Correction to: Scientific Reports https://doi.org/10.1038/s41598-025-14641-5, published online 30 September 2025

The original version of this Article contained errors in Table 2, where four equations were incorrect. The incorrect and correct equations appear below.

Incorrect:

No

References

Equations

4

Innorta et al. (1980)38

\(\begin{array}{c}S=0.2624-1.73\times {10}^{-3}T+8.69\times {10}^{-6}{T}^{2}\end{array} +8.69\times {10}^{-6}{T}^{2}\)

8

Wu et al. (2010)42

\(\begin{array}{c}S=-1.024+0.00754T\end{array}+0.00754T-1.149\times {10}^{-5}{T}^{2}\)

11

Krumgalz (2018)45

\(\begin{array}{l}S=1.277\times {10}^{-2}+1.761\times {10}^{-4}T-3.462\times {10}^{-6}{T}^{2}+2.157\times {10}^{-8}{T}^{3}-5.054\times {10}^{-11}{T}^{4}\\-3.462\times {10}^{-6}{T}^{2}+2.157\times {10}^{-8}{T}^{3}-5.054\times {10}^{-11}{T}^{4}-5.054\times {10}^{-11}{T}^{4}\end{array}\)

12

Ezuber et al. (2023)13

\(S=[\begin{array}{c}exp({a}_{0}+{a}_{1}\cdot T+{a}_{2}\cdot {T}^{2}\end{array}{+{a}_{3}\cdot P+{a}_{4}\cdot I+{a}_{5}\cdot {I}^{0.5}+{a}_{6}\cdot {I}^{0.5}T}^{0.5}]\)

Correct:

No

References

Equations

4

Innorta et al. (1980)38

\(\begin{array}{c}S=0.2624-1.73\times {10}^{-3}T+8.69\times {10}^{-6}{T}^{2}\end{array}\)

8

Wu et al. (2010)42

\(\begin{array}{c}S=-1.024+0.00754T\end{array}-1.149\times {10}^{-5}{T}^{2}\)

11

Krumgalz (2018)45

\(S=1.277\times {10}^{-2}+1.761\times {10}^{-4}T-3.462\times {10}^{-6}{T}^{2}+2.157\times {10}^{-8}{T}^{3}-5.054\times {10}^{-11}{T}^{4}\)

12

Ezuber et al. (2023)13

\(S=[\begin{array}{c}exp({a}_{0}+{a}_{1}\cdot T+{a}_{2}\cdot {T}^{2}\end{array}+{a}_{3}\cdot P+{a}_{4}\cdot I+{a}_{5}\cdot {I}^{0.5}+{a}_{6}\cdot {I}^{0.5}T){]}^{0.5}\)

In addition, Equation 12 contained errors. Consequently,

$${N}_{3}=0.0148363-0.394805 \, {N}_{4}+0.671073 \, {N}_{5}+5.81608{N}_{9}^{2}$$

now reads:

$$N_{3} = 0.0148363 - 0.394805 \, N_{4} + 0.671073 \, N_{5} { + }5.81608 \, N_{4}^{2}$$
$${N}_{4}=0.00401049-0.731636 \, {N}_{6}+1.40403 \, {N}_{8}-67.7609{N}_{4}{N}_{8}+53.7624{N}_{6}^{2}+14.1122{N}_{8}^{2}$$

now reads:

$$N_{4} = 0.00401049 - 0.731636 \, N_{6} + 1.40403 \, N_{8} - 67.7609 \, N_{6} \, N_{8} + 53.7624 \, N_{6}^{2} + 14.1122 \, N_{8}^{2}$$
$${N}_{5}=0.0695009-0.000171121 \, T-0.00225487 \, T{N}_{7}+9.72296\times {10}^{-8}{T}^{2}{N}_{8}+21.9375{N}_{7}^{2}$$

now reads:

$$N_{5} = 0.0695009 - 0.000171121 \, T - 0.00225487 \, T \, N_{7} + 9.72296 \times 10^{ - 8} \, T^{2} + 21.9375 \, N_{7}^{2}$$
$${N}_{7}=-0.000666812-0.856323{N}_{9}+0.0750963{N}_{10}+55.0989{N}_{9}{N}_{10}-1.24928{N}_{9}^{2}-7.44268{N}_{{10}^{2}}$$

now reads:

$$N_{7} = - 0.000666812 - 0.856323 \, N_{9} + 0.0750963 \, N_{10} + 55.0989 \, N_{9} \, N_{10} - 1.24928 \, N_{9}^{2} - 7.44268 \, N_{10}^{2}$$
$${N}_{8}=0.0651995-0.000682133 \, MW-0.0124249 \, I-5.87111\times {10}^{-5} \, MWI+1.84848\times {10}^{-6} \, M{W}^{2}-0.000367581 \, {I}^{2}$$

now reads:

$$N_{8} = 0.0651995 - 0.000682133 \, MW + 0.0124249 \, I - 5.87111 \times 10^{ - 5} \, MW \, I + 1.84848 \times 10^{ - 6} \, MW^{2} - 0.000367581 \, I^{2}$$
$${N}_{10}=-0.119205+0.000812485 \, T+0.00334223 \, I+5.26927\times {10}^{-6} \, TI-1.06148\times {10}^{-6} \, {T}^{2}-0.000365208 \, {I}^{2}-9.19219\times {10}^{-7} \, M{W}^{2}$$

now reads:

$$N_{10} = - 0.119205 + 0.000812485 \, T + 0.00334223 \, I + 5.26927 \times 10^{ - 6} \, T \, I - 1.06148 \times 10^{ - 6} \, T^{2} - 0.000365208 \, I^{2}$$

The original Article has been corrected.