DETERMINING SUITABLE DROUGHT MONITORING INDEXES AND DEVELOPING A MIXED METHOD (Case Study, Ardabil Province, North-west of Iran) Alireza Pilpayeh, Naser Almasi Bigdiloo ABSTRACT The objective of this study was to determine suitable drought monitoring indexes using the approach of systematic simulation and evaluation of interactions between water resources and historical drought in a region and to develop a mixed method. One of the important and efficient tools in drought monitoring systems is monitoring indexes, which in the case of compatibility with the conditions of application environment has a considerable effect on monitoring, pre-warning and often predicting this phenomenon. This is only possible if the mentioned indexes are selected based on the need and conditions of the application location. In this research, the studied region was Ardabil province in north-west of Iran and the objective was to determine severity and range of drought in the region. Three indexes were utilized for monitoring drought: PNPI (Percent of Normal Precipitation Index), DPI (Deciles Precipitation Index) and SPI (Standardized Precipitation Index). Information of 0 stations in the study area were used. The results showed that SPI clearly indicated drought condition in Ardabil province in 3 and 6 month scales since, in the selected dry years, values of this index illustratively decreased to the undernormal value. Oscillation trend of SPI corresponded to hydrologic oscillations in snowy regions in 6 months scale and, in farther regions, it was in 3 months scale. Through constant use and monthly analysis of SPI values in 3 and 6 months periods, reliability coefficient of this index could be increased and validated and also a kind of 3 to 6 months pre-warning system could be obtained prior to the drought. Keywords: Drought indexes, Drought monitoring, SPI, Agricultural drought, Probability distribution, Ardabil province, Iran.. INTRODUCTION Drought indexes are used in monitoring drought conditions and helping in its management. Often, the reliability for the indeses may become questionable due to the mathematical basis for calculating them. However, considering that each index is developed for a specific application in a specific region; the index chosen for a certain region may not be applicable to another region. Therefore, selecting a suitable index is a sensitive and complicated procedure which depends on several conditions. Trenka et al. (006) studied a new index (CDI) in Czech Republic by combining three main methods of SPI, PDSI and ZIND in drought studies. The results showed that approximately 3% of the country was in high risk area,.3% faced 50 to 60% risk probability and drought prone areas were concentrated in the main areas of agricultural production in the north-west and south-east parts. Bordi et al. (009) analyzed linear and nonlinear trends of drought and wet years based on SPI in Europe. According to the results, surface coverage of drought and Department of Water Science and Engineering, Parsabad Branch, Islamic Azad University, Parsabad, Iran. Corresponding Author: a.pilpayeh54@yahoo.com Moghan Company for Operation and Maintenance of Irrigation & Drainage Systems, Parsabad, Iran.
wet year time series had a linear trend up to the end of current century, which was reversed during 997 to 009; becoming nonlinear. Sirdas and Şen, (003), found a direct relationship between duration and magnitude of drought using time-spatial analysis in Trakya, Turkey, by RUN and Z-SCORE statistical methods and Kriging interpolation method. Yildiz (009) estimated time and location characteristics of droughts in Turkey in order to first calculate frequency curve-surface range-drought for different return periods and then determine severity. The return periods of old droughts were then investigated in the region and assessment of drought severity was presented. Barlow et al. (00) studied drought in middle and south-east Asia and showed that, during winter, there was a reverse relationship between precipitation anomalies in Indian Ocean, middle and south-west Asia. Ceasation of precipitation in middle and south-west Asia was compatible with the reaction between local storms and energy wave created by increased tropical precipitation in eastern Indian Ocean. Yahiaui et al. (009) analyzed frequency of hydrological drought in west of Algeria and showed that drought frequency and severity was a random phenomenon. After recent droughts in Iran, use of indexes and zoning of drought have become common. Abarghoei et al (00). drew severity and zoning maps of drought for Yazd province. Ghatreh (00) studied drought trend in Chaharmahal and Bakhtiari province and drew drought distribution map. Lashizadeh and Kharamian determined zoning of climatic drought in Lorestan province based on the severity of drought and drew it by SURFER software; then, they studied the area of drought ranges in the province during this period. The current study was done to determine suitable indexes for monitoring drought, using systematic simulation and evaluation approach of interactions between water resources and historical droughts and to develop a mixed method in Ardabil province, located in north-west of Iran.. MATERIALS AND METHODS Drought monitoring methods may be categorized in 5 main groups: Water balance precipitation data analysis, river flow and groundwater analysis, synoptic analysis and geomorphic and historical information method. Precipitation data analysis method: It is the most widely used due to: Easy access to precipitation data in compared with other data Instability of precipitation compared with other climatic parameters, particularly in dry areas Direct input to soil humidity, surface flows, groundwater beds, etc. from precipitation; thus, it can be considered in every drought condition. Meteorological indexes are utilized for drought monitoring, which use the precipitation data to monitor this event. In Ardabil Province, the time series of precipitation data do not fit to any statistical distributions due to its erratic nature and prolonged no precipitation periods. Only, in the time scales of greater than 3 months, Gamma distribution acceptably fits the data. Considering the existing limitations, precipitation
monitoring indexes of PNPI, DPI and SPI were used to evaluate efficiency of precipitation indexes for drought monitoring in this area and the relationship between the obtained values from calculation of these indexes and historical droughts of the region was studied. In some of these studies in universal scale, statistical analysis tools have been applied to establish a correlation between meteorological drought monitoring indexes and agricultural and hydrological droughts; but, implementation of these studies is discussed in the spatial scale of basins. For more reliability of the results, the calculation method studied the above three indexes and selected the most suitable one for the province. 3. PERCENT OF NORMAL PRECIPITATION INDEX (PNPI) Percent of normal precipitation index is one of the simplest in a region and is very effective when used for studying drought or wet year in a specific location or season. This index is calculable for different time scales from to several months or even the whole year. This index is obtained by dividing actual precipitation by normal precipitation and its multiplication by 00. Pi PNPI 00 P in which: P i precipitat ion in the desired month or period, and P mean long term precipitat ion in the desired period Using this index requires mean of precipitation to correspond to the median or normal participation distribution. Studies have shown that monthly and seasonal precipitations do not usually follow a normal distribution, which is one of the disadvantages of this method. High comprehensiveness and flexibility of this index have made many researchers use them. 3. Deciles Precipitation Index (DPI) Arranging monthly precipitation data in deciles is another widespread technique for drought monitoring. Index of deciles was first utilized by Gibbs and Maher (967) to avoid some weak points of percent of normal precipitation method. General principles of calculating deciles are as follows:. Arranging monthly precipitation data in an ascending order. Determining domain of deciles using the equation: Di = i x (n + )/0, where Di is the i th decile, n is number of precipitation data. 3. Estimating values of precipitation related to each decile (final limit) 4. Determining statistical years placed in different deciles The data must have normal distribution to be used in this method and, since the precipitation data do not usually have normal distribution, the data should be normalized by one of the appropriate methods. 3. Standardized Precipitation Index (SPI) McKee et al. (993) presented the SPI for defining and monitoring drought. The characteristic of SPI allows the analyzer to determine rare drought and also wet year phenomena in a specific time scale at any point in the world. 3
SPI is calculated for every region according to the record of long-term precipitations in that region (Edwards & McKee, 997). Basically, SPI is designed to identify shortage in the amount of precipitation in multiple time scales. These time scales reflect particular effects of drought on accessibility of different water resources. Humidity conditions of soil react to relatively short-term abnormalities in precipitation while groundwater, river flows and reservoirs are affected by long-term abnormalities in precipitation. As a result, McKee et al. (993) first used this index for 3, 6, and 4 month time scales. Edwards and McKee (997) stated that, having the time series of monthly precipitation data for each location, SPI could be calculated for l earlier months, where, l =,, 3,,,, 4,, 48 months. 3.3 Methodology of SPI Calculation First, the appropriate statistical distribution is fitted on long-term precipitation data. Then, cumulative distribution function is converted into normal distribution using equal probabilities so that it is standardized and its mean becomes zero for each desired region and period (Edwards & McKee, 997). Positive SPI values indicate the precipitation of more than the mean and negative values indicate the reverse. According to this method, drought occurs when SPI is constantly negative and reaches - or less and stops when SPI becomes positive. Therefore, the drought period is determined by the beginning and ending of negative values for SPI and cumulative values of SPI indicate magnitude and severity of the drought period. Thom (996) realized that Gamma distribution has a good fitting on meteorological precipitation time series (Edwards & McKee, 997). Gamma distribution function is defined as pdf with the following frequency: for x o, g(x) α β τ( ) α o, α is shape factor, β o, α x / β x e β is scale factor, x and τ ( ) is the Gamma function, calculated using : α y τα y e dy 0 0, x is precipitat ion amount, Calculation of SPI consists of fitting Gamma probability function on frequency distribution of total precipitation for a specific station. Then, parameters α and β of Gamma pdf are estimated for each station in each time scale (3, 6,, 4, 48 months, etc.) and for each month of the year. The following equations were used for optimal estimation of α and β (i.e., αˆ and βˆ ) : 4A αˆ and 4A 3 Ln (x) Where: A Ln X and n is number of observations. n In the next stage, ( αˆ βˆ) and are are used for obtaining cumulative probability function of precipitation for the desired month and specific time scale in the studied station. Cumulative Gamma function is defined as: βˆ X αˆ G (x) g(x)dx 0 βˆ αˆ Γ(αˆ) x αˆ x/ βˆ x e dx 0 4
If x t, the above equation would be the incomplete Gamma function: βˆ G(x) Γ(αˆ) x 0 t αˆ e t dt Since the Gamma function is not defined for x = 0 (0 mm precipitation) and precipitation distribution could have negative values, the cumulative probability function which also contains zero is obtained using: H(x) q ( q) G(x) Where q is the probability that precipitation is zero. Thom (966) stated that, if m is the number of precipitation data with value of zero in equivalent time series, then q is calculated as: q = m/n. Thom (996) used the incomplete Gamma function table to determine cumulative probability of G (x). After calculation of total cumulative function H (x), transformation of co-probability of Gamma cumulative function into standard normal random variable Z (or SPI) with mean of 0 and variance of was done. Panofsky and Beier (985) stated that the transformation of co-probability of one variable (like Gamma) into another variable with another distribution (like standard normal) was possible if probability was less than the specified value of those two similar variables. Precipitation data are arranged in ascending order; and the probability values are calculated as: Experimental cumulative probability = (K) / (n + ) Where K is the specific row number of precipitation so that the smallest value has number, and n is the sample size. For easy access to SPI values, it is better to use the following approximation. This approximation converts cumulative probability into a standard normal random variable as follows: C C t C t Z SPI t 0 for 0 H(x) 0.5 d d d 3 t t 3 t C 0 C t C t Z SPI t for 0.5 H(x).0 3 d t d t d3 t Where; t t Ln {H(X)} Ln {( H(X)} for 0 H(x) 0.5, and for 0.5 H(x).0 and, constants are: C0=.5557, C= 0.80853, C= 0.0038, d=.43788, d= 0.8969 and d3= 0.00308 5
In fact, SPI is a standardized variable which shows deviations higher or lower than the mean. Anyway, this condition is not quite correct for short-term comparison because primary distribution of precipitation contains skewness. 3.4 Case Study This research was conducted in Ardabil province in north-west of Iran. This province is located between two basins of Aras and Sefidrood with a large part of its area in Aras basin. 4. RESULTS In this research, precipitation data of the desired station were studied in a statistical period and a data matrix was formed after testing for homogeneity. SPI was adopted for the study, as it is precipitation based, multi-dimensional and drought monitoring is possible from agricultural, meteorological and hydrological perspective. It is standard and can categorize pervasive and severe drought events for any location and any time scale because of following normal distribution, independence from humidity of soil, possibility of application in all months of the year and flexibility of SPI toward different time scales; thus, it was selected as the suitable index. Then, long-term variations of SPI in different time scale were drawn and the value of frequency was calculated for each category according to SPI categorization; finally, it was calculated using the ranking method: Tr = (N + )/M, where N is the number of years of data and M is the number of wet years. Methodology stages used in SPI are shown in Figure Monthly Time 3Month Time 6Month Time Database Creation According to Sketc hing Long- Month 8Mont h Time 4Mont h Time Data Homogenei Determinat ion of Time Deter minatio n of Formation of Data Selection of a Suitable Determi nation of Determination of Severity, Duration, and Continuity of Meteorological Drought Determin ation of Suitable Drought Characteristi cs Determinin g the severity of change, Continuity and return Study of Drought Characteristics due to Change in Climate Figure. Methodology stages used in SPI 6
CONCLUSION This study was conducted to identify a method for monitoring and possibly prewarning drought in Ardabil province and the following results were achieved: SPI in 3 and 6 months time scale indicated drought situation in Ardabil province because, in the selected dry years, SPI decreased to below-normal level. Oscillation trend of SPI in snowy regions in 6 months time scale and in a distance from these regions in 3 months time scales matched hydrological oscillations. In northern areas of the province, impacts of cumulative precipitation were effective on watering the rivers and occurrence of hydrological drought. Considering the above issues, through constant use and monthly analysis of 3 and 6 months SPI, reliability coefficient of this index can be increased and validated; also, it can be used as a kind of pre-warning (3 to 6 months prior to the drought). According to more than 90% dependence on surface water reservoirs, drought of Ardabil province was hydrological drought of surface waters. According to the conducted studies, hydrological drought monitoring indexes cannot be used in this province in the current time section due to various reasons including the decrease in hydrological data. Because of the inapplicability of hydrological drought indexes in Ardabil province, using meteorological drought monitoring indexes is recommended in this province. Due to the mixture of precipitation in province (snow and rain in two precipitation seasons during the year), specific considerations were taken into account for drought analysis of the province. Among the meteorological drought indexes, SPI is recommended because of its cumulative nature in calculations (basically, in hydrological drought monitoring through meteorological drought indexes, indexes with cumulative nature are recommended). From among time scales of SPI for northern regions of the province, using 3 months time scales is recommended for all the seasons in central and southern regions by this scale for the first half of the year. 6.0 REFERENCES Abarghoei, H., Tavakoli, M., Talebi, M. 00 Analysis of Climatic Changes and Frequency Percentage of Drought in Yazd Province. Proceedings of First National Conference on Strategies to Cope with Water Shortage and Drought in Kerman, Vol.. Abramowitz, M., and Stegun, I.A. 965 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, Inc. New York,NewYork. Barlow, M., Cullen, H., Lyon, B. 00 Drought in Central and Southwest Asia: La Nina, the Warm Pool, and Indian Ocean Precipitation. Journal of climate. Volume 5(7), 697-700. Bordi. I, Fraedrich. K, Sutera. A, 009 Observed drought and wetness trends in Europe: an update, Journal of Hydrol. Earth Syst. Sci, 3, 59 530. Edwards, D.C, Mc Kee, T. B. 997 Characteristics of 0th century drought in theunited States at multiple time scales, Climatology Report. No. -97, Colorado, Colorado State Univ. Farajzadeh, M., 997 Drought and its Studying Methods. Journal of Forest and Grasslands, No. 3, pp.. Ghatreh Samani, S. 00 Analysis of drought trend in Chaharmahal and Bakhtiari Province, 7
Proceedings of First National Conference on Strategies to Cope with Water Shortage and Drought in Kerman, 7. Gibbs, W.J. & Maher, J. V. 967 Rainfall deciles as drought indicators. Bureau of Meteorology Bulletin. No. 48, Commonwealth of Australia, Melbourne. Lashizadeh, M., Kharamian N. 00 Climatic Drought Zoning in Lorestan Province using Statistical ndexes, Proceedings of First National Conference on Strategies to Cope with Water Shortage and Drought in Zabol, Vol.. Mckee, T. B., Doesken, N. J. & Kleist, J. 993 The relationship of drought frequency and duration to time scales, Preprints 8th conference on applied climatology. Morid, S. 00 Assessing America's Performance in Coping with Drought and the Congress' Perspectives, Proceedings of First National Conference on Strategies to Cope with Water Shortage and Drought in Zabol, Vol.. NDMC;000 National drought mitigation center, URL, http://enso.unl.edu /ndmc/watch/watch.htm, Panofsky, H. A., and G. W. Brier. 958 Some applications of statistics to meteorology Pennsylvania State University, University Park, 4 pp. Sirdas. S. and Şen. Z. 003. Spatio-temporal drought analysis in the Trakya region, Turkey, Hydrological Sciences, Volume 48, 5:809-80. Journal of Smith, D. I., Hutchinson, M. F. & Mc Arthur, R. J. 993 Australian climatic and agricultural drought payments and policy. Drought Network News, No. 3. Thom, H.C.S. 966 Some Methods of Climatological Analysis WMO Technical Note No 8, Secretariat of the World Meteoro-logical Organization, Geneva. Trenka. M, Dubrovský. M, Semerádová. D, Žalud. Z, Svoboda. M, Hayes. M, Wilhite. D. 006 New Method for Assessment of the Drought Climatology - Czech Republic as a Case Study, Geophysical Research Abstracts, Vol. 8,, SRef-ID: 607-796/gra/EGU06-A- 0338. Yahiaoui. A, Touaïbia. B, Bouvier, C. 009 Frequency analysis of the hydrological drought regime. Case of oued Mina catchment in western of Algeria, Revue Nature et Technologie, : 3-5. Yildiz, O. 009 Assessing temporal and spatial characteristics of droughts in the Hirfanli dam basin, Turkey, Academic Journal of Scientific Research and Essay, Volume 4, 4: 49-55. 8