Investigation of Monthly Pan Evaporation in Turkey with Geostatistical Technique

The aim of this study is to evaluate the spatial variations of monthly average pan evaporation amounts throughout Turkey by applying Geostatistical methods. Monthly averages of Class A pan evaporation data are reported by the General Directorate of State Meteorological Works using series of record lengths between 20 and 45 years at about 200 stations scattered over an 814.578 km2 surface area of Turkey. The data belonging to the summer months of June, July, and August are used in this study because the evaporation in this three-month period is greater than the sum of those of the other nine months. Monthly averages of the observed pan evaporation data are considered and the spatial variation of evaporation is analyzed. Kriging estimate maps are drawn and interpreted for the summer months. The study indicates that the spatial variation of monthly average pan evaporation values can be reasonably estimated by the geostatistical method based on observed pan evaporation data. It is suggested that this map may be used by decision-makers for accurate estimation of monthly pan evaporation in any reservoir management or irrigation projects where data availability is limited

Modifying Ritchie equation for estimation of reference evapotranspiration at coastal regions of Anatolia

Evapotranspiration (ET) is of great importance in many disciplines, including irrigation system design, irrigation scheduling and hydrologic and drainage studies. A large number of more or less empirical methods have been developed to estimate the evapotranspiration from different climatic variables. The Food and Agriculture Organization (FAO) rates the Penman- Monteith equation as the major model for estimation of reference (grass) evapotranspiration (ET0) because of the fact that it gives more accurate and consistent results as compared to the other empirical models. However, the main disadvantage of this method is that it cannot be used when the sufficient data are not available. The FAO-56 PM equation requires quite a few independent variables such as solar radiation, air temperature, wind speed, and relative humidity in predicting ET0. Worldwide, the weather stations measuring all these variables are few as the majority measure air temperature only. Therefore, for regions which may not be measuring all these meteorological variables, the temperature based models like Ritchie, Hargreaves-Samani and Thornthwaite equations is necessarily used instead of the FAO-56 PM equation. In this study, the Ritchie equation is applied on the measured data recorded at 158 stations at the Coastal are of Turkey (Mediterranean, Aegean, Marmara and Black Sea regions of Anatolia), and the monthly ET0 values computed by it are observed to be smaller than those given by the Penman-Monteith equation. Next, average values for the coefficients of the Ritchie equation, which are constants originally developed in [6], are recomputed using the ET0 values given by the FAO-56 PM equation at all weather stations in coastal regions of Anatolia (Turkey). The Ritchie equation modified in such manner is observed to yield greater determination coefficients (R2), smaller root mean square errors (MSE), and smaller mean absolute relative errors (MARE) as compared to the original versions of Ritchie equation suggested by [6]. It is concluded that for estimation of reference evapotranspiration at coastal regions of Anatolia where the meteorological measurements are scarce, the modified Ritchie equation can be easily used for estimating the ET0 values

Three-step N-R algorithm for the maximum-likelihood estimation of the general extreme values distribution parameters

First, starting out with the magnitudes of both the scale and location parameters given by the method of moments (MOMs), and assuming they are constants, the root of the single equation formed by equating the partial derivative of the log-likelihood function (LLF) with respect to the shape parameter (a) to zero is solved, partial derivative LLF/partial derivative a = 0. Next, with this value for the shape parameter and the MOMs estimate for the location parameter (c), the root of the single equation formed by equating the partial derivative of the LLF with respect to the scale parameter (b) to zero is solved, partial derivative LLF/partial derivative b = 0. Next, with the recently computed values for the shape and scale parameters, the root of the single equation formed by equating the partial derivative of the LLF with respect to the location parameter to zero is solved, partial derivative LLF/partial derivative c = 0. Next, with the recently computed values for the other two parameters, these single equations are solved once again, in the same order. As a result of these two cycles, the roots of the single equations turn out to be close to the roots of the simultaneous system of equations of partial derivative LLF/partial derivative a = 0 and partial derivative LLF/partial derivative b = 0 and partial derivative LLF/partial derivative c = 0. Finally, the system of three equations is solved by the Newton-Raphson (N-R) algorithm with those values used as initial estimates. (c) 2007 Elsevier Ltd. All rights reserved