Simple and quick answer, the monsoon variability comes from internal and/or external processes. A good example of external forcing is ENSO's teleconnection with Indian Monsoon rainfall. Please refer to 'On the Weakening Relationship Between the Indian Monsoon and ENSO (Kumar, et al., 1999, Science). For the internal forcing, some papers focusing on monsoon onset variability could be found on my ResearchGate page, like 'The Onset of the Monsoon over the Bay of Bengal: The Year-to-Year Variations (Yu, et al., 2012, AOSL)', and 'Structures and mechanisms of the first-branch northward-propagating intraseasonal oscillation over the tropical Indian Ocean (Li et al, 2013, CD)'. Hope they are helpful.
The atmospheric dust appears to be the strongest impact on clouds and rainfall on the planet, if you overlay the dust over the monsoonal moisture between India and Arabia each year, for example. The Pakistan-Arabia Dust Cloud forms a wall that either stalls the monsoon in India or Pakistan and causes floods, or the lands on the other side of the dust wall experiences drought.
Overlaying the Pakistan-Arabia Dust Cloud with the moisture of the Category-5 cyclone GONU, you can see the direct effect of the dust, ripping the cyclone in two on June 6, 2007 at 06:00Z and eating the cyclone like icecream. You can see this epic battle at http://www.ecoseeds.com/newGONU.html and there are other dust-rainfall battles at http://www.ecoseeds.com/contents.html.
The amazing action of the atmospheric dust, is that it can have an measurable effect on rainfall and droughts at very low levels, like only 40 micrograms per cubic meter. And it is also remarkable that any amount of dust has the power to extinguish a Category-5 cyclone, that is a real eye-opener.
We need to start incorporating the atmospheric dust into all of our computer climate models, and when we do so, we may get a really big surprise.
The interface between the Indian monsoon summer moisture and the Pakistan-Arabia Dust Cloud would be a good place to start, because the interaction is so easily and clearly available for modeling, and that interface interaction means drought or floods for over a billion people on the planet.
Conversely, if we could eliminate the Pakistan-Arabia Dust Cloud by ecological restoration with local native plants in the source countries producing that dust, that could modify weather in a very positive direction for the whole northern hemisphere, and can help contribute to subtract some of the global climate warming effects.