Define time dependent variable in a netcdf file using python

I'll explain a bit my situation: I am trying to edit some variables of a netcdf file and write out a new netcdf file that shows me the new edited variables. My problem is that variables are time-dependent and I don't know how to include this in my code:

import netCDF4
import numpy as np

 ncfile = netCDF4.Dataset('toread.nc', 'r')
 u = ncfile.variables['u'][:,:,:]
 v = ncfile.variables['v'][:,:,:]

 nx = np.shape(u)[0] - 1 
 ny = np.shape(v)[1] - 1 
 nz = np.shape(u)[2] 

 u_center = 0.5 * (u[0:nx,:,:] + u[1:nx+1,:,:]) 
 v_center = 0.5 * (v[:,0:ny,:] + v[:,1:ny+1,:])


 ncfile_out = netCDF4.Dataset('./output.nc', 'w')
 ncfile_out.createDimension('longitude', nx)
 ncfile_out.createDimension('latitude', ny)
 ncfile_out.createDimension('level', nz)
 u_out = ncfile_out.createVariable('u_center', 'f4', ('longitude', 'latitude', 'level'))
 v_out = ncfile_out.createVariable('v_center', 'f4', ('longitude', 'latitude', 'level'))
 u_out[:,:,:] = u_center[:,:,:]
 v_out[:,:,:] = v_center[:,:,:]
 ncfile_out.close()

I tried to compile this but it showed a Value Error talking about a dimension problem. I think my variables are 4D including time-dependence but I don't know how to define it and finish my code.

ncdump info:

   netcdf state.global {
dimensions:
    T = UNLIMITED ; // (10001 currently)
    Xp1 = 61 ;
    Y = 1 ;
    Z = 20 ;
    X = 60 ;
    Yp1 = 2 ;
    Zl = 20 ;
variables:
    double Xp1(Xp1) ;
        Xp1:long_name = "X-Coordinate of cell corner" ;
        Xp1:units = "meters" ;
    double Y(Y) ;
        Y:long_name = "Y-Coordinate of cell center" ;
        Y:units = "meters" ;
    double Z(Z) ;
        Z:long_name = "vertical coordinate of cell center" ;
        Z:units = "meters" ;
        Z:positive = "up" ;
    double X(X) ;
        X:long_name = "X-coordinate of cell center" ;
        X:units = "meters" ;
    double Yp1(Yp1) ;
        Yp1:long_name = "Y-Coordinate of cell corner" ;
        Yp1:units = "meters" ;
    double Zl(Zl) ;
        Zl:long_name = "vertical coordinate of upper cell interface" ;
        Zl:units = "meters" ;
        Zl:positive = "up" ;
    double T(T) ;
        T:long_name = "model_time" ;
        T:units = "s" ;
    int iter(T) ;
        iter:long_name = "iteration_count" ;
    double U(T, Z, Y, Xp1) ;
        U:units = "m/s" ;
        U:coordinates = "XU YU RC iter" ;
    double V(T, Z, Yp1, X) ;
        V:units = "m/s" ;
        V:coordinates = "XV YV RC iter" ;
    double Temp(T, Z, Y, X) ;
        Temp:units = "degC" ;
        Temp:long_name = "potential_temperature" ;
        Temp:coordinates = "XC YC RC iter" ;
    double S(T, Z, Y, X) ;
        S:long_name = "salinity" ;
        S:coordinates = "XC YC RC iter" ;
    double Eta(T, Y, X) ;
        Eta:long_name = "free-surface_r-anomaly" ;
        Eta:units = "m" ;
        Eta:coordinates = "XC YC iter" ;
    double W(T, Zl, Y, X) ;
        W:units = "m/s" ;
        W:coordinates = "XC YC RC iter" ;

// global attributes:
        :MITgcm_version = "****************" ;
        :build_user = "************" ;
        :build_host = "**************" ;
        :build_date = "*******************" ;
        :MITgcm_URL = "***************" ;
        :MITgcm_tag_id = "*******************" ;
        :MITgcm_mnc_ver = 0.9 ;
        :sNx = 30 ;
        :sNy = 1 ;
        :OLx = 2 ;
        :OLy = 2 ;
        :nSx = 2 ;
        :nSy = 1 ;
        :nPx = 1 ;
        :nPy = 1 ;
        :Nx = 60 ;
        :Ny = 1 ;
        :Nr = 20 ;
}