AGU2020 Yohei Sawada1 and Risa Hanazaki1 1 The University of Tokyo Socio-hydrologic data assimilation: Analyzing human-flood interactions by model-data integration ȁ ∝ ȁ x: model states, y: observation

AGU2020 1. Introduction

AGU2020 1.1. Socio-hydrological modeling vs observation [Di Baldassarre et al. 2013 HESS] [Gironz Lopez et al. 2017 WRR] Socio-hydrological modeling Socio-hydrological observation [Fanta et al. 2019 Nat. Comm.] [Mostert 2018 HESS]

AGU2020 1.2. Model-data integration in the socio-hydrologic domain Socio-hydrologic simulation Socio-hydrologic observation VS. Good: • Spatiotemporally continuous social state. • Improving understanding by simulating unrealized scenario. Bad: • Inaccurate, many hypothesis Good: • Accurate. Bad: • Spatiotemporally sparse • Difficult to quantify causal relationship → Model-data integration is crucially important to push the limit of socio-hydrologic approach!

AGU2020 1.3. Goals Exploring the potential of sequential data assimilation as the model-data integration in the socio-hydrologic domain.

AGU2020 2. Method

AGU2020 2.1. Flood risk model [Di Baldassarre et al. 2013 HESS]

AGU2020 2.2. Sequential data assimilation In data assimilation, we sequentially execute Bayes’ theorem between simulation and observation ȁ ∝ ȁ x: model states, y: observation prior: probability of model’s state before looking at observations Likelihood: consistency between simulation and observation Posterior: probability of model’s state after looking at observations time prior observation posterior Sampling-Importance-Resampling Particle Filter (SIRPF) [e.g., Moradkhani et al. 2005 WRR] was used in this study

AGU2020 3. Idealized experiments

AGU2020 3.1. Observation System Simulation Experiment (OSSE) External forcing (High water level) Flood risk model: f + 1 = , , x: model variables (e.g., levee height, settlement size) Observation Simulated observation Operator True world OSSE is the idealized numerical experiment to check if the proposed algorithm properly works. Model parameter: (e.g., social memory decay rate) External forcing (High water level) Flood risk model: f + 1 = , , x: model variables (e.g., levee height, settlement size) Simulated observation Operator Model parameter: (e.g., social memory decay rate)

AGU2020 3.2.1. Scenario 1: Uncertain high water level - setup External forcing (High water level) Flood risk model: f + 1 = , , x: model variables (e.g., levee height, settlement size) Observation Simulated observation Operator Model parameter: (e.g., social memory decay rate) In the scenario 1, we have added noise to the “true” high water level. The structure of the model and parameters are assumed to be perfect (same as “truth”). Observation of all 4 state variables can be obtained every 10 years.

AGU2020 3.2.2. Scenario 1: Uncertain high water level - Results 5000-ensemble simulation of flood risk model. Black: Truth, Gray: ensembles, red: ensemble mean No data assimilation data assimilation Uncertainty in high water level induces uncertainty in social processes, which is greatly mitigated by data assimilation

AGU2020 3.3.1. Scenario 2: Uncertain high water level, parameters, and model structure - setup External forcing (High water level) Flood risk model: f + 1 = , , x: model variables (e.g., levee height, settlement size) Observation Simulated observation Operator Model parameter: (e.g., social memory decay rate) In scenario 2, we have 4 unknown parameters and 2 of them temporally change in the “true” world. We assume that we do not know the rule to control the dynamics of parameters Unknown time-invariant parameters Unknown time-variant parameters

AGU2020 3.3.2. Scenario 2: Uncertain high water level, parameters, and model structure – Results (1) 5000-ensemble simulation of flood risk model. Black: Truth, Gray: ensembles, red: ensemble mean No data assimilation data assimilation Our data assimilation correctly simulates model states even if we have unknown dynamics.

AGU2020 3.3.3. Scenario 2: Uncertain high water level, parameters, and model structure – Results (2) 5000-ensemble simulation of flood risk model. Black: Truth, Gray: ensembles, red: ensemble mean data assimilation Our data assimilation correctly estimates model parameters. Advantage of data assimilation is that we can track the change in parameters. Time-varying parameters driven by unresolved dynamics may often exist in socio- hydrological models Estimation of model parameters

AGU2020 4. Real-data experiment

AGU2020 4.1. Real-data experiment Social data collected by Ciullo et al. [2017, HSJ] Study area: Tiber river flood plain in Rome, Italy Study period: 1800-2010 Observation data: • High water level (input) • Population • Levee height

AGU2020 4.2. Results 5000-ensemble simulation of flood risk model. Gray: ensembles, red: ensemble mean, Green: observation No data assimilation data assimilation Our data assimilation can be applied to real-world social dynamics.

AGU2020 5. Conclusions • We developed the sequential data assimilation system in the socio-hydrologic domain. • We demonstrated the potential of data assimilation to reconstruct historical flood- human interactions by idealized and real-data experiments. • Sequential data assimilation is effective with imperfect models and imperfect observations Sawada, Y. and Hanazaki, R.: Socio-hydrological data assimilation: analyzing human–flood interactions by model–data integration, Hydrol. Earth Syst. Sci., 24, 4777– 4791, https://doi.org/10.5194/hess-24-4777-2020, 2020.