Classifying dynamical forcing mechanisms using a climatology of extratropical cyclones

A climatology of almost 700 extratropical cyclones is compiled by applying an automated feature tracking algorithm to a database of objectively identified cyclonic features. Cyclones are classified according to the relative contributions to the midlevel vertical motion of the forcing from upper and lower levels averaged over the cyclone intensification period (average U/L ratio) and also by the horizontal separation between their upper-level trough and low-level cyclone (tilt). The frequency distribution of the average U/L ratio of the cyclones contains two significant peaks and a long tail at high U/L ratio. Although discrete categories of cyclones have not been identified, the cyclones comprising the peaks and tail have characteristics that have been shown to be consistent with the type A, B, and C cyclones of the threefold classification scheme. Using the thresholds in average U/L ratio determined from the frequency distribution, type A, B, and C cyclones account for 30\%, 38\%, and 32\% of the total number of cyclones respectively. Cyclones with small average U/L ratio are more likely to be developing cyclones (attain a relative vorticity $\ge 1.2 \times 10^{-4} \mbox{s}^{-1}$) whereas cyclones with large average U/L ratio are more likely to be nondeveloping cyclones (60\% of type A cyclones develop whereas 31\% of type C cyclones develop). Type A cyclogenesis dominates in the development region East of the Rockies and over the gulf stream, type B cyclogenesis dominates in the region off the East coast of the USA, and type C cyclogenesis is more common over the oceans in regions of weaker low-level baroclinicity.

Determining the effect of asymmetric data on the variogram. I. Underlying asymmetry

Matheron's usual variogram estimator can result in unreliable variograms when data are strongly asymmetric or skewed. Asymmetry in a distribution can arise from a long tail of values in the underlying process or from outliers that belong to another population that contaminate the primary process. This paper examines the effects of underlying asymmetry on the variogram and on the accuracy of prediction, and the second one examines the effects arising from outliers. Standard geostatistical texts suggest ways of dealing with underlying asymmetry; however, this is based on informed intuition rather than detailed investigation. To determine whether the methods generally used to deal with underlying asymmetry are appropriate, the effects of different coefficients of skewness on the shape of the experimental variogram and on the model parameters were investigated. Simulated annealing was used to create normally distributed random fields of different size from variograms with different nugget:sill ratios. These data were then modified to give different degrees of asymmetry and the experimental variogram was computed in each case. The effects of standard data transformations on the form of the variogram were also investigated. Cross-validation was used to assess quantitatively the performance of the different variogram models for kriging. The results showed that the shape of the variogram was affected by the degree of asymmetry, and that the effect increased as the size of data set decreased. Transformations of the data were more effective in reducing the skewness coefficient in the larger sets of data. Cross-validation confirmed that variogram models from transformed data were more suitable for kriging than were those from the raw asymmetric data. The results of this study have implications for the 'standard best practice' in dealing with asymmetry in data for geostatistical analyses. (C) 2007 Elsevier Ltd. All rights reserved.

Determining the effect of asymmetric data on the variogram. II. Outliers

Asymmetry in a distribution can arise from a long tail of values in the underlying process or from outliers that belong to another population that contaminate the primary process. The first paper of this series examined the effects of the former on the variogram and this paper examines the effects of asymmetry arising from outliers. Simulated annealing was used to create normally distributed random fields of different size that are realizations of known processes described by variograms with different nugget:sill ratios. These primary data sets were then contaminated with randomly located and spatially aggregated outliers from a secondary process to produce different degrees of asymmetry. Experimental variograms were computed from these data by Matheron's estimator and by three robust estimators. The effects of standard data transformations on the coefficient of skewness and on the variogram were also investigated. Cross-validation was used to assess the performance of models fitted to experimental variograms computed from a range of data contaminated by outliers for kriging. The results showed that where skewness was caused by outliers the variograms retained their general shape, but showed an increase in the nugget and sill variances and nugget:sill ratios. This effect was only slightly more for the smallest data set than for the two larger data sets and there was little difference between the results for the latter. Overall, the effect of size of data set was small for all analyses. The nugget:sill ratio showed a consistent decrease after transformation to both square roots and logarithms; the decrease was generally larger for the latter, however. Aggregated outliers had different effects on the variogram shape from those that were randomly located, and this also depended on whether they were aggregated near to the edge or the centre of the field. The results of cross-validation showed that the robust estimators and the removal of outliers were the most effective ways of dealing with outliers for variogram estimation and kriging. (C) 2007 Elsevier Ltd. All rights reserved.