Cloud fraction affects both shortwave and longwave cloud radiative effects, strongly regulating the Earth's energy budget and thus climate change in both observation and model simulations. This study evaluates two diagnostic cloud-fraction parameterization schemes, namely the Xu-Randall scheme and the Sundqvist scheme, using a novel approach. Unlike previous evaluation studies that compared schemes embedded in a climate model and could not identify the exact sources for the biases, this study obtained all inputs to the schemes by upscaling the CloudSat (quasi) observations. Hence, the scheme-observation discrepancies can be mostly attributed to deficiencies of the cloud-fraction parameterization, providing clear insights for model improvement.Results show that both schemes predict total cloud fraction close to the observation, overestimate high-level cloud fraction over the tropics, and underestimate low- and middle-level cloud fraction around 60°S and 60°N. Overall, the Xu-Randall scheme is relatively closer to the observation than the Sundqvist scheme. The Xu-Randall scheme produces a relatively more-realistic seasonal variation of cloud fraction, while the Sundqvist scheme underestimates low-level cloud fraction at all latitudes in all seasons. It is further revealed that the observed cloud fraction tends to vary with relative humidity (RH) in a non-monotonous way for clouds of any phase. Neither scheme can capture this non-monotonicity. Both schemes tend to overestimate the change rate of cloud fraction with RH and predict excessive cloud fraction when RH approaches 100%, especially for the ice-phase clouds. In addition, the biases are exacerbated in both schemes when the horizontal/vertical grid sizes are decreased/increased, respectively. Implications for future cloud-fraction parameterization improvement are also discussed.
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