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Abstract Bulk microphysics schemes continue to face challenges due in part to the necessary simplification of hydrometeor properties and processes that is inherent to any parameterization. In all operational bulk schemes, one such simplification is the division of liquid water into two subcategories (cloud and rain) when predicting the evolution of warm clouds. It was previously found that biases in collisional growth in a bulk scheme with these separate liquid water categories can be mitigated with a unified liquid water category in which cloud and rain are contained within the same category. In this study, we examine the effect of artificially separating the liquid water category on other microphysical processes and in more realistic settings. Both our idealized 1D and 3D results show that a unified category bulk scheme is fundamentally better at predicting the timing and intensity of rain from warm‐phase cumulus clouds compared to a traditional (separate) category bulk scheme. This is because a unified category bulk scheme allows a bimodal distribution to exist within one traditional “rain” category, whereas separate category bulk scheme only have one mode per category. This advantage allows the unified bulk scheme to retain the information of the largest droplets even as they fall through a layer of small raindrops. A separate category bulk scheme fails to represent this bimodal feature in comparison.
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This content will become publicly available on March 1, 2026
Hecke categories, idempotents, and commuting stacks
Abstract We formulate a connection between a topological and a geometric category. The former is the idempotent completion of the (horizontal) trace of the affine Hecke category, while the latter is the equivariant derived category of the (semi-nilpotent) commuting stack. This provides a more precise and improved version of our proposal in Gorsky and Neguț (Proc Lond Math Soc (3) 126(6): 2013–2056, 2023).
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- Award ID(s):
- 2302305
- PAR ID:
- 10613595
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Mathematische Zeitschrift
- Volume:
- 309
- Issue:
- 3
- ISSN:
- 0025-5874
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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