Then watch thou for the Day that the sky will bring forth a kind of smoke (or mist) plainly visible, (Quran 44:10)

It obviously refers to great calamity, and from the wording it is to be a great calamity in the future, seen with the prophetic eye. The word yagsha in verse 11 may be compared to gashiya in 88:1, which obviously refers to the final Day of Judgment. But verse 15 below ("We shall remove the Penalty for a while") shows that it is not the final Judgment referred to here, but some calamity that was to happen soon afterwards, Perhaps it was a famine.
The "smoke" or "mist" is interpreted on good authority to refer to a severe famine in Makkah, in which men were so pinched with hunger that they saw mist before their eyes when they looked at the sky. Ibn Kathir in his Tarikh mentions two famines in Makkah, one in the 8th year of the Mission, say the fourth year before the Hijrah, and another about the 8th year after the Hijrah. But as either or both of these famines lasted as many as seven years, the dates are to be taken very roughly. It is even possible that the two famines were continuous, of varying severity from year to year. Bukhari mentions only the post-Hijrah famine, which was apparently so severe that men began to eat bones and carrion. Abu Sufyan (about 8 A.H.) approached the holy Prophet to intercede and pray for the removal of the famine, as the Pagans attributed it to the curse of the Prophet. Surah 23., which is also Makkan, but of later date than the present Surah, also refers to a famine: see 23:75. As Surahs were not all revealed entire, but many came piecemeal, it is possible that particular verses in a given Surah may be of different dates from the Surah as a whole.

Enveloping the people: this will be a Penalty Grievous. (Quran 44:11)

We shall indeed remove the Penalty for a while, (but) truly ye will revert (to your ways). (Quran 44:15)

One day We shall seize you with a mighty onslaught: We will indeed (then) exact Retribution! (Quran 44:16)

Although there is an explanation for the famine that afflicted the people of Mecca and it is true that there is a connection between aya and famine, however when interpreting the Quran, we cannot deviate from seeing a future event affecting not only Mecca but also the whole humanity. For the Surah does not stick on the pagan, earthly behavior of Mecca, but illustrates the great calamities of the past, where the reason is the same: the pride and arrogance of human supremacy, what is the seed of many sins.
Following the above verses comes the story of Moses and the Pharaoh, then the Himyar dynasty in Yemen, whose destruction was caused by their own arrogance.

The verses here are reference to the pride of Pharaoh and his Egyptians, and their fall, rather than to the story of Moses himself; just as in 44:30-33 the reference is to the blessings bestowed on Israel, contrasted with their pride, unbelief, and fall; and in 44:37, to the ancient Himyar kingdom in Yemen, which similarly fell for its sins.
Most honorable: this epithet is specially applied to Moses here, as expressing the truth, in contrast to the Pharaoh's false characterization of him as "a contemptible wretch". (43:52).

Tubba' is understood to be a title or family name of Himyar kings in Yemen, of the tribe of Hamdan. The Himyar were an ancient race. At one time they seem to have extended their hegemony over all Arabia and perhaps beyond, to the East African Coast. Their earliest religion seems to have been Sabianism, or the worship of the heavenly bodies. They seem at different times, later on, to have professed the Jewish and the Christian religion. Among the Embassies sent by the holy Prophet in A.H. 9-10 was one to the Himyar of Yemen, which led to their coming into Islam. This was of course much later than the date of this Surah.
Great Dam of Ma'rib built by the Himyars in the 8th century BC. It was one of the engineering wonders of the ancient world. Once the dam broke and nothing remained afterwards except drought, famine and destruction.

Remember: verse 10 refers to the smoke that covers the whole sky and verses 15-16 refer to a punishment that comes from time to time, but if humans will not change their behavior, they will suffer of a final blow. Can't you see the Signs of that?