Determination of Holocene cave temperatures from Kr and Xe concentrations in stalagmite fluid inclusions

From the concentrations of dissolved atmospheric noble gases in water, a so-called “noble gas temperature” (NGT) can be determined that corresponds to the temperature of the water when it was last in contact with the atmosphere. Here we demonstrate that the NGT concept is applicable to water inclusions in cave stalagmites, and yields NGTs that are in good agreement with the ambient air temperatures in the caves. We analysed samples from two Holocene and one undated stalagmite. The three stalagmites originate from three caves located in different climatic regions having modern mean annual air temperatures of 27 °C, 12 °C and 8 °C, respectively. In about half of the samples analysed Kr and Xe concentrations originated entirely from the two well-defined noble gas components air-saturated water and atmospheric air, which allowed NGTs to be determined successfully from Kr and Xe concentrations. One stalagmite seems to be particularly suitable for NGT determination, as almost all of its samples yielded the modern cave temperature. Notably, this stalagmite contains a high proportion of primary water inclusions, which seem to preserve the temperature-dependent signature well in their Kr and Xe concentrations. In future work on stalagmites detailed microscopic inspection of the fluid inclusions prior to noble gas analysis is therefore likely to be crucial in increasing the number of successful NGT determinations.

Describing seasonal variability in the distribution of daily effective temperatures for 1985-2009 compared to 1904-1984 for De Bilt, Holland

This paper proposes a method for describing the distribution of observed temperatures on any day of the year such that the distribution and summary statistics of interest derived from the distribution vary smoothly through the year. The method removes the noise inherent in calculating summary statistics directly from the data thus easing comparisons of distributions and summary statistics between different periods. The method is demonstrated using daily effective temperatures (DET) derived from observations of temperature and wind speed at De Bilt, Holland. Distributions and summary statistics are obtained from 1985 to 2009 and compared to the period 1904–1984. A two-stage process first obtains parameters of a theoretical probability distribution, in this case the generalized extreme value (GEV) distribution, which describes the distribution of DET on any day of the year. Second, linear models describe seasonal variation in the parameters. Model predictions provide parameters of the GEV distribution, and therefore summary statistics, that vary smoothly through the year. There is evidence of an increasing mean temperature, a decrease in the variability in temperatures mainly in the winter and more positive skew, more warm days, in the summer. In the winter, the 2% point, the value below which 2% of observations are expected to fall, has risen by 1.2 °C, in the summer the 98% point has risen by 0.8 °C. Medians have risen by 1.1 and 0.9 °C in winter and summer, respectively. The method can be used to describe distributions of future climate projections and other climate variables. Further extensions to the methodology are suggested.

Impact of anthropogenic heat emissions on London's temperatures

We investigate the role of the anthropogenic heat flux on the urban heat island of London. To do this, the time-varying anthropogenic heat flux is added to an urban surface-energy balance parametrization, the Met Office–Reading Urban Surface Exchange Scheme (MORUSES), implemented in a 1 km resolution version of the UK Met Office Unified Model. The anthropogenic heat flux is derived from energy-demand data for London and is specified on the model's 1 km grid; it includes variations on diurnal and seasonal time-scales. We contrast a spring case with a winter case, to illustrate the effects of the larger anthropogenic heat flux in winter and the different roles played by thermodynamics in the different seasons. The surface-energy balance channels the anthropogenic heat into heating the urban surface, which warms slowly because of the large heat capacity of the urban surface. About one third of this additional warming goes into increasing the outgoing long-wave radiation and only about two thirds goes into increasing the sensible heat flux that warms the atmosphere. The anthropogenic heat flux has a larger effect on screen-level temperatures in the winter case, partly because the anthropogenic flux is larger then and partly because the boundary layer is shallower in winter. For the specific winter case studied here, the anthropogenic heat flux maintains a well-mixed boundary layer through the whole night over London, whereas the surrounding rural boundary layer becomes strongly stably stratified. This finding is likely to have important implications for air quality in winter. On the whole, inclusion of the anthropogenic heat flux improves the comparison between model simulations and measurements of screen-level temperature slightly and indicates that the anthropogenic heat flux is beginning to be an important factor in the London urban heat island.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

On increasing global temperatures: 75 years after Callendar

In 1938, Guy Stewart Callendar was the first to demonstrate that the Earth’s land surface was warming. Callendar also suggested that the production of carbon dioxide by the combustion of fossil fuels was responsible for much of this modern change in climate. This short note marks the 75th anniversary of Callendar’s landmark study and demonstrates that his global land temperature estimates agree remarkably well with more recent analyses.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

An improved sum-product estimate for general finite fields

An improved sum-product estimate for subsets of a finite field whose order is not prime is provided. It is shown, under certain conditions, that max{∣∣∣A+A∣∣∣,∣∣∣A⋅A∣∣∣}≫∣∣A∣∣12/11(log2∣∣A∣∣)5/11. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev

Proteolysis of milk heated at high temperatures by native enzymes analysed by trinitrobenzene sulphonic acid (TNBS) method

Native enzymes play a significant role in proteolysis of milk during storage. This is significant for heat resistant native enzymes. Plasmin is one of the most heat resistant enzymes found in milk. It has been reported to survive several heat treatments, causing spoilage during storage. The aim of this study was to assess susceptibility of high temperature heated milk to proteolysis by native enzymes. The trinitrobenzene sulphonic acid (TNBS) method was used for this purpose. Raw milk was heated at 110, 120, 130,142°C for 2 s and 85°C for 15 s and milk processed at low temperature (85°C /15s) was selected to mimic pasteurisation. TNBS method confirmed that raw milk and milk processed at 85°C /15s were the most proteolysed, whereas treatment of milk at high temperatures (110, 120, 130 and 142°C for 2 s) inactivated the native enzymes. It may thus be concluded that high temperature processing positively affects proteolysis by lowering its susceptibility to spoilage during storage.