Stochastic Forecasting of Drought Probabilities (Case Study on Northwest of Iran)

1. In recent years, droughts have been occurring more frequently, and their impacts are being aggravated by the rise in water demand and the variability in hydro-meteorological variables due to climate change. As a result, probabilities of different characteristics of drought have a great importance in planning and managing water resource systems to cope with the effects of droughts [1]. A lot of researchers have focused to investigate drought frequency analysis, and most of them are based on historical data record or Markov chain model. But the Markov first order model cannot reproduce the observed persistence of annual rainfalls and the correlation structure among rainfalls in different months, although the correlation between any two consecutive months is reproduced. Therefore, both short and long timescale drought behavior investigation must be accomplished using a stochastic procedure such as Valencia-Schaake disaggregation model that is able to reproduce both characteristics of annual rainfalls and all correlations among monthly rainfalls in the same year [2].2. Methodology2.1. Study area and data analysis:In this study, the monthly and annual time series of rainfall of twelve synoptic stations were used as base stations geographically located in the northwest of Iran. The rainfall data series had a 50-year statistical period (1961-2010). First, the rainfall data records were checked using a number of initial statistical tests. Then, the Pearson type III is found the most appropriate distribution of monthly and annual rainfalls at all stations using the PPCC test.2.2. Stochastic data generation procedure:In this study, annual and monthly rainfall data are required to investigate drought characteristics at both annual and monthly levels. However, efforts must be made to ensure that annual and within year statistical characteristics are equally preserved in the generated sequences; hence rather than generating monthly rainfalls directly, annual rainfalls were first generated based on AR (1) model and later disaggregated to monthly rainfalls using the Valencia- Schaake approach. For each of the twelve synoptic stations, 1000 possible sequences of annual and monthly rainfalls were generated. Then, the probabilities of different characteristics of drought, including duration, intensity, interarrival time, transition probability matrix and convergence of annual and monthly drought events were estimated and predicted by using of Standardized Precipitation Index (SPI).3. Results and discussion3.1. Probability of nonexceedance:drought Probability of non-exceedance of various drought durations derived from the generated and historical time series shown in Fig. 1 for Urmia station. Fig. 1 shows that the non-exceedance drought probability increases with increasing drought duration, so that, for drought duration of more than 5-years, it approaches to unity (100%). Also, according to Fig. 1, expected probabilities from historical data have a significant deviation from the generated data and this irregular behavior has also been obtained for other stations. Fig. 2 compares the probability density function of SPI drought classes between historical and generated data for Urmia station. The figure shows that the probability density function of SPI drought classes according to the generated data adapts more closely to the normal distribution. Considering the drought as a natural phenomenon, it is justified that the longer data series would result in the more fitness of drought probabilities to the normal distribution.3.2. Drought intensity:According to RUN theory, drought intensity is determined by dividing deficiency of a drought parameter below the critical level to duration. Fig. 3 show the absolute values of drought intensities for periods of 1-10 year by SPI values for all stations. It is observed that, the 1-year drought intensity values for all sites are very close to 1.59, but these values for the 2-years period are very significantly for different sites. We found that the 2-year drought intensity highly correlates with serial correlation lag-1 of annual data and with increasing the serial correlation lag-1 of annual data, the 2-year drought intensity increases.3.3. Probability of drought interarrival time:Fig. 4 shows the probability of drought interarrival time between any two continuous droughts for all stations. It is observed that the probability function of drought interarrival time is nonlinear and the probability of 2-years interarrival time between two continuous droughts has the maximum value for all sites. This value decreases as the drought interarrival time increases. 3.4. Joint probability of drought duration severity:Drought duration and severity are both random in nature, and are significantly correlated. The relationship between these two parameters is an important feature of the drought characteristics investigations. Fig. 4 as an example, shows the joint probability distribution of drought duration and severity for Urmia station. According to Fig. 4, joint probabilities distribution of drought duration and severity are follow a bivariate exponential function. Values of expected drought probabilities with less duration and intensity are more and rapidly decrease with increasing duration and intensity.3.5. Transition probability matrix: Transition probabilities can be determined for short and long-term planning, and for the probabilistic characterization of the progression and recession of droughts. Table 1 shows the probability matrix values based on the distinction between generated and historical data in three drought classes for Urmia station (i.e. dry (D), normal (N) and wet (W) periods). It is seen that, probability of “normal” state after all different drought states for generated and historical data are equal and quite similar results have also been obtained for other stations. However, the results for the historical data for all stations have complete disagreement with each other and very different results from generated data. 3.4. Convergence of annual, season and monthly drought events: Annual drought is generally affected by the deficits of rainfall in the different months. The effect of each month and season on the annual drought is presented in Figure 13 for all sites within the study area. The results indicate that the dryness of the year is mostly affected by the rainy month (wet periods) rather than the dry periods. In other words, rainy months like November to May play a major role in determining drought status and the rest of the months of the year known as low rainfall months are considered as almost to have a negligible role.4. -The results suggest that there are serious doubts to cite the results of historical data and using stochastic simulation approach in the more accurate analysis of drought seems necessary and according to the results of historical data in such analyzes would be highly unreliable and with high error. -Non-exceedance drought probabilities increase with increasing drought duration and its value for more than 5- years drought duration is unity.-Change in drought intensities follows an urceolate asymmetric relationship, so that, maximum drought intensity is related to 2-year drought in most sites of study area. Nevertheless, significant difference between drought intensities in all sites and has a very high affinity with serial correlation Lag-1.-Joint probabilities distribution of drought duration and severity are follow a bivariate exponential function and values of expected drought probabilities with less duration and intensity are more and rapidly decrease with increasing duration and intensity.-According to the transition probability matrix, there is a high chance that a ‘normal’ state would follow an extreme ‘dry’ or ‘wet’ period in the study area and not spatial.- Results show that rainy month played a major role in determining the drought status and the rest of the months of the year known as low rainfall months are considered as almost to have a negligible role.