Multivariate Drought Assessment Considering the ...

Multivariate Drought Assessment Considering the Antecedent Drought Conditions Muhammad Waseem, Muhammad Ajmal, Joo Heon Lee & Tae-Woong Kim

Water Resources Management An International Journal - Published for the European Water Resources Association (EWRA) ISSN 0920-4741 Water Resour Manage DOI 10.1007/s11269-016-1416-5

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Author's personal copy Water Resour Manage DOI 10.1007/s11269-016-1416-5

Multivariate Drought Assessment Considering the Antecedent Drought Conditions Muhammad Waseem 1 & Muhammad Ajmal 1,2 & Joo Heon Lee 3 & Tae-Woong Kim 4

Received: 22 June 2015 / Accepted: 21 June 2016 # Springer Science+Business Media Dordrecht 2016

Abstract Several drought indices have been developed based on a single variable or multiple variables using very complex calculations. Antecedent conditions are quite significant for analyzing physical processes involved in the conceptual rainfall-runoff modeling and for proper assessment of drought. However, not much attention has been paid to these conditions in the development of drought indices. Hence, we developed an alternative index for drought assessment, i.e., the antecedent condition-based multivariate drought index (AMDI), by taking into consideration all of the forms of drought, including meteorological, agricultural, and hydrological drought, in combination with the antecedent drought conditions. By comparing the AMDI with the standardized precipitation index (SPI) and reconnaissance drought index (RDI), it was revealed that in most cases, the drought trend was more or less the same. However, some discrepancies were also observed. Moreover, by considering additional factors, i.e., the antecedent soil moisture conditions and balance, an approximately 6 % difference in the drought frequency was observed compared to that of the SPI and RDI results, leading to a significant and proper drought assessment. The AMDI was also identified as a multi-scalar, multivariate index, which aggregates the effects of multiple drought forms by maintaining the continuity during month-to-month transitions. Hence, we concluded that the AMDI could be considered as an alternative tool for significant drought assessment. Keywords Antecedent condition . Drought . Multivariate index . Soil-water balance

* Tae-Woong Kim [email protected]

1

Department of Civil and Environmental Engineering, Hanyang University, Seoul 04763, Republic of Korea

2

Department of Agricultural Engineering, University of Engineering and Technology, Peshawar 25120, Pakistan

3

Department of Civil Engineering, Joongbu University, Goyang 102790, Republic of Korea

4

Department of Civil and Environmental Engineering, Hanyang University, Ansan 15588, Republic of Korea

Author's personal copy M. Waseem et al.

1 Introduction Drought is a reoccurring and region-wide phenomenon with spatial and temporal characteristics that vary significantly from one environmental region to another (Zargar et al. 2011). Unlike other natural disasters, drought is hard to detect at its onset because it creeps slowly and affects a significant area. A drought index is a quantitative measure used to characterize drought severity by assimilating data from one or several indicators such as precipitation, streamflow, and evapotranspiration, into a single numerical value (Zargar et al. 2011). Various drought indices have been developed to provide a holistic representation of historical droughts and then place current conditions into historical perspectives. The nature of drought indices reflects different events and conditions associated with delayed agricultural and hydrological impacts such as soil moisture loss, less of vegetation, lowered reservoir level, or low streamflow. During the last few decades, numerous drought severity indices have been suggested in the literature and have been extensively used in many geographical regions of the world (Mishra and Singh 2011; Zargar et al. 2011; Tigkas et al. 2012; Jiang et al. 2015). However, we unfortunately cannot say that a certain index is absolutely better than the other indices (Kim et al. 2014; Waseem et al. 2015). Some drought indices specifically reflect one type of impact or application, while others can be configured to correspond to varying impacts and drought types (Zargar et al. 2011). For example, even though the standardized precipitation index (SPI) is a meteorological drought index, it can be applied for longer time scales to reflect agricultural and hydrological drought/ impacts (Zargar et al. 2011). SPI is based on the precipitation amount in 3, 6, 9, 12, 24, and 48 month periods (Narasimhan and Srinivasan 2005; Logan et al. 2010). However, the dependence only on precipitation, which is loosely connected to ground conditions and the absence of evapotranspiration decrease its effectiveness (Zargar et al. 2011; Gocic and Trajkovic 2014). From the global warming viewpoint, the rise in temperature increases the rate of evapotranspiration, and the actual water stress becomes more evident in the warmer climate. Therefore, drought occurrence may decrease when only taking into consideration the change in a single variable, e.g., precipitation. However, available water can also be diminished by an increase in evapotranspiration; hence, evapotranspiration could be a valuable additional indicator for drought assessment. Tsakiris et al. (2007) introduced a new drought index called the reconnaissance drought index (RDI) and claimed it was a more effective tool than the SPI for drought assessment. The RDI incorporates temperature data to take water balance and evapotranspiration into consideration. The RDI has been well tested and widely used due to its good performance and capability to describe drought at the regional and commercial levels (Zargar et al. 2011; Banimahd and Khalili 2013; Tigkas et al. 2013; Vangelis et al. 2013; Tigkas et al. 2015). However, it is incapable of taking soil water balance into consideration, which is an important factor, particularly in semi-arid and arid areas (Sohrabi et al. 2015). Likewise, Vicente-Serrano et al. (2010) developed the standardized precipitation evapotranspiration index (SPEI), which is sensitive to long-term trends in temperature change. However, the SPEI is nearly equivalent to SPI or other precipitation based drought indices, when there are no apparent temporal trends in temperature (Zargar et al. 2011). In addition, SPEI application for drought assessment also suffers some unanticipated problems, e.g., in the case of parameter fitting, evapotranspiration model selection, very arid areas, or areas with a high latitude (cold desert) and altitude (Beguería et al. 2014). Paulo et al. (2012) also claimed that the Palmer drought severity index (PDSI) responds more clearly to precipitation anomalies

Author's personal copy Multivariate drought assessment considering the antecedent

by taking soil water retention into consideration and significantly identifies the supply-demand dynamics more effectively than the SPEI and SPI. The PDSI is principally based on soil water balance rather than only climatic water balance. The PDSI is usually estimated using a twolayer bucket type model to obtain data on water balance components. However, the effects of factors, such as the vegetation cover, spatial variability of soil, and topography, on catchment hydrological processes are not considered in this model (Yan et al. 2013). Furthermore, the estimation of PDSI was primarily based on the records of meteorological stations at the point scale, having the limitation of acquiring long-time serial soil moisture and actual evapotranspiration on a large scale and not clearly reflecting the regional difference in the drought (Yan et al. 2013). However, these drought indices are normally used for drought assessment and share a common characteristic called time independency. Consequently, they are developed for a specific month (e.g., January, February, etc.) and do not indeed maintain the continuity during month-to-month transitions (Sohrabi et al. 2015). The development of a reliable drought index requires proper consideration of precipitation, time lag continuity, vegetation type, soil properties, antecedent moisture conditions, evapotranspiration, and temperature (Narasimhan and Srinivasan 2005). In addition, the single variable-based assessment of drought may not be sufficient for significant and reliable drought assessment (Waseem et al. 2015). Hence, the creation of a new multi-variate, multi-scalar, drought index that can incorporate and more effectively exploit readily available information regarding soil, water balance as well as climatic water balance with a time lag effect is needed for the proper assessment of drought (Zargar et al. 2011). Considering the points mentioned above, we introduced a new multivariate, multi-scalar, drought index, known as the antecedent condition-based multivariate drought index (AMDI), which is primarily based on antecedent soil conditions and soil water balance as well as climatic water balance with a time lag effect. The motivation behind the development of the new drought index was to provide an alternative to specialized drought indices by assessing the overall availability of water contents, i.e., the meteorological, agricultural and hydrological regimes of drought with subsequent time steps instead of a targeted month.

2 Methodology After a systematic review of the plethora of indices used for the monitoring and assessment of drought, it was determined that all of the indices were useful and configured to correspond to varying impacts or applications of drought. However, the indices do not seem to be attractive for universal applicability (Kim et al. 2014). In the current study, based on antecedent soil conditions, the soil water balance and the climatic water balance considering a time lag effect (the prior 5 days in this study), a new drought index (AMDI) was developed to provide a reliable and simple alternative to specialized drought indices. The primary step involved in the mathematical formulation of AMDI was to estimate the daily potential evapotranspiration (PE) of the study area using the Hargreaves equation (Hargreaves and Samani 1985). Estimation of the PE involves numerous parameters, e.g., surface temperature, air humidity, water pour pressure, soil incoming radiation and latent and sensible heat flux (Vicente-Serrano et al. 2010). However, these meteorological data are not available at the site of interest in the majority of areas. Hence, we used the Hargreaves equation


for practical estimation of the PE, since it required only daily temperature data. The Hargreaves equation estimates the potential evapotranspiration (PEJ) for the Jth Julian day as given in Eq. 1. PE J ¼ 0:0023Ra T 0:5 ð1Þ D T avg −17:8 where J stands for the Julian day, TD is the temperature difference between the maximum and min ) in oC, and Ra minimum temperature (°C), Tavg is an average daily temperature (i.e., T max þT 2 stands for the water equivalent of extraterrestrial radiation (mm/day), which is usually calculated as a function of the month of the year and the latitude as given in Eq. 2. Ra ¼

1444 GSC d r ½ψS sinðφÞsinðδÞ þ cosðφÞcosðδÞsinðψS Þ π

ð2Þ

where GSC is the extraterrestrial radiation constant, dr is the Earth-sun inverse relative distance, ψs is the sun set hour angle (rad), φ is the location latitude, and δ is the solar delineation (rad). In the next step, the daily water budget (WB) was calculated from the difference in the observed Jth Julian day precipitation (PJ) and the respective PEJ as depicted in Eq. 3. Irrespective of the specific target month, the Julian day concept was introduced in this study leading to the conceptualization of a continuous index based on water budget temporal transition, which is normally not considered in the PDSI or SPEI (Sohrabi et al. 2015) W B J ¼ P J −PE J

ð3Þ

In this study, the previous five Julian days’ cumulative water budget corresponding to the 5

Jth day, WB5 (= ∑ W B J ), was introduced to calculate the Jth day runoff (RJ) that resulted J ¼1

from current Julian day rainfall (PJ) considering antecedent soil-moisture conditions. The Natural Resources Conservation Service (NRCS) Curve Number (CN) model is one of the practical rainfall-runoff models, which is well documented based on wide experience (Woodward et al. 2003). This model involves parameters, such as CN mainly from watershed characteristics, land cover conditions, and soil types, which are used to predict the soil water balance (Mishra et al. 2005). The traditional NRCS model is also a part of very well known hydrological models, such as the soil and water assessment tool (SWAT), used to estimate the surface runoff. Some researchers (e.g., Yan et al. 2013; Sohrabi et al. 2015) have used the NRCS model via SWAT to provide an alternative for the PDSI for drought assessment. However, the NRCS model has been criticized by numerous researchers (Mishra et al. 2006; Ajmal and Kim 2015). Hence, plethora of modifications can be found in the literature (Mishra and Singh 2002; Mishra et al. 2005, 2006; Ajmal and Kim 2015). Within the framework of the referenced NRCS literature, the modified parameters associated with the NRCS model have been estimated in this study. The antecedent water-content (AWC) is generally measured based on the prior 5 days’ rainfall. However, the AWC was estimated based on the previous 5 days’ water budget (WB5) in the current study instead of previous 5 days’ rainfall as given in Eq. 4. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi AWC ¼ 0:5 −ð1 þ λÞS þ ð1−λÞ2 S 2 þ 4W B5 S

ð4Þ


where λ is the initial abstraction coefficient, traditionally assumed to be 0.2. However, Woodward et al. (2003) found λ = 0.05 was more effective than λ = 0.2. Hence, λ = 0.05 was adopted in the current study for further analysis. S is the potential maximum retention, which is mainly based on the antecedent soil conditions and the converted value of CN. Using the concept of the antecedent degree of soil saturation and the traditional NRCS model, the Jth day runoff (RJ) that resulted from the current Julian day rainfall (PJ) and the antecedent AWC was estimated as given in Eq. 5.

RJ ¼

ðP J −I a þ AWC Þ2 P J −I a þ S þ AWC

ð5Þ

where Ia is the initial abstraction (mm), normally calculated by Ia=λS. However, the modified λS 2 form based on the prior 5 days’ conditions was used as follows: I a ¼ SþAWC . In order to account for the soil water balance as well as water content balance, the effective daily water content deficiency (EDJ) was calculated using Eq. 6 with the daily series of WBJ and RJ that resulted from Eqs. 3 and 5, respectively, as follows: ED J ¼ W B J −R J

ð6Þ

To apply the proposed drought index (AMDI) for multiple time scales, the daily EDJ ’s were aggregated to the desired time window, such as monthly or yearly, and are denoted by ED*K , where K represents the time window. For example, in the case of a monthly window, ED*K is the sum of 30 daily EDJ’s of a particular K month as illustrated in Eq. 7. ED*K ¼

30 X

ED J

ð7Þ

J ¼1

Last, but not least, the AMDI was computed by incorporating the standardization concept of SPI as depicted by the mathematical expression in Eq. 8. In addition, categorization of the intensity of drought was defined by adopting the SPI classification (McKee et al. 1993; Mallya et al. 2013) as follows:

AMDI ¼

ED*K −ED*K SK

ð8Þ

where ED*K and SK are the long-term mean and standard deviation of the effective deficiency ED*K for a time window K, respectively. Although the AMDI is similar to the SPI and RDI in that they have been developed based on the same concept, they contain some additional significant factors. Consequently, the comparison of these indices could provide a significant measure to validate the appropriateness of the AMDI findings. Hence, the AMDI findings were compared to the SPI and RDI results to understand the performance of AMDI in quantifying the drought events and to verify how AMDI responds to variations in the individual drought attributes (e.g., rainfall and evapotranspiration).


3 Application 3.1 Study Area For the application and evaluation of the proposed drought index, we selected a sub-basin located near the east coast of South Korea at 38.25°N and 128.56°E, as shown in Fig.1. The selected study area covers an area of 1852.93 km2 with a maximum altitude of 1705 m. Daily precipitation and temperature data for the period of 2000–2014 were collected from the Water Resources Management Information System (WAMIS) of Korea (http://www.wamis.go.kr/eng/ main.aspx). Whereas, the additional information, e.g., land covers and soil type, were extracted from the Korea Meteorological Administration (KMA) (http://web.kma.go.kr/eng/) and Ministry of Land, Infrastructure, and Transport (MOLIT) (http://english.molit.go.kr/intro.do). The statistical summary indicated that the maximum, minimum, and averaged values of rainfall within the study area were 294.20 mm, 0.10 mm, and 4.12 mm, respectively, while the respective temperature values were 30 °C, −5 °C, and 14 °C. Moreover, the composite averaged value of the curve number (CN) obtained from land characteristics was 63.

3.2 Results In order to assess the performance of the proposed AMDI drought index in quantifying drought during the selected duration (2000–2014), the AMDI time series for the study area was estimated based on the methodology noted above and then compared with other wellknown univariate and multivariate drought indices.

Fig. 1 Case study area (Sockcho basin) for application of the proposed drought index (AMDI)


In order to verify the performance of AMDI, an initial inspection was carried out to compare the results of the AMDI methodology with the historical drought record. With the application of AMDI methodology, it was observed that May 2001, June 2004, and July 2007 were the driest months, while April 2010, February 2013, and December 2013 were the wettest months. Moreover, statistical analysis indicated that 2000–2001, 2004–2005, and 2008–2009 were the driest years, and 2002– 2003, 2010–2011, and 2013–2014 were the wettest years amongst data records (2000–2014) in the selected study area. On average, March, April, and May were the driest months, while August and September were the wettest months. These results seemed quite similar to the historical record of drought events that happened during the selected study period (http://203.237.1.38/index.aspx). Comparisons with existing univariate drought indices, such as the SPI, and multivariate drought indices, such as the RDI, are depicted in Fig. 2 to identify the response of the AMDI to variability in the individual drought attributes. The preliminary comparative assessment using the Pearson correlation coefficient (PCC) indicated that a significant correlation (PCC = 0.73) existed between the AMDI and SPI, whereas a weak correlation (PCC = 0.35) existed between 3.00

AMDI

SPI

RDI

2.00

Drought Index

1.00 0.00 -1.00 -2.00 -3.00 -4.00 Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan

2000

2001

2002

2003

2004

2005

2006

2007

Time

(a)

3.00

AMDI

SPI

RDI

Drought Index

2.00 1.00 0.00 -1.00 -2.00 -3.00 Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan Nov Sep Jul May Mar Jan

2008

2009

2010

2011

2012

2013

Time

(b)

Fig. 2 AMDI, SPI and RDI time series for the study area during (a) 2000–2007 and (b) 2008–2014

2014


the AMDI and RDI. The study area experienced a very low temperature in winter, which generally affected the RDI prediction and could be the reason for the low correlation between the AMDI and RDI. In most cases, all of the indices indicated more or less a symmetrical drought trend. However, the intensity varied quite a bit. Moreover, the monthly time series comparison shown in Fig. 2 clearly indicates that abrupt variability in AMDI outputs was less than that of the SPI and RDI, since it is based on an additional factor of antecedent conditions, which is lacking in the SPI and RDI. It is worth noting that the SPI characterizes droughts that may start and end rapidly, while the AMDI indicates the combined effects of the soil and water balance with the time lag effect. Therefore, the onset and ending, as well as the intensity of drought predicted by the different drought indices, could be different as can be observed specifically in the case of Oct 2000, Dec 2001, and Apr 2013. In addition, the statistical summary for the indices is shown in Fig. 3 using a box plot representation. The box plot representation indicates that the central value of RDI is quite different than those of the SPI and AMDI. Moreover, the dotted lines indicate the classification, i.e., exceptionally dry (D4), extremely dry (D3), severely dry (D2), moderately dry (D1), and abnormally dry (D0) conditions, of the drought events. The assessment of drought classification frequency using the AMDI indicated that approximately 72 % of the time periods could be classified as normal or wet conditions (NC), while

Fig. 3 Statistical distribution and classification of drought events resulted from AMDI, SPI and RDI time series during 2000–2014 (whereas exceptional dry (D4), extreme dry (D3), severe dry (D2), moderate dry (D1), abnormally dry (D0) and wet conditions are drought classification)


1 %, 2 %, 3 %, 14 %, and 8 % were identified as exceptionally dry (D4), extremely dry (D3), severely dry (D2), moderately dry (D1), and abnormally dry (D0) conditions, respectively. In the case of the SPI, the frequencies of D4, D3, D2, D1, D0, and NC were determined to be 2 %, 4 %, 3 %, 10 %, 8 %, and 78 %, respectively, and they were 5 %, 3 %, 3 %, 5 %, 6 %, and 78 %, respectively, in the case of RDI (Fig. 4). Hence, considering additional factors, i.e., antecedent soil-moisture conditions and balance, an approximately 6 % difference in the drought frequency among the AMDI, SPI, and RDI results was noted, which is quite important for significant and proper drought assessment and mitigation. It is important to note that different indices might predict different onset and termination times for the event. Therefore, it is expected that the severity and duration values may also be different. Figure 5 shows the number of drought events along with the respective duration for the selected study area during 2000–2014. It was determined that if we only relied on the specific drought indices of the SPI or RDI, we could estimate the actual drought conditions to be normal or wet. However, the AMDI resulted in longer drought duration and more drought events. Moreover, the comparison revealed that simplicity, an aggregation of all of the soil water balance values, consideration of antecedent conditions, and the equal responses to all of the variables were significant features of the AMDI contributing to the proper drought assessment. We concluded that the developed AMDI provided a physically sound, temporally flexible and unbiased index associated with all the possible variants.

AMDI

D4 D3 1% 2%

D2 3%

D4 2%

SPI D1 14% D0 8%

D3 D2 4% 3%

D1 10% D0 3%

NC 72%

NC 78%

(a)

(b) D4 5%

RDI

D3 3%

D2 3%

D1 5%

D0 6%

NC 78%

(c) Fig. 4 Frequency of drought events resulted from (a) AMDI, (b) SPI and (c) RDI during 2000–2014


Drought Duration

Drought Events

50

50

40

40

30

30

20

20

10

10

0

AMDI

SPI Drought Index

RDI

Drought Events

Drought Duration

Fig. 5 Numbers of drought events with their respective duration

0

4 Conclusions Antecedent conditions play a crucial role in the analysis of the physical processes involved in conceptual rainfall-runoff modeling and demonstrate the soil-wateratmosphere interaction. In addition, these factors also play an important role in providing a reliable assessment of drought. Joint consideration of all forms of drought, i.e., agricultural, hydrological, and meteorological drought with the involvement of antecedent soil water conditions triggered the development of a new drought index, which was called AMDI in the current study. The newly developed drought index complimented the weaknesses of the existing drought indices (i.e., SPI and RDI) by taking into consideration all of the drought variables in the form of precipitation, evapotranspiration, antecedent soil and water conditions, and runoff that are generally involved in water balance for significant drought assessments. The key strengths involved in the development of the AMDI formulation were: (a) to consider a multivariate perspective that accounts for the causative variables and aggregates the effects of multiple drought forms; (b) to construct a technically sound mathematical formulation behind the multivariate drought index development; (c) to develop a multi-scalar index that can be developed for multiple time scales; and (d) to be statistically robust with very simple and clear mathematic computational procedures using readily available information. Based on comparative analyses, it was determined that the AMDI could significantly capture the variation in precipitation and evapotranspiration as well as the antecedent soil water conditions. Several discrepancies were observed between the time series of the proposed AMDI and the comparative SPI and RDI. However, the drought trend was found be more or less the same in most of the cases. Hence, it was concluded that the AMDI could be considered as an alternative tool for specific drought indices, e.g., the SPI, RDI, or even the PDSI, and it may be a step forward for significant drought assessment. Acknowledgments This article is based on research supported by a grant (14AWMP-B082564-01) from Advanced Water Management Research Program funded by the Ministry of Land, Infrastructure and Transport of Korea. Compliance with Ethical Standards Conflict of Interest The authors declare that they have no conflict of interest.


References Ajmal M, Kim T (2015) Quantifying excess stormwater using SCS-CN–based rainfall runoff models and different curve number determination methods. J Irrig Drain Eng 141(3):04014058 Banimahd SA, Khalili D (2013) Factors influencing Markov chain predictability characteristics, utilizing SPI, RDI, EDI and SPEI drought indices in different climatic zones. Water Resour Manag 27:3911–3928 Beguería S, Vicente-Serrano SM, Reig F, Latorr B (2014) Standardized precipitation evapotranspiration index (SPEI) revisited: parameter fitting, evapotranspiration models, tools, datasets and drought monitoring. Int J Climatol 34(10):3001–3023 Gocic M, Trajkovic S (2014) Drought characterization based on water surplus variability index. Water Resour Manag 28(10):3179–3191 Hargreaves GL, Samani ZA (1985) Reference crop evapotranspiration from temperature. Appl Eng Agric 1: 96–99 Jiang R, Xie J, He H, Luo J, Zhu J (2015) Use of four drought indices for evaluating drought characteristics under climate change in Shaanxi, China: 1951–2012. Nat Hazards 75(3):2885–2903 Kim BS, Park IH, Ha SR (2014) Future projection of droughts over South Korea using representative concentration pathways (RCPs). Terr Atmos Ocean Sci 25:673–688 Logan KE, Brunsell NA, Jones AR (2010) Assessing spatio-temporal variability of drought in the U.S. central plains. J Arid Environ 74:247–255 Mallya G, Tripathi S, Kirshner S, Govindaraju R (2013) Probabilistic assessment of drought characteristics using hidden Markov model. J Hydrol Eng 18(7):834–845 McKee TB, Doesken NJ, Kleist, J (1993) The relationship of drought frequency and duration to time scales. 8th Conference on Applied Climatology, Anaheim, Calif. 17–22 January 1993. American Met. Society. Mishra SK, Singh VP (2002) SCS-CN-based hydrologic simulation package, in: Singh, V.P., Frevert, D.K. (Eds), Mathematical models in small watershed hydrology and applications. Water Resour. Publ., P.O. Box 2841, Littleton, Colorado 80161, pp.391–464 Mishra AK, Singh VP (2011) Drought modelling-a review. J Hydrol 403(1–2):157–175 Mishra SK, Jain MK, Pandey RP, Singh VP (2005) Catchment area-based evaluation of the AMC-dependent SCS-CN-based rainfall–runoff models. Hydrol Process 19(14):2701–2718 Mishra SK, Sahu RK, Eldho TI, Jain MK (2006) An improved Ia-S relation incorporating antecedent moisture in SCS-CN methodology. J Water Resour Manag 20:643–660 Narasimhan B, Srinivasan R (2005) Development and evaluation of soil moisture deficit index (SMDI) and evapotranspiration deficit index (ETDI) for agricultural drought monitoring. Agric For Meteorol 133:69–88 Paulo AA, Rosa RD, Pereira LS (2012) Climate trends and behavior of drought indices based on precipitation and evapotranspiration in Portugal. Nat Hazards Earth Syst Sci 12(5):1481–1491 Sohrabi MM, Ryu JH, Abatzoglou J, Tracy J (2015) Development of soil moisture drought index to characterize drought. J Hydrol Eng doi:10.1061/(ASCE) HE.1943-5584.0001213, 04015025. Tigkas D, Vangelis H, Tsakiris G (2012) Drought and climatic change impact on streamflow in small watersheds. Sci Total Environ 440:33–44 Tigkas D, Vangelis H, Tsakiris G (2013) The RDI as a composite climatic index. Eur Water 41:17–22 Tigkas D, Vangelis H, Tsakiris G (2015) DrinC: a software for drought analysis based on drought indices. Earth Sci Inf 8(3):697–709 Tsakiris G, Pangalou D, Vangelis H (2007) Regional drought assessment based on the reconnaissance drought index (RDI). Water Resour Manag 21(5):821–833 Vangelis H, Tigkas D, Tsakiris G (2013) The effect of PET method on reconnaissance drought index (RDI) calculation. J Arid Environ 88:130–140 Vicente-Serrano SM, Beguería S, López-Moreno JI (2010) A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. J Clim 23(7):1696–1718 Waseem M, Ajmal M, Kim TW (2015) Development of new composite drought index for multivariate drought assessment. J Hydrol. doi:10.1016/j.jhydrol.2015.04.044 Woodward DE, Hawkins, RH, Jiang, R, Hjelmfelt, AT Jr, Van Mullem, JA, Quan, DQ (2003) Runoff curve number method: Examination of the initial abstraction ratio. World Water & Environ Resour Congress 2003 and Related Symposia, EWRI, ASCE, Philadelphia, Pennsylvania, USA Yan D, Shi X, Yang Z, Li Y, Zhao K, Yuan Y (2013) Modified palmer drought severity index based on distributed hydrological simulation. Math Probl Eng. doi:10.1155/2013/327374 Zargar A, Sadiq R, Naser B, Khan FI (2011) A review of drought indices. Environ Rev 19:333–349