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.

Model complexity versus ensemble size: allocating resources for climate prediction.

A perennial question in modern weather forecasting and climate prediction is whether to invest resources in more complex numerical models or in larger ensembles of simulations. If this question is to be addressed quantitatively, then information is needed about how changes in model complexity and ensemble size will affect predictive performance. Information about the effects of ensemble size is often available, but information about the effects of model complexity is much rarer. An illustration is provided of the sort of analysis that might be conducted for the simplified case in which model complexity is judged in terms of grid resolution and ensemble members are constructed only by perturbing their initial conditions. The effects of resolution and ensemble size on the performance of climate simulations are described with a simple mathematical model, which is then used to define an optimal allocation of computational resources for a range of hypothetical prediction problems. The optimal resolution and ensemble size both increase with available resources, but their respective rates of increase depend on the values of two parameters that can be determined from a small number of simulations. The potential for such analyses to guide future investment decisions in climate prediction is discussed.

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.

Development of probability density functions for future South American rainfall.

*We estimate probability density functions (PDFs) for future rainfall in five regions of South America, by weighting the predictions of the 24 Coupled Model Intercomparison Archive Project 3 (CMIP3) General Circulation Models (GCMs). The models are rated according to their relative abilities to reproduce the inter-annual variability in seasonal rainfall. *The relative weighting of the climate models is updated sequentially according to Bayes' theorem, based on the biases in the mean of the predicted time-series and the distributional fit of the bias-corrected time-series. *Depending on the season and the region, we find very different rankings of the GCMs, with no single model doing well in all cases. However, in some regions and seasons, differential weighting of the models leads to significant shifts in the derived rainfall PDFs. *Using a combination of the relative model weightings for each season we have also derived a set of overall model weightings for each region that can be used to produce PDFs of forest biomass from the simulations of the Lund-Potsdam-Jena Dynamic Global Vegetation Model for managed land (LPJmL).

MEP and planetary climates: insights from a two-box climate model containing atmospheric dynamics.

A two-box model for equator-to-pole planetary heat transport is extended to include simple atmospheric dynamics. The surface drag coefficient CD is treated as a free parameter and solutions are calculated analytically in terms of the dimensionless planetary parameters eta (atmospheric thickness), omega (rotation rate) and xi (advective capability). Solutions corresponding to maximum entropy production (MEP) are compared with solutions previously obtained from dynamically unconstrained two-box models. As long as the advective capability xi is sufficiently large, dynamically constrained MEP solutions are identical to dynamically unconstrained MEP solutions. Consequently, the addition of a dynamical constraint does not alter the previously obtained MEP results for Earth, Mars and Titan, and an analogous result is presented here for Venus. The rate of entropy production in an MEP state is shown to be independent of rotation rate if the advective capability xi is sufficiently large (as for the four examples in the solar system), or if the rotation rate omega is sufficiently small. The model indicates, however, that the dynamical constraint does influence the MEP state when xi is small, which might be the case for some extrasolar planets. Finally, results from the model developed here are compared with previous numerical simulations in which the effect of varying surface drag coefficient on entropy production was calculated.

Increasing risk of Amazonian drought due to decreasing aerosol pollution.

The Amazon rainforest plays a crucial role in the climate system, helping to drive atmospheric circulations in the tropics by absorbing energy and recycling about half of the rainfall that falls on it. This region (Amazonia) is also estimated to contain about one-tenth of the total carbon stored in land ecosystems, and to account for one-tenth of global, net primary productivity. The resilience of the forest to the combined pressures of deforestation and global warming is therefore of great concern, especially as some general circulation models (GCMs) predict a severe drying of Amazonia in the twenty-first century. Here we analyse these climate projections with reference to the 2005 drought in western Amazonia, which was associated with unusually warm North Atlantic sea surface temperatures (SSTs). We show that reduction of dry-season (July-October) rainfall in western Amazonia correlates well with an index of the north-south SST gradient across the equatorial Atlantic (the 'Atlantic N-S gradient'). Our climate model is unusual among current GCMs in that it is able to reproduce this relationship and also the observed twentieth-century multidecadal variability in the Atlantic N-S gradient, provided that the effects of aerosols are included in the model. Simulations for the twenty-first century using the same model show a strong tendency for the SST conditions associated with the 2005 drought to become much more common, owing to continuing reductions in reflective aerosol pollution in the Northern Hemisphere.