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 𝑅𝐿 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 𝑅𝐿 on pressure, whereas previous studies have reported constant 𝑅𝐿. 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) β€œUnsupervised 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

Errata

Errors were "published with respect to the value of the moving average window, β„“. Each value of β„“ used in the study was in fact one fourth the value reported (e.g. instances of β€œβ„“ = 100 dbar” should instead read β€œβ„“ = 25 dbar”). Additionally, instances of β€œ20 times the typical layer thickness” should instead read β€œfive times the typical layer thickness.” The authors apologize for this error. This does not affect the results or interpretations in the text.

The specific instances where this error is present are enumerated below:

  • p. 7

    • Caption of Figure 2, β€œβ„“ = 100 dbar” should be β€œβ„“ = 25 dbar”

  • p. 8

    • Caption of Figure 3, β€œβ„“ = 100 dbar” should be β€œβ„“ = 25 dbar”

    • β€œ...highest score occurring for β„“ = 100 dbar.” should be β€œ...highest score occurring for β„“ = 25 dbar.”

    • β€œThe choice β„“ = 100 dbar, where the largest DBCV score occurs, thus corresponds to approximately 20 times the typical layer thickness.” should be β€œThe choice β„“ = 25 dbar, where the largest DBCV score occurs, thus corresponds to approximately five times the typical layer thickness.”

    • β€œWe obtain the values β„“ = 100 dbar and ...” should be β€œWe obtain the values β„“ = 25 dbar and ...”

  • p. 9

    • Table 2, Both instances of β€œ100 dbar” in the β„“ column should be β€œ25 dbar”

  • p. 11

    • Caption of Figure 4, β€œβ„“ = 100 dbar” should be β€œβ„“ = 25 dbar”

In the supplementary materials:

  • p. 2

    • Caption of Figure S.1, β€œβ„“ = 100 dbar” should be β€œβ„“ = 25 dbar”

  • p. 3

    • β€œ...moving average profile with the values of β„“: 10, 50, 100, and 150 dbar. ... When β„“ = 10 dbar, the moving average profile still clearly contains some of the larger stair steps. When β„“ = 150 dbar, ...” should be β€œ...moving average profile with the values of β„“: 2.5, 12.5, 25, and 37.5 dbar. ... When β„“ = 2.5 dbar, the moving average profile still clearly contains some of the larger stair steps. When β„“ = 37.5 dbar, ...”

    • β€œIf we always choose β„“ to be approximately twenty times the typical layer thickness, ...” should be β€œIf we always choose β„“ to be approximately five times the typical layer thickness, ...”

  • p. 4

    • Caption of Figure S.3, β€œ...4 different values ofβ„“: (a) 10 dbar, (b) 50 dbar, (c) 100 dbar, and (d) 150 dbar.” should be β€œ...4 different values of β„“: (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, β€œ...4 different values of β„“: (a) 10 dbar, (b) 50 dbar, (c) 100 dbar, and (d) 150 dbar.” should be β€œ...4 different values of β„“: (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, β€œβ„“ = 100 dbar” should be β€œβ„“ = 25 dbar”

  • p. 7

    • Caption of Figure S.6, β€œβ„“ = 100 dbar” should be β€œβ„“ = 25 dbar”