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As the resolution of global climate model increases, whether trigger functions in current convective parameterization schemes still work remains unknown. In this study, the scale dependence of undilute and dilute dCAPE, Bechtold, and heated condensation framework (HCF) triggers is evaluated using the cloud-resolving model (CRM) data. It is found that all these trigger functions are scale dependent, especially for dCAPE-type triggers, with skill scores dropping from similar to 0.6 at the lower resolutions (128, 64, and 32 km) to only similar to 0.1 at 4 km. The average convection frequency decreases from 14.1% at 128 km to 2.3% at 4 km in the CRM data, but it increases rapidly in the dCAPE-type triggers and is almost unchanged in the Bechtold and HCF triggers across resolutions, all leading to large overpredictions at higher resolutions. In the dCAPE-type triggers, the increased frequency is due to the increased rate of dCAPE greater than the threshold (65 J kg(-1) h(-1)) at higher resolutions. The box-and-whisker plots show that the main body of dCAPE in the correct prediction and overprediction can be separated from each other in most resolutions. Moreover, the underprediction is found to be corresponding to the decaying phase of convection. Hence, two modifications are proposed to improve the scale dependence of the undilute dCAPE trigger: 1) increasing the dCAPE threshold and 2) considering convection history, which checks whether there is convection prior to the current time. With these modifications, the skill at 16 km, 8 km, and 4 km can be increased from 0.50, 0.27, and 0.15 to 0.70, 0.61, and 0.53, respectively.