Applicability of SPI and RDI for forthcoming drought events: a non-parametric trend and one way ANOVA approach Free

Bundelkhand has been historically known as a drought-prone region of India, but the frequent and intense droughts have increased in recent decades. The scarcity of water in the semi-arid region, with poor soil and low productivity, further aggravates the problem of food security (Gupta et al. 2014). Hence, further study is expected to be alert to such drought events happening in the future. Analysis of trends is a primary tool to predict future drought scenarios. Yue et al. (2002) studied two non-parametric ranked based tests, namely the Mann–Kendall test and Spearman's rho test. Both tests were compared based on the power of the test by Monte Carlo simulation and gave very similar results of the trend. It is noted that the distribution of Mann–Kendall approaches more quickly than Spearman's rho. These tests become more powerful with an increase in the sample size and decrease when the number of variation grows. The Mann–Kendall trend test and Sen's slope estimator are helpful to find trends effectively for data of more than 30 years. The increasing and decreasing trend shows climate trend and helps to foresee future climate variables (Birara et al. 2018). The main advantage of the Mann–Kendall trend test is that it can be performed at any time scale. It is robust against distribution-free and has low sensitivity to sudden breaks in time series.

Jain & Kumar (2012) performed the Mann–Kendall trend test for the whole of India for rainfall and temperature. The magnitude of the trend in a time series is determined using Sen's estimator method. The test represents both positive and negative trends in the area, although they are not very significant. The test can be performed to determine the pattern for drought indices also. Two relevant drought indices; RDI (Reconnaissance Drought Index) and SPI (Standardized Precipitation Index) were used for 3, 6, 9, 12, 18 and 24-month time scales in 40 meteorological stations in Iran and it was seen that the correlation coefficient (R) decreases with an increase in the time scales between SPI and RDI and can be easily differentiated in the wetter climate for all time scales (Zarch et al. 2011). For the semi-arid region, SPI and RDI can both be performed for trend detection. This study is expected to organize region-specific drought monitoring by identifying the trend of precipitation and temperature along with the significant trend in drought. The kriging interpolation has been adopted to plot the change of temperatures (maximum and minimum), SPI and RDI on the ArcGIS tool. Kriging is one of the geospatial interpolation techniques based on statistics and it is a more advanced tool (Childs 2004). While plotting the Sen's slope values over the study area on the ArcGIS tool, there are many raster interpolation methods available such as inverse distance weightage (IDW), kriging and natural neighbor interpolation, etc. Of all the processes, kriging shows a better representation of spatial figures. The one way ANOVA method is chosen to discriminate both SPI and RDI indices. This method can compare more than two groups. ANOVA uses the F statistic to test if all groups have the same mean (Park 2009; Skidmore & Thompson 2013). It gives better comparative results than other methods such as the t-test.

Sagar division comes under the Bundelkhand region in Madhya Pradesh, India. It consists of five districts (Sagar, Chhatarpur, Tikamgarh, Panna and Damoh). It is situated at 23°49′48″ N latitude and 78°42′36″ E longitude where the nearest city is Sagar, which is the headquarters of the division. The area lies in the heart of India, found below the Indo-Gangetic Plain to the north, with the undulating Vindhyan mountain range spreads from the northwest to the south (Gupta et al. 2014). The location of the Sagar division can be seen in Figure 1.

Daily rainfall data of 35 rain gauge stations in the Sagar division were collected from the Department of Water Resources (BODHI), Bhopal (M.P.), India. Daily gridded data (0.5 × 0.5° resolution) of maximum and minimum temperature for 31 years (1988–2018) were collected from NASA (https://power.larc.nasa.gov/data-access-viewer/) for 35 stations in the Sagar division. The description of rainfall data along with the rain gauge stations in the Sagar division is shown in Table 1.

Trend analysis is the prediction of future outcomes by using historical results based on their trend. The non-parametric Mann–Kendall test is used to obtain patterns using historical data and its magnitude is evaluated using Sen's slope estimator (Mondal et al. 2012; Rahmat et al. 2015). The increase or decrease in trend is checked, which is based on the normalized test statistics (Z) value. When Z is positive, the trend is said to be increasing and when Z is negative, it is said to be decreasing. The trend's slope gives the annual rate and direction of change.

The DrinC (Drought Indices Calculator) model is used to evaluate two drought indices, SPI and RDI (Tigkas et al. 2015). The model was developed at the National Technical University of Athens for providing an adaptable and straightforward interface to calculate drought indices. The model is applicable for several locations, especially for arid and semi-arid regions. Sagar division comes under the semi-arid region. SPI is calculated only by rainfall data (McKee et al. 1993), while RDI uses both rainfall and temperature data. It makes it more effective as two meteorological elements are involved there (Tsakiris & Vangelis 2005; Tigkas et al. 2015). SPI is based on the probability of precipitation at any time scale (Tian et al. 2018), while RDI is based on both cumulative rainfall (P), and potential evapotranspiration (PET), in which P is measured and PET is calculated using the Hargreaves method (Tsakiris et al. 2007).

ANOVA is a statistical technique that is used to check if the means of two or more groups are remarkably different from each other (Skidmore & Thompson 2013). Statistician and evolutionary biologist Ronald Fisher developed it. ANOVA verifies the effect of one or more factors by comparing the means of different samples at a significance level α = 0.05.

The null hypothesis in ANOVA is valid when all the sample means are equal, or they do not have any significant difference. ANOVA follows F-distribution which does not have any negative values because between and within-group, variability is always positive due to each deviation's square.

The non-parametric Mann–Kendall trend tests of rainfall and temperature were analyzed on monthly, seasonal and annual time series. If the normalized test statistics Z > 1.96 or Z < –1.96, null hypothesis (H_O) is rejected at the 95% significance level.

Monthly, annual and seasonal non-parametric trends of rainfall evaluation for 35 rain gauge stations (Table 1) of Sagar division are mentioned in Table 1. Out of five districts, Sagar has the maximum number of stations with a significant increasing and decreasing trend (nine stations). Sagar station showed a negative rainfall trend in August (β = –3.783 mm/year) and in the spring season (β = –1.053 mm/year). Jaisinagar and Rahatgarh stations showed a higher decreasing trend in August at β = –7.263 mm/year and β = –10.62 mm/year, respectively, as shown in Figure 2.

Baldevgarh station in Tikamgarh district indicated a higher negative trend in rainfall in August (β = –6.379 mm/year), annual (β = –11.737 mm/year) and also in the rainy season (β = –13.044 mm/year). That means a significant deficiency is seen in future rainfall in the month of August, annually and in the rainy season. Similarly, Nowgaon and Gaurihar stations saw a massive decreasing trend in August.

The less increasing rainfall rate has been seen in most of the rain gauge stations (<1 mm/year). Deori station was the only station that showed β as 4.75 mm/year in July.

It is noticed that the decreasing trend is more dominant compared to the increasing trend of rainfall for most of the stations of the Sagar division, as shown in Figure 3.

Temperature is one of the prime keys responsible for climate change. Daily maximum and minimum temperature data of five districts of Sagar division (Sagar, Chhatarpur, Tikamgarh, Panna, and Damoh) over 31 years (1988–2018) were collected and arranged in a monthly, seasonal and annual basis. It is evident that temperature has been increasing day by day which means that the increasing trend in the results was expected. The non-parametric test displayed no significant trend for maximum temperature but a significant increasing trend for minimum temperature for most of the stations on the monthly time scale.

April became warmer in terms of the lower temperature range for almost all of the districts except Panna station. Sagar district mostly suffered due to the increasing minimum temperature in April (β = 0.045 °C/year) and May (β = 0.03 °C/year) and also in summer (β = 0.031 °C/year) and spring (β = 0.016 °C) seasons. Panna district showed a negative trend in the month of May (β = 0.03 °C/year) and annually (β = 0.012 °C/year), as shown in Figure 4. The results of the significant trend of temperature at seasonal and annual scales are presented in Figure 5.

The results revealed that the minimum temperature had increased more as compared to the maximum temperature over the last 31 years. Increasing temperature affects the capability of the plant to produce grain efficiently which means a rise in minimum temperature has a bigger effect on crop yield than a maximum temperature rise. Hence, it becomes necessary to carry out a broad range study of temperature behavior and its impact, which will be seen in the future climate by predicting them.

Monthly and annual trends of SPI and RDI indices performed for 35 stations were both evaluated using the DrinC model (Tigkas et al. 2015). The results of the significant trend of SPI and RDI are presented in Table 2. Sen's slope of rainy months JJAS (June, July, August and September) over the study area were plotted using kriging interpolation on ArcGIS, as shown in Figure 6.

The four stations of Tikamgarh had a significant trend (out of seven) for either SPI or RDI or both. Baldevgarh station presented an annual decreasing trend (β = –0.046) of SPI, while Prithvipur also had an annual negative trend (β = –0.031) of SPI. For Palera and Orcha, both stations had a diminishing trend in RDI for the month of August.

Six stations in Sagar (out of 12) displayed a significant trend of either SPI or RDI or for both. Jaisinagar showed a decreasing trend for both SPI (β = –0.056) and RDI (β = –0.052) in August while Khurai and Bina stations showed a negative trend of both SPI and RDI in August. Rehli was the only station which showed a significant trend of both SPI and RDI in two months (August and September) simultaneously. Four stations in Chhatarpur (out of eight) had a significant trend of either SPI or RDI or both. Baxwaha and Gaurihar stations showed a negative trend for both SPI and RDI in August.

It is noticed that no significant trend is seen for any of the stations of Damoh and Panna for both SPI and RDI. There are many similarities found in the results of Sen's slope of SPI and RDI, as shown in Table 2. SPI depends only on rainfall while RDI depends on rainfall as well as temperature. Hence, RDI can give better results for the trend with two variables.

The performance of RDI with two meteorological variables (rainfall and temperature) was found to be quite good, along with the SPI with one meteorological variable (rainfall). Hence, RDI can replace SPI if better correlation is shown between both of them. Sen's slope of both indices showed nearly similar results on an 85% significance level while Z < 1.44 or Z > –1.44. The ANOVA test was performed to see the level of discrimination of both SPI and RDI.

For all the stations, values of SPI and RDI are nearly equal, but the discrimination of SPI and RDI is necessary based on their increasing and decreasing behavior. Thus, Sen's slope values were taking for the ANOVA test on an 85% significance level. There are two groups with a single variable, and that is why one way ANOVA is applied, shown in Table 3.

There was a deficient level of discrimination found between Sen's slope of SPI and RDI (Hypothesis is accepted, F ≪ Fcrit), as shown in Table 4. That means RDI shows substantial accuracy towards projections of future drought with two climate variables.

It is concluded that the decreasing trend of rainfall is more dominant as compared to the increasing trend for most of the stations of the Sagar division, especially Baldevgarh station, which showed the higher negative trend of rainfall in August (β=–6.379 mm/year), annual (β=–11.737 mm/year) and also in the rainy season (β = –13.044 mm/year). That means significant deficiency was seen in future rainfall in August, annually and in the rainy season. Similarly, Jaisinagar, Rahatgarh, Nowgaon and Gaurihar stations showed a massive decreasing rainfall trend in August.

The minimum temperature had increased more as compared to the maximum temperature during the last 31 years of the study region. No significant trend was seen for maximum temperature in the study region, but for minimum temperature an increasing trend was observed for all stations, in particular the month of April gets warmer in the lower temperature range for almost all of the districts. Sagar district mostly suffered in April (β = 0.045 °C/year) and May (β = 0.03 °C/year) as well as in summer (β = 0.031 °C/year) and spring (β = 0.016 °C/year) seasons.

For most of the stations of the Sagar division, the trend of drought was found to be significant, especially in August. It was also noticed that no significant trend was seen for any of the stations of Damoh and Panna districts. There are many similarities found in SPI, and RDI values at the level of severity of drought and also similar results are seen in Sen's slope of SPI and RDI.

Sen's slope values of SPI and RDI for August presented a very similar magnitude. The significant trend was mostly seen in this month. Figure 6 represented the Sen's slope of rainy months JJAS (June, July, August and September) over the study area.

The ANOVA result of SPI and RDI also displayed substantial similarity to Sen's slope. It means RDI can give better results of the trend with two meteorological variables along with SPI. The study also helps to choose a suitable drought index to project future drought using the general circulation models (GCMs) or regional climate models (RCMs) in meteorological drought as well as the agricultural drought category. At the same time, the SPI indicated the meteorological drought only.

The focus of the current study was to check the applicability of drought indices for the Sagar division so that further drought could be forecast using specific climate models such as GCMs and RCMs. Specific bias correction methods could be applied such as linear scaling (LS), general quantile mapping (GEQM), gamma quantile mapping (GAQM), and power transmission (PT) to downscale the model data (Homsi et al. 2020). Drought indices could also be modeled by the support vector regression (SVR), SVR model coupled with firefly algorithm (SVR-FA), Gene Expression Programming (GEP), and M5 model trees (MT) to forecast drought (Moazenzadeh et al. 2018; Shamshirband et al. 2020).

All relevant data are included in the paper or its Supplementary Information.