Geostatistical analysis of rainfall

Rainfall can be modeled as a spatially correlated random field superimposed on a background mean value; therefore, geostatistical methods are appropriate for the analysis of rain gauge data. Nevertheless, there are certain typical features of these data that must be taken into account to produce useful results, including the generally non-Gaussian mixed distribution, the inhomogeneity and low density of observations, and the temporal and spatial variability of spatial correlation patterns. Many studies show that rigorous geostatistical analysis performs better than other available interpolation techniques for rain gauge data. Important elements are the use of climatological variograms and the appropriate treatment of rainy and nonrainy areas. Benefits of geostatistical analysis for rainfall include ease of estimating areal averages, estimation of uncertainties, and the possibility of using secondary information (e.g., topography). Geostatistical analysis also facilitates the generation of ensembles of rainfall fields that are consistent with a given set of observations, allowing for a more realistic exploration of errors and their propagation in downstream models, such as those used for agricultural or hydrological forecasting. This article provides a review of geostatistical methods used for kriging, exemplified where appropriate by daily rain gauge data from Ethiopia.

Climate model calculations of the impact of aerosols from road transport and shipping

Road transport and shipping are copious sources of aerosols, which exert a 9 significant radiative forcing, compared to, for example, the CO2 emitted by these sectors. An 10 advanced atmospheric general circulation model, coupled to a mixed-layer ocean, is used to 11 calculate the climate response to the direct radiative forcing from such aerosols. The cases 12 considered include imposed distributions of black carbon and sulphate aerosols from road 13 transport, and sulphate aerosols from shipping; these are compared to the climate response 14 due to CO2 increases. The difficulties in calculating the climate response due to small 15 forcings are discussed, as the actual forcings have to be scaled by large amounts to enable a 16 climate response to be easily detected. Despite the much greater geographical inhomogeneity 17 in the sulphate forcing, the patterns of zonal and annual-mean surface temperature response 18 (although opposite in sign) closely resembles that resulting from homogeneous changes in 19 CO2. The surface temperature response to black carbon aerosols from road transport is shown 20 to be notably non-linear in scaling applied, probably due to the semi-direct response of clouds 21 to these aerosols. For the aerosol forcings considered here, the most widespread method of 22 calculating radiative forcing significantly overestimates their effect, relative to CO2, 23 compared to surface temperature changes calculated using the climate model.

Examination of long-wave radiative bias in general circulation models over North Africa during May–July

Satellite data are used to quantify and examine the bias in the outgoing long-wave (LW) radiation over North Africa during May–July simulated by a range of climate models and the Met Office global numerical weather prediction (NWP) model. Simulations from an ensemble-mean of multiple climate models overestimate outgoing clear-sky long-wave radiation (LWc) by more than 20 W m−2 relative to observations from Clouds and the Earth's Radiant Energy System (CERES) for May–July 2000 over parts of the west Sahara, and by 9 W m−2 for the North Africa region (20°W–30°E, 10–40°N). Experiments with the atmosphere-only version of the High-resolution Hadley Centre Global Environment Model (HiGEM), suggest that including mineral dust radiative effects removes this bias. Furthermore, only by reducing surface temperature and emissivity by unrealistic amounts is it possible to explain the magnitude of the bias. Comparing simulations from the Met Office NWP model with satellite observations from Geostationary Earth Radiation Budget (GERB) instruments suggests that the model overestimates the LW by 20–40 W m−2 during North African summer. The bias declines over the period 2003–2008, although this is likely to relate to improvements in the model and inhomogeneity in the satellite time series. The bias in LWc coincides with high aerosol dust loading estimated from the Ozone Monitoring Instrument (OMI), including during the GERBILS field campaign (18–28 June 2007) where model overestimates in LWc greater than 20 W m−2 and OMI-estimated aerosol optical depth (AOD) greater than 0.8 are concurrent around 20°N, 0–20°W. A model-minus-GERB LW bias of around 30 W m−2 coincides with high AOD during the period 18–21 June 2007, although differences in cloud cover also impact the model–GERB differences. Copyright © Royal Meteorological Society and Crown Copyright, 2010

Rossby waves and two-dimensional turbulence in a large-scale zonal jet

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field. Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ[identical with] (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ [identical with] (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences. The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to K Kβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [double less-than sign] κ for typical eddy length and velocity scales.

Inhomogeneous two-dimensional turbulence in the atmosphere

Faced with the strongly nonlinear and apparently random behaviour of the energy-containing scales in the atmosphere, geophysical fluid dynamicists have attempted to understand the synoptic-scale atmospheric flow within the context of two-dimensional homogeneous turbulence theory (e.g. FJØRTOFT [1]; LEITH [2]). However atmospheric observations (BOER and SHEPHERD [3] and Fig.1) show that the synoptic-scale transient flow evolves in the presence of a planetary-scale, quasi-stationary background flow which is approximately zonal (east-west). Classical homogeneous 2-D turbulence theory is therefore not strictly applicable to the transient flow. One is led instead to study 2-D turbulence in the presence of a large-scale (barotropically stable) zonal jet inhomogeneity.

A finite element-spherical harmonics model for radiative transfer in inhomogeneous clouds. Part II. some applications

EVENT has been used to examine the effects of 3D cloud structure, distribution, and inhomogeneity on the scattering of visible solar radiation and the resulting 3D radiation field. Large eddy simulation and aircraft measurements are used to create realistic cloud fields which are continuous or broken with smooth or uneven tops. The values, patterns and variance in the resulting downwelling and upwelling radiation from incident visible solar radiation at different angles are then examined and compared to measurements. The results from EVENT confirm that 3D cloud structure is important in determining the visible radiation field, and that these results are strongly influenced by the solar zenith angle. The results match those from other models using visible solar radiation, and are supported by aircraft measurements of visible radiation, providing confidence in the new model.

A regime-dependent parametrization of subgrid-scale cloud water content variability

The subgrid-scale spatial variability in cloud water content can be described by a parameter f called the fractional standard deviation. This is equal to the standard deviation of the cloud water content divided by the mean. This parameter is an input to schemes that calculate the impact of subgrid-scale cloud inhomogeneity on gridbox-mean radiative fluxes and microphysical process rates. A new regime-dependent parametrization of the spatial variability of cloud water content is derived from CloudSat observations of ice clouds. In addition to the dependencies on horizontal and vertical resolution and cloud fraction included in previous parametrizations, the new parametrization includes an explicit dependence on cloud type. The new parametrization is then implemented in the Global Atmosphere 6 (GA6) configuration of the Met Office Unified Model and used to model the effects of subgrid variability of both ice and liquid water content on radiative fluxes and autoconversion and accretion rates in three 20-year atmosphere-only climate simulations. These simulations show the impact of the new regime-dependent parametrization on diagnostic radiation calculations, interactive radiation calculations and both interactive radiation calculations and in a new warm microphysics scheme. The control simulation uses a globally constant f value of 0.75 to model the effect of cloud water content variability on radiative fluxes. The use of the new regime-dependent parametrization in the model results in a global mean which is higher than the control's fixed value and a global distribution of f which is closer to CloudSat observations. When the new regime-dependent parametrization is used in radiative transfer calculations only, the magnitudes of short-wave and long-wave top of atmosphere cloud radiative forcing are reduced, increasing the existing global mean biases in the control. When also applied in a new warm microphysics scheme, the short-wave global mean bias is reduced.

Reducing noise associated with the Monte Carlo Independent Column Approximation for weather forecasting models

The Monte Carlo Independent Column Approximation (McICA) is a flexible method for representing subgrid-scale cloud inhomogeneity in radiative transfer schemes. It does, however, introduce conditional random errors but these have been shown to have little effect on climate simulations, where spatial and temporal scales of interest are large enough for effects of noise to be averaged out. This article considers the effect of McICA noise on a numerical weather prediction (NWP) model, where the time and spatial scales of interest are much closer to those at which the errors manifest themselves; this, as we show, means that noise is more significant. We suggest methods for efficiently reducing the magnitude of McICA noise and test these methods in a global NWP version of the UK Met Office Unified Model (MetUM). The resultant errors are put into context by comparison with errors due to the widely used assumption of maximum-random-overlap of plane-parallel homogeneous cloud. For a simple implementation of the McICA scheme, forecasts of near-surface temperature are found to be worse than those obtained using the plane-parallel, maximum-random-overlap representation of clouds. However, by applying the methods suggested in this article, we can reduce noise enough to give forecasts of near-surface temperature that are an improvement on the plane-parallel maximum-random-overlap forecasts. We conclude that the McICA scheme can be used to improve the representation of clouds in NWP models, with the provision that the associated noise is sufficiently small.

Effects of Crossing Saddle Coil Conductors: Electric Length X Mutual Inductance

In magnetic resonance imaging (MRI), either on human or animal studies, the main requirements for radiofrequency (RF) coils are to produce a homogeneous RF field while used as a transmitter coil and to have the best signal-to-noise ratio (SNR) while used as a receiver. Besides, they need to be easily frequency adjustable and have input impedance matching 50 Omega to several different load conditions. New theoretical and practical concepts are presented here for considerable enhancing of RF coil homogeneity for MRI experiments on small animals. To optimize field homogeneity, we have performed simulations using Blot and Savart law varying the coil`s window angle, achieving the optimum one. However, when the coil`s dimensions are the same order of the wave length and according to transmission line theory, differences in electrical length and effects of mutual inductances between adjacent strip conductors decrease both field homogeneity and SNR. The problematic interactions between strip conductors by means of mutual inductance were eliminated by inserting crossings at half electrical length, avoiding distortion on current density, thus eliminating sources of field inhomogeneity. Experimental results show that measured field maps and simulations are in good agreement. The new coil design, dubbed double-crossed saddle described here have field homogeneity and SNR superior than the linearly driven 8-rung birdcage coil. One of our major findings was that the effects of mutual inductance are more significant than differences in electrical length for this frequency and coil dimensions. In vitro images of a primate Cebus paela brain were acquired, confirming double-crossed saddle superiority. (C) 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 193-201, 2010

Thomas-Fermi ground state of dipolar fermions in a circular storage ring

Recent developments in the field of ultracold gases has led to the production of degenerate samples of polar molecules. These have large static electric-dipole moments, which in turn causes the molecules to interact strongly. We investigate the interaction of polar particles in waveguide geometries subject to an applied polarizing field. For circular waveguides, tilting the direction of the polarizing field creates a periodic inhomogeneity of the interparticle interaction. We explore the consequences of geometry and interaction for stability of the ground state within the Thomas-Fermi model. Certain combinations of tilt angles and interaction strengths are found to preclude the existence of a stable Thomas-Fermi ground state. The system is shown to exhibit different behavior for quasi-one-dimensional and three-dimensional trapping geometries.

Malformação arteriovenosa uterina após doença trofoblástica gestacional

OBJETIVO: investigar a presença e resultados de malformações vasculares uterinas (MAVU) após doença trofoblástica gestacional (DTG). MÉTODOS: estudo retrospectivo com inclusão de casos diagnosticados entre 1987 e 2004; 2764 pacientes após DTG foram acompanhadas anualmente com ultra-sonografia transvaginal e Doppler colorido no Centro de Neoplasia Trofoblástica Gestacional da Santa Casa da Misericórdia (Rio de Janeiro, RJ, Brasil). Sete pacientes tiveram diagnóstico final de MAVU baseado em análise ultra-sonográfica - índice de pulsatilidade (IP), índice de resistência (IR) e velocidade sistólica máxima (VSM) - e achados de imagens de ressonância nuclear magnética (RNM). Dosagens negativas de beta-hCG foram decisivas para estabelecer o diagnóstico diferencial com DTG recidivante. RESULTADOS: a incidência de MAVU após DTG foi 0,2% (7/2764). Achados ultra-sonográficos de MAVU: IP médio de 0,44±0,058 (extremos: 0,38-0,52); IR médio de 0,36±0,072 (extremos: 0,29-0,50); VSM média de 64,6±23,99 cm/s (extremos: 37-96). A imagem de RNM revelou útero aumentado, miométrio heterogêneo, espaços vasculares tortuosos e vasos parametriais com ectasia. A apresentação clínica mais comum foi hemorragia transvaginal, presente em 52,7% (4/7) dos casos. Tratamento farmacológico com 150 mg de acetato de medroxiprogesterona foi empregado para controlar a hemorragia, após a estabilização hemodinâmica. Permanecem as pacientes em seguimento, assintomáticas até hoje. Duas pacientes engravidaram com MAVU, com gestações e partos exitosos. CONCLUSÃO: presente sangramento transvaginal em pacientes com beta-hCG negativo e história de DTG, deve-se considerar a possibilidade de MAVU e solicitar avaliação ultra-sonográfica com dopplervelocimetria. O tratamento conservador é a melhor opção na maioria dos casos de MAVU pós-DTG.

Dynamics of bright matter-wave solitons in a Bose-Einstein condensate with inhomogeneous scattering length

We investigate dynamical effects of a bright soliton in Bose-Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross-Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.

Dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that for big enough initial inhomogeneity of density, interplay of nonlinear and dispersion effects leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations.

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

Bose-Einstein condensates with inhomogeneous scattering length in one and two dimensions

We report on investigations of the properties of bright solitons in Bose-Einstein condensates in the presence of point-like spatial inhomogeneities, in one and two dimensions. By considering an analytical variational approach and full numerical simulations, we describe such processes due to interactions between the soliton and the inhomogeneity as the trapping, reflection, and transmission of bright matter solitons. We also study the critical number of particles as a function of the magnitude of the impurity.