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Explora: Environment
and Resource Stratification and mixed layer deepening

as defined in time series theory. From this derived series, This reduction can lead to cases where the type of
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we generated a binary series composed of 1s or 0s using the alternation in the binary series indicates an interaction
following conventions: with a specific entity, even when there is no strong
• 1: Indicates positive difference, that is, an increase in correlation in the original time series. Conversely, a robust
stratification compared to the previous semester. correlation between the original series may not correspond
• 0: Indicates no increase in stratification. to a shared alternation pattern in the binary series. These
two types of information are fundamentally different and
Next, we examined whether the frequencies of 0s and 1s
were approximately equal to 0.5, suggesting that increases complementary:
(i) Quantitative variations: Insights into the overall
and decreases in stratification are equiprobable. This
observation, combined with the finding that stratification dynamics driving the changes in the series, which help
differences can be modeled as white noise, supports formulate or refute hypotheses about its underlying
“engine.”
the hypothesis that the binary series (0s and 1s) can be (ii) Qualitative alternation patterns: Understanding the
modeled as a Markov process.
factors influencing the rhythm of the alternation
We considered three potential scenarios for the Markov between increases and decreases in the phenomenon.
process: An analogy can help illustrate the distinction between
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(i) Markov-0 binomial model: Each value is these two types of information. Consider a musician using
independent of the previous one, resulting in a an electronic synthesizer: They can lengthen the cumulative
binomial distribution governed by parameters n duration of the ascending and descending phases of the
(number of elements) and p = 0. sound power (analogous to alternation patterns) or adjust
(ii) Markov-1 lengthening case: Each value depends on the average sound power using the potentiometer on their
the previous one such that if the previous value is 0 (or amplifier (analogous to quantitative variations). These are
1), the next value is more likely to remain 0 (or 1). two distinct processes: the average sound power is directly
(iii) Markov-1 alternating case: Each value depends on the influenced by the potentiometer, while the alternation
previous one such that if the previous value is 0 (or 1), speed is governed by the musician’s rhythmic choices.
the next value is more likely to be 1 (or 0).
To distinguish among these scenarios, we analyzed 3. Results and discussion
the average lengths of successive runs of 1s (or 0s) and 3.1. Description of data used for global stratification
compared them to the theoretical average length of 1.94 (upper 0 – 2000 m) and upper layer stratification
expected under the Markov-0 binomial model. The (upper 0 – 200 m)
classification criteria were as follows: 1
• Less than 1.80: Markov-1 alternating case We used stratification data provided by Li et al.,
• Between 1.80 and 2.10: Markov-0 binomial model initially published in 2020 and subsequently updated
• Greater than 2.10: Markov-1 lengthening case. by the authors. The dataset is publicly accessible at
the following link: https://pan.cstcloud.cn/web/share.
If necessary, we confirmed the calculation by calculating html?hash=E0zjDQOeRfs
the probability under a binomial distribution. When
the binary series is classified as Markov-1 alternating The dataset primarily relies on data from the Institute
or Markov-1 lengthening, this classification implies an of Atmospheric Physics at Chinese Academy of Sciences
interaction with another entity that exhibits a similar type (China), covering the period from 1955 to the present. It is
available with a horizontal resolution of 1° × 1° and includes
of signal. In such cases, it is necessary to identify a potential 41 vertical levels for the upper 0 – 2000 m of the ocean. The
interacting entity and justify this choice using additional researchers applied several quality assurance techniques,
arguments, which, in our study, are primarily climatological.
including instrumental bias correction, an advanced
As demonstrated in Zeltz , Zeltz , and Zeltz, this gap-filling algorithm for reconstructing temperature
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method of time series analysis enables the identification and salinity changes, and validation against recent Argo
of interactions that are undetectable by traditional data (available at https://argo.ucsd.edu). In addition, the
approaches. It provides valuable insights into the type of data include 95% confidence intervals calculated using
alternation within the series and its potential dependence a Monte Carlo approach that accounts for all sources of
on another series. However, this approach also results in error. Figure 2 presents the global monthly anomalies of
a significant loss of information, as the original series is stratification for upper 0 – 2000 m, updated by the authors
reduced to a derived binary series composed solely of 0s through the end of 2023 and calculated relative to the 1981
and 1s. – 2010 reference period.

Volume 1 Issue 1 (2024) 3 doi: 10.36922/eer.4578