Zekai Sen

First-order markov chain approach to wind speed modelling

Abstract Hourly wind speed data in northwestern region of Turkey are simulated by using transition matrix approach of the first-order Markov chain method. For this purpose, the wind speed time series is divided into various states depending on the arithmetic average and the standard deviation. Once the control and validation of the model is confirmed, it is then used for generating synthetic series of various lengths of any desired duration. Wind speed measurement parameters are used to generate synthetic series with the preservation of the statistical parameters and the first-order autocorrelation coefficient. It is observed that for short periods, the parametric results obtained from the synthetic time series are close to the measured values. It is concluded in this paper that first-order Markov chain, despite its simplicity, accounts for more than 90% of the statistical parameters in the synthetic wind speed time series at most of the 10 stations considered. However, the discrepancy of the results is due to the use of first-order Markov chain as a first approximation. Since, hourly wind speed data are used in addition to the first-order autocorrelation coefficient second and even third-order autocorrelation coefficients are also significant. Therefore, in the future hourly wind speed modelling at least second- or preferably third-order, Markov chain must be tried.

Spatio-temporal drought analysis in the Trakya region, Turkey

Abstract Since droughts are natural phenomena, their occurrence cannot be predicted with certainty and thus it must be treated as a random variable. Once drought duration and magnitude have been found objectively, it is possible to plan for the transport of water in known quantities to drought-stricken areas either from alternative water resources or from water stored during wet periods. The summation of deficits over a particular period is referred to as the drought magnitude. Drought intensity is the ratio of drought magnitude to its duration. These drought properties at different truncation levels provide significant hydrological and hydrometeorological design quantities. In this study, the run analysis and z-score are used for determining drought properties of given hydrological series. In addition, kriging is used as a spatial drought analysis for mapping. This study is applied to precipitation records for Istanbul, Edirne, Tekirdag and Kirklareli in the Trakya region, Turkey and then the drought period, magnitude and standardized precipitation index (SPI) values are presented to depict the relationships between drought duration and magnitude.

Investigation of fatigue behaviour of asphalt concrete pavements with fuzzy-logic approach

Fatigue life and deformation are intimately related phenomena and a model involving a relationship between them can best be derived by methods that explicitly take vagueness into account. In this paper, the theory of fuzzy sets, especially fuzzy modeling, is employed to represent fatigue life and deformation relations as a set of fuzzy rules. A fuzzy logic algorithm has been devised for estimating the fatigue life from deformation measurements. The main advantage of fuzzy models is their ability to describe the knowledge in a descriptive human-like manner in the form of simple rules using linguistic variables only. In this manner the classical power relationship between the fatigue life and deformation variable can be replaced by a set of fuzzy rule bases. The fuzzy approach is applied for test data obtained in Isparta city, Turkey.

Solar Irradiation Estimation from Sunshine Duration by Geno-Fuzzy Partial Approach

Terrestrial solar irradiation estimations are obtained mostly from the sunshine duration measurements through almost linear models such as the classical Angstrom formulation. The parameters of such model are estimated through the least squares technique in practical studies. In this article, more efficient model based on the fuzzy system concept is proposed for the architecture of solar irradiation estimation from the sunshine duration measurements. Especially, partial fuzzy modeling accounts for the possible local nonlinearities in the form of piece-wise linearizations. The parameters estimation of such a fuzzy model is achieved through the application of genetic algorithm technique. The fuzzy part of the model provides treatment of vague information about the sunshine duration data whereas the genetic part furnishes an objective and optimum estimation procedure. The application of geno-fuzzy model as proposed in this article is presented for three stations in Turkey and the results are constrasted by the previous classical approaches.

Wind energy directional spatial correlation functions and application for prediction

In planning, design, operation and maintenance of wind farms, the spatial variations in wind velocity become significant. Although there are many wind energy studies at a single location, spatial assessment evaluation methods are scanty. Wind velocity maps may provide a common basis for regional assessment and interpretations, but they do not yield means of regional prediction. Hence, the main purpose of this paper is to propose some new concepts and methods that are useful prior to regional wind energy potential calculations. Among these are Directional Point Cumulative Semivariogram (DPCSV) concepts, which provide information concerning local spatial wind velocity and/or elevation changes. It is possible to obtain the radius of wind velocity influence around each station, along desired directions, based on the DPCSV concept. The implementation of the proposed methodology is presented for some wind velocity measurement stations in Turkey. For the application, the sample DPCSVs are first obtained from the available data, and then converted to Local Spatial Dependence Functions (LSDF). These functions are the basic ingredients for the regional wind velocity estimations. The reliability of the methodology is measured through the cross validation procedure and it is observed that the procedure is valid with less than 20% error.

Spatial Dependence Measures

Rather than geometrical weighting functions as in Chapter 2, it is preferable to obtain spatial dependence function from a set of measurements points. Prior to such a functional derivation, it is necessary to examine the isotropy and homogeneity of the spatial data directionally and the point-wise features of the regionalized variable (ReV). The basics of semivariogram (SV), with its different components such as sill, nugget, and radius of influence, are presented in descriptive and application manners. Similar to SV cumulative SV (CSV) and point CSV (PCSV), concepts are explained with applications to groundwater quality data. It is emphasized that PCS helps to depict the spatial behavior features around any sampling point by taking into consideration the contribution from the surrounding measurement points. It is shown that for each location of measurement it is possible to obtain the radius of influence, if necessary along any direction, and their regional contour maps provide the radius of influence at non-measurement locations. Once the radius of influence is known, then it is possible to depict which nearby measurement locations should be taken into consideration in the calculation of unknown data value. The validity of any method can be decided on the basis of cross-validation error minimization. A new concept of spatial dependence function (SDF) is developed without the need that regional data have normal (Gaussian) probability distribution. The application of SDF is presented for earthquake and precipitation data from Turkey.

A Short Note on Wind Speed with Height Exponent Estimation by considering Time Series Variations

Height extrapolation of wind velocity is frequently used in practical studies, such as wind energy calculations and air pollution modelling. The mean wind profile, i.e. measurements of wind speed as a function of height, is often described for engineering purposes by a “power law”, where there is an exponent value dependent on the atmospheric eddy fluctuations, meteorological lapse rate, and the environmental and topographical conditions. In practical studies, depending on the environmental conditions, the value is obtained rather arbitrarily and subjectively with a typical value of 0.14. In this short Note, perturbation methodology is applied to the power law, and consequently, an objective way of exponent determination is presented on the basis of the wind speed measurements at different heights. Finally, it is observed that the exponent is a function of the wind speed averages, standard deviations and the correlation coefficients between two wind speed time series at different heights.

Forecast errors in the Florida State University atmospheric boundary layer model (FSU1DPBL). Part I: Thermal advection effects

Short range weather forecasting and atmospheric boundary layer (ABL) processes are studied by using a one-dimensional ABL model where the horizontal advection terms are neglected. The ability of the model, the Florida State University atmospheric boundary layer (FSU1DPBL) model, to forecast minimum temperature is investigated in terms of thermal advection effects. The model is used for 12-, 24-, and 36-h forecasts of minimum temperatures. The minimum temperatures obtained from the model forecasts are compared with observations. The investigation is confined to days meeting criteria representative of clear and calm synoptic conditions. Errors between observations and model results are determined using thermal advection analysis in the boundary layer since horizontal thermal advection affects cooling rates at night. The errors are found to be strongly correlated with thermal advection in the lowest part of the ABL. By carrying out some case studies, it is seen that the model is more prone to errors in dry conditions. It is also confirmed that the strong thermal advection aloft getting closer and closer to the ground largely explains the difference in minimum temperatures between the model and observations. The results show that the model is also a useful tool for the short-range weather forecasting since it is not computationally expensive. The model is able to simulate well the nighttime minimum temperatures, and can be used operationally.

Data Types and Logical Processing Methods

Not only numerical but also linguistic data are necessary in the modeling of earth sciences events. Measurements are sources of numerical data whereas observations lead to linguistic data. Numerical data include randomness and errors but linguistic data are rather fuzzy, which means that there are uncertainties in both data types. Accordingly, the final model results as predictions or estimations include errors that must be confined within ±5% limits in practical applications. Spatial estimations can be obtained either on point basis or on sub-areal basis depending on the refinement of the problem at hand and purpose. In general, longitude (easting), latitude (northing), and regionalized variable (ReV) value at this location are necessary for a complete description and establishment of a point-wise spatial model, where these three values are referred to as triplicate; but in the case of pixel location its size is also necessary, which leads to four variables (quadruple) for the description of ReV. Simple classical triangularization, polygonalization techniques are used in addition to innovative percentage polygon methodology. Droughts are a kind of spatial earth sciences with coverage area that can be modeled by probabilistic approaches.

Classical Spatial Variation Models

Men have tried to model spatial behavior of the natural phenomena since a long time, with initiative simple models such as the weighting functions, which are supposed to represent regional dependence structure of the phenomenon concerned. Unfortunately, commonly employed weighting functions are not actually data-dependent and hence they are applicable invariably in each spatial prediction, which is not convenient since each spatial phenomenon will have its own spatial dependence function. Spatial data distribution can be uniform, randomly uniform, homogeneous, isotropic, clustering, etc., which should be tested by a convenient test as described in the text. Besides statistically it is also possible to depict the spatial variation through trend surface fit methods by using least squares technique. In this chapter, finally, adaptive least squares techniques is suggested in the form of Kalman filter for spatial estimation.