Could detection and attribution of climate change trends be spurious regression?

Since the 1970s, scientists have developed statistical methods intended to formalize detection of changes in global climate and to attribute such changes to relevant causal factors, natural and anthropogenic. Detection and attribution (D&A) of climate change trends is commonly performed using a variant of Hasselmann's "optimal fingerprinting" method, which involves a linear regression of historical climate observations on corresponding output from numerical climate models. However, it has long been known in the field of time series analysis that regressions of "non-stationary" or "trending" variables are, in general, statistically inconsistent and often spurious. When non-stationarity is caused by "integrated" processes, as is likely the case for climate variables, consistency of least-squares estimators depends on "cointegration" of regressors. This study has shown, using an idealized linear-response-model framework, that if standard assumptions hold then the optimal fingerprinting estimator is consistent, and hence robust against spurious regression. In the case of global mean surface temperature (GMST), parameterizing abstract linear response models in terms of energy balance provides this result with physical interpretability. Hypothesis tests conducted using observations of historical GMST and simulation output from 13 CMIP6 general circulation models produced no evidence that standard assumptions required for consistency were violated. It is therefore concluded that, at least in the case of GMST, detection and attribution of climate change trends is very likely not spurious regression. Furthermore, detection of significant cointegration between observations and model output indicates that the least-squares estimator is "superconsistent", with better convergence properties than might previously have been assumed. Finally, a new method has been developed for quantifying D&A uncertainty, exploiting the notion of cointegration to eliminate the need for pre-industrial control simulations.

A Probabilistic Paradigm for the Parametric Insurance of Natural Hazards.

There is a pressing need for simple and reliable risk transfer mechanisms that can pay out quickly after natural disasters without delays caused by loss estimation, and the need for long historical claims records. One such approach, known as parametric insurance, pays out when a key hazard variable exceeds a predetermined threshold. However, this approach to catastrophe risk, based on making deterministic binary predictions of loss occurrence, is susceptible to basis risk (mismatch between payouts and realized losses). A more defensible approach is to issue probabilistic predictions of loss occurrence, which then allows uncertainty to be properly quantified, communicated, and evaluated. This study proposes a generic probabilistic framework for parametric trigger modeling based on logistic regression, and idealized modeling of potential damage given knowledge of a hazard variable. We also propose various novel methods for evaluating the quality and utility of such predictions as well as more traditional trigger indices. The methodology is demonstrated by application to flood-related disasters in Jamaica from 1998 to 2016 using gridded precipitation data as the hazard variable. A hydrologically motivated transformation is proposed for calculating potential damage from daily rainfall data. Despite the simplicity of the approach, the model has substantial skill at predicting the probability of occurrence of loss days as demonstrated by traditional goodness-of-fit measures (i.e., pseudo-R2 of 0.55) as well as probabilistic verification diagnostics such as receiver operating characteristics. Using conceptual models of decisionmaker expenses, we also demonstrate that the system can provide considerable utility to involved parties, e.g., insured parties, insurers, and risk managers.

A geostatistical extreme-value framework for fast simulation of natural hazard events.

We develop a statistical framework for simulating natural hazard events that combines extreme value theory and geostatistics. Robust generalized additive model forms represent generalized Pareto marginal distribution parameters while a Student's t-process captures spatial dependence and gives a continuous-space framework for natural hazard event simulations. Efficiency of the simulation method allows many years of data (typically over 10 000) to be obtained at relatively little computational cost. This makes the model viable for forming the hazard module of a catastrophe model. We illustrate the framework by simulating maximum wind gusts for European windstorms, which are found to have realistic marginal and spatial properties, and validate well against wind gust measurements.

Evaluating probabilistic dengue risk forecasts from a prototype early warning system for Brazil.

Recently, a prototype dengue early warning system was developed to produce probabilistic forecasts of dengue risk three months ahead of the 2014 World Cup in Brazil. Here, we evaluate the categorical dengue forecasts across all microregions in Brazil, using dengue cases reported in June 2014 to validate the model. We also compare the forecast model framework to a null model, based on seasonal averages of previously observed dengue incidence. When considering the ability of the two models to predict high dengue risk across Brazil, the forecast model produced more hits and fewer missed events than the null model, with a hit rate of 57% for the forecast model compared to 33% for the null model. This early warning model framework may be useful to public health services, not only ahead of mass gatherings, but also before the peak dengue season each year, to control potentially explosive dengue epidemics.

Dengue outlook for the World Cup in Brazil: an early warning model framework driven by real-time seasonal climate forecasts.

BACKGROUND: With more than a million spectators expected to travel among 12 different cities in Brazil during the football World Cup, June 12-July 13, 2014, the risk of the mosquito-transmitted disease dengue fever is a concern. We addressed the potential for a dengue epidemic during the tournament, using a probabilistic forecast of dengue risk for the 553 microregions of Brazil, with risk level warnings for the 12 cities where matches will be played. METHODS: We obtained real-time seasonal climate forecasts from several international sources (European Centre for Medium-Range Weather Forecasts [ECMWF], Met Office, Meteo-France and Centro de Previsão de Tempo e Estudos Climáticos [CPTEC]) and the observed dengue epidemiological situation in Brazil at the forecast issue date as provided by the Ministry of Health. Using this information we devised a spatiotemporal hierarchical Bayesian modelling framework that enabled dengue warnings to be made 3 months ahead. By assessing the past performance of the forecasting system using observed dengue incidence rates for June, 2000-2013, we identified optimum trigger alert thresholds for scenarios of medium-risk and high-risk of dengue. FINDINGS: Our forecasts for June, 2014, showed that dengue risk was likely to be low in the host cities Brasília, Cuiabá, Curitiba, Porto Alegre, and São Paulo. The risk was medium in Rio de Janeiro, Belo Horizonte, Salvador, and Manaus. High-risk alerts were triggered for the northeastern cities of Recife (p(high)=19%), Fortaleza (p(high)=46%), and Natal (p(high)=48%). For these high-risk areas, particularly Natal, the forecasting system did well for previous years (in June, 2000-13). INTERPRETATION: This timely dengue early warning permits the Ministry of Health and local authorities to implement appropriate, city-specific mitigation and control actions ahead of the World Cup. FUNDING: European Commission's Seventh Framework Research Programme projects DENFREE, EUPORIAS, and SPECS; Conselho Nacional de Desenvolvimento Científico e Tecnológico and Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro.

The development of an early warning system for climate-sensitive disease risk with a focus on dengue epidemics in Southeast Brazil.

Previous studies demonstrate statistically significant associations between disease and climate variations, highlighting the potential for developing climate-based epidemic early warning systems. However, limitations include failure to allow for non-climatic confounding factors, limited geographical/temporal resolution, or lack of evaluation of predictive validity. Here, we consider such issues for dengue in Southeast Brazil using a spatio-temporal generalised linear mixed model with parameters estimated in a Bayesian framework, allowing posterior predictive distributions to be derived in time and space. This paper builds upon a preliminary study by Lowe et al. but uses extended, more recent data and a refined model formulation, which, amongst other adjustments, incorporates past dengue risk to improve model predictions. For the first time, a thorough evaluation and validation of model performance is conducted using out-of-sample predictions and demonstrates considerable improvement over a model that mirrors current surveillance practice. Using the model, we can issue probabilistic dengue early warnings for pre-defined 'alert' thresholds. With the use of the criterion 'greater than a 50% chance of exceeding 300 cases per 100,000 inhabitants', there would have been successful epidemic alerts issued for 81% of the 54 regions that experienced epidemic dengue incidence rates in February-April 2008, with a corresponding false alarm rate of 25%. We propose a novel visualisation technique to map ternary probabilistic forecasts of dengue risk. This technique allows decision makers to identify areas where the model predicts with certainty a particular dengue risk category, to effectively target limited resources to those districts most at risk for a given season.

On the visualization, verification and recalibration of ternary probabilistic forecasts.

We develop a graphical interpretation of ternary probabilistic forecasts in which forecasts and observations are regarded as points inside a triangle. Within the triangle, we define a continuous colour palette in which hue and colour saturation are defined with reference to the observed climatology. In contrast to current methods, forecast maps created with this colour scheme convey all of the information present in each ternary forecast. The geometrical interpretation is then extended to verification under quadratic scoring rules (of which the Brier score and the ranked probability score are well-known examples). Each scoring rule defines an associated triangle in which the square roots of the score, the reliability, the uncertainty and the resolution all have natural interpretations as root mean square distances. This leads to our proposal for a ternary reliability diagram in which data relating to verification and calibration can be summarized. We illustrate these ideas with data relating to seasonal forecasting of precipitation in South America, including an example of nonlinear forecast calibration. Codes implementing these ideas have been produced using the statistical software package R and are available from the authors.

Temporal clustering of tropical cyclones and its ecosystem impacts.

Tropical cyclones have massive economic, social, and ecological impacts, and models of their occurrence influence many planning activities from setting insurance premiums to conservation planning. Most impact models allow for geographically varying cyclone rates but assume that individual storm events occur randomly with constant rate in time. This study analyzes the statistical properties of Atlantic tropical cyclones and shows that local cyclone counts vary in time, with periods of elevated activity followed by relative quiescence. Such temporal clustering is particularly strong in the Caribbean Sea, along the coasts of Belize, Honduras, Costa Rica, Jamaica, the southwest of Haiti, and in the main hurricane development region in the North Atlantic between Africa and the Caribbean. Failing to recognize this natural nonstationarity in cyclone rates can give inaccurate impact predictions. We demonstrate this by exploring cyclone impacts on coral reefs. For a given cyclone rate, we find that clustered events have a less detrimental impact than independent random events. Predictions using a standard random hurricane model were overly pessimistic, predicting reef degradation more than a decade earlier than that expected under clustered disturbance. The presence of clustering allows coral reefs more time to recover to healthier states, but the impacts of clustering will vary from one ecosystem to another.

Stratospheric memory and skill of extended-range weather forecasts.

We use an empirical statistical model to demonstrate significant skill in making extended-range forecasts of the monthly-mean Arctic Oscillation (AO). Forecast skill derives from persistent circulation anomalies in the lowermost stratosphere and is greatest during boreal winter. A comparison to the Southern Hemisphere provides evidence that both the time scale and predictability of the AO depend on the presence of persistent circulation anomalies just above the tropopause. These circulation anomalies most likely affect the troposphere through changes to waves in the upper troposphere, which induce surface pressure changes that correspond to the AO.