Global Warming Has Been Accelerating Since At Least 1990

Technical Summary: Global Warming Has Been Accelerating Since At Least 1990

Problem Statement
Recent literature has reported that Global Mean Surface Temperature (GMST) has accelerated, with some studies suggesting this acceleration began around 2015. However, existing methodologies for detecting acceleration possess limitations. The standard quadratic trend specification ($xt = \alpha + \lambda t + \beta t^2 + \epsilon_t$) imposes a rigid functional form where the warming rate increases at a constant rate, which may not reflect reality. Furthermore, quadratic models often require two-step procedures (filtering data for El Niño and solar effects before trend estimation), which can reduce the precision of parameter estimates. Conversely, piecewise linear trends allow for structural breaks but assume discrete shifts at specific dates, potentially misinterpreting a continuously increasing rate as a series of breaks. The paper seeks to address these issues by developing a more flexible statistical framework to test for supralinear (greater-than-linear) trends and to determine the onset of acceleration more robustly.

Methodology
The authors propose a linearithmic specification as a flexible alternative to the quadratic trend. The model is defined as:
$$x_t = \alpha + \beta \log(t)t + \epsilon_t$$
where $x_t$ is the GMST anomaly at time $t$. The presence of acceleration is tested by evaluating the hypothesis $\beta > 0$. Theoretically, the linearithmic term $\log(t)t$ grows faster than a linear trend but slower than any polynomial trend with a degree $\delta > 1$, providing a lower bound for supralinear acceleration.

The study utilizes five major temperature datasets (HadCRUT, GISTEMP, NOAA, Berkeley Earth, and ERA5) covering the period from January 1970 to December 2025. The analysis employs a single-step estimation procedure that includes control variables for the El Niño effect ($N_t$) and solar irradiance ($S_t$) directly within the regression, rather than using a two-step filtering approach. The models are estimated using Ordinary Least Squares (OLS) with Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors (Newey-West estimator) to account for serial correlation and heteroskedasticity.

To determine the timing of acceleration, the authors employ an expanding window framework, starting with a sample from 1970–1990 and incrementally extending the end date to 2025. To address the multiple testing problem inherent in this approach, they utilize a max-|t| wild-bootstrap procedure to calculate critical values and adjust p-values, ensuring robustness against false positives.

Key Contributions

1. Novel Statistical Specification: The paper introduces the linearithmic specification ($\beta \log(t)t$) as a robust test for acceleration. Unlike the quadratic model, it does not assume a constant rate of increase in the warming rate and avoids the multicollinearity issues often found between linear and quadratic terms.
2. Theoretical Insight on Structural Breaks: The authors provide a theoretical proof (Theorem 0.3) demonstrating that if the true underlying trend is supralinear, standard structural break tests will eventually detect changes in the slope of a linear trend model. This suggests that reported "structural breaks" in GMST (e.g., in the 1970s or 2015) may be statistical artifacts of fitting a linear model to a supralinear trend, rather than evidence of discrete shifts in the warming rate.
3. Refined Timing of Acceleration: By applying the expanding window framework with bootstrap adjustments, the study re-evaluates the onset of acceleration, challenging the notion that it is solely a post-2015 phenomenon.

Results

• Linearithmic Specification: The results indicate statistically significant evidence of acceleration ($\beta > 0$) across all five datasets using the linearithmic specification. This significance holds both with and without additional control variables. Crucially, the expanding window analysis shows that evidence for acceleration is present since at least 1990, with the statistical significance strengthening as more recent data (up to 2025) is included.
• Quadratic Specification: In contrast, the quadratic specification yields significant results only in the longest estimation windows and primarily when additional control variables are included. Without controls, the quadratic coefficient is significant in only three of the five datasets.
• Polynomial Exponent Estimation: An additional exercise estimating the exponent $\delta$ in a general polynomial trend ($t^\delta$) suggests that the true exponent is less than two (the quadratic case) but greater than one. This supports the use of the linearithmic model as a more appropriate lower bound for the observed dynamics.
• Structural Breaks: The theoretical results suggest that the detection of structural breaks in linear trend models is consistent with an underlying supralinear trend, offering an alternative explanation for previously reported change points in GMST trends.

Significance and Claims
The paper claims that global warming acceleration is not merely a recent phenomenon starting around 2015 but has been present for several decades, detectable since at least 1990. The authors argue that the linearithmic specification provides a more robust and flexible framework for testing acceleration compared to the rigid quadratic model.

The study highlights that the observed acceleration implies an increasing rate of warming over time, which has implications for ecosystems, human health, and the economy. The authors note that their findings are consistent with other physical evidence, such as the increasing airborne fraction of anthropogenic carbon emissions and the doubling of Earth's energy imbalance in recent decades.

Finally, the paper emphasizes the importance of distinguishing between supralinear trends and structural breaks for policy and modeling. If the true trend is supralinear, piecewise linear models may underrepresent the true dynamics of GMST by capturing only discrete slope changes rather than a continuously increasing rate. The authors conclude that the presence of acceleration underscores the urgency of mitigation and adaptation strategies.