Eos Trans Research Articles

Strahler number of natural language sentences in comparison with random trees

The Strahler number was originally proposed to characterize the complexity of river bifurcation and has found various applications. This article proposes a computation of the Strahler number’s upper and lower limits for natural language sentence tree structures. Through empirical measurements across grammatically annotated data, the Strahler number of natural language sentences is shown to be almost 3 or 4, similar to the case of river bifurcation as reported by Strahler (1957 Eos Trans. Am. Geophys. Union 38 913–20). Based on the theory behind this number, we show that there is a kind of lower limit on the amount of memory required to process sentences. We consider the Strahler number to provide reasoning that explains reports showing that the number of required memory areas to process sentences is 3–4 for parsing (Schuler et al 2010 Comput. Linguist. 36 1–30), and reports indicating a psychological ‘magical number’ of 3–5 (Cowan 2001 Behav. Brain Sci. 24 87–114). An analytical and empirical analysis shows that the Strahler number is not constant but grows logarithmically. Therefore, the Strahler number of sentences is derived from the range of sentence lengths. Furthermore, the Strahler number is not different for random trees, which could suggest that its origin is not specific to natural language.

Engineering better science education

Thanks to Stephen Pompea and Pedro Russo for their comprehensive overview of science education activities (Physics Today, September 2021, page 26). The authors mention in passing that the evaluation of innovative science education projects was included in their studies of educational transformation. It would be interesting to learn what was found in their evaluations and in others that may have been performed. NSF alone spends some $1 billion on STEM (science, technology, engineering, and mathematics) education, so it is important to assess what effects those activities have had on science appreciation and competence.I constructed a small observatory in my town and operated it with NSF and NASA support for over 20 years. The opportunity to increase the awareness of astronomy in my community was enjoyable.11. P. Foukal, Eos Trans. AGU 95, 63 (2014). https://doi.org/10.1002/2014EO070004 But the experience raised some concerns about the current emphasis in science education. For one, I was surprised to find that while there are many astronomy projects on the Web focused on specific topics like building a model solar system or a rocket, the one resource that elementary or middle school teachers might most need—a comprehensive introduction to astronomy at that level—seems to have been overlooked. The only such general introduction that my colleagues and I were able to find at that time was an excellent textbook by Jay Pasachoff22. J. Pasachoff, Science Explorer: Astronomy, Prentice-Hall (2000). that wasn’t available anymore, although a revised edition has since appeared. An experienced teacher working with me commented that the currently popular emphasis of Web-based resources for teachers and students on relatively narrow topics makes it difficult to present a subject like astronomy cohesively.Another concern is the impact of too many curriculum changes on teachers. Our daughter teaches third grade, and one wonders how many enthusiasts of frequently revamping STEM curricula understand how much work goes into handling 25 rambunctious kids and their sometimes-difficult parents. Attrition of experienced teachers is a serious problem, and finding out that they need to master yet another way to teach math or science could be the last straw for some.It would be interesting to hear from the authors whether such concerns have been covered in past evaluations or how they might be addressed in the future.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. P. Foukal, Eos Trans. AGU 95, 63 (2014). https://doi.org/10.1002/2014EO070004, Google ScholarCrossref2. J. Pasachoff, Science Explorer: Astronomy, Prentice-Hall (2000). Google Scholar© 2022 American Institute of Physics.

Subdiffusive flow in a composite medium with a communicating (absorbing) interface

Two-dimensional subdiffusion in media separated by a partially communicating interface is considered. Starting with the appropriate Green’s functions, solutions are developed in terms of the Laplace transformation reflecting two circumstances at the interface: situations where there is perfect contact and situations where the interface offers a resistance. Asymptotic solutions are derived; limiting forms of the expressions reduce to known solutions for both classical diffusion and subdiffusion. Specifics are analyzed in depth with reference to flow in porous media with potential applications to the evaluation of the role of subsurface faults and flow in fractured rocks. Characteristics of the derivative responses are documented extensively as they are the linchpin for evaluation of pressure tests. Results given here may be used for evaluation at the Theis (1935; Eos Trans. AGU 2, 519–524) scale along with geological and geophysical properties, and production statistics. Yet a subdiffusive model does not imply a single value for properties. The method presented here may be extended to multiple contiguous media and to subdiffusive transport in many contexts (complex wellbores such as inclined, fractured and horizontal wells, situations such as sequestration, production of geothermal systems, etc.).

Is public awareness and perceived threat of climate change associated with governmental mitigation targets?

Social scientists and science communicators are concerned about the apparent discrepancy between the scientific consensus on climate change (Anderegg et al. Proc Natl Acad Sci 107:12107–12109, 2010; Doran and Zimmerman EOS Trans Am Geophys Union 90:22–3, 2009) and the general public’s views (Knight Environ Sociol 2:101–113, 2016; Lee et al. Nat Clim Chang 5:1014–1020, 2015). It is reasoned that increased public awareness and perceived threat of climate change may pressure governments to enact policy to counteract climate change (e.g. setting stringent carbon emissions targets). Despite a logical link between public awareness and government-set emissions targets, this relationship remains untested. We examined the relationship between public awareness about and perceived threat of climate change and governmental emissions targets across 71 countries and 1 region. We found a positive association between the proportions of a country’s population that are aware of climate change and the unconditional emissions reduction targets set by that country in the Paris Agreement (Rogelj et al. Nature 534:631–639, 2016). However, the proportion of people in a country who perceive climate change as a personal threat was not associated with higher emissions reduction targets. Our results suggest that public awareness may be an important part of garnering the public support required for policies designed to mitigate climate change to succeed.

Locations and magnitudes of earthquakes in Central Asia from seismic intensity data

We apply the Bakun and Wentworth (Bull Seism Soc Am 87:1502–1521, 1997) method to determine the location and magnitude of earthquakes occurred in Central Asia using MSK-64 intensity assignments. The attenuation model previously derived and validated by Bindi et al. (Geophys J Int, 2013) is used to analyse 21 earthquakes that occurred over the period 1885–1964, and the estimated locations and magnitudes are compared to values available in literature. Bootstrap analyses are performed to estimate the confidence intervals of the intensity magnitudes, as well as to quantify the location uncertainty. The analyses of seven significant earthquakes for the hazard assessment are presented in detail, including three large historical earthquakes that struck the northern Tien-Shan between the end of the nineteenth and the beginning of the twentieth centuries: the 1887, M 7.3 Verny, the 1889, M 8.3 Chilik and the 1911, M 8.2 Kemin earthquakes. Regarding the 1911, Kemin earthquake the magnitude values estimated from intensity data are lower (i.e. MILH = 7.8 and MIW = 7.6 considering surface wave and moment magnitude, respectively) than the value M = 8.2 listed in the considered catalog. These values are more in agreement with the value M S = 7.8 revised by Abe and Noguchi (Phys Earth Planet In, 33:1–11, 1983b) for the surface wave magnitude. For the Kemin earthquake, the distribution of the bootstrap solutions for the intensity centre reveal two minima, indicating that the distribution of intensity assignments do not constrain a unique solution. This is in agreement with the complex source rupture history of the Kemin earthquake, which involved several fault segments with different strike orientations, dipping angles and focal mechanisms (e.g. Delvaux et al. in Russ Geol Geophys 42:1167–1177, 2001; Arrowsmith et al. in Eos Trans Am Geophys Union 86(52), 2005). Two possible locations for the intensity centre are obtained. The first is located on the easternmost sub-faults (i.e. the Aksu and Chon-Aksu segments), where most of the seismic moment was released (Arrowsmith et al. in Eos Trans Am Geophys Union 86(52), 2005). The second location is located on the westernmost sub-faults (i.e. the Dzhil'-Aryk segment), close to the intensity centre location obtained for the 1938, M 6.9 Chu-Kemin earthquake (MILH = 6.9 and MIW = 6.8).

History of Geophysics Fellowship awarded

Inspired by an article in an issue of Eos from April 1970, Gabe Henderson discovered a legacy of correspondence from former AGU president Helmut Landsberg detailing his views in the early days of the climate science debate. Thanks to AGU donors and the creation of a new fellowship by AGU's History of Geophysics Committee, Henderson, a Ph.D. candidate at Michigan State University, is conducting research on Landsberg's papers at the University of Maryland, College Park, continuing his study of the broad history of geophysics and the link between the past and future of climate science. In April 1970, Henderson says, AGU president Helmut Landsberg called for S. Fred Singer to lead a special committee on environmental quality to evaluate the geophysical aspects of environmental problems, dispassionately (H. E. Landsberg,Eos Trans. AGU, 51, 243, doi:10.1029/EO051i004p00243). Because environmental problems were hardly given a second thought at that time, Landsberg's request could have faded from the consciousness of geoscientists and from the pages of history.

Another exchange on climate change

Although I enjoyed most of Steve Sherwood’s article on science controversy, I was a bit surprised to read a jab at geologists that sounded more like what I’d expect to hear from physicist caricature Sheldon Cooper of CBS’s The Big Bang Theory than from an article in a serious publication. Sherwood suggests that traditional geologists “emphasize empiricism and classification” and “consider ab initio theoretical approaches to be hopeless.” (A more derogatory phrasing I’ve heard from other physicists is that “geology is just stamp collecting.”) Especially since the advent of plate tectonic theory, academic geology has in fact emphasized testing hypotheses about Earth processes and not simple classification.Sherwood’s claim that geologists are as skeptical about global warming as the general public is also misleading. The article he cites11. P. T. Doran, M. K. Zimmerman, Eos Trans. Am. Geophys. Union 90 (3), 22 (2009). https://doi.org/10.1029/2009EO030002 does note that only 47% of 103 surveyed economic geologists—those who study mining, oil and gas, and so forth—agree that “human activity is a significant contributing factor in changing mean global temperatures,” but the same survey showed that among 1749 publishing geoscientists surveyed, 89% agree.22. M. K. Zimmerman, “The consensus on the consensus—An opinion survey of Earth scientists on global climate change,” MS thesis, University of Illinois, Chicago (2008). The resistance of some geologists to accept anthropogenic warming may be related to their financial reliance on the fossil-energy industry, but aspersions on geologists’ use of the scientific method are not warranted.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. P. T. Doran, M. K. Zimmerman, Eos Trans. Am. Geophys. Union 90 (3), 22 (2009). https://doi.org/10.1029/2009EO030002, Google ScholarCrossref2. M. K. Zimmerman, “The consensus on the consensus—An opinion survey of Earth scientists on global climate change,” MS thesis, University of Illinois, Chicago (2008). Google Scholar© 2012 American Institute of Physics.

NASA scientific integrity policy

On 16 December, NASA became the latest U.S. federal agency to issue a scientific integrity policy. It was issued less than 10 days after the U.S. National Oceanic and Atmospheric Administration (NOAA) issued its policy on the same topic (see “NOAA issues scientific integrity policy,” Eos Trans. AGU, 92(50), 467, doi:10.1029/2011EO500004, 2011). The agency policies respond to earlier White House memos on the topic issued in 2009 and 2010. NASA is the fifth federal department or agency that has finalized a scientific integrity policy; the Department of the Interior and the National Science Foundation also have finalized their policies. As Eos went to press, 13 other policies were in near–final draft form, including those from the departments of Agriculture and Energy; the Environmental Protection Agency and the Department of Labor had indicated that they expected to submit their policies to the White House Office of Science and Technology Policy (OSTP) soon, OSTP director John Holdren wrote in a 21 December note on the office's Web site.

NOAA administrator reviews agency progress and challenges

The approach of the new year is a traditional time to tally up successes, failures, and the path ahead. Jane Lubchenco, administrator of the U.S. National Oceanic and Atmospheric Administration (NOAA), examined some agency advances and significant challenges during the 7 December Union Agency Lecture at the AGU Fall Meeting, during a press briefing, and in an interview with Eos. Lubchenco focused on several key areas including the concern about monitoring, mitigating, and managing extreme events; budgetary pressures the agency faces in current fiscal year (FY) 2012 and in FY 2013, with President Barack Obama on 18 November having signed into law a bill, HR 2112, following congressional agreement on a budget legislation conference report; and NOAA's newly released scientific integrity policy (see “NOAA issues scientific integrity policy,” Eos Trans. AGU, 92(50), 467, doi:10.1029/2011EO500004, 2011).

NOAA issues scientific integrity policy

The U.S. National Oceanic and Atmospheric Administration (NOAA) announced the agency's first‐ever scientific integrity policy at a 7 December news briefing at the AGU Fall Meeting in San Francisco, Calif. The policy follows a December 2010 White House memorandum that issued guidance to federal agencies implementing scientific integrity policies (see “White House issues scientific integrity policies,” Eos Trans. AGU, 91(51), 503, doi:10.1029/2010EO510003, 2010). The purpose of the NOAA policy is “to promote a continuing culture of scientific excellence and integrity, and to establish a policy on the integrity of scientific activities that the agency conducts and uses to inform management and policy decisions,” the agency's administrative order states. “In addition, the intent of the policy is to strengthen widespread confidence—from scientists, to decisionmakers, to the general public—in the quality, validity, and reliability of NOAA science and to denote the agency's commitment to a culture of support for excellence of NOAA's principal science asset, its employees.”

Environmental impacts of shale-gas production

David Kramer, in the Physics Today0031-92286472011 https://doi.org/10.1063/PT.3.1159.July 2011 issue of Physics Today (page 23), presented a fairly thorough review of the status and issues associated with the extraction of shale gas in the US. Much is still unknown about the environmental effects of shale-gas production. Eight federal and state government agencies are currently working together to collect baseline data on a future shale-gas drill site in southwestern Pennsylvania, with the intent of monitoring environmental impacts through the drilling and fracturing process and for some time afterward.11. For a summary and details of the study, see D. J. Soeder, Eos Trans. Am. Geophys. Union 91 (32), 277 (2010). https://doi.org/10.1029/2010EO320001Several statements in Kramer’s news story are misleading or incorrect. The piece mentions gas industry claims that no case of groundwater contamination caused by hydraulic fracturing (fracking) has ever been documented. In the next paragraph, Anthony Ingraffea of Cornell University is quoted as stating that “thousands of cases” of groundwater contamination due to oil and gas drilling have been documented. Despite requests, Ingraffea has not shared that documentation or published it in the peer-reviewed literature.Although the two statements regarding groundwater sound contradictory, they are, in fact, two separate issues. In most instances, fracking takes place at such great depths that it is highly unlikely to affect shallow aquifers in any way. Detailed microseismic data in both the Marcellus and Barnett shales22. 2. K. Fisher, American Oil and Gas Reporter 53 (7), 30 (2010). showed that none of the induced fractures in the shales approached within several thousand vertical feet of the deepest freshwater aquifers overlying them. On the other hand, a surface spill of fracturing fluid, followed by ground infiltration and percolation down to an aquifer used for drinking water, is a much more likely contamination route. Indeed, that is how many common contaminants—from gasoline additives to agricultural fertilizers—have entered the groundwater.The Kramer account also overstates that Marcellus shale fracking operators must find the means to dispose of up to 7 million gallons of wastewater generated per well. Drillers typically use 3 million to 5 million gallons of water to frac a multistage well, and only about a quarter to a third of that total volume of water is recovered. Because of higher disposal costs under new regulations, flowback is now essentially 100% recycled into the next well as a standard practice. After the final frac treatment, the recycled water is injected down a separate disposal well, as stated in the article.The issue of methane in groundwater requires much more data and analysis before any conclusions can be drawn. Each case probably has unique circumstances and requires a forensic-type investigation to determine the source of the gas and the route by which it may have migrated into a domestic water well. The Duke University study33. S. G. Osborn, A. Vengosh, N. R. Warner, R. B. Jackson, Proc. Natl. Acad. Sci. USA 108, 8172 (2011). https://doi.org/10.1073/pnas.1100682108 Kramer cites suffers from several flaws, including a lack of predrilling baseline data and no assessment of the local geology or hydrology. Alternative explanations, such as gas migration from shallow bedrock into aquifers, were not explored.It is important for the scientific and regulatory communities to focus on protecting water resources, air quality, habitat, and ecosystems during shale-gas production. Objective data are needed to update state oil and gas regulations, identify environmental concerns, and define mitigation strategies for the production of this important resource. Misleading or inaccurate statements do little except shift focus away from the real problems and needlessly worry the public.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. For a summary and details of the study, see D. J. Soeder, Eos Trans. Am. Geophys. Union 91 (32), 277 (2010). https://doi.org/10.1029/2010EO320001, Google ScholarCrossref2. 2. K. Fisher, American Oil and Gas Reporter 53 (7), 30 (2010). Google Scholar3. S. G. Osborn, A. Vengosh, N. R. Warner, R. B. Jackson, Proc. Natl. Acad. Sci. USA 108, 8172 (2011). https://doi.org/10.1073/pnas.1100682108, Google ScholarCrossref, ISI© 2011 American Institute of Physics.

Museum exhibit on climate change draws from National Research Council reports

With all of science to choose from for topics, the Marian Koshland Science Museum of the National Academy of Sciences (NAS) has mounted its second exhibit about climate change since the museum's founding, in 2004, emphasizing the importance it places on the subject. The new exhibit, “Earth Lab: Degrees of Change,” which officially opened in the museum's compact quarters in downtown Washington, D. C., on 15 September, presents some in‐depth interactive displays about climate change, including a centerpiece “decision table,” a mitigation simulation game that challenges visitors to lower carbon dioxide emissions while also balancing costs and other factors. The exhibit is based in part on the America's Climate Choices Reports from the National Research Council, which, along with NAS, is part of the National Academies. Those reports indicate that climate change is occurring, is very likely caused by human activities, and poses significant risks for a broad range of human and natural systems. Further, the reports include a series of recommended steps to respond to those risks (see R. Showstack, Climate change report calls for iterative risk management framework, Eos Trans. AGU, 92(21), 178–179, doi:10.1029/2011EO210002, 2011).

Timescales for the evolution of oxygen isotope compositions in the solar nebula

We review two models for the origin of the calcium-, aluminum-rich inclusion (CAI) oxygen isotope mixing line in the solar nebula: (1) CO self-shielding, and (2) chemical mass-independent fractionation (MIF). We consider the timescales associated with formation of an isotopically anomalous water reservoir derived from CO self-shielding, and also the vertical and radial transport timescales of gas and solids in the nebula. The timescales for chemical MIF are very rapid. CO self-shielding models predict that the Sun has Δ 17O SMOW ∼ −20‰ (Clayton, 2002), and chemical mass-independent fractionation models predict Δ 17O SMOW ∼0‰. Preliminary Genesis results have been reported by McKeegan et al. (McKeegan K. D., Coath C. D., Heber, V., Jarzebinski G., Kallio A. P., Kunihiro T., Mao P. H. and Burnett D. S. (2008b) The oxygen isotopic composition of captured solar wind: first results from the Genesis. EOS Trans. AGU 89(53), Fall Meet. Suppl., P42A-07 (abstr)) and yield a Δ 17O SMOW of ∼ −25‰, consistent with a CO self-shielding scenario. Assuming that subsequent Genesis analyses support the preliminary results, it then remains to determine the relative contributions of CO self-shielding from the X-point, the surface of the solar nebula and the parent molecular cloud. The relative formation ages of chondritic components can be related to several timescales in the self-shielding theories. Most importantly the age difference of ∼1–3 My between CAIs and chondrules is consistent with radial transport from the outer solar nebula (>10 AU) to the meteorite-forming region, which supports both the nebular surface and parent cloud self-shielding scenarios. An elevated radiation field intensity is predicted by the surface shielding model, and yields substantial CO photolysis (∼50%) on timescales of 0.1–1 My. An elevated radiation field is also consistent with the parent cloud model. The elevated radiation intensities may indicate solar nebula birth in a medium to large cluster, and may be consistent with the injection of 60Fe from a nearby supernova and with the photoevaporative truncation of the solar nebula at KBO orbital distances (∼47 AU). CO self-shielding is operative at the X-point even when H 2 absorption is included, but it is not yet clear whether the self-shielding signature can be imparted to silicates. A simple analysis of diffusion times shows that oxygen isotope exchange between 16O-depleted nebular H 2O and chondrules during chondrule formation events is rapid (∼minutes), but is also expected to be rapid for most components of CAIs, with the exception of spinel. This is consistent with the observation that spinel grains are often the most 16O-rich component of CAIs, but is only broadly consistent with the greater degree of exchange in other CAI components. Preliminary disk model calculations of self-shielding by N 2 demonstrate that large δ 15N enrichments (∼ +800‰) are possible in HCN formed by reaction of N atoms with organic radicals (e.g., CH 2), which may account for 15N-rich hotspots observed in lithic clasts in some carbonaceous chondrites and which lends support to the CO self-shielding model for oxygen isotopes.

Biochar: Carbon Mitigation from the Ground Up

As multibillion-dollar projects intended to sequester carbon dioxide (CO2) in deep geologic storage continue to seek financial support, the fertile black soils in the Amazon basin suggest a cheaper, lower-tech route toward the same destination. Scattered patches of dark, charcoal-rich soil known as terra preta (Portuguese for “black earth”) are the inspiration for an international effort to explore how burying biomass-derived charcoal, or “biochar,” could boost soil fertility and transfer a sizeable amount from the atmosphere into safe storage in of CO2 topsoil. Although burial of biochar is just beginning to be tested in long-term, field-scale trials, studies of Amazonian terra preta show that charcoal can lock up carbon in the soil for centuries and improve soil fertility. Charcoal is made by heating wood or other organic material with a limited supply of oxygen (a process termed “pyrolysis”). The products of the pyrolysis process vary by the raw material used, burning time, and temperature, but in principle, volatile hydrocarbons and most of the oxygen and hydrogen in the biomass are burned or driven off, leaving carbon-enriched black solids with a structure that resists chemical and microbial degradation. Christoph Steiner, a research scientist at the University of Georgia, says the difference between charcoal and biochar lies primarily in the end use. “Charcoal is a fuel, and biochar has a nonfuel use that makes carbon sequestration feasible,” he explains. “Otherwise there is no difference between charcoal carbon and biochar carbon.” Charcoal is traditionally made by burning wood in pits or temporary structures, but modern pyrolysis equipment greatly reduces the air pollution associated with this practice. Gases emitted from pyrolysis can be captured to generate valuable products instead of being released as smoke. Some of the by-products can be condensed into “bio-oil,” a liquid that can be upgraded to fuels including biodiesel and synthesis gas. A portion of the noncondensable fraction is burned to heat the pyrolysis chamber, and the rest can provide heat or fuel an electric generator. Pyrolysis equipment now being developed at several public and private institutions typically operate at 350–700°C. In Golden, Colorado, Biochar Engineering Corporation is building portable $50,000 pyrolyzers that researchers will use to produce 1–2 tons of biochar per week. Company CEO Jim Fournier says the firm is planning larger units that could be trucked into position. Biomass is expensive to transport, he says, so pyrolysis units located near the source of the biomass are preferable to larger, centrally located facilities, even when the units reach commercial scale.

Teaching and Learning Guide for: The Current Debate on the Linkage between Global Warming and Hurricanes

Teaching and Learning Guide for: The Current Debate on the Linkage between Global Warming and Hurricanes

Integration of reflection seismic and sediment grain-size data from Lake Khubsugul (Northern Mongolia): a reply to Prokopenko and Kendall

Prokopenko and Kendall (J Paleolimnol doi:10.1007/s10933-008-9219-1, 2008) criticise the work presented in Fedotov et al. (J Paleolimnol 39:335–348, 2008), and instead propose an alternative interpretation for the grain-size evolution recorded in the KDP-01 core, retrieved from the central part of Lake Khubsugul. Their interpretation is based (i) on a seismic-stratigraphic re-interpretation of sparker seismic profile khub012 (which they copied from Fedotov et al. (EOS Trans 87:246–250, 2006)), (ii) on the presupposition that changes in lake level are the dominant control on facies distribution in Lake Khubsugul, and (iii) on the invalidation of our age-depth model. In this reply to their comment, we demonstrate that they interpreted seismic artefacts and geometries caused by changes in profile orientation as true stratigraphic features and that the lake-level reconstruction they derive from this interpretation is therefore incorrect. We also demonstrate that their grain-size predictions, which they consider to be predominantly driven by changes in lake level, are inconsistent with the measured sulphate concentration, which is a demonstrated proxy of lake level in Lake Khubsugul, and with the measured grain-size record. Finally, we point out that even if there would be a problem with the age-depth model, this problem would not affect the part of the sedimentary sequence discussed in Fedotov et al. (J Paleolimnol 39:335–348, 2008).

An advanced approach to finding magnetometer zero levels in the interplanetary magnetic field

For a magnetometer that measures weak interplanetary fields, the in-flight determination of zero levels is a crucial step of the overall calibration procedure. This task is more difficult when a time-varying magnetic field of the spacecraft interferes with the surrounding natural magnetic field or when the spacecraft spends only short periods of time in the interplanetary magnetic field. Thus it is important to examine the algorithms by which these zero levels are determined, and optimize them. We find that the method presented by Davis and Smith (1968 EOS Trans. AGU 49 257) has significant mathematical advantages over that published by Belcher (1973 J. Geophys. Res. 71 5509) as well as over the correlation technique published by Hedgecock (1975 Space Sci. Instrum. 1 83–90). We present an alternative derivation of the Davis–Smith method which illustrates that it is also a correlation technique. It also works with first differences as well as filtered data as input. In contrast to the postulate by Hedgecock (1975 Space Sci. Instrum. 1 83–90), we find that using first differences in general provides no advantage in determining the zero levels. Our new algorithm obtains zero levels by searching for pure rotations of the interplanetary magnetic field, with a set of sophisticated selection criteria. With our algorithm, we require shorter periods (of the order of a few hours, depending on solar wind conditions) of interplanetary data for accurate zero level determination than previously published algorithms.

40Ar– 39Ar dating of plagioclase grain size separates from silicate inclusions in IAB iron meteorites and implications for the thermochronological evolution of the IAB parent body

In order to better constrain the thermochronological evolution of the IAB parent body we performed a 40Ar/ 39Ar age study on individual silicate inclusions of the IAB irons Caddo County, Campo del Cielo, Landes, and Ocotillo. In contrast to earlier studies, several plagioclase separates of different grain sizes and quality grades were extracted from each inclusion to reduce the complexity of the age spectra and study the influence of these parameters on the Ar–Ar ages. In nearly all inclusions we found significantly different Ar–Ar ages among the separates (Caddo County: 4.472 ± 0.02–4.562 ± 0.02 Ga; Campo del Cielo 2: 4.362 ± 0.04–4.442 ± 0.03 Ga; Landes 2: 4.412 ± 0.05–4.522 ± 0.04 Ga; Ocotillo: 4.382 ± 0.04–4.462 ± 0.03 Ga). These ages were calculated using the new 40K decay constant published by [Mundil R., Renne P. R., Min K. and Ludwig K. R. (2006) Resolvable miscalibration of the 40Ar/ 39Ar geochronometer. Eos Trans. AGU 87, Fall Meet. Suppl., Abstract V21A-0543]. The ages did not systematically correlate with the respective grain size of the separate as expected, i.e., smaller grains did not necessarily show younger ages due to later closure to Ar diffusion or easier re-opening of the system in the course of a reheating event compared to larger grains. Based on the large range of Ar–Ar ages we suggest that the individual inclusions are composed of silicate grains from different locations within the IAB parent body. While some grains remained in a hot (deep) environment that allowed Ar diffusion over an extended time period—in some cases combined with grain coarsening—, others cooled significantly earlier (near surface) through the K/Ar blocking temperature. These different grains where brought together during an impact followed by mixing and reassembly of the debris as proposed by Benedix et al. [Benedix G. K., McCoy T. J., Keil K. and Love S. G. (2000) A petrologic study of the IAB iron meteorites: constraints on the formation of the IAB-Winonaite parent body. Meteorit. Planet. Sci. 35, 1127–1141]. Due to rapid cooling after the impact some of the age differences among the grains could be preserved. Based mainly on our Caddo County Ar–Ar age information, the IAB parent body was destroyed by impact and reassembled between ∼4.5 and 4.47 Ga. However, IAB silicate Ar–Ar ages should depend much more on the pre- and post-impact cooling rate and burial depth than on the time of the actual impact. This is supported by a compilation of our and literature IAB and winonaite Ar–Ar ages ranging smoothly from the time of accretion of the chondritic IAB parent body down to the time of its final cooling through the K–Ar blocking temperature after impact and reassembly, instead of showing a peak in Ar–Ar ages at the time of the destructive impact.

Numerical evaluation of volumetric weighted mean transmissivity estimates in laterally heterogeneous aquifers

Most previous investigations to evaluate the “effective” or average transmissivity in heterogeneous environments have used calculations based on areas to weight the effects of each heterogeneity. Analysis of spatial volumetric variations within the cone of depression expressed at the potentiometric surface offers a more general solution to evaluate the meaning of transmissivity ( T ) and storativity ( S ) values derived from aquifer tests in these environments. The [Cooper Jr., H.H., Jacob, C.E. 1946. A generalized graphical method for evaluating formation constants and summarizing well-field history. Eos Trans. AGU, 27(4), 526–534] method is used to demonstrate that T variations reflected in slope changes in plots of the pumping well drawdown data correspond to changes in the volumetric weighted mean transmissivity ( VWMT ) over time. Lognormal distributions of transmissivity are represented by block heterogeneities within two simulated aquifers, for both spatially random and spatially correlated data sets. By analyzing the volumetric evolution of the cone of depression observed in the potentiometric surface, the nature of T averaging within the cone of depression as a function of time is illustrated. Volumetric analysis shows that the average aquifer T varies with time as the cone of depression progressively envelops different heterogeneities. The initial trend is controlled primarily by the heterogeneities directly surrounding the pumping center. If steady-shape conditions are not achieved, late-time VWMT values do not approach an asymptotic limit.

Establishing Rights over the Arctic Ocean

Establishing Rights over the Arctic Ocean