the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 01 Jul 2025
Revisited heat budget and probability distributions of turbulent heat fluxes in the Mediterranean Sea
Abstract. Understanding the surface heat budget of the Mediterranean Sea is essential for assessing its role in regional climate and ocean circulation. Under the steady-state heat budget closure hypothesis, the Mediterranean should exhibit a net surface heat loss to balance the heat gained through the inflow of warm Atlantic water at the Gibraltar Strait. However, literature estimates of the net heat flux vary widely, raising questions about the accuracy of existing reanalysis products. In this study, we compute the net surface heat flux over the Mediterranean using two atmospheric datasets: high-resolution (0.125°) ECMWF analysis and lower-resolution (0.25°) ERA5 reanalysis. By applying the same sea surface temperature fields and bulk formulas in both cases, we isolate the impact of atmospheric resolution and data quality. We find that the ECMWF analysis yields a basin-averaged net heat flux of –3.6 ± 1.3 W m⁻2, consistent with the closure hypothesis, while ERA5 gives a spurious positive flux of +5 ± 1.2 W m⁻2. Furthermore, beyond simply assessing the net heat budget, this study delves into the probability distributions of air-sea heat fluxes, aiming to gain a deeper understanding of associated uncertainties and extreme values in turbulent heat fluxes. The probability distributions for turbulent heat flux components exhibit characteristics such as skewness and kurtosis, respectively, varying across the basin. To assess the influence of extremes, we apply the Interquartile Range (IQR) method within statistical models that account for the skewed nature of turbulent heat flux distributions, enabling a consistent treatment of outliers. Our results reveal that extreme negative heat flux events play a critical role in determining the net heat flux direction; excluding these extremes leads to a spurious positive heat budget. This highlights the importance of high-resolution atmospheric data for accurately capturing air-sea interactions and ensuring physically consistent climate modelling over the Mediterranean Sea. And we demonstrate that the Mediterranean heat budget closure hypothesis is connected to extreme heat loss events occurring in key regions of the basin, such as the Gulf of Lion, the Adriatic Sea, the Aegean Sea, and the southern Turkish coasts.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-2867', Anonymous Referee #1, 08 Aug 2025
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RC2: 'Comment on egusphere-2025-2867', Anonymous Referee #2, 04 Sep 2025
The paper of Ghani et al., entitled ‘Revisited heat budget and probability distributions of turbulent heat fluxes in the Mediterranean Sea’ compared two surface heat budget estimates for the 2006-2020 period over the Mediterranean Sea recomputed by the authors with ECMWF and ERA5 bulk outputs (but the same SST). The paper presents also a statistical analyse of the sensible and latent heat fluxes with a characterization of their distributions and finally investigates the role of heat loss extremes.
This study has questioning conclusive remarks:
- The mention that the heat budget closure hypothesis can not be satisfied with coarse resolution (lines 457-458) is not fully exact as shown by Table 1 where previous studies prove their quality to obtain negative heat loss in surface balanced by Gibraltar heat inflow. Possibly you would like to argue that a better representation of the heat budget is related to horizontal resolution; But, there are many sources of improvements for representation of the heat budget terms: one is likely resolution, but sea surface and clouds/radiative schemes are also very important. This conclusion must be more carefully discussed in my opinion.
- The statement that the Mediterranean is still losing heat but only if using a(the) high-resolution ECMWF analysis (lines 459-460) puzzles me. I am not sure this is a way to promote the results. The fact the Mediterranean Sea losses or not heat is something that can not be settle by only looking on one dataset. A very large analyse of a large amount of data is mandatory.
Please also clarify paragraph p10, lines 273-279. It is confusing to put here the finding is that the Mediterranean Sea still looses heat in surface, as you decided to follow the heat budget closure hypothesis that imposes this.
I have also main concerns related to:
- the LH distribution (section 4.2). Fig. 5a shows surprisingly a quite large number of positive LH values for all locations. This means condensation, and surpersaturation of air mass. This phenomenon is quite rare. It appears mandatory to check the LH values in these distributions. Also, for turbulent fluxes, the computation uses transfer coefficients independent from the wind (equation 9/10). Does this may affect your results in terms of SH/LH distribution shapes.
- There are very large differences in SW (Fig. 1d,h). This is the main reason for the ERA5 positive budget (Tab. 1). From equation 2, I understand the differences come only from the cloud coverage C. Did you compare the cloud coverage fields in the two atmospherical dataset? Should the threshold to define clear sky be adapted and?
For these two remarks, a larger discussion of what is mentioned p10, line 263-366 would be greatly useful.
Finally, even if I understand and find fair the objective of having the same fluxes computation method and same SST for both dataset, I would have appreciated a brief comparison with the SW, LW, LH and SH fluxes directly taken from ECMWF and ERA5.
I put below some minor comments.
According to my main remarks, I recommend a major revision of the paper.
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Minor comments:
p5, eq.2: add information in text about the threshold; and unit for C.
p5, line 140: what is sec ?
p6, eq 8: why did you not use directly the specific humidity?
p7, line 189: ... the following atmospheric near-surface variables…
Fig. 1: Could a column with difference maps for each term be added?
P8, line 210-212: ... The largest mean sensible heat gain is observed… Gulf of Lion loss more… [negative is heat loss]
p8, lines 221-223: The first reason for SW differences between Western Mediterranean and Eastern Mediterranean is the latitudinal position of each sub-basin.
P8, line 227: … presumably due to the warm Atlantic surface inflow…
p13, line 328: From Fig. 4b μ is mostly positive. Please modify the sentence.
P15, line 395: ...with long term climatology values for the extreme heat losses days… : Could you precise how is built this climatology?
P16, line 400-401: The differences in Qnet between ECMWF and ERA5 is mostly due to differences in SW. Please review the whole paragraph.
P17, line 424: … of -289 W/m2 (for k=0.75)...
p17, line 427: Please add the map of differences between Fig8 and Fig. 3a to put in evidence this result.
P19, line 486: minus sign is missing.
Citation: https://doi.org/10.5194/egusphere-2025-2867-RC2 -
EC1: 'Comment on egusphere-2025-2867', Yonggang Liu, 18 Sep 2025
Both Reviewers provided constructive comments aiming at improving the manuscript. I would like to encourage the authors revise the manuscript by properly addressing all of the comments.
It seems that there is not much in situ data of air-sea heat fluxes for the Mediterranean Sea and the reanalysis products are used to examine heat budgets. Note that these products may have biases that are hard to know without comparing to observations. If there are some long-term moored observations available (e.g., similar to Sorinas et al., 2023), it would be better to use them to evaluate the reanalysis products. If not available for now, it would be good to call for such sustained ocean observations in the discussion.
Reference:
Sorinas, L., Weisberg, R.H., Liu, Y., Law, J. (2023), Ocean-atmosphere heat exchange seasonal cycle on the West Florida Shelf derived from long term moored data, Deep-Sea Research Part II, 212, https://doi.org/10.1016/j.dsr2.2023.105341
Citation: https://doi.org/10.5194/egusphere-2025-2867-EC1 -
AC1: 'Reply on EC1', Mahmud Hasan Ghani, 29 Sep 2025
Dear Editor,
Many thanks for your response and feedback. Yes, we are reviewing and preparing our revisions to the comments provided by the reviewers. Hopefully, I would able to upload our response soon here.
And, we have taken consideration your suggestion on the necessity of ocean observations and will add some texts in our discussion.
Citation: https://doi.org/10.5194/egusphere-2025-2867-AC1
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AC1: 'Reply on EC1', Mahmud Hasan Ghani, 29 Sep 2025
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- 1
Summary : The manuscript investigates several aspects of heat flux dynamics in the Mediterranean Sea. First the manuscript compares the long-term mean heat flux from two reanalysis products with different spatial resolutions (ERA5 and ECMWF) and the higher resolution reanalysis (ECMWF) is found to provide a heat flux consistent with the ‘closure hypothesis’. The authors attributed this difference to spatial resolution. Then the authors looks at the PDF of the turbulent heat fluxes and also look at the impact of extreme events on the heat budget. The authors find reasonable PDFs that capture the statistical patterns in the heat fluxes terms and that fall/winter cooling events are criteria to achieving the negative long-term mean of ECMWF that is consistent with the ‘closure’ hypothesis.
The work is interesting and will likely be of interest to a broad range of scientists. Couple of questions that I think should be address in some fashion.
Major comments
Seems like there's an issue with using the closure hypothesis as evidence for which result is 'correct' . Finding data/results that fit the expectation assumes the hypothesis is truth which seems a bit problematic to me. It seems like the authors should be framing the results differently
It's not clear that the spatial difference in the reanalysis products is the only potential cause of the difference. Could there be other possible causes? For example, could the cloud physics be the issue. Looking at Figure 1, the long wave and short wave radiation are the terms that look most different. Since SST is the same in both cases, the differences in long wave radiation could point to the cloud cover parameters, maybe? Is cloud representation done the same way in these two reanalysis products. It is not clear to me the only difference in this reanalysis products is the spatial resolution. Maybe I missed that though.
Why are the statistical distributions just the turbulent heat fluxes explored. Its fine, but it seems like the author should comment on why these are the target and why the distributions of the longwave and shortwave radiation are not explored.
With regard to the extreme events. I guess it should not be surprising that if you remove the most extreme negative values and then average the heat flux the mean will get warmer. However, potential feedbacks may not be accounted for that should be mentioned. For example, if the extreme heat flux events are removed but there impacts on SST is not, then the subsequent fluxes may be lower than should be if the extreme event in the heat flux never occurred. So the relative gain associated with the extreme event may not be as significant indicated by just removing the extreme heat flux. There maybe other potential feedbacks that the removal methodology does not full consider that should be mentioned.
Can more details or discussion be provided on why spatial resolution limits the ability of ERA5 to represent extreme heat loss in fall and winter?
Similarly related – Figure 7 shows the Qnet, but what is driving the extreme Qnet – typically I assume latent heat flux (and reduced shortwave) is the main driver of fall/winter cooling events but Figure 1 suggests that these are quite similar between ERA5 and ECMWF at least in terms of the mean… Is that the case in the extreme events?
Minor comments
Line 50-51 Awkward phasing
Line 83 ‘have shown large deviation’ - revise phrasing
Line 162 Was ρ (rho) defined?
Line 400 ‘ that this is the reason why…’
Line 404-405 I don’t really understand this sentence.
Line 453 ‘Differences appear…’ The main difference were in the long and short wave radiation. Figure 1 showed that latent and sensible heat fluxes were not that different.
Line 485-487 These sentence are confusing to me. I suggest revising them in some way.
Line 493 poor phrasing – this sentence should be revised.