There are diverse and different climate regions in Türkiye due to the irregular topography. Turkey has seven local climate regions as the Black Sea, Marmara Sea, Aegean Sea, Mediterranean Sea, Central Anatolia, Eastern Anatolia and Southeastern Anatolia as in Fig. 3. Black Sea region is under the effect of North Atlantic Oscillation (NAO) variations which provide cyclonic rainfall occurrences. It is also subject to Siberian cold air movement during winter months winter seasons. This eastern Black Sea region has more than 2,000 mm of total annual precipitation. Along the region mountains are extensive parallelly to the sea coastal area and thus orographic type of rainfall events also take place. The Marmara region plays a transitional role between the Black Sea and Mediterranean Sea climate zones through Marmara inland and Aegean Sea regions. During summer (winter) months the region has warm to hot (cool) conditions. There are also snow events during winter months. Over the region annual average precipitation is about 850 mm. The Aegean Region has a type of climate especially along the coastal areas, where summer months are hot, dry, mild to cold whereas winter months show semi-arid continental climate. In this region the mountains are perpendicular to the coastal areas and thus interior parts has hot and dry summer months followed by cold and snowy winter months. The average annual precipitation amounts vary between 450 mm and 1,000 mm. The Mediterranean Region falls within the Eastern Mediterranean basin, which is reported by IPCC (2007, 2013,2019) among the most climate change impact subjective regions. In the Mediterranean region Taurus mountains run parallel to the coastal line and therefore rain clouds cannot enter the Central Anatolian part of the country. This region receives about 1,050 mm average annual precipitation. The central Anatolian region is surrounded by Black Sea and Mediterranean Sea mountains in the north and south, respectively. The western part is surrounded by the Aegean Sea region mountains and in the east is the Eastern Anatolian region high mountains. The clouds that penetrate to the Central Anatolian part from the Black Sea and Mediterranean Sea climate regions cannot produce significant rain. The average annual precipitation amounts are around 250 mm. The Eastern Anatolian region the mountain elevations reach more than 2,500-3,000 m. Eastern Black Sea and Caucasian Mountains does not pass rain clouds to enter the Eastern Anatolian climate region and thus the precipitation events take place as a result of continental climate regime with long winter months. The southeastern Anatolian region in the south of Türkiye is under the effect of a semiarid continental climate that is harsher than Central Anatolia, where hot summers, and cold and often snowy winters prevail.
The application of the proposed methodology is presented for monthly and annual precipitation records from different climate regions of the country. As for the further rectification of the classical SPI drought effect calculations Fig. 4 presents one representative meteorology station with monthly precipitation records and the final
A first glance at the graphs in this figure provides a set of useful information about the application of the classical and rectified SPI.
- In each graph the theoretical Cumulative probability distribution (CD) functions are confirmed with empirical monthly data CDF availability. Visually it is clear that the match between the data scatter and the theoretical CDF is perfect. The validity of this view is confirmed with the Kolmogorov-Smirnov method, which tests the comparison of two distributions to determine if they are originating from the same underlying CDFs. The maximum probability difference between these two CDFs fall within the acceptable range,
- Two-parameter Gamma CDF curves in each graph have unacceptable Kolmogorov-Smirnov test result as for the difference from the theoretical and empirical CDFs. The two-parameter Gamma CDFs are results of the classical SPI application, which does not take into consideration theoretical CDF of the data as explained in Section 2,
- In graph related to 17270 Şanlıurfa although empirical, theoretical and two-parameter CDFs have the same types, even then their parameters are different from each other. This point implies that the theoretical CDF in this paper are calculated according to maximum likelihood procedure, but SPI CDF are calculated according to statistical lower order moments like mean and standard deviation only,
- A general pattern appears in the comparison of theoretical and two-parameter Gamma CDFs, which are very close to each other around 0.50 probability on the vertical axis. In cases of less (more) than about 0.50 probability level for the same probability levels two-parameter Gamma CDF leads to more (less) than the corresponding theoretical CDF line,
- In order to give an idea about the quantitative difference between theoretical CDF and the two-parameter Gamma CDF 17636 Istanbul meteorology station graph is provided in a bigger scale as follows.
Two extreme points at 0.10 and 0.90 probability level are considered for the comparison based on corresponding monthly precipitation amounts along the horizontal axis. For 0.10 level theoretical CDF yields 10 cm and the two-parameter Gamma CDF value is 42. The relative error between these two parameters is 100(42–10) / 42 = 76%, which is not acceptable. Similar calculation for 0.90 probability level leads to 63% that is also very big value for acceptance. These percentages have different values in other graphs in Fig. 3 and they are all outside practically acceptable \(\pm 5\text{\%} \text{o}\text{r} \pm 10\text{\%}.\)
6. In the light of the previous steps, it becomes clear that without considering the most suitable theoretical CDF to empirical data CDF the results are in biased. Conversion of any precipitation time series to two-parameter Gamma CDF is not recommendable in practical works.
In general, it is recommended to calculate SPI values for 1-month, 3-month, 6-month, 9-month and 12-month periods. In order to make comparison and to save space in this paper 12-month results are presented for few meteorology stations as in Figure 5.
Comparison of the corresponding graphs with the ones in Figure 3 graphs provides the following points.
- As the duration increases the two-parameter Gamma CDF approaches the theoretical CDF, but still there are significant differences between the two CDFs,
- The same meteorology stations may have different theoretical CDFs in monthly and annual precipitation cases. For example, this is obvious for 17636 Florya/Istanbul precipitation case,
- In some cases, the theoretical CDFs do not change whether monthly or annually, but their parameters are completely different from each other (see 17130 Ankara precipitation theoretical graphs). The same is valid for the two-parameter Gamma CDF cases at the same stations,
- Comparison of the theoretical and the two-parameter Gamma CDFs in each annual graph has the same tendency as for the monthly CDFs in Figure 3.