Accumulation rate and stable oxygen isotope ratios of the ice cores from the North Greenland Traverse

We present for the first time all 12 d18O records obtained from ice cores drilled in the framework of the North Greenland Traverse (NGT) between 1993 and 1995 in northern Greenland. The cores cover an area of 680 km × 317 km, 10 % of the Greenland ice sheet. Depending on core length (100-175 m) and accumulation rate (90-200 kg/m**2/a) the single records reflect an isotope-temperature history over the last 500-1100 years. Lowest d18O mean values occur north of the summit and east of the main divide as a consequence of Greenland's topography. In general, ice cores drilled on the main ice divide show different results than those drilled east of the main ice divide that might be influenced by secondary regional moisture sources. A stack of all NGT records and the NGRIP record is presented with improved signal-to-noise ratio. Compared to single records, this stack represents the mean d18O signal for northern Greenland that is interpreted as proxy for temperature. Our northern Greenland d18O stack indicates distinctly enriched d18O values during medieval times, about AD 1420 ± 20 and from AD 1870 onwards. The period between AD 1420 and AD 1850 has depleted d18O values compared to the average for the entire millennium and represents the Little Ice Age. The d18O values of the 20th century are comparable to the medieval period but are lower than that about AD 1420.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.