We use 3-D cloud-resolving model (CRM) simulations of two mesoscale convective systems at mid-latitudes and a simple statistical ensemble method to diagnose the scale dependency of convective momentum transport (CMT) and CMT-related properties, and evaluate a parameterization scheme for convection-induced pressure gradient (CIPG) developed by Gregory et al. (GKI97). GKI97 relates CIPG to a constant coefficient multiplied by mass flux and vertical mean wind shear. CRM results show that mass fluxes and CMT exhibit strong scale dependency in temporal evolution and vertical structure. The prevalent understandings of CMT characteristics in terms of upgradient/downgradient transport are applicable to updrafts but not downdrafts across a wide range of grid spacings (4-512 km). For the small-to-median grid spacings (4~64 km), GKI97 reproduces some aspects of CIPG scale dependency except for underestimating the variations of CIPG as grid spacing decreases. However, for large grid spacings (128~512 km), GKI97 might even less adequately parameterize CIPG because it omits the contribution from either the nonlinear shear or buoyancy forcings. Further diagnosis of CRM results suggests that inclusion of nonlinear shear forcing in GKI97 is needed for the large grid spacings, and use of the three updraft and one downdraft approach proposed in an earlier study may help a modified GKI97 capture more variations of CIPG as grid spacing decreases for the small-to-median grid spacings. Further, the optimal coefficients used in GKI97 seems insensitive to grid spacings, but they might be different for updrafts and downdrafts, for different MCS types, and for zonal and meridional components.
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