This repository includes the codes used in the paper: Optimal Life-Cycle Adaptation of Coastal Infrastructure under Climate Change by Bhattacharya, Papakonstantinou, Warn, McPhillips, Bilec, Forest, Hasan, and Chavda (Accepted in Nature Communications. Currently in print).

Abstract: Climate change-related risk mitigation is typically addressed using cost-benefit analysis that evaluates mitigation strategies against a wide range of simulated scenarios and identifies a static policy to be implemented, without considering future observations. Due to the substantial uncertainties inherent in climate projections, this identified policy will likely be sub-optimal with respect to the actual climate trajectory that evolves in time. In this work, we thus formulate climate risk management as a dynamic decision-making problem based on Markov Decision Processes (MDPs) and Partially Observable MDPs, taking real-time data into account for evaluating the evolving conditions and related model uncertainties, in order to select the best possible life-cycle actions in time, with global optimality guarantees, for the formulated optimization problem. The framework is developed for coastal adaptation applications, considering a wide variety of possible actions, including various forms of nature-based infrastructure. Related environmental impacts of carbon emissions and uptake are also incorporated and social cost of carbon implications are discussed, together with several future directions and supported features.

This repository contains the steps along with the necessary codes for generating components of the MDP and POMDP models for flood management and for generating the input for dynamic programming solvers like FRTDP. The workflow for generating the MDP and POMDP input files for the coastal city setting application with the two floodwall options for the SSP:245 scenario, as described in the paper, using the provided code, is outlined below.

• The IPCC projection dataset (for Battery tide gauge in New York) used to simulate SLR models is available at: IPCC slr projections. These datasets, if used directly, are to be cited properly as documented in IPCC SLR projections.
• The dataset for SLR trends (for Battery tide gauge in New York) used to fit the noise present in the past SLR observations is taken from: NOAA slr trends

The SLR trajectories are simulated using the slr_simulations.m file. This file requires the SLR projections to be stored in the format as is provided in SLR_245.mat file. This file provides sea-level rise (SLR) projections across various years (years.mat) and quantile values (quantiles.mat) for the SSP245 scenario at the New York Battery tidal gauge (downloaded from IPCC slr projections). The SLR projections for other SSP scenarios can also be found at IPCC slr projections. The generated simulations are used to inform SLR state transitions.

The dataset of annual extremes (for Battery tide gauge in New York) used to fit a GEV model for storm surges is taken from: NOAA Extremes

To generate discrete-state transition probabilities, the SLR and storm surge levels are suitably discretized into 77 and 72 discrete states, respectively. The discrete-state transitions for Sea Level Rise (SLR) and storm surge are generated using the codes, as:

1. slr_transitions.m for SLR transitions
2. surge_transitions.m for storm surge transitions

The SLR transition probability matrices derived and used in this paper can be found at t_slr_245.mat file. The storm surge transitions derived from the GEV model is uploaded here as t_surge.mat file. The SLR and storm surge transition probabilities need to be combined to obtain transition probabilities over combined SLR and storm surge states using the cal_transitions_total.m file.

The full state space of the problem needs to account for non-stationary sea level rise trends and different system configurations possible with different sets of actions. The complete state space of the problem is derived in the paper. After generating the SLR and surge transitions, the full transition model over the complete MDP state space is generated considering state-space augmentation with time and systems, using transition_model_MDP.m file.

Generate the rewards for states in the different systems for all the actions in the application setting, along with the social cost of carbon considerations, using the rewards_with_scc_systems.m file. After generating the rewards for the different systems, the rewards for the full MDP state space are generated using the rewards_model_MDP.m file. This file calls rewards_fp.m file to shape the rewards in such a way so as to use the fast parser for the input file in the solver used. The fast parser is used to efficiently parse large input files for the dynamic programming solver to be used.

After generating the transitions and rewards components of the MDP model in the above steps, the MDP input file is generated using inp_mdp_file_generator.m file. The generated input is solved using the FRTDP solver. The solver is publicly available at: FRTDP. The details related to the solver and the input file formats can be found in this GitHub.

For the POMDP formulation, the MDP state space is further expanded to include all relevant states within each of the climate scenario models under consideration. The transition matrices need to be obtained as outlined above for each of the climate models under consideration. The underlying climate model is not known with certainty in this framework and is inferred based on observations in time. We consider two possible climate model scenarios in this work, SSP2-4.5 and SSP5-8.5, without loss of generality, and the belief over these models is updated using SLR states, which are fully observable in time. For any given SLR state, there exists a probability of observing that specific SLR state under each of the considered climate models. These probabilities are represented in the observation likelihood matrices and can be generated using obs_likelihood_models.m file.

The POMDP input file is generated using inp_pomdp_file_generator.m file. The config options files for the FRTDP solver are also provided here as config_options_mdp and config_options_pomdp for the MDP and POMDP formulations, respectively. These options can be changed according to user preference. More details about the options can be found at FRTDP.

• Fox-Kemper, B., H.T. Hewitt, C. Xiao, G. Aðalgeirsdóttir, S.S. Drijfhout, T.L. Edwards, N.R. Golledge, M. Hemer, R.E. Kopp, G. Krinner, A. Mix, D. Notz, S. Nowicki, I.S. Nurhati, L. Ruiz, J.-B. Sallée, A.B.A. Slangen, and Y. Yu, 2021: Ocean, Cryosphere and Sea Level Change. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 1211–1362, doi:10.1017/9781009157896.011.
• Kopp, R. E., Garner, G. G., Hermans, T. H. J., Jha, S., Kumar, P., Reedy, A., Slangen, A. B. A., Turilli, M., Edwards, T. L., Gregory, J. M., Koubbe, G., Levermann, A., Merzky, A., Nowicki, S., Palmer, M. D., & Smith, C. (2023). The Framework for Assessing Changes To Sea-Level (FACTS) v1.0: A platform for characterizing parametric and structural uncertainty in future global, relative, and extreme sea-level change. Geoscientific Model Development, 16, 7461–7489. https://doi.org/10.5194/gmd-16-7461-2023
• Garner, G. G., T. Hermans, R. E. Kopp, A. B. A. Slangen, T. L. Edwards, A. Levermann, S. Nowikci, M. D. Palmer, C. Smith, B. Fox-Kemper, H. T. Hewitt, C. Xiao, G. Aðalgeirsdóttir, S. S. Drijfhout, T. L. Edwards, N. R. Golledge, M. Hemer, G. Krinner, A. Mix, D. Notz, S. Nowicki, I. S. Nurhati, L. Ruiz, J-B. Sallée, Y. Yu, L. Hua, T. Palmer, B. Pearson, 2021. IPCC AR6 Sea Level Projections. Version 20210809. Dataset accessed [2024-10-27] at https://doi.org/10.5281/zenodo.5914709.

If you use this repository in your research or projects, please cite our paper as follows:

@article{bhattacharya2024optimal,
    author = {Bhattacharya, A. and Papakonstantinou, K.G., and Warn, G.P., McPhillips, L.,
    Bilec, M.M., and Forest, C.E., and Hasan, R. and Chavda, D.},
    title = {Optimal Life-Cycle Adaptation of Coastal Infrastructure under Climate Change},
    journal = {Nature Communications},
    year = {2024},
    note = {Accepted and currently in print}
}