Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Helium isotope geochemistry of mid-ocean ridge basalts from the South Atlantic

We report new helium isotope results for 49 basalt glass samples from the Mid-Atlantic Ridge between 1°N and 47°S.³He/⁴He in South Atlantic mid-ocean ridge basalts (MORB) varies between 6.5 and 9.0 R_A (R_A is the atmospheric ratio of1.39 × 10⁻⁶), encompassing the range of previously reported values for MORB erupted away from high³He/⁴He hotspots such as Iceland. He, Sr and Pb isotopes show systematic relationships along the ridge axis. The ridge axis is segmented with respect to geochemical variations, and local spike-like anomalies in³He/⁴He, Pb and Sr isotopes, and trace element ratios such as(La/Sm)_N are prevalent at the latitudes of the islands of St. Helena, Tristan da Cunha and Gough to the east of the ridge. The isotope systematics are consistent with injection beneath the ridge of mantle “blobs” enriched in radiogenic He, Pb and Sr, derived from off-axis hotspot sources. The variability in³He/⁴He along the ridge can be used to refine the hotspot source-migrating-ridge sink model.

MORB from the 2–7°S segment are systematically the least radiogenic samples found along the mid-ocean ridge system to date. Here the depleted mantle source is characterized by⁸⁷Sr/⁸⁶Sr of 0.7022, Pb isotopes close to the geochron and with²⁰⁶Pb/²⁰⁴Pb of 17.7, and³He/⁴He of 8.6–8.9 R_A. The “background contamination” of the subridge mantle, by radiogenic helium derived from off-ridge hotspots, displays a maximum between 20 and 24°S. The HePb and HeSr isotope relations along the ridge indicate that the³He/⁴He ratios are lower for the hotspot sources of St. Helena, Tristan da Cunha and Gough than for the MORB source, consistent with direct measurements of³He/⁴He ratios in the island lavas. Details of the HeSrPb isotope systematics between 12 and 22°S are consistent with early, widespread dispersion of the St. Helena plume into the asthenosphere, probably during flattening of the plume head beneath the thick lithosphere prior to continental breakup. The geographical variation in theHe/Pbratio deduced from the isotope systematics suggests only minor degassing of the plume during this stage. Subsequently, it appears that the plume component reaching the mid-Atlantic ridge was partially outgassed of He during off-ridge hotspot volcanism and related melting activity.

Overall, the similar behavior of He and Pb isotopes along the ridge indicates that the respective mantle sources have evolved under conditions which produced related He and Pb isotope variations.     

The Dublin Gulch intrusion-hosted gold deposit, Tombstone plutonic suite, Yukon Territory, Canada

The Dublin Gulch intrusion is a member of the Tombstone plutonic suite, a linear belt of middle Cretaceous intrusions that extend across the Yukon Territory. Like many of the intrusions in this suite, the Dublin Gulch intrusion is associated with several different zones of gold and tungsten mineralization, within and immediately adjacent to the intrusion. The Eagle zone (50.3 Mt @ 0.93 g/t gold), located in the southwestern part of the Dublin Gulch intrusion, hosts the most significant concentration of gold in the area. The gold occurs in a broadly east-west-striking, steeply south-dipping series of sheeted veins. The veins consist of early quartz-scheelite-pyrrhotite-pyrite-arsenopyrite, and are associated with K-feldspar-albite alteration envelopes. These grade out to and are overprinted by sericite-carbonate-chlorite alteration. The same assemblage also occurs in veinlets that refracture sheeted quartz veins and contain the majority of the gold. The gold occurs with molybdenite, lead-bismuth-antimony sulfosalts, galena, and bismuthinite. Gold correlates strongly with bismuth (r²=0.9), a relationship common to several intrusion-related gold deposits, but has a poor correlation with all other elements. Tungsten and molybdenum have a weak inter-element correlation (r²=0.55) and paragenetically pre-date the majority of gold precipitation. Lead, zinc, copper, silver, antimony, and arsenic have moderate to strong inter-element correlations (0.58 to 0.93). The change from tungsten-bearing mineralization through to gold-bismuth-rich ores with elevated syn- to post-ore lead, zinc, copper, silver, antimony, and arsenic can be grossly correlated with a change in hydrothermal fluid composition. Early scheelite-bearing quartz contains primary CO₂-rich fluid inclusions, which are post-dated by secondary inclusions with higher salinities (up to 15 wt% NaCl equiv.) and less CO₂. These latter inclusions are interpreted to coincide with the later gold-bismuth and base metal mineralization. The favored genetic model is one in which early CO₂-rich fluids exsolved from a magma with an initially high CO₂ content, but progressively became more saline and H₂O-rich as the system evolved.     

The Aristarchus-Harbinger region of the moon: Surface geology and history from recent remote-sensing observations

The region including the Aristarchus Plateau and Montes Harbinger is probably the most diverse, geologically, of any area of comparble size on the Moon. This part of the northwest quadrant of the lunar near side includes unique dark mantling material; both the densest concentration and the largest of the sinuous rilles; apparent volcanic vents, sinks, and domes; mare materials of various ages and colors; one of the freshest large craters (Aristarchus) with ejecta having unique colors and albedos; and three other large craters in different states of flooding and degradation (krieger, Herodotus, and Prinz). The three best-authenticated lunar transient phenomena were also observed here.This study is based principally on photographic and remote sensing observations made from Earth and Apollo orbiting space craft. Results include (1) delineation of geologic map units and their stratigraphic relationships; (2) discussion of the complex interrelationships between materials of volcanic and impact origin, including the effects of excavation, redistribution and mixing of previously deposited materials by younger impact craters; (3) deduction of physical and chemical properties of certain of the geologic units, based on both the remote-sensing information and on extrapolation of Apollo data to this area; and (4) development of a detailed geologic history of the region, outlining the probable sequence of events that resulted in its present appearance.A primary concern of the investigation has been anomalous red dark mantle on the Plateau. Based on an integration of Earth- and lunar orbit-based data, this layer seems to consist of fine-grained, block-free material containing a relatively large fraction of orange glass. It is probably of pyroclastic origin, laid down at some time during the Imbrian period of mare flooding.     

Temporal and Spatial Dynamics of Diel-Cycling Hypoxia in Estuarine Tributaries

The distribution and intensity of hypoxia (low dissolved oxygen) in estuaries is increasing worldwide due to cultural eutrophication. This study quantifies the strength of associations between the duration of diel-cycling severe hypoxia (≤2 mg O₂ l⁻¹) in bottom water (∼15 cm above bottom) of a shallow (<2 m) coastal lagoon estuary (Delaware, USA) and abiotic environmental variables (water temperature, insolation, tide, streamflow, and wind) and predicts the duration of severe hypoxia given different combinations of these variables. The intensity and spatial extent and dynamics of diel-cycling severe hypoxia events were defined. Vertical variability in dissolved oxygen (DO) concentration during the daytime was also determined. During the summers of 2001–2005, bottom DO data were collected for periods of weeks to months at multiple sites using automated sondes. Multiple linear regression (MLR) and regression tree analysis (RTA) were used to determine the relative importance of the environmental variables in predicting the number of hours of severe hypoxia per day. Key findings of the study were that severe hypoxia events of minutes to hours in duration occurred frequently in all four tributaries sampled, primarily between 0200 and 1000 hours. Severe hypoxia duration and diel-cycling amplitudes of DO concentration increased in the up-tributary direction. Hierarchically, the duration of severe hypoxia was influenced mostly by the mean daily water temperature, then by preceding days’ total insolation, percentage of morning hours (02:00 to 10:00 a.m.) ebb tide, and daily streamflow. Collectively, the variables examined by the MLR and the RTA approaches accounted for 62% and 65% of the variability in the duration of severe hypoxia, respectively. RTA demonstrated that daily mean water temperature above 26.3°C and previous day’s total insolation below 13.6 kW m⁻² were associated with the longest lasting severe hypoxic events (9.56 h). The environmental variables and combinations of conditions that modulate or augment diel-cycling hypoxia presented in this paper enhance understanding of this widespread and growing phenomenon and provide additional insight regarding the extent to which it can impact food webs in very shallow estuarine waters that often serve as nursery habitat.     

Tectonothermal events in the Olympic IOCG Province constrained by apatite and REE-phosphate geochronology

The Olympic iron oxide–copper–gold province in South Australia contains numerous deposits and prospects, including the Olympic Dam Cu–U–Au–Ag deposit and the Acropolis prospect. The Acropolis prospect comprises massive, coarse-grained magnetite–apatite veins partly replaced by a hematite-stable assemblage. The apatite grains in the veins contain zones with abundant inclusions of other minerals (including monazite and xenotime) and low trace-element concentrations relative to the inclusion-free zones. The inclusion-rich apatite zones are interpreted to be formed from the recrystallisation of the inclusion-free apatite and remobilisation of U, Th and rare earth element (REE) from apatite into monazite and xenotime. Apatite, monazite and xenotime are all established U–Th–Pb geochronometers and offer the potential to constrain the alteration history of the Acropolis prospect. The LA-ICPMS U–Pb age of inclusion-free apatite is within error of the age of the host volcanic units (ca 1.59 Ga). Inclusion-rich apatite yields both near-concordant analyses that are within error of the inclusion-free apatite as well as highly disturbed (discordant) analyses. The most concordant analyses of monazite (Th–Pb) inclusions and xenotime (U–Pb) inclusions and rim grains indicate an alteration event occurred at ca 1.37 Ga and possibly also at ca 500 Ma. The disparity in age of the inclusion-rich apatite and the REE-phosphate inclusions (and rim grains) is suggested to be owing to the apatite being initially recrystallised at ca 1.59 Ga and modified again by a later event that also formed (or coarsened) most of the inclusions. Partial resetting of the majority of the monazite inclusions as well as the presence of significant amounts of common Pb has complicated the interpretation of the monazite results. In contrast, xenotime is a more robust geochronometer in this setting. The ages of the two post-1.59 Ga events that appear to have affected the Acropolis prospect do not correspond to any events known to have occurred in the Gawler Craton. The earlier (ca 1.37 Ga) age instead corresponds best with metamorphic–magmatic–hydrothermal activity in Laurentia, consistent with the proximity of Laurentia and the Gawler Craton inferred from palaeogeographic reconstructions. The later (ca 500 Ma) event corresponds to the Delamerian Orogeny and has been shown by prior studies to have also affected the Olympic Dam deposit.     

δ18O record and temperature change over the past 100 years in ice cores on the Tibetan Plateau

The 213 m ice core from the Puruogangri Ice Field on the Tibetan Plateau facilitates the study of the regional temperature changes with its δ18O record of the past 100 years. Here we combine information from this core with that from the Dasuopu ice core (from the southern Tibetan Plateau), the Guliya ice core (from the northwestern Plateau) and the Dunde ice core (from the northeastern Plateau) to learn about the regional differences in temperature change across the Tibetan Plateau. The δ18O changes vary with region on the Plateau, the variations being especially large between South and North and between East and West. Moreover, these four ice cores present increasing δ18O trends, indicating warming on the Tibetan Plateau over the past 100 years. A comparative study of Northern Hemisphere (NH) temperature changes, the δ18O-reflected temperature changes on the Plateau, and available meteorological records show consistent trends in overall warming during the past 100 years.     

GLAST large area telescope multiwavelength planning

Gamma-ray astrophysics depends in many ways on multiwavelength studies. The Gamma-ray Large Area Space Telescope (GLAST) Large Area Telescope (LAT) Collaboration has started multiwavelength planning well before the scheduled 2007 launch of the observatory. Some of the high-priority multiwavelength needs include: (1) availability of contemporaneous radio and X-ray timing of pulsars; (2) expansion of blazar catalogs, including redshift measurements; (3) improved observations of molecular clouds, especially at high galactic latitudes; (4) simultaneous broad-band blazar monitoring; (5) characterization of gamma-ray transients, including gamma ray bursts; (6) radio, optical, X-ray and TeV counterpart searches for reliable and effective sources identification and characterization. Several of these activities are needed to be in place before launch.