The Mishnah describes the circumstance of rain during Sukkos as if the servant came to mix the master's cup of wine, but the master rejected the wine and threw the cup back in the servant's face. The Vilna Gaon explained the comparison. The Days of Awe are times of strict judgment. Sukkos, however, is a merciful time that softens the severity of Rosh Hashanah and Yom Kippur.

If it rains during the festival of Sukkos, it is an indication that Hashem does not want to soften the judgment. This is an unfortunate sign. It is similar to the servant who cannot mix the cup; wine is strong, the mixing of the cup indicates the diluting of its potency. The servant who cannot mix the cup runs the risk of facing a harsh year....

We had a heavy rain this week in NYC but the Big Apple is always on the road to hell anyway.

But Shemini Atzeret isn't just about rain, although no one is sure what it is about besides hanging out one last time before packing up our booths and going home.

Rashi seems to indicate that there is no real reason for Shemini Atzeret. Rather, God says, as it were: “Please remain with Me just one more day, for your departure is difficult for Me to endure.” The Ramban suggests that the eighth day of Sukkot alludes to the idea that the Jewish people are the partner to the seventh day – Shabbat – and thus it is observed as a holiday.

. . . . Targum Yonatan Ben Uziel in Parashat Pinchas explains the significance of Shmini Atzeret as follows: “On the eighth day you shall gather in joy as you leave your sukka and return to your home.” There is certainly much joy when we enter the sukka and bask in the presence of the Shechina, but why should leaving the sukka be cause for celebration? Rav Ferrer explains that the sukkah represents God’s protection as we wandered in the desert for forty years; by living in a temporary dwelling, we reaffirm the fact that God always protects His nation. When were we able to leave the sukka, to build our permanent homes and lives? That occurred when we arrived in Eretz Israel.

This lengthy holy season (which really began with the 17th of Tammuz) gradually conditions us to let go of our preconceptions about ourselves, and exist in the state of uncertainty when one has rejected old patterns of behavior but not yet integrated the new ones. During this liminal time our emotions naturally swing from optimism to despair. During Sukkot we live in the wilderness, learning that even without permanence and control we can be happy. Shemini Atzeret is a gradual reintroduction to the concrete world in which our new behaviors are exercised, never as perfectly as they existed in our imaginiations.

The traditional Ashkenaz Geshem is at the end of this post.
The Sephardi Geshem.

Like the High Holy Day piyyut Hu ya'aneynu, Geshem has been influenced by feminism; now there are versions invoking the matriarchs as well. Here's a beautiful one by the same rabbi who adapted the piyyut Hu ya'aneynu, which I linked to during Ellul.