Fig 1.
Diagram detailing the Matilda workflow to compute probabilistic projections. Dotted lines indicate opportunities for the user to define their own program specification. The dashed line in step 3 indicates the ability of the user to evaluate ensemble members repeatedly with different scoring criterion.
Table 1.
Hector parameters used in Matilda.
Hector parameters used to generate parameter sets in this work. The distributions are indicated as mean ± standard deviation. References from where distributions are derived are included.
Fig 2.
Decay rates from varying sensitivity values.
Root-mean-square error (RMSE) plotted against likelihood, conditional upon observed data. Different colors indicate decay rates for different sensitivity values in score_bayesian(). Setting higher values to sensitivity decreases the deviation penalty applied to ensemble members.
Fig 3.
Example of decay method for score_ramp() where w1 = 5 and w2 = 10. Ensemble members with an average deviation from observation < 5 will score 1 and ensemble members with an average deviation > 10 will score 0. Scores of ensemble members with average deviation between w1 and w2 will decrease from 1 linearly as average deviation approaches w2.
Fig 4.
Weighted ensemble members using different scoring algorithms.
Perturbed parameter ensemble (PPE) projections using 25 parameter sets plotted for atmospheric CO2 concentration from 1960–2100 weighted using the A) score_ramp() and B) score_bayesian() algorithms. Ensemble member weights are indicated by color shading with the solid red line representing observed atmospheric CO2 concentrations from 1959–2021.
Fig 5.
Likelihood of ensemble members given different sensitivity values.
Likelihood of perturbed parameter ensemble (PPE) members for an example emissions scenario based on root mean square error (RMSE) using the score_bayesian() algorithm. Blue line shows the use of default sensitivity value: The algorithm penalizes ensemble members as RMSE values deviate from one unit of standard deviation. Red line shows the use of a customized sensitivity value: Setting sensitivity = 2 indicating two units of standard deviation and thus assigns weight to ensemble members falling within this acceptable deviation range. Black dots represent individual ensemble members.
Fig 6.
Global mean surface temperature projections and warming probabilities across four emissions scenarios.
A) 1000-member perturbed parameter ensemble (PPE) projecting global mean surface temperature from 1950–2100 for each SSP scenario. Darker blue ensemble members represent those members that best reflect historical temperature observations. B) Stacked bars blocked by the probability of different temperature ranges for each SSP scenario. Lower emissions scenarios (SSP1-1.9 and SSP1-2.6) have a higher probability of temperature remaining below 2.0°C than higher emissions scenarios (SSP2-4.5 and SSP3-7.0).