Determination of Distributional Changes of Annual Rainfall in Some Semi-Northern Stations in Iran

In addition to the limitations of conventional for investigation of rainfall trend tests (OLR, Mann-Kendall, Sen), these are only provided to estimate the conditional mean or median and do not consider different quantiles. Investigation of trend of changes of empirical probability distribution function (EPDF) and empirical cumulative distribution function (ECDF) can lead to more detailed information in comparison with conventional methods. The objectives of this study are application of quantile regression for estimation of changes in EPDF and ECDF of five annual rainfall series in northern Iran and interpreting their results.
The linear regression lines were estimated using quantile regression considering quantiles (0.05-0.95 with 0.01 steps). Then slope-quantiles curve were extracted based on slopes of quantile regression lines and considering 0.05 statistical significance level. The graphs of trends of different annual rainfall series were presented considering selected quantiles 0.9, 0.7, 0.5, 0.3 and 0.1 and the results were analyzed. The curves of EPDF and ECDF belonging to first and last years of data recorded periods estimated with concept of quantile regression and their curves were plotted and comparison between first and last year curves were done.
The numbers of lines with positive slopes were considerably more than negative slopes considering 0.05 statistical significance level. Investigation of quantile regression lines showed decreasing and increasing trend lines for upper and lower quantiles respectively for Mashhad series but increasing and decreasing trend lines for upper and lower quantiles of other series. In addition, the magnitude of slope lines for lower quantiles were more than those belonging to upper quantiles for Gorgan, Bandar-Anzali, Tabriz and Urmia series but there were inverse pattern for Mashhad series. Comparative assessment of ECDF curves belonging to first and last recoded years revealed apparent difference in lower level of probability for Tabriz, Gorgan, Urmia and (to some extent) Bandar-Anzali but a limited difference for Mashhad series. Assessment of changes pattern of EPDF showed relatively constant location parameters but changes in scale parameters that resulted in peakness for last year EPDF of Mashahad but flatness for Gorgan, Bandar-Anzali, Tabriz and Urmia series. In addition, most of the changes related to end part of EPDF for Mashhad and Bandar-Anzali series while related to beginning for Gorgan, Tabriz and Urmia series.
Thequantile regression can be used without affecting the limitations of conventional methods for trend analysis to access a wider range of applied analysis. There were apparent differences between signs of quantile regression lines belonging to upper and lower levels in all of five investigated series that showed Conventional methods could not be a useful tool for trend assessment of extreme events. The results of this study showed quantile regression is a suitable method to analyses changes in EPDF and ECDF of time series and this type of analysis present more useful results with comparison to conventional trend analysis methods.