While it is entirely possible for heavy precipitation to occur with an initially shallow layer of moisture at the surface overlain by drier air aloft, it is more common for precipitation to be associated with a relatively deep layer of moisture in the lower half of the atmosphere. One strategy to use in forecasting precipitation is to assess how close to saturation the lower atmosphere may be. The variable that gives this information is the relative humidity. If the average relative humidity in the layer between 850 mb and 500 mb is at least 70%, there is a reasonable probability that precipitation will occur. If the value is higher, precipitation is more likely. The links for this section will take you to multi-panel plots of forecast 850 to 500 mb mean relative humidity.