The Laws of the Aravah (Willow), 2 Seifim: 1. "Willows of the stream" mentioned in the Torah is a known species that is called that. Its leaf is long like a stream, its leaf edge is smooth, and its stem is red (and even when it is still green it is valid (Beit Yosef)). Most of this species grows by streams, which is why it is called "willows of the stream." Even if it were to grow in the desert or the mountains, it is valid. There is another species similar to the willow but with round leaves with edges serrated like a massar (meaning a sickle, siga in the vernacular) and a non-red stem. This is the tzaftzfa, and it is invalid. There is a kind of willow whose leaf edge is not smooth but rather has many small protrusions like a small sickle, and it is valid.
2. If a willow dried out, had most of its leaves fall off or had its top severed, it is invalid. If it only partially dried out or had some of its leaves fall off, it is valid. The Ramba"m validates one with a severed top.