We develop a methodology for identification of candidate observables that best constrain the parameterization of physical processes in numerical models. This methodology consists of three steps: (i) identifying processes that significantly impact model results, (ii) identifying observables that best constrain the influential processes, and (iii) investigating the sensitivity of the model results to the measurement error and vertical resolution of the constraining observables. This new methodology is applied to the Jet Propulsion Laboratory stochastic multi-plume Eddy-Diffusivity/Mass-Flux (JPL-EDMF) model for two case studies representing non-precipitating marine stratocumulus and marine shallow convection. The uncertainty of physical processes is characterized with uncertainty of model parameters. We find that the most uncertain processes in the JPL-EDMF model are related to the representation of lateral entrainment for convective plumes and parameterization of mixing length scale for the eddy-diffusivity part of the model. The results show a strong interaction between these uncertain processes. Measurements of the water vapor profile for shallow convection and of the cloud fraction profile for the stratocumulus case are among those measurements that best constrain the uncertain JPL-EDMF processes. The interdependence of the required vertical resolution and error characteristics of the observational system are shown. If the observations are associated with larger error, their vertical resolution has to be finer and vice versa. We suggest that the methodology and results presented here provide an objective basis for defining requirements for future observing systems such as future satellite missions to observe clouds and the planetary boundary layer.