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Soap and water?

Water and a soft brush on a stick would probably work

Rain?

Upvoted. I watched my panels turn yellow from pollen a few weeks ago. It all washed away in the rain.

Granted, I live in an area where we get rain on a regular basis.

A whole lot of rain will pour down on those panels every year. You should be fine unless you live in a really dry and dusty area. Or if you have trees overhead which leave sticky leaves on your roof.

Involved in large scale, long term solar testing in the past:

I was almost always better to let the rain clean the panels in the field, even in some pretty dusty and arid climates.

The deciding factor was usually the labor cost of the cleaning. (Think very depressed labor prices) Even then the risk of damage from the cleaning ops might sway away from manual cleaning.