In telling Noach to enter the Teivah (א:ז) ויאמר ה' לנח בא אתה וכל ביתך אל התיבה Hashem uses the name י-ה-ו-ה which indicates His mercy. Later on, when telling Noach to leave the Teivah after approximately a year of being inside of it Hashem uses the name "Elokim" which denotes judgment. In addition to the aforementioned popular meaning this name is also used to refer to the God who dominates nature and uses it to carry out His ends. Just like judgment proceeds along clear and specifically defined rules, so too nature has its clear and specifically defined laws, within which Hashem guides the world through these rules unless He decides to override them and perform a miracle. The name Elokim refers to this aspect of Hashem's total mastery. This is because it describes him as "Mighty one who wields authority over the beings above and below." Tur (Orach Chaim 5) and the Baal Heichalot also describes Hashem as the Omnipotent one (Shulchan Aruch, ibid).
Here, when Hashem called to Noach to leave the Teivah and build a new world, He appeared as the God who created and preserves the natural world, and who would reconstruct and rejuvenate the universe that had lain almost totally dormant for a year (Haamek Davar). The word Elokim in Gematria equals that of הטבע, the nature. This indicates the He controls all of the natural phenomena.
It is quite strange how Hashem uses the name of judgment when telling Noach to leave the Teiva. Whom was He judging? There were not many people left in the world to judge. Besides which, the Mabul was supposed to cleanse the world of it's evil. It would have been a failure if Hashem had to judge even before the Mabul was over. One of the possible interpretations of this could be that someone must have sinned while inside of the Teivah or Hashem was judging Noach in the good sense. In other words he wasn't judging him to see if he was righteous or bad but rather he was judging him to find out the status of his righteousness. Before the flood Noach was referred to asאיש צדיק בדורותו - a righteous man in his generation. Perhaps while Noach was in the Teivah he had time to think and be more devoted to Hashem. However this is probably not the case because the Teivah was not a luxurious hotel of any kind. Rather it was an uncomfortable place to be in. Perchance Noach and some of his family lost some of his faith in Hashem while he was in the Teivah. Hashem put them into this horrible place for almost a year when He could have just performed some other miracle which wouldn't have been so detrimental to Noach and his family. This may be why Hashem was using the Shem of judgment rather than that of Rachamim. In the beginning Hashem used the Shem Harachamim because he was having mercy on Noach and his family. But now after the Mabul Hashem had to judge them on their actions and ideas inside of the Teivah.
Another possibility could be that Hashem was judging Noach's family according to each other. In the first pasuk of Noach the Torah say's that Noach was a Tzadik in his generation. We have the famous opinion that if Noach were to be in Avraham's generation he would not have been such a tzadik. Another opinion suggests that Noach's family may have may not have been considered evil in contrast to the wicked people who lived in his time. But now there aren't that many people in the world and the people that are in the world must live up to higher standards. Noach's family may not have lived up to the status of Noach while they were in the Teivah and therefore Hashem needed to judge them.