A possible way, I have tested, could be :
The green part is a network done using a part of a semi-circle.
You do a profile, here in magenta.
This profile is extruded to have a surface. here the orange surface.
The blue part is a blending between the edges of green surface and the orange surface.
Next the orange surface could be hide or delete.
The green part and blue one could be mirrored.
A first way to be near the result you want.
If you tune this method perhaps you will have the result you want.
This test is only a test... The curves are not perfect of course but the idea is here.

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