Uniform factorial decay estimate for the remainder of rough Taylor expansion

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

Datasets related to in-land water for limnology and remote sensing applications: distance-to-land, distance-to-water, water-body identifier and lake-centre co-ordinates

Datasets containing information to locate and identify water bodies have been generated from data locating static-water-bodies with resolution of about 300 m (1/360 deg) recently released by the Land Cover Climate Change Initiative (LC CCI) of the European Space Agency. The LC CCI water-bodies dataset has been obtained from multi-temporal metrics based on time series of the backscattered intensity recorded by ASAR on Envisat between 2005 and 2010. The new derived datasets provide coherently: distance to land, distance to water, water-body identifiers and lake-centre locations. The water-body identifier dataset locates the water bodies assigning the identifiers of the Global Lakes and Wetlands Database (GLWD), and lake centres are defined for in-land waters for which GLWD IDs were determined. The new datasets therefore link recent lake/reservoir/wetlands extent to the GLWD, together with a set of coordinates which locates unambiguously the water bodies in the database. Information on distance-to-land for each water cell and the distance-to-water for each land cell has many potential applications in remote sensing, where the applicability of geophysical retrieval algorithms may be affected by the presence of water or land within a satellite field of view (image pixel). During the generation and validation of the datasets some limitations of the GLWD database and of the LC CCI water-bodies mask have been found. Some examples of the inaccuracies/limitations are presented and discussed. Temporal change in water-body extent is common. Future versions of the LC CCI dataset are planned to represent temporal variation, and this will permit these derived datasets to be updated.

Translation, decay and splitting of Agulhas rings in the southeastern Atlantic Ocean

All Agulhas rings that were spawned at the Agulhas retrofiec- tion between 1993 and 1996 (a total of 21 rings) have been monitored using TOPEX/Poseidon satellite altimetry and followed as they moved through the southeastern Atlantic Ocean, decayed, interacted with bottom topography and each other, or dissipated completely. Rings preferentially crossed the Walvis Ridge at its deepest parts. After having crossed this ridge they have lower translational speeds, and their decay rate decreases markedly. Half the decay of long-lived rings takes place in the first 5 months of their lifetimes. In addition to the strong decay of rings in the Cape Basin, about one third of the observed rings do not seem to leave this region at all but totally disintegrate here. The interaction of rings with bottom topography, in particular with the Verna Seamount, is shown frequently to cause splitting of rings. This will enhance mixing of the rings' Indian Ocean water into that of the southern Atlantic. This localized mixing may well provide a considerable source of warm and salty Indian Ocean water into the Atlantic overturning circulation.