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Explora: Environment
and Resource Stratification and mixed layer deepening

enabling them to perform simulations and gain a concrete y =m y +x t (XVI)
t
t+1
understanding of the dynamics of climate change. This In contrast, the Z.3 model is guided by “signals” detected
represents a significant improvement over the reliance in the climate system. Specifically, it identifies Markov-1
on near-blind trust that non-specialists have traditionally alternating-type signals in atmospheric (monthly)
placed in the results of more complex and effective and oceanic (quarterly) temperatures. The Z.2 model,
models. Such advanced models, while powerful, are often developed in Zeltz, hypothesizes a direct interaction
8
inaccessible due to their dependence on sophisticated between these signals, where the difference in their periods
computing equipment, lengthy computation times, and is attributed to the vastly different climatic memories of the
a lack of transparency regarding the relationships and atmosphere and ocean.
parameters employed.
Building on this interaction, the Z.3 model is
However, the Z.3 model’s simplicity also imposes
inherent limitations. While it can simulate a few key fundamentally deterministic, incorporating random
coefficients only to account for natural variability. This
parameters essential for understanding climate change,
its rudimentary nature restricts its scope. Notably, it contrasts with Hasselmann’s approach, which is more
does not account for local changes in salinity caused by inherently stochastic. Despite these differences, both
models underscore the importance of climate memory in
melting ice, precipitation anomalies, or increased river understanding system dynamics.
runoff driven by global warming, all of which affect
stratification. Furthermore, the model, in its current form, 4. Conclusion
cannot incorporate the potential to change the large-scale
circulation of the global ocean, including its overturning This study demonstrates, through a detailed analysis of
circulation and horizontal flows (thermohaline circulation probabilistic signals present in relevant time series, that the
[THC]/meridional overturning circulation [MOC], ENSO exerts a significant influence on the biannual cycles
commonly known as the “global conveyor belt”). These of rise and fall in global average oceanic stratification.
39
limitations present two interesting perspectives for future Conversely, the long-term increase in stratification and
improvement of the Z.3 model, with undoubtedly many the deepening of the mixed layer r are predominantly
additional areas for refinement. explained by the warming of the UOS.
The Z.3 model, as it currently stands, integrates the Our calculations indicate that the excess heat entering
mechanisms detailed in this article and previous works. the UOS is dissipated as follows: out of a total of 40 units of
7,8
It is capable of producing reliable simulations of five additional heat, 34 units contribute to warming the UOS,
key climatic parameters – arguably the most critical five units are released as latent heat into the atmosphere,
for understanding the global climate – at a very low and one unit deepens the mixed layer by forming new lower
computational cost. However, it cannot replace the more strata, as described in Sections 3.3 and 3.4. This mechanism
sophisticated and comprehensive models employed by provides the primary explanation for the observed dual
major climate institutes. Instead, it serves as a valuable phenomenon of increasing stratification and deepening of
complementary tool for climate research. the lower boundary layer. Additional factors, such as the
intensification of storms (accounted for in the model) and
3.10. Comparison with the stochastic Hasselmann the displacement of water masses from their regions of
model formation by ocean currents and eddies, also play a role.
42
The stochastic Hasselmann model, developed in 1976, However, certain phenomena, particularly those related
40
41
remains in use today (e.g., Lin et al. ). Like the Z.3 model, to changes in double diffusion driven by climate change
it is based on the differing climatic “memories” of the – such as diffusive convection or salinization occurring
oceans and the atmosphere and employs Markov chains. in the expanding basins of the world’s oceans 42-45 – are

It is, therefore, worthwhile to highlight the key differences not included in this work. This omission constitutes a
between the two approaches. significant limitation, adding to those noted in Section 3.9.
In Hasselmann’s theory, short-term random noise The Z.3 modeling, which builds on this and prior
(e.g., atmospheric weather) drives longer-term variations studies, incorporates five key climatic parameters:
7,8
(e.g., red spectra at the ocean level). Mathematically, this is atmospheric temperature (t), UOS temperature (θ),
represented by an autoregressive process of the first order, oceanic cloudiness(cl), stratification (s), and the depth(S)
where the next step, y , of the long variation depends on of the mixed layer. The model reveals a common behavior
t+1
the previous state, y , scaled by the ocean’s climatic memory, across these parameters: growth toward an asymptotic
t
m, and disturbed by short-term variation x : t threshold. The magnitude of variations projected for the

Volume 1 Issue 1 (2024) 11 doi: 10.36922/eer.4578