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Linear transformation of scaling factors

YL Y. T. Eunice Lo
AC Andrew J. Charlton-Perez
FL Fraser C. Lott
EH Eleanor J. Highwood
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For the two-fingerprint experiments, TLS regression against the G4 and RCP4.5 simulations, xG4 and xRCP, was used instead of xSAI and xRCP, due to a lack of SAI-only simulations. We extracted the scaling factors for the SAI and RCP4.5 forced signals from that of xG4 by transforming scaling factors after regression18. Assuming xG4 = xSAI + xRCP:

where An external file that holds a picture, illustration, etc. Object name is srep39169-m3.jpg’s are best-estimate scaling factors. Linear transformation in matrix form is thus:

Equation 3 was used to estimate both the best estimates and uncertainty ranges of scaling factors for hypothesis testing in TfNo, TfC0 and TfC1.

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