Page 108 - EER-1-1

Explora: Environment
and Resource Stratification and mixed layer deepening

temperature increase is faster, approximately 0.008°C/year, is strongly correlated with the increase in heat (C )
n
as shown in Desbruyères et al. 34 absorbed by the UOS. This relationship occurs directly
The thermal energy Q’ responsible for the annual through heat penetration and indirectly through the
1
warming of the 0 – 200 m mixed layer is approximately: addition of melted freshwater, which alters salinity.
This relationship is expressed as:
Q’ ≈ 1027 × C× 200 × 3.6 × 10 × 0.008 ≈ 2.36 × 10 J (V)
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14
s = s +μ(θ - θ ) (VII)
This value represents approximately 71.5% of the n+1 n n+1 n
additional thermal energy absorbed annually by the where μ is a constant estimated through calibration
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oceans. Half of the remaining energy (26%, or 0.26 × 3.3× with data from Li et al.
10 ≈ 0.858 × 10 J) dissipates as latent heat through • Line 18 (added): We define L as the global average
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21
n
evaporation, while the other half offsets the cooling caused distance during month n between the base of the
by evaporation. This process accounts for the surface mixed layer and the sea surface. Estimating Ln reliably
temperature rise of 0.008°C. Consequently, the total energy is technically challenging due to the diverse criteria
used for surface warming is approximately 71.5% + 13% ≈ used (e.g., water pressure, temperature, salinity, or
84.5%, while 13% escapes as latent heat to the atmosphere specific thresholds). However, the change in depth,
37
– approximately 5 times the energy dissipated into the defined as:
thermocline. S L - L (VIII)
n = n n-1
The amount of additional water evaporated, E, can be On the other hand, for fairly obvious mathematical
calculated as: reasons, the depth S of the layer defined by following
n
E = (0.5× 0.858 × 10 )/l (VI) Equation VIII depends much less on the techniques and
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criteria used.
where l ≈ 2470 kJ/kg is the latent heat of water at
the relevant temperatures. Substituting values yields S = S + λ(θ -θ ) + L (IX)
31
n
n-1
>Th
n+2
n+3
E ≈ 1.73 × 10 kg, or approximately 168 km of seawater. Here, θ – θ reflects the interaction between
3
14
n-1
n
This amount represents only a small fraction (≈0.035%) of UOS temperature variations and the deepening of the
the total oceanic evaporation rates, which is estimated at thermocline and mixing layer (Section 3.6). The 3-month
480 km³ ± 10%. 36 lag between S and θ -θ n -1 accounts for the significant
n+3
n
Table S1 summarizes the primary results obtained in thermal inertia of ocean water. 31,38 The constant λ is
2
this section. estimated through calibration with data from Sallée et al.
L denotes additional deepening (L) caused by thermal
>Th
3.5. Modeling the deepening of the mixed layer energy inputs exceeding a certain threshold Th, driven by
Table S2 summarizes the relationships used by the Z.3 violent winds.
model, which is employed to simulate the deepening of the 3.6. The Z.3 model: Confidence intervals and
mixed layer. Most of the relationships remain unchanged simulations
from the Z.2 model, which previously enabled simulations
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of changes in atmospheric temperature, the UOS, and Using a sample of 250 simulations from the Z.3 model, we
oceanic cloud cover. Compared to the Z.2 model, only line determined point estimates (μ and σ ) for the means (μ)
e
e
9 has been modified, and one new line (line 18) has been and standard deviations (σ) of monthly changes in S , s ,
n
n
added. t , θ , and cl over the period 1955 – 2095. After verifying
n
n
n
normality, these estimates allowed us to calculate95%
Consequently, lines 1 – 8 and 10 – 17 are identical confidence intervals. Table S3 summarizes the results.
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to those in the table, which outlines the relationships
underlying the Z.2 model. Their detailed explanations, Figures 6-9 illustrate Z.3 model simulations for:
primarily derived from Zeltz, and supplementary • Deepening (S ) in meters (Figure 6)
7,8
n
information provided in Table S2, are discussed in Zeltz, • Stratification (s ) in percentage (Figure 7)
7
n
8
except for lines 6 and 6 , which are explained in Zeltz. • Temperature anomalies (t and θ ) in °C (Figure 8),
b
a
n
n
The constants employed in the model have been calibrated and
using observational data, incorporating the ratios • Oceanic cloudiness (cl ) in percentage (Figure 9).
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determined in Section 3.4.
Each figure includes the following components:
The modifications and additions are described below: • A simulation curve of the variable,
• Line 9 (modified): The growth of stratification (s ) • Two extreme curves delimiting the 95% confidence
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Volume 1 Issue 1 (2024) 8 doi: 10.36922/eer.4578