As far as velocity measurements are concerned, we may anticipate progress in the near future on the question of the depth of supergranulation thanks to local helioseismology applied to higher-resolution observations. However, characterising vertical flows at the supergranulation scale is a more complex task since such flows are faint and very localised in space. Improving the diagnostics of the latitudinal dependence of the supergranulation pattern may also prove useful, in particular to help understand if subsurface shear plays a significant role in shaping the supergranulation flow.
Another point worth studying in more detail is the distribution of kinetic energy at scales between supergranulation and the Sun’s radius. This has already been attempted using supergranules as passive tracers of larger-scale velocity patterns (Švanda et al., 2006, 2008). Even more accurate studies of this kind could become feasible soon by using tracking techniques applied to images obtained with wide-field cameras imaging the full solar disc with sub-granulation resolution.
The case of the interactions with magnetic fields deserves a lot of further attention on the observational side in our view. It is now well established that flows at scales larger than granulation advect internetwork fields and tend to concentrate magnetic elements into the network, along the boundaries of supergranules. This process is essentially kinematic, in the sense that the magnetic field only has a very weak feedback on the flow. But what we observe ultimately is probably a nonlinear statistically steady magnetised state, in which the magnetic field provides significant feedback on the flow. Hence, it would be useful to have more quantitative observational results on the relations between the properties of supergranules and the surrounding magnetic fields (internal and boundary flux, filling factors, strength, size) to characterise this feedback more precisely (we refer the reader to Section 8 for an exhaustive discussion on supergranulation and MHD). Most importantly, a precise determination of the magnetic energy spectrum of the quiet Sun over a very wide range of scales would be extremely precious to understand the nature of MHD interactions between supergranulation, network and internetwork fields. Finally, it would also be interesting to have more documented observational examples of the interactions of supergranulation with magnetic regions of various strengths (active regions, polar regions) to gain some insight into the dynamical processes at work in the problem. This latter point is important from the perspective of the global solar dynamo problem, as it would help better constrain the transport of magnetic field by turbulent diffusion at the surface of the Sun.
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