A Framework for Spatiotemporal Uncertainty & Sensitivity Analysis of Geographical Models

Piotr Jankowski, Arika Ligmann-Zielinska San Diego State University, Michigan State University

Uncertainty Analysis vs. Sensitivity Analysis • Uncertainty Analysis (UA) assesses the uncertainty of model output resulting from model input factors.
UA does not explain a relationship between uncertain factors and their share in model’s overall output uncertainty

• Sensitivity Analysis (SA) evaluates the contribution of each input factor to uncertainty in model output.

An Integrated Approach to UA & SA

Motivation for i-USA • Managing model output uncertainty through: – Identifying input factors that influence output variance.

• Model simplification through: – Identifying non-influential factors (factor fixing).

• Gaining insights into model behavior in space & time: – Identifying regions of low/high model output uncertainty and their changes in time.

• Providing insights on where further data collection is needed.

Steps of i-USA Uncertainty Analysis 1. Identify uncertain input factors in a model. 2. Generate a list of N input samples for k input factors. The size of N depends on model complexity. 3. Run the model N times to simulate N model output realizations. 4. Aggregate the N model output realizations computing model output mean and variance (measure of output uncertainty).

Steps of i-USA Sensitivity Analysis 5. Decompose the unconditional (total) variance of model output into conditional variances and calculate: - First-order sensitivity index (Si) that quantifies the contribution to output variance of a given factor i taken independently from other factors. - Total effect sensitivity index (STi) that quantifies the contribution to outcome variance of factor i accounting for its interactions with other factors.

i-USA Workflow

i-USA Example

Ligmann-Zielinska, A., Jankowski, P. 2014. Environmental Modeling & Software. 57, 235-247

Modeling Land Suitability • Spatial Multiple Criteria Evaluation Model: – Ideal Point multiple criteria aggregation function – Seven suitability criteria – Criteria weights as uncertain input factors

Ligmann-Zielinska, A., Jankowski, P. 2014. Environmental Modeling & Software. 57, 235-247

Results of UA

Ligmann-Zielinska, A., Jankowski, P. 2014. Environmental Modeling & Software. 57, 235-247

Results of UA

Ligmann-Zielinska, A., Jankowski, P. 2014. Environmental Modeling & Software. 57, 235-247

Results of SA: First Order (Si) Sensitivity Index

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Ligmann-Zielinska, A., Jankowski, P. 2014. Environmental Modeling & Software. 57, 235-247

Results of SA: Dominance Map of Si Indices

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Ligmann-Zielinska, A., Jankowski, P. 2014. Environmental Modeling & Software. 57, 235-247

Results of SA: Interaction Effects Based on STi Indices

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Ligmann-Zielinska, A., Jankowski, P. 2014. Environmental Modeling & Software. 57, 235-247

A Framework for Spatiotemporal i-USA

Challenges Associated with spatiotemporal i-USA • Number of random samples N needs to be quite high to obtain a reliable approximation of the variance-based sensitivity indexes: – The authors present a land suitability model, where N = 15,360, factors (k) = 9, resulting in 138,240 samples

• Number of model simulations increases as a function of spatial units representing the study area: – In the land suitability model the study area comprises 73,170 cells requiring to compute over 109 suitability scores (73170 * 138240); one score for each cell

• Large number of simulations N∙(K+2)∙m∙t can become problematic in computationally complex models

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Conclusion • Advantages of employing the framework in space-time geographical models – Factor prioritization (importance), – Model simplification, – Identification of the drivers of uncertainty

• Computational cost limiting model complexity and level of detail in representing space and time. • Need to develop intelligent ways of representing uncertain inputs and taking advantage of high performance computing environments. 17

ACKNOWLEDGMENT Financial support for this work was provided in part by the U.S. National Science Foundation Geography and Spatial Sciences Program Grant No. BCS 1263477. Any opinion, findings, conclusions, and recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation.