The Cable equation is one of the most fundamental equations for modeling neuronal dynamics. In this article, we consider a high order compact finite difference numerical solution for the fractional Cable equation, which is a generalization of the classical Cable equation by taking into account the anomalous diffusion in the movement of the ions in neuronal system. The resulting finite difference scheme is unconditionally stable and converges with the convergence order of
Bin and bulk schemes are the two primary methods to parameterize cloud microphysical processes. This study attempts to reveal how their structural differences (size‐resolved vs. moment‐resolved) manifest in terms of cloud and precipitation properties. We use a bulk scheme, the Arbitrary Moment Predictor (AMP), which uses process parameterizations identical to those in a bin scheme but predicts only moments of the size distribution like a bulk scheme. As such, differences between simulations using AMP's bin scheme and simulations using AMP itself must come from their structural differences. In one‐dimensional kinematic simulations, the overall difference between AMP (bulk) and bin schemes is found to be small. Full‐microphysics AMP and bin simulations have similar mean liquid water path (mean percent difference <4%), but AMP simulates significantly lower mean precipitation rate (−35%) than the bin scheme due to slower precipitation onset. Individual processes are also tested. Condensation is represented almost perfectly with AMP, and only small AMP‐bin differences emerge due to nucleation, evaporation, and sedimentation. Collision‐coalescence is the single biggest reason for AMP‐bin divergence. Closer inspection shows that this divergence is primarily a result of autoconversion and not of accretion. In full microphysics simulations, lowering the diameter threshold separating cloud and rain category in AMP from
- Award ID(s):
- 2025103
- PAR ID:
- 10400070
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Advances in Modeling Earth Systems
- Volume:
- 15
- Issue:
- 3
- ISSN:
- 1942-2466
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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