## 2 Science Rationale  
Convective transition statistics serve as model diagnostics for the parameterization of convection in climate and weather forecast models [6; 25; 26]. These statistics characterize the distribution of precipitation rate (\(P\)) as a function of water vapor (denoted by \(q\))  
Figure 2: Example of a three-RO coincidence from COSMIC-2 on 5 May 2020. (**a**) Temperature (dashed) and relative humidity (solid lines) profiles from each RO, color-coded according to their location. (**b**). Locations of each of the RO tangent point locations and a 200-km segment of the occultation plane, overlaid on top of the nearest 30-min IMERG precipitation product (the IMERG color scale maximum is set to 10 mm h\({}^{-1}\) for enhancement). The RO ray path associated outside of the precipitation (green line) is displaced from (and roughly “parallel to”) the other two RO ray paths which intersect precipitation (red and black lines). and temperature (\(T\)), with the transition to deep convection seen as a threshold in this thermodynamic space where a strong \"pickup\" of precipitation is noted. Figure 3 shows one example, highlighting the current disparity in the precipitation dependence on water vapor [5] produced by 10 models from the CMIP6 program [27]. Here, conditional averages of precipitation on the LFT water vapor (integrated between two pressure levels, 750 to 900 hPa), and expressed as equivalent water depth in mm), relative to the Atmospheric Radiation Measurement (ARM) best estimate [28] for the Nauru ARM observation site in the tropical Western Pacific, are shown in the following [29]. The layer-integrated water vapor value at which the precipitation pickup occurs has a dependence on temperature that is more complex than constant relative humidity (RH), with larger subsaturation at warmer temperatures [6] (Figure 1), [25]. The relationship between precipitation and water vapor in different free tropospheric layers across the tropical latitudes was investigated by the authors of [7] using globally distributed COSMIC RO temperature and moisture profiles, collocated with GPM IMERG precipitation. Similar to results at specific tropical locations [8; 30], sharp pickups of conditionally averaged \(P\) as a function of layer \(q\) were noted in different tropospheric layers for a variety of tropical ocean and land regions. More recent studies have refined this relationship via relative contributions to conditional instability from different free-tropospheric layers above the boundary layer, in terms of dynamic entrainment profiles [8; 31; 32]. Since these convective transition statistics capture the fast time scale associated with convective development, these diagnostics provide a set of constraints on the convective parameterizations used in climate models [6; 29]. For deep convective regions, the precipitation-water vapor-temperature relationships arise from conditional instability of entraining convective updrafts. Figure 4 illustrates the relationship between vertical thermodynamic profiles and conditional stability--this helps to clarify why precipitation dependence on layer-average water vapor and temperature is more complex than simply reaching a saturation value given by the Clausius-Clapeyron relationship. Saturation equivalent potential temperature \(\theta_{es}\) (which depends only on the temperature profile) is the quantity that a raised convective parcel must exceed to be buoyant. The comparison between this and the profile of equivalent potential temperature \(\theta_{e}\), which is conserved under moist adiabatic motions, provides information on conditional instability for convection. The orange shaded area is closely related to the traditional  
Figure 3: Precipitation rate (mm h\({}^{-1}\)) conditionally averaged as a function of lower free-tropospheric water vapor q\({}_{\text{LFT}}\) (units of mm) from ten CMIP6 models (colored lines), relative to the ARM Best-Estimate observations (solid black line).