插值

If you regrid your data to a coarser lat/lon grid using e.g. bilinear interpolation, this will result in a smoother field.

The NCAR ClimateData guide has a nice introduction to regridding (general, not Python-specific).

The most powerful implementation of regridding routines available for Python is, to my knowledge, the Earth System Modeling Framework (ESMF) Python interface (ESMPy). If this is a bit too involved for your application, you should look into

1. EarthPy tutorials on regridding (e.g. using Pyresample, cKDTree, or Basemap).
2. Turning your data into an Iris cube and using Iris' regridding functions.

Perhaps start by looking at the EarthPy regridding tutorial using Basemap, since you are using it already.

The way to do this in your example would be

from mpl_toolkits import basemap
from netCDF4 import Dataset

filename = '/Users/Nick/Desktop/SST/SST.nc'
with Dataset(filename, mode='r') as fh:
   lons = fh.variables['LON'][:]
   lats = fh.variables['LAT'][:]
   sst = fh.variables['SST'][:].squeeze()

lons_sub, lats_sub = np.meshgrid(lons[::4], lats[::4])

sst_coarse = basemap.interp(sst, lons, lats, lons_sub, lats_sub, order=1)

This performs bilinear interpolation (order=1) on your SST data onto a sub-sampled grid (every fourth point). Your plot will look more coarse-grained afterwards. If you do not like that, interpolate back onto the original grid with e.g.

sst_smooth = basemap.interp(sst_coarse, lons_sub[0,:], lats_sub[:,0], *np.meshgrid(lons, lats), order=1)

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Cube interpolation and regridding

cressman 第三章插值方法比较
参考
胡金义. 基于ArcGIS的Cressman插值算法研究[A]. 中国水利学会.中国水利学会2010学术年会论文集（上册）[C].中国水利学会:中国水利学会,2010:8.