Question: Is the beracha on rain said in Israel when rain comes after a drought?
Does the berach on rain have an introduction containing shem and malchus, as a beracha usually does unless it preceded by another beracha.
If it is not introduced by shem and malchus is it really a beracha just because it has the concluding phrase of a beracha?
(a) The Halachah is that the Berachah is recited in Israel when rain comes after a drought, as the SHULCHAN ARUCH (OC 221:1-2) rules.
(In fact, the MISHNAH BERURAH there wants to rule that since Israel is always suffering from drought, every year when it rains for the first time in the rain season, we should say this blessing. However, the PRI MEGADIM argues, and the ELIYAH RABAH is in doubt, and therefore the Mishnah Berurah (in BI'UR HALACHAH) concludes that one who wants to recite the blessing on the first rains of every year should not say Shem u'Malchus.)
In practice, though, many people recite the blessing without Shem u'Malchus on rains that fall after a drought, presumably because the amount of rain that needs to fall is not clear.
(b) No, the Berachah does not have an introduction containing Shem u'Malchus. This problem is addressed by TOSFOS in Berachos (46a, DH ul'Man d'Amar), who explains that a Berachah of Hoda'ah, a Berachah of praise to Hash-m (as opposed to Birchas ha'Nehenin or Birchas ha'Mitzvos), does not need to open with the text of a Berachah with Shem u'Malchus.
(Another explanation could be based on the Rishonim who explain that a Berachah which, in its normal place, is Samuch l'Chavertah and thus is considered to open with the text of a Berachah, may be recited without its opening Berachah in another context. For example, since the normal place of the Berachah of Shome'a Tefilah is in the Shemoneh Esreh, where it is preceded by another Berachah, one may say the Berachah of Tefilas ha'Derech (which opens with no Berachah and concludes with Shome'a Tefilah) without reciting a Berachah before it. Similarly, the Berachah of "Modim Anachnu Lach" is normally recited by someone who owns a field, who first says the Berachah of "Ha'Tov v'Ha'Meitiv" or "She'he'cheyanu," and then he recites "Modim," and that "Modim" is preceded by the first Berachah. Therefore, one may say "Modim" out of its "normal" place, even when there is no Berachah preceding it.)
(c) Yes, as long as it has the Shem u'Malchus somewhere in the Berachah, it counts as a Berachah.
The Shem is obviously there. But where is Malchus? The word Melech does not appear. Is it implicit in the Shem?
(a) The word "Malkeinu" appears in the Berachah (granted, not in the Chasimah itself, but right before the Chasimah). We find that, according to some Rishonim, appearances of Malchus, even when not in the actual Chasimah (or Pesichah), still count as the necessary Malchus, as the Beis Yosef, citing from the Rosh and Tosfos, mentions in OC 214.
(b) It is interesting to note, though, that the RAN (Ta'anis 2a, DH Amar Rav Papa) says that the end of the Berachah should indeed include the word "Melech" ("Baruch... Melech Rov ha'Hoda'os") for this reason.
(c) The RA'AVAD (on the Ba'al ha'Me'or in Maseches Berachos), as quoted by the TUR (OC 218), maintains that a Birchas Hoda'ah does not require Malchus like other types of Berachos do. Although all of the Rishonim argue with the Ra'avad, the PERISHAH there (218:4) writes that, "[The opinion of the Ra'avad] is the source for the common practice that in a number of Berachos, we do not say Malchus."
(The MISHNAH BERURAH (214:1) says that the Halachah that a Berachah without Shem u'Malchus is not a Berachah applies to "both Birchos ha'Mitzvos and Birchos ha'Nehenin." He leaves out Birchos ha'Hoda'os, though, and it may be that he means to imply, like the Perishah, that Birchos ha'Hoda'os (such as the Berachah for rain in Eretz Yisrael) do not need Malchus.)