| 05 Feb 2026
First global assessment of the Eddy-Diffusivity Mass-Flux (EDMF) parameterization for oceanic convection in NEMO: implications for global temperature and surface heat fluxes
Abstract. The Eddy-Diffusivity Mass-Flux (EDMF) parameterization provides a unified framework to represent both local (diffusive) and non-local (convective) vertical mixing in the ocean. While EDMF has been evaluated in idealized and regional configurations, its performance in global ocean models has not yet been assessed. We present the first global-scale evaluation of the EDMF scheme implemented in NEMO and compare it with the widely used Enhanced Vertical Diffusion (EVD) and Mixed Layer Penetration (MLP) parameterizations. Three global 1/4° simulations for 1999–2020 are analyzed, focusing on convective regimes, upper-ocean temperature and mixed-layer depth.
EDMF successfully reproduces both shallow diurnal convection in the tropics and deep wintertime convection in subpolar regions, with modelled plume timing, penetration depth and vertical velocities consistent with available observations. In the tropics, EDMF captures the observed penetrative cooling and depth variability of nocturnal cold plumes, in contrast to the instantaneous adjustment produced by EVD. In deep-convection regions such as the Labrador Sea, EDMF simulates realistic interannual variability in convective depth and intensity.
The improved representation of convective regimes leads to a ~30 % reduction in global upper-ocean (0–700 m) temperature biases in EDMF compared to EVD-based simulations. Changes in latent heat loss, driven by SST differences, dominate the associated changes in net surface heat flux between EDMF and EVD simulations, corresponding to ~6.5 % of the global average net climatological surface heat balance.
These findings demonstrate that EDMF provides a more physically consistent representation of oceanic convection and offers an alternative to traditional and empirical EVD- and MLP- based approaches.
Review of "First global assessment of the Eddy-Diffusivity Mass-Flux (EDMF) parameterization for oceanic convection in NEMO: implications for global temperature and surface heat fluxes" by Piton et al.
Major issues:
A) It is tacitly assumed that open water deep convection by the parameterization is what is needed to more accurately simulate the Labrador Sea and other deep convection sites. However, there is substantial observational and theoretical evidence that convection influenced by lateral boundaries is more important for the overturning mass flux (e.g., https://doi.org/10.1175/2011JCLI4130.1, https://doi.org/10.1175/JPO-D-24-0019.1).
B) I think you may be missing a major source of convection in under-resolved "Ekman buoyancy flux" that is known to induce strong submesoscale convection (https://doi.org/10.1175/JPO2737.1). This can be included into convective parameterizations straightforwardly (http://dx.doi.org/10.1016/j.ocemod.2016.12.003). This lateral transport can overwhelm the surface buoyancy fluxes in the presence of strong fronts (e.g., https://doi.org/10.1016/j.dsr2.2013.02.025).
C) Figures 2&3 lack a "control case". Outside of the EDMF parameterization, it is not clear how to interpret the w_p. I suggest comparing the vertical diffusive, total, and convective heat fluxes in the time window shown in Fig. 2 to the vertical total heat fluxes in the EVD simulation at the same location and time. I guess the point is that the MF parameterization will go deeper than the ED flux, but what fraction of the total is it, and is it deeper than in the EVD simulation? In examining KPP variants, we often find that the "deeper" schemes end up being similar to the "shallower" versions under the same surface forcing--it is quite hard to do this comparison fairly (see http://dx.doi.org/10.1175/JPO-D-22-0107.1 and http://dx.doi.org/10.1029/2019MS001810), especially so in a GCM with feedbacks present. Figure 9 does this comparison more effectively than the earlier figures.
D) Introduction: A paragraph on the dangers of over-interpreting bias reduction in global models as evidence for improved parameterization physics should be added. The key point is that because of compensating errors in global models, it is often the case that improved physics initially leads to increased bias rather than a reduction. In this case, because of past work on idealized models, care is taken to avoid overinterpretation by comparison to the conclusions drawn in those more controlled settings. Discussion of Figures 5 & 7 should also mention this context, because it is likely that if other parameterizations (e.g., GM) were retuned after implementation of the EDMF scheme, the bias and RMSD reduction might be greater than shown there. Also, you should revise the sentence "Overall, this first global-scale validation demonstrates that EDMF provides a more coherent and physically
consistent representation of oceanic convection." correspondingly, as this GCM-bias reduction study does not show coherence nor physically consistent representation, it shows the impacts of those physical principles that are established in the process papers leading up to this one.
E) I'm confused by how large the JJASO bias in the global MLD is for the EDMF scheme vs de Boyer-Montegut, as it seems smaller than that in all of the 3 regions. In the global comparison only, the TKE+EVD seems to be closer to observations during JAS, while in all of the three regional panels the EDMF is closer. Also, you are showing the deB-M and Holte MLDs as though both are comparable to the model, but doesn't NEMO use the deB-M definition of MLD as suggested in Treguier et al. (2023; http://dx.doi.org/10.5194/gmd-16-3849-2023)?
Minor issues:
L67: Please clarify if these are vertical or horizontal length scales intended, and whether the relevant phenomena are expected to be approximately isotropic or not.
L75: It is a bit peculiar to cite the Large et al. 1994 paper for only the diffusive part of the transport, as the majority of the discussion in that paper is about the nondiffusive part of the KPP scheme. The distinctions between the KPP non-diffusive/convective parameterization and the EDMF approach taken here should be delineated nearby.
L93: author's -> authors' (there is more than one author here)
L120: are any submesoscale parameterizations used? Are any other parameterizations known to impact ML properties (e.g., penetrating radiation, low cloud physics, etc.) used? These should be laid out.
L140: Please clarify which of these papers is the relevant first source for the MLP parameterization by adding the reference to the sentence ending on L133.
L166: Why are you using rho for pressure and for density? That is really confusing. Please use p_h for hydrostatic pressure if that symbol is correctly defined in the text.
Eq (2) and subsequent. I am very confused by the dimensions of the properties in this equation and the related notation. Cursive L (suggesting a length) is an inverse length scale while epsilon and delta are described as entrainment "rates" when indeed they are also inverse length scales, as the beta parameters are dimensionless. Please clarify that all of these are the vertical decay scale for the exponential functions, which may increase area (if entrainment plus slowing dominates) or decrease area (in the case of dominant detrainment). The slowing rate (cursive L) is meant to capture the cross-sectional momentum adjustment of the plume as it widens in the absence of entrainment or detrainment.
L200: this comment about T_p vs. T at the second half time step makes it quite confusing what the implied flux of heat, salt and freshwater are in this scheme. Please clarify how these are set at the surface for both the diffusive and mass flux portions of the scheme so as to ensure conservation.
Figure 10 caption should mention that the sign convention for the Delta metrics is given in Equation (12). Also, Panels a&b should have 2 y-axis labels, one in temperature units for Delta T and one in W/m^2 for SURF. I have no idea what W/m^2 numbers are given the normalization of the tables and the lack of this second vertical axis label. Ideally, SURF in c & d should be given in both temperature and W/m^2 units.