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An alternative solution to the asymptotic Taylor statistical diffusion theorem (variance of particle dispersion) and the asymptotic variance quantifying convergence of averages is presented. The solution approach is to identify a representation of the Dirac delta function for large times in the same integral occurring in both variances. This particular function acts as an effective filter and provides a way to obtain an analytical solution. Considering these asymptotic dispersion parameters in a Gaussian diffusion model, analysis of the simulated concentration results shows that the model reproduces well the experimental ground-level concentration data. The variance between the temporal and ensemble averages is evaluated using turbulent observational data collected in a convective boundary layer. The results show that the difference between the temporal and ensemble means is of the order of 5% for an average time window of 1800 s. The present development can be used in a variety of situations involving different types of turbulence.

The primary focus of this article is to derive a solution to obtain the asymptotic turbulent dispersion parameter provided by the spectral Taylor statistical diffusion model. Unlike previous articles, which employed the Dirac delta function to solve the eddy diffusivity formula, in this study, we used the Dirac delta function properties to obtain directly the asymptotic turbulent dispersion parameter from the particles’ spatial dispersion variance described in terms of the Eulerian turbulence spectrum and of the scale factor defined formally as the ratio between Lagrangian and Eulerian timescales. From the Kolmogorov 1941 theory, a detailed derivation for this scale factor is presented. Furthermore, using high mean wind speed data generated by local topographic features, a magnitude for the Kolmogorov constant for the neutral atmospheric boundary layer is evaluated. Thus, this magnitude when added to other values obtained from the selected studies found in the literature provides an average value for the Kolmogorov constant that agrees with large eddy simulation data results. Therefore, this average value allows to obtain a more reliable description of this scale factor. Finally, employing analytical formulations for the observed neutral turbulent spectra and for the velocity variances as well as turbulent statistical quantities measured in a surface neutral atmospheric boundary layer, a vertical dispersion parameter is derived. This vertical dispersion parameter when utilized in a simple Gaussian diffusion model is able to reproduce well contaminant observed concentrations.The Gaussian simulated concentrations also compare well with those simulated by a Lagrangian stochastic particle dispersion model that uses observed vertical spectral peak frequency values at distinct levels of the neutral surface boundary layer. Therefore, the present study shows that the observational determination of a single vertical spectral peak frequency is sufficient to obtain a realistic vertical dispersion parameter characterizing the dispersive effect in the turbulent environment of the surface neutral atmospheric boundary layer.

In this contribution, motivated by the quest to understand cosmic acceleration, based on the theory of Hořava–Lifshitz and on the branch-cut gravitation, we investigate the effects of non-commutativity of a mini-superspace of variables obeying the Poisson algebra on the structure of the branch-cut scale factor and on the acceleration of the Universe. We follow the guiding lines of a previous approach, which we complement to allow a symmetrical treatment of the Poisson algebraic variables and eliminate ambiguities in the ordering of quantum operators. On this line of investigation, we propose a phase-space transformation that generates a super-Hamiltonian, expressed in terms of new variables, which describes the behavior of a Wheeler–DeWitt wave function of the Universe within a non-commutative algebraic quantum gravity formulation. The formal structure of the super-Hamiltonian allows us to identify one of the new variables with a modified branch-cut quantum scale factor, which incorporates, as a result of the imposed variable transformations, in an underlying way, elements of the non-commutative algebra. Due to its structural character, this algebraic structure allows the identification of the other variable as the dual quantum counterpart of the modified branch-cut scale factor, with both quantities scanning reciprocal spaces. Using the iterative Range–Kutta–Fehlberg numerical analysis for solving differential equations, without resorting to computational approximations, we obtained numerical solutions, with the boundary conditions of the wave function of the Universe based on the Bekenstein criterion, which provides an upper limit for entropy. Our results indicate the acceleration of the early Universe in the context of the non-commutative branch-cut gravity formulation. These results have implications when confronted with information theory; so to accommodate gravitational effects close to the Planck scale, a formulation à la Heisenberg’s Generalized Uncertainty Principle in Quantum Mechanics involving the energy and entropy of the primordial Universe is proposed.

Abstract During the cold season, episodes of a windstorm known as Vento Norte (VNOR) are frequently observed in the city of Santa Maria, situated in the central region of Rio Grande do Sul (RS). The onset of this windstorm is characterized by strong gusts with northerly component which are accompanied by a sharp increase in temperature and abrupt drying. A methodology based on the observed behavior of the standard deviation of temperature during VNOR was successful in identifying the onset and demise of the windstorm. Additionally, the research shows the results of different micrometeorological variables during the event. Early morning and evening atmospheric profiles exhibit an elevated mixed layer over central RS in association with the strong VNOR winds, indicating the presence of mechanically-forced mixing during nighttime hours.

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigate a formulation of quantum gravity using the Hořava–Lifshitz theory of gravity, which is General Relativity augmented by counter-terms to render the theory regularized. We are then led to the Wheeler–DeWitt (WDW) equation combined with the classical concepts of the branch-cut gravitation, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction and expansion phases. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched gravitation as well as the corresponding conjugate momentum to the category of quantum operators. Ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted, to make contact with similar approaches, to the integers α=[0,1,2], allowing this way a broader class of solutions for the wave function of the Universe. In addition to a branched universe filled with underlying background vacuum energy, primordial matter and radiation, in order to connect with standard model calculations, we additionally supplement this formulation with baryon matter, dark matter and quintessence contributions. Finally, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early Universe in contrast to the classic branched cosmology view of a smooth transition.

This study investigates a summer heat wave (HW) associated with downslope winds (DWs) affecting the central region of the state of Rio Grande do Sul (RS), Brazil. The temporal evolution of both phenomena is analyzed in the atmospheric boundary layer (ABL) using a combination of micrometeorological and rawinsonde data. For spatial characterization, ERA-5 reanalysis data are used. The HW covered a large area in southern Brazil, Argentina, and Paraguay. The main features of the HW were locally enhanced in the central region of RS by the development of DWs. The establishment of DWs near the surface depends on the dynamics of the ABL and local topographic features. The results showed that DWs that occurred during the HW contributed to the extreme temperatures and were associated with strong northerly winds, low relative humidity, and a drop in the dew points. Together, these extreme events influenced the turbulent and mean flow patterns of the ABL. The increase in turbulent activity associated with the warming of the ABL favored enhanced growth of morning ABL, while at night the simultaneous effects of radiative and turbulence cooling inhibited the formation of a strong stable ABL. The analysis highlights the complex interplay of synoptic and local factors associated with DWs and HW.

Land surface/ecosystem models (LSEMs) play a key role in understanding the Earth’s climate. They represent ecosystem dynamics by simulating fluxes occurring between the biosphere and atmosphere. However, for a correct flux simulation, it is critical to calibrate the model using robust and state-of-the-art calibration techniques. In this work, we optimize parameters of the Integrated Model of Land Surface Processes (INLAND) using the hierarchical multi-objective calibration method (AMALGAM) to improve the representation of surface processes in a natural ecosystem over the Pampa biome in South America. The calibration was performed using experimental data of energy and CO2 flux collected in a native field located in southern Brazil. We compared simulations using the default and calibrated parameter set. The results show that the calibration of the model significantly improved all fluxes analyzed. The mean errors and bias values were significantly reduced, and the seasonality of fluxes was better represented. This work is one of the first to apply a multi-objective calibration in an LSEM to represent surface fluxes in the Pampa biome, presenting a consistent set of parameters for future applications used in studies of biome land use and land cover.

The processes of water transfer in the soil-plant-atmosphere system are strongly affected by soil use and management. Differences in the dynamics of soil water transfer between no-tillage (NT) and conventional tillage (CT) practices during a soybean (Glycine max) growing season in southern Brazil were assessed in this study. All the water balance components were analyzed during the soybean growing season (2009/2010). Rainfall, runoff, soil water storage and hydro-physical soil properties were analyzed under two tillage systems. The land-atmosphere water vapor exchanges, obtained from eddy covariance stations, were analyzed with regard to the soybean agroecosystem. Characterizations of soil water storage were also formulated in the 2006/2007 and 2008/2009 soybean growing seasons under the NT system. During the periods without rain, the soil water content under NT was greater than under CT. The soil superficial layer, more porous under NT, contributed to less runoff during rainy events. Moreover, under NT conditions the water supply was always high, between 0.2 - 0.5 m. The total evapotranspiration in the soybean agroecosystem growing season was 410.8 mm.

Soil thermal conductivity is an important parameter for understanding soil heat transfer. It is difficult to measure in situ with available instruments. This work aims to propose a numerical model to estimate the thermal conductivity from the experimental measurements of soil heat flux and soil temperature. The new numerical model is based on the Fourier Law adding a constant empirical parameter to minimize the uncertainties contained in the data from field experiments. Numerically, the soil thermal conductivity is obtained by experimental linear data fitting by the Least Squares Method (LSM). This method avoids numerical indetermination when the soil temperature gradient or soil heat flux is very close to zero. The new model is tested against the different numerical methodology to estimate the soil heat flux and validated with field experimental data. The results indicate that the proposed model represents the experimental data satisfactorily. In addition, we show the influence of the different methodologies on evaluating the dependence of the thermal conductivity on the soil water content.

This study aims to review the physical theory and parametrizations associated to Turbulent Kinetic Energy Density Function (STKE). The bibliographic references bring a broad view of the physical problem, mathematical techniques and modeling of turbulent kinetic energy dynamics in the convective boundary layer. A simplified model based on the dynamical equation for the STKE, in an isotropic and homogeneous turbulent flow regime, is done by formulating and considering the isotropic inertial energy transfer and viscous dissipation terms. This model is described by the Cauchy Problem and solved employing the Method of Characteristics. Therefore, a discussion on Linear First Order Partial Differential Equation, its existence, and uniqueness of solution has been presented. The spectral function solution obtained from its associated characteristic curves and initial condition (Method of Characteristics) reproduces the main features of a modeled physical system. In addition, this modeling allows us to obtain the scaling parameters, which are frequently employed in parameterizations for turbulent dispersion.

Este artigo apresenta dois estudos de caso com objetivo de investigar a interação do vento local no interior de um vale, com o vento sinótico. A direção e a velocidade do vento local são obtidas de dados de resposta lenta medidos em um trecho leste/oeste do vale do rio da Prata, localizado na região de Nova Roma do Sul, Estado do Rio Grande do Sul. Os dados sinóticos da direção e velocidade dos ventos foram observados às 00, 12 e 18 TMG, em três estações meteorológicas de superfície localizadas na mesorregião do vale estudado. O padrão sinótico é avaliado através de campos meteorológicos construídos com a reanálise do NCEP-NCAR. A análise sinótica e a avaliação empírica do vento local são realizadas com a ajuda de outras variáveis medidas no fundo do vale, tais como radiação solar incidente e temperatura do ar. Os resultados mostram a existência de superposição das forçantes, térmica e canalizada, durante a madrugada e parte da manhã. Porém, quando a temperatura do ar durante a madrugada é baixa, o efeito térmico parece ser mais pronunciado do que o efeito do vento sinótico canalizado. O vento sinótico de norte proporciona um padrão característico do vento local no interior do vale. O escoamento vale abaixo é relativamente mais forte entre a madrugada e a manhã devido à soma dos efeitos, térmico e canalizado. Por outro lado, esses efeitos anulam-se a partir das 12 - 13 h, provocando calmaria no interior do vale.This paper shows two case studies to investigate the interaction of the local wind within a valley with the synoptic-scale wind. The direction and velocity of the local wind are obtained from slow response data measured within an east/west section of Prata valley in Nova Roma do Sul, Rio Grande do Sul State, Brazil. The synoptic direction and velocity wind were observed at 00, 12 and 18 TMG at three meteorological surface stations, situated in the studied valley. The synoptic pattern is evaluated by the NCEP-NCAR reanalysis of meteorological fields. The synoptic analysis and empirical evaluation of local wind are done with the use of others variables in the bottom of the valley, as incident solar radiation and air temperature. The results showed that there is a superposition of the thermal and the channeled flow forcings within the valley during the first hours and part of the morning. However, when the air temperature during the early morning is low, the thermal effect seems to be more pronounced than the synoptic channeled wind effect. The down-valley wind flow is relatively stronger during the early and the late morning due to the superposition of both thermal and channeled effects. On the other hand, these effects cancel each other from 12-13 hour, causing calm winds within the valley.

Um modelo estocástico Lagrangeano é utilizado para simular a dispersão e o transporte de contaminantes, sob condições estáveis, com velocidade do vento fraco, no experimento traçante realizado no Idaho National Engineering Laboratory (INEL). Neste trabalho é testada uma nova parametrização dos parâmetros que representam as freqüências associadas ao fenômeno de meandro do vento, presentes nas equações de Langevin para as componentes do vento horizontal. Esta nova parametrização é descrita em termos de uma quantidade adimensional que controla a freqüência de oscilação de meandro do vento e da escala de tempo, associada às estruturas coerentes em uma turbulência bem desenvolvida. As simulações demonstram que o modelo Lagrangeano considerado, incorporando esta nova parametrização, reproduz corretamente a difusão de escalares passivos em uma camada limite atmosférica estável com velocidade do vento fraco.A Lagrangian stochastic particle model is utilized to simulate the dispersion and the transport of contaminants under low wind stable conditions in the tracer experiment carried in the Idaho National Engineering Laboratory (INEL). In this work a new parameterization for the parameters representing the frequencies associated to the meandering phenomenon is tested. The new parameterization is expressed in terms of a non-dimensional quantity that controls the frequencies of the meandering oscillation and of the time scale associated to a coherent structure in a fully developed turbulence. The simulations show that the considered Lagrangian model, incorporating this new parameterization, reproduces correctly the diffusion of passive scalars in a low wind speed stable atmospheric boundary layer.

A Lagrangian particle model is used to study the dispersion of pollutants released in two different tracer experiments: Prairie Grass and Copenhagen. The model is based on a generalized form of the Langevin equation. Turbulence inputs are parameterized according to a scheme able to generate continuous values in all stability conditions and in all heights in the planetary boundary layer. Predicted values of ground-level concentration agree quite well with observed ones. The major progress of this paper is as follows: For air quality modeling it is highly necessary to include a parameterization that allows a correct description of the turbulent transport of contaminants released simultaneously from low and tall sources.