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We develop a geometrical interpretation of ternary probabilistic forecasts inwhich forecasts and observations are regarded as points inside a triangle.Within the triangle, we define a continuous colour palette in which hue andcolour saturation are defined with reference to the observed climatology. Incontrast to current methods, forecast maps created with this colour schemeconvey all of the information present in each ternary forecast. The geometricalinterpretation is then extended to verification under quadratic scoring rules(of which the Brier Score and the Ranked Probability Score are well--knownexamples). Each scoring rule defines an associated triangle in which the squareroots of the score, the reliability, the uncertainty and the resolution allhave natural interpretations as root--mean--square distances. This leads to ourproposal for a Ternary Reliability Diagram in which data relating toverification and calibration can be summarised. We illustrate these ideas withdata relating to seasonal forecasting of precipitation in South America,including an example of nonlinear forecast calibration. Codes implementingthese ideas have been produced using the statistical software package R and areavailable from the authors.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

On the visualisation, verification and recalibration of ternary probabilistic forecasts