I've ROMS model data of ocean surface current, which has a very High resolution. But still, near the coasts of a partially isolated island I don't have data(for context see the image below).
If I want data somewhat more into near to the land, then what method should be approached.
If my assumption is correct, that the subtitle of your question is: which method of interpolation is most appropriate to deduce the missing values, then there are some considerations to mention.
The mask that I see in your figure has a resolution of about 8 km. I cannot tell whether this is the resolution of the velocity field itself or the resolution of the shoreline/landmask. I would argue that an 8 km resolution is relatively coarse for coastal applications, and even if your velocity field is of higher resolution, I have serious doubts on whether an interpolation method could reproduce a field which is realistic close to the shoreline, in a physical sense.
ROMS has a minimum depth input, which in combination with the landmask, the bathymetry, the horizontal resolution and the vertical discretization among others, plays a crucial role in the hydrodynamics close to the shoreline, and is closely related to the general fields that you get.
If you didn't run the model with a higher resolution landmask, or in other words, if the model is not covering areas as close to the shoreline as you would want to, I suggest that it is not correct in a physical sense to deduce these values offline and you should rerun the model using a higher resolution landmask or use it to force an other model with a smaller grid.
Unless you just want to fill the gaps for illustration purposes, in which case either a bilinear or cubic interpolation would work fine.
Stamatios Petalas Thanks for the detailed response. I understand that the approach to fill the gaps just for the sake of it would be misleading. I was curious if this could be achieved without reruning model, but your answer made it much clear.