Comments on "Revisiting Regression Methods for Estimating Long-Term Trends in Sea Surface Temperature"

In this manuscript, the authors compare the ability of several regression techniques to recover underlying long-term trends in daily SST (Sea Surface Temperature) records. They find that the ordinary least squares (OLS) method could be biased due to an imbalanced phase associated with seasonal cycles. They further propose a 7-step approach to account for imbalanced seasonal cycles to obtain a less-biased estimator. Despite the interesting technical discussion, the manuscript, in my view, does not provide sufficient methodological advances. The atmospheric and climate community already has other approaches to address this issue, potentially more efficiently (please refer to my second comment below). Moreover, I am concerned that the topic of this paper might not fall within the scope of this journal, which focuses on Natural Hazards. As a result, I would suggest that the authors compare their methods to the approach I suggest below and consider submitting this work to a more technical journal.

1. I appreciate the authors' careful introduction of OLS2, GMR, and OR, but this discussion may not be entirely relevant in this context because the timing of SST measurements should be well-known. The authors also point this out in line 115. On the other hand, the STL (Seasonal-Trend Decomposition procedure based on Loess) probably deserves a more detailed introduction, including the mathematics and equations.

2. In atmospheric, ocean, and climate research, the first step of an analysis typically involves removing the seasonal cycle. Long-term trends are then estimated from the anomalies. When using daily data, directly calculating daily climatology often results in noisy estimates. Hence, the community uses sine and cosine functions to fit the amplitude and shape of seasonal cycles. For a problem that also estimates long-term trends, the model would be:

T = μ + k*yr + ∑_{i=1}^{N}(a_i * sin(i*yr*2π)) + ∑_{i=1}^{N}(b_i * cos(i*yr*2π)),

where the goal is to fit for μ, k, a_i, and b_i from the data, with i = 1, 2, ..., N. In practice, this is simply a multi-linear regression, and N can be determined if increasing N does not further improve the fitting (using, for example, an F-test). Fitting sine and cosine functions simultaneously captures different phases. Hence, unless the authors demonstrate that their method outperforms the community's common practice, I am not fully convinced that the method they propose would make a significant methodological improvement.

Please see the attached .pdf file.