Intensity and spatiotemporal variations of drought in Tumakuru district, India using drought indices

Abstract Depletion of water resources and soil moisture leading to drought is a global concern and the effective assessment and monitoring using a drought model has become essential. A detailed account of frequency, run length and temporal trend of the drought events are presented in the study from 1981 to 2019 at the 1-, 3-, 6-, 9-, 12- and 24-month timescale using the Standardized Precipitation Index and Standardized Precipitation Evapotranspiration Index. SPI recorded more drought months in the extreme category with 14 months at Gubbi station for example, while SPEI showed only 5 months. SPEI showed longer drought length in moderate and severe categories for agricultural and hydrological drought. At a 1-month timescale, both the indices reported extreme drought events where Tiptur station in May 2016 (–4.75) and Chikkanayakanahalli station in March 1992 (–2.76) were the worst-case scenarios. The study aims at providing practical results to facilitate decision-makers for drought risk management.


Introduction
Climate change has paved way for the increase in the frequency of extreme weather conditions driving the community towards vulnerability. In recent years, such events make a severe impact not only on the environment but also on the world economy. At varying intensities and magnitudes, hydro-meteorological disasters have been occurring all over the world. Fluctuations in the temporal and spatial distribution of rainfall along with the rise in temperature have caused persistent aridity with long-lasting environmental consequences like drought. Drought is one of the most influencing phenomena and poses a threat to human lives more than other natural disasters and it is broadly considered the least understood and the most complex of all environmental hazards (Shen et al. 2019). Drought identification and its assessments are most difficult to explore because of the lack of a universally accepted method for qualifying and measuring drought effects (Moradi et al. 2011). Drought has long-term severe impacts on water resources, ecosystem, economies, society and agriculture that leads to loss of the economy, shortage of food availability and drinking water, increased land degradation and forest fire that causes diseases and epidemics . As per the International Disaster Database statistics, the worldwide loss of nearly 221 billion dollars per annum from 1960 to 2016 was caused by drought (Guo 2012). The frequency, intensity and severity of drought have noticed a significant positive trend due to the increasing global warming (Giannakopoulos et al. 2009). Accordingly, it is necessary to monitor the drought occurrences and understand the indices of drought assessment to reduce and avoid the unnecessary loss of money and lives.
Various indices are developed and suggested for drought assessment, e.g. Standardized Precipitation Index (McKee et al. 1993), Palmer Drought Severity Index (Palmer 1965), Standardized Streamflow Index (Shukla and Wood 2008), Percent of Normal Precipitation Index (Werick et al. 1994), Regional Drought Area Index (Fleig et al. 2011) andStandardized Precipitation Evapotranspiration Index (Vicente-Serrano et al. 2010). Every index defines specific characteristics. A standardized precipitation index (SPI) can recognize the characteristics of drought activity within a region and can quantify the drought severity at multiple timescales. The SPI indicates that rainfall is the only major variable affecting the duration, frequency and intensity of drought. Vicente-Serrano et al. (2010) proposed the first improved index for drought identification and analysis as SPEI to study the effects of climate change on drought parameters. SPEI takes into consideration the impact of evapotranspiration on drought characteristics, while the different timescale nature of the SPEI empowers the identification of various types of droughts and their impacts (Vicente-Serrano et al. 2011, 2012. Various studies have been carried out on SPEI and SPI in recent years. An increase in the duration, occurrences and severity of drought in India was witnessed under the warming climate situation when studied at different time periods (Naresh Kumar et al. 2012;Bisht et al. 2019) analyzed the drought variability using SPI in India. The result indicated an increasing trend in July and highlighted the severe drought year of 1987. The study regarding the changes in the drought characteristics with respect to the geomorphology was carried out using SPI and SPEI in China at differing time and space scales (Pei et al. 2020;Liu et al. 2021) stated that there was consistency in SPI and SPEI values with the increasing timescale while there was a larger difference in between the indices at shorter timescales. Falzoi et al. (2019) used the meteorological indices to follow the progress of the extreme drought event of 2018 in Ireland. It was the most severe event in the 1981 to 2018 period when the soil moisture deficit index reached a maximum value of 94.3 mm. The influence of the atmospheric circulation pattern on the drought scenario is studied using SPI (Irannezhad et al. 2017). The analysis showed that the dry event had a higher frequency in December month. The drought pattern of Oklahoma at a 6-month timescale is studied using SPEI by Tian and Quiring (2019). The moisture conditions varied sustainably which was evident in the shorter timescales. Over the mainland of Spain, Dom ınguez-Castro et al. (2019) characterized the drought events using SPI and SPEI. The duration and magnitude of drought were higher for SPEI than SPI at the 1-, 3-and 6-month time scales. The study of the long-term hydroclimatic condition in Chile was assessed by Serrano-Notivoli et al. (2021) using the SPEI. A breaking point was seen in the mid-twentieth century with an increase in interannual variability and less intense wet events. The impact of climate change with respect to the groundwater drought was investigated by Secci et al. (2021) using SPI and SPEI and realized that there was a negative effect on the groundwater levels. The intensity-duration-frequency curve is employed to obtain better knowledge about the relationship between the parameters (Aksoy et al. 2021).
In general, some major factors such as topography, atmospheric circulation, geology, distance from the ocean and geography are highly responsible for climate change and the climate of the Tumakuru district which is characterized as arid and semiarid. An assessment of the spatial and temporal pattern of the meteorological drought in Tumakuru is studied by Kumar et al. (2022) which revealed that most of the drought occurred during the southwest monsoon season resulting in a devastating outcome. The dry season starts in November lasting till the end of May and the rainy season extends from June to October in Tumakuru. Due to the arid and semiarid climatic zone of the Tumakuru district, the ecological environment conditions are very delicate and permeable to climate change (John et al. 2013). Drought conditions are a frequent meteorological hazard in Tumakuru and affect the agriculture production that causes the agricultural drought. Therefore, it is crucial to examine and observe the varying conditions of drought characteristics over time to avoid disaster risk. How do the SPEI and SPI describe the different characteristics and behavior of drought varieties in the study area? What are the applicability and characteristics of both these indices at multiple timescales? These discoveries need further investigation. The major aim of this study is the computations of the SPEI and SPI of 11 meteorological grid stations at 1-, 3-, 6-, 9-, 12-and 24-month timescale in the Tumakuru district from 1981 to 2019. The study analyzes and compares the performance and reliability of these indices. The primary goals of the study are: (1) to examine the differences in the spatial and temporal characteristics of drought computed through SPEI and SPI at different time scales and (2) to investigate the consistency and relevance of the SPEI and SPI in drought assessment and the relationship between drought intensity, severity and frequency at Tumakuru district. There has been no prior research regarding drought in the study area hence making it of greater importance for a better water management system. It is expected that the study would give the appropriate ideas to select the feasible index for drought monitoring.

Study area and dataset
The studied region lies in the arid steppe hot and tropical savannah zone according to the Koppen-Geiger climate classification between 12 44 0 31 00 to 14 21 0 2 00 North latitude and 76 21 0 2 00 to 77 30 0 12 00 East longitude, situated in Southeast Karnataka, India with covering of 10,603 km 2 geographical area which is classified into 10 taluks Figure 1. The Mean rainfall of the area was 668.74 mm during 1981-2019. Generally, the district is affected by two major seasons; dry and rainy domination of the rainy season exists from June to October, and the rest of the months last as dry seasons. The topography of the district is diverse with the composition of hills and undulating plains where the altitude range is about 434 m at the minimum and 1191 m at the maximum highest point from the mean sea level which is idealized for urbanization, industry and agriculture. The eastern part is surrounded by granite hills with a narrow range and the western part is covered by the long range of hills of the district. The maximum temperature reaches its highest in April at around 33 C and the minimum at 18 C in December. Annual rainfall for the time period of 39 years reached about 2282 mm at maximum in Turuvekere and 223 mm at least at Pavagada station (Table 1). The monthly rainfall data in this research are from India Meteorological Department (https://www.imdpune. gov.in/Clim_Pred_LRF_New) Climate Prediction Group, Climate Research and Service, the monthly rainfall data of 11 meteorological grid stations with long time series from 1981 to 2019 are obtained (Pai et al. 2014). The temperature data are acquired from POWER j Data Access Viewer (nasa.gov) to compute the SPEI. The MERRA-2 temperature data which is assimilated using the GEOS-DAS (Goddard Earth Observation System -Data Assimilation System) is a reanalysis product and has been in operation since 1979.

Methodology
In this study, R studio software (Beguer ıa and Vicente-Serrano 2013) has been used with the SPEI version 1.7 package which has a different program to compute both SPI and SPEI. Fitting the P (precipitation) and P-PET (potential evapotranspiration) data series to an appropriate probability distribution is the main function of computing these indices. Then, this fitted data series is converted into a standard value that defines the SPEI and SPI (Table 2).

SPI
The index was firstly introduced by (McKee et al. 1993) that has been generally utilized to monitor the spatio-temporal pattern of drought. SPI can demonstrate the amount of rainfall at a particular time period in a selected region and is suggested by World Meteorological Organization to be utilized globally. The stable result, simple calculation and dependency of only rainfall data are some advantages of SPI. SPI depends on the probability distribution of rainfall utilizing the gamma probability. For the chosen frequency distribution of rainfall, a gamma probability density function is defined as: where a defines the shape and b defines the scale parameter.
x is the quantity of precipitation and the gamma function is defined as Using the maximum likelihood method, the suitable values of a and b are calculated.
where n denotes the total number of samples of rainfall. A function can then be derived to calculate the cumulative probability of rainfall for a given month using: The SPI is calculated as: where x denotes the amount of rainfall and G(x) is the precipitation probability distribution concerning the C function. S indicates the minus and plus coefficients of the Moderately wet -1.0 to 1.0 Nearly normal -1.49 to À1.0 Moderate dry -2.0 to À1.5 Severe dry À2.0 Extreme dry cumulative probability distribution. When G(x) > 0.5, S ¼ 1 and when G(x)

SPEI
The method to compute the SPEI was first developed by Vicente-Serrano et al. (2010) as the enhancement of the SPI. Taking into account the change in surface evaporation and the impact of the temperature, SPEI improves on the SPI by replacing the monthly rainfall in SPI with the difference between the Potential Evapotranspiration (PET) and rainfall data. The following method demonstrates the probability distribution function of loglogistic probability which makes SPEI provide a characterized and suitable analysis of drought severity. The probability density function is expressed by the following equation: where a denotes scale, b the shape and c the origin. The probability distribution function can, therefore, be given as Following which SPEI can be calculated as when P 0.5, w¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi À2 lnðPÞ p and when P > 0.5, w ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi À2 lnð1ÀPÞ p , c 0 ¼2.5155, c 1 ¼0.8028, c 2 ¼0.0203, d 1 ¼ 1.4327, d 2 ¼ 0.1892, d 3 ¼ 0.0013.

Drought frequency
The purpose of this research was to compute the frequency distribution to recognize the frequently affected area by drought, on the premise of the frequency of the SPI and SPEI for individual eleven stations and various timescales. The frequency was determined based on the occurrences percentage distribution of drought categories (moderate, severe and extreme) at various timescales (1-, 3-, 6-, 9-, 12-and 24-month) over the Tumakuru region from 1981 to 2019 (As per Table A in Supporting Information). The spatial distribution and extent of drought events (%) for different SPI and SPEI timescales with drought categories are shown in Figures 2 and 3. The outcomes of this study stated that for a selected timescale extreme drought happened less frequently at every station and mild drought existed more frequently than other drought categories. Time-series comparison of both indices indicates the sensitivity and ability to find out the temporal and spatial pattern of drought in any specified region. In this research, both SPI and SPEI concurred on the pattern and directional variability of drought although the indices showed different intensities. When comparing the SPEI to SPI, SPEI recognized the more frequent drought spells in the moderate and severe categories while SPI discovered the greater number of dry months and frequency under the mild and extreme categories. The result of the SPEI expresses the significant role portrayed by the temperature fluctuation in the drought analysis but the SPI claims importance in drought analysis when temperature data is missing. The frequency of drought at various timescales was analyzed from the spatial distribution perspective. The SPI and SPEI results for the frequency analysis barely showed any similarity at any of the timescales barring a few exceptions at 1and 3-month for moderate drought and 6-month for severe drought. For SPI, at the 1-month timescale, the maximum drought event of moderate intensity occurred in the southern part of the district, the severe intensity at Chikkanayakanahalli and Madhugiri, and extreme intensity at Tumakuru. At the 3-month timescale, severe drought expanded in Chikkanayakanahalli and extreme drought at Kunigal and Tumakuru stations while moderate drought noted the highest frequency of about 10%. A major chunk of the South and Southeastern part of the area is affected by a 6-month severe drought. As per the 9-month timescale, Kunigal was highly affected by severe drought, and extreme drought affected Chikkanayakanahalli, Gubbi, Tumakuru and Tumakuru-1. Kunigal, Tiptur and Chikkanayakanahalli were influenced by severe drought and Tumakuru and Tumakuru-1 by extreme drought at the 12-month timescale. Extreme drought condition tends to occur at higher frequency as the timescale is increased from 1-month to 24-month. The 24-month severe drought occurred frequently in the Northwest direction and moderate drought in the North and Southwest region of the district.
The spatial distribution of SPEI with moderate drought occurred over 40% of the area majorly in the South and Southeast parts for a 3-month timescale. Pavagada station recorded the highest frequency of moderate drought at all the timescales featuring the effect of the climatic condition as the region lies in the arid steppe hot climatic zone according to K€ oppen-Geiger Climate classification. The severe drought frequency is predominantly indicated in the greater part of the South and Southeastern region at the 6-, 9-, 12-and 24-month timescale. Extreme drought is evident in Madhugiri for all the timescales and extreme drought at slightly less intensity is observed at Chikkanayakanahalli for all the timescales except for the 3-month. For all the timescale except 12-month, moderate and severe drought finds better representation in SPEI while SPI tends to give better results for the extreme drought category. The similarity in SPI and SPEI was observed for the moderate, severe and extreme intensities at the 12-month timescale. Pavagada station receives the least mean rainfall in the study area and the frequency of the moderate drought is high in the area whereas apart from significant extreme meteorological drought, the rest of the timescale does not express intense dry periods as seen in SPI and SPEI. Although Kunigal recorded the highest mean rainfall, there is a higher frequency of moderate meteorological drought. There is a greater frequency of severe category of agricultural and hydrological drought as discovered by SPI and SPEI. From this observation, we can deduce that the mean rainfall although highest at Kunigal station may have occurred over a very short period of time giving room to the more frequent occurrence of drought events. There is also no clear association of the fluctuation of the drought frequency with the mean rainfall in the area.

Run length of drought
The SPI and SPEI values were calculated in hopes of finding their potential application in the analysis of the dry periods and also drought risk monitoring and management for the timescales 1-, 3-, 6-, 9-, 12-and 24-months from 1981 to 2019 were utilized to construct the graphs portraying the maximum run length (in months) for various drought categories. The period over which a certain level of wetness persists denotes the duration of drought and serves as a crucial tool in the planning of water resources. According to Figure 4, for the hydrological and agricultural drought conditions SPI showed greater drought months in the extreme category than SPEI while at the same time, SPEI observed longer drought run length than SPI in the moderate and severe category.
Mudhugiri station experienced a prolonged drought of extreme intensity throughout the year 2019 from January to December which is upheld by the consistently negative Gubbi. Rabi season was greatly affected by severe drought as seen from the SPEI value at 6-month timescale while Madhugiri faced extreme drought. The SPEI value for 1-and 3month are more pronounced than SPI.
During the years 2002 and 2003 most of the study area suffered drought conditions categorized using SPI as severe and extreme mostly in 6-, 9-, 12-and 24-month timescale. This pattern was recorded prominently during the southwest monsoon season (July to December). The longest run length of nearly 46 months for moderate and severe drought was observed at Sira station from September 1983 to July 1987 for the 24-month timescale. Meteorological drought persisted from August to December in 2002 and 2003 at the stations Tumakuru and Tumakuru-1, which was moderate, severe and extreme in character along with Tumakuru enduring severe drought from April 1990 to November 1990. Tumakuru is the sole station that witnessed extreme 6-month drought in continuity during  January-December of 1990. At the shorter time scale, the meteorological drought has a good representation in SPEI in comparison to SPI. When comparing the agricultural drought, more stations revealed severe and some extreme events in SPEI. The variation of results from SPI and SPEI though inevitable finds similarities when it comes to a longer time scale indicating the hydrological drought. The key factor that sets SPEI apart from SPI is the inclusion of evapotranspiration parameters by including the temperature data. This brings about a huge change in the resulting value. The evaporation of water from the surface also affects the onset of drought which can be quantified using the SPEI. The evapotranspiration creates a demand on the available water, which is clearly observed during periods of water scarcity which is further reflected in the increased SPEI values. Also, the drought period found in SPI was further amplified when seen in SPEI. With rainfall being the only parameter, more of extreme drought condition is extracted than when the potential evapotranspiration (PET) is included. The longer timescale holds a greater duration than the shorter timescale of drought in 55% of the stations for SPEI. The rest of the station at the longer timescale noted a lower duration of drought which greatly impacted the shortterm water resource than the long term. It is not necessary that the longest drought period causes the most impact as the intensity of the drought needs to be taken into consideration. The relationship between the duration of drought and mean rainfall is erratic in the region. Table B showing drought duration and severity is attached in the Supporting Information.

Temporal evolution of dry period at different timescale
The drought occurrence in the study area over the years has seen fluctuations and these are directly related to the meteorological parameters affecting the region. The analysis of the temporal pattern at various time scales (1-, 3-, 6-, 9-, 12-and 24-month) from 1981 to 2019 is shown in Figure 5. helps us obtain a better understanding of the dry conditions in the area which in turn paves a way to monitor and mitigate further deterioration in the condition. From 1981 to 2019, the early 1990s, the early 2000s and the late 2010s are the years that stand out in the entire study area showing prominent dry periods.
The worst of extreme drought event at the 1-month scale according to SPI and SPEI occurred in Tiptur in May 2016 (-4.75) and Chikkanayakanahalli in March 1992 (-2.76), respectively. For the 3-month timescale, the lowest value for SPI was at Chikkanayakanahalli in July 2001 (-4.21) and for SPEI at Gubbi in April 1983 (-2.71). SPI at Koratagere in May 2003 (-4.16) and SPEI at Gubbi in September 2003 (-2.79) are the minimum at the 6-month timescale. Chikkanayakanahalli in September 2003 noted an SPI value of À3.38 and Madhugiri in May 2019 noted an SPEI value of À2.59 for the 9-month timescale. SPI for Tumakuru in July 1990 was À3.91 and SPEI for Chikkanayakanahalli in February 2017 was À2.54 which were the least values in the 12-month timescale. At the timescale of 24-month, Tumakuru in September 1990 showed À3.61 and Madhugiri in May 2019 showed À2.28. The intensity of drought is significantly more in SPI in comparison to SPEI at all the stations and timescales which is denoted by the negative value of the indices. A common trend is seen where the extreme drought event at all the stations and at every time scale was prominently featured by SPI than SPEI. The smaller time scales showed lower values for both SPI and SPEI and the value increased when proceeding toward the longer timescale. May to July seem to be the worst affected months across the timescales for SPI and February and March as per SPEI values. Tumakuru station did not record any extreme drought events successively for the 9-, 12-and 24-month timescale for SPEI. Koratagere and Tumakuru-1 at the 9-and 12-month timescale showed zero extreme drought events. SPI did not capture any extreme drought events at Pavagada for 9-and 24-month and at Turuvekere for 12-and 24-month timescales. A stark difference between SPI and SPEI can be observed from the temporal graph at the various timescale. A similar dry spell was found at all the stations in 2016 and 2017 for the SPEI value whereas, at the same time, SPI recorded mostly no drought condition. SPI value is prominent in 2003 showing extreme conditions at all stations except Sira, while SPEI showed mainly mild drought conditions. The large fluctuation was frequently observed in the indices at the shorter timescale which also showed a large difference between the intensities (Table  3). For the longer timescale, there was a slight difference between the SPI and SPEI intensity, and the fluctuation tended to be gentle. The climate change and subsequent increase in global warming find better representation in SPEI rather than SPI, as the former includes the effects of temperature on PET along with precipitation, while the latter shows no attention to the effect of evaporation on drought.

Conclusion
Drought being one of the hydro-meteorological disasters has been a successively recurring event across the state of Karnataka with varying magnitude and intensity. Climate change resulting in the spatial and temporal variation of temperature and precipitation has been the driving force for such events. The major difference between the indices is that SPEI includes the evapotranspiration parameter along with rainfall while SPI is solely dependent on rainfall only. This difference is minor when concerning the meteorological drought but when dealing with agricultural and hydrological drought, the climatic water balance comes into question drawing prominence to SPEI over SPI. This study analyzed the drought severity at the 1-, 3-, 6-, 9-, 12-and 24-month timescales by drawing a comparison between SPI and SPEI.
a. The outcome of the drought frequency study indicated that SPI showed more frequent extreme dry periods while SPEI gave a better result for moderate and severe drought in all the timescale. b. SPI and SPEI showed greater fluctuation and had a poor correlation for the shorter timescale representing the meteorological drought as there was a large difference in their values; SPEI gives the best result since it deals with the increase in the water demand caused by the PET as a result of rising temperature. For the longer time scale, there is a mild fluctuation between the indices, and the difference between them also considerably decreased. By this, we can conclude that the drought conditions at the longer timescale given by SPI and SPEI tend to be more consistent. c. Although precipitation has a great role in the determination of drought, evapotranspiration has an unforgettable part to play in the spatio-temporal variability of soil moisture giving rise to agricultural drought which is best portrayed in the 6-and 9month timescale of SPEI. While SPI and SPEI serve different purposes, the former needs to be utilized with caution and whereas the latter is extremely useful wherever the effects of evapotranspiration are in play.
The present study aims at defining the difference between the two indices SPI and SPEI by evaluating the data of the Tumakuru District, India. As they serve different purposes, no clear conclusion can be drawn on which index is the better identifier of the drought condition. The research gives an understanding of the most suitable index to criticize drought in the study area but this may not be extended to other regions as the index is dependent on the variability of climatic conditions and regional characteristics. The correlation of SPEI and SPI facilitates policymakers and planners in the planning and execution of innovative water conservation structures and effective drought mitigation structures.