عنوان مقاله [English]
Background and Objectives: The rainfall Intensity–Duration–Frequency (IDF) relationships are among the most important requirements in the field of planning, design and operation of hydraulic structures and water resources different projects. Mainly the creation of IDF curves requires statistical analysis of precipitation data at different durations and so when the study basin is no data or has limited statistics, the survey is difficult. However, in most basins, availability to daily precipitation data is easily possible. Therefore, aim of present study is an evaluation and comparison of IDF curves derived from the integrating fractal theory and generalized extreme value distribution relationship for ungaged site on the basis concept of fractal properties of precipitation with the empirically common relationships and determination of the error rate and calculation accuracy and reliability of this relationship into other relationships.
Materials and Methods: In this research, by using of data of maximum depth of annual rainfall at daily duration, construction of IDF curves with the method based on the approach of an integrated of fractal nature of rainfall data and generalized extreme value distribution was done. Then, IDF curves was created by applying Ghahraman method of the empirical relationship was given for this method and at the conventional method of statistical analysis of extreme annual rainfall data at different durations for study station. Ultimately, evaluation and quantitative and qualitative comparison of results of fractal theory method with Ghahraman empirical relationship was done. This research was applied for the Chenaran rain gauge station at latitude 〖36〗^° 〖 38〗^' 〖 38〗^" and longitude 〖59〗^° 〖07〗^' 〖53.1〗^".
Results: Investigation of Fractal behavior in precipitation data at the Chenaran rain gauge station showed precipitation properties at time range from 1 to 7 days, follows from the simple scaling hypothesis (Monofractal) and the estimated design storm by fractal theory has a good agreement with the precipitation observed data. The results at Chenaran rain gauge station shows the accuracy superiority of an integrated of fractal theory and generalized extreme value distribution relationship with an error average 9.34 than the Ghahraman empirical relationship with an error average 16.43. In addition, estimation error of quantities IDF by the fractal theory relationship to the conventional method that is based on the real data at 24 hours duration was calculated zero. So far as the construction of IDF curves by an integrated of fractal theory and generalized extreme value distribution relationship, only is done by using the 24-hour maximum rainfall intensity data; it can be concluded; the mentioned method has the suitable accuracy and acceptable results.
Conclusion: The present research is an attempt to increase the use of IDF scaling relationship than to using of compiled empirical relationships that conducted without regard to geographical and hydrological conditions; for using in regions that are faced with deficiency or the lack of rainfall data. The important characteristics of this relationship is the foundation of it based on the fractal properties of rainfall and in contrast, prepared of IDF curves in both experimental and conventional method is only depends on the statistical and mathematical analysis without attention to physical principles of precipitation process, and thus will follow increase the uncertainty of the results.