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The Biur Halacha (229:1) writes
הרואה הקשת וכו' - לא נתבאר אם בעינן דוקא שיראהו בתמונת קשת דהוא כחצי גורן עגולה או אפילו מקצת ממנו די - It's not explained whether you need to specifically see the full half-circle [of a rainbow] or a part of it is sufficient.
Do Poskim allow one to make a beracha on seeing a portion of a rainbow but a significant percentage of it is blocked by trees or houses, or do we say safek berachos l'hakel?
In my personal experience, I have seen that the common practice is to recite the blessing over any visible rainbow in the sky.
In the additions to Peninei Halacha (Berachot 15:10), Rabbi Ma'or Kayam supports this view by citing a number of contemporary authorities who are lenient (in some regard) for one to recite the blessing even if they cannot see the entire semicircle, including:
Rabbi Kayam himself agrees with the lenient view, and supports his conclusion by noting that even a partial rainbow causes memory of the covenant, which is what the blessing is about.
From Halachapedia:
Some say that one must see the entire rainbow in order to make the bracha.[4] Others, however, hold that there is what to rely on if one makes the bracha upon seeing a part of the rainbow.[5]
Sources [4] Teshuvot Vehanhagot 3:76 concludes that therefore, one may not make the blessing on anything less than a full semicircle rainbow. Vezot HaBracha (pg 156, chapter 17) writes that Rav Elyashiv rules that if one saw the entire semicircle one can make the Bracha even if it’s missing a piece.
Sources [5] Chazon Ovadia (Brachot p. 473), Halacha Brurah 229:2, Birkat Hashem (v. 4, 4:35)
