After a dry Monday and Tuesday, there will be a high probability of rainfall on Wednesday and Thursday as an area of low currently in the Great Basin region in combination with a low off the Pacific Northwest help draw in moisture from the Gulf of Mexico.
The mean upper-level flow has been frequently from the west or northwest over the past several months. That tends to be a very dry flow for North Dakota and that certainly has been the case. But a southwest flow, tends to be a wet flow in the state as any storm system that rides along the mean storm track in that situation will draw in Gulf of Mexico moisture as it moves into the north central part of the United States.
The low pressure center(s) that will move through the region this week will be just the first wave of moisture, as yet another storm is expected on Sunday. The first waves of moisture on Wednesday and Thursday will in turn draw in cooler air behind the rain, leaving Friday and Saturday dry, albeit much cooler than the weather that has dominated the region for the past week. Another low pressure center with more rain potential on Sunday will in turn draw in additional cool air meaning that will some moisture will also come a period of below average temperatures from Saturday through Wednesday of next week.
Rainfall from the first waves on Wednesday and Thursday are expected to drop on average between 0.25 and 0.75 inches rain. Usual caveats apply as rainfall variation is great in most events and that is the range I expect most gauges to read by the end of Thursday. Some localized 1 inch amounts will probably happen as well as the spots that stay on the low side, but at this time a good percentage of the region should get a welcomed useful rain with an additional threat on Sunday.