Revisiting regression methods for estimating long-term trends in sea surface temperature

Global warming has enduring consequences in the ocean, leading to increased sea surface temperatures (SSTs) and subsequent environmental impacts, including coral bleaching and intensified tropical storms. It is imperative to monitor these trends to enable informed decision-making and adaptation. In this study, we comprehensively examine the methods for extracting long-term temperature trends, including STL, seasonal-trend decomposition procedure based on LOESS (locally estimated scatterplot smoothing), and the linear regression family, which comprises the ordinary least-squares regression (OLSR), orthogonal regression (OR), and geometric-mean regression (GMR). The applicability and limitations of these methods are assessed based on experimental and simulated data. STL may stand out as the most accurate method for extracting long-term trends. However, it is associated with notably sizable computational time. In contrast, linear regression methods are far more efficient. Among these methods, GMR is not suitable due to its inherent assumption of a random temporal component. OLSR and OR are preferable for general tasks but require correction to accurately account for seasonal signal-induced bias resulting from the phase-distance imbalance. We observe that this bias can be effectively addressed by trimming the SST data to ensure that the time series becomes an even function before applying linear regression, which is named "evenization". We compare our methods with two commonly used methods in the climate community. Our proposed method is unbiased and better than the conventional SST anomaly method. While our method may have a larger degree of uncertainty than combined linear and sinusoidal fitting, this uncertainty remains within an acceptable range. Furthermore, linear and sinusoidal fitting can be unstable when applied to natural data containing significant noise.