Table 1 Regression results and performance metrics for various model configurations using different inputs for predictor Γ and equivalent calculations for the Global Carbon Project between 1960 and 2020

From: Surprising stability of recent global carbon cycling enables improved fossil fuel emission verification

Parameter

Weighted-T model

Tropical-T model

ENSO model

Global Carbon Project

Model configuration: input used for predictor Γ

Globally integrated, γ-weighted and detrended land temperature anomalies

Tropical average detrended land temperature anomalies

Niño 3.4 index

Not a regression result

a (GtC yr−1 K−1)

−4.384 ± 0.408

−3.880 ± 0.467

−0.810 ± 0.241

 

b (yr−1)

0.00839 ± 0.00131

0.00895 ± 0.00132

0.01020 ± 0.00142

 

c (GtC yr−1)

−5.293 ± 0.974

−5.731 ± 0.971

−6.613 ± 1.074

 

r2

0.749 ± 0.059

0.638 ± 0.074

0.472 ± 0.207

 

RMSE (GtC yr−1)

0.50 ± 0.09

0.60 ± 0.10

0.74 ± 0.21

0.76 ± 0.11

Decadal RMSE (GtC yr−1)

0.16 ± 0.04

0.20 ± 0.03

0.24 ± 0.07

0.36 ± 0.14

  1. Uncertainties (1σ) coefficients a, b, and c from the regression model in equation (2) as well as the model’s coefficient of determination r2 are obtained by jackknifing with five-year non-overlapping blocks. RMSE values represent the true generalization error and are derived using cross-validation on the same blocks. Decadal RMSE is calculated analogously after smoothing the residual model errors ϵ (or the GCP budget imbalance δ) with a ten-year moving average. Uncertainty of the generalization error (that is, uncertainty on RMSE) is approximated following the method of Nadeau and Bengio38. See Methods for details.
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