The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Estimating surface CO2 fluxes from space-borne dry air mole fraction observations using an Ensemble Kalman filter

We have developed an ensemble Kalman Filter (EnKF) to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2) and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO). The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a) the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths <0.3; and b) scene-dependent averaging kernels that relate the CO2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1) bias and unbiased errors, 2) alternative duty cycles, 3) measurement density and correlations, 4) the spatial resolution of estimated flux estimates, and 5) reducing the length of the lag window and the size of the ensemble. At the revision stage of this manuscript, the OCO instrument failed to reach its orbit after it was launched on 24 February 2009. The EnKF formulation presented here is also applicable to GOSAT measurements of CO2 and CH4.

Land surface anomaly simulations and predictions with a climate model: an El Nino Southern Oscillation case study

The ability of climate models to reproduce and predict land surface anomalies is an important but little-studied topic. In this study, an atmosphere and ocean assimilation scheme is used to determine whether HadCM3 can reproduce and predict snow water equivalent and soil moisture during the 1997–1998 El Nino Southern Oscillation event. Soil moisture is reproduced more successfully, though both snow and soil moisture show some predictability at 1- and 4-month lead times. This result suggests that land surface anomalies may be reasonably well initialized for climate model predictions and hydrological applications using atmospheric assimilation methods over a period of time.

The four major N- and C-terminal splice variants of the excitatory amino acid transporter GLT-1 form cell surface homomeric and heteromeric assemblies

The L-glutamate transporter GLT-1 is an abundant CNS membrane protein of the excitatory amino acid transporter (EAAT) family which controls extracellular L-glutamate levels and is important in limiting excitotoxic neuronal death. Using RT-PCR, we have determined that four mRNAs encoding GLT-1 exist in mouse brain, with the potential to encode four GLT-1 isoforms that differ in their N- and C-termini. We expressed all four isoforms (termed MAST-KREK, MPK-KREK, MAST-DIETCI and MPK-DIETCI according to amino acid sequence) in a range of cell lines and primary astrocytes and show that each isoform can reach the cell surface. In transfected HEK-293 or COS-7 cells, all four isoforms support high-affinity sodium-dependent L-glutamate uptake with identical pharmacological and kinetic properties. Inserting a viral epitope (V5, HA or FLAG) into the second extracellular domain of each isoform allowed co-immunoprecipitation and tr-FRET studies using transfected HEK-293 cells. Here we show for the first time that each of the four isoforms are able to combine to form homomeric and heteromeric assemblies, each of which are expressed at the cell surface of primary astrocytes. After activation of protein kinase C by phorbol ester, V5-tagged GLT-1 is rapidly removed from the cell surface of HEK-293 cells and degraded. This study provides direct biochemical evidence for oligomeric assembly of GLT-1 and reports the development of novel tools to provide insight into the trafficking of GLT-1.

A Bayesian approach to estimate sensible and latent heat over vegetated land surface

Sensible and latent heat fluxes are often calculated from bulk transfer equations combined with the energy balance. For spatial estimates of these fluxes, a combination of remotely sensed and standard meteorological data from weather stations is used. The success of this approach depends on the accuracy of the input data and on the accuracy of two variables in particular: aerodynamic and surface conductance. This paper presents a Bayesian approach to improve estimates of sensible and latent heat fluxes by using a priori estimates of aerodynamic and surface conductance alongside remote measurements of surface temperature. The method is validated for time series of half-hourly measurements in a fully grown maize field, a vineyard and a forest. It is shown that the Bayesian approach yields more accurate estimates of sensible and latent heat flux than traditional methods.

Ex Vivo Construction of an Artificial Ocular Surface by Combination of Corneal Limbal Epithelial Cells and a Compressed Collagen Scaffold Containing Keratocytes

We have investigated the use of a laminin coated compressed collagen gel containing corneal fibroblasts (keratocytes) as a novel scaffold to support the growth of corneal limbal epithelial stem cells. The growth of limbal epithelial cells was compared between compressed collagen gel and a clinically proven conventional substrate, denuded amniotic membrane. Following compression of the collagen gel, encapsulated keratocytes remained viable and scanning electron microscopy showed that fibres within the compressed gel were dense, homogeneous and similar in structure to those within denuded amniotic membrane. Limbal epithelial cells were successfully expanded upon the compressed collagen resulting in stratified layers of cells containing desmosome and hemidesmosome structures. The resulting corneal constructs of both the groups shared a high degree of transparency, cell morphology and cell stratification. Similar protein expression profiles for cytokeratin 3 and cytokeratin 14 and no significant difference in cytokeratin 12 mRNA expression levels by real time PCR were also observed. This study provides the first line of evidence that a laminin coated compressed collagen gel containing keratocytes can adequately support limbal epithelial cell expansion, stratification and differentiation to a degree that is comparable to the leading conventional scaffold, denuded amniotic membrane.

Evaluating the efficacy of planktonic foraminifer calcite and 18O data for sea surface temperature reconstruction for the Late Miocene

This study examines the efficacy of published δ18O data from the calcite of Late Miocene surface dwelling planktonic foraminifer shells, for sea surface temperature estimates for the pre-Quaternary. The data are from 33 Late Miocene (Messinian) marine sites from a modern latitudinal gradient of 64°N to 48°S. They give estimates of SSTs in the tropics/subtropics (to 30°N and S) that are mostly cooler than present. Possible causes of this temperature discrepancy are ecological factors (e.g. calcification of shells at levels below the ocean mixed layer), taphonomic effects (e.g. diagenesis or dissolution), inaccurate estimation of Late Miocene seawater oxygen isotope composition, or a real Late Miocene cool climate. The scale of apparent cooling in the tropics suggests that the SST signal of the foraminifer calcite has been reset, at least in part, by early diagenetic calcite with higher δ18O, formed in the foraminifer shells in cool sea bottom pore waters, probably coupled with the effects of calcite formed below the mixed layer during the life of the foraminifera. This hypothesis is supported by the markedly cooler SST estimates from low latitudes—in some cases more than 9 °C cooler than present—where the gradients of temperature and the δ18O composition of seawater between sea surface and sea bottom are most marked, and where ocean surface stratification is high. At higher latitudes, particularly N and S of 30°, the temperature signal is still cooler, though maximum temperature estimates overlap with modern SSTs N and S of 40°. Comparison of SST estimates for the Late Miocene from alkenone unsaturation analysis from the eastern tropical Atlantic at Ocean Drilling Program (ODP) Site 958—which suggest a warmer sea surface by 2–4 °C, with estimates from oxygen isotopes at Deep Sea Drilling Project (DSDP) Site 366 and ODP Site 959, indicating cooler than present SSTs, also suggest a significant impact on the δ18O signal. Nevertheless, much of the original SST variation is clearly preserved in the primary calcite formed in the mixed layer, and records secular and temporal oceanographic changes at the sea surface, such as movement of the Antarctic Polar Front in the Southern Ocean. Cooler SSTs in the tropics and sub-tropics are also consistent with the Late Miocene latitude reduction in the coral reef belt and with interrupted reef growth on the Queensland Plateau of eastern Australia, though it is not possible to quantify absolute SSTs with the existing oxygen isotope data. Reconstruction of an accurate global SST dataset for Neogene time-slices from the existing published DSDP/ODP isotope data, for use in general circulation models, may require a detailed re-assessment of taphonomy at many sites.

Quantifying time scales of pedogenic calcrete formation using U-series disequilibria

Time scales of pedogenic calcrete development are quantified by subsampling carbonate from within a mature (stage V) pedogenic calcrete profile from southeast Spain and dating the material by U-series disequilibria. The location of the earliest and latest cements can be estimated by comparing previous studies of calcrete morphological development with micromorphological analysis of the study profile. Carbonate was sampled and dated from three locations within the profile: (1) below the lower surface of clasts within the hardpan (representing the earliest cement present-207 +/- 11 ka), (2) from the centre of cement filled pores within the hardpan (reflecting the final plugging of the calcrete hardpan-155 +/- 9 ka) and (3) from the laminar calcrete overlying the hardpan (representing the latest cement-112 +/- 15 ka). These results show that the hardpan took between 73 and 31 ka to form, whilst the mature stage V profile took between 121 and 69 ka to form. This is the first time that rates of mature calcrete development have been established by direct radiometric dating of the authigenic carbonate. The technique is appropriate for dating mature calcretes in dryland regions worldwide and offers the opportunity of increasing our understanding of the spatial and temporal variability in rates of pedogenic calcrete development. (C) 2004 Elsevier B.V. All rights reserved.

Does reactive surface area depend on grain size? Results from pH 3, 25 circle C far-from-equilibrium flow-through dissolution experiments on anorthite and biotite

Laboratory determined mineral weathering rates need to be normalised to allow their extrapolation to natural systems. The principle normalisation terms used in the literature are mass, and geometric- and BET specific surface area (SSA). The purpose of this study was to determine how dissolution rates normalised to these terms vary with grain size. Different size fractions of anorthite and biotite ranging from 180-150 to 20-10 mu m were dissolved in pH 3, HCl at 25 degrees C in flow through reactors under far from equilibrium conditions. Steady state dissolution rates after 5376 h (anorthite) and 4992 h (biotite) were calculated from Si concentrations and were normalised to initial- and final- mass and geometric-, geometric edge- (biotite), and BET SSA. For anorthite, rates normalised to initial- and final-BET SSA ranged from 0.33 to 2.77 X 10(-10) mol(feldspar) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 5.74 to 8.88 X 10(-10) mol(feldspar) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.11 to 1.65 mol(feldspar) g(-1) s(-1). For biotite, rates normalised to initial- and final-BET SSA ranged from 1.02 to 2.03 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 3.26 to 16.21 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric edge SSA ranged from 59.46 to 111.32 x 10(-12) mol(biotite) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.81 to 6.93 X 10(-12) mol(biotite) g(-1) s(-1). For all normalising terms rates varied significantly (p <= 0.05) with grain size. The normalising terms which gave least variation in dissolution rate between grain sizes for anorthite were initial BET SSA and initial- and final-geometric SSA. This is consistent with: (1) dissolution being dominated by the slower dissolving but area dominant non-etched surfaces of the grains and, (2) the walls of etch pits and other dissolution features being relatively unreactive. These steady state normalised dissolution rates are likely to be constant with time. Normalisation to final BET SSA did not give constant ratios across grain size due to a non-uniform distribution of dissolution features. After dissolution coarser grains had a greater density of dissolution features with BET-measurable but unreactive wall surface area than the finer grains. The normalising term which gave the least variation in dissolution rates between grain sizes for biotite was initial BET SSA. Initial- and final-geometric edge SSA and final BET SSA gave the next least varied rates. The basal surfaces dissolved sufficiently rapidly to influence bulk dissolution rate and prevent geometric edge SSA normalised dissolution rates showing the least variation. Simple modelling indicated that biotite grain edges dissolved 71-132 times faster than basal surfaces. In this experiment, initial BET SSA best integrated the different areas and reactivities of the edge and basal surfaces of biotite. Steady state dissolution rates are likely to vary with time as dissolution alters the ratio of edge to basal surface area. Therefore they would be more properly termed pseudo-steady state rates, only appearing constant because the time period over which they were measured (1512 h) was less than the time period over wich they would change significantly. (c) 2006 Elsevier Inc. All rights reserved.

Degradation of atrazine and isoproturon in surface and sub-surface soil materials undergoing different moisture and aeration conditions

The influence of different moisture and aeration conditions on the degradation of atrazine and isoproturon was investigated in environmental samples aseptically collected from surface and sub-surface zones of agricultural land. The materials were maintained at two moisture contents corresponding to just above field capacity or 90% of field capacity. Another two groups of samples were adjusted with water to above field capacity, and, at zero time, exposed to drying-rewetting cycles. Atrazine was more persistent (t(1/2) = 22-3S days) than isoproturon (t(1/2) = 5-17 days) in samples maintained at constant moisture conditions. The rate of degradation for both herbicides was higher in samples maintained at a moisture content of 90% of field capacity than in samples with higher moisture contents. The reduction in moisture content in samples undergoing desiccation from above field capacity to much lower than field capacity enhanced the degradation of isoproturon (t(1/2) = 9-12 days) but reduced the rate of atrazine degradation (t(1/2) = 23-35-days). This demonstrates the variability between different micro-organisms in their susceptibility to desiccation. Under anaerobic conditions generated in anaerobic jars, atrazine degraded much more rapidly than isoproturon in materials taken from three soil profiles (0-250 cm depth). It is suggested that some specific micro-organisms are able to survive and degrade herbicide under severe conditions of desiccation. (C) 2004 Society of Chemical Industry.

The development and contribution of surface charge by crop residues in two Malawian acid soils

The effects of maize and soya bean residues on the pH and charge of a loamy sand (Kawalazi) and a sandy clay loam (Naming'omba) from Malawi were measured to determine both the indirect effect of the residues on soil charge through the changes in pH, and the direct contribution of charge carried on the residue surfaces. The soils had pH values (10 mM CaCl2) of 4.3 and 5.0 and organic matter contents were 1.4% and 2.7%, respectively. The clay fractions were dominated by kaolinite and goethite, and mica was present in both samples. The soils were incubated for 28 days with maize (Zea mays) and soya bean (Glycine max) residues. The maximum addition of residue (12.0%) in the Kawalazi and Naming'omba soils increased the pH from 4.3 and 5.0 to 4.8 and 5.3 (maize) and to 9.0 and 8.8 (soya bean), respectively. Negative charge increased from 2.1 and 4.7 cmol(c) kg(-1) to 3.8 and 7.5 (maize) and to 5.3 and 9.3 cmol(c) kg(-1) (soya bean). Positive charge increased from 0.72 and 0.62 to 0.87 and 0.85 cmol(c) kg(-1) (maize) and to 0.75 and 0.68 (soya bean). The charge contribution by the residues was calculated by difference between the charge on a sample incubated with residue and the charge on a soil without residue limed to the same pH value. Up to 100 cmolc negative charge and 10 cmol(c) of positive charge per kg of residue were directly contributed to the soil-residue mixture, the amounts depending on the type of residue, the extent to which the residue was decomposed in the soil and the pH of the mixture. The Anderson and Sposito method [Soil Sci. Soc. Am. J. 55 (1991) 1569] was used to partition the permanent negative charge (holding Cs+) from variable negative charge (holding Li+). In the pH range 3.7-6.5 the maize residue contributed between 3 and 26 cmol(c) of variable charge per kg of residue in the Kawalazi soil and between 6 and 25 cmol(c) per kg of residue in the Naming'omba soil. For soya bean the values were between I and 28 and between 4 and 68 cmolc per kg of residue, respectively. At a given pH value, the charge tended to increase with time of incubation and for a given addition of residue, pH decreased during incubation. Addition of residues contributed no permanent negative charge and the charge on the soil measured by Cs adsorption was independent of pH change caused by the residue showing that the method is valid for soil-residue mixtures. With time there was a decrease in the amount of permanent charge probably due to masking as humic material become adsorbed on mineral surfaces. (C) 2003 Elsevier Science B.V. All rights reserved.

Evaluating the efficacy of planktonic foraminifer calcite and 18O data for sea surface temperature reconstruction for the Late Miocene

This study examines the efficacy of published δ18O data from the calcite of Late Miocene surface dwelling planktonic foraminifer shells, for sea surface temperature estimates for the pre-Quaternary. The data are from 33 Late Miocene (Messinian) marine sites from a modern latitudinal gradient of 64°N to 48°S. They give estimates of SSTs in the tropics/subtropics (to 30°N and S) that are mostly cooler than present. Possible causes of this temperature discrepancy are ecological factors (e.g. calcification of shells at levels below the ocean mixed layer), taphonomic effects (e.g. diagenesis or dissolution), inaccurate estimation of Late Miocene seawater oxygen isotope composition, or a real Late Miocene cool climate. The scale of apparent cooling in the tropics suggests that the SST signal of the foraminifer calcite has been reset, at least in part, by early diagenetic calcite with higher δ18O, formed in the foraminifer shells in cool sea bottom pore waters, probably coupled with the effects of calcite formed below the mixed layer during the life of the foraminifera. This hypothesis is supported by the markedly cooler SST estimates from low latitudes—in some cases more than 9 °C cooler than present—where the gradients of temperature and the δ18O composition of seawater between sea surface and sea bottom are most marked, and where ocean surface stratification is high. At higher latitudes, particularly N and S of 30°, the temperature signal is still cooler, though maximum temperature estimates overlap with modern SSTs N and S of 40°. Comparison of SST estimates for the Late Miocene from alkenone unsaturation analysis from the eastern tropical Atlantic at Ocean Drilling Program (ODP) Site 958—which suggest a warmer sea surface by 2–4 °C, with estimates from oxygen isotopes at Deep Sea Drilling Project (DSDP) Site 366 and ODP Site 959, indicating cooler than present SSTs, also suggest a significant impact on the δ18O signal. Nevertheless, much of the original SST variation is clearly preserved in the primary calcite formed in the mixed layer, and records secular and temporal oceanographic changes at the sea surface, such as movement of the Antarctic Polar Front in the Southern Ocean. Cooler SSTs in the tropics and sub-tropics are also consistent with the Late Miocene latitude reduction in the coral reef belt and with interrupted reef growth on the Queensland Plateau of eastern Australia, though it is not possible to quantify absolute SSTs with the existing oxygen isotope data. Reconstruction of an accurate global SST dataset for Neogene time-slices from the existing published DSDP/ODP isotope data, for use in general circulation models, may require a detailed re-assessment of taphonomy at many sites.

A surface energy perspective on climate change

A surface forcing response framework is developed that enables an understanding of time-dependent climate change from a surface energy perspective. The framework allows the separation of fast responses that are unassociated with global-mean surface air temperature change (ΔT), which is included in the forcing, and slow feedbacks that scale with ΔT. The framework is illustrated primarily using 2 × CO2 climate model experiments and is robust across the models. For CO2 increases, the positive downward radiative component of forcing is smaller at the surface than at the tropopause, and so a rapid reduction in the upward surface latent heat (LH) flux is induced to conserve the tropospheric heat budget; this reduces the precipitation rate. Analysis of the time-dependent surface energy balance over sea and land separately reveals that land areas rapidly regain energy balance, and significant land surface warming occurs before global sea temperatures respond. The 2 × CO2 results are compared to a solar increase experiment and show that some fast responses are forcing dependent. In particular, a significant forcing from the fast hydrological response found in the CO2 experiments is much smaller in the solar experiment. The different fast response explains why previous equilibrium studies found differences in the hydrological sensitivity between these two forcings. On longer time scales, as ΔT increases, the net surface longwave and LH fluxes provide positive and negative surface feedbacks, respectively, while the net surface shortwave and sensible heat fluxes change little. It is found that in contrast to their fast responses, the longer-term response of both surface energy fluxes and the global hydrological cycle are similar for the different forcing agents.

A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

Surface determination of the air-earth electrical current density using co-located sensors of different geometry

A vertical conduction current flows in the atmosphere as a result of the global atmospheric electric circuit. The current at the surface consists of the conduction current and a locally generated displacement current, which are often approximately equal in magnitude. A method of separating the two currents using two collectors of different geometry is investigated. The picoammeters connected to the collectors have a RC time constant of approximately 3 s, permitting the investigation of higher frequency air-earth current changes than previously achieved. The displacement current component of the air-earth current derived from the instrument agrees with calculations using simultaneous data from a co-located fast response electric field mill. The mean value of the nondisplacement current measured over 9 h was 1.76 +/- 0.002 pA m(-2). (c) 2006 American Institute of Physics.