Periodic time series modeling of environmental proxy records with guaranteed positive growth rate estimation

Identifying a periodic time-series model from environmental records, without imposing the positivity of the growth rate, does not necessarily respect the time order of the data observations. Consequently, subsequent observations, sampled in the environmental archive, can be inversed on the time axis, resulting in a non-physical signal model. In this paper an optimization technique with linear constraints on the signal model parameters is proposed that prevents time inversions. The activation conditions for this constrained optimization are based upon the physical constraint of the growth rate, namely, that it cannot take values smaller than zero. The actual constraints are defined for polynomials and first-order splines as basis functions for the nonlinear contribution in the distance-time relationship. The method is compared with an existing method that eliminates the time inversions, and its noise sensitivity is tested by means of Monte Carlo simulations. Finally, the usefulness of the method is demonstrated on the measurements of the vessel density, in a mangrove tree, Rhizophora mucronata, and the measurement of Mg/Ca ratios, in a bivalve, Mytilus trossulus.

Faunal evidence of a Holocene pluvial phase in Southern Arabia with remarks on the morphological variability of Helenina anderseni

Although foraminifera have been found living in inland saline lakes isolated from the sea, this phenomenon has rarely been recognized in the fossil record. This study documents the occurrence of benthic foraminifera in Holocene lake sediments located nearly 500 km inland from the Red Sea, in the Al-Mundafan region of southern Saudi Arabia. The lake formed during a regional pluvial period, 10,500–6000 yr BP. The presence of foraminifera and brackish charophytes in the studied section represent an interval when the lake was slightly brackish due to high evaporation. The studied sediments yielded a bispecific benthic foraminiferal fauna comprised of Helenina anderseni and Trichohyalus aguayoi, as well as the brackish charophyte genus Lamprothamnium. The benthic foraminifera are species characteristic of mangrove swamps, salt marshes, and lagoons, which are environments currently widespread along the Red Sea coasts. Because the Al Mundafan area was never connected to the sea during the Quaternary, wading birds must have been the vector that transported the foraminifera to the paleolake.