Serial clustering of extratropical cyclones MAILIER, Pascal J; STEPHENSON, David B; FERRO, Christopher A. T ...
Monthly weather review,
08/2006, Letnik:
134, Številka:
8
Journal Article
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The clustering in time (seriality) of extratropical cyclones is responsible for large cumulative insured losses in western Europe, though surprisingly little scientific attention has been given to ...this important property. This study investigates and quantifies the seriality of extratropical cyclones in the Northern Hemisphere using a point-process approach. A possible mechanism for serial clustering is the time-varying effect of the large-scale flow on individual cyclone tracks. Another mechanism is the generation by one "parent" cyclone of one or more "offspring" through secondary cyclogenesis. A long cyclone-track database was constructed for extended October-March winters from 1950 to 2003 using 6-h analyses of 850-mb relative vorticity derived from the NCEP-NCAR reanalysis. A dispersion statistic based on the variance-to-mean ratio of monthly cyclone counts was used as a measure of clustering. It reveals extensive regions of statistically significant clustering in the European exit region of the North Atlantic storm track and over the central North Pacific. Monthly cyclone counts were regressed on time-varying teleconnection indices with a log-linear Poisson model. Five independent teleconnection patterns were found to be significant factors over Europe: the North Atlantic Oscillation (NAO), the east Atlantic pattern, the Scandinavian pattern, the east Atlantic-western Russian pattern, and the polar-Eurasian pattern. The NAO alone is not sufficient for explaining the variability of cyclone counts in the North Atlantic region and western Europe. Rate dependence on time-varying teleconnection indices accounts for the variability in monthly cyclone counts, and a cluster process did not need to be invoked. PUBLICATION ABSTRACT
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Abstract
In the forecasting of binary events, verification measures that are “equitable” were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, ...including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weights are independent of the entries in the table, apart from the base rate. The authors demonstrate that the widely used “equitable threat score” (ETS), as well as numerous others, satisfies neither of these requirements and only satisfies the first requirement in the limit of an infinite sample size. Such measures are referred to as “asymptotically equitable.” In the case of ETS, the expected score of a random forecasting system is always positive and only falls below 0.01 when the number of samples is greater than around 30. Two other asymptotically equitable measures are the odds ratio skill score and the symmetric extreme dependency score, which are more strongly inequitable than ETS, particularly for rare events; for example, when the base rate is 2% and the sample size is 1000, random but unbiased forecasting systems yield an expected score of around −0.5, reducing in magnitude to −0.01 or smaller only for sample sizes exceeding 25 000. This presents a problem since these nonlinear measures have other desirable properties, in particular being reliable indicators of skill for rare events (provided that the sample size is large enough). A potential way to reconcile these properties with equitability is to recognize that Gandin and Murphy’s two requirements are independent, and the second can be safely discarded without losing the key advantages of equitability that are embodied in the first. This enables inequitable and asymptotically equitable measures to be scaled to make them equitable, while retaining their nonlinearity and other properties such as being reliable indicators of skill for rare events. It also opens up the possibility of designing new equitable verification measures.
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Inference for clusters of extreme values Ferro, Christopher A. T.; Segers, Johan
Journal of the Royal Statistical Society. Series B, Statistical methodology,
01/2003, Letnik:
65, Številka:
2
Journal Article
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Inference for clusters of extreme values of a time series typically requires the identification of independent clusters of exceedances over a high threshold. The choice of declustering scheme often ...has a significant effect on estimates of cluster characteristics. We propose an automatic declustering scheme that is justified by an asymptotic result for the times between threshold exceedances. The scheme relies on the extremal index, which we show may be estimated before declustering, and supports a bootstrap procedure for assessing the variability of estimates.
A number of realizations of one or more numerical weather prediction (NWP) models, initialised at a variety of initial conditions, compose an ensemble forecast. These forecasts exhibit systematic ...errors and biases that can be corrected by statistical post‐processing. Post‐processing yields calibrated forecasts by analysing the statistical relationship between historical forecasts and their corresponding observations. This article aims to extend post‐processing methodology to incorporate atmospheric circulation. The circulation, or flow, is largely responsible for the weather that we experience and it is hypothesized here that relationships between the NWP model and the atmosphere depend upon the prevailing flow. Numerous studies have focussed on the tendency of this flow to reduce to a set of recognisable arrangements, known as regimes, which recur and persist at fixed geographical locations. This dynamical phenomenon allows the circulation to be categorized into a small number of regime states. In a highly idealized model of the atmosphere, the Lorenz ‘96 system, ensemble forecasts are subjected to well‐known post‐processing techniques conditional on the system's underlying regime. Two different variables, one of the state variables and one related to the energy of the system, are forecasted and considerable improvements in forecast skill upon standard post‐processing are seen when the distribution of the predictand varies depending on the regime. Advantages of this approach and its inherent challenges are discussed, along with potential extensions for operational forecasters.
The properties of weather forecasts depend upon the large‐scale atmospheric state and therefore conditioning statistical post‐processing methods on this state can be expected to offer more skilful forecasts than standard calibration approaches. Several new extensions of standard methods are proposed that provide more flexibility when calibrating dynamical weather forecasts. The new techniques are trialled in the Lorenz ‘96 system and prominent improvements upon standard post‐processing are found when the distribution of the predictand varies conditional on the system's underlying regime.
A new framework is introduced for measuring the performance of probability forecasts when the true value of the predictand is observed with error. In these circumstances, proper scoring rules favour ...good forecasts of observations rather than of truth and yield scores that vary with the quality of the observations. Proper scoring rules thus can favour forecasters who issue worse forecasts of the truth and can mask real changes in forecast performance if observation quality varies over time. Existing approaches to accounting for observation error provide unsatisfactory solutions to these two problems. A new class of ‘error‐corrected’ proper scoring rules is defined that solves both problems by producing unbiased estimates of the scores that would be obtained if the forecasts could be verified against the truth. A general method for constructing error‐corrected proper scoring rules is given for the case of categorical predictands, and error‐corrected versions of the Dawid–Sebastiani scoring rule are proposed for numerical predictands. The benefits of accounting for observation error in ensemble post‐processing and in forecast verification are illustrated in three data examples that include forecasts for the occurrence of tornadoes and of aircraft icing.
A new framework is introduced for measuring the performance of probability forecasts when the true value of the predictand is observed with error. The new class of ‘error‐corrected’ proper scoring rules provides unbiased estimates of the scores that would be obtained if forecasts could be verified against the truth. These scores favour good forecasts of the truth, rather than of the observations, and are insensitive to changes in observation quality.
The generalized extreme value (GEV) distribution has often been used to describe the distribution of daily maximum precipitation in observed and climate model data. The model developed in this paper ...allows the GEV location parameter to vary over the region, while the dispersion coefficient (the ratio of the GEV scale and location parameters) and the GEV shape parameter are assumed to be constant over the region. This corresponds with the index flood assumption in hydrology. It is further assumed that all three GEV parameters vary with time, such that the relative change in a quantile of the distribution is constant over the region. This nonstationary model is fitted to the 1‐day summer and 5‐day winter precipitation maxima in the Rhine basin in a simulation of the Regional Atmospheric Climate Model (RACMO) for the period 1950–2099, and the results are compared with gridded observations. Except for an underestimation of the dispersion coefficient of the 5‐day winter maxima by about 35%, the GEV parameters obtained from the observations are reasonably well reproduced by RACMO. A positive trend in the dispersion coefficient is found in the summer season, which implies that the relative increase of a quantile increases with increasing return period. In the winter season there is a positive trend in the location parameter and a negative trend in the shape parameter. For large quantiles the latter counterbalances the effect of the increase of the location parameter. It is shown that the standard errors of the parameter estimates are significantly reduced in the regional approach compared to those of the estimated parameters from individual grid box values, especially for the summer maxima.
The probabilistic skill of seasonal prediction systems is often inferred using reanalysis data, assuming these benchmark observations to be error free. However, an increasing number of studies report ...non‐negligible levels of uncertainty affecting reanalysis observations, especially when it comes to variables like precipitation or wind speed. We consider different possibilities to account for such error in forecast quality assessment, either exploiting the newly produced ensemble reanalyses (e.g., European Centre for Medium‐Range Weather Forecasts Reanalysis version 5–Ensemble of Data Assimilations, ERA5 ‐ EDA) or applying methodologies that use scores that take observational uncertainty into account. We illustrate the benefits of employing ensemble reanalyses over traditional reanalyses and show how the true skill can be approximated, whatever the observational reference. We ultimately emphasise the perils and quantify the error committed when the observational reference, either reanalysis or point dataset, is selected arbitrarily for verifying a seasonal prediction system.
Brier skill score of the lead‐zero SEAS5 monthly predictions (1981–2017) for surface wind speeds exceeding the 90th percentile of the climatological distribution (BSS90), at a subset of HadISD locations before (left) and after (right) adjusting for observation error. The BSS90 for the observational datasets with an asterisk is computed using the Candille and Talagrand (2008) method. F17: method of Ferro (2017). ERAI: European Centre for Medium‐Range Weather Forecast (ECMWF) Reanalysis‐Interim; JRA55: Japanese 55‐year Reanalysis; HRES: ECMWF Reanalysis version 5 (ERA5)‐High Resolution; MERRA‐2: Modern‐Era Retrospective analysis for Research and Applications, version 2; R1: National Centers for Environmental Prediction–National Center for Atmospheric Research Reanalysis 1; HadISD: Hadley Centre Integrated Surface Database; MR‐MEAN: multi‐reanalysis mean; ERA5‐EDA: Ensemble of Data Assimilations; MR: multi‐reanalysis.
Understanding the relationship between climate and crop productivity is a key component of projections of future food production, and hence assessments of food security. Climate models and crop yield ...datasets have errors, but the effects of these errors on regional scale crop models is not well categorized and understood. In this study we compare the effect of synthetic errors in temperature and precipitation observations on the hindcast skill of a process-based crop model and a statistical crop model. We find that errors in temperature data have a significantly stronger influence on both models than errors in precipitation. We also identify key differences in the responses of these models to different types of input data error. Statistical and process-based model responses differ depending on whether synthetic errors are overestimates or underestimates. We also investigate the impact of crop yield calibration data on model skill for both models, using datasets of yield at three different spatial scales. Whilst important for both models, the statistical model is more strongly influenced by crop yield scale than the process-based crop model. However, our results question the value of high resolution yield data for improving the skill of crop models; we find a focus on accuracy to be more likely to be valuable. For both crop models, and for all three spatial scales of yield calibration data, we found that model skill is greatest where growing area is above 10-15 %. Thus information on area harvested would appear to be a priority for data collection efforts. These results are important for three reasons. First, understanding how different crop models rely on different characteristics of temperature, precipitation and crop yield data allows us to match the model type to the available data. Second, we can prioritize where improvements in climate and crop yield data should be directed. Third, as better climate and crop yield data becomes available, we can predict how crop model skill should improve.
Forecasts of “normal” Mason, Simon J.; Ferro, Christopher A. T.; Landman, Willem A.
Quarterly journal of the Royal Meteorological Society,
January 2021 Part B, 2021-01-00, 20210101, Letnik:
147, Številka:
735
Journal Article
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The difficulty of forecasting “normal” climate conditions is demonstrated in the context of bivariate normally distributed forecasts and observations. Deterministic and probabilistic skill scores for ...the normal category are less than for the outer category for all‐but‐perfect models. There are two important mathematical properties of the normal category in a three‐category climatologically equiprobable forecast system that affect the scores for this category. First, the normal category can achieve the highest probability less frequently than the outer categories, and far less frequently in contexts of weak to moderate skill. Second, there are upper limits to the probability the normal category can reach. These mathematical constraints suggest that summary measures of skill may underestimate the predictability and forecast‐skill of extreme events, and that subjective inputs to probabilistic forecasts may need to take greater account of limitations to the predictability of normal conditions.
Maximum possible forecast probability for the normal category as a function of the correlation skill for bivariate normally distributed predictions and observations given different sample sizes, n is shown in the figure above. The effects of sample size on the maximum forecast probability for the normal category are indicated in the figure is small (reducing the maximum probability by less than 1% for sample sizes larger than 20), so the primary control on the maximum probability is the correlation skill.
Calibration Strategies Ho, Chun Kit; Stephenson, David B.; Collins, Matthew ...
Bulletin of the American Meteorological Society,
01/2012, Letnik:
93, Številka:
1
Journal Article
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... HadRM3 simulated present-day temperatures are more positively skewed compared to observations in parts of this region, a feature observed in simulations of a number of other regional climate ...models. ... HadRM3 projects temperatures to become even more positively skewed with time over northern continental Europe.
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