Learn Finnish: Viljelijän on tarkoitus kylvää ohra aikaisin keväällä. - The farmer intends to sow the barley early in the spring.

This sentence uses the structure [Genitive subject] + on tarkoitus + [1st infinitive], which expresses intention. Just like necessity structures (such as minun täytyy), the "doer" of the action is put into the genitive case. So, viljelijä becomes viljelijän.

Why is the object ohra in the basic nominative form instead of the genitive-looking accusative (ohran)?

When a sentence has a genitive subject and expresses necessity or intention (like with on tarkoitus), a total object drops its normal -n ending and looks exactly like the nominative. Since the farmer intends to sow all the relevant barley, it's a total object, making it ohra instead of ohran.

How would the meaning change if the sentence used on määrä instead of on tarkoitus?

While both express a scheduled plan, on tarkoitus focuses on the subject's own intention or purpose ("The farmer intends to"). If you used on määrä, it would sound more like an external schedule or expectation ("The farmer is scheduled to" or "The farmer is supposed to").

Look at the time expression aikaisin keväällä. Why don't the words match in case?