Integrating 2D data with nans using numpy trapz

Question

I have a 2D matrix U of data that looks something like this:

0   0.5   0.1   0.3 
0   nan   0.4   0.1
nan nan   0.2   nan

The rows index corresponds to height axis data points zz = [0, 2, 10] and the columns are the horizontal axis data points yy = [0, 3, 7, 9] (not fixed intervals). I want to integrate this matrix U over the zz and yy axes. In order to do that I thought about using numpy trapz in the following way:

Uy = np.zeros(len(yy))

for y in range(len(yy)):
        U_step = U[:,y][~np.isnan(U[:,y])]
        x = zz[0:len(U_step)]
        Uy[y] = np.trapz(U_step, x=x)

I = np.trapz(Uy, x=yy)

However, the result I get is not similar to what I expect (value is too low), so I wonder if there is something wrong with the way I integrate, or maybe I should use other functions?