Understanding drought dynamics and variability over ...

Understanding drought dynamics and variabilityover Bundelkhand region

MD SAQUIB SAHARWARDI, ALAM SHWETA MAHADEO and PANKAJ KUMAR*

Department of Earth and Environmental Sciences, Indian Institute of Science Education and Research,Bhopal, India.*Corresponding author. e-mail: [email protected]

MS received 23 September 2020; revised 16 December 2020; accepted 21 February 2021

This study provides an evaluation of the past, present, and future spatiotemporal variability of droughtsin the Bundelkhand region of central India. The assessment has been made by analyzing the existing(1951–2018) drought dynamics with gridded observational and reanalysis datasets. The future projectionis presented using a multi-model ensemble from 21 simulations of regional climate model over CORDEXSouth-Asia domain under the highest carbon concentration, i.e., RCP8.5 emission scenario. The Stan-dardized Precipitation Index (SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI)indices are used for short and long-term monitoring of droughts. Spatiotemporal statistical analysis isperformed to examine the relationship between drought indices, i.e., SPI, SPEI and driving parameterssuch as temperature, precipitation, etc. It is noticed that the frequency of drought has increased since thebeginning of the 21st century. In particular, the northern part of the Bundelkhand region is more vul-nerable to drought due to overall less precipitation and more temperature. The composite analysis ofdrought year indicates that moisture-laden wind from the Arabian Sea branch generally weakened inmonsoon season. Teleconnections of drought over Bundelkhand region reveal that nearly 40% of thedroughts are linked to El-Nino events that have become stronger in recent decades. The model ensemblerealistically represents the regional climate reasonably well over the region. The projected change in nearfuture drought shows more frequent events using both SPI and SPEI indices that are also detected in theobservational analysis.

Keywords. Bundelkhand drought; SPI and SPEI; drought frequency; drought projection; drivers.

1. Introduction

Drought is a severe and unpredictable naturalthreat due to low rainfall (Dai 2011). The keychallenge in the study of drought is to describe thebeginning and end of drought events as it pro-gresses and recedes very gradually and stays for avariable time span, often months to years (Mishraand Singh 2010; Dai 2011). Growing occurrence ofdrought has attracted the attention of meteoro-logists and climatologists to consider this

phenomenon across the globe. India is one amongthe various drought-prone countries where at leastone drought event has been reported in every 3 yrssince the last Bve decades (Mishra and Singh 2010).Primarily, precipitation is considered as a maincause of drought occurrences along with certainother parameters (Dai 2011). Below normal rainfallduring the monsoon season creates water scarcity.Indian subcontinent receives 70%–90% of itsannual rainfall during monsoon months June, July,August, September (JJAS) (Parthasarathy et al.

J. Earth Syst. Sci. (2021) 130:122 � Indian Academy of Scienceshttps://doi.org/10.1007/s12040-021-01616-z (0123456789().,-volV)(0123456789().,-volV)

1987; Kumar et al. 2013). Delayed onset, earlywithdrawal of southwest monsoon, and its longbreaks trigger agricultural droughts in India(Gautam and Bana 2014). This monsoon variabil-ity is largely teleconnected with the coupled air–sea mechanism that aAects the moisture transportalong the Indian subcontinent (Chattopadhyayand Bhatla 1996; Chattopadhyay and Bhatla 2002;Bhatla et al. 2006). In addition, increase evapora-tive demands due to accelerated warming climatemay further increase the drought stress and severeheat-like condition over the region (Pattanaik et al.2013; Bhatla et al. 2020). Rajasthan and Bun-delkhand are known for their history of droughts,along with Karnataka and Odisha (Gupta andSingh 2011). InefBcient water management andagriculture practices have led to significant agri-cultural droughts in Punjab, Haryana, andChhattisgarh (Gupta et al. 2011).In central India, the Bundelkhand region has

experienced multiple extreme drought events inrecent decades (Thomas et al. 2016b). Every yearthousands of farmers migrate to urban areas due tothe losses incurred in agriculture caused by intensedrought conditions in the region (Ahmed et al.2019). It is therefore important to understand themechanism and characteristics of drought in theregion. Various studies have been carried out usingmultiple drought indices to classify meteorological,hydrological, and soil moisture droughts (Nair andSingh 2013; Thomas et al. 2015, 2016a). The pro-gression and withdrawal of each drought event aredifferent and depend on the monthly rainfall cycle(Thomas et al. 2015). A recent study on theseverity of drought events in the region revealsvariations across the entire Bundelkhand duringthe monsoon season of the drought year (Thomaset al. 2015). In addition to severity, drought onsetand duration, drought-affected area, varied signif-icantly for each observed drought event. Alongwith studies in Bundelkhand region as a whole,individual basin level study also reveals increaseddrought frequency every 3–4 years (Thomas et al.2016a). Besides, drought frequency and intensity inthe Bundelkhand region is changing for meteoro-logical, hydrological and agricultural droughts(Nair and Singh 2013).Though earlier studies of drought assessment

over the Bundelkhand region have addressed theissues regarding the drought variability; there arevery few attempts to analyze the regional droughtdrivers. In recent decades, the region has experi-enced multiple severe drought events. Hence to

explore processes causing dryness, requires a betterunderstanding of the nature of drought eventswhich will also help to monitor upcoming droughtevents. Furthermore, projecting potential droughtevents will be helpful for better planning, prepa-ration and mitigation of droughts. The three-broadobjectives of this study are to Bnd out: (i) assess-ment of spatiotemporal variability of past andrecent drought occurrences, (ii) analyzing thecauses of drought using multiple meteorologicalvariables, and (iii) future drought projection usingregional climate models.

2. Study area

The outline map of Bundelkhand region is shown inBgure 1. It lies in the north-central region of Indiabetween the north–south boundary of Indo-Gangetic plain and Vindhyan Ranges, respectively.It is comprised of 13 districts separated by twostates – Madhya Pradesh and Uttar Pradesh. Dis-tricts in Madhya Pradesh are Sagar, Chhatarpur,Panna, Damoh, Tikamgarh, Datia and in UttarPradesh: Lalitpur, Mahoba, Jalaun, Hamirpur,Banda, Jhansi, and Chitrakoot. According to2011 census, Bundelkhand has a population of18,311,896, out of which 14,198,668 live in ruralareas of Bundelkhand region. The geographicposition is between 238200–268200N latitude and788200–818400E longitude. Rivers are the primarysource of water for both agriculture and everydaylife use. The major perennial rivers Cowing throughthe region are the Yamuna, Ken, Betwa, Sind andPahuj. About 70% of the region’s population eco-nomically depends on agriculture. Wheat, pulses,and soybeans are major crops cultivated in theregion despite lower productivity compared to theother leading states. The average annual surfaceair temperature is over *25�C and average annualrainfall is 998 mm for the period 1951–2018. Morethan 90% of the annual rainfall occurs in themonsoon season, and the surface air temperatureranges between 22� and 25�C, and in summer thetemperature rises beyond 40�C, attain maximumtemperature in May and June (Gupta et al. 2014).

3. Methodology

3.1 Datasets

For this study, droughts were analyzed using var-ious meteorological variables, such as surface air

122 Page 2 of 16 J. Earth Syst. Sci. (2021) 130:122

temperature, precipitation, wind, sea surfacetemperature, etc. The surface air temperature(Srivastava et al. 2009) used are minimum, maxi-mum, and mean temperature along with the pre-cipitation station data is obtained from the IndiaMeteorological Department (IMD) (Rajeevan et al.2006) with a spatial grid resolution of 1�91� for theperiod 1951–2018. The NCEP-NCAR reanalysisdataset is used at 2.5� 9 2.5� spatial resolution formeridional and zonal wind at 850 hPa used tostudy the circulation pattern in the monsoonseason (Kalnay et al. 1996). Hadley Centre SeaIce and Sea Surface Temperature (HadISST)dataset (Titchner and Rayner 2014) for the sameperiod at 1� 9 1� has been used to identify tele-connection of drought with El Nino years. A setof 21 CORDEX Regional climate model’s data at0.5� 9 0.5� has been used to study the futuredrought assessment over the study region. Anensemble mean is used for the same using RCP8.5emission scenario for temperature, precipitationas well as drought indices for reference(1976–2005) and near-future period (2006–2030).The RCM ensemble comprises of nine SMHI-RCA (Swedish Meteorological and HydrologicalInstitute – Rossby Centre regional Atmosphericclimate model) (Rummukainen et al. 1998), BveRegCM4 (Regional Climate Model 4) (Giorgiet al. 2012), six CCAM (Conformal CubicAtmospheric Model) (Mcgregor 2005) and oneREMO (REgional MOdel) (Jacob and Podzun1997) simulations having forcing from differentglobal climate models.

3.2 Calculation of drought indices

SPI (McKee et al. 1993) and SPEI (Vicente-Serrano et al. 2010) are common indices used tostudy the short- and long-term meteorologicaldrought that develops within 3–4 months and 12months or more. Both SPI and SPEI are used forpreferable time scales and applicable for wide cli-matic zones. The spatiotemporal analysis has beencarried out using SPI and SPEI to identify thesuitable drought index for the region. Both theindices use the precipitation as an input source, butSPEI uses additional parameter Potential Evapo-transpiration (PET) along with precipitation,which has been calculated using the Hargreavesmethod (Hargreaves and Samani 1985). Thedetailed values of SPI and SPEI have been tabu-lated in table 1. Negative (positive) values repre-sent the episodes of a dry (wet) type. The detaileddescriptions about the calculation methodology ofboth the indices are given in Appendix.

Figure 1. Index map of the Bundelkhand Region.

Table 1. SPI and SPEI index values.

Index severity Types of events

2.0 + Extremely wet

1.5 to 1.99 Very wet

1.0 to 1.49 Moderately wet

–0.99 to 0.99 Near normal

–1.5 to –1.99 Severely dry

–2.0 and less Very dry

J. Earth Syst. Sci. (2021) 130:122 Page 3 of 16 122

4. Results and discussions

4.1 Drought variability and its characteristics

Figure 2(a) shows the inter-annual variability forJJAS mean standardized rainfall anomaly for theperiod 1951–2018. The orange (green) colour barsbelow (above) the negative (positive) truncation–1 (+1) represent the drought years. The fre-quency of drought has increased from the begin-ning of the 21st century and droughts wererecorded in the years: 1965, 1966, 1979, 1989,2006, 2007, 2009, 2014, 2015 and 2017. Thesedrought years have very much similarity withalready reported studies (Shrestha et al. 2020).After 2000, six drought events were observed,resulting in a significant rise of around 50% indrought years against four drought events in thelast 50 years before 2000. These drought yearsconsist of a number of short-term droughts withina year. In the recent decade, continuous two timesconsecutive intense drought experienced in2006–2007 and 2014–2015, which has intensiBedthe regional water scarcity. The 11-yr runningaverage also shows a progressive trajectory of adeclining trend for precipitation later in 2000. Thepositive slope (0.0068) indicates the rising trend insurface air temperature till 2018, whereas thenegative slope (–0.0105) represents the decreasingtrend in precipitation, though not significant. Theresult shows the increasing trend in temperaturefor the period 1951–2018 in Bgure 2(b). Therefore,the temperature is one of the factors that play akey role in the drought occurrences along withprecipitation. It is observed that the temperaturein the northern part of the Bundelkhand region isrelatively more than the southern part (Bgure 3a).

At the same time, the northern part is experi-encing less rainfall than the southern part(Bgure 3b). This lower precipitation, along withextreme drought activity over the northern partof Bundelkhand is also reported in a previousstudy (Deo et al. 2015; Shrestha et al. 2020). Thisrelatively higher temperature and lower precipi-tation in the northern region causes intense dry-ness and even more during the summer seasonaAecting regional hydrological balance. The situ-ation gets critical when the region receives lessthan normal rainfall for consecutive years, leadingto severe drought conditions. The extreme pre-cipitation under changing climate may furtherlead to enhanced surface runoA and subsequently,less water available for recharge (Bhatla et al.2019).Figure 4 shows the time-series of SPI and SPEI

for 04 and 12 months timescale, respectively.

Interestingly, both the indices detected a similar

number of drought events though differences were

observed in their severity (table 2). The SPI12

variability has a considerable match with station

observatory, which was detected in a previous

study (Alam et al. 2014). This variation in severity

arises due to additional parameter potential evapo-

transpiration in SPEI. It is noticed that significant

severe and extreme droughts occurred during the

1970s and at the beginning of 2000s for SPI, and

SPEI. SPI and SPEI are closely linked. The cor-

relation between SPI04 and SPEI04 is 0.897, while

0.936 is between SPI12 and SPEI12, which is quite

significant. Long-term droughts are more intense,

with a low frequency of occurrence than short-termdroughts. Therefore, for shorter time scales, thedrought severity as obtained by SPI and SPEI is

Figure 2. Anomalies over Bundelkhand region for the period 1951–2018. (a) Standardized rainfall anomaly and (b) temperatureanomaly.


comparable, but for longer time scales of 12-monthor more, the differences in the drought severitybecome pronounced. A significant decreasing trend([95% conBdence level) is observed for all fourdrought indices detected by the negative slope ofthe regression line except SPEI04. This indicatesthat there is an increasing drought trend in whichis observed by all the four indices.

Figure 4. SPI and SPEI time series for the period 1951–2018. (a) 04–m SPI, (b) 12–m SPI, (c) 04–m SPEI, and (d) 12–m SPEI.

Figure 3. Annual mean of daily data for the period 1951–2018. (a) Mean surface air temperature (oC) and (b) meanprecipitation (mm/day).

Table 2. Number of drought events with severity level.

Drought severity SPI04 SPI12 SPEI04 SPEI12

Moderate (–1 to –1.49) 24 6 21 7

Severe (–1.5 to –1.9) 10 4 14 3

Extreme (–2 and less) 2 1 1 1

Total events 36 11 36 11


4.2 Comparative Cood and drought analysis

Figure 5 shows the spatial distribution of Coodcomposite (1952, 1961, 1967, 1971, 1978, 1980,1982, 1983, 1990, 1999, 2003, 2013, 2016) anddrought composite (1965, 1966, 1979, 1989, 2006,2007, 2009, 2014, 2015, 2017) years over Bun-delkhand region. As expected, in all seasons, Coodcomposites show more rainfall except March–April–May (MAM). The mean rainfall is 3–4mm/day higher for Cood in comparison to droughtyears. However, in both the cases, the southernregion received more rainfall in comparison to thenorth. Hence northern part is more prone todrought and higher severity.From the annual cycle of rainfall anomaly for

Cood (Bgure 6a) and drought (Bgure 6b) compositeyears, it is evident that JJAS in Cood compositeyears received a considerable rainfall which causedinundation in the region while drought compositeyears received relatively less rainfall. Hence, duringCood composite years, region witnessed Cood andvice-versa. Moreover, the Cood years show maxi-mum rainfall in August, whereas a drought yearexhibits maximum rainfall in July. Spatial vari-ability of SPI and SPEI for Cood composite and

drought composite years is given in Bgure 7(a andb), respectively. During Cood composite years,both the indices show the entire region havingnormal to wet conditions, while in drought com-posite years 4 and 12 months SPI and SPEI showthe entire region to be under normal to dryconditions.

4.3 Regional rainfall variability in ENSOassociated

It is interesting to note that the region receivesmonsoon rainfall mainly from the Arabian Seabranch both during Cood and drought compositeyears. Figure 8 shows the circulation pattern overthe Bundelkhand region for composite years at 850hPa and their difference (Bgure 8c). The wind inthe Cood composite years is two-fold stronger thanthe drought. Now it is quite evident that the Ara-bian Sea branch of monsoon is the major driver fordrought/Cood over the region. This Westernbranch of monsoon has a great impact on precipi-tation pattern over the Bundelkhand region ishighlighted in an earlier study as well (Deo et al.2015). However, they only focused on the Uttar

Figure 5. Spatial distribution of precipitation for all seasons. (a) Flood composite years and (b) drought composite years.


Pradesh part of the region. Since ENSO has animpact on all India JJAS monsoon rainfall inter-annual variability, ENSO teleconnection over thestudy region is analyzed to explore their impacts onseasonal rainfall variability. Interestingly, approxi-mately 40% of total drought events are associatedwith El-Nino events (Bgure 9). In addition, therelationship has become stronger in recent decades.The correlation between the Bundelkhand regionprecipitation and ENSO region sea surface tem-perature (SST) interannual variability is –0.28. Anegative correlation indicates warmer SST inthe eastern PaciBc will lead to a reduction in pre-cipitation. To further investigate the drought dri-vers, seasonal rainfall variability is analyzed for ElNino and non-El Nino drought composite years(Bgure 10). It is observed that El Nino droughtscausing long-term break during the peak monsoonseason, however, no such pattern was detected fornon-El Nino droughts. However, the correlationwith PaciBc SST as well as monsoon circulation hassignificant impact over the region. The regionalsubsurface properties and topography also have animportant role in this region for drought occur-rence. The impermeable rock in this region causesto move most of the perceptible water via surfacerunoA, and as a result, the groundwater recharge isvery less. Secondly, the hilly topography furtherenhances the water runoA in a short time period.Under the changing climate, the increase inextreme precipitation has enhanced further theseactivities to a great extent.

4.4 Future projection of drought

4.4.1 Model validation

The RCMs ensemble mean (hereafter referred to asRCM) for surface air temperature and annualprecipitation cycles are shown in Bgure 11. Bothare showing good agreement with the observationsIMD, though JJAS precipitation is underesti-mated. However, the correlation between IMD andRCM annual cycle in terms of temperature (pre-cipitation) is 0.99 (0.98), which is quite significant.This strong relationship indicates that the model isable to replicate the observational variability withslight systematic underestimation during JJASseason. The spatial distribution of mean tempera-ture and precipitation has been plotted for RCMtogether with IMD for the historical period1976–2005 (Bgure 12). In comparison to observa-tion, the model is able to capture the spatiotem-poral variability quite realistically with a slightlower magnitude for both. This underestimation islargely due to the smoothing of multiple RCMsimulations. Figure 13 shows the spatial differencebetween RCM and observations. It illustrates thatRCM simulated historical temperature is higherthan the IMD in the northern part and lower in thesouth. For precipitation, has slightly higher rainfallthan observations in the northern and westernpart, the central region shows less rainfall whencompared to observations. Overall RCM canreplicate the observational variability reasonablywell.

Figure 6. Annual cycle of rainfall anomaly for the period 1951–2018. (a) Flood composite years and (b) drought compositeyears.


Figure

7.SpatialmeanofSPIandSPEIfor04-and12-m

onth

timescale.(a

)Floodcomposite

years

and(b

)droughtcomposite

years.


4.4.2 Projected changes in drought

As present drought frequency is increasing, it iscrucial to investigate future drought projections fortaking adaptive measures to reduce the risks, anddrought inCicts over the region. The analysis isperformed for a near-future scenario for tempera-ture and precipitation, including drought indices,SPI and SPEI for the period 2006–2030 are pro-jected relative to the reference period 1976–2005.Figures 14 shows the near future projection oftemperature and precipitation for the period2006–2030. With respect to the base climate, it isnoticed overall, an increase in rainfall is projectedwith the eastern and southwestern relatively get-ting more. However, as expected, the temperatureis showing an increase throughout the region with ahigher magnitude in the north. Interestingly, theenhanced temperature magnitude in the projectedclimate over the northern region is consistent withearlier study though differences were observed inmagnitude (Prajapati et al. 2018).The projected trend in future drought

(2006–2030) is shown in Bgure 15. The droughtevents are projected to increase in the near futurebased on all the indices. SPI-based projectionsshow a more frequent drought in comparison toSPEI. The variability of both is quite similar withlittle differences in magnitude. This indicates thatprecipitation will be still the dominant driver ofdrought in future. The PET will only aAect themagnitude of drought severity which is an impor-tant parameter. In future projection, we cannotignore the role of increasing temperature underchanging climate. Therefore, SPEI can be consid-ered to be a better indicator of future droughtprojections. Both the indices exhibit frequentdrought activity nearby 2020, which is also obviousfrom the observational results. Surprisingly forSPI04 and SPI12, overall, no trend is observed. Inaddition, both SPEI04 and SPEI12 show a slightlynegative trend in the time series. Despite higherdrought frequency, these lower trends indicate thatthe drought conditions will be a normal activity inthe future.

5. Summary and conclusion

In this study, past, present and near future droughtvariability in the Bundelkhand region of centralIndia has been studied for the period 1951–2018.

Figure 8. Wind Pattern in JJAS month at 850 hPa. (a) Floodcomposite years, (b) drought composite years, and (c)difference in the wind pattern between Cood and droughtcomposite years.


Figure 9. Relationship between standardized rainfall anomaly with SST.

Figure 10. Comparison of daily monsoon season precipitation over Bundelkhand region for the period 1951–2018. (a) El-Ninodrought composite years and (b) non El-Nino drought composite.

Figure 11. Annual cycle of IMD and RCM for the period 1976–2005. (a) Mean surface air temperature annual cycle and(b) precipitation annual cycle.


An investigation has revealed that later in 2000,the frequency of drought has increased. Theincreasing trend in temperature and decreasingtrend in precipitation is notable as both have avital role in modulating the regional droughtoccurrence, which implies swift changes in the

drought driving variables over the period of time.Therefore, from the spatial distribution of tem-perature and precipitation, it is concluded that thenorthern region of Bundelkhand is more suscepti-ble to the dryness during pre- and post-monsoonseasons. SPI and SPEI have been considered for the

Figure 12. Comparison of annual mean of daily data of IMD and RCM for the period 1976–2005. (a) Mean surface airtemperature (oC) and (b) mean precipitation (mm/day).

Figure 13. Difference in RCM and IMD data for the period 1976–2005. (a) Mean surface air temperature (oC) and (b) meanprecipitation (mm/day).


investigation of drought occurrences because theironset and termination can be better comprehendedby these indices. Both indices for 04- and 12-monthrunning mean produced equal drought events withvarying severity and intensity. The spatial patternof drought composite years derived from SPI showsthat maximum area is aAected by both short andlong-term drought, but the SPEI pattern exhibitless severity as compared to SPI for short and long-term drought due to the PET eAects, which slightlyreduces the severity. Hence, considering the

drought characteristics solely based on precipita-tion may cause a discrepancy in the drought spa-tiotemporal pattern. Comparative Cood anddrought analysis show that year which has receivedless rainfall has created severe drought conditions.The significant Bnding of this study is that rainfallintensity across the region is interestingly con-trolled by the moisture-carrying wind from boththe Arabian Sea branch, and the weaker wind cir-culation causes a lowering in the amount of rainfall.Seasonal (JJAS) rainfall has also been correlated

Figure 14. The mean projected change for the period 2006–2030 based on RCM ensemble. (a)Mean surface air temperature (8C)and (b) mean precipitation (mm/day).

Figure 15. SPI and SPEI time series plot of the time period 2006–2030. (a) 04–m SPI, (b) 12–m SPI, (c) 04–m SPEI, and(d) 12–m SPEI.


with the warming of the PaciBc SST. This resultconBrms that approximately 40% of droughts arerelated to the El-Nino, though all dry spells and itsassociated drought are not always related toEl-Nino.Future projection of short and long-term

droughts carried out using an ensemble of the high-resolution regional climate model. The potentialincrease in temperature and precipitation has beenanalyzed under the high concentration of carbonemission scenario RCP 8.5. The base climate modelwas able to simulate the observational variabilityrealistically. For near-future projection, SPI exhi-bits no trend, whereas SPEI shows a slightlydecreasing trend, though drought frequencies areprojected to increase. This discrepancy arises dueto drought events become so normal that no orlittle trend is observed. Moreover, under thechanging climate, the impact of temperature can-not be ignored. Therefore, SPEI should be consid-ered as a more suitable index compared to SPI forfuture drought projections. The interannualdrought variability in the present climate is notmuch sensitive to temperature compared to futureprojection under the RCP8.5 scenario, which isclearly visible from the observational and projecteddrought pattern.The present study investigated the spatiotem-

poral variability of the drought only based onmeteorological variables; however, regional geol-ogy, land-use, and land-cover processes may aAectthe regional hydrology significantly. This needs amore integrated modelling approach to compre-hensively address the future projections. Detailedanalysis is required to address the variability ofagriculture and hydrological droughts. The newgeneration of models simulated in CMIP6 orregional coupled RCMs may further enhancegreater conBdence in regional projections.

Acknowledgements

MSS acknowledges the fellowship from Dept. ofScience and Technology (DST), Govt. of IndiaINSPIRE Fellowship no. IF160281. PK acknowl-edges funding from the Science and EngineeringResearch Board (SERB), Govt. of India grantnumber SB/S2/RJN-080/2014 and DST, Govt. ofIndia grant number DST/CCP/NCM/69/2017.Authors are thankful to the India MeteorologicalDepartment and Regional modelling group for

providing the observational and model datasets,respectively.

Author statement

PK convinced the idea. All the authors contributedto the designing of the manuscript. ASM and MSSprepared the Bgures with help from PK. Allauthors contributed to the writing of the manu-script and its result interpretations.

A. Appendix

A.1 SPI Calculation

SPI is derived by Btting gamma distributionfunction. It is then transformed into standardnormal distribution where the mean value is zeroand variance is one (McKee et al. 1993).The gamma distribution is deBned by probabil-

ity density function (p.d.f.) as

g xð Þ ¼ ½1= ba � CðaÞ� � xa�1 � e�x=b ðA:1Þ

where a[ 0, a is a shape parameter; b[ 0, b is ascale parameter; x [ 0, x is the precipitationamount.

ðaÞ ¼Z 1

0

ya�1e�ydy; ðaÞ is a gamma function:

The cumulative probability distributionfunction G(x) is obtained from integrating p.d.f.as:

G xð Þ ¼Z x

0

g xð Þdx ¼ 1

baC að Þ

Z x

0

x a�1e�x=bdx

ðA:2Þ

where

a ¼ 1

4A1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 4A

3

r !

b ¼ x

a

A ¼ ln ðxÞ �P

ln xð Þn

n is the number of precipitation observations.

Let t = x/ b, putting it in G(x)


G xð Þ ¼ 1

C að Þ

Z x

0

ta�1e�tdt: ðA:3Þ

For x = 0, the gamma function is undeBnedtherefore the cumulative probability becomes

H xð Þ ¼ q þ 1�qð ÞG xð Þ: ðA:4Þ

Here q is the value when the probability at x = 0.To get SPI value, the cumulative probability

function has to be converted into a standard nor-mal cumulative distribution function having meanvalue zero and variance as one. Then SPI is cal-culated using Abramowitz and Stegun (1965)approximation as:

SPI ¼ � t � C0 þ C1t þ C2t2

1þ d1t þ d2t þ d3t3

� �

for 0\HðxÞ\0:5 ;

ðA:5Þ

SPI ¼ þ t � C0 þ C1t þ C2t2

1þ d1t þ d2t þ d3t3

� �

for 0:5\HðxÞ\ 1:0 ;

ðA:6Þ

where

t ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiln

1

H xð Þð Þ2

!vuut for 0\HðxÞ\0:5 ;

t ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiln

1

1:0�H xð Þð Þ2

!vuut for 0:5\H xð Þ\1:0

C0 ¼ 2:515517, C1 ¼ 0:802853, C2 ¼ 0:010328,d1 ¼ 1:432788, d2 ¼ 1:89269 and d3 ¼ 0:001308.

A.2 SPEI calculation

The SPEI is calculated as

Di ¼ Pi � PETi ; ðA:7Þ

where Di is aggregate at different time scale, Pi ismonthly precipitation and PET is the monthlypotential evapotranspiration.The probability density function (for log logistic

distributed variable) is given by

f xð Þ ¼ ba

x � ca

� �b�1

1þ x � ca

� �b� ��2

; ðA:8Þ

where a is a scale parameter for D values

a ¼ W0 � 2W1ð ÞbC 1þ 1

b

� �C 1� 1

b

� � ;

b is a shape parameter for D values

b ¼ 2W1 �W0

6W1 �W0 � 6W2;

c is an origin parameter for D values

c ¼ W0� aC 1þ 1b

� �C 1� 1

b

� �.

Probability weighted moments (PWMs) calcu-lated by

xs ¼1

N

XNi¼1

1� Fið ÞSDi ; ðA:9Þ

where S is an order of PWMs, N is the number ofdata, Fi is the frequency estimator and can beexpressed as:

Fi ¼i � 0:35

N;

where i is a range of observations.The unbiased PWMs calculated as:

xs ¼1

N

XNi¼1

N � is

� �Di

N � is

� � : ðA:10Þ

Therefore now p.d.f. is given by according to loglogistic distribution for D is given as:

F xð Þ ¼ 1þ ax � c

� �b" #�1

: ðA:11Þ

The standard value of F(x) is SPEI. Therefore,

SPEI ¼ W� C0 þ C1W þ C2W2

1þ d1W þ d2W 2 þ d3W 3ðA:12Þ

where

W ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�2 ln Pð Þ

pfor P� 0:5:

Constants hold the same value as in SPI forC0;C1;C2 and d1; d2; d3 mentioned above in SPIcalculation section.

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Corresponding editor: KAVIRAJAN RAJENDRAN


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