The GPS Toolbox

The GPS Toolbox is dedicated to highlighting algorithms utilized by GPS engineers and scientists. If you have an interesting algorithm you would like to share with our readers or if you have a topic you would like to see covered in a future column, contact us at gps-toolbox@ngs.noaa.gov. To comment on the algorithms presented here, or to leave a request for an algorithm you may be looking for, visit our Web site (http://www.ngs.noaa.gov/gps-toolbox). ? 2000 John Wiley & Sons, Inc.     

Inversion of electromagnetic data: An overview of new techniques

This paper explores some of the newer techniques for acquiring and inverting electromagnetic data. Attention is confined primarily to the 2d magnetotelluric (MT) problem but the inverse methods are applicable to all areas of EM induction. The basis of the EMAP technique of Bostick is presented along with examples to illustrate the efficacy of that method in structural imaging and in overcoming the deleterious effects of near-surface distortions of the electric field. Reflectivity imaging methods and the application of seismic migration techniques to EM problems are also explored as imaging tools. Two new approaches to the solution of the inverse problem are presented. The AIM (Approximate Inverse Mapping) inversion of Oldenburg and Ellis uses a new way to estimate a perturbation in an iterative solution which does not involve linearization of the equations. The RRI (Rapid Relaxation Inverse) of Smith and Booker shows how approximate Fréchet derivatives and sequences of 1d inversions can be used to develop a practical inversion algorithm. The overview is structured to provide insight about the latest inversion techniques and also to touch upon most areas of the inverse problem that must be considered to carry out a practical inversion. These include model parameterization, methods of calculating first order sensitivities, and methods for setting up a linearized inversion.     

The place of rural, remote and least-wealthy small islands in international water development: the nexus of geography–technology sustainability in Chuuk State, Federated States of Micronesia

Many least-wealthy, rural, remote and resource-poor small island communities are unlikely to benefit from high-profile global water improvement initiatives. Their small landmasses, geologic composition, geography, social and technological isolation, colonial history, and weak educational and financial resources constitute significant barriers to improving access to safe drinking water. This paper discusses the relatively unique position of such island societies in the international community, providing a case study of the Federated States of Micronesia that integrates data and information pertaining to water resources management and governance, spanning from the island village to national scale. A vision is offered regarding the interaction between small island human and biophysical water systems, manifesting ways to pursue water resource development to improve public health which are constructed to be economically, physically and culturally sustainable.     

Pyroxene-Olivine-Quartz Assemblages in Rocks Associated with the Nain Anorthosite Massif, Labrador

Unusually iron-rich pyroxene and olivine occur in rocks associatedwith the Nain anorthosite massif, Labrador. Adamellite and granodioritecontain orthopyroxene (inverted from pigeonite) as iron-richas Ca₆Fe₈₂Mg₁₂; comparison with experimental data suggests aminimum pressure of crystallization of 5 kb. Some of these iron-richpyroxene crystals have broken down, apparently upon decreasingpressure, to yield intergrowths of less iron-rich orthopyroxene(near Ca₇Fe₇₂Mg₂₁), ferroaugite, fayalite (near Fo₉), and quartz.Other rocks, monzonites, contain pyroxenes with calcium-poorcores and ferroaugite rims, as well as crystals composed ofbroad lamellae of ferroaugite and orthopyroxene in sub-equalproportions. Analysis of one such crystal with unusually thinand closely spaced lamellae yielded a bulk composition of Ca₂₄Fe₅₈Mg₁₈.Such pyroxenes probably crystallized near or above the crestof the augite-pigeonite two-phase region, probably above 925°C. This high temperature suggests that the monzonites crystallizedfrom relatively dry magmas. If they represent a residual fractionderived from the same magma as the anorthosite, then that magmamust have been nearly anhydrous. Pigeonite rather than orthopyroxene was the primary magmaticCa-poor pyroxene in most of the Nain rocks studied here. Nucleationrates apparently were low under subsolidus conditions, and low-Capigeonite (Ca₂Fe₇₈Mg₂₀) is present in grains where orthopyroxenedid not nucleate as pigeonite cooled and exsolved ferroaugite.Iron-rich orthopyroxene (Ca₂Fe₇₉M₁₉) crystallized instead ofpigeonite in a Greenland quartz syenite that contains more abundanthydrous phases.     

Trace Element and Isotope Geochemistry of the Volcanic Rocks of Bequia, Grenadine Islands, Lesser Antilles Arc: a Study of Subduction Enrichment and Intra-crustal Contamination

Pliocene volcanics on the island of Bequia comprise two interbeddedsuites of basalts and andesites. The isotopically homogeneoussuite (IHS) has a limited range of Sr—Nd—Pb isotopes(⁸⁷Sr/⁸⁶Sr 0.7040–0.7046, ¹⁴³ Nd/¹⁴⁴ Nd 0.5130 and ²⁰⁶Pb/²⁰⁴Pb 19.36–19.51), and mantle-like ¹⁸O values (5.5in clinopyroxene). The isotopically diverse suite (IDS) is characterizedby much wider ranges of radiogenic isotopes (⁸⁷ Sr/⁸⁶Sr 0.7048–0.7077,¹⁴³ Nd/¹⁴⁴ Nd 0.5128–0.5123 and ²⁰⁶ Pb/²⁰⁴ Pb 19.7–20.2),in which all of the Sr and Pb ratios are higher and Nd ratiosare lower than those of the IHS. The IDS is also characterizedby high ¹⁸ O values, up to 7.6 in clinopyroxene. The Sr andPb isotope ratios are too high, and the Nd isotope ratios aretoo low in the IDS for any of these lavas to be derived fromunmodified depleted mantle. Both suites are petrologically very similar and their majorelement compositions and phenocryst contents suggest that theywere formed largely by fractional crystallization of a hydroustholeiitic melt at pressures <3 kbar. The isotopic ratiosand enrichments in large ion lithophile elements (LILE), andto some extent light rare earth elements (LREE), as comparedwith mid-ocean ridge basalts (MORB), of the IHS lavas suggestthat they were derived from a depleted mantle source which hadbeen re-enriched by the addition of 1–4% of a subductioncomponent. This component probably comprised a mixture of dehydrationfluids, and perhaps minor siliceous melts, released from subductingsediments and mafic crust. The extreme isotopic ranges, largeenrichments in incompatible elements, more fractionated LREEpatterns and higher ¹⁸ O values of the IDS lavas are interpretedas resulting from 10–55% assimilation—fractionalcrystallization of sediments, derived from the Guyana Shield,which are present in the arc crust, by IHS type melts. KEY WORDS: trace elements; radiogenic isotopes; arc lavas; Lesser Antilles ^*Corresponding author.     

Real-time multi-model decadal climate predictions

We present the first climate prediction of the coming decade made with multiple models, initialized with prior observations. This prediction accrues from an international activity to exchange decadal predictions in near real-time, in order to assess differences and similarities, provide a consensus view to prevent over-confidence in forecasts from any single model, and establish current collective capability. We stress that the forecast is experimental, since the skill of the multi-model system is as yet unknown. Nevertheless, the forecast systems used here are based on models that have undergone rigorous evaluation and individually have been evaluated for forecast skill. Moreover, it is important to publish forecasts to enable open evaluation, and to provide a focus on climate change in the coming decade. Initialized forecasts of the year 2011 agree well with observations, with a pattern correlation of 0.62 compared to 0.31 for uninitialized projections. In particular, the forecast correctly predicted La Niña in the Pacific, and warm conditions in the north Atlantic and USA. A similar pattern is predicted for 2012 but with a weaker La Niña. Indices of Atlantic multi-decadal variability and Pacific decadal variability show no signal beyond climatology after 2015, while temperature in the Niño3 region is predicted to warm slightly by about 0.5 °C over the coming decade. However, uncertainties are large for individual years and initialization has little impact beyond the first 4 years in most regions. Relative to uninitialized forecasts, initialized forecasts are significantly warmer in the north Atlantic sub-polar gyre and cooler in the north Pacific throughout the decade. They are also significantly cooler in the global average and over most land and ocean regions out to several years ahead. However, in the absence of volcanic eruptions, global temperature is predicted to continue to rise, with each year from 2013 onwards having a 50 % chance of exceeding the current observed record. Verification of these forecasts will provide an important opportunity to test the performance of models and our understanding and knowledge of the drivers of climate change.     

Availability of suitable land-fast ice and predation as factors limiting ringed seal populations, Phoca hispida, in Svalbard

We examined the stability of fast ice areas in western and northern Spitsbergen, the area north of Nordaustlandet, the bays and sounds of Hinlopen Stretet and the large area in the northern part of Storfjorden. NOAA satellite imagery from 1974 and 1988 and NOAA (AVHRR) imagery from 1980-87 were used to determine the dates of freeze-up and break-up. The number of days of fast ice present before the nominal birth date of ringed seal pups were computed for all major bays and fjords. Ice thickness was then computed from these data. Known prime breeding habitat in Svalbard is found in areas near glacier fronts in protected fjords and bays, where densities of birth lairs are 5.46 km⁻², corresponding to a ringed seal female density of 2.6 km⁻². Most of the ringed seal breeding habitat in Svalbard, however, consists of flat fjord ice where snow accumulation is rarely deep enough to permit birth lair construction. In these areas pups are often born in the open. Based on breathing hole densities, the density of adult females in the flat ice areas in the breeding period was estimated to 0.98 km⁻². A preliminary estimate is that approximately 19,500 pups could be born annually in the fast ice of Svalbard. Annual recruitment could be quite variable given the unpredictable nature of the fast ice areas and the high predation mortality on newborn pups. Discrepancies between our calculated ringed seal production and numbers of seals required to feed the large polar bear population in the area signal cause for management concern.