Overview
Recently, significant advances have been made in modeling compound flood risk associated with tropical cyclones, extending the existing Joint Probability Method with Optimal Sampling (JPM-OS) previously applied to surge- and wave-driven flooding to further account for rainfall and rainfall-runoff dynamics mediated by soil moisture. Publication of this method is pending, and a preprint can be found here, referred to below as Bartlett et al.
The Problem
While much of the proposed work represents a rigorous step forward in modeling compound flood risk associated with tropical cyclones, the rainfall model used in these efforts is problematic to the point of being largely invalid. The rainfall model in question is published here. This published work starts with an existing model of TC-driven rainfall by the Interagency Performance Evaluation Task Force (IPET). This model of expected rainfall assumes that rainfall around the eye of a tropical storm is effectively axisymmetric—a circular blob of rainfall which smooths out the peaked spiral bands of precipitation that tropical cyclones are known to generate. The rainfall model now used for compound flood risk analysis in Louisiana and elsewhere along the Gulf Coast creates a bias-adjustment to correct the total areal rainfall generated by the IPET model (that is, the total rainfall per tropical cyclone event on a pixel-wise basis), and parameterizes the residual (multiplicative) error in total rainfall on a pixel-wise basis as a mixture of Gaussians with correlation structure captured via meta-Gaussian copula. The "probabilistic generator" then draws from this error distribution a random field of spatially varying but temporally fixed multipliers which are applied to the temporally varying IPET model. As a result, this rainfall model accounts for rainfall variability in space but not in time. Rather than converting the axisymmetric (i.e. with circular level sets) IPET model into the realistic rotating spiral pattern as seen in real tropical cyclones in a way that aligns with real time-series data, it instead multiplies that moving blob of the IPET model by a temporally static sequence of spatial blobs. It does not lead to spatiotemporally varying rainfall fields that align with real data or even attempt to do so, but rather generates wildly unrealistic time series data, adjusting the moving blob of the IPET model up or down on a pixel-wise fashion for the entire duration of the storm to match the rainfall totals associated with real tropical cyclone data. Previous analysis has suggested that this model reasonably captures peak 12-hour rainfall rates associated with tropical cyclones but severely underestimates shorter-duration peaks such as the 3-hour peak which are known to drive flashy localized flooding.
It should be noted that this approach for generating spatiotemporally varying rainfall fields is not described in full detail in the peer-reviewed publication. The publication introducing this rainfall model discussed only storm-wise rainfall totals, which the generator does accurately capture. Its use in generating spatiotemporally varying rainfall fields therefore represents a bit of a bait-and-switch, in which the valid peer-reviewed results are presented as justifying the use of the generator for spatiotemporally varying rainfall fields when they plainly do not.
Additionally, it should be clear to anyone with significant statistical training that when performing Monte Carlo sampling on the convolution of two distributions such as the distribution of tropical cyclone features and the distribution of rainfall conditioned on those features, the conditional draws on the latter should be independent. This was made clear to collaborators involved in both the paper and in applications of the extended JPM-OS method for use in resilience planning in the state of Louisiana and city of Jacksonville, Florida, projects requiring roughly a quarter of a million rainfall fields over ~500 synthetic tropical cyclones. However, collaborator Gabrielle Villarini of Princeton did not generate ~250,000 random fields but only 2,000 random fields which were randomly reused, underestimating the conditional variance of rainfall and likely harming the validity of the clustering-driven optimal sampling approach used to reduce the ~250,000 storm events to a smaller and more tractable set of hydrodynamic simulations. Collaborators refused to address this issue, which to the best of our knowledge persisted through production and delivery.
Pending Documentation
Pending documentation will clearly and empirically illustrate the problems described, and demonstrate that a straightforward extension of existing methods which were applied in two-dimensional cartesian coordinates (x, y) to three dimensions (time, radius from storm center, angle relative to storm heading) with an appropriate approach to Monte Carlo sampling can resolve these issues.