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Cloud fraction parameterizations are beneficial to regional, convection-permitting numerical weather prediction. For its operational regional midlatitude forecasts, the Met Office uses a diagnostic cloud fraction scheme that relies on a unimodal, symmetric subgrid saturation-departure distribution. This scheme has been shown before to underestimate cloud cover and hence an empirically based bias correction is used operationally to improve performance. This first of a series of two papers proposes a new diagnostic cloud scheme as a more physically based alternative to the operational bias correction. The new cloud scheme identifies entrainment zones associated with strong temperature inversions. For model grid boxes located in this entrainment zone, collocated moist and dry Gaussian modes are used to represent the subgrid conditions. The mean and width of the Gaussian modes, inferred from the turbulent characteristics, are then used to diagnose cloud water content and cloud fraction. It is shown that the new scheme diagnoses enhanced cloud cover for a given gridbox mean humidity, similar to the current operational approach. It does so, however, in a physically meaningful way. Using observed aircraft data and ground-based retrievals over the southern Great Plains in the United States, it is shown that the new scheme improves the relation between cloud fraction, relative humidity, and liquid water content. An emergent property of the scheme is its ability to infer skewed and bimodal distributions from the large-scale state that qualitatively compare well against observations. A detailed evaluation and resolution sensitivity study will follow in Part II.

A Bimodal Diagnostic Cloud Fraction Parameterization. Part I: Motivating Analysis and Scheme Description