Using Fractal Interpolation Functions for Temporal Downscaling of Temperature Data

For optimal management of a catchment، the time and space downscaling of hydrological properties is essential. To achieve accurate energy and water budget equations in every time or space resolution، spatial and temporal downscaled information of water budget''s components are used. The fractal geometry is a branch of mathematics which has been utilized in discrete and periodic fields to generate data with different scales from observed data. In this research، the fractal interpolation functions were used for temporal downscaling of daily temperature data. The fractal dimension was used to express the rate of irregularities or fluctuations in the quatity. The fractal dimension of Mashhad daily temperature datasets for the period of 1992- 2007 was calculated. The mean of the fractal dimension was obtained 1. 54. Moreover، using the fractal interpolation functions and the midday temperature dataset with 15 days resolution، hourly temperature dataset has been estimated and compared with observed dataset. It was shown that despite the considerable time interval between two consecutive measurements (as 15 days)، the temperature time series with 3 hours resolution were obtained. The determination coefficient and the root mean square error of the model are 0. 77 and 7، respectively.