If the authorities calculate zakaah as less than it should be

It is proven that the Prophet (peace and blessings of
Allaah be upon him) said concerning zakaah on produce of the earth: “For
that which is watered by the sky or a spring, or by its roots, (the rate of
zakaah) is one-tenth, and for that which is watered by a camel, (the rate of
zakaah) is half of one-tenth.”  

The Muslim must give this amount of zakaah on that which is
produced by the earth, if it reached the nisaab (minimum threshold). 

If it so happens that those who are in charge of zakaah –
namely the committee that estimates the crops and takes zakaah from them –
underestimated it, then the owner must give zakaah on the additional amount
of crops, whether this extra amount reaches the nisaab or not. That is
because the Prophet (peace and blessings of Allaah be upon him)
enjoined a specific share as stated above, one tenth or half of one tenth,
so this must be paid. 

Majmoo’ Fataawa Ibn ‘Uthaymeen
(18/64). 

And Allaah knows best.