The first issue we consider in developing our five year hurricane number prediction schemes is how to estimate the current climate state. Recent historical data is likely to be more relevant to making such estimates than earlier historical data. We therefore address the question of exactly how much of the historical data one should use, and with what weight. The next issue we consider in our model development is how to model potential future changes over the next five years. We include some methods that assume that the future will not change from the current state, and others that model systematic future changes. Some of our methods, for example, attempt to model a trendand extrapolate it into the future, while other models estimate the probability of future climate shifts. We note, however, that all of our models incorporate any past effects of trends and variability when they attempt to capture the current level of activity.

To keep things simple, the goal we set for our predictions is to minimize the root mean square error (RMSE) between the predicted and actual numbers of hurricanes. We note that one might eventually want to move beyond RMSE as a metric because, among other reasons, RMSE gives equal weight to errors on both sides of the prediction, while the consequences of overpredicting and underpredicting may not have symmetric affects. Furthermore, we note that one might ultimately want to consider making probabilistic forecasts and evaluating them using a probabilistic metric. We have taken this approach in Hall and Jewson, 2006.

Most of our analysis uses simple classical statistical methods, with the addition of some use of model shrinkage (which is described in section 5). Given that the amount of data is rather small, the signals are weak, and the parameter uncertainty is high one might consider using more elements of Bayesian statistics (Litterman, 1979, 1986) to attack this problem. However, Bayesian methods tend to be both complex and controversial and we are not yet convinced that the potential benefits of using them, in terms of greater scientific accuracy, would outweigh the loss of transparency for the problem at hand. This is partly because one of our goals is to introduce methods that can be widely understood by meteorologists, climate modelers, and insurance industry practitioners. We feel that at this early stage in the development of the ideas presented here it is more important to focus on the discussion of what methods fundamentally make sense, and what assumptions the different methods depend on, rather than taking the level of technical and statistical sophistication as far as it could be taken.

In the following sections, we present the methods developed for predicting the number of Atlantic hurricanes that will make U.S. landfall in the periods 2006-2010,

2007-2011 and 2008-2012. These predictions are made given data up to the end of the hurricane seasons in 2005 and 2006 and using an estimate for the 2007 season given information up to 15 Oct, 2007. The data used is described in section two. In section three we describe what we call 'long baseline methods'. In section four we discuss issues related to the non-stationarity of the hurricane number time-series. In this section we describe what we call 'short baseline methods', and introduce the idea of direct and indirect predictions of landfall numbers. In section five we describe what we call 'mixed baseline' methods that mix the historical levels of hurricane activity in an optimal way. Our climate-shift models are also introduced in this section. In section six we describe prediction methods based on sea-surface temperature (SST) and in section seven we describe a model which uses both SST and windshear to predict hurricane numbers. In all cases, predictions are made for the expected numbers of category 1-5 and category 3-5 hurricanes hitting the U.S. coastline for five years ahead. The estimated model skill for each of the models, determined by the root mean squared error, is shown in section 8. We present predictions for 2006-2010,2007-2011 and 2008-2012. The 2006-2010 predictions are those that were used in the RMS 2006 expert elicitation. The 2007-2011 predictions are made from the same models but also include data from 2006. The

2008-2012 predictions are made from the slightly different (and hopefully improved) set of models that were used in the RMS 2007 expert elicitation. Tables of the predictions from all the models are shown, and discussed, in the summary section 9.

All the methods we present have been described in detail in Risk Management Solutions technical reports, and are available from the Arxiv preprint server at arxiv.org. They can also be accessed by following links from www.rms-research. com and are cited throughout this article. Relative to those reports, this article summarizes the methods used, explains the connections between them, and publishes the results from all the methods side by side for the first time.

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