Interpolate in 1D a 3D masked array in python

Question

I need a faster solution to interpolate a 3D array in one dimension to a 2D surface. My data is gridded (k, j, i): the horizontal grid is regular (j, i), but the vertical grid is not (i.e depth points are different at each i, j point). Additionally, my array has a 2D horizontal mask. My current solution is:

from scipy.interpolate import interp1d

def interpz(depths, var, z_levs):
    var_z = np.zeros_like(var[0,:,:])
    for j in range(var_z.shape[0]):
        for i in range(var_z.shape[1]):
            if var_z.mask[j,i]==False:
                f = interp1d(depths[:,j,i], var[:,j,i])
                var_z[j,i] =  f(z_levs[j,i])   
    return var_z

It works, but it's too slow (my horizontal grid is about 200x600, and the number of interpolations reduces quite a lot with the mask but it still takes about one hour).

I've looked into griddata, but there is one issue, and one problem: the issue, it uses all the values to interpolate the point, when I actually only require 1D interpolation in the z direction (which, whatever), BUT the problem is that apparently, it doesn't like nans (in fact. not actual NaNs, but masked values):

z, y, x = depths.flatten(), y.flatten(), x.flatten()
data =  var.flatten()
var_z = griddata((z, y, x), data, (z_levs.flatten(), y[0,:,:].flatten(), 
...: x[0].flatten()), method='linear')

I get:

in griddata(points, values, xi, method, fill_value, rescale)
    215     elif method == 'linear':
    216         ip = LinearNDInterpolator(points, values, fill_value=fill_value,
--> 217                                   rescale=rescale)
    218         return ip(xi)
    219     elif method == 'cubic' and ndim == 2:

scipy/interpolate/interpnd.pyx in scipy.interpolate.interpnd.LinearNDInterpolator.__init__ (scipy/interpolate/interpnd.c:5530)()

scipy/spatial/qhull.pyx in scipy.spatial.qhull.Delaunay.__init__ (scipy/spatial/qhull.c:18174)()

scipy/spatial/qhull.pyx in scipy.spatial.qhull._Qhull.__init__ (scipy/spatial/qhull.c:4788)()

ValueError: Points cannot contain NaN

Suggestions are deeply appreciated