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 (α_k) at different time scales. This paper aims to address the question of how a probability distribution may fit better to the α_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 α_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 (RDI_log) and the best (RDI_App) 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 RDI_log and RDI_App 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.