Strengthening High Pressure will keep conditions cold & dry with calm winds for the coming week. The coldest morning temperatures should continue to drop to the 20s with afternoon high temperatures in the 40s. The inversion (a layer of warm air trapping cold air near the ground) means that the air will continue to stagnate and pollutants will build each day until a brisk wind arrives to scour it out of the valleys. This doesn’t look likely until Friday.
A weak system Tuesday will not stir the wind enough to resolve the issue. By Friday, the high pressure finally weakens enough to allow a front to approach from the north. This front will stay parked over Northern Washington & Idaho sending enough moisture to prohibit fog formation and send in clouds. At this point, it looks like it will be Monday before the atmosphere moistens enough for a chance of rain.