Simple d8 Weather

To establish, either start with preexisting weather or roll a d8*, interpret high results as clear weather, low results as appropriate nasty weather (a table for this region might be handy), and middling results as indicative of upcoming weather; wind starts picking up, light sprinkling, etc. 

Once weather has been established, roll a d8*, on a high result the weather is either favorite to the players (or to their predictions) or it abates or clears up, on a low result it continues or gets worse, on a middling result it looks like it might change, and either goes down an increment in intensity (ex: thunderstorm to light shower) or becomes another weather type (ex: rain becomes sleet). Repeat** rolling this oracle ad infinitum.

An example in practice:

It starts out a clear, sunny day above a temperate floodplain. 

(rolls a 5) 

But there's a faint humidity in the air, a pressure from the east.

(rolls a 5) 

It remains sunny and clear however, seems the clouds are clustering and passing by somewhere over the horizon.

(rolls a 4)

They lurk ominously. Reports of torrential rains in the neighboring kingdom.

(rolls a 3)

The humidity is beginning to climax and the sky is darkened by stray clouds, soft rains fall.

(rolls a 2)

The clouds break and sheets of rain fall drenching everything, the sky is black and roiling thick with clouds, it's a springtime rainstorm at its fullest. 

(rolls a 6)

The rain weans and becomes sporadic, sun breaks through patches in the sky.

(rolls a 5)

A chilling wind picks up, blowing many of the clouds away.

(rolls a 4)

All the clouds and their rains have gone, replaced by cold wind blowing down from the uplands.

(rolls a 5)

The wind slows a little, mild gusts is all. 

(rolls a 7)

The wind dies completely, a warm sunny day out, the birds sing and hop about.

(rolls a 7) 

The sun comes out in full force warming everything to a pleasant degree.

This system should produce weather that runs for long stretches, tweakible to the roller's taste, and which hopefully lets weather build up and die down. The d8 makes it run with preference towards middling, a d6 might make things swingier! 

*****

*Or really any die bigger than a d4 should work well for this since its oracular

** Rolls can be made once a day, or if you want a bit more granularity, twice or thrice per day (morning/afternoon or morning/noon/evening)