In this paper, we investigate the parameters controlling the precipitation for a two-dimensional conditionally unstable flow over a two-dimensional mountain by conducting idealized numerical simulations using the Weather and Research Forecast (WRF) model. As found in Chu and Lin (2000), three moist flow regimes, namely, (I) regime with upstream-propagating convective systems, (II) regime with quasi-stationary upslope and downslope convective systems, and (III) regime with stationary upslope and downstream propagating convective systems, are identified by the moist Froude number. In this study, we propose to use a new nondimensional control parameter, CAPE-U=(2CAPE)**0.5/U, to represent the characteristics of the conditional instability. Physically, this control parameter compares the convective available potential energy and the kinetic energy of the incoming conditional unstable flow. When CAPE-U increases, the area of precipitation concentration moves further upstream. That is, the flow shifts from higher-number regime to lower-number regime. Physically, this indicates that the upward motion induced by the instability is able to overcome the advection effect of the basic flow, thus the convective system is able to anchor over the upslope and then propagate against the basic flow.

In addition to the moist Froude number and CAPE-U, the flow is also controlled by the mountain height-width aspect ratio, h/a, and the amount of moisture in the layer or the mean relative humidity. With a smaller h/a, i.e. lower or wider mountain, for a constant Froude number, there are more, but weaker, convective cells generated by the orography. The idealized numerical experiments also indicate that as the amount of moisture increases, the flow tends to shift from higher-number regime to lower-number regime. Physically, this means that a stronger convective system is generated, which is able to produce stronger upward motion to overcome the advection effect of the basic flow, in a way similar to the increase of the CAPE of the basic flow.