Using stochastically generated skewed distributions to represent hourly nontidal residual water levels at United States tide gauges

Abstract

The daily likelihood of High Tide Flooding (HTF) predicted by the National Oceanic and Atmospheric Administration (NOAA) for leads up to one year is expressed as the sum of a long-term trend, tides, and nontidal residuals (NTRs) whose probability density functions (PDFs) are assumed to be Gaussian (i.e., normally distributed). We analyzed observed detrended hourly NTR distributions at 148 NOAA tide gauges along the U.S. coastline and show that 98.7% of them are better characterized by ‘Stochastically Generated Skewed’ (SGS) distributions, a class of non-Gaussian (skewed, heavy-tailed) PDFs. In contrast to other methods that generate PDFs by fitting observed raw histograms, SGS distributions are determined through time series analysis. Observations are fit to a simple linear (autoregressive) time series model, driven by stochastic noise with a linear dependence upon the NTR anomaly. The PDF is then determined from the fitted model parameters. The SGS distributions improve upon the Gaussian PDF high-water probabilities at varying thresholds throughout the year along all U.S. coasts, with significantly better estimates along the U.S. East and Gulf coasts during summer (apart from large hurricane events) and along the U.S. West Coast during winter (even though variability there is often dominated by monthly time scales and many locations have nearly Gaussian PDFs). For evaluating extreme high-water event probabilities, the SGS distribution is no more sensitive to limited observations than kernel density estimation or Generalized Extreme Value methods. Tail probabilities for all three methods are generally similar. Our results may contribute to more robust and accurate HTF forecasts and, more broadly, provide additional insight in developing adaptation and mitigation strategies for future sea level conditions.