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ABSTRACT We present a novel method for generating sequential parameter estimates and quantifying epistemic uncertainty in dynamical systems within a data‐consistent (DC) framework. The DC framework differs from traditional Bayesian approaches due to the incorporation of the push‐forward of an initial density, which performs selective regularization in parameter directions not informed by the data in the resulting updated density. This extends a previous study that included the linear Gaussian theory within the DC framework and introduced the maximal updated density (MUD) estimate as an alternative to both least squares and maximum a posterior (MAP) estimates. In this work, we introduce algorithms for operational settings of MUD estimation in real‐ or near‐real time where spatio‐temporal datasets arrive in packets to provide updated estimates of parameters and identify potential parameter drift. Computational diagnostics within the DC framework prove critical for evaluating (1) the quality of the DC update and MUD estimate and (2) the detection of parameter value drift. The algorithms are applied to estimate (1) wind drag parameters in a high‐fidelity storm surge model, (2) thermal diffusivity field for a heat conductivity problem, and (3) changing infection and incubation rates of an epidemiological model. 

In this study, ADCIRC is configured to run using a test mesh based on the Shinnecock Inlet on the Outer Barrier of Long Island, NY, USA. External forcing for the model is given by tidal forcing reconstructed from the TPXO9.1 harmonic tidal constituents using OceanMesh2D, constant air pressure of 1013 millibars, and free surface stress from winds computed from a 0.25 deg hourly CFSv2 10-m wind fields for a period of 16 days (29 December 2017 - 31 January 2018). Winds are modified for the purposes of the numerical experiment to simulate a more extreme (Category 4) event, with winds scaled radially down to zero from the point of interest, i.e. the center of the inlet (see figure in figures folder). Water elevation at an artificial recording station inside the inlet was recorded over a period of 14 days (1 January 2018 - 14 January 2018) at 3 hour intervals for different wind drag parameter samples. These water elevation values and wind drag parameters, compiled into a singular dataset, is then used to solve inverse problems. 

This simulation is a collection of 446 ADCIRC storm surge simulations for synthetic storms in the Gulf of Mexico. The output includes both water elevation and velocity time-series. The data could be used for structural impacts, flood risk studies, environmental impacts, disease vectors, among other uses. The total size of the output is on the order of a few terabytes - and provides a wealth of training data for future machine learning applications.