Rank histograms of stratified Monte-Carlo ensembles

The application of forecast ensembles to probabilistic weather prediction has spurred considerable interest in their evaluation. Such ensembles are commonly interpreted as Monte Carlo ensembles meaning that the ensemble members are perceived as random draws from a distribution. Under this interpretation, a reasonable property to ask for is statistical consistency, which demands that the ensemble members and the verification behave like draws from the same distribution. A widely used technique to assess statistical consistency of a historical dataset is the rank histogram, which uses as a criterion the number of times that the verification falls between pairs of members of the ordered ensemble. Ensemble evaluation is rendered more specific by stratification, which means that ensembles that satisfy a certain condition (e.g., a certain meteorological regime) are evaluated separately. Fundamental relationships between Monte Carlo ensembles, their rank histograms, and random sampling from the probability simplex according to the Dirichlet distribution are pointed out. Furthermore, the possible benefits and complications of ensemble stratification are discussed. The main conclusion is that a stratified Monte Carlo ensemble might appear inconsistent with the verification even though the original (unstratified) ensemble is consistent. The apparent inconsistency is merely a result of stratification. Stratified rank histograms are thus not necessarily flat. This result is demonstrated by perfect ensemble simulations and supplemented by mathematical arguments. Possible methods to avoid or remove artifacts that stratification induces in the rank histogram are suggested.

The determination of total nitrogen and total phosphorus concentrations in freshwaters from land use, stock headage and population data: testing of a model for use in conservation and water quality management

1. Nutrient concentrations (particularly N and P) determine the extent to which water bodies are or may become eutrophic. Direct determination of nutrient content on a wide scale is labour intensive but the main sources of N and P are well known. This paper describes and tests an export coefficient model for prediction of total N and total P from: (i) land use, stock headage and human population; (ii) the export rates of N and P from these sources; and (iii) the river discharge. Such a model might be used to forecast the effects of changes in land use in the future and to hindcast past water quality to establish comparative or baseline states for the monitoring of change. 2. The model has been calibrated against observed data for 1988 and validated against sets of observed data for a sequence of earlier years in ten British catchments varying from uplands through rolling, fertile lowlands to the flat topography of East Anglia. 3. The model predicted total N and total P concentrations with high precision (95% of the variance in observed data explained). It has been used in two forms: the first on a specific catchment basis; the second for a larger natural region which contains the catchment with the assumption that all catchments within that region will be similar. Both models gave similar results with little loss of precision in the latter case. This implies that it will be possible to describe the overall pattern of nutrient export in the UK with only a fraction of the effort needed to carry out the calculations for each individual water body. 4. Comparison between land use, stock headage, population numbers and nutrient export for the ten catchments in the pre-war year of 1931, and for 1970 and 1988 show that there has been a substantial loss of rough grazing to fertilized temporary and permanent grasslands, an increase in the hectarage devoted to arable, consistent increases in the stocking of cattle and sheep and a marked movement of humans to these rural catchments. 5. All of these trends have increased the flows of nutrients with more than a doubling of both total N and total P loads during the period. On average in these rural catchments, stock wastes have been the greatest contributors to both N and P exports, with cultivation the next most important source of N and people of P. Ratios of N to P were high in 1931 and remain little changed so that, in these catchments, phosphorus continues to be the nutrient most likely to control algal crops in standing waters supplied by the rivers studied.

Volume-based size distribution of accumulation and coarse particles (PM0.1–10) from cooking fume during oil heating

Particulate matter generated during the cooking process has been identified as one of the major problems of indoor air quality and indoor environmental health. Reliable assessment of exposure to cooking-generated particles requires accurate information of emission characteristics especially the size distribution. This study characterizes the volume/mass-based size distribution of the fume particles at the oil-heating stage for the typical Chinese-style cooking in a laboratory kitchen. A laser-diffraction size analyzer is applied to measure the volume frequency of fume particles ranged from 0.1 to 10 μm, which contribute to most mass proportion in PM2.5 and PM10. Measurements show that particle emissions have little dependence on the types of vegetable oil used but have a close relationship with the heating temperature. It is found that volume frequency of fume particles in the range of 1.0–4.0 μm accounts for nearly 100% of PM0.1–10 with the mode diameter 2.7 μm, median diameter 2.6 μm, Sauter mean diameter 3.0 μm, DeBroukere mean diameter 3.2 μm, and distribution span 0.48. Such information on emission characteristics obtained in this study can be possibly used to improve the assessment of indoor air quality due to PM0.1–10 in the kitchen and residential flat.

A model of the three-dimensional evolution of Arctic melt ponds on first-year and multiyear sea ice

During winter the ocean surface in polar regions freezes over to form sea ice. In the summer the upper layers of sea ice and snow melts producing meltwater that accumulates in Arctic melt ponds on the surface of sea ice. An accurate estimate of the fraction of the sea ice surface covered in melt ponds is essential for a realistic estimate of the albedo for global climate models. We present a melt-pond–sea-ice model that simulates the three-dimensional evolution of melt ponds on an Arctic sea ice surface. The advancements of this model compared to previous models are the inclusion of snow topography; meltwater transport rates are calculated from hydraulic gradients and ice permeability; and the incorporation of a detailed one-dimensional, thermodynamic radiative balance. Results of model runs simulating first-year and multiyear sea ice are presented. Model results show good agreement with observations, with duration of pond coverage, pond area, and ice ablation comparing well for both the first-year ice and multiyear ice cases. We investigate the sensitivity of the melt pond cover to changes in ice topography, snow topography, and vertical ice permeability. Snow was found to have an important impact mainly at the start of the melt season, whereas initial ice topography strongly controlled pond size and pond fraction throughout the melt season. A reduction in ice permeability allowed surface flooding of relatively flat, first-year ice but had little impact on the pond coverage of rougher, multiyear ice. We discuss our results, including model shortcomings and areas of experimental uncertainty.

Housing densities and consumer choice

From 2001, the construction of flats and high-density developments increased in England and the building of houses declined. Does this indicate a change in taste or is it a result of government planning policies? In this paper, an analysis is made of the long-term effects of the policy of constraint which has existed for the past 50 years but the increase in density is identified as occurring primarily after new, revised, planning guidance was issued in England in 2000 which discouraged low-density development. To substantiate this, it is pointed out that the change which occurred in England did not occur in Scotland where guidance was not changed to encourage high-density residential development. The conclusion that the change is the result of planning policies and not of a change in taste is confirmed by surveys of the occupants of new high-rise developments in Leeds. The new flat-dwellers were predominantly young and childless and expressed the intention, in the near future, when they could, of moving out of the city centre and into houses. From recent changes in guidance by the new coalition government, it is expected that the construction of flats in England will fall back to earlier levels over the next few years.

Hollow structures with bilayer graphene walls

The formation of three-dimensional shell-like structures with bilayer graphene walls is described. The structures are produced by the passage of an electric current through graphite in an arc-discharge apparatus. High resolution transmission electron microscopy is used to characterize the carbon, and provides evidence that the structures are three-dimensional rather than flat. A striking feature of the material is that it contains bilayer nanotubes seamlessly joined to larger shell-like regions. The possible growth mechanism of the carbon is discussed, and potential applications considered.

Displacement of methane by coadsorbed carbon dioxide is facilitated in narrow carbon nanopores

By using simulation methods, we studied the adsorption of binary CO2-CH4 mixtures on various CH4 preadsorbed carbonaceous materials (e.g., triply periodic carbon minimal surfaces, slit-shaped carbon micropores, and Harris's virtual porous carbons) at 293 K. Regardless of the different micropore geometry, two-stage mechanism of CH4 displacement from carbon nanospaces by coadsorbed CO2 has been proposed. In the first stage, the coadsorbed CO2 molecules induced the enhancement of CH4 adsorbed amount. In the second stage, the stronger affinity of CO2 to flat/curved graphitic surfaces as well as CO2-CO2 interactions cause the displacement of CH4 molecules from carbonaceous materials. The operating conditions of CO2-induced cleaning of the adsorbed phase from CH4 mixture component strongly depend on the size of the carbon micropores, but, in general, the enhanced adsorption field in narrow carbon ultramicropores facilitates the nonreactive displacement of CH4 by coadsorbed CO2. This is because in narrow carbon ultramicropores the equilibrium CO2/CH4 selectivity (i.e., preferential adsorption toward CO2) increased significantly. The adsorption field in wider micropores (i.e., the overall surface energy) for both CO2 and CH4 is very similar, which decreases the preferential CO2 adsorption. This suppresses the displacement of CH4 by coadsorbed CO2 and assists further adsorption of CH4 from the bulk mixture (i.e., CO2/CH4 mixing in adsorbed phase).

Noise propagation from a cutting of arbitrary cross-section and impedance

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

An assessment of a three-beam Doppler lidar wind profiling method for use in urban areas

Currently there are few observations of the urban wind field at heights other than rooftop level. Remote sensing instruments such as Doppler lidars provide wind speed data at many heights, which would be useful in determining wind loadings of tall buildings, and predicting local air quality. Studies comparing remote sensing with traditional anemometers carried out in flat, homogeneous terrain often use scan patterns which take several minutes. In an urban context the flow changes quickly in space and time, so faster scans are required to ensure little change in the flow over the scan period. We compare 3993 h of wind speed data collected using a three-beam Doppler lidar wind profiling method with data from a sonic anemometer (190 m). Both instruments are located in central London, UK; a highly built-up area. Based on wind profile measurements every 2 min, the uncertainty in the hourly mean wind speed due to the sampling frequency is 0.05–0.11 m s−1. The lidar tended to overestimate the wind speed by ≈0.5 m s−1 for wind speeds below 20 m s−1. Accuracy may be improved by increasing the scanning frequency of the lidar. This method is considered suitable for use in urban areas.

On the power amplifier nonlinearity in MIMO transmit beamforming systems

In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT.

Compensation for HPA nonlinearity and I/Q imbalance in MIMO beamforming systems

In this paper, we investigate the effects of high-power amplifier (HPA) nonlinearity and in-phase and quadrature-phase (I/Q) imbalance on the performance of multiple-input multiple-output (MIMO) transmit beamforming (TB) systems. Specifically, we propose a compensation method for HPA nonlinearity and I/Q imbalance together in MIMO TB systems. The performance of the MIMO TB system under study is evaluated in terms of the average symbol error probability (SEP) and system capacity, considering transmission over uncorrelated frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, such as the HPA parameters, image-leakage ratio, numbers of transmit and receive antennas, length of pilot symbols, and modulation order of phase-shift keying (PSK), on performance.