08 Jun 2023
 | 08 Jun 2023
Status: this preprint is currently under review for the journal ESD.

Temperature Trends, Climate Attribution and the Nonstationarity Question

Ross McKitrick, Timothy Vogelsang, and John Christy

Abstract. The standard trend model for measuring climate warming assumes error terms are mean-reverting and stationary. But the climate econometrics literature has argued that if anthropogenic forcing is a dominant driver of climate, temperature trends must have nonstationary (unit root) error terms, which may be considered a “fingerprint” for anthropogenic forcing. Herein we explain this paradox and apply some tools from time series econometrics to resolve it. We formalize a previously proposed hypothesis for why past results have been unclear, namely that temperatures contain both a nonstationary forcing component and a stationary “weather noise” component that may bias unit root tests towards over-rejection. Our analysis yields a diagnostic method for assessing whether this problem matters in practice. We apply unit root tests to observed and modeled temperature series at surface and tropospheric layers. We find observed temperatures are stationary around a trend after allowing for a single structural break in trend, with no evidence of testing bias due to weather noise. Unit root tests applied to model-generated temperatures also indicate trend stationarity however we find evidence of testing bias due to weather noise. This implies that time series models for climate attribution need to deal carefully with the requirements for establishing cointegration. We discuss the implications for understanding the relationship between greenhouse gas forcing and atmospheric temperatures over time.

Ross McKitrick et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on esd-2023-11', Anonymous Referee #1, 30 Jun 2023
    • AC1: 'Reply on RC1', Ross McKitrick, 15 Aug 2023
  • RC2: 'Comment on esd-2023-11', Anonymous Referee #2, 03 Jul 2023
    • AC2: 'Reply on RC2', Ross McKitrick, 15 Aug 2023

Ross McKitrick et al.

Ross McKitrick et al.


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Short summary
The climate econometrics field has shown that attribution of warming to anthropogenic forcings requires temperature data to have a property called “nonstationarity” whereas trend detection assumes the data are stationary. Detailed testing shows temperatures are best described as stationary deviations around a linear trend. This is not consistent with anthropogenic forcings being the dominant driver of observed trends over time in the empirical framework commonly used in climate econometrics.