growing complexity: the modeling trilemma
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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
12
[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.]
18
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.]
20
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
23
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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