Practical Use of Computationally Frugal Model Analysis Methods

Three challenges compromise the utility of mathematical models of groundwater and other environmental systems: (1) a dizzying array of model analysis methods and metrics make it difficult to compare evaluations of model adequacy, sensitivity, and uncertainty; (2) the high computational demands of many popular model analysis methods (requiring 1000's, 10,000 s, or more model runs) make them difficult to apply to complex models; and (3) many models are plagued by unrealistic nonlinearities arising from the numerical model formulation and implementation. This study proposes a strategy to address these challenges through a careful combination of model analysis and implementation methods. In this strategy, computationally frugal model analysis methods (often requiring a few dozen parallelizable model runs) play a major role, and computationally demanding methods are used for problems where (relatively) inexpensive diagnostics suggest the frugal methods are unreliable. We also argue in favor of detecting and, where possible, eliminating unrealistic model nonlinearities—this increases the realism of the model itself and facilitates the application of frugal methods. Literature examples are used to demonstrate the use of frugal methods and associated diagnostics. We suggest that the strategy proposed in this paper would allow the environmental sciences community to achieve greater transparency and falsifiability of environmental models, and obtain greater scientific insight from ongoing and future modeling efforts.     

Late Holocene climatic changes in Tierra del Fuego based on multiproxy analyses of peat deposits

A ca. 1400-yr record from a raised bog in Isla Grande, Tierra del Fuego, Argentina, registers climate fluctuations, including a Medieval Warm Period, although evidence for the ‘Little Ice Age’ is less clear. Changes in temperature and/or precipitation were inferred from plant macrofossils, pollen, fungal spores, testate amebae, and peat humification. The chronology was established using a ¹⁴C wiggle-matching technique that provides improved age control for at least part of the record compared to other sites. These new data are presented and compared with other lines of evidence from the Southern and Northern Hemispheres. A period of low local water tables occurred in the bog between A.D. 960-1020, which may correspond to the Medieval Warm Period date range of A.D. 950-1045 generated from Northern Hemisphere tree-ring data. A period of cooler and/or wetter conditions was detected between ca. A.D. 1030 and 1100 and a later period of cooler/wetter conditions estimated at ca. cal A.D. 1800-1930, which may correspond to a cooling episode inferred from Law Dome, Antarctica.     

Sea Ice Dynamics Induced by External Stochastic Fluctuations

The influence of stochastic fluctuations in the atmosphere and in the ocean caused by different occasional phenomena (noises) on dynamic processes of sea ice growth with a mushy layer is studied. It is shown that atmospheric temperature variances substantially increase the sea ice thickness, whereas dispersion variations of turbulent flows in the ocean to a great extent decrease the ice content produced by false bottom evolution.     

Hf isotope compositions and HREE variations in off-craton garnet and spinel peridotite xenoliths from central Asia

Garnet-facies continental mantle is poorly understood because the vast majority of mantle xenoliths in continental basalts are spinel peridotite. Peridotite xenoliths from Vitim (southern Siberia) and Mongolia provide some of the best samples of garnet and garnet-spinel facies off-craton lithospheric mantle. Garnets in those fertile to moderately depleted lherzolites show a surprisingly broad range of HREE abundances, which poorly correlate with modal and major oxide compositions. Some garnets are zoned and have Lu-rich cores. We argue that these features indicate HREE redistribution after the partial melting, possibly related to spinel-garnet phase transition on isobaric cooling. Most peridotites from Vitim have depleted to ultra-depleted Hf isotope compositions (calculated from mineral analyses: ε_Hf(0) = +17 to +45). HREE-rich garnets have the most radiogenic ε_Hf values and plot above the mantle Hf-Nd isotope array while xenoliths with normal HREE abundances usually fall within or near the depleted end of the MORB field. Model Hf isotope ages for the normal peridotites indicate an origin by ancient partial melt extraction from primitive mantle, most likely in the Proterozoic. By contrast, an HREE-rich peridotite yields a Phanerozoic model age, possibly reflecting overprinting of the ancient partial melting record with that related to a recent enrichment in Lu. Clinopyroxene-garnet Lu-Hf isochron ages (31-84 Ma) are higher than the likely eruption age of the host volcanic rocks (∼16 Ma). Garnet-controlled HREE migration during spinel-garnet and garnet-spinel phase transitions may be one explanation for extremely radiogenic ¹⁷⁶Hf/¹⁷⁷Hf reported for some mantle peridotites; it may also contribute to Hf isotope variations in sub-lithospheric source regions of mantle-derived magmas.     

Geomagnetically induced currents in power lines according to data on geomagnetic variations

The time derivative (d H/dt) of the geomagnetic field horizontal component (H) for seven intervals of high geomagnetic activity in 2003–2005 has been calculated, based on the data of Alma-Ata, Novosibirsk, and Irkutsk observatories, in order to estimate the probability of appearance of geomagnetically induced current (GIC), the value of which is linearly dependent on d H/dt, in power lines on the territory of Kazakhstan. The distributions of the H and d H/dt directions have been constructed; in this case it was most interesting that these distributions were narrow and extended along the magnetic meridian for Alma-Ata and were wider angular for Novosibirsk and Irkutsk. It has been indicated that large H values, determining significant GIC values, took place at a sudden commencement of strong storms, which had a character of a pulsed disturbance of the geomagnetic field, and during large-amplitude geomagnetic field pulsations. The duration of the periods of large |d H/dt| values exceeding the threshold (30 nT/min), when GIC could cause unwanted consequences in power circuits, has been determined.     

Trace element distribution in peridotite xenoliths from Tok, SE Siberian craton: A record of pervasive, multi-stage metasomatism in shallow refractory mantle

Spinel peridotite xenoliths in alkali basalts at Tok, SE Siberian craton range from fertile lherzolites to harzburgites and wehrlites; olivine-rich (70-84%) rocks are dominant. REE patterns in the lherzolites range from nearly flat for fertile rocks (14-17% cpx) to LREE-enriched; the enrichments are positively correlated with modal olivine, consistent with high-permeability of olivine-rich rocks during melt percolation. Clinopyroxene in olivine-rich Tok peridotites typically has convex-upward trace element patterns (La/Nd_PM < 1 and Nd/Yb_PM ? 1), which we consider as evidence for equilibration with evolved silicate liquids (with higher REE and lower Ti contents than in host basalts). Whole-rock patterns of the olivine-rich xenoliths range from convex-upward to LREE-enriched (La/Nd_PM > 1); the LREE-enrichments are positively correlated with phosphorus abundances and are mainly hosted by accessory phosphates and P-rich cryptocrystalline materials. In addition to apatite, some Tok xenoliths contain whitlockite (an anhydrous, halogen-poor and Na-Mg-rich phosphate), which is common in meteorites and lunar rocks, but has not been reported from any terrestrial mantle samples. Some olivine-rich peridotites have generations of clinopyroxene with distinct abundances of Na, LREE, Sr and Zr. The mineralogical and trace element data indicate that the lithospheric mantle section represented by the xenoliths experienced a large-scale metasomatic event produced by upward migration of mafic silicate melts followed by percolation of low-T, alkali-rich melts and fluids. Chromatographic fractionation and fractional crystallisation of the melts close to the percolation front produced strong LREE-enrichments, which are most common in the uppermost mantle and are related to carbonate- and P₂O₅-rich derivatives of the initial melt. Reversal and gradual retreat of the percolation front during thermal relaxation to ambient geotherm (“retrograde” metasomatism) caused local migration and entrapment of small-volume residual fluids and precipitation of volatile-rich accessory minerals. A distinct metasomatic episode, which mainly produced “anhydrous” late-stage interstitial materials was concomitant with the alkali basaltic magmatism, which brought the xenoliths to the surface.     

Compositional variations and heterogeneity in fertile lithospheric mantle: peridotite xenoliths in basalts from Tariat,Mongolia

Clinopyroxene-rich, poorly metasomatised spinel lherzolites are rare worldwide but predominate among xenoliths in five Quaternary basaltic eruption centres in Tariat, central Mongolia. High-precision analyses of the most fertile Tariat lherzolites are used to evaluate estimates of primitive mantle compositions; they indicate Mg#_PM = 0.890 while lower Mg# in the mantle are likely related to metasomatic enrichments in iron. Within a 10 × 20 km area, and between ~45 and ≥60 km depth, the sampled xenoliths suggest that the Tariat mantle does not show km-scale chemical heterogeneities and mainly consists of residues after low-degree melt extraction at 1–3 GPa. However, accessory (<1%) amphibole and phlogopite are unevenly distributed beneath the eruption centres. Ca abundances in olivine are controlled by temperature whereas Al and Cr abundances also depend on Cr/Al in coexisting spinel. Comparisons of conventional and high-precision analyses obtained for 30 xenoliths show that high-quality data, in particular for whole-rocks and olivines, are essential to constrain the origin of mantle peridotites. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Impacts of frontal stability and topography on cross-shelf exchange in the Northern Gulf of Mexico

The shelfbreak wintertime thermal front in the Northeastern Gulf of Mexico often exhibits meandering, eddy formation and warm-water intrusion. A high level of frontal variability plays an essential role in exchange processes across the shelf. This study examines the impacts of local frontal instability and bottom topography on turbulent heat exchange across the front using the results of two numerical models. Analysis of a series of numerical experiments reveals that the flow is baroclinically unstable. Predicted frontal instability contributes significantly to cross-frontal exchange and accounts for about 35% of the total eddy heat flux. Onshore eddy heat flux has the highest intensity at the frontal position. In addition, eddy activity and heat flux are sensitive to variation of bottom topography. For topographic features and frontal characteristics that are typical of the area, bottom steepness enhances the flux and is nearly proportional to the cross-frontal heat exchange. The study attempts to explain physical mechanisms that drive frontal circulation in the area and to quantify heat transport across the shelf. Estimated heat fluxes can provide important information for climate and ecosystem modeling of the Mississippi Bight.     

Lithospheric mantle beneath the south-eastern Siberian craton: petrology of peridotite xenoliths in basalts from the Tokinsky Stanovik

We provide petrographic, major and trace element data for over 30 spinel peridotite xenoliths from the Tokinsky Stanovik (Tok) volcanic field on the Aldan shield to characterize the lithospheric mantle beneath the south-eastern margin of the Siberian craton, which formed in the Mesoproterozoic. High equilibration temperatures (870–1,010°C) of the xenoliths and the absence of garnet-bearing peridotites indicate a much thinner lithosphere than in the central craton. Most common among the xenoliths are clinopyroxene-poor lherzolites and harzburgites with Al₂O₃ and CaO contents nearly as low as in refractory xenoliths from kimberlite pipes (Mir, Udachnaya) in the central and northern Siberian craton. By contrast, the Tok peridotites have higher FeO, lower Mg-numbers and lower modal orthopyroxene and are apparently formed by shallow partial melting (3 GPa). Nearly all Tok xenoliths yield petrographic and chemical evidence for metasomatism: accessory phlogopite, amphibole, phosphates, feldspar and Ti-rich oxides, very high Na₂O (2–3.1%) in clinopyroxene, LREE enrichments in whole-rocks.Electronic Supplementary Material Supplementary material is available for this article at