Rain falls on an almanac, a book people use to predict the weather and the seasons, and the speaker reads this as "a doubtful sign." There's a quiet irony in it: the book meant to forecast the future gets soaked by the very weather it tries to foresee, and its certainty runs.
That wetness turns into "wet ink," which the speaker sees as a "rain-drawn dog." The smeared marks seem to take an animal shape. The title suggests the black dog often used as an image for depression, though the poem never says so outright. Instead, the last lines have the dog refuse to "answer / to the name melancholy." It won't be labeled.
The mood is hushed, wry, and a little uneasy. The speaker seems to feel a low, shapeless sadness, and the poem suggests that naming a feeling doesn't capture it. The blurred ink and the unpredictable rain suggest the same thing: some moods can't be pinned down or forecast.