Unable to achieve an Earth-like tsurf gradient using SOCRATES and and frierson_solar_rad = True

[DavidM-source]

Description

Hello! I'm currently working on creating an aseasonal Earth-like aquaplanet for a project. But, I seem to running into some issues. Assuming the default values of del_sol = 1.4 and del_sw = 0.0, I'm unable to obtain realistic tropical and polar temperatures when imposing an annual-mean insolation profile to the simulation. I have tried varying the del_sol parameter, but it just results in temperatures being too warm or too cold for both regions. Additionally, the surface temperature gradient, particularly in the tropics, appear to be too sharp with the default del_sol value that I mentioned previously. Using the SOCRATES radiation module and an annual-mean insolation profile, Is there any way to achieve (1) realistic tropical and polar temperatures and (2) a realistic surface temperature gradient for an aseasonal Earth-like aquaplanet? A script is provided below. I also added an zonal-mean plot of surface tempertaure (with varying del_sol) for context.

Screenshots

Minimal reproducible example

soc_earth_like_aquaplanet.txt