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Phytoplankton are not to be taken for granted. Not only do they form the core of marine food webs around the world, they also release half of the world's oxygen. But phytoplankton, being plant-like organisms, need nutrients for their blooms to survive and thrive into populations large enough to be visible from space. For many, the origins of those nutrients come from one of the least likely sources: desert dust storms swept up from far away by deserts. As the dust settles down to the oceans, they drop down enough nutrients to create these vast blooms on an annual basis.

But what else could feed a plankton bloom on a global scale and an annual basis?

You could say that volcanic ash could be the answer, but there's a problem--unlike dust storms, volcanoes don't erupt at once or regularly. Two eruptions from one same volcano could be years or even decades apart, and that sort of duration gap won't do for plankton blooms. So what else could feed a plankton bloom on a global scale and an annual basis?

EDIT--NO manmade processes! Everyting MUST be natural!

Rivers.

https://earthobservatory.nasa.gov/images/1257/mississippi-river-sediment-plume

Depicted: the Mississippi dumping its load of sediment into the Gulf of Mexico. River flow is cyclical in most places, with high flow during rainy season or spring melt and low flow during dry season / winter or summer. During high flow, nutrients move from the land to the river and on to the sea. With the advent of synthetic fertilizer this can be too much of a good thing - so much nitrogen and phosphorus that they produce massive blooms, that then die.

Icebergs.

Icebergs generation is periodic, both intrayear and over longer periods.

https://www.nationalgeographic.org/media/iceberg-frequency/

Icebergs that have scraped along the land can ferry nutrients out to sea, releasing them slowly as the ice melts.

https://phys.org/news/2019-03-mystery-green-icebergs.html

The green icebergs have been a curiosity to scientists for decades,
but now glaciologists report in a new study that they suspect iron
oxides in rock dust from Antarctica's mainland are turning some
icebergs green... Iron is a key nutrient for phytoplankton,
microscopic plants that form the base of the marine food web. But iron
is scarce in many areas of the ocean.

If experiments prove the new theory right, it would mean green
icebergs are ferrying precious iron from Antarctica's mainland to the
open sea when they break off, providing this key nutrient to the
organisms that support nearly all marine life.

Eventually, phytoplankton don't really feed on dust, but on nitrogen (N), phosphorus (P), iron(Fe), and the various other nutrients plants need, that may compose it. But if a desert hold such nutrients, it will not stay a desert for long.

An example of a yearly massive bloom could be a mass migration of ground animal, on shore, for reproductive purpose (a bit like toad, that need water even if they are most the time ground animal). They will stay on the shore for some weeks, defecating and urinating, and releasing a massive dose of nitrates, phosphate and so on...

Second example, industrial activity, mainly agriculture, may lead to algae bloom (like in Brittany, France, with the famous green and smelly algae). And since plants grow on yearly cycle, fertilizer are used on a yearly basis

Up-welling. Nutrients tend to sink to the bottom, or to deep water where not enough light reaches to keep photosynthetic life forms thriving. If there is some mechanism to vigorously return deep water to the surface then it can bring the nutrients with it.

Up-welling might well be a seasonal thing. For example, currents could flow in one direction half the year when the snow melts in this hemisphere and builds up in the other. Then in the other direction for the other half of the year. This could produce a seasonal stirring of the deeper ocean layers.

Up-welling could be driven by temperature differences produced by geological heating that does not rise to the level of volcanoes. Water is at its highest density at close to 1.5°C. So if you have something that warms the depths it will bring the deep water back to the surface. This probably isn't seasonal.

In exotic places with exotic tides, that might do it. If a large moon had an exceedingly eccentric orbit, you could have extreme tides for the portion of the moon's orbit when it was closest, then far weaker tides the rest of the time.