I am specifically looking for a article talk about maize. because we are working on a MS that try to show that water productivity is changing along the season.
The attached paper is the one you are possibly looking for. It is on maize and one of the main issues discussed on it is that WP varies during the growing season of maize. See Fig. 2 and page 446 (last paragraph at the right hand) of the paper about the results on WP variation during the growing season.
In addition look at page 430 of the file (426.pdf) last paragraph at the left hand side that argues about WP variation during the growing season. Probably you may find more in the literature.
Zhenjiang, If you are also interested in articles on other crops (rice) for water productivity. There is this one which talks about seasonal variations in water productivity for rice.
Article Atmospheric CO2 concentration effects on rice water use and ...