Approximating method of frames

In this paper, the well-known method of frames approach to the signal decomposition problem is reformulated as a certain bilevel goal-attainment linear least squares problem. As a consequence, a numerically robust variant of the method, named approximating method of frames, is proposed on the basis of a certain minimal Euclidean norm approximating splitting pseudo-iteration-wise method.

Precipitation over the past four centuries in the Dieshan Mountains as inferred from tree rings: An introduction to an HHT-based method

To improve our understanding of the Asian monsoon system, we developed a hydroclimate reconstruction in a marginal monsoon shoulder region for the period prior to the industrial era. Here, we present the first moisture sensitive tree-ring chronology, spanning 501 years for the Dieshan Mountain area, a boundary region of the Asian summer monsoon in the northeastern Tibetan Plateau. This reconstruction was derived from 101 cores of 68 old-growth Chinese pine (Pinus tabulaeformis) trees. We introduce a Hilbert–Huang Transform (HHT) based standardization method to develop the tree-ring chronology, which has the advantages of excluding non-climatic disturbances in individual tree-ring series. Based on the reliable portion of the chronology, we reconstructed the annual (prior July to current June) precipitation history since 1637 for the Dieshan Mountain area and were able to explain 41.3% of the variance. The extremely dry years in this reconstruction were also found in historical documents and are also associated with El Niño episodes. Dry periods were reconstructed for 1718–1725, 1766–1770 and 1920–1933, whereas 1782–1788 and 1979–1985 were wet periods. The spatial signatures of these events were supported by data from other marginal regions of the Asian summer monsoon. Over the past four centuries, out-of-phase relationships between hydroclimate variations in the Dieshan Mountain area and far western Mongolia were observed during the 1718–1725 and 1766–1770 dry periods and the 1979–1985 wet period.

Loss on ignition as a method for estimating organic and carbonate content in sediments: reproducibility and comparability of results

Five test runs were performed to assess possible bias when performing the loss on ignition (LOI) method to estimate organic matter and carbonate content of lake sediments. An accurate and stable weight loss was achieved after 2 h of burning pure CaCO3 at 950 °C, whereas LOI of pure graphite at 530 °C showed a direct relation to sample size and exposure time, with only 40-70% of the possible weight loss reached after 2 h of exposure and smaller samples losing weight faster than larger ones. Experiments with a standardised lake sediment revealed a strong initial weight loss at 550 °C, but samples continued to lose weight at a slow rate at exposure of up to 64 h, which was likely the effect of loss of volatile salts, structural water of clay minerals or metal oxides, or of inorganic carbon after the initial burning of organic matter. A further test-run revealed that at 550 °C samples in the centre of the furnace lost more weight than marginal samples. At 950 °C this pattern was still apparent but the differences became negligible. Again, LOI was dependent on sample size. An analytical LOI quality control experiment including ten different laboratories was carried out using each laboratory's own LOI procedure as well as a standardised LOI procedure to analyse three different sediments. The range of LOI values between laboratories measured at 550 °C was generally larger when each laboratory used its own method than when using the standard method. This was similar for 950 °C, although the range of values tended to be smaller. The within-laboratory range of LOI measurements for a given sediment was generally small. Comparisons of the results of the individual and the standardised method suggest that there is a laboratory-specific pattern in the results, probably due to differences in laboratory equipment and/or handling that could not be eliminated by standardising the LOI procedure. Factors such as sample size, exposure time, position of samples in the furnace and the laboratory measuring affected LOI results, with LOI at 550 °C being more susceptible to these factors than LOI at 950 °C. We, therefore, recommend analysts to be consistent in the LOI method used in relation to the ignition temperatures, exposure times, and the sample size and to include information on these three parameters when referring to the method.