Yocheved took for Moshe a reed basket, smeared it with clay and tar, put him into it and placed it amongst the reeds at the Nile's edge. The Medrash explains that her strategy was that the Egyptian astrologers will see that their prediction that the savior of the Jewish Nation will die by water has already been fulfilled and the decree of throwing new born babies into the Nile can now be terminated. The Chasam Sofer adds to say that this is the reason why Yocheved chose to place Moshe in a reed basket instead of wood because she feared that maybe the astrologers would somehow realize that although the savior is in the water but nevertheless was alive because he was floating in a wooden vessel. She therefore chose a reed basket whose material grows in the water and therefore it would be undetectable to them.
A parallel story to this drama is Noach and his Taiva (ark). By the command of Hashem Noach built a boat in which all the earth's creatures and his family entered and were saved from perishing in the Flood. At first glance one might not see any association between the two floating vessels outside of the common theme that in both stories there was a vessel in which they were protected and which saved them from dying. However, if we take a closer look at some of the details we will find a number of similarities between the vessels and the individuals who were being saved Noach and Moshe.
(1) Yocheved placed Moshe in a basket fashioned from גמא - reeds. The length of Noach's Taiva was three hundred amos שלשה מאה אמות ארך. If we take the acronym of Moshe's גמא it spells ג מאות אמות (ארך) .
(2)The gematriah of גמא (with the kollel) equals מאד. In describing the waters of the Flood the Torah says והמים גברו מאד מאד על הארץ .
(3) Noach was saved by the תיבה he constructed and Moshe was saved by בתיה the daughter of Pharaoh which share the same letters.
(4) Furthermore, the passuk describing the light in the Taiva says צהר תעשה לתבה. The Chizkuni learns that this word can be rendered as oil a derivative of יצהר . Noach illuminated the ark with oil lamps ע"כ. We can say that the entire Ark and its contents were likened to oil. For the nature of oil is that when it comes in contact and mixed with water and other liquids it separates itself and rises to the top. So too, the Taiva is compared to oil in that its inhabitants were saved by rising above the waters of the Flood. Take the gematriah of תיבה and you will get זית olive.
In Moshe's reed basket there also resided a light. The passuk says that Basya opened the basket ותפתח ותראהו את הילד and she saw the child. Chazal (Sotah 12) comment that she saw the Shechinah with him (Rashi). As soon as Moshe was born the Shechinah resided by him as the Torah says after Yocheved gave birth to him ותרא אתו כי טוב הוא that the house in which he was born was full of light. Moshe Rabbeinu also possessed a special relationship with the oil used to light the Menorah as the passuk says ואתה תצוה את בני ישראל ויקחו אליך שמן זית זך להעלת נר תמיד. The Menorah symbolizes the wisdom of the Torah and Moshe was the one who brought the Torah down and delivered it to Am Yisrael. Even in his little Taiva he radiated that same light. A remez to this is the gematriah of אליך עה"כ which equals כי טוב הוא with the three words.
Noach knew that the Mabbul waters had subsided by the episode of the dove bringing back to him a torn leaf from an olive tree. It was now safe to go out for the danger was gone. So too when בתיה who is gematriah זית opened the basket and saw Moshe Rabbeinu and his radiance she removed him from the basket and the danger of the water.
בתיה is gematriah זית to hint to us the words of Chazal that her presence that day in the Nile River was to toveil and convert, removing herself and rising above the idol worship of her father like the nature of olive oil. In one aspect she was like the dove who returned to Noach with an olive leaf sending him the message that I would rather eat sustenance that is bitter from the hand of Hashem than food that is sweet given to me from man (Rashi). It was at that moment of geirus that she found Moshe and saw the Shechinah. Basya wanted to be connected and dependent upon Hashem and not her father and the Nile River. What a hashgacha that she saved and sustained Moshe the very person who merited bringing to Yisrael the מן in the desert delivered daily by the hand of Hashem.
(5) Before Hashem brought the Mabbul on the world, the Torah relates that Hashem said .לא ידון רוחי באדם לעלם בשגם הוא בשר והיו ימיו מאה ועשרים שנה My spirit will not remain in conflict over (whether to destroy) for a long time. He is flesh and still does not humble himself before Me. I will give him 120 years to live (in order to repent and if not he will be perished from earth). Chazal say (Chullin 139b) that Moshe is alluded to in this passuk being that בשגם is gematriah .משה This is followed with the passuk נח מצא חן בעיני ה' that Noach found favor in the eyes of Hashem to be spared from the obliteration of Mankind. Moshe was saved by the Taiva of גמא and including the word the gematriah comes out to גמב which shares three letters of Moshe's gematriah בשגם. The fact that Moshe's existence is hinted to in Hashem's decision of mankind's demise conveys that Moshe and Noach have some deep relationship with each other.
(6) From the time that Noach was told about his task to build a Taiva in order to save himself from the Flood waters, and the actual period that the Flood began, there was a period of 120 years. Similarly, from the time that Moshe was placed in his taivah that saved him from the waters of the Nile until his death there also passed 120 years.
(7) One more similarity between Moshe and Noach's water vessels is that they both brought about refuos. Chazal tell us that Basya was afflicted with tzaras and for that reason she went to bathe in the Nile. When she saw the reed basket she touched it and immediately her tzaraas was healed. This is one of the reasons given why she was motivated to save Moshe even though her father decreed that all Jewish babies should be drowned - Hakaras Tov.
The Taivah of Noach also had a healing effect. The passuk says that when the animals left the Taivah למשפחתהם יצאו מן התבה vowing to mate only with their own species (Rashi). The Meshech Chachma brings the Chazal that Rav Yochanan said ולא הם "and not them." Rav Meir Simcha ztl explains that these animals possessed perverted natures due to the influence received by the decadence of the generation. It took a year of toil and constant hashgacha to rehabilitate them back to their G-d given nature. When they left the Taiva לא הם their former selves were not recognizable at all. They were like new creations. Here we see the parallel between the reed basket and the Taivah for they both were vehicles of healing, by correcting deviances of nature back to their former realities and natural selves.
We have demonstrated clearly that these two salvations, one through the Taivah of Noach and the other through the Taiva of Moshe, share similar themes and details. Now we must now ask the question why was it so? The answer to all of this is what the Megaleh Amukos writes that Noach had to undergo a gilgul neshama (reincarnation) in Moshe for his aveirah of not davening to Hashem on behalf of mankind that they should not perish in the Flood. Chazal comment on Noach the passuk found in Aishes Chayil שקר החן that finding grace in Hashem's eyes is referring to Noach (Bereishis 6,8) which indicates that without grace he also would have perished in the Mabbul. If one looks at the Haftorah of Parshas Noach (Yechezkail 54,9) כי מי נח זאת לי the waters of the Flood are called the Waters of Noach because he failed to daven on behalf of humanity. That is why we find that Moshe Rabbeinu went out on the ledge surrendering his life in order to save Bnei Yisrael after the chait of the Aigel. He boldly told Hashem to erase his name from Hashem's Torah if Yisrael will not be saved from annihilation. He used the term מחני נא erase me. This is the same term used during the Mabbul (Bereishis 6,7;7,4,23) ומחיתי את כל היקום. By Moshe using the word מחני while davening for the perpetuation of Klal Yisrael, he corrected what Noach failed to do in his generation thereby repairing the letters of מי נח with Moshe's letters of מחני bringing a tikkun to the neshama of Noach.
In the sefer Shevilei Pinchus (תשעט) he brings a passuk in Parshas Noach where Hashem is addressing Noach yet it is hinting a future connection to Moshe Rabbeinu
"ויאמר ה' לנח בא אתה וכל ביתך אל התבה כי אותך ראיתי צדיק לפני בדור הזה"
Come into the Taivah because I see you as a tzaddik before me in this generation. The word הזה is gematriah 17. From Noach until Moshe Rabbeinu there passed 17 generations. In the 17th generation Moshe Rabbeinu brought a tikkun to Noach to be called now a tzaddik by his own plea to Hashem to save Yisrael with the word מחני.
Following this thought we can find another allusion to Moshe bringing the gilgul of Noach to its tikkun. It says in Bereishis 7,11 the day that the Mabbul מי נח began, was
בשנת שש מאות שנה לחיי נח בשנה בחודש השני בשבעה עשר יום לחודש ביום הזה נבקעו כל מעינות תהום רבה
We find that Moshe Rabbeinu is also called הזה (Shmos 2,9) when Basya tells Yocheved הליכי את הילד הזה והניקהו לי Take this child and nurse him for me. The מי נח was fixed by Moshe who is also called הזה gematriah טוב.
We can add another hinting to Moshe's future tikkun of Noach. It is from the passuk ונח מצא חן בעיני יהוה which is gematriah .הוא משה It will be Moshe who will fix the status of Noach from being saved only because he found chein שקר)) in the eyes of Hashem to after his tikkun reaching the level of tzadik.
One might ask why didn't Hashem just tell Noach straight out that he must daven on behalf of mankind. He surely would have done it and then he wouldn't have needed a gilgul neshama in Moshe. The answer is Hashem did tell him in the form of using the word Taivah over and over again. Taivah means word as the Baal Shem Tov said on the passuk בא אל התיבה go into the word that you are davening and don't say it superficially. Hashem expected Noach to think of this interpretation by himself which would have made him into the tzadik he was destined to be but he failed to do so. The Torah calls Noach איש צדיק. This is gematriah .תפלה This is about his potential. Had he davened to stop the Mabbul he would have reached איש צדיק תמים.
Many times Hashem sends us hints along the way, messages signaling that we have to correct certain failures and shortcomings. If one is willing to take the time and analyze the events and words that are spoken, we can become inspired and on his way to repair himself with the tikkun awaiting him.