Unsupervised clustering identifies thermohaline staircases in the Canada Basin of the Arctic Ocean
Abstract: Thermohaline staircases are a widespread stratification feature that impacts the vertical transport of heat and nutrients and are consistently observed throughout the Canada Basin of the Arctic Ocean. Observations of staircases from the same time period and geographic region form clusters in temperature-salinity (T–S) space. Here, for the first time, we use an automated clustering algorithm called the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN), to detect and connect individual well-mixed staircase layers across profiles from Ice-Tethered Profilers (ITPs). Our application only requires an estimate of the typical layer thickness and expected salinity range of staircases. We compare this method to two previous studies that used different approaches to detect layers and reproduce several results, including the mean lateral density ratio $R_L$ and that the difference in salinity between neighboring layers is a magnitude larger than the salinity variance within a layer. We find that we can accurately and automatically track individual layers in coherent staircases across time and space between different profiles. In evaluating the algorithm’s performance, we find evidence of different physical features, namely splitting or merging layers and remnant intrusions. Further, we find a dependence of $R_L$ on pressure, whereas previous studies have reported constant $R_L$. Our results demonstrate that clustering algorithms are an effective and parsimonious method of identifying staircases in ocean profile data.
Schee, M.G., E. Rosenblum, J.M. Lilly, and N. Grisouard (2024) “Unsupervised clustering identifies thermohaline staircases in the Canada Basin of the Arctic Ocean,” Environmental Data Science, 3:e13, 1-19, DOI: 10.1017/eds.2024.13
Corrigendum
Errors were published with respect to the value of the moving average window, $\ell$. Each value of $\ell$ used in the study was in fact one fourth the value reported (e.g. instances of “$\ell$ = 100 dbar” should instead read “$\ell$ = 25 dbar”). Additionally, instances of “20 times the typical layer thickness” should instead read “five times the typical layer thickness.” The authors apologize for this error. This does not affect the results or interpretations in the text.
Schee, M.G., E. Rosenblum, J.M. Lilly, and N. Grisouard (2025) “Unsupervised clustering identifies thermohaline staircases in the Canada Basin of the Arctic Ocean - CORRIGENDUM,” Environmental Data Science, 4:e8, 1, DOI: 10.1017/eds.2024.56
In the version of this article available above on this page, all the instances of the error related to the values of $\ell$ have been corrected. However, in the version available through Environmental Data Science, several instances were not corrected in the article and no instances were corrected in the supplementary materials. All such instances are detailed below.
Instances of this error still present in the published version:
- p. 8
- Figure 3(a), all values of $\ell$ on the x-axis should be divided by 4.
- “…with the choices $\ell=100$ and $m_{pts}=170$ leads to…” should be “…with the choices $\ell=25$ and $m_{pts}=170$ leads to…”
- p. 9
- Table 2, Both instances of “100 dbar” in the $\ell$ column should be “25 dbar”
- This instance has been corrected in the pdf version available from Environmental Data Science, however the table displayed on the webpage version of the article is still incorrect.
- Table 2, Both instances of “100 dbar” in the $\ell$ column should be “25 dbar”
All instances of this error in the original version of the article:
- p. 7
- Caption of Figure 2, “$\ell = 100$ dbar” should be “$\ell = 25$ dbar”.
- p. 8
- Figure 3(a), all values of $\ell$ on the x-axis should be divided by 4.
- This instance is still present in the published version.
- Caption of Figure 3, “$\ell = 100$ dbar” should be “$\ell = 25$ dbar”
- “…highest score occurring for $\ell = 100$ dbar.” should be “…highest score occurring for $\ell = 25$ dbar.”
- “The choice $\ell = 100$ dbar, where the largest DBCV score occurs, thus corresponds to approximately 20 times the typical layer thickness.” should be “The choice $\ell = 25$ dbar, where the largest DBCV score occurs, thus corresponds to approximately five times the typical layer thickness.”
- “…with the choices $\ell=100$ and $m_{pts}=170$ leads to…” should be “…with the choices $\ell=25$ and $m_{pts}=170$ leads to…”
- This instance is still present in the published version.
- “…we obtain the values $\ell = 100$ dbar and …” should be “We obtain the values $\ell = 25$ dbar and …”
- Figure 3(a), all values of $\ell$ on the x-axis should be divided by 4.
- p. 9
- Table 2, Both instances of “100 dbar” in the $\ell$ column should be “25 dbar”
- This instance has been corrected in the pdf version available from Environmental Data Science, however the table displayed on the webpage version of the article is still incorrect.
- Table 2, Both instances of “100 dbar” in the $\ell$ column should be “25 dbar”
- p. 11
- Caption of Figure 4, “$\ell = 100$ dbar” should be “$\ell = 25$ dbar”
All instances of this error present in the supplementary materials:
- p. 2
- Caption of Figure S.1, “$\ell = 100$ dbar” should be “$\ell = 25$ dbar”
- p. 3
- “…moving average profile with the values of $\ell$: 10, 50, 100, and 150 dbar. … When $\ell$ = 10 dbar, the moving average profile still clearly contains some of the larger stair steps. When $\ell$ = 150 dbar, …” should be “…moving average profile with the values of $\ell$: 2.5, 12.5, 25, and 37.5 dbar. … When $\ell$ = 2.5 dbar, the moving average profile still clearly contains some of the larger stair steps. When $\ell$ = 37.5 dbar, …”
- “If we always choose $\ell$ to be approximately twenty times the typical layer thickness, …” should be “If we always choose $\ell$ to be approximately five times the typical layer thickness, …”
- p. 4
- Caption of Figure S.3, “…4 different values of$\ell$: (a) 10 dbar, (b) 50 dbar, (c) 100 dbar, and (d) 150 dbar.” should be “…4 different values of $\ell$: (a) 2.5 dbar, (b) 12.5 dbar, (c) 25 dbar, and (d) 37.5 dbar.” and similarly for the titles of each subplot
- p. 5
- Caption of Figure S.4, “…4 different values of $\ell$: (a) 10 dbar, (b) 50 dbar, (c) 100 dbar, and (d) 150 dbar.” should be “…4 different values of $\ell$: (a) 2.5 dbar, (b) 12.5 dbar, (c) 25 dbar, and (d) 37.5 dbar.” and similarly for the titles of each subplot
- p. 6
- Caption of Figure S.5, “$\ell = 100$ dbar” should be “$\ell = 25$ dbar”
- p. 7
- Caption of Figure S.6, “$\ell = 100$ dbar” should be “$\ell = 25$ dbar”
- p. 8
- Caption of Figure S.7, “$\ell = 100$ dbar” should be “$\ell = 25$ dbar”