Nonhomogeneous hidden Markov models (NHMMs) provide a relatively simple framework for simulating precipitation at multiple rain gauge stations conditional on synoptic atmospheric patterns. Building on existing NHMMs for precipitation occurrences, we propose an extension to include precipitation amounts. The model we describe assumes the existence of unobserved (or hidden) weather patterns, the weather states, which follow a Markov chain. The weather states depend on observable synoptic information and therefore serve as a link between the synoptic-scale atmospheric patterns and the local-scale precipitation. The presence of the hidden states simplifies the spatio-temporal structure of the precipitation process. We assume the temporal dependence of precipitation is completely accounted for by the Markov evolution of the weather state. The spatial dependence of precipitation can also be partially or completely accounted for by the existence of a common weather state. In the proposed model, occurrences are assumed to be conditionally spatially independent given the current weather state and, conditional on occurrences, precipitation amounts are modeled independently at each rain gauge as gamma deviates with gauge-specific parameters. We apply these methods to model precipitation at a network of 24 rain gauge stations in Washington state over the course of 17 winters. The first 12 yr are used for model fitting purposes, while the last 5 serve to evaluate the model performance. The analysis of the model results for the reserved years suggests that the characteristics of the data are captured fairly well and points to possible directions for future improvements.

Some recent developments in the stochastic modelling of single site and spatial rainfall are summarised. Alternative single site models based on Poisson cluster processes are introduced, fitting methods are discussed, and performance is compared for representative UK hourly data. The representation of sub-hourly rainfall is discussed, and results from a temporal disaggregation scheme are presented. Extension of the Poisson process methods to spatial-temporal rainfall, using radar data, is reported. Current methods assume spatial and temporal stationarity; work in progress seeks to relax these restrictions. Unlike radar data, long sequences of daily raingauge data are commonly available, and the use of generalized linear models (GLMs) (which can represent both temporal and spatial non-stationarity) to represent the spatial structure of daily rainfall based on raingauge data is illustrated for a network in the North of England. For flood simulation, disaggregation of daily rainfall is required. A relatively simple methodology is described, in which a single site Poisson process model provides hourly sequences, conditioned on the observed or GLM-simulated daily data. As a first step, complete spatial dependence is assumed. Results from the River Lee catchment, near London, are promising. A relatively comprehensive set of methodologies is thus provided for hydrological application.

Probabilistic risk assessment systems for tropical cyclone hazards rely on large ensembles of model simulations to characterize cyclones tracks, intensities, and the extent of the associated damaging winds. Given the computational costs, the wind field is often modeled using parametric formulations that make assumptions that are based on observations of tropical systems (e.g., satellite, or aircraft reconnaissance). In particular, for the Northern Hemisphere, most of the damaging contribution is assumed to be from the right of the moving cyclone, with the left-hand-side winds being much weaker because of the direction of storm motion. Recent studies have highlighted that this asymmetry assumption does not hold for cyclones undergoing extratropical transitions around Japan. Transitioning systems can exhibit damaging winds on both sides of the moving cyclone, with wind fields often characterized as resembling a horseshoe. This study develops a new parametric formulation of the extratropical transition phase for application in risk assessment systems. A compromise is sought between the need to characterize the horseshoe shape while keeping the formulation simple to allow for implementation within a risk assessment framework. For that purpose the tropical wind model developed by Willoughby et al. is selected as a starting point and parametric bias correction fields are applied to build the target shape. Model calibration is performed against a set of 37 extratropical transition cases simulated using the Weather Research and Forecasting Model. This newly developed parametric model of the extratropical transition phase shows an ability to reproduce wind field features observed in the western North Pacific Ocean while using only a restricted number of input parameters.

The risk from natural catastrophes is typically estimated using complex simulation models involving multiple stochastic components in a nested structure. This risk is principally assessed via the mean annual loss, and selected quantiles of the annual loss. Determining an appropriate simulation strategy is important in order to achieve satisfactory convergence of these statistics, without excessive computation time and data storage requirements. This necessitates an understanding of the relative contribution of each of the stochastic components to the total variance of the statistics. A simple framework using random effects models and analysis of variance is used to partition the variance of the annual loss, which permits calculation of the variance of the mean annual loss with varying numbers of samples of each of the components. An extension to quantiles is developed using the empirical distribution function in combination with bootstrapping. The methods are applied to a European flood model, where the primary stochastic component relates to the frequency and severity of flood events, and three secondary components relate to defence levels, exposure locations and building vulnerability. As expected, it is found that the uncertainty due to the secondary components increases as the size of the portfolio of exposures decreases, and is higher for industrial and commercial business, compared with residential for all statistics of interest. In addition, interesting insights are gained as to the impact of flood defences on convergence.

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Risk-assessment systems for wind hazards (e.g., hurricanes or typhoons) often rely on simple parametric wind field formulations. They are built using extensive observations of tropical cyclones and make assumptions about wind field asymmetry. In this framework, maximum winds are always simulated to the right of the cyclone, but analysis of the Climate Forecast System Reanalysis database for the western North Pacific Ocean suggests that wind fields from cyclones undergoing extratropical transition around Japan often present features that cannot be adequately simulated under these assumptions. These ''left-hand-side contribution'' (LHSC) wind fields exhibit strong winds on both sides of the moving cyclone with the maximum magnitude often located to the left. Classification of cyclones in terms of their most frequent patterns reveals that 67% of cases that make a transition around Japan are dominantly LHSC. They are more likely in autumn and have more intense maximum winds. The results from this study show the need for a new approach to the modeling of transitioning wind fields in the context of risk-assessment systems.

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ABSTRACT:The interannual prediction of the number of hurricanes to strike the US coastline is of vital interest to those who live on the coast, those who insure property along the coast and policy makers who make decisions about infrastructure and mitigation measures. Here it is shown that these predictions can be made more accurate when information about the total number of Atlantic Basin hurricanes is considered. The proportion of Atlantic hurricanes that make landfall in the USA is a measure of the relationship between landfalling and basin hurricane numbers. In order to use basin numbers to help make predictions of landfalling numbers, we must first investigate the nature of this relationship. Here we run a number of statistical tests and find that there is a significant change in the relative proportion of Atlantic hurricanes that hit the US coastline between the first and second halves of the 20th century. This difference is ostensibly due to the lack of basin observations in the earlier period. However, after 1948, the proportion of Atlantic hurricanes that hit the US coast shows no evidence of change. By assuming that the proportion is constant, we are able to then use information about the total number of hurricanes in the Atlantic Basin and make more accurate estimates of landfalling hurricane activity.