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.