Studying and applying the Standardized Precipitation Evapotranspiration Index (Case study: Tabriz Meteorological Station)

The present paper introduces new drought indices with caption standardized precipitation evapotranspiration index (SPETI) that the first by Vicente-Serrano et al (2009) is presented. The SPETI is based on precipitation and temperature data, and it has the advantage of combining multiscalar character with the capacity to include the effects of temperature variability on drought assessment. The procedure to calculate the index is detailed and involves a climatic water balance, the accumulation of deficit/surplus at different time scales, and adjustment to a log-logistic probability distribution. Mathematically, the SPETI is similar to the standardized precipitation index (SPI), but it includes the role of temperature. Because the SPETI is based on a water balance, it can be compared to the self-calibrated Palmer drought severity index (sc-PDSI). Time series of the three indices were compared for a set of observatories with different climate characteristics, located in different parts of the world. Under global warming conditions, only the sc-PDSI and SPETI identified an increase in drought severity associated with higher water demand as a result of evapotranspiration. Relative to the sc-PDSI, the SPETI has the advantage of being multiscalar, which is crucial for drought analysis and monitoring.
Material and We describe here a simple multiscalar drought index (the SPETI) that combines precipitation and temperature data. The SPETI is very easy to calculate, and it is based on the original SPI calculation procedure. The SPETI uses the monthly (or weekly) difference between precipitation and PET. This represents a simple climatic water balance (Thornthwaite, 1948) that is calculated at different time scales to obtain the SPETI. The first step, the calculation of the PET, is difficult because of the involvement of numerous parameters, including surface temperature, air humidity, soil incoming radiation, water vapor pressure, and ground–atmosphere latent and sensible heat fluxes. Different methods have been proposed to indirectly estimate the PET from meteorological parameters measured at weather stations. We followed the simplest approach to calculate PET (Thornthwaite 1948), which has the advantage of only requiring data on monthly-mean temperature.
With a value for PET, the difference between the precipitation P and PET for the month i is calculated using which provides a simple measure of the water surplus or deficit for the analyzed month. Tsakiris et al. (2007) proposed the ratio of P to PET as a suitable parameter for obtaining a drought index that accounts for global warming processes. This approach has some shortcomings: the parameter is not defined when PET = 0 (which is common in many regions of the world during winter), and the P/PET quotient reduces dramatically the range of variability and deemphasizes the role of temperature in droughts. The calculated values are aggregated at different time scales, following the same procedure as that for the SPI.
For calculation of the SPI at different time scales, a probability distribution of the gamma family is used (the two-parameter gamma or three-parameter Pearson III distributions), because the frequencies of precipitation accumulated at different time scales are well modeled using these statistical distributions. Although the SPI can be calculated using a two-parameter distribution, such as the gamma distribution, a three-parameter distribution is needed to calculate the SPETI. In two-parameter distributions, the variable x has a lower boundary of zero whereas in three-parameter distributions, x can take values in the range where is the parameter of origin of the distribution; consequently, x can have negative values, which are common in D series.
The probability density function of a three-parameter log-logistic distributed variable is expressed as where , , and are scale, shape, and origin parameters, respectively, for D values in the range ().
Parameters of the log-logistic distribution can be obtained following different procedures. Among them, the L-moment procedure is the most robust and easy approach (Ahmad et al. 1988). When L moments are calculated, the parameters of the Pearson III distribution can be obtained following Singh et al. (1993).
The probability distribution function of the D series, according to the log-logistic distribution, is given by The F(x) values for the D series at different time scales adapt very well to the empirical F(x) values at the different observatories, independently of the climate characteristics and the time scale of the analysis. With F(x) the SPETI can easily be obtained as the standardized values of F(x).
Where and P is the probability of exceeding a determined D value, P =1- F(x). If P >0.5, then P is replaced by 1- P and the sign of the resultant SPETI is reversed. The constants are ,,,,and .
The average value of SPETI is 0, and the standard deviation is 1. The SPETI is a standardized variable, and it can therefore be compared with other SPETI values over time and space. An SPETI of 0 indicates a value corresponding to 50% of the cumulative probability of D, according to a log-logistic distribution.
The result of monthly calculated of SPETI and SPI for the 12-month time scale in Tabriz station for period 1951-2010 shows despite the little difference between two indicies but in last 16 year the SPETI shows drought better than the SPI so the number of drought years in SPETI is greater than SPI due to using temperature in SPETI, the severe wet( severe drought) years that SPI shows because of high temperature( low temperature) are adjusted and the opposite is also true. This means that when the SPI shows normal or near normal condition the SPETI shows drought (wet) years because of high (low) temperature.
The last 16 years is an example of situation due to rising temperature which the SPETI the more drought year than SPI. For example, when the SPI is in normal condition in 2002 and 2007 years, the SPI indicates the drought condition for those years.
According to the results the SPETI has more advantages than SPI for monitoring drought because of being multiscalar and using a few meteorological parameters for calculation. Last 16 years shows this difference because of decreasing rainfall and rising temperature.