Depending on the volume of material ejected, the size of the particles and the height they achieve, there could be some climate impacts.
From the AP:
Alaska's Mount Redoubt volcano erupted five times overnight, sending an ash plume more than 9 miles into the air in the volcano's first emissions in nearly 20 years. Residents in the state's largest city were spared from falling ash, though fine gray dust was falling Monday morning on small communities north of Anchorage. The ash began falling around daybreak and continued into midmorning. They were supposed to end by noon....MOREThe Redoubt webcam is showing the ash haze.
The hut webcam, located 7 1/2 miles from the summit crater is not operative:
"WE ARE CURRENTLY NOT RECEIVING ANY DATA FROM THIS CAMERA."