0 is a scale factor, and is the gamma function. Parameters and of the gamma function are estimated for each time scale (k) and for each location. The estimated parameters are then used to find the cumulative probability of for a given year for the location under study.
3. Reference Evapotranspiration Equations
For purpose of this paper, we selected the most commonly used ETo methods including Blaney-Criddle (Blaney-Criddle, 1950), Thornthwaite (Thornthwaite, 1948), Hargreaves (Hargreaves & Samani, 1985), Penman-Montieth with Hargreaves radiation term (Allen et al., 1998) and FAO-56 Penman-Montieth (Allen et al., 1998). In this study, the latest method was used as the reference method.
4. Statistical indicators
For each station, Mean Bias Error (MBE) and Root Mean Square Error (RMSE) were calculated to compare the impact of the different ETo methods on RDI values. The smaller RMSE and MBE indicate the better model's performance.
Results
The values of ETo estimations obtained with four methods were compared with those calculated by the FAO56 P-M equation. In Bandar Anzali, the ETo values estimated by Blaney-Criddle equation were the highest among selected methods with a rather significant difference of about 500 mm in mean values. In Sharekord and Kerman, the Thorentwaite equation estimated the lower values, wherease in Ahvaz the highest ones were estimated by this method.
In the next step, assuming k is equal to 12, the RDIst series were calculated using the ETo values estimated by the methods under study. The comparison over the 39 last years revealed that the RDIst values calculated by the ETo methods under study are very close to those estimated by ETo reference method. In the other hand, in the most cases, the differences between RDI values were relatively small and do not exceed any drought severity threshold.
Since 3, 6, 9, 12, 24 or 48 months are the typical time scales for precipitation deficits to affect the five type of usable water sources (soil moisture, ground water, snowpack, steamflow and reservoir storage),the impact of various ETo methods on the severity of drought calculated by RDIst for shorter time scale than a year were also discussed. The analysis and comparisons are performed for the 6-month and 3-month time scales. The results of the comparison of the RDIst values calculated by four ETo methods against those obtained using FAO56 P-M suggested that there are reasonably good agreements between the 6-monthly RDIst series in all stations. The RMSE values were less than 0.51 and MBE values which can be practically considered as zeros. In the case of the four 3-month time scale, the most accurate results in Kerman and Sharekourd stations are provided by PMT and HS equations in relation to the other models.
Conclusion
The RDI is an important and useful tool for indicating meteorological drought. However, prior to apply this index, its sensitivity to ETo methods must be identified. This paper concludes that the differences between RDIst calculated by the selected ETo equations and those computed by reference method have no effects on the characterizations of drought severity class through RDIst series.The PMT and HS equations performed relatively better than the other models in semi arid stations (Kerman and Sharekourd) Therefore even if minimum data are available (P, T), the severity of drought can be reliably assessed by this index. These results are similar to those reported by Vangelis et al. (2013) for two stations in Greece.
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