Temperature Trends, Climate Attribution and the Nonstationarity Question

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.