arXiv subjects
Publications and source records attributed to Stephen Jewson.
In previous work we have analysed the Atlantic basin hurricane number time-series to identify decadal time-scale change points. We now repeat the analysis but for US landfalling hurricanes. The results are very different.
In earlier work we considered methods for predicting future levels of hurricane activity based on the assumption that historical mean activity was at one constant level from 1900 to 1994, and has been at another constant level since then. We now make this model a little more subtle, and account for the possibility of four different levels of mean hurricane activity since 1900.
We perform an objective change-point analysis on 106 years of historical hurricane number data. The algorithm we use looks at all possible combinations of change-points and compares them in terms of the variances of the differences between real and modelled numbers. Overfitting is avoided by using cross-validation. We identify four change-points, and show that the presence of temporal structure in the hurricane number time series is highly statistically significant.
We compare classical and Bayesian methods for fitting the poisson distribution to the number of hurricanes making landfall on sections of the US coastline.
One possible method for the year-ahead prediction of hurricane numbers would be to make a year-ahead prediction of sea surface temperature (SST), and then to apply relationships that link SST to hurricane numbers. As a first step towards setting up such a system this article compares three simple statistical methods for the year-ahead prediction of the relevant SSTs.
In previous work, we have shown how to combine long and short historical baselines to make predictions of future hurricane numbers. We now ask: how should such combinations change if we are interested in predicting the future number of intense hurricanes?
We present results from the sixth stage of a project to build a statistical hurricane model. Previous papers have described our modelling of the tracks, genesis, and lysis of hurricanes. In our track model we have so far employed a normal distribution for the residuals when computing innovations, even though we have demonstrated that their distribution is not normal. Here, we test to see if the track model can be improved by including more realistic non-normal innovations. The results are mixed. Some features of the model improve, but others slightly worsen.
Annual levels of US landfalling hurricane activity averaged over the last 11 years (1995-2005) are higher than those averaged over the previous 95 years (1900-1994). How, then, should we best predict hurricane activity rates for next year? Based on the assumption that the higher rates will continue we use an optimal combination of averages over the long and short time-periods to produce a prediction that minimises MSE.
We describe results from the fifth stage of a project to build a statistical model of tropical cyclone tracks. The previous stages considered genesis and the shape of tracks. We now consider in more detail how to represent the lysis (death) of tropical cyclones. Improving the lysis model turns out to bring a significant improvement to the track model overall.
We continue with our program to derive simple practical methods that can be used to predict the number of US landfalling hurricanes a year in advance. We repeat an earlier study, but for a slightly different definition landfalling hurricanes, and for intense hurricanes only. We find that the averaging lengths needed for optimal predictions of numbers of intense hurricanes are longer than those needed for optimal predictions of numbers of hurricanes of all strengths.
As part of a project to develop more accurate estimates of the risks due to tropical cyclones, we describe a non-parametric method for the statistical simulation of the location of tropical cyclone genesis. The method avoids the use of arbitrary grid boxes, and the spatial smoothing of the historical data is constructed optimally according to a clearly defined merit function.
We describe results from the third stage of a project to build a statistical model for hurricane tracks. In the first stage we modelled the unconditional mean track. In the second stage we modelled the unconditional variance of fluctuations around the mean. Now we address the question of how to model the autocorrelations in the standardised fluctuations. We perform a thorough diagnostic analysis of these fluctuations, and fit a type of AR(1) model. We then assess the goodness of fit of this model in a number of ways, including an out-of-sample comparison with a simpler model, an in-sample residual analysis, and a comparison of simulated tracks from the model with the observed tracks. Broadly speaking, the model captures the behaviour of observed hurricane tracks. In detail, however, there are a number of systematic errors.
We present a simple method for the year-ahead prediction of the number of hurricanes making landfall in the US. The method is based on averages of historical annual hurricane numbers, and we perform a backtesting study to find the length of averaging window that would have given the best predictions in the past.
The empirical covariance matrix is not necessarily the best estimator for the population covariance matrix: we describe a simple method which gives better estimates in two examples. The method models the covariance matrix using truncated PCA with white noise residuals. Jack-knife cross-validation is used to find the truncation that maximises the out-of-sample likelihood score.
We describe results from the second stage of a project to build a statistical model for hurricane tracks. In the first stage we modelled the unconditional mean track. We now attempt to model the unconditional variance of fluctuations around the mean. The variance models we describe use a semi-parametric nearest neighbours approach in which the optimal averaging length-scale is estimated using a jack-knife out-of-sample fitting procedure. We test three different models. These models consider the variance structure of the deviations from the unconditional mean track to be isotropic, anisotropic but uncorrelated, and anisotropic and correlated, respectively. The results show that, of these models, the anisotropic correlated model gives the best predictions of the distribution of future positions of hurricanes.
We present a statistical model for the unconditional mean tracks of hurricanes. Our model is a semi-parametric scheme that averages together observed hurricane displacements. It has a single parameter that defines the averaging length scale, and we derive the optimum value for this parameter using a jackknife. The main purpose of this model is as a starting point for developing a statistical model of hurricanes for use in the estimation of the wind, rainfall and flooding risks. The model also acts as an optimal filtering tool for estimating mean hurricane tracks.
Spread regression is an extension of linear regression that allows for the inclusion of a predictor that contains information about the variance. It can be used to take the information from a weather forecast ensemble and produce a probabilistic prediction of future temperatures. There are a number of ways that spread regression can be formulated in detail. We perform an empirical comparison of four of the most obvious methods applied to the calibration of a year of ECMWF temperature forecasts for London Heathrow.
The spread of ensemble weather forecasts contains information about the spread of possible future weather scenarios. But how much information does it contain, and how useful is that information in predicting the probabilities of future temperatures? One traditional answer to this question is to calculate the spread-skill correlation. We discuss the spread-skill correlation and how it interacts with some simple calibration schemes. We then point out why it is not, in fact, a useful measure for the amount of information in the ensemble spread, and discuss a number of other measures that are more useful.