Direct Component Analysis Research Articles

Developing Representative Impact Scenarios From Climate Projection Ensembles, With Application to UKCP18 and EURO‐CORDEX Precipitation

AbstractCalculating impacts from climate projection ensembles can be challenging. A simple approach might consider just the ensemble mean, but this ignores much of the information in the ensemble and does not explore the range of possible impacts. A more thorough approach would consider every ensemble member, but may be computationally unfeasible for many impact models. We investigate the compromise in which we represent the ensemble by the mean and a single deviation from the mean. The deviation from the mean would ideally be representative both of variability in the ensemble, and have a significant impact, according to some impact metric. We compare methods for calculating the deviation from the mean, based on traditional compositing and a statistical method known as Directional Component Analysis (DCA). DCA is based on linearizing the impact metric around the ensemble mean. We illustrate the methods with synthetic examples, and derive new mathematical results that clarify the interpretation of DCA. We then use the methods to derive scenarios from the UKCP18 and EURO‐CORDEX projections of future precipitation in Europe. We find that the worst ensemble member is not robust, but that deviations from the ensemble mean calculated using compositing and DCA are robust. They thus give robust insight into the patterns of change in the ensemble. We conclude that mean and representative deviation methods may be suitable for climate projection users who wish to explore the implications of the uncertainty around the ensemble mean without having to calculate the impacts of every ensemble member.

Robust worst-case scenarios from ensemble forecasts

AbstractTo extract the most information from an ensemble forecast, users would need to consider the possible impacts of every member in the ensemble. However, not all users have the resources to do this. Many may opt to consider only the ensemble mean and possibly some measure of spread around the mean. This provides little information about potential worst-case scenarios. We explore different methods to extract worst-case scenarios from an ensemble forecast, for a given definition of severity of impact: taking the worst member of the ensemble, calculating the mean of the N worst members, and two methods that use a statistical tool known as directional component analysis (DCA).We assess the advantages and disadvantages of the four methods in terms of whether they produce spatial worst-case scenarios that are not overly sensitive to the finite size and randomness of the ensemble or small changes in the chosen geographical domain. The methods are tested on synthetic data and on temperature forecasts from ECMWF. The mean of the N worst members is more robust than the worst member, while the DCA-based patterns are more robust than either. Furthermore, if the ensemble variability is well-described by the covariance matrix, the DCA patterns have the statistical property that they are just as severe as those from the other two methods, but more likely. We conclude that the DCA approach is a tool that could be routinely applied to extract worst-case scenarios from ensemble forecasts.

An Alternative to PCA for Estimating Dominant Patterns of Climate Variability and Extremes, with Application to U.S. and China Seasonal Rainfall

Floods and droughts are driven, in part, by spatial patterns of extreme rainfall. Heat waves are driven by spatial patterns of extreme temperature. It is therefore of interest to design statistical methodologies that allow the rapid identification of likely patterns of extreme rain or temperature from observed historical data. The standard work-horse for the rapid identification of patterns of climate variability in historical data is Principal Component Analysis (PCA) and its variants. But PCA optimizes for variance not spatial extremes, and so there is no particular reason why the first PCA spatial pattern should identify, or even approximate, the types of patterns that may drive floods, droughts or heatwaves, even if the linear assumptions underlying PCA are correct. We present an alternative pattern identification algorithm that makes the same linear assumptions as PCA, but which can be used to explicitly optimize for spatial extremes. We call the method Directional Component Analysis (DCA), since it involves introducing a preferred direction, or metric, such as “sum of all points in the spatial field”. We compare the first PCA and DCA spatial patterns for U.S. and China winter and summer rainfall anomalies, using the sum metric for the definition of DCA in order to focus on total rainfall anomaly over the domain. In three out of four of the examples the first DCA spatial pattern is more uniform over a wide area than the first PCA spatial pattern and as a result is more obviously relevant to large-scale flooding or drought. Also, in all cases the definitions of PCA and DCA result in the first PCA spatial pattern having the larger explained variance of the two patterns, while the first DCA spatial pattern, when scaled appropriately, has a higher likelihood and greater total rainfall anomaly, and indeed is the pattern with the highest total rainfall anomaly for a given likelihood. The first DCA spatial pattern is arguably the best answer to the question: what single spatial pattern is most likely to drive large total rainfall anomalies in the future? It is also simpler to calculate than PCA. In combination PCA and DCA patterns yield more insight into rainfall variability and extremes than either pattern on its own.

A single-trial analytic framework for EEG analysis and its application to target detection and classification

Modern neuroimaging technologies afford a non-invasive view into the functions of the human brain with great spatial (fMRI) and temporal resolution (EEG). However, common signal analytic methods require averaging over many trials, which limits the potential for practical application of these technologies. In this paper we advance a novel single-trial analysis method for EEG and demonstrate this approach with a target detection task. The method utilizes a framework consisting of multiple processing modules that can be applied in whole or in part, including noise mitigation, source–space transformation, discriminant analysis, and performance evaluation. The framework introduces an enhanced noise mitigation technology based on Directed Components Analysis (DCA) that improves upon existing spatial filtering techniques. Source–space transformation, utilizing a finite difference model (FDM) of the human head, estimates activity measures of the cortical sources involved in task performance. Such a source–space discrimination provides measurement invariance between training and testing sessions and holds the promise of providing a degree of classification not possible with scalp-recorded EEG. The framework's discrimination modules interface with performance evaluation modules to generate classification performance statistics. When applied to EEG acquired during performance of a target detection task, this method demonstrated that neural signatures of target recognition correctly classified up to 87% of targets in a rapid serial visual presentation (RSVP) of target/non-target images. On average, the single-trial classification method resulted in greater than 60% improvement over behavioral performance for target detection.