On the quality of RS41 radiosonde descent data

Radiosonde descent profiles have been available from tens of stations for several years now – mainly from Vaisala RS41 radiosondes. They have been compared with the ascent profiles, with ECMWF short-range forecasts and with co-located radio-occultation retrievals. Over this time our understanding of the data has grown, and the comparison also shed some light on radiosonde ascent data. It has become clear that the fall rate is very variable and that it is an important factor, with high fall rates being associated with temperature biases, especially at higher altitudes. Ascent winds are affected by pendulum motion, on average descent winds are less affected by pendulum motion and are smoother. It is plausible that the true wind variability in the vertical lies between that shown by ascent and descent profiles. The discrepancy indicates the need for reference wind measurements.

Descent and Galois theory for Hopf categories

Descent theory for linear categories is developed. Given a linear category as an extension of a diagonal category, we introduce descent data, and the category of descent data is isomorphic to the category of representations of the diagonal category, if some flatness assumptions are satisfied. Then Hopf–Galois descent theory for linear Hopf categories, the Hopf algebra version of a linear category, is developed. This leads to the notion of Hopf–Galois category extension. We have a dual theory, where actions by dual linear Hopf categories on linear categories are considered. Hopf–Galois category extensions over groupoid algebras correspond to strongly graded linear categories.

Demazure Descent and Representations of Reductive Groups

We introduce the notion of Demazure descent data on a triangulated category C and define the descent category for such data. We illustrate the definition by our basic example. Let G be a reductive algebraic group with a Borel subgroup B. Demazure functors form Demazure descent data on DbRepB and the descent category is equivalent to DbRepG.

Assessment of GPS radiosonde descent data

Radiosondes are widely used to obtain basic meteorological parameters such as pressure (P), temperature (T), relative humidity (RH) and horizontal winds during the balloon ascent up to the altitude of balloon burst, usually ~ 32–35 km. Data from the radiosondes released from Gadanki (13.5° N, 79.2° E), a tropical station in India, have been collected during the ascent and during the descent as well without attaching any parachute or its equivalent since the year 2008. In the present study an attempt has been made to characterize the radiosonde descent data with the main objective of exploring its usefulness and reliability for scientific purposes. We compared the data obtained during ascent and descent phases of the same sounding. The mean differences in T, RH and horizontal winds between ascent and descent data are found to be small and are sometimes even within the uncertainty of the measurements and/or expected diurnal variation itself. The very good consistency observed between the ascent and the descent data shows that one more profile of the meteorological parameters can be constructed within 3 h of time of balloon launch practically at no additional cost. Further checks are done by utilizing the 3-hourly radiosonde observations collected during the Tropical Tropopause Dynamics campaigns conducted at Gadanki. In the process of checking the consistency between the radiosonde ascent and descent data, several new findings are arrived at and are reported in this study. In general, it has taken more than half an hour for the balloon to reach the ground from the burst altitude. It is also observed that the fall velocity is close to 10 m s−1 near the surface. Finally, it is suggested to record the observations also when the balloon is descending as this information is useful for scientific purposes.