**4. Discussion**

In this paper, the author combines components of a Lagrangian basin-scale ocean model with the dynamical core of a global Lagrangian atmospheric model to create a new global Lagrangian ocean model (GLOM). Rather than numerically solving partial differential equations that describe fluid flow, this model predicts the motions of individual fluid parcels using ordinary differential equations and classical physics. The GLOM has variable bottom topography and spherical geometry, so it can be used to simulate general circulations of the global ocean. It also has a unique convective parameterization, in which the vertical positions of parcels are sorted by density to remove convective instability.

When forced with idealized surface temperature restoring and wind stress, the GLOM generates much of the circulation structure seen in nature in the global oceans, including mid-latitude gyres with western boundary currents, shallow wind-driven cells at low latitudes, a deep overturning in the Atlantic Ocean, and an Antarctic Circumpolar Current. The GLOM also produces thermocline structure and water mass distributions that are similar to those seen in nature. When interior mixing is removed, the large-scale ocean circulation, stratification, and water mass distributions are similar, with the main difference being that circulations, thermocline structure and upper-level water masses are slightly shallower. These results support the primary conclusion of [15] (and earlier papers such as [34,35]) that the leading-order solution for ocean stratification and circulation can be reproduced without interior tracer mixing, and that including tracer diffusivity creates first-order perturbations.

The work presented here and in previous Lagrangian modeling studies supports the idea that the Lagrangian approach would complement existing numerical methods used to study climate dynamics and climate change. This paper highlights several unique features of the GLOM: (1) the ability to conduct simulations with zero tracer diffusivity; (2) the unique convective parameterization which restacks parcels in convectively unstable regions, and (3) ease in tracking every mass element in the ocean and determining locations where water masses form. For these reasons, the author is continuing to refine and improve the GLOM, and he will soon be coupling it to a Lagrangian atmospheric model for coupled ocean–atmosphere climate dynamics experiments.

Of course, the GLOM has a number of disadvantages as well, so it would not be well suited for every climate application. For example, the model, as it is currently configured, uses a high degree of gravity wave retardartion (GWR) [29] which amounts to assuming that there is a layer of fluid above the ocean with a density slightly lower than that of salt water, and which slows externing gravity waves, allowing the model to have a large time step. The main side effect of GWR is that it greatly enhances the amplitude of free surface perturbations, which would be a problem for modeling circulations in shallow estuaries, for example. A second drawback to the Lagrangian approach used here is that there is a potential energy barrier to starting circulations in a pile of parcels [25], so it could have problems simulating weakly forced circulations.

The simulations presented in this paper are also limited in the sense that they use very large water parcels, with horizontal scales of a few degrees, and vertical scales on the order of 100 m. Owing to the lack of numerical tracer diffusion in the model, the equivalent resolution in an Eulerian ocean model is probably somewhat finer. For example, Haertel et al. [25] found that circulations and stratification in a 3-degree basin-scale Lagrangian ocean model compared favorably to those in a 1-degree z-coordinate model that was exposed to the same surface forcing. However, this resolution is still very coarse, and it represents the low end of expected climate applications (i.e., for millennial time-scale, single-processor, global simulations). Fortunately, there is reason to believe that the GLOM will have the capacity to be run at much finer resolution once it is coded in parallel. For example, Haertel et al. [24] found nearly linear scaling in a predecessor to the GLOM, which had similar computational costs to a sigma-coordinate ocean model for simulating circulations in a large lake. Moreover, it is encouraging that even at the very coarse resolution used in this paper, the GLOM was able to reproduce the gross circulation patterns and stratification seen in the world ocean, with the Lagrangian convective parameterization and random parcel motions apparently adequately representing buoyancy driven convective circulations and mesoscale eddy transports that occur at much smaller scales in nature.

Considering that the GLOM is in a relatively early stage of development when compared with other climate modeling tools, it is too early to fully understand its advantages and disadvantages at this time. Moreover, there are probably many other potential applications for the GLOM and its fully Lagrangian atmospheric counterpart that will take years to explore. For example, the recent study of Paparella and Popolizio [36] suggests that Lagrangian models will have advantages for simulating the mixing of biogeochemical tracers. However, one thing is clear already—Lagrangian models, as well as the physical parameterizations that go along with them, are fundamentally different from Eulerian models and methods, and they make a significant contribution to the diversity of climate modeling tools.

**Funding:** This research was supported by NSF gran<sup>t</sup> AGS-1561066.

**Conflicts of Interest:** The author declares no conflict of interest.
