Changes in meltwater chemistry over a 20-year period following a thermal regime switch from polythermal to cold-based glaciation at Austre Broggerbreen, Svalbard

Our long-term study gives a rare insight into meltwater hydrochemistry following the transition of Austre Brøggerbreen from polythermal to cold-based glaciation and its continued retreat. We find that the processes responsible for ion acquisition did not change throughout the period of records but became more productive. Two regimes before and after July/August 2000 were identified from changes in solute concentrations and pH. They resulted from increased chemical weathering occurring in ice-marginal and proglacial environments that have become progressively exposed by glacier retreat. Carbonate carbonation nearly doubled between 2000 and 2010, whilst increases in the weathering of silicate minerals were also marked. In addition, the end of ablation season chemistry was characterized by reactions in long residence time flow paths like those in subglacial environments, in spite of their absence in the watershed. Furthermore, the retreat of the glacier caused the sudden re-routing of meltwaters through its immediate forefield during 2009, which more than doubled crustal ion yields in this particular year and influenced chemical weathering in 2010 regardless of a low water flux. Such a “flush” of crustally derived ions can be meaningful for downstream terrestrial and marine ecosystems. We therefore find that, during glacier retreat, the recently exposed forefield is the most chemically active part of the watershed, making high rates of weathering possible, even when ice losses have caused a switch to cold-based conditions with no delayed subglacial drainage flowpaths. In addition, the drainage system reorganization events result in significant pCO2 depletion in an otherwise high pCO2 system

Basic Methods for Computing Special Functions

This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website