Abarim Publications' online Biblical Hebrew Dictionary
The roots גיח and גיא are officially not related, but their form seems somewhat adjacent and their meanings overlap:
The verb גיח (giah) — also spelled גוח (gwh) — meaning to burst forth, is used to describe a vivaciously flowing river (Job 40:23) or a child coming forth from the womb (Job 38:8, Psalm 22:10). This verb occurs about half a dozen times and has no derivatives.
The root גיא (gy') isn't used as verb in the Bible, but its derived masculine (and sometimes feminine) noun גיא (gai'), meaning valley, occurs all over. The relationship to the previous is obvious as valleys often have rivers at the bottom.
There are several Hebrew words that describe a valley, but, as HAW Theological Wordbook of the Old Testament notes, the noun גיא (gai') appears to be used most often to describe "elongated and flat-bottom depressions" (Joshua 8:11, 1 Samuel 17:3, Micah 1:6). It's this word that is used in the familiar phrases "the valley of the shadow of death" (Psalm 23:4) and the "valley of vision" (Isaiah 22:1 and 22:5).
There are several valleys or plains named in the Bible:
- The valley of Iphtahel (Joshua 19:14).
- The valley of Zeboim (1 Samuel 13:18).
- The valley of Melah (or "salt"; 2 Samuel 8:13, see the name Ge-melah below).
- The valley of craftsmen, of Charashim, often wholly transliterated as Ge-harashim (1 Chronicles 4:14).
- The valley of Zephathah (2 Chronicles 14:10).
- The valley of Hamon-gog (Ezekiel 39:11).
- The valley of Hinnom (Joshua 15:8). The name of this valley, Ge-hinnom, became transliterated as Gehenna, one of a few New Testament words for hell.