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Abstract
Cluster analysis is a technique frequently used in climatology for grouping cases to define classes (synoptic types or climate regimes, for example), or for grouping stations or grid points to define regions. Cluster analysis is based on some form of distance matrix, and the most commonly used metric in the climatological field has been Euclidean distances. Arguments for the use of Euclidean distances are in some ways similar to arguments for using a covariance matrix in principal components analysis: the use of the metric is valid if all data are measured on the same scale. When using Euclidean distances for cluster analysis, however, the additional assumption is made that all the variables are uncorrelated, and this assumption is frequently ignored. Two possible methods of dealing with the correlation between the variables are considered: performing a principal components analysis before calculating Euclidean distances, and calculating Mahalanobis distances using the raw data. Under certain conditions calculating Mahalanobis distances is equivalent to calculating Euclidean distances from the principal components. It is suggested that when cluster analysis is used for defining regions, Mahalanobis distances are inappropriate, and that Euclidean distances should be calculated using the unstandardized principal component scores based on only the major principal components.
Abstract
Cluster analysis is a technique frequently used in climatology for grouping cases to define classes (synoptic types or climate regimes, for example), or for grouping stations or grid points to define regions. Cluster analysis is based on some form of distance matrix, and the most commonly used metric in the climatological field has been Euclidean distances. Arguments for the use of Euclidean distances are in some ways similar to arguments for using a covariance matrix in principal components analysis: the use of the metric is valid if all data are measured on the same scale. When using Euclidean distances for cluster analysis, however, the additional assumption is made that all the variables are uncorrelated, and this assumption is frequently ignored. Two possible methods of dealing with the correlation between the variables are considered: performing a principal components analysis before calculating Euclidean distances, and calculating Mahalanobis distances using the raw data. Under certain conditions calculating Mahalanobis distances is equivalent to calculating Euclidean distances from the principal components. It is suggested that when cluster analysis is used for defining regions, Mahalanobis distances are inappropriate, and that Euclidean distances should be calculated using the unstandardized principal component scores based on only the major principal components.
The International Research Institute for Climate Prediction (IRI) net assessment seasonal temperature and precipitation forecasts are evaluated for the 4-yr period from October–December 1997 to October–December 2001. These probabilistic forecasts represent the human distillation of seasonal climate predictions from various sources. The ranked probability skill score (RPSS) serves as the verification measure. The evaluation is offered as time-averaged spatial maps of the RPSS as well as area-averaged time series. A key element of this evaluation is the examination of the extent to which the consolidation of several predictions, accomplished here subjectively by the forecasters, contributes to or detracts from the forecast skill possible from any individual prediction tool.
Overall, the skills of the net assessment forecasts for both temperature and precipitation are positive throughout the 1997–2001 period. The skill may have been enhanced during the peak of the 1997/98 El Niño, particularly for tropical precipitation, although widespread positive skill exists even at times of weak forcing from the tropical Pacific. The temporally averaged RPSS for the net assessment temperature forecasts appears lower than that for the AGCMs. Over time, however, the IRI forecast skill is more consistently positive than that of the AGCMs. The IRI precipitation forecasts generally have lower skill than the temperature forecasts, but the forecast probabilities for precipitation are found to be appropriate to the frequency of the observed outcomes, and thus reliable. Over many regions where the precipitation variability is known to be potentially predictable, the net assessment precipitation forecasts exhibit more spatially coherent areas of positive skill than most, if not all, prediction tools. On average, the IRI net assessment forecasts appear to perform better than any of the individual objective prediction tools.
The International Research Institute for Climate Prediction (IRI) net assessment seasonal temperature and precipitation forecasts are evaluated for the 4-yr period from October–December 1997 to October–December 2001. These probabilistic forecasts represent the human distillation of seasonal climate predictions from various sources. The ranked probability skill score (RPSS) serves as the verification measure. The evaluation is offered as time-averaged spatial maps of the RPSS as well as area-averaged time series. A key element of this evaluation is the examination of the extent to which the consolidation of several predictions, accomplished here subjectively by the forecasters, contributes to or detracts from the forecast skill possible from any individual prediction tool.
Overall, the skills of the net assessment forecasts for both temperature and precipitation are positive throughout the 1997–2001 period. The skill may have been enhanced during the peak of the 1997/98 El Niño, particularly for tropical precipitation, although widespread positive skill exists even at times of weak forcing from the tropical Pacific. The temporally averaged RPSS for the net assessment temperature forecasts appears lower than that for the AGCMs. Over time, however, the IRI forecast skill is more consistently positive than that of the AGCMs. The IRI precipitation forecasts generally have lower skill than the temperature forecasts, but the forecast probabilities for precipitation are found to be appropriate to the frequency of the observed outcomes, and thus reliable. Over many regions where the precipitation variability is known to be potentially predictable, the net assessment precipitation forecasts exhibit more spatially coherent areas of positive skill than most, if not all, prediction tools. On average, the IRI net assessment forecasts appear to perform better than any of the individual objective prediction tools.
Abstract
Probabilistic forecasts of variables measured on a categorical or ordinal scale, such as precipitation occurrence or temperatures exceeding a threshold, are typically verified by comparing the relative frequency with which the target event occurs given different levels of forecast confidence. The degree to which this conditional (on the forecast probability) relative frequency of an event corresponds with the actual forecast probabilities is known as reliability, or calibration. Forecast reliability for binary variables can be measured using the Murphy decomposition of the (half) Brier score, and can be presented graphically using reliability and attributes diagrams. For forecasts of variables on continuous scales, however, an alternative measure of reliability is required. The binned probability histogram and the reliability component of the continuous ranked probability score have been proposed as appropriate verification procedures in this context, but are subject to some limitations. A procedure is proposed that is applicable in the context of forecast ensembles and is an extension of the binned probability histogram. Individual ensemble members are treated as estimates of quantiles of the forecast distribution, and the conditional probability that the observed precipitation, for example, exceeds the amount forecast [the conditional exceedance probability (CEP)] is calculated. Generalized linear regression is used to estimate these conditional probabilities. A diagram showing the CEPs for ranked ensemble members is suggested as a useful method for indicating reliability when forecasts are on a continuous scale, and various statistical tests are suggested for quantifying the reliability.
Abstract
Probabilistic forecasts of variables measured on a categorical or ordinal scale, such as precipitation occurrence or temperatures exceeding a threshold, are typically verified by comparing the relative frequency with which the target event occurs given different levels of forecast confidence. The degree to which this conditional (on the forecast probability) relative frequency of an event corresponds with the actual forecast probabilities is known as reliability, or calibration. Forecast reliability for binary variables can be measured using the Murphy decomposition of the (half) Brier score, and can be presented graphically using reliability and attributes diagrams. For forecasts of variables on continuous scales, however, an alternative measure of reliability is required. The binned probability histogram and the reliability component of the continuous ranked probability score have been proposed as appropriate verification procedures in this context, but are subject to some limitations. A procedure is proposed that is applicable in the context of forecast ensembles and is an extension of the binned probability histogram. Individual ensemble members are treated as estimates of quantiles of the forecast distribution, and the conditional probability that the observed precipitation, for example, exceeds the amount forecast [the conditional exceedance probability (CEP)] is calculated. Generalized linear regression is used to estimate these conditional probabilities. A diagram showing the CEPs for ranked ensemble members is suggested as a useful method for indicating reliability when forecasts are on a continuous scale, and various statistical tests are suggested for quantifying the reliability.
Abstract
Potential and real predictive skill of the frequency of extreme rainfall in southeastern South America for the December–February season are evaluated in this paper, finding evidence indicating that mechanisms of climate variability at one time scale contribute to the predictability at another scale; that is, taking into account the interference of different potential sources of predictability at different time scales increases the predictive skill. Part I of this study suggested that a set of daily atmospheric circulation regimes, or weather types, was sensitive to these cross–time scale interferences, conducive to the occurrence of extreme rainfall events in the region, and could be used as a potential predictor. At seasonal scale, a combination of those weather types indeed tends to outperform all the other candidate predictors explored (i.e., sea surface temperature patterns, phases of the Madden–Julian oscillation, and combinations of both). Spatially averaged Kendall’s τ improvements of 43% for the potential predictability and 23% for real-time predictions are attained with respect to standard models considering sea surface temperature fields alone. A new subseasonal-to-seasonal predictive methodology for extreme rainfall events is proposed based on probability forecasts of seasonal sequences of these weather types. The cross-validated real-time skill of the new probabilistic approach, as measured by the hit score and the Heidke skill score, is on the order of twice that associated with climatological values. The approach is designed to offer useful subseasonal-to-seasonal climate information to decision-makers interested not only in how many extreme events will happen in the season but also in how, when, and where those events will probably occur.
Abstract
Potential and real predictive skill of the frequency of extreme rainfall in southeastern South America for the December–February season are evaluated in this paper, finding evidence indicating that mechanisms of climate variability at one time scale contribute to the predictability at another scale; that is, taking into account the interference of different potential sources of predictability at different time scales increases the predictive skill. Part I of this study suggested that a set of daily atmospheric circulation regimes, or weather types, was sensitive to these cross–time scale interferences, conducive to the occurrence of extreme rainfall events in the region, and could be used as a potential predictor. At seasonal scale, a combination of those weather types indeed tends to outperform all the other candidate predictors explored (i.e., sea surface temperature patterns, phases of the Madden–Julian oscillation, and combinations of both). Spatially averaged Kendall’s τ improvements of 43% for the potential predictability and 23% for real-time predictions are attained with respect to standard models considering sea surface temperature fields alone. A new subseasonal-to-seasonal predictive methodology for extreme rainfall events is proposed based on probability forecasts of seasonal sequences of these weather types. The cross-validated real-time skill of the new probabilistic approach, as measured by the hit score and the Heidke skill score, is on the order of twice that associated with climatological values. The approach is designed to offer useful subseasonal-to-seasonal climate information to decision-makers interested not only in how many extreme events will happen in the season but also in how, when, and where those events will probably occur.
Abstract
The complex structure of the vertical velocity field inside an anticyclonic eddy located just south of the Canary Islands is analyzed through a high-resolution ocean model. Based on the flow divergence, vertical velocity is decomposed into various forcing components. The analysis reveals that advection and stretching of vorticity are the most important forcing contributions to the vertical velocity within the eddy. In the mixed layer, a small-scale multipolar vertical velocity pattern dominates. This is the result of vertical mixing effects that enhance the surface vertical velocity by increasing the ageostrophic velocity profile. As a result, an ageostrophic secondary circulation arises that acts to restore thermal-wind balance, inducing strong vertical motions. Nonlinear Ekman pumping/suction patterns resemble the small-scale vertical velocity field, suggesting that nonlinear Ekman effects are important in explaining the complex vertical velocity, despite an overestimate of its magnitude. In the eddy thermocline, the vertical velocity is characterized by a dipolar pattern, which experiences changes in intensity and axisymmetrization with time. The dipolar vertical velocity distribution arises from the imbalance between the advection and stretching of the vorticity forcing terms. A vertical velocity dipole is also obtained by solving a generalized omega equation from density and horizontal velocity fields, which also shows a preponderance of the ageostrophic term. The ubiquity of dipolar vertical velocity distributions inside isolated anticyclones is supported by recent observational findings in the same oceanic region.
Abstract
The complex structure of the vertical velocity field inside an anticyclonic eddy located just south of the Canary Islands is analyzed through a high-resolution ocean model. Based on the flow divergence, vertical velocity is decomposed into various forcing components. The analysis reveals that advection and stretching of vorticity are the most important forcing contributions to the vertical velocity within the eddy. In the mixed layer, a small-scale multipolar vertical velocity pattern dominates. This is the result of vertical mixing effects that enhance the surface vertical velocity by increasing the ageostrophic velocity profile. As a result, an ageostrophic secondary circulation arises that acts to restore thermal-wind balance, inducing strong vertical motions. Nonlinear Ekman pumping/suction patterns resemble the small-scale vertical velocity field, suggesting that nonlinear Ekman effects are important in explaining the complex vertical velocity, despite an overestimate of its magnitude. In the eddy thermocline, the vertical velocity is characterized by a dipolar pattern, which experiences changes in intensity and axisymmetrization with time. The dipolar vertical velocity distribution arises from the imbalance between the advection and stretching of the vorticity forcing terms. A vertical velocity dipole is also obtained by solving a generalized omega equation from density and horizontal velocity fields, which also shows a preponderance of the ageostrophic term. The ubiquity of dipolar vertical velocity distributions inside isolated anticyclones is supported by recent observational findings in the same oceanic region.
Abstract
There is growing awareness among governments, businesses, and the general public of risks arising from changes to our climate on time scales from months through to decades. Some climatic changes could be unprecedented in their harmful socioeconomic impacts, while others with adequate forewarning and planning could offer benefits. There is therefore a pressing need for decision-makers, including policy-makers, to have access to and to use high-quality, accessible, relevant, and credible climate information about the past, present, and future to help make better-informed decisions and policies. We refer to the provision and use of such information as climate services. Established programs of research and operational activities are improving observations and climate monitoring, our understanding of climate processes, climate variability and change, and predictions and projections of the future climate. Delivering climate information (including data and knowledge) in a way that is usable and useful for decision-makers has had less attention, and society has yet to optimally benefit from the available information. While weather services routinely help weather-sensitive decision-making, similar services for decisions on longer time scales are less well established. Many organizations are now actively developing climate services, and a growing number of decision-makers are keen to benefit from such services. This article describes progress made over the past decade developing, delivering, and using climate services, in particular from the worldwide effort galvanizing around the Global Framework for Climate Services under the coordination of UN agencies. The article highlights challenges in making further progress and proposes potential new directions to address such challenges.
Abstract
There is growing awareness among governments, businesses, and the general public of risks arising from changes to our climate on time scales from months through to decades. Some climatic changes could be unprecedented in their harmful socioeconomic impacts, while others with adequate forewarning and planning could offer benefits. There is therefore a pressing need for decision-makers, including policy-makers, to have access to and to use high-quality, accessible, relevant, and credible climate information about the past, present, and future to help make better-informed decisions and policies. We refer to the provision and use of such information as climate services. Established programs of research and operational activities are improving observations and climate monitoring, our understanding of climate processes, climate variability and change, and predictions and projections of the future climate. Delivering climate information (including data and knowledge) in a way that is usable and useful for decision-makers has had less attention, and society has yet to optimally benefit from the available information. While weather services routinely help weather-sensitive decision-making, similar services for decisions on longer time scales are less well established. Many organizations are now actively developing climate services, and a growing number of decision-makers are keen to benefit from such services. This article describes progress made over the past decade developing, delivering, and using climate services, in particular from the worldwide effort galvanizing around the Global Framework for Climate Services under the coordination of UN agencies. The article highlights challenges in making further progress and proposes potential new directions to address such challenges.
