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

Abstract. 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 commonly used methods for extracting long-term temperature trends, including the seasonal-trend decomposition procedure based on loess (STL) and the linear regression family, which comprises ordinary least square 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 stands out as the most accurate method for extracting long-term trends. However, it is associated with a notably sizeable 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. We introduced and evaluated an implementation using both simulated and realistic data.