import numpy as np
import xarray as xr

def f1(x, y, z):
    return 2*x+3*y+4*z

def f2(x, y, z):
    return x/2+y/3+z/4

TestArray=xr.Dataset({'f1Res':(['xCoord', 'yCoord', 'zcoord'], f1(*np.meshgrid(x, y, z))),
            'f2Res':(['xCoord', 'yCoord', 'zCoord'], f2(*np.meshgrid(x, y, z)))},
                  coords={'xCoord':x, 'yCoord':y, 'zCood':z})

TestArray