10Be isotope amount changes during ice ages?

10be isotope ice agesA study has suggested or found that global weathering rates do not seem to have changed in total during ice ages over the last couple of millions of years.

Or could the beryllium isotope 10Be amount being created or sent into our planets atmosphere have changed during ice ages?

And if its flux has changed then what process or events could have changed it?

a geochemical technique that compares the concentration of two forms, or isotopes, of the element beryllium (Be). 9Be is found naturally in silicate rocks on Earth; 10Be is a radioactive cosmogenic isotope produced by the collision of cosmic rays with nitrogen and oxygen molecules in the atmosphere.

"Because 10Be rains down onto Earth's continents and oceans at more or less a constant rate, it's like a clock that can be used to time processes," von Blanckenburg said. "9Be, on the other hand, can be used to calculate how much dissolved rock has washed into the oceans from rivers."
Weathering and river discharge surprisingly constant during Ice Age cycles

The ratio of the cosmogenic isotope 10Be, which is produced in the atmosphere and deposited to the oceans and the land surface, to 9Be, which is introduced to the oceans by the riverine silicate weathering flux, can be used to track relative weathering fluxes. Here we apply this proxy to marine sediment beryllium records spanning the past two million years, and find no detectable shifts in inputs from global silicate weathering into the oceans.
Stable runoff and weathering fluxes into the oceans over Quaternary climate cycles

Could the 10Be isotope be a marker or trigger for ice ages or climate changes?

"Our results suggested that globally the aggregate change in discharge from all the rivers was effectively zero between the glacial and interglacial times. That was surprising," Maher said.

The models offered a likely explanation for this: they showed that while the change in water discharge for rivers at higher latitudes in the northern hemisphere could vary wildly between glacial and interglacial times, the flux for rivers in the tropics-which remained temperate even during ice ages-did not change by more than a few percent.
Stable runoff and weathering fluxes into the oceans over Quaternary climate cycles

Or is it actually explained by the geology models? But if the colder rivers stop flowing then why does an increase of only a few percent in the warmer areas make up for it?