Parameter estimation for computationally intensive nonlinear regression with an application to climate modeling

Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by maximum likelihood is not feasible. The method presented in this paper proposes to construct a faster running surrogate for such a computationally intensive nonlinear function, and to use it in a related nonlinear statistical model that accounts for the uncertainty associated with this surrogate. A pivotal quantity in the Earth's climate system is the climate sensitivity: the change in global temperature due to doubling of atmospheric $\mathrm{CO}_2$ concentrations. This, along with other climate parameters, are estimated by applying the statistical method developed in this paper, where the computationally intensive nonlinear function is the MIT 2D climate model.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS210 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Assessing the Impact of Retreat Mechanisms in a Simple Antarctic Ice Sheet Model Using Bayesian Calibration

The response of the Antarctic ice sheet (AIS) to changing climate forcings is an important driver of sea-level changes. Anthropogenic climate change may drive a sizeable AIS tipping point response with subsequent increases in coastal flooding risks. Many studies analyzing flood risks use simple models to project the future responses of AIS and its sea-level contributions. These analyses have provided important new insights, but they are often silent on the effects of potentially important processes such as Marine Ice Sheet Instability (MISI) or Marine Ice Cliff Instability (MICI). These approximations can be well justified and result in more parsimonious and transparent model structures. This raises the question of how this approximation impacts hindcasts and projections. Here, we calibrate a previously published and relatively simple AIS model, which neglects the effects of MICI and regional characteristics, using a combination of observational constraints and a Bayesian inversion method. Specifically, we approximate the effects of missing MICI by comparing our results to those from expert assessments with more realistic models and quantify the bias during the last interglacial when MICI may have been triggered. Our results suggest that the model can approximate the process of MISI and reproduce the projected median melt from some previous expert assessments in the year 2100. Yet, our mean hindcast is roughly 3/4 of the observed data during the last interglacial period and our mean projection is roughly 1/6 and 1/10 of the mean from a model accounting for MICI in the year 2100. These results suggest that missing MICI and/or regional characteristics can lead to a low-bias during warming period AIS melting and hence a potential low-bias in projected sea levels and flood risks.Comment: v1: 16 pages, 4 figures, 7 supplementary files; v2: 15 pages, 4 figures, 7 supplementary files, corrected typos, revised title, updated according to revisions made through publication proces

Optimization of multiple storm surge risk mitigation strategies for an Island City On a Wedge

Managing coastal flood risks involves choosing among portfolios of different options. Analyzing these choices typically requires a model. State-of-the-art coastal risk models provide detailed regional information, but can be difficult to implement, computationally challenging, and potentially inaccessible to smaller communities. Simple economic damage models are more accessible, but may not incorporate important features and thus fail to model risks and trade-offs with enough fidelity to effectively support decision making. Here we develop a new framework to analyze coastal flood control. The framework is computationally inexpensive, yet incorporates common features of many coastal cities. We apply this framework to an idealized coastal city and assess and optimize two objectives using combinations of risk mitigation strategies against a wide range of future states of the world. We find that optimization using combinations of strategies allows for identification of Pareto optimal strategy combinations that outperform individual strategy options.Comment: 22 pages, 5 figures, supplemental discussio

Trade-offs and synergies in managing coastal flood risk: A case study for New York City

Decisions on how to manage future flood risks are frequently informed by both sophisticated and computationally expensive models. This complexity often limits the representation of uncertainties and the consideration of strategies. Here we use an intermediate complexity model framework that enables us to analyze a richer set of strategies, a wider range of objectives, and greater levels of uncertainty than are typically considered by more sophisticated and computationally expensive models. We find that allowing for more combinations of risk mitigation strategies can help expand the solution set, help explain synergies and trade-offs, and point to strategies that can improve outcomes