Kenzu Abdella

A New Second-Order Turbulence Closure Scheme for the Planetary Boundary Layer

A new turbulence formulation for the planetary boundary layer (PBL) is presented and compared with largeeddy simulations (LES) for the dry PBL. The new scheme contains a prognostic equation for the turbulent kinetic energy. Other second-order moments are determined diagnostically through a parameterization of the third-order moments that is based on a convective mass-flux argument. For the heat flux this leads to a nonlocal formulation with the usual down-gradient term and a counter-gradient term. The counter-gradient term turns out to be a combination of well-established formulations with an additional new term. The performance of the new scheme is tested in a variety of cloud-free PBL conditions by comparing the results with corresponding LES simulations. The scheme is able to accurately reproduce the LES results of the mean as well as the turbulent quantities including third moments.

Local quaternion Fourier transform and color image texture analysis

Color images can be treated as two-dimensional quaternion functions. For analysis of quaternion images, a joint space-wavenumber localized quaternion S transform (QS) is presented in this study for a simultaneous determination of the local color image spectra. The QS transform uses a two-dimensional Gaussian localizing window that scales with wavenumbers. Rotation invariance, invertibility and computational aspects of the QS transform are discussed. The power map of the QS transform is presented here as a powerful tool in color image texture and pattern analysis. Examples are presented.

The trinion Fourier transform of color images

Any color may be represented in terms of three components (RGB or HSL) or four components (CMYK). For the four component color representation the use of quaternions, with one real and three imaginary components, is natural. By setting one component to zero, quaternions have been used in RGB or HSL representation of colors and color images. In this paper a new quantity, trinion, with one real and two imaginary components, is introduced and its use in color image representation is examined. The goal is to see if significant efficiencies in representation, analysis and computation involving three component color images accrue with the use of trinions. Two versions of the trinion Fourier transform (TFT) are introduced and it is shown that using TFT is preferable for combined analysis of three component color images rather than separate monochromatic analysis of each component and use of quaternions. Joint space-wavenumber localized trinion S (TS) transform with a two-dimensional Gaussian window function that scales with wavenumbers is also presented. Invertibility, rotation invariance, and computational aspects of the TS transform are discussed.

Modelling Boundary-Layer Clouds With a Statistical Cloud Scheme and a Second-Order Turbulence Closure

We present a second-order turbulence model for the cloudy planetary boundary layer (PBL), which includes a statistical scheme of the sub-grid scale condensation. The model contains prognostic equations for the turbulent kinetic energy, total water, and liquid water temperature, the latter two being assumed to be conservative variables. Using these conservative thermodynamic variables the condensation process is formulated as a function of the departure of the total water from saturation and its variance. The computation of the variance requires second moment correlations which are modelled through the parameterization of the third-order moments using a convective mass-flux formulation. The inclusion of these third moments and new assumptions on heat flux transport lead to a nonlocal turbulence scheme with counter-gradient effects. The final form for the heat flux turns out to be a linearized version of a previously established result. For the statistical cloud formulation, a linear combination of a Gaussian and a positively skewed distribution function is used with a modified liquid water flux expression to account fornon-Gaussian behaviour.The effect of the turbulence scheme on the boundary-layer cloud structure is discussed and the performance of the model is tested by comparing it against the large eddy simulation (LES) of the undisturbed period of the Atlantic Stratocumulus Transition Experiment (ASTEX). The model is able to produce both mean and turbulent quantities that are in reasonable agreement with the LES output of ASTEX.

Non‐iterative surface flux parametrization for the unstable surface layer

Abstract This study presents a semi‐analytic non‐iterative solution for the Monin‐Obukhov similarity equations under unstable surface conditions. The solution is represented in terms of the non‐dimensional Monin‐Obukhov stability parameter z/L. This parameter is given as a function of the bulk Richardson number and other surface parameters including the heat and momentum roughness lengths which are generally assumed to be different in this formulation. The proposed formulations give results that are both quantitatively and qualitatively consistent with the fully iterated numerical solution for a wide range of surface parameters.

The application of the Sinc-Collocation approach based on derivative interpolation in numerical oceanography

Abstract In this paper, the application of a Sinc-Collocation approach based on first derivative interpolation in numerical oceanography is presented. The specific model of interest involves a hydrodynamic model of wind-driven currents in coastal regions and semi-enclosed seas with depth-dependent vertical eddy viscosity. The model is formulated in two different but equivalent systems; a complex-velocity system and a real-valued coupled system. Even in the presence of singularities that are often present in oceanographic problems involving boundary layers, the Sinc-Collocation technique provides exponentially convergent approximations. Moreover, the first derivative interpolation approach which uses Sinc-based integration to approximate the unknown has advantages over the customary Sinc method of interpolating the unknown itself since integration has the effect of damping out numerical errors that are inherently present in numerical approximations. Moreover, the approach presented in this paper preserves the appropriate endpoints behaviors of the Sinc bases, resulting in a highly accurate and computationally efficient method. The accuracy and stability of the proposed method is demonstrated through the solution of several model problems. It is further shown that the proposed approach is more accurate and computationally less expensive than those obtained by the Sinc-Galerkin approach reported in previous studies.

Modeling Drought Option Contracts

We introduce a new financial weather derivative—a drought option contract—designed to protect agricultural producers from potential income loss due to agricultural drought. The contract is based on an index that reflects the severity of drought over a long period. By modeling temperature and precipitation, we price a hypothetical drought contract based on data from the Jinan climate station located in a dry region of China.

Analysis and Calibration of Empirical Relationships for Estimating Evapotranspiration in Qatar: Case Study

AbstractKnowledge of evapotranspiration (ETo), which is the process of water loss from vegetated soils due to evaporation and transpiration, is important in real-time irrigation management and water-resource allocation, particularly in water-scarce regions. In this study, several methods used in estimating evapotranspiration, including the Blaney-Criddle, Hargreaves-Samani, Jensen-Haise, Linacre, and Turc methods were calibrated and validated against the Penman-Monteith model, which is considered as the standard method of estimating evapotranspiration. The paper utilizes data from the Doha International Airport meteorological station over a period of 30 years (January 1985–December 2014). ETo values were estimated using the different methods. These values were then compared to those obtained by the Penman-Monteith method. Using appropriate indicators, the Turc method was found to be the best for estimating ETo over Doha (R2=0.9519, RMSE=1.4511  mm day−1, and MAE=1.1633  mm day−1). The Turc method comes in...

Modelling the Effects of Pollution on a Population and a Resource in a Polluted Environment

A model for the effect of pollution on an animal population partially dependent on a plant resource is examined. Using a system of ordinary differential equations, the model tracks and relates changes in an animal population and its internal pollution levels, a plant population and its internal pollution levels, and the overall environmental pollution level. The model system is analysed using standard mathematical techniques, including the direct Lyapunov method and numerical simulations. Criteria for the stability of the system are found and numerically tested. Three inequalities are sufficient to establish global stability, and a parameter range exists in which these criteria are satisfied. The stability criteria dictate that the system will be globally stable provided that the removal rate of the pollution from the environment, the intrinsic growth rate of the plant population, and the rate the animal population relieves itself of its pollution are all sufficiently large.