Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

Physicochemical sea ice and water characteristics near Point Barrow 2005-2006

Photosynthetic parameters of phytoplankton and sea ice algae from landfast sea ice of the Chukchi Sea off Point Barrow, Alaska, were assessed in spring 2005 and winter through spring 2006 using Pulse Amplitude Modulated (PAM) fluorometry including estimates of maximum quantum efficiency (Fv/Fm), maximum relative electron transport rate (rETRmax), photosynthetic efficiency (alpha), and the photoadaptive index (Ek). The use of centrifuged brine samples allowed to document vertical gradients in ice algal acclimation with 5 cm vertical resolution for the first time. Bottom ice algae (0-5 cm from ice-water interface) expressed low Fv/Fm (0.331-0.426) and low alpha (0.098-0.130 /(µmol photons/m**2/s)) in December. Fv/Fm and alpha increased in March and May (0.468-0.588 and 0.141-0.438 /(µmol photons/m**2/s), respectively) indicating increased photosynthetic activity. In addition, increases in rETRmax (3.3-16.4 a.u.) and Ek (20-88 µmol photons/m**2/s) from December to May illustrates a higher potential for primary productivity as communities become better acclimated to under-ice light conditions. In conclusion, photosynthetic performance by ice algae (as assessed by PAM fluorometry) was tightly linked to sea ice salinity, temperature, and inorganic nutrient concentrations (mainly nitrogen).

Dissolved organic carbon (DOC) in Arctic ground ice, from northwest Canada, east Siberia, and Alaska

Thermal permafrost degradation and coastal erosion in the Arctic remobilize substantial amounts of organic carbon (OC) and nutrients which have accumulated in late Pleistocene and Holocene unconsolidated deposits. Permafrost vulnerability to thaw subsidence, collapsing coastlines and irreversible landscape change are largely due to the presence of large amounts of massive ground ice such as ice wedges. However, ground ice has not, until now, been considered to be a source of dissolved organic carbon (DOC), dissolved inorganic carbon (DIC) and other elements which are important for ecosystems and carbon cycling. Here we show, using biogeochemical data from a large number of different ice bodies throughout the Arctic, that ice wedges have the greatest potential for DOC storage, with a maximum of 28.6 mg/L (mean: 9.6 mg/L). Variation in DOC concentration is positively correlated with and explained by the concentrations and relative amounts of typically terrestrial cations such as Mg2+ and K+. DOC sequestration into ground ice was more effective during the late Pleistocene than during the Holocene, which can be explained by rapid sediment and OC accumulation, the prevalence of more easily degradable vegetation and immediate incorporation into permafrost. We assume that pristine snowmelt is able to leach considerable amounts of well-preserved and highly bioavailable DOC as well as other elements from surface sediments, which are rapidly frozen and stored in ground ice, especially in ice wedges, even before further degradation. We found that ice wedges in the Yedoma region represent a significant DOC (45.2 Tg) and DIC (33.6 Tg) pool in permafrost areas and a freshwater reservoir of 4200 km**3. This study underlines the need to discriminate between particulate OC and DOC to assess the availability and vulnerability of the permafrost carbon pool for ecosystems and climate feedback upon mobilization.

Mean dynamic topography and oceanographic parameters estimated from an inverse model and satellite geodesy, with link to model result in one single NetCDF file (392 MB), including the inverse data error covariance

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography-the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99-110, 2012, doi:10.1016/j.jog.2011.07.0069; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie, 2012, http://nbn-resolving.de/nbn:de:hbz:5n-29199). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.