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Abstract In a previous paper, we identified a “notch” in unstable layers at Koror (7.3°N, 134.5°E), where there was a relative deficiency in thin unstable layers and a corresponding relative excess in thicker layers, at altitudes centered at 12 km. We hypothesized that this feature was associated with the previously identified stability minimum in the tropics at that same altitude. In this paper, we extend our studies of this notch and its association with the tropical stability minimum by examining other stations in the deep tropics and also some stations at higher latitudes within the tropics. We find that this notch feature is found at all the other radiosonde stations in the deep tropics that we examined. We also find that the annual variations in unstable layer occurrences at stations at higher latitudes within the tropics show variations consistent with our hypothesis that this notch is associated with the region of minimum stability in the tropics at altitudes centered around 12 km, in that the annual variation in this notch feature is consistent with the annual variation of minimum stability in this region. Two factors contribute to the notch feature. One is that the data quality control procedure of the analysis rejects many thin layers due to the small trend-to-noise ratio in the region of minimum stability. The other is that the cloud-top outflow, which was previously identified with the stability minimum, advects thicker unstable layers throughout the deep tropics at the altitudes of the notch. Significance StatementPrevious papers have separately identified a stability minimum in the tropics and a “notch” feature in the thicknesses of unstable atmospheric layers where there are less thin unstable layers and a corresponding excess of thicker unstable layers, both at altitudes around 12 km. We previously hypothesized that these two features were associated with one another. In this paper, we examine this notch feature and the minimum in atmospheric stability at both deep tropical radiosonde stations and stations located at higher latitudes in the tropics, and we find that the annual variation of this notch feature is consistent with the latitudinal migration of the latitudes of the stability minimum. Turbulence associated with this notch feature might be significant for aircraft operations.
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Tangent developable surfaces and the equations defining algebraic curves
This is an introduction, aimed at a general mathematical audience, to recent work of Aprodu, Farkas, Papadima, Raicu, and Weyman. These authors established a long-standing folk conjecture concerning the equations defining the tangent developable surface of the rational normal curve. This in turn led to a new proof of a fundamental theorem of Voisin on the syzygies of generic canonical curves. The present note, which is the write-up of a talk given by the second author at the Current Events seminar at the 2019 JMM, surveys this circle of ideas.
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- Award ID(s):
- 1801870
- PAR ID:
- 10422599
- Date Published:
- Journal Name:
- Bulletin of the American Mathematical Society
- Volume:
- 57
- Issue:
- 1
- ISSN:
- 0273-0979
- Page Range / eLocation ID:
- 23 to 38
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1090/bull/1683
