I believe that scale-aware cumulus parameterisations to be used at such high-resolutions are an active area of research, although my knowledge on them is limited.

What I can comment on is on the use of explicit convection at those scales. There are a number of papers that use explicit convection at reasonably coarse resolutions (up to 12km), and while they have issues of their own, they solve a number of problems that are common for parameterisations, in particular they have a much better diurnal cycle, and a better distribution of rainfall, as they can reproduce mesoscale propagating systems, as opposed to parameterisations of convection which tend to produce drizzle everywhere.

A couple of examples:

http://onlinelibrary.wiley.com/doi/10.1002/grl.50347/abstract

http://dx.doi.org/10.1002/2013JD020887

These two papers analyze continental-scale runs over west africa at 4 and 12km resolution with explicit convection, and 12 and 40 with parameterised convection.

http://journals.ametsoc.org/doi/abs/10.1175/2009jcli2890.1

This paper shows model results for a global run at 7km resolution (with explicit convection), also showing the improvements in the diurnal cycle.

Ultimately, it probably depends on what you want to look at. I'm currently working on investigating differences between parameterised and explicit convection at these resolutions, so let me know if you want to discuss this more!

Thanks Luis for your valuable comments! I'll take a look at the suggested papers.

One more question, for the simulation on tropical cyclones where small scale (eg., ~1km) convection systems usually exists, do you have any experience or suggestion on "explicit" convection at 3km resolution or higher. If so, how does the convection trigger work in the "explicit" simulation?

A recent research was performed by Ridick Roland TAKONG on the use of CP schemes in squall line simulation, which supports the CP implementation on grid scale greater than 0.25km.

https://www.researchgate.net/publication/262972646_Improving_the_Kain-Fritsch_convection_scheme_in_simulating_a_squall_line_sensitivity_to_convective_time_scale?pli=1&loginT=8B18DFXJqgVff7QnOI3RZzw_t3N9LEDM-vhmuKRUOdI*&uid=54e63efc-2d57-496a-9518-eaaf5cad4fd9&cp=re243_x_p11&ch=reg

Thesis Improving the Kain-Fritsch convection scheme in simulating a...