Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition

In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone op- erator. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. The advantage to an earlier algorithm is demonstrated. Furthermore an example is given which shows how to analyze a given perturbed interconnected system.Comment: 30 pages, 7 figures, 4 table

Persistence of full glacial conditions in the central Pacific until 15,000 years ago

The magnitude of atmospheric cooling during the Last Glacial Maximum and the timing of the transition into the current interglacial period remain poorly constrained in tropical regions, partly because of a lack of suitable climate records. Glacial moraines provide a method of reconstructing past temperatures, but they are relatively rare in the tropics. Here we present a reconstruction of atmospheric temperatures in the central Pacific during the last deglaciation on the basis of cosmogenic ^3He ages of moraines and numerical modelling of the ice cap on Mauna Kea volcano, Hawaii—the only highland in the central Pacific on which moraines that formed during the last glacial period are preserved. Our reconstruction indicates that the Last Glacial Maximum occurred between 19,000 and 16,000 years ago in this region and that temperatures at high elevations were about 7 °C lower than today during this interval. Glacial retreat began about 16,000 years ago, but temperatures were still about 6.5 °C lower than today until 15,000 years ago. When combined with estimates of sea surface temperatures in the central Pacific Ocean, our reconstruction indicates that the lapse rate during the Last Glacial Maximum was higher than at present, which is consistent with the proposal that the atmosphere was drier at that time. Furthermore, the persistence of full glacial conditions until 15,000 years ago is consistent with the relatively late and abrupt transition to warmer temperatures in Greenland5, indicating that there may have been an atmospheric teleconnection between the central Pacific and North Atlantic regions during the last deglaciation

Noncommutative polynomial maps

Accepté pour publication dans "Journal of Algebra and its applications"; 16 pages.Polynomial maps attached to polynomials of an Ore extension are naturally defi ned. In this setting we show the importance of pseudo-linear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a fi nite fi eld F_q[t;S ], where S is the Frobenius automorphism, are translated into factorizations in the usual polynomial ring F_q[x]

Argo data 1999-2019: two million temperature-salinity profiles and subsurface velocity observations from a global array of profiling floats.

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Wong, A. P. S., Wijffels, S. E., Riser, S. C., Pouliquen, S., Hosoda, S., Roemmich, D., Gilson, J., Johnson, G. C., Martini, K., Murphy, D. J., Scanderbeg, M., Bhaskar, T. V. S. U., Buck, J. J. H., Merceur, F., Carval, T., Maze, G., Cabanes, C., Andre, X., Poffa, N., Yashayaev, I., Barker, P. M., Guinehut, S., Belbeoch, M., Ignaszewski, M., Baringer, M. O., Schmid, C., Lyman, J. M., McTaggart, K. E., Purkey, S. G., Zilberman, N., Alkire, M. B., Swift, D., Owens, W. B., Jayne, S. R., Hersh, C., Robbins, P., West-Mack, D., Bahr, F., Yoshida, S., Sutton, P. J. H., Cancouet, R., Coatanoan, C., Dobbler, D., Juan, A. G., Gourrion, J., Kolodziejczyk, N., Bernard, V., Bourles, B., Claustre, H., D'Ortenzio, F., Le Reste, S., Le Traon, P., Rannou, J., Saout-Grit, C., Speich, S., Thierry, V., Verbrugge, N., Angel-Benavides, I. M., Klein, B., Notarstefano, G., Poulain, P., Velez-Belchi, P., Suga, T., Ando, K., Iwasaska, N., Kobayashi, T., Masuda, S., Oka, E., Sato, K., Nakamura, T., Sato, K., Takatsuki, Y., Yoshida, T., Cowley, R., Lovell, J. L., Oke, P. R., van Wijk, E. M., Carse, F., Donnelly, M., Gould, W. J., Gowers, K., King, B. A., Loch, S. G., Mowat, M., Turton, J., Rama Rao, E. P., Ravichandran, M., Freeland, H. J., Gaboury, I., Gilbert, D., Greenan, B. J. W., Ouellet, M., Ross, T., Tran, A., Dong, M., Liu, Z., Xu, J., Kang, K., Jo, H., Kim, S., & Park, H. Argo data 1999-2019: two million temperature-salinity profiles and subsurface velocity observations from a global array of profiling floats. Frontiers in Marine Science, 7, (2020): 700, doi:10.3389/fmars.2020.00700.In the past two decades, the Argo Program has collected, processed, and distributed over two million vertical profiles of temperature and salinity from the upper two kilometers of the global ocean. A similar number of subsurface velocity observations near 1,000 dbar have also been collected. This paper recounts the history of the global Argo Program, from its aspiration arising out of the World Ocean Circulation Experiment, to the development and implementation of its instrumentation and telecommunication systems, and the various technical problems encountered. We describe the Argo data system and its quality control procedures, and the gradual changes in the vertical resolution and spatial coverage of Argo data from 1999 to 2019. The accuracies of the float data have been assessed by comparison with high-quality shipboard measurements, and are concluded to be 0.002°C for temperature, 2.4 dbar for pressure, and 0.01 PSS-78 for salinity, after delayed-mode adjustments. Finally, the challenges faced by the vision of an expanding Argo Program beyond 2020 are discussed.AW, SR, and other scientists at the University of Washington (UW) were supported by the US Argo Program through the NOAA Grant NA15OAR4320063 to the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) at the UW. SW and other scientists at the Woods Hole Oceanographic Institution (WHOI) were supported by the US Argo Program through the NOAA Grant NA19OAR4320074 (CINAR/WHOI Argo). The Scripps Institution of Oceanography's role in Argo was supported by the US Argo Program through the NOAA Grant NA15OAR4320071 (CIMEC). Euro-Argo scientists were supported by the Monitoring the Oceans and Climate Change with Argo (MOCCA) project, under the Grant Agreement EASME/EMFF/2015/1.2.1.1/SI2.709624 for the European Commission

Equatorial Atlantic Ocean dynamics in a coupled ocean–atmosphere model simulation

The ocean temperatures and zonal currents at the equatorial Atlantic simulated by an improved version of the Brazilian earth system model (BESM), with changes in the cloud cover scheme and optical properties of the atmospheric component, are analyzed and compared to those obtained from a previous version of BESM and also from other seven selected CMIP5 models. It is shown that this updated version of BESM, despite some persistent biases, more accurately represents the surface temperature variation at the Equator and the equatorial thermocline east–west slope. These improvements are associated to a more realistic seasonal cycle achieved for the Atlantic equatorial undercurrent, as well as sea surface temperatures and zonal wind stress. The better simulation of the equatorial undercurrent is, in its turn, credited to a more realistic representation of the surface wind position and strength at the tropical Atlantic by the coupled model. With many of the systematic errors noticed in the previous version of the model alleviated, this version of BESM can be considered as a useful tool for modelers involved in Atlantic variability studies

The Lake CHAd Deep DRILLing project (CHADRILL) - targeting ~ 10 million years of environmental and climate change in Africa

At present, Lake Chad ( ~13°0 N, ~14° E) is a shallow freshwater lake located in the Sahel/Sahara region of central northern Africa. The lake is primarily fed by the Chari-Logone river system draining a ~600 000 km2 watershed in tropical Africa. Discharge is strongly controlled by the annual passage of the intertropical convergence zone (ITCZ) and monsoon circulation leading to a peak in rainfall during boreal summer. During recent decades, a large number of studies have been carried out in the Lake Chad Basin (LCB). They have mostly focused on a patchwork of exposed lake sediments and outcrops once inhabited by early hominids. A dataset generated from a 673m long geotechnical borehole drilled in 1973, along with outcrop and seismic reflection studies, reveal several hundred metres of Miocene-Pleistocene lacustrine deposits. CHADRILL aims to recover a sedimentary core spanning the Miocene-Pleistocene sediment succession of Lake Chad through deep drilling. This record will provide significant insights into the modulation of orbitally forced changes in northern African hydroclimate under different climate boundary conditions such as high CO2 and absence of Northern Hemisphere ice sheets. These investigations will also help unravel both the age and the origin of the lake and its current desert surrounding. The LCB is very rich in early hominid fossils (Australopithecus bahrelghazali; Sahelanthropus tchadensis) of Late Miocene age. Thus, retrieving a sediment core from this basin will provide the most continuous climatic and environmental record with which to compare hominid migrations across northern Africa and has major implications for understanding human evolution. Furthermore, due to its dramatic and episodically changing water levels and associated depositional modes, Lake Chad's sediments resemble maybe an analogue for lake systems that were once present on Mars. Consequently, the study of the subsurface biosphere contained in these sediments has the potential to shed light on microbial biodiversity present in this type of depositional environment. We propose to drill a total of ~1800m of poorly to semi-consolidated lacustrine, fluvial, and eolian sediments down to bedrock at a single on-shore site close to the shoreline of present-day Lake Chad. We propose to locate our drilling operations on-shore close to the site where the geotechnical Bol borehole (13°280 N, 14°440 E) was drilled in 1973. This is for two main reasons: (1) nowhere else in the Chad Basin do we have such detailed information about the lithologies to be drilled; and (2) the Bol site is close to the depocentre of the Chad Basin and therefore likely to provide the stratigraphically most continuous sequence