Quantifying Changes in Reconnaissance Drought Index using Equiprobability Transformation Function

The Reconnaissance Drought Index (RDI) is obtained by fitting a lognormal probability density function (PDF) to the ratio of accumulated precipitation over potential evapotranspiration values (alpha(k)) at different time scales. This paper aims to address the question of how a probability distribution may fit better to the alpha(k) values than a lognormal distribution and how RDI values may change in shorter (i.e., 3-month, and 6-month) and longer (i.e., 9-month, and annual) time scales during 1960-2010 period over various climate conditions (arid, semi-arid, and humid) in Iran. For this purpose, the series of RDI were initially computed by fitting a lognormal PDF to the alpha(k) values and the Kolmogorov-Smirnov (K-S) test was implemented to choose the best probability function in different window sizes from 3 to 12-months. The corresponding RDI values for the best distribution were then deriven based on an equiprobability transformation function. The differences between RDI values (the lognormal (RDIlog) and the best (RDIApp) distributions) were compared based on Nash-Sutcliffe efficiency (NSE) criterion. The results of goodness of fit test based on threshold value in the K-S test showed that the goodness of fit in the lognormal distribution may not be rejected at 0.01 and 0.05 significance levels while may only be rejected in a short term (Apr.-Jun.) period at humid station (Rasht station), and three-month (Oct.-Dec. and Apr.-Jun.) and six-month (Apr.-Sep.) periods in semi-arid station (Shiraz station) at significance levels of 0.10 and 0.20, correspondingly. Further a difference between RDIlog and RDIApp performed that RDI values may change if the best distribution employs and this may therefore lead to significant discrepant and/or displacement of drought severity classes in the RDI estimation.