I have lived in the land of Israel for at least half of the year over the last decade.
The word "over" in this sentence means Through the period or duration of: records maintained over two years. and NOT More than in degree, quantity, or extent: over a thousand dollars.
The definite article in front of "year" is the first clue that tells us the author meant that for the last decade they have spent at least six months (maybe more) of each year in Israel. If the author had written "at least half a year" we might think they meant six months over the last decade instead of six months every year. I interpret "half the year" as half of each year of the last decade. I would interpret "half a year" as six months and it would be less clear whether they meant each year of the decade or just six months total.
The second clue is "at least" and the use of "over" the last decade. The context tells us that the author is trying to impress us with how much time they have spent in Israel. Six months in ten years doesn't seem like a lot of time. At least 6 months (maybe more) every year for the last decade seems like much more time. Someone who visited a place every year for 6 months would probably know a lot about it. If they had lived in Israel six months in the past ten years, they might have written "only half a year in the last decade".
A more idiomatic way to express the same thing:
I have lived in Israel at least six months of every year for the last decade.