evaluating ecological resilience in multimodal

probability distribution functions

GSUA PDF allows estimation of probabilities that the

system will remain in its initial state (0)

[Perz, Muñoz-Carpena, Kiker, Holt. 2013. Ecological Modelling Volume 263:174-186]

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CASE STUDY 1: CATTAIL MIGRATION IN THE EVERGLADES NP, FL

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Water Conservation Area

2A (WCA2A), in the

northern Everglades, FL.

Green squares represent

inlet and outlet control

structures; blue lines

represent canal structures.

Triangles represent the

mesh used for RSM

numerical simulation.

Test site & Model28

G.Lagerwall , G.Kiker , R.Muñoz-Carpena , N.Wang. 2014. Ecological Modelling 275:22-30

Processes Inputs Level 1 Level 2 Level 3 Level 4 Level 5

CATTAIL DIFFUSION

Cattail initial densities

Yes Yes Yes Yes Yes

Cattail growth rate

Yes Yes Yes Yes Yes

WATER DEPTHRegional water depth

No Yes Yes Yes Yes

P IN WATERRegional soil phosphorus concentration

No No Yes Yes Yes

SAWGRASS COMPETITION

Sawgrass initial densities

No No No Yes Yes

CATTAIL COMPETITION

Sawgrass growth rate

No No No No Yes

Cattails migration & invasion

Relevance

Cattail invasion

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CASE STUDY 2: LINKING GSUA TO MANAGEMENT OUTCOMES-

FUTURE FLORIDA SNOWY PLOVER MIGRATION AND SURVIVAL WITH SEA LEVEL RISE

[Poster]

informing management decisions by MC filtering of important factors.

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Thank you for your attention!

Questions?

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