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Updated: May 25, 2026
05:37
An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
On the visualization, verification and recalibration of ternary probabilistic forecasts
Tim E Jupp1, Rachel Lowe, Caio A S Coelho
1Mathematics Research Institute, University of Exeter, Exeter, UK. t.e.jupp@ex.ac.uk
Summary
We present a new graphical method for interpreting probabilistic weather forecasts using triangles. This approach visually represents all forecast data and aids in forecast verification and calibration, improving accuracy.
Area of Science:
- Meteorology and Atmospheric Sciences
- Data Visualization
- Statistical Modeling
Background:
- Ternary probabilistic forecasts are complex to visualize.
- Current methods often fail to convey all forecast information.
- Verification and calibration of probabilistic forecasts require robust graphical tools.
Purpose of the Study:
- To develop a novel graphical interpretation for ternary probabilistic forecasts.
- To create a visualization method that displays complete forecast information.
- To extend geometrical interpretation for forecast verification and calibration.
Main Methods:
- Representing forecasts and observations as points within a triangle.
- Defining a continuous color palette based on observed climatology.
- Extending geometrical interpretation to quadratic scoring rules (e.g., Brier score, ranked probability score).
- Proposing a ternary reliability diagram for verification and calibration data.
Main Results:
- The proposed color scheme conveys all information in ternary forecasts.
- Scoring rules define associated triangles where score components are interpretable as distances.
- The ternary reliability diagram effectively summarizes verification and calibration data.
- Demonstrated application in seasonal precipitation forecasting for South America, including nonlinear calibration.
Conclusions:
- The graphical interpretation offers a comprehensive way to visualize ternary probabilistic forecasts.
- The geometrical framework provides natural interpretations for forecast verification metrics.
- The ternary reliability diagram is a valuable tool for assessing forecast performance and calibration.
- The developed methods and R codes are available for practical application in meteorological forecasting.
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