The standardized precipitation index

Monthly precipitation records from the island of Crete in Greece were used for the assessment of drought with the aid of the Standardized Precipitation Index (SPI) to study both temporal and spatial evolution characteristics for the period 1974-2005. The SPI analysis revealed that Crete has faced a drought period at northern part and two drought periods at southern and eastern parts. The multiple linear regression method was performed to form the relationship between annual precipitation, elevation and longitude. The precipitation is of orographic type and it strongly depends on longitude with decreasing magnitude in West-East direction. It was also found that the correlation coefficient R2 is higher for precipitation when both dependent variables, e.g. elevation and longitude are used. Elevation-rainfall gradients for a spatial variability of northern, southern and eastern parts are for an average year 0.8, 0.5 and 1 mm/m and for 30-year average 0.7, 0.5 and 0.7 mm/m respectively. Longitude-rainfall gradients are for an average year -3.2, -1.8 and 0.9 mm/km in northern, southern and eastern parts respectively, while the results obtained from 30-year average study are -3.3, -3.9 and -0.4 mm/km in northern, southern and eastern parts, respectively. This multilevel drought climatology will definitely serve as a basis for assessing the impacts of climate change on droughts, as it is indispensable for developing an appropriate policy for sustainable water resources.

Key words: Precipitation, drought, SPI, multiple linear regression


Drought is a recurrent climatic feature that is more frequent in the Mediterranean region, one of the most vulnerable areas concerning the future precipitation extreme conditions, since it lies in the transitional zone between Northern Africa and Southern Europe. Recent severe and prolonged droughts have highlighted Europe's vulnerability to this natural hazard and alerted the public, governments and operational agencies to the many socio-economic problems accompanying water shortage and to the need for drought mitigation measures (Lloyd-Hughes and Saunders, 2002). Several definitions of drought are given in the literature in terms of meteorological, hydrological, agricultural, and socio-economic conditions. However, all points of view seem to agree that drought is characterized by a significant decrease of water availability caused by a deficit in precipitation during a significant period over a large area (Rossi, 2000). It is difficult to determine the beginning of a drought, as its progress is slow and "creeping". Moreover, the effects of a drought can linger over many years after it has ended (Vicente-Serrano, 2006).

In spite of the fact that precipitation is the principal factor controlling the generation and persistence of drought conditions, other factors such as evapotranspiration, high temperature or dry winds contribute to the amplification of its intensity. The severity of drought depends on the duration of the phenomenon, the moisture deficit degree, and its spatial extend. Drought impacts first arise on agriculture which is prone to be affected by soil moisture decrease and high evapotranspiration. During extended dry periods, soil water depletes fairly rapidly. On the other hand, surface water and subsurface water resources are considered as the last to be affected from an extended dry period (Snmez et al., 2005).

Most of the methods that are used to assess droughts use indices to represent the levels of drought severity. A large number of studies are included in the international literature on examining the effectiveness of various drought indices regarding detection and monitoring drought events and regional drought analysis (Palmer, 1965; McKee et al., 1993; Rumman et al., 2009). Among the developed drought indices, Standardized Precipitation Index (SPI), Palmer Drought Severity Index (PDSI) and Reconnaissance Drought Index (RDI) are the most commonly used. This paper describes the calculation of drought climatology for the island of Crete in Greece based upon the SPI after a brief comparison between SPI, PDSI and RDI.

Many studies performed, include the application of the SPI index over the last decades (Hayes et al., 1999; Bonaccorso et al., 2003; Loukas and Vasiliades, 2004; Moreira et al., 2006). Paulo et al. (2005) applied the SPI for a region in Southern Portugal estimating the probability and the expected time of different drought severity classes. Furthermore, Bacanli et al. (2008) provided a comprehensive picture for the time scale used according to which when time scale increases drought is observed less but lasts longer, noting that there are short term conditions with seasonal variation for 3 and 6 months periods, while 9 and 12 months periods used showed drought with average duration and long term drought is assessed when using 24 months period.

Several studies deal with the relationship between mean annual precipitation and elevation (Basist et al., 1994; Harris et al., 1996; Naoum and Tsanis, 2004; Guan et al., 2005), finding significant increasing relations between these characteristics. A common belief that precipitation amounts increase with elevation has then adopted, thereby proving that the mountainous environment is prone to extreme and frequent precipitation events (Allamano et al., 2009). This phenomenon, called the orographic effect, is worldwide common. The orographic influence takes place only near high grounds under conditions of stable atmosphere. There are three principal mountain effects: orographic lifting, thermal forcing and obstacle effects which include mountain blocking and flow diversion (Naoum and Tsanis, 2004).

The intensity of cyclonic precipitation can be increased in a mountain or range of mountains by decreasing the rate of movement of the storm and causing uplifting activity of the air mass (Barry and Chorley, 1976; Marwitz, 1987). Log-linear or exponential functions may be better describe the relationship between precipitation and elevation in terms of other conditions, but the linear form is preferable to use and seems to be an acceptable approximation in most cases (Naoum and Tsanis, 2004).

Precipitation is measured in time and space and varies according to the general atmospheric circulation system and to local factors. The use of measured precipitation is practical in a variety of hydrological applications. The key factors in assessing extreme events like floods and droughts, are rainfall duration and intensity; the estimation of irrigation water needs is linked to a water balance that includes available water, represented by rain, and losses by crop evapotranspiration and other factors. Precipitation is characterized by a seasonal and a geographical variation. When the annual oscillation of the atmospheric circulation changes the amount of moisture inflow over the regions, seasonal variation occurs (Chow et al., 1988). The geographical distribution of precipitation depends on orographic factors and latitude. Rainfall amounts are greater near the Equator while diminish as the air moves toward higher latitudes. According to several reports in literature, other components that may affect the variability of precipitation include topography, orientation of topography and aspect, direction of wind and continentality (Naoum and Tsanis, 2003).

The objective of this study is to assess drought events over Crete in both spatial and temporal scale and connect them with precipitation variability. More specifically, the comprehension of the evolution of this climatic phenomenon and identification of important drought episodes are provided. Moreover, topographic factors and precipitation were correlated using multiple linear regression to ascertain the degree of influence of each factor.


2.1 The Standardized Precipitation Index (SPI)

In the present paper, the SPI is used for assessing drought occurrence in Crete. The index offers the advantage of assessing drought conditions over a wide spectrum of time scales, while comparison between dry and wet periods on different locations is possible. Moreover, it is based on precipitation alone, so that a drought could be assessed even if other meteo-hydrological data are not available (Bonaccorso et al., 2003).

There is a general agreement about the fact that the SPI computed on shorter time scales (3 or 6 months) describes drought events that affect agricultural activities, whereas on the longer ones (12, 24 or 48 months) describes the effects of precipitation deficit on different water resources components such as soil moisture, streamflow, groundwater, reservoir storage. In this paper, the longest time scale (48 months) is set in the calculation of the SPI.

The SPI index was developed by McKee et al. (1993). In its original version, precipitation for a long period at a station is fitted to a Gamma probability distribution, which is then required to be transformed into a normal distribution such that the mean SPI value equals to zero. The index values are then the standardized deviations of the transformed precipitation totals from the mean. The gamma distribution is defined by its frequency or probability density function:

Positive SPI values denote greater than median precipitation whereas negative values denote less than median precipitation. Periods with drought conditions are represented by relatively high negative deviations. Specifically, the ''drought'' part of the SPI range is arbitrary divided in four categories; mildly dry (0 > SPI > -0.99), moderately dry (-1.0 > SPI > -1.49), severely dry (-1.5 > SPI > -1.99) and extremely dry conditions (SPI < -2.0). A drought event is considered to start when SPI value reaches -1.0 and ends when SPI becomes positive again (McKee et al., 1993). Thresholds of the SPI for drought characterization are presented in Table 1.

2.2 The Reconnaissance Drought Index

The index is described as the ratio between two aggregated quantities of precipitation and potential evapotranspiration. The initial value of the index for a certain period, indicated by a certain month (k) during a year, is calculated by the following equation: where Pij and PETij represent the precipitation and the potential evapotranspiration of month j of year i, starting usually from October (customary for Mediterranean countries) and N is the total number of years of the available data.

The initial formulation of RDIst (Tsakiris and Vangelis, 2005) is based on the assumption that RDIo values follow the lognormal distribution and RDIst is calculated as: where y is the ln(RDIo), is its arithmetic mean and is its standard deviation.

The analysis of data from several locations and different time steps (3, 6, 9 and 12 months) showed that while ak values fit sufficiently to both lognormal and gamma distributions in almost all locations and time scales, in most of the cases the gamma distribution has a better fit. Therefore, the performance of RDIst could be more effective in many cases by fitting the gamma probability density function to the given frequency distribution of ak. In addition, this approach gives an answer to the issue of calculating RDIst for small time steps, such as monthly, which may include null precipitation values (ak = 0), for which equation (2) cannot be applied. The thresholds of this index are the same with SPI.

2.3 The Palmer Drought Severity Index

The Palmer Drought Severity Index (PDSI) is a measure of regional moisture availability. It has been used extensively to estimate drought events and wet spells in the United States, particularly as the primary indicator of the severity and extent of recent year droughts (Palmer, 1965; Heim, 2002), with applications in other parts of the world in the past decade (Briffa et al., 1994; Dai et al., 1998; Dai et al., 2004; Lloyd-Hughes and Saunders, 2002). The procedure considers meteorological variables such as monthly precipitation, evapotranspiration [computed using the Thornthwaite (1948) method] and soil moisture conditions that determine hydrological and agricultural drought.

In general, monthly PDSI values range between -9 and +9, where severe and extreme conditions are characterized by absolute values greater than 4 and 6, respectively (Szep et al., 2005). These thresholds may vary among the diverse geographic regions of the world, whereas 4 is considered to be the original extremity threshold (Brzdil et al., 2008) (Table 1). Furthermore, negative PDSI values correspond to drought events while positive values imply wet conditions. Compared to other traditional drought indices, PDSI offers several advantages: simulation of the moisture content of the soil in a monthly basis can be realized and it is suitable for examining the severity of drought events at regions with rather different climatic characteristics. The equations based on a rather complex water budget system are included in the calculation of PDSI and are analyzed in various studies (Palmer, 1965; Guttman, 1998; Wells et al., 2004; Szep et al., 2005; Van der Schrier et al., 2005).

Based on potential values for the quantities involved in the calculation of the index, Palmer (1965) defined the "climatically appropriate for existing conditions" precipitation, and here lies the difference between the latter and the actual precipitation which is the core of PDSI. The self-calibrating PDSI (SC-PDSI) as suggested by Wells et al. (2004) is more suitable for geographical comparison of different regions with different climates. Wells et al. (2004) improved the performance of the PDSI by incorporating automatic estimations of the empirical constants in the PDSI algorithm. That was achieved by determining a climatic characteristic weighting factor using data from each location (rather than by using data of a small number of stations from different climates as it was originally done). The deviation from normal precipitation was then multiplied by this weighting factor to produce a "moisture anomaly index." The weighting aimed to adjust the deviations of normal precipitation to be comparable amongst different areas and different months (Van der Schrier et al., 2005). Finally, the SC-PDSI is the most common PDSI version, while consists a more appropriate way of comparing the spatial relationships between areas of differing climates in terms of moisture because the SC-PDSI illustrates a more realistic index for drought periods or excessive moisture supply.

2.4 Multiple linear regression

Regression analysis is used to understand which among the independent raw data variables are related to the dependent variable, and to explore the forms of these relationships and hence, providing information for planning the collection of data when needed.

Least square regression was used for the analysis on the present study, which objective function is the minimization of the deviations of sum of squares between the observed response and the fitted response (Naoum and Tsanis, 2003). This involves the initial assumption that the relationship between the unknown parapeters is linear. The model function shapes a specified form that includes both the predictor variables (elevation and longitude) and the parameters considering that precipitation is the dependent (response) variable. Interaction effects between the variables also can be taken into account by being represented in the models with the addition of three more terms. The use of a second-order model could be also possible resulting in a ten-parameter model. The general form of the model used is: where p is precipitation (mm/year), x1 is elevation (m), x2 is longitude (km).

Study area and data description

The island of Crete is located in the southeastern part of the Mediterranean region and it is well known that comprises an area which has been characterized as one of the most drought prone areas of Greece. The island covers an area of 8336 km2, the mean elevation is 460 m and the average slope is 22.8%. Crete is divided into four prefectures, namely from west to east: Chania, Rethymnon, Heraklio and Lassithi. The mean annual precipitation is estimated to be 750 mm, varies from east - 440 mm (Ierapetra - elevation: 10 m) to west - 2118 mm (Askifou - elevation: 740 m) and the potential renewable water resources reach 2650 Mm3. The public belief that water resources are inadequate and that some kind of drought is imminent originates from political interests and disputes among the four prefectures and the more than 100 municipalities of the island, as well as poor water management (Manios and Tsanis, 2006).

The actual water use is about 485 Mm3/year. The main water use in Crete covers irrigation, with a high percentage of 83.3% of the total consumption. The domestic use, including tourism, covers 15.6% and the industrial use 1% of the total consumption (Region of Crete, 2002). The eastern and southern parts are more arid than the west and northern parts, as there is higher precipitation in the Northwestern coastal areas and lower in the Southeastern part of the island, a fact that confirms regional variations in water availability (Chartzoulakis et al., 2005). There are significant effects when the uneven spatial and temporal precipitation distributions of Crete, although common in many Mediterranean areas, are related to intensive agricultural activities and the tourism industry (Tsanis and Naoum, 2003).

Several studies have been performed for the application of the SPI. Especially in the area of Crete, Tsakiris and Vangelis (2004) concluded that the eastern part of the island suffers more frequently from droughts according to a method based on the estimation of the SPI and its use for characterizing drought. A digital terrain model based on spatial distribution utilizing a grid analysis and a simple computer calculating process was used and it was deduced that the proposed procedure could be easily applied to an area of mesoscale dimensions. It was concluded that a significantly persistent drought occurrence was noted during the period 1987 to 1994, while distinct drought events were observed in the years 1973-74, 1976-77, 1985-86 and 1999-00. Additionally, Tsakiris et al. (2007) estimated drought areal extent for Eastern Crete using the SPI and RDI and deduced that the driest year during the examined period from 1962-63 to 1991-92 is 1989-90. Naoum and Tsanis (2004) introduced a multiple linear regression model to derive the relationship between annual precipitation, elevation and longitude.

Monthly precipitation data was compiled by the WRDPC service (Water Resources Department of the Prefecture of Crete) for 56 precipitation stations (Figure 1). The stations mainly cover the eastern part of the island which has a higher level of agricultural and tourism activity than the western part. The gauges were located at elevations that ranged from sea level, in the prefecture of Iraklion (central Crete), to 905m a.s.l, in the prefecture of Lassithi (eastern Crete) (Region of Crete, 2009). These data cover a thirty (30) years time period for each month of the hydrological year (September to August), from 1974 to 2005.

Results and discussion

The selection of the most appropriate drought index was performed through comparison between SPI, RDI and SC-PDSI for 3 representative stations (Palea Rumata, Gergeri, Pachia Ammos). Graphical examination of temporal evolution of the pre-mentioned indices (Figure 2) showed that SPI and RDI conform better in all stations, whereas there is less coherence between SPI and SC-PDSI, as Table 2 shows. The extra components of temperature and AWC that are being taken into account during the SC-PDSI calculation affect the correlation with the other indices. On the basis of these plots and considering the easy applicability and worldwide use of the indices, SPI was finally selected for assessing drought analysis.

Long period characteristics represented by 48-month time scale values of SPI, were calculated for eighteen (18) representative stations, in order to provide an overview of prolonged drought occurrences in relation to the factor of elevation and longitude during the period 1974-2005. The island was divided into three parts (northern, south-central and eastern), so as orientation of topography factors is taken into account. The results of drought analysis in the the island of Crete during this period show a definite tendency towards prolongation and greater severity of drought episodes. Figure 3a and 3b illustrate the drought conditions of some representative stations in the northern part of Crete. The period 1988-1998 was recorded to be a period of drought for Palea Rumata, Kalives, Askifou and Anogia, while the intensity of wet periods of 1978-1985 and 1999-2004 vary between Palea Rumata (severely dry) and Kalives/Askifou (mildly dry) and vice versa respectively. Unlike the other stations, Muri and Finikia introduce an extra dry period during 1980-1986. The SPI peaks of each period correspond to the peaks of precipitation. It is obvious that Askifou and Muri have high precipitation values with an increasing trend due to topographic features, while in Palea Rumata precipitation decreases and in Kalives remains steady. The moving average method confirms the number of drought periods at each station.

The south-central part experiences an extra drought period during 2000-2002 concerning Gergeri, Pompia, Pretoria, Melabes and Lefkogia, while severely wet periods follow the second drought period (2002-2004) (Figure 4). Extreme drought spells were recorded in the year 1992 for Pompia, Melabes, Pretoria and Gergeri, during which precipitation was significantly decreased.

Finally, as Figure 5 shows, the eastern part of Crete experiences the most long-term drought period, especially in Sitia, that signs its beginning in 1990 and ends in 2003. It is important to stress that Agios Georgios -with three drought periods- appears the afore-mentioned drought period 8 years earlier. There is a significant extra wet period during 1986-1989 for Mithoi, Pachia Ammos and Sitia, a fact attributed to high precipitation values the referring period. In general, the southern and eastern parts of Crete suffer more from drought events.

Graphical examination of spatial evolution of precipitation confirm that there is variability according to the general pattern of atmospheric circulation; air masses moving from the south-west cover the west part of the island and move upwards, leaving the central-east part intact. However, differences between stations with different elevations lie on the orographic effect, so stations with high elevation represent higher precipitation values. Generally speaking, for the 30-year period, there are 26 stations with downward precipitation trend, 24 follow upward precipitation trend while 6 remain stable.

Two parameters (elevation, longitude) were proposed and adopted to perform simple linear regression individually for 55 stations. The station of Askifou was excluded from this method in order to obtain more reasonable results, as Askifou (with elevation 740 m) exemplifies a special case of a region with orographic precipitation. Upon examining the correlation between precipitation and elevation taking into consideration the northern, south-central and eastern part, it was found that the regression plot for all stations justifies the positive correlation (Figure 6). The plots based on elevation provided a more physically meaningful interpretation of the effect of this variable on precipitation; the presence of the orographic effect at high elevations. It is obvious that the eastern part provides the strongest correlation with a R2 value reaching 67%. Contrarily, the south-central part represents the lowest R2 value of 23%, a fact attributed to various local peaks due to the existent atmospheric circulation pattern.

On the other hand, further analysis covering the parameter of longitude showed that there is a negative correlation between the afore-mentioned parameter and precipitation. Four plots of longitude versus annual precipitation were constructed, as shown in Figure 7. The R2 value ranged from 9% in the case of eastern part to 13% in the case of northern part. The noticeable downward gradient of precipitation from one part to another denotes a statistical evidence of the geographical factor. In other words, the decrease of precipitation is responsive to longitude increasing. It is then deduced that topographic and geographic factors determine the spatial association in precipitation variations.

Multiple linear regression was used to study the level of association between the two variables for a dry year (1992-1993), a wet year (1980-1981), an average year (1978-1979) and a long-term average (1974-1975 to 2004-2005) (Table 3). The coefficient of determination (R2) is used to determine the adequacy of the regression equation. The relationship between precipitation and elevation is not as strong for the whole island (55 stations) as it is for individual parts, especially the eastern part for all years assessed. This is attributable to the relatively high elevations of stations in this part, which is likely to result in a higher association than the other parts. The R2 for the whole island varies between 16% and 40% for the one-variable model (maximum in average year) while a range of R2 34% to 49% is obtained for the two-variable model (maximum in wet year).

Results reported by Naoum and Tsanis (2003) demonstrated that, for a typical dry year, the island of Crete would receive up to 800 mm of precipitation, for an average year, precipitation has a range between 800 and 1100 mm and finally for a wet year, the island would receive precipitation greater than 1100 mm. Based on these values, the range of elevation-precipitation gradient (b1) is 0.29-0.68, 0.52-0.94 and 0.5-1 mm/m for dry, wet and average years, respectively. The range of longitude precipitation gradient (b2) for a dry year is -5.04 to 0.89 mm/ km, -5.41-1.3 mm/km for a wet year and -3.23-0.94 mm/km for an average year.

In brief, the results show that there is a general increase in the coefficient of determination from the one-variable equation to the two-variable equation for all years under study.

Following the multiple linear regression method, another form of analysis was carried out and included precipitation characteristics of 56 stations. The results are summarized in Table 4. Crete and especially the eastern part, experiences the lowest mean annual precipitation, the minimum number of rainy days and events during the dry year 1992-1993. On the other hand, the wet year 1980-1981 includes the highest mean annual precipitation and the maximum number of rainy days. The average year 1978-1979 represents average values of annual precipitation, rainy days and events number.

The number of rainy days varies according to two variables; space and time. Obviously, the dry year is characterized of the minimum of rainy days and events, whereas the maximum takes place during the wet year (Figure 8). In terms of the spatial component, there is a decreasing gradient of the rainy days and events from west to east. There are 52, 61 and 67 rainy days during the dry, wet and average year respectively and 23, 26 and 34 precipitation events on average occur during the dry, wet and average year respectively, a fact attributable to the low frequency and the high intensity of events in wet years in comparison to the higher frequency and lower intensity of events in average years. The dashed lines indicate lack of data the corresponding period of time. Figure 9 indicates the spatial distribution of precipitation during a dry, wet and average year. According to the atmospheric circulation pattern, air masses originate from 3 directions: north-west, south-west and west. The maps show that western Crete receives higher amounts of precipitation than eastern Crete. This is due to the complex orography of the west part (Lefka Ori Mountains), the regional northwest to southeast dominant meteorological atmospheric patterns and the higher elevation and steepest slope morphology of the western Crete in comparison with the eastern region of the island.

Upon examining two representative extreme precipitation events for the island for the years 1986 and 2001 (Figure 10), it was found that in 1986 case, three parts along the island suffered a maximum of daily precipitation up to 294 mm (Anogia) whereas in 2001 case the western part is covered with a maximum of daily precipitation at Askifou up to 160 mm. Obviously, in the latter event air masses pass over the western part of Crete and deliver high amount of mainly orogenic precipitation.


The selection of the most appropriate drought index was carried out through comparison between SPI, RDI and SC-PDSI for 3 stations in the island of Crete. The SPI was therefore selected for the drought assessment due to its worldwide applicability. The proposed methodology is easy to be applied and interpreted the precipitation deficit and thus can become a practical tool for the assessment of regional drought events. Accordingly, the SPI is a statistically coherent index for sensitively measuring drought.

The SPI was successfully applied in the island of Crete for drought assessment for the period 1974 - 2005 as for 18 stations. The SPI analysis revealed that Crete has faced a drought period at northern part and two drought periods at southern and eastern parts.

Results of simple linear regression demonstrated that precipitation and elevation are correlated through a positive rate, whereas a negative correlation lies between precipitation and longitude. It is then deduced that topographic and geographic factors determine the spatial association in precipitation variations.

The multiple linear regression method has been used to develop correlations to estimate the spatial distribution of orographic precipitation for complex territory such as that of the island of Crete in Greece using the parameters of elevation and longitude. The two-variable model is more reliable and realistic, especially when dealing with a relatively small number of rain gauges. The correlation coefficient R2 is lower when the one-variable model is used, whereas R2 is higher for precipitation when both dependent variables, e.g. elevation and longitude are used. Spatially, it was obvious that precipitation is of orographic type (precipitation is strongly correlated with elevation). Elevation-rainfall gradients for a spatial variability of northern, southern and eastern parts are for an average year 0.8, 0.5 and 1 mm/m and for 30-year average 0.7, 0.5 and 0.7 mm/m, respectively. Longitude-rainfall gradients are for an average year -3.2, -1.8 and 0.9 mm/km in northern, southern and eastern parts respectively, while the results obtained from 30-year average study are -3.3, -3.9 and -0.4 mm/km in northern, southern and eastern parts, respectively.

Results showed that western Crete receives higher amounts of precipitation than eastern Crete and this is due to the complex orography of the west part (Lefka Ori Mountains), the regional northwest to southeast meteorological atmospheric patterns and the higher elevation and steepest slope morphology of western Crete in comparison with the eastern region of the island.

The statistical tools that were used proved to be very effective in the evaluation of the spatio-temporal variability of precipitation and accordingly of drought in the island of Crete. These analyses should be valuable for the purpose of water resources management, especially in regions where orographic precipitation predominates. Finally, the climatology will provide a useful resource for assessing the regional vulnerability to drought in order to set the predictability of the phenomenon feasible.

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