Uncertainty Quantification and Risk

Uncertainty quantification and risk analysis for geophysical hazard models, emphasizing scalable methods and decision-relevant interpretation under climate change.

Overview

Uncertainty is inherent in computational models of geophysical systems, arising from incomplete observations, model assumptions, and future climate conditions. This project focuses on quantifying, propagating, and interpreting uncertainty in computational models, with the goal of producing risk-relevant and decision-supporting outputs rather than single deterministic predictions.

My work emphasizes uncertainty-aware modeling strategies that remain computationally feasible for large-scale, high-resolution simulations. It builds upon earlier contributions to uncertainty quantification and inverse problems for geophysical systems, extending these ideas to modern, large-scale risk assessment under climate change.

Left: Monotone decomposition for transport aware model reduction from (Rim et al., 2023). Right: Changes in the return curves for Jamaica Bay NYC for the current climate (blue), projected climate in 2050 (orange), and projected climate in 2100 (red) from (Sarhadi et al., 2024).

Core Questions

How should uncertainty in storms, sea level rise, and model parameters be represented in coastal hazard models?
What uncertainty information is most relevant for risk assessment and decision-making?
How can uncertainty be propagated efficiently in computationally expensive geophysical models?
How do climate-driven nonstationarities alter traditional risk metrics?

Methods & Approaches

My research integrates uncertainty quantification techniques with numerical simulation and data-driven modeling, including:

Polynomial chaos and surrogate modeling for efficient uncertainty propagation
Bayesian inference and inverse methods for parameter estimation in geophysical models
Ensemble-based approaches for storm surge and compound flooding scenarios
Reduced-order and transport-aware models for computationally intensive systems
Risk and exceedance analysis under nonstationary climate assumptions

These methods are often developed in close connection with large-scale numerical models, ensuring consistency between uncertainty treatment and underlying physics.

Foundations & Early Work

My work in uncertainty quantification builds on earlier contributions to polynomial chaos methods, Bayesian inference, and inverse problems for geophysical and transport-dominated systems. These efforts focused on quantifying parametric uncertainty, inferring poorly constrained model inputs, and developing surrogate models compatible with large-scale numerical solvers.

This foundation continues to inform my current work on risk-aware coastal hazard modeling, particularly in settings where uncertainty is high and data are limited.

Applications

Representative applications include:

Probabilistic flood risk assessment for urban infrastructure
Climate-driven changes in compound flooding risk
Evaluation of coastal protection strategies under uncertain future conditions
Interpretation of hazard uncertainty for stakeholder-facing studies

Many of these efforts are closely linked to the Coastal Flooding & Storm Surge Modeling project, where uncertainty-aware methods are applied at scale. This work also draws on foundational numerical methods described in Numerical Methods for Hyperbolic PDEs.

Outcomes

Scientific Contributions

Frameworks for uncertainty-aware coastal hazard modeling
Methods for integrating uncertainty quantification with high-resolution simulations

Impact

Risk metrics that move beyond deterministic flood maps
Improved communication of uncertainty to interdisciplinary collaborators
Support for climate adaptation and resilience planning under deep uncertainty

Representative Publications

Foundations of Uncertainty Quantification

Quantifying uncertainties in tsunami source inversion (Sraj et al., 2017; Giraldi et al., 2017)
Bayesian inference of geophysical parameters (Sraj et al., 2014)
Polynomial chaos surrogates for transport-dominated systems (Rim & Mandli, 2018)

Risk, Climate, and Coastal Applications

Climate change contributions to compound flooding (Sarhadi et al., 2024)
Coastal flood hazards under climate change (Hemmati et al., 2025)
Optimization of coastal protection under uncertainty (Miura et al., 2025)

References

2025

Assessment of Caribbean Coastal Hazard Posed by Tropical Cyclones

Mona Hemmati, Chia-Ying Lee, Kyle T. Mandli, Adam H. Sobel, Suzana J. Camargo, and 1 more author

Journal of Applied Meteorology and Climatology, Nov 2025

DOI
Coastal storm-induced flooding risk of the New York City subway amid climate change

Yuki Miura, Christine Y. Blackshaw, Michelle S. Zhang, Kyle T. Mandli, and George Deodatis

Transportation Research Part D: Transport and Environment, Nov 2025

Abs DOI

Coastal areas face worsening storm-induced flooding due to climate change, threatening critical below-ground infrastructure like subway systems, as seen from Hurricane Sandy’s catastrophic impact on New York City (NYC)’s subway system in 2012. Stakeholders must urgently address these risks to protect infrastructure and assets. Simulating future flood scenarios is crucial for estimating flood risk and damage efficiently and for identifying reliable and effective protective measures. This article uses the GIS-based Subdivision-Redistribution (GISSR) methodology, a high-speed, physics-based flood estimation tool, that is now extended to model subway system flooding and associated economic impacts. It identifies flooded tunnels and stations and quantifies indirect economic losses from subway inoperability using an input–output model. The model is validated against observed subway flooding during Hurricane Sandy. Each analysis, covering both above- and below-ground flooding in Lower Manhattan, takes less than 90 s on a single 4-core Intel Core i7-13620H CPU machine. Scenario analyses were conducted with NYC stakeholders, incorporating sea level rise projections and various protective measures. Results, benchmarked against NYC’s ongoing resiliency projects, demonstrate the effectiveness of adaptation/protective strategies, particularly when subway system-specific and coastal measures are combined, highlighting the model’s value as a practical guide for stakeholders.

2024

Climate Change Contributions to Increasing Compound Flooding Risk in New York City

Ali Sarhadi, Raphaël Rousseau-Rizzi, Kyle Mandli, Jeffrey Neal, Michael P Wiper, and 2 more authors

Bulletin of the American Meteorological Society, Nov 2024

Abs DOI

Abstract Efforts to meaningfully quantify the changes in coastal compound surge- and rainfall-driven flooding hazard associated with tropical cyclones (TCs) and extratropical cyclones (ETCs) in a warming climate have increased in recent years. Despite substantial progress, however, obtaining actionable details such as the spatially and temporally varying distribution and proximal causes of changing flooding hazard in cities remains a persistent challenge. Here, for the first time, physics-based hydrodynamic flood models driven by rainfall and storm surge simultaneously are used to estimate the magnitude and frequency of compound flooding events. We apply this to the particular case of New York City. We find that sea level rise (SLR) alone will increase the TC and ETC compound flooding hazard more significantly than changes in storm climatology as the climate warms. We also project that the probability of destructive Sandy-like compound flooding will increase by up to 5 times by the end of the century. Our results have strong implications for climate change adaptation in coastal communities.

2023

Manifold Approximations via Transported Subspaces: Model Reduction for Transport-Dominated Problems

Donsub Rim, Benjamin Peherstorfer, and Kyle T. Mandli

SIAM Journal on Scientific Computing, Nov 2023

Abs DOI

This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as hyperbolic conservation laws typically exhibit nonlinear structures, which means that traditional model reduction methods based on linear approximations are inefficient when applied to these problems. In contrast, the approach introduced in this work derives reduced approximations that are nonlinear by explicitly composing global transport dynamics with locally linear approximations of the solution manifolds. A time-stepping scheme evolves the nonlinear reduced models by transporting local approximation spaces along the characteristic curves of the governing equations. The proposed computational procedure allows an offline/online decomposition and is online-efficient in the sense that the complexity of accurately time stepping the nonlinear reduced model is independent of that of the full model. Numerical experiments with transport through heterogeneous media and the Burgers equation show orders of magnitude speedups of the proposed nonlinear reduced models based on transported subspaces compared to traditional linear reduced models and full models.

2018

Displacement Interpolation Using Monotone Rearrangement

Donsub Rim and Kyle T. Mandli

SIAM/ASA Journal on Uncertainty Quantification, Nov 2018

Abs DOI

When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters proves ineffective. This is particularly true for responses from hyperbolic partial differential equations (PDEs) where linear, low-dimensional bases are difficult to construct. We propose the use of displacement interpolation, where the interpolation is done on the optimal transport map between the functions at nearby parameters, to achieve an effective dimensionality reduction of hyperbolic phenomena. We further propose a multidimensional extension by using the intertwining property of the Radon transform. This extension is a generalization of the classical translational representation of Lax and Phillips [P. D. Lax and R. S. Phillips, Bull. Amer. Math. Soc., 70 (1964), pp. 130–142].

2017

Quantifying uncertainties in fault slip distribution during the Tōhoku tsunami using polynomial chaos

Ihab Sraj, Kyle T. Mandli, Omar M. Knio, Clint N. Dawson, and Ibrahim Hoteit

Ocean Dynamics, Nov 2017

Abs DOI

An efficient method for inferring Manning’s n coefficients using water surface elevation data was presented in Sraj et al. (Ocean Modell 83:82–97 2014a) focusing on a test case based on data collected during the Tōhoku earthquake and tsunami. Polynomial chaos (PC) expansions were used to build an inexpensive surrogate for the numerical model GeoClaw, which were then used to perform a sensitivity analysis in addition to the inversion. In this paper, a new analysis is performed with the goal of inferring the fault slip distribution of the Tōhoku earthquake using a similar problem setup. The same approach to constructing the PC surrogate did not lead to a converging expansion; however, an alternative approach based on basis pursuit denoising was found to be suitable. Our result shows that the fault slip distribution can be inferred using water surface elevation data whereas the inferred values minimize the error between observations and the numerical model. The numerical approach and the resulting inversion are presented in this work.
Bayesian inference of earthquake parameters from buoy data using a polynomial chaos-based surrogate

Loïc Giraldi, Olivier P. Le Maître, Kyle T. Mandli, Clint N. Dawson, Ibrahim Hoteit, and 1 more author

Computational Geosciences, Apr 2017

Abs DOI

This work addresses the estimation of the parameters of an earthquake model by the consequent tsunami, with an application to the Chile 2010 event. We are particularly interested in the Bayesian inference of the location, the orientation, and the slip of an Okada-based model of the earthquake ocean floor displacement. The tsunami numerical model is based on the GeoClaw software while the observational data is provided by a single DARTⓇ buoy. We propose in this paper a methodology based on polynomial chaos expansion to construct a surrogate model of the wave height at the buoy location. A correlated noise model is first proposed in order to represent the discrepancy between the computational model and the data. This step is necessary, as a classical independent Gaussian noise is shown to be unsuitable for modeling the error, and to prevent convergence of the Markov Chain Monte Carlo sampler. Second, the polynomial chaos model is subsequently improved to handle the variability of the arrival time of the wave, using a preconditioned non-intrusive spectral method. Finally, the construction of a reduced model dedicated to Bayesian inference is proposed. Numerical results are presented and discussed.

2014

Uncertainty quantification and inference of Manning’s friction coefficients using DART buoy data during the Tōhoku tsunami

Ihab Sraj, Kyle T. Mandli, Omar M. Knio, Clint N. Dawson, and Ibrahim Hoteit

Ocean Modelling, Apr 2014

Abs DOI

Tsunami computational models are employed to explore multiple flooding scenarios and to predict water elevations. However, accurate estimation of water elevations requires accurate estimation of many model parameters including the Manning’s n friction parameterization. Our objective is to develop an efficient approach for the uncertainty quantification and inference of the Manning’s n coefficient which we characterize here by three different parameters set to be constant in the on-shore, near-shore and deep-water regions as defined using iso-baths. We use Polynomial Chaos (PC) to build an inexpensive surrogate for the GeoClaw model and employ Bayesian inference to estimate and quantify uncertainties related to relevant parameters using the DART buoy data collected during the Tōhoku tsunami. The surrogate model significantly reduces the computational burden of the Markov Chain Monte-Carlo (MCMC) sampling of the Bayesian inference. The PC surrogate is also used to perform a sensitivity analysis.