Below is further info on the above issue borrowed from an appendix in the Aramaic English New Testament by Andrew Gabriel Roth:
The first season of year is of course, Spring, called Aviv in Scripture. The characteristics of Spring involve the earth returning to a state of greenness, which is why we are told in Exodus to observe that moment of the year as its beginning. The Karaites also believe, quite correctly, that the sign of Spring is the tender and green ears of the barley, the first of the produce to ripen in Israel. However, they are incorrect that Aviv has started when the barley ripens, at the end of the lunar year. Barley is the earth sign, but it needs the sky sign to precede it before the season can officially begin.
It is important to point out that the first two commands to "observe Aviv" don't take place in Israel. The first Aviv occurred in Egypt and the second was in the Wilderness. Such a pattern begs several questions of the Karaite position. Which barley "counts" since it ripens gradually over several weeks? Is one part of Israel superior to others? What about the places where the command was originally given, that were both outside of Israel? Where is the biblical procedure that tells us where we get the barley? Who does it and who judges?
There are, of course, basic answers to these questions. However, this is assumed by the Karaites who add their own details to Torah, even while criticizing the Rabbis for the very same thing! However, if we know there is a sky sign that will always point to when the barley is ripe, and this is in harmony with the Torah in places like Genesis 1:14-19, then no additional procedures are required. We simply wait for the sky sign, get the barley, and go!
What we can also say about the moedim (appointed times) is that once the time is set, the moon controls the ordering of the sacred festivals: "The moon marks off the seasons, and the sun knows when to go down." (Psalm 104:19) Philo has a very interesting commentary on this verse:
"And before now some men have predicted disturbances and commotions from the motions of the earth, from the revolutions of the heavenly bodies, and innumerable other events that have turned out most exactly true; so that it is a most veracious saying that "the stars were created to act as signs and moreover to mark the seasons." And by the word seasons the divisions of the year are intended. And why may not this be reasonably affirmed? For what other idea of opportunity can there be except that it is the time for success? And the seasons bring everything to perfection, and set everything right; giving perfection to the sowing and planting of fruits and to the birth and growth of animals. They were also created to serve as the measure of time; for it is by the appointed periodic revolutions of the sun and moon and other stars that the days, months and years are determined. (Philo Judaeus, On Creation, 59-60 p. 9 CD Yonge Translation)
However, the moon is still subject to the solar year, because without it these same holidays that are keyed to harvest and planting will occur out of season. So as long as those appointed times stay on track, the moon is in charge. When it needs help, however, to keep the festivals at their proper time, the sun takes over. In so doing, both the sun and the moon mark the year, again as Scripture says.
(For more, please check out the Aramaic English New Testament.)