Meteorological drought analysis with different indices for the Betwa River basin, India

Climate change is adversely affecting the development, management, and planning of surface and groundwater resources. The meteorological drought becomes a severe natural problem, and it can occur in any climatic region of the world. Thus, monitoring and minimizing drought is crucial for analyzing and predicting drought impacts. The meteorological drought is considered basin or region-specific since atmospheric conditions are highly variable from region to region. However, agricultural drought links the various characteristics of hydrological or meteorological drought to agricultural impacts focusing on groundwater deficit, soil moisture deficit, etc. A single drought index cannot assess each aspect of the meteorological drought. In this study, we considered seven drought indices such as the Standardized Precipitation Index (SPI), China Z Index (CZI), Modified China Z Index (MCZI), Percent Normal Drought Index (PNI), Deciles Index (DI), Rainfall Anomaly Index (RAI), and Z-score Index (ZSI). The drought was analyzed for 3, 6, 9, and 12 months’ time step, and drought classification and threshold values were estimated. SPI showed maximum correlation values (0.389, 0.412, 0.560, and 0.996) for 3, 6, 9, and 12 month time steps compared to the other drought indices. The value of correlation is increased with the increase in time step for all drought indices; therefore, the accuracy of drought assessment also increases with an increase in time step. The Mann–Kendall’s trend test was analyzed at a 5% significance level for drought assessments. The drought magnitude and the severity of the Betwa River basin were estimated based on the meteorological data (Rainfall) from 1970 to 2014.


Introduction
Research must link different meteorological drought indices with the impact of drought on society. Previously, some researchers have established this link with narrow impact measures. A period of abnormally dry weather leads to drought in a specific climatic region, and it can be observed that the vegetation cover in that region is changed. It was observed that the frequency and intensity of the droughts were increased in the last three decades. So, many parts of the world suffered from severe water crises (Dai et al. 2004;Ghulam et al. 2008). Intergovernmental Panel on Climate Change (IPCC) projected the severe drought increase in the future, especially during the summer months. McKee et al. (1993) and Guttman (1999) recommended standardized precipitation drought indices as a candidate drought index in their study. The SPI was selected because the European researchers were predominantly recommended for meteorological studies. It became a popular choice among the researchers because it is probabilistic, simple, depends on a single variable (precipitation), and is consistent in the interpretation. This technique can be easily used in risk management and decision analysis at different periods. Knutson et al. (1998) showed the adverse effect of drought on society's environment, social, and economic aspects. Obasi (1994) studied that the meteorological and hydrological extremes are directly or indirectly responsible for 85% of natural disasters. Drought is the least understood natural hazard phenomenon that affects more people than any other natural hazard. Although it is a slow-developing phenomenon (Wilhite 2000), several researchers developed computer-based programs to estimate drought indices (Wu et al. 2001). Smakhtin and Hughes (2007) used a software package to estimate the Deciles Index, Effective Drought Index, and SPI. It provided several options such as month selection and type of drought study. Ji and Peters (2003) established a link between the meteorological drought indices and the vegetation response.
SPI is considered a new drought index and is widely accepted in all continents of the Earth to monitor real-time drought events. Morid et al. (2006) used historical meteorological and hydrological data to estimate and compare drought indices. Most of the drought indices are calculated based on the Gamma distribution. The possibility of the precipitation of all stations and regions may not be appropriate for the Gamma distribution (Blain 2011). Tsakiris et al. (2013) suggested an operational management system for drought-prone areas. This system established a relationship between specific variables and drought. The consequences of each aspect of the system were discussed because the drought was considered a natural hazard phenomenon. Jain et al. (2015) compared the SPI, EDI, CZI, RD, and statistical Z-score drought indices in the drought-prone area of the Ken River basin, India. The severity of drought indices was estimated for 1-, 3-, 6-, 9-, and 12-month time step and index values compared with each other.
China-Z Index (CZI) was introduced for monitoring the drought and severity. Initially, it was used for a 1-month time scale to monitor China (Ju et al. 1997). Shahabfar and Eitzinger (2009) showed that the CZI was helpful in monitoring the field-based drought indices with significant statistical significance. Salehnia et al. (2017) assessed several drought indices to estimate the severity of the drought events for the Kashafrood Basin of Iran. The drought indices were correlated with the AgMERRA precipitation data. Li et al. (2017) studied that drought risk mitigation can be effectively understood by using meteorological drought analysis on a global scale. Kao and Govindaraju (2008) suggested that the dependence structure of the hydroclimatic variables can be modeled by using Copula with any form of the marginal distribution. Tencer et al. (2014) recognized that precipitation significantly impacts agricultural, environmental, and industrial activities. These activities govern the droughts and the water shortage in the soil moisture and groundwater (Najafi et al. 2017). Haied et al. (2017 conducted a drought characterization study for the Wadi Djelfa-Hadjia sub-basin of Algeria, and SPI, DI, and RDI drought indices for intensity and magnitude of drought estimation. Daneshmand and Mahmoudi (2017) observe that the rainfall increase caused the variation in the properties of spatial-temporal droughts in Iran. Mahmoudi et al. (2019) evaluated the sensitivity of the precipitation drought indices at annual, monthly, and seasonal scales. The correlation coefficient of each index was obtained above the time scale. Abbasian et al. (2021) studied the precipitation-temperature Deciles Index bivariate by using Copula to assess the severity and intensity of future drought. The Copula model projected that the numbers of the hot and dry months would appear between 2060 and 2080.
The natural phenomenon could be considered the primary cause behind the droughts. Still, some of the studies are showing that the water resources (groundwater, surface water) which are directly under the impact of humans are two times more vulnerable than the less interference water resources (precipitation, snow cover) (Shaban 2009). Edossa et al. (2010) conducted a drought analysis for the Awash River basin, Ethiopia. Hydrological and meteorological data were considered for this study. SPI indices were estimated using spatial and temporal meteorological data sets and Arc-GIS software for the severity map generation. Dogan et al. (2012) estimated that drought in multiple time steps played a significant role in regional level estimation. Patel et al. (2007) analyzed the 160 rainfall station precipitation data in the Gujrat region and emphasized SPI 3 for spatial patterns of meteorological droughts and severity. Surendran et al. (2019) estimated drought indices for India's arid, semi-arid, and humid regions using DrinC software. SPI indices showed seven drought years in arid and four drought years in semi-arid and humid regions. Similarly, RDI indices showed 11 drought years in semi-arid and humid regions and 10 years in arid regions. The frequency of drought is increased in northern China, the USA, and Southern Australia. This is a significant evidence that global warming plays a vital role in extreme climatic events (Sheffield and Wood 2008). Roy and Hirway (2007) and GOI (2016) analyzed that India faced the worst meteorological droughts in 1917-1918, 1965-1966, 1986-1987, 2009, and 2012 in the last century. Hangshing and Dabral (2018) used Archimedean and meta-elliptical copulas to model SPI drought indicators at multiple time scales. These copulas were used for trivariate and bivariate joint distribution. Schwarz information criterion (SCI) and Akaike information criterion were used for model selection. Standardized Precipitation Index and Reconnaissance Drought Index are considered to be recently developed indices. Most of the drought studies in Korea were conducted based on these indices (Jang 2018). Khan et al. (2018) considered four drought indices to detect drought variability. This study was conducted at five and two meteorological stations of the Songhua River basin and Indus River basin. The result showed a 6-month time scale for the Indus River basin, and the 12-month time scale for the Songhua River basin was most appropriate for drought indices. Droughts are a very common phenomenon in the Betwa River basin. The past records of rainfall patterns 1 3 show a decreasing rainfall trend in most of the districts. The decrease in rainfall falls in the range of 0.674 to 6.46 mm/year. Hamirpur, Mahoba, and Jhansi districts exhibited increasing rainfall trends in the range of 0.854 to 1.474 mm/ year (Desai et al. 2019). However, the summer rainfall has no trend in seasonal and yearly rainfall. In the case of summer rainfall, a decreasing trend was observed in the basin (Suryavanshi et al. 2014). Bhunia et al. (2020) used SPI to quantify drought in the Purulia, Bankura, and Midnapur districts of West Bengal. Gumbel type I distribution and Mann-Kendal's tests were applied for drought frequency and trend analysis. They found that most of the rain gauges of the study area found negative SPI values. It means that the study area comes under a drought-prone area. Mishra and Desai (2006), Belayneh et al. (2014), and Xu et al. (2020) used the ARIMA model to forecast the SPI indices at different time steps and compared them with the artificial neural network (ANN) and support vector regression (SVR) statistical methods. Khan et al. (2020) used Artificial Neural Network (ANN) and ARIMA model to predict drought in Malesia's Langat River basin. SPI and Standard Index for Annual Precipitation (SIAP) were used to analyze the historical drought events. The Hybrid ANN-ARIMA model showed an improved correlation coefficient over ANN and ARIMA models. Alsubih et al. (2021) studied the meteorological drought conditions integrating the particle swarm optimization ensemble with the ANN, and trend analysis of the drought indices was carried out using the Mann-Kendall's test and sequential Mann-Kendall's test. Singh and Sharma (2021) applied an auto-regressive moving average (ARMA) linear model for drought forecasting in the Betwa River basin. SPI was used as a Drought Severity Index. They found that ARMA (2,0) was the best suitable model for this study area, and observed precipitation was compared with the estimated precipitation. Wu et al. (2021) used multitime scale SPI and standardized streamflow (SSI) for the estimation of hydrological and meteorological drought. The correlation analysis of precipitation and non-linear response were compared, and possible differences in the propagation threshold were analyzed. They have also conducted a drought study at the sub-basin level in South China.
The aim of the present study is to compute the qualitative state of drought events in the river basin. Drought monitoring at various time scales plays a significant role in the identification of short-term drought periods within the long-term wet period or short-term wet period within long-term drought. Drought indices can simplify complex meteorological events and effective communication tools for diverse public audiences. Irrespective of the available potential of water resources in India, some catchments have been facing droughts. Betwa River basin is one of them, and the frequency of droughts in this basin has increased in the past few decades. The mean average precipitation of the Betwa River basin is used in the study, and the arithmetic mean approach is used to calculate mean precipitation from all rain gauges.

A brief description of the study area and rainfall data set
The present study has been carried for the Betwa River basin, a tributary of the Yamuna River. Most of the region of this basin is considered to be drought-prone in Central India. The basin lies between the latitude 23 with the elevation between 300 to 700m from mean sea level (Fig. 1). The study area is located in the sub-humid and semi-arid regions with four seasons: rainy, dry, winter, and very dry. Most of the rainfall occurred during the rainy season (June-September), and the average annual rainfall of the basin varies from 700 to 1200mm.
The rainfall in the Betwa region is non-uniform in regard to space and time, as the upper half of the basin receives more rainfall than the lower half. Rainfall forms a significant source of groundwater recharge in the area. Hence, the development of the groundwater recharge in the basin is very poor due to the rugged topography and inconsistent rainfall pattern in the basin. Groundwater recharge is highly uneven and unpredictable throughout the year and has to be estimated separately for monsoon and non-monsoon. Recharge from the rainfall in the whole river basin for the monsoon alone since this season receives 80-85% of total rainfall. Groundwater recharge from rainfall in the monsoon season accounts for about 80-85% of the total annual rainfall, and just 15-20%of rainfall occurs in non-monsoon seasons. Recharge in non-monsoon can be assumed to be negligible (Jeet et al. 2019). The average area precipitation of the Betwa River basin is used in the study (Fig. 2), and the mean monthly rainfall of the basin can be downloaded from http:// www. mpwrd. gov. in/ betwa-basin website. Kaliasote, Bah, Halali, Budhna, and Bina are the major tributaries of this river basin.

Methodology
In the study, monthly precipitation (Rainfall) data from 1970 to 2014 is used to estimate meteorological drought indices. Seven meteorological events are applied for the severity and duration analysis of droughts. These drought indices are Standardized Precipitation Index (SPI), Percent of Normal Precipitation (PN), Deciles Index (DI), China Z-Index (CZI), Modified China Z-Index, Rainfall Anomaly Index (RAI), and Z-score. These indices are the numerical representation and technical indicator of the drought severity. It is assessed using rainfall as a meteorological input. A brief description of all the above drought indices is given below.

Standardized Precipitation Index (SPI)
The SPI of any rain gauge station is calculated based on the historical long-term precipitation data. This precipitation data is fitted in the Gamma probability distribution and transformed into the normal distribution. So, the mean SPI of the desired rain gauge data becomes zero (Mckee et al. 1993). Multiple time scales such as 1, 3, 9, and 12 month can identify various types of droughts. SPI has been successfully used in the various regions of the world because of its reliability and ability to address drought for various time scales (Guttman 1999;Vicente-Serrano et al. 2004;Pandey et al. 2008;Edossa et al. 2010;Zhai et al. 2010;Singh and Sharma 2021;etc.). The probability distribution of the Gamma function can be defined as follows: x > 0, > 0 , shape parameter ( ) , and scale parameter ( ) are estimated from the likelihood function such as: The cumulative probability of the precipitation for desired rain gauge and time scale can be defined as follows: The rainfall event may contain zero value, but the Gamma function cannot be defined at x = 0 . Thus, the cumulative probability distribution of the Gamma function is described as given below: where q is the probability of zero precipitation. After that H(x) is transformed into the normal distribution with zero mean and unit variance.

Percent of normal (PN) precipitation
Percent normal is the straightforward drought measurement index. It is the ratio of the normal precipitation p i to the actual precipitation (p) , and they are expressed in the percentage. At least 30 years of data is required to estimate the percent normal index, and it can be calculated for various time scales such as weekly, monthly, seasonally, and yearly. Although it is the simplest index to calculate alone, it cannot be used for decision-making statements (Willeke et al. 1994). PN drought index is calculated at a station using the following formula: Gibbs and Maher (1967) developed the Deciles Index for drought estimation from the historical data in Australia. Long-term precipitation (monthly, seasonally, or annually) data can be used for the study. The data set is arranged into descending or ascending order to formulate the frequency distribution. If precipitation data does not follow the normal distribution, then normalization methods are used to normalize it. The data is divided into several groups of the normal distribution, and each group is known as Decile. The first Decile is less than 10% precipitation of total precipitation. The second Decile is less than 20% precipitation of total precipitation. The fifth and last Decile is less than 50% precipitation of the total precipitation (Table 1).

Z-score Index (ZSI)
Z-score Index does not require the transformation of the precipitation data in the Pearson type-III distribution or Gamma distribution. Morid et al. (2006), Patel et al. (2007), etc. were analyzed drought by using ZSI. Z-score Index is computed by the following equation. (7)

China Z-Index (CZI) and Modified China-Z Index (MCZI)
China-Z Index is related to the Wilson-Hilferty cube root transformation (Wilson and Hilferty 1931). Assuming that the precipitation follows the person type III distribution, the following equations compute the CZI.  1970 1975 1980 1985 1990 1995  where C s is the coefficient of skewness and is the standard deviation of n number of observations.
The Modified China Z-Index is calculated similarly as China Z-Index, while the median of the precipitation is used instead of the mean of the precipitation data.

Rainfall Anomaly Index (RAI)
Rainfall Anomaly Index (RAI) was introduced by Van Rooy (1965). It is basically a ranking procedure to assign the degree of positive and negative precipitation between + 3 and −3 . It can be applied for both monthly and annual precipitation time scale. RAI is computed by using the following equations.
And if p < p , then where p and p are the precipitation and mean precipitation value and m and X are the mean of ten maximum and ten minimum precipitation values of the data set. Mann (1945) and Kendall (1975) specified the Mann-Kendall's trend statistics. MK test is used for statistically increasing or decreasing trends in long-term temporal data 1970 1975 1980 1985 1990 1995 2000 2005   where x i and x j values of the data series and x j > x i . For sample size (n > 10) , the variance is considered to be zero.

The Mann-Kendall's (MK) trend analysis test
where m and i are the numbers of tie t i extent and tie group z s is computed as: On the basis of 5% significance level, if ≤ 0.05 ( s value), i.e., z s = 1.96 , then the alternate hypothesis is rejected, or the alternate hypothesis is accepted. While ≥ 0.05 , the null hypothesis is accepted.

Sen's slope estimator
Sen slope ( Q ) was developed to estimate the magnitude of trend in the long time-series data (Sen 1968). It precisely ;ifs < 0 detects the linear relationship because it cannot be affected by the outliners in the data. Positive Sen's slope indicated the increasing trend, while negative Sen's slope indicated the decreasing trend in the data.
If the number of observations (n) is only one datum in each time period, then N = n(n−1 2 , and if more time period, then N < n(n−1 2 . The N value of the Sen's slope is arranged from smallest to largest, and the median of the Sen's slope is estimated as given below:

Pearson correlation coefficient
The Pearson correlation coefficient measures the linear dependence of two series of random variables. It is the ratio of the covariance of series to the products of standard deviations, and it ranges between + 1 and − 1 (Lee Rodgers and Nicewander 1988).

Results and discussion
The Standardized Precipitation Index (SPI) is the most widely used drought index across various parts of the world. It is also found suitable for the Asian region (Smaktin and Hughes 2004). China Z Index, Modified China Z Index, and Z-score Index are primarily used in Asian regions. DI, PN, and RAI are used in the study due to their simplicity in the calculation. Most of the rainfall occurred during the monsoon period in the study area and showed high rainfall variability from month to month. Therefore, we decided to compute the different drought indices in 3-, 6-, 9-, and 12 -month time steps for the average area rainfall of the basin. One-month time step cannot describe drought situation appropriately (Jain et al. 2015). So, it is not included in the study. The drought indices have a different range of values to  Table 1.
The SPI, CZI, and MCZI can be classified on a similar drought severity scale, ranging between −3 and +3 . This study shows that SPI, CZI, and MCZI have an almost similar number of months in each type of severity (moderate, severe, and extreme severe) for each time step. Most of the SPI, CZI, and MCZI values were falling under near normal and moderately drought zone. A few months of various time steps showed under severe drought zone, and 3 months of the year 1979 have extremely drought in each time step, while 1 month of the year 2014 showed extremely drought for 6-, 9-, and 12-month time step. The single-single month of the year 2002 and 2006 showed extreme drought for 3-and 6 -month time steps, respectively (Fig. 3).
The DI, PN, RAI, and ZSI have different drought classification scales. Most of the indices lie in the range of near normal and moderate droughts, and a significant number of values also lie in the range of severe and extreme droughts (Fig. 4). Therefore, drought indices showed high severity than the SPI, CZI, and MCZI. The DI showed almost similar severity for each time step, and 1 month in each year, it occurs in the extreme drought range. This trend cannot be observed in the other indices; thus, it seems to be a hypothetical estimation. For the 12-month time step, PN does not show any value in the extreme drought range. Apart from these other time steps, a significant number of indices values range in the extreme and severe drought zone. RAI and ZSI drought indices showed most of their values in the near normal and moderate drought range similar to the SPI, CZI, and MCZI, but these indices also have significant numbers in the extreme and severe drought zone.
Mann-Kendall's trend test showed a negative value for each drought indices, while p value of trend is positive. A similar hypothesis was found for each index, i.e., the null hypothesis is accepted with decreasing trend at a 5% level of significance. The Sen's slope represents the magnitude of the increasing or decreasing slope of the MK trend test. It was found to be the negative value (declining) for all indices except for PN 3, DI 3, DI 6, DI 9, and DI 12 (Table 2).
All drought indices are positively correlated except MCZI at a 3-month step size, and they can be compared based on Pearson's correlation for the same time step. SPI was highly correlated in each time step precipitation data compared with the remaining indices. The correlation coefficient values of SPI were 0.389, 0.412, 0.560, and 0.996 for 3-, 6-, 9-, and 12-month time steps, respectively. Apart from SPI, several other indices such as CZI, RAI, ZSI, and MCZI were also showed good correlation except MCZI 3. So, MCZI cannot be considered for the smaller time step. It was observed that the correlation of all indices is increasing with an increase in time (Fig. 5). It means drought estimation is more accurate for higher time steps compared to the smaller time step.
It was found to be very interesting that the number of extremely drought months of SPI, CZI, MCZI, ZSI, and RAI indices is increasing with an increase in 3-, 6-, and 9 -month time steps. While severely and moderately number of drought months are increasing in 3-and 6-month time step and decrease in 12-month time step. For DI indices, extremely, severely, and moderately drought months are almost the same in each time step, while the PN index showed the decreasing trend in the number of drought months as we described earlier that the type of droughts is characterized based on severity and duration. The drought months in 3-, 6-, 9-, and 12-month time steps for various indices during 1970 to 2014 for the Betwa River basin are presented in Table 3.
It can be noted from Fig. 6 that the occurrence of the extreme, severe, and moderate drought events showed a  . 6 Percentage of drought severities at 3-, 6-, 9-, and 12-month time step for a SPI, b CZI, c MCZI, d PN, e DI, f RAI, and g ZSI decreasing trend in 3-, 6-, 9-, and 12-month time steps. Figure 6a-c showed that extremely and severely drought events range from 0.56 to 2.78% , while moderately drought events are comparatively more, i.e., ranging from approximately 1 to 11% . Also, in Fig. 6d-f, the extreme drought events range from 17.41 to 34% , while severe and moderately drought events range from approximately 5.51 to 32.59% . Figure 6g showed that extreme, severe, and moderate drought events are ranging from 2 to 5%, 9 to 11%, and 10 to 25%, respectively. It can be observed that the extreme drought events are very less than the severe and moderate drought events during 1970 to 2014 in the Betwa River basin. It was observed that if drought occurred during the monsoon period, it could be continued until the next monsoon period unless excess rainfall occurred during the non-monsoon period. This phenomenon has happened because most of the rainfall occurred during the monsoon period in this basin. The indices used in the study are computed based on the area average monthly precipitation data. Drought management and trend analysis are necessary because it controls climate change. All indices were showed good correlation and Mann-Kendall's trend test. It is appropriate to say that the SPI is the best-suited drought index for drought forecasting in the Betwa River basin, but RAI, CZI, ZSI, and MCZI can also be considered because their indices follow a similar trend as SPI. But MCZI cannot consider smaller time steps. It is recommended that these groups of indices can be considered for other river basins with similar morphological and hydrographic features.

Conclusions
This study used a group of seven drought indices (SPI, CZI, MCZI, DI, PN, RAI, and CZI) for drought estimation in the Betwa River basin. Based on the study, following conclusion remarks are given below: 3. It was found to be the negative value (decreasing) for all indices except for PN 3, DI 3, DI 6, DI 9, and DI 12, i.e., the null hypothesis H 0 is accepted with decreasing trend in the data. The Pearson's correlation coefficient of SPI was 0.389, 0.412, 0.560, and 0.996 for 3-, 6-, 9-, and 12-month time steps. Apart from SPI, several other indices such as CZI, RAI, ZSI, and MCZI were also showed good correlation except MCZI 3. 4. The number of extremely drought months for SPI, CZI, MCZI, ZSI, and RAI is increasing with the increase in time step, while severely and moderately numbers of drought months are increasing in 3-and 6-month time steps and decrease in 12-month time step. 5. The occurrence of the extreme, severe, and moderate drought events showed a decreasing trend in 3-, 6-, 9-, and 12-month time steps. The extreme drought events are very less than the severe and moderately drought events from 1970 to 2014 in the Betwa River basin.
Finally, it is concluded that the SPI is the best drought index compared to other indices for the management and modeling of drought. Apart from SPI, RAI and CZI can also be used for drought assessment. Furthermore, more studies are required on local climatic conditions with meteorological data to uncertainty in drought assessment to suggest a better tool for managing and planning water resources in the Betwa River basin.