UNCERTAINTY BASED ASSESSMENT OF DROUGHT USING STANDARDIZED PRECIPITATION INDEX-A CASE STUDY
M.F. Rabby1*, S.K. Adhikary2
1Lecturer, Department of Civil Engineering, Z. H. Sikder University of Science & Technology, Madhupur, Shariatpur, Bangladesh, Email: [email protected]
2Professor, Department of Civil Engineering, Khulna University of Engineering & Technology (KUET), Khulna-9203, Bangladesh, Email: [email protected]
*Corresponding Author
Abstract
Drought is a recurrent extreme hydrological event occurring almost every year in Bangladesh. Particularly, the northwest region of the country has been severely affected by the frequent occurrence of droughts. Standardized Precipitation Index (SPI) is the most widely used index for meteorological drought assessment because of its modest data requirement and ease of use. However, SPI's reliability in drought assessment has been questioned due to the presence of uncertainty in its computational process. Although past studies have identified various sources of uncertainty, a few have explored their influence on drought calculation. Therefore, the aim of this study is to identify the uncertainty sources in SPI based drought assessment and analyse their effects on drought characteristics. The current study is demonstrated through two selected climate stations, namely Bogra and Ishurdi located in the northwest region of Bangladesh. Two probability distribution functions, such as Gamma and Log-normal distributions, are used to calculate SPI over 6, 12 and 24-month time scales. The maximum likelihood method is adopted to find parameters of the distribution functions and the Run's theory are employed to determine the drought characteristics. The results indicate that the uncertainty in SPI calculation is greater at smaller time scales and usually decreases with the increase in time scale and length of data series. It is also evident from the results that the standard gamma distribution performs similarly to the log-normal distribution at larger time scales. This demonstrates that the log-normal distribution can be adopted as a viable alternative over the standard gamma distribution for drought assessment in the study area. The results also show that the uncertainty greatly affects extreme droughts. The higher the SPI value becomes, the larger the chances of uncertainty introduced. It is also found that the uncertainty sources greatly impact the drought characteristics and categorization. The current study thus concludes that correct and reliable assessment of drought using SPI can be achieved by considering diverse sources of uncertainty and their impacts on the drought assessment.
Keywords
Uncertainty; SPI; Drought; Maximum likelihood; Gamma distribution; Log-normal distribution 1. Introduction
Drought is a naturally occurring extreme hydrological event, which is mainly caused by the scarcity of precipitation. Due to high spatial and temporal variability of precipitation caused by climate change, drought has become an important concern to researchers all over the world. Drought is recurrently occurring almost every year in Bangladesh. Considering the country’s unique geographical location, dense population, low income and uncontrolled urbanization as well as high dependency of major income generating sectors on precipitation patterns such as agriculture and fishing in the country, this is regarded as one of the most pressing disasters in Bangladesh. In recent years, there have been an increase in the frequency of droughts and a significant number of droughts are occurred ever in the country since its independence in 1971 [1]. In particular, the northwest region of the country are prone to drought since the region usually receives very less precipitation than the rest of the country [1-2]. The region regularly experiences meteorological drought, which is associated with the precipitation pattern and other climatic factors [1, 3]. It has been observed that natural droughts have impacted about 53% of people and around 47% of the nation in the past [4]. The effect of droughts may be minimized through drought preparation and mitigation strategies in which drought indices act as one of the vital factors and effective risk control techniques [5–7].
Drought indices are the simplest way to monitor drought conditions as they can provide a numerical depiction of the beginning and end of a drought event along with its severity [8]. During the last several decades, numerous statistical approaches have been employed to quantify meteorological, agricultural, and hydrological droughts
[9-10]. Among them, standardized precipitation index (SPI) is the most widely adopted index all over the world [11] to monitor precipitation-based meteorological droughts because it requires only precipitation records and can analyze droughts across different time periods [12-13]. However, there are some questionable issues with how SPI is calculated. Several factors including the length of data series, the time scales, the probability distribution function used to fit the data, the parameter estimation approach could be responsible for the induced uncertainty in drought assessment using SPI [13–17]. It has been understood that the mostly used Gamma distribution function should not be adopted extensively since other distribution functions often perform better than the standard gamma distribution function. For example, Guttman [18] demonstrates that the Pearson Type- III distribution is the optimal fit for American precipitation data whereas Sienz et al. [19], Angelidis et al. [20], and Blain & Meschiatti [21] found that the weibull, log-normal, and generalized-normal distributions are the most appropriate fits for European, Guadiana (Portugal), and Brazilian precipitation data, respectively. Bhakar [22] showed that the Gumbel distribution is suited best for maximum monthly precipitation in India whereas Mandal & Choudhury [23] found the log-normal distribution as the best fitting distribution function for pre- monsoon precipitation in Bangladesh.
Variability in parameter estimation methods also induces uncertainty as it would yield different SPI values which would eventually affect the drought estimation. Parameter stability and validity have been the focus of research in several published works. Carbone et al. [24] discovered that there is a non-linear relationship between the record length and the stability of parameter estimation. Moreover, it has been shown that the duration and diversity of precipitation data used to fit the probability distribution contribute to the uncertainty, and that the larger the variability of precipitation, the greater the uncertainty [25]. World Meteorological Organization (WMO, 2012) suggests a minimum time series of 50 or 60 years for this purpose; nevertheless, a 30-year time series is regarded enough for most purposes.
Even though all of the aforementioned research has contributed much to enhance the uncertainty analysis in drought assessments, the majority of it focused on the implications of sources of uncertainty on drought index itself and the failure to take into account their effects on occurrences and characteristics of droughts. Although Zhang and Li [13] considered the effects of uncertainty but it was limited to a 12-month time scale and 55-year data period. To the best knowledge of authors, there has not been any previous research conducted in Bangladesh that takes into consideration the consequences of uncertainty in drought estimation. Therefore, the objective of the current research is to evaluate the implications of uncertainty in drought assessment, particularly concerning the SPI values and the characteristics of drought.
2. Materials and Methods 2.1 Study Area and Data Used
The northwest region of Bangladesh is particularly drought prone and receives less rainfall compared to the other part of the country. Thus the current study is mainly focused on the two important stations namely Bogra and Ishurdi in this region, which is shown in Fig. 1. The area includes very pronounced seasonal shifts and has high temperatures, moderate rainfall, and typically considerable humidity. Precipitation amounts vary both geographically and seasonally in this region. In the study area, the highest mean annual rainfall is recorded about 1743 mm in Bogra and 1545 mm at Ishurdi.
Since SPI based drought estimation requires only the precipitation data, the precipitation data for the Bogra and Ishurdi stations are collected from Bangladesh Meteorological Department (BMD) for a period of 45 years from 1975 to 2019. The details of the two aforementioned stations are given in Table 1.
Table 1: Details of the BMD climatic stations in the study area
Station Area covered (km2) Latitude (Deg.) Longitude (Deg.) Data used Data Period
Bogra 2898.68 24.88 89.39 Precipitation 1975-2019
Ishurdi 2376.13 24.12 89.04 Precipitation 1975-2019
2.2 Standardized Precipitation Index (SPI) Calculation
The SPI [26] is a widely used indicator to assess meteorological drought at different time scales (e.g., 3, 6, 12, 18, 24-months). The procedure of calculating SPI is outlined in the following:
a) Given a certain time scale a, the cumulative precipitation at the nth month during different years is calculated by:
( ) ∑ ( )
( ) (1)
where, x is the monthly precipitation record of N years, t is the annual index (from 1 to N), and m is a given month (January, February,..., December)
b) Then the cumulative precipitation series are fitted by a probability density function where Gamma distributions and Lognormal distributions are taken into consideration for the current study, which are represented by Eq. (2) and Eq. (3), respectively.
( | )
( )( ) (2)
( | )
√
( ( ) )
(3)
where, is the Gamma function and are the shape and scale parameters, respectively.
c) The cumulative probability of a certain precipitation event is then determined for a specified time scale and month. The SPI value is obtained by using the Eq. (4) to convert the cumulative probability distribution (CDF) into a standard normal distribution with a mean of zero and a variance of one.
( ) (4)
Where, the quantile of the cumulative probability k, denoted by , and the inverse function of the CDF for a normal distribution is denoted by . The SPI-based drought classification is presented in Table 2.
Table 2: Drought classification according to SPI values SPI Value Drought category Probability (%)
-0.99 to 0.00 Mild drought 34.1
-1.49 to -1.00 Moderate drought 9.2
-1.99 to -1.50 Severe drought 4.4
2.00 Extreme drought 2.3
2.3 Assessment of Drought Characteristics
Drought can be described in a variety of ways, including its drought event number, and severity, intensity, peak, duration, frequency, etc., are recommended by various researchers to use for drought assessments [13, 27–29]
and thus selected for this study. According to [30–32] a drought event is defined as a period when SPI is continuously below 0 with the lowest SPI value less than −1.0. Once drought events are identified, the drought characteristics can be calculated by run’s theory [33]. Run’s theory demonstrated that the total sum of all the SPI readings below a threshold level represent the severity (Se) which is shown in Eq. (5). Duration is the length of the time during which the SPI value is continuously below the threshold level. The intensity of a drought event (DIe) is the mean value of SPI below the threshold level which may be obtained by using Eq. (6). The worse the drought, the higher the DIe value. The peak is the minimum value of SPI below the threshold level.
|∑
| (5)
(6)
where, e is regarded as a drought event; is a month; is the SPI value in month ; are the duration, severity and intensity of a drought event e, respectively. The frequency of drought can be obtained by Eq. (7) given in the following.
(7)
where, is the number of drought events, is the number of years in study period and s represents a station.
3. Results and Discussion
The SPI values obtained by using two different types of distributions such as Gamma and Lognormal distributions at different time scales for the 45 year period at Bogra and Ishurdi station produces same type of results. Drought estimation in Bogra station by SPI-6 (i.e., SPI values for 6 month time scales) and SPI-24 (i.e., SPI values for 24 month time scales) are shown Fig. 2. As can be seen from the figure, the SPI values found using these distributions are almost identical to each other for a particular type of time scale except at some extreme ends. Furthermore, it is seen that the droughts are more frequent at shorter time scales and gets reduced as the time scale gets increased. It is also evident that the lognormal distribution is primarily responsible for yielding the higher values of SPI at the extreme ends.
Figure 2: SPI based drought calculation at Bogra station using Gamma and Lognormal distributions The differences derived from SPILognormal minus SPIGamma for the selected SPI time scales were compared to analyze the irregularity of the SPI values for both Bogra and Ishurdi stations, which are shown in Fig. 3. It is seen from the figure that the disturbances are more obvious for the extremes and least for the normal and moderate classifications of dry and wet period. Furthermore, it is observed that this induced uncertainty tends to reduce as the time scale gets larger. On the other hand, the parameters of the distributions (i.e., shape and scale) are greatly affected by the type of estimation used along with the data length, time scales considered to compute
it. It is found that the parameters vary significantly when the distribution is changed from the Gamma to Lognormal distribution as well as when the time scales and the data period changes.
Figure 3: Residuals of SPI calculations for different time scales for Bogra and Ishurdi stations
The shape (µ) and scale (σ) parameters as given by Eqs. (2) and (3) can be varied based on different time scales and data ranges, which results in the different values of probability distributions (i.e., Gamma and Lognormal distributions in the current study) and hence computations of different SPI values. This ultimately influences the drought assessment using SPI. The variation of shape and scale parameters for different time scales at Bogra station in presented in Fig. 4. It is observed from the figure that due to the change in distribution the shape parameter varies from 74 to 80% while it varies almost 88% when the time scales changes. Furthermore, it varies from 4 to 29% when the data period gets changed. Similarly, the scale parameters changes almost 97%, 60% and 19% maximum as the distribution, time scale and data period changes, respectively.
Figure 4: Variation of shape and scale parameters for different time scales at Bogra station
The effect of uncertainty has been observed on drought characteristics. The drought characteristics obtained for both Ishurdi and Bogra stations is shown in Fig. 5. It is evident from the figure that the lognormal distribution yields slightly greater number of drought events, duration, severity, intensity and drought peak in comparison to that of the gamma distribution for a specific time scale and length of data period. In addition to this, it is seen that the drought characteristics tends to decrease as the time scale increases for a particular length of data period.
Furthermore, most of the drought characteristics are found as higher when considering the 45 year data period.
The result also shows that the uncertainty has less effect on drought frequency. However, almost same frequency of drought is encountered using both Gamma and Lognormal distributions. Though the highest frequency of drought obtained is for mild category whereas it becomes less for the moderate, severe and extreme category and this tends to remain more or less constant as the time scales and data period changes. It is also evident from the results that the most severe type of drought is found at 24-month time scale for both stations.
Note: a. changes in probability distribution used at 12-month time scale, b. changes in time scales used in between 6-month and 12-month, c. changes in data records from 35-year to 45-year ranges
Figure 5: SPI based drought characteristics at Ishurdi and Bogra stations
Table 3 presents the severity of drought at 35- and 45-year periods for 24-month time scale and their corresponding intensity, duration and the distribution used to result in that severity for both stations.
Table 3: Most severe droughts obtained in the study area Time
Period Station Start-End Most severe
drought
Duration
(months) Intensity Distribution used
35 Y Bogra July 1979- April 1984 42.38 23 -1.84 Lognormal
Ishurdi April 1994- September 1996 38.39 25 -1.54 Lognormal
45 Y Bogra April 2012- March 2015 59.12 35 -1.69 Lognormal
4. Conclusions
The current study focuses on the identification of the sources of uncertainty in SPI based drought assessment and analyse their effects on drought characteristics. The study is demonstrated through two selected climate stations, namely Bogra and Ishurdi located in the northwest region of Bangladesh. Gamma and Log-normal distributions are adopted for SPI calculation for 6-, 12- and 24-month time scales. Parameters of the distribution functions are obtained by the maximum likelihood method and the drought characteristics are determined using the Run's theory. It is evident from the obtained results that the estimation process of SPI includes uncertainty that cannot be eliminated. These uncertainties are attributable to SPI's probability distribution functions, parameter estimation techniques, time scales, and length of data period. The current study incorporates the aforementioned uncertainties into SPI calculation process and evaluates their influence on SPI values and the corresponding drought characteristics. This study also uses the lognormal distribution in addition to the standard gamma distribution to fulfill its goals. It is evident from the results that the lognormal distribution behaves similarly to the gamma distribution at larger time scales, but exhibits more sensitivity at the extreme ends. This demonstrates that the log-normal distribution can be adopted as a viable alternative over the standard gamma distribution for drought assessment. The results also show that the uncertainty greatly affects extreme droughts.
The higher the SPI value becomes, the larger the chances of uncertainty introduced. As extremes are a matter of concern nowadays and uncertainties tend to reduce at extremes at greater time scales and longer data periods, it is recommended to take this into account for the SPI based drought assessment.
References
1. Habiba U, Shaw R, Takeuchi Y (2011) Drought risk reduction through a socio-economic, institutional and physical approach in the northwestern region of Bangladesh. Environmental Hazards 10:121–138. DOI:
10.1080/17477891.2011.582311
2. Shahid S, Behrawan H (2008) Drought risk assessment in the western part of Bangladesh. Natural Hazards 46:391–413. DOI: 10.1007/s11069-007-9191-5
3. Shahid S, Chen X, Hazarika MK (2005) Assessment aridity of Bangladesh using geographic information system. GIS Development 9(12):40–43.
4. Dey N, Alam MS, Sajjan AK, Bhuiyan MA, Ghose L, Ibaraki Y, Karim F (2012) Assessing environmental and health impact of drought in the Northwest Bangladesh. Journal of Environmental Science and Natural Resources 4(2):89–97. DOI: 10.3329/jesnr.v4i2.10141
5. Wilhite DA (2003) Moving toward drought risk management: The need for a global strategy. National Drought Mitigation Center University of Nebraska: Lincoln, USA.
6. Wilhite DA, Sivakumar MVK, Pulwarty R (2014) Managing drought risk in a changing climate: The role of national drought policy. Weather and Climate Extremes 3:4–13. DOI: 10.1016/j.wace.2014.01.002 7. Das S, Das J, Umamahesh NV (2021) Nonstationary Modeling of Meteorological Droughts: Application to
a Region in India. Journal of Hydrologic Engineering 26:05020048. DOI: 10.1061/(ASCE)HE.1943- 5584.0002039
8. Tabari H, Nikbakht J, Hosseinzadeh TP (2013) Hydrological Drought Assessment in Northwestern Iran Based on Streamflow Drought Index (SDI). Water Resources Management 27:137–151. DOI:
10.1007/s11269-012-0173-3
9. Wells N, Goddard S, Hayes MJ (2004) A Self-Calibrating Palmer Drought Severity Index. Journal of Climate 17:2335–2351. DOI: 10.1175/1520-0442(2004)017<2335:ASPDSI>2.0.CO;2
10. Jain SK, Keshri R, Goswami A, Sarkar A (2010) Application of meteorological and vegetation indices for evaluation of drought impact: a case study for Rajasthan, India. Natural Hazards 54:643–656. DOI:
10.1007/s11069-009-9493-x
11. Kumar MN, Murthy CS, Sesha Sai MVR, Roy PS (2009) On the use of standardized precipitation index (SPI) for drought intensity assessment. Meteorological Applications 16: 381-389. DOI: 10.1002/met.136 12. Zhang Y, Li W, Chen Q, Pu X, Xiang L (2017) Multi-models for SPI drought forecasting in the north of
Haihe River Basin, China. Stochastic Environmental Research and Risk Assessment 31:2471–2481. DOI:
10.1007/s00477-017-1437-5
13. Zhang Y, Li Z (2020) Uncertainty analysis of standardized precipitation index due to the effects of probability distributions and parameter errors. Frontiers in Earth Science 8:76. DOI: 10.3389/
feart.2020.00076.
14. Wu H, Hayes MJ, Wilhite DA, Svoboda MD (2005) The effect of the length of record on the standardized precipitation index calculation. International Journal of Climatology 25:505–520. DOI: 10.1002/joc.1142.
15. Vergni L, di Lena B, Todisco F, Mannocchi F (2017) Uncertainty in drought monitoring by the Standardized Precipitation Index: the case study of the Abruzzo region (central Italy). Theoretical and Applied Climatology 128:13–26. DOI: 10.1007/s00704-015-1685-6.
16. Stagge JH, Tallaksen LM, Gudmundsson L, van Loon AF, Stahl K (2015) Candidate Distributions for Climatological Drought Indices ( <scp>SPI</scp> and <scp>SPEI</scp> ). International Journal of Climatology 35:4027–4040. DOI: 10.1002/joc.4267.
17. Beyaztas U, Bickici Arikan B, Beyaztas BH, Kahya E (2018) Construction of prediction intervals for Palmer Drought Severity Index using bootstrap. Journal of Hydrology 559:461–470. DOI:
10.1016/j.jhydrol.2018.02.021.
18. Guttman NB (1999) ACCEPTING THE STANDARDIZED PRECIPITATION INDEX: A CALCULATION ALGORITHM 1. JAWRA Journal of the American Water Resources Association 35:311–322. DOI: 10.1111/j.1752-1688.1999.tb03592.x.
19. Sienz F, Bothe O, Fraedrich K (2012) Monitoring and quantifying future climate projections of dryness and wetness extremes: SPI bias. Hydrology and Earth System Sciences 16:2143–2157. DOI: 10.5194/hess- 16-2143-2012.
20. Angelidis P, Maris F, Kotsovinos N, Hrissanthou V (2012) Computation of Drought Index SPI with Alternative Distribution Functions. Water Resources Management 26:2453–2473. DOI: 10.1007/s11269- 012-0026-0.
21. Blain GC, Meschiatti MC (2015) Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index. Revista Brasileira de Engenharia Agrícola e Ambiental 19:1129–1135. DOI:
10.1590/1807-1929/agriambi.v19n12p1129-1135.
22. Bhakar S, Iqbal M, Devanda M, Chhajed N, Bansal A (2008) Probability analysis of rainfall at Kota.
Indian Journal of Agricultural Research 42:
23. Mandal S, Choudhury BU (2015) Estimation and prediction of maximum daily rainfall at Sagar Island using best fit probability models. Theoretical and Applied Climatology 121:87–97. DOI: 10.1007/s00704- 014-1212-1.
24. Carbone GJ, Lu J, Brunetti M (2018) Estimating uncertainty associated with the standardized precipitation index. International Journal of Climatology 38:e607–e616. DOI: 10.1002/joc.5393.
25. Ghasemnezhad F, Bazrafshan O, Fazeli M, Parvinnia M, Singh V (2021) Uncertainty Analysis of Hydrological Drought due to Record Length, Time Scale, and Probability Distribution Functions Using Monte-Carlo Simulation Method. DOI: 10.21203/rs.3.rs-131396/v1.
26. McKee TB, Doesken NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales.
Proc. of the Ninth Conference on Applied Climatology, American Meteorological Society, 17-22.
27. He Z, Liang H, Yang C, Huang F, Zeng X (2018) Temporal–spatial evolution of the hydrologic drought characteristics of the karst drainage basins in South China. International Journal of Applied Earth Observation and Geoinformation 64:22–30. DOI: 10.1016/j.jag.2017.08.010.
28. Sheffield J, Wood EF (2008) Global Trends and Variability in Soil Moisture and Drought Characteristics, 1950–2000, from Observation-Driven Simulations of the Terrestrial Hydrologic Cycle. Journal of Climate 21:432–458. DOI: 10.1175/2007JCLI1822.1.
29. Loukas A, Vasiliades L (2004) Probabilistic analysis of drought spatiotemporal characteristics inThessaly region, Greece. Natural Hazards and Earth System Sciences 4:719–731. DOI: 10.5194/nhess-4-719-2004.
30. Mesbahzadeh T, Mirakbari M, Mohseni Saravi M, Soleimani Sardoo F, Miglietta MM (2020) Meteorological drought analysis using copula theory and drought indicators under climate change scenarios (RCP). Meteorological Applications 27. DOI: 10.1002/met.1856.
31. Nedealcov M, Răileanu V, Sîrbu R, Cojocari R (2015) The Use Of Standardized Indicators (SPI And SPEI) In Predicting Droughts Over The Republic Of Moldova Territory. Present Environment and Sustainable Development 9:149–158. DOI: 10.1515/pesd-2015-0032.
32. Lee S-H, Yoo S-H, Choi J-Y, Bae S (2017) Assessment of the Impact of Climate Change on Drought Characteristics in the Hwanghae Plain, North Korea Using Time Series SPI and SPEI: 1981–2100. Water (Basel) 9:579. DOI: 10.3390/w9080579.
33. Yevjevich VM (1969) An objective approach to definitions and investigations of continental hydrologic droughts: Vujica Yevjevich: Fort Collins, Colorado State University, 1967, 19 p. (Hydrology paper no. 23).
Journal of Hydrology 7:353. DOI: 10.1016/0022-1694(69)90110-3.