Understanding drought dynamics and variability over Bundelkhand region

Abstract

This study provides an evaluation of the past, present, and future spatiotemporal variability of droughts in 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 projection is presented using a multi-model ensemble from 21 simulations of regional climate model over CORDEX South-Asia domain under the highest carbon concentration, i.e., RCP8.5 emission scenario. The Standardized Precipitation Index (SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI) indices are used for short and long-term monitoring of droughts. Spatiotemporal statistical analysis is performed to examine the relationship between drought indices, i.e., SPI, SPEI and driving parameters such as temperature, precipitation, etc. It is noticed that the frequency of drought has increased since the beginning of the 21st century. In particular, the northern part of the Bundelkhand region is more vulnerable to drought due to overall less precipitation and more temperature. The composite analysis of drought year indicates that moisture-laden wind from the Arabian Sea branch generally weakened in monsoon season. Teleconnections of drought over Bundelkhand region reveal that nearly 40% of the droughts are linked to El-Nino events that have become stronger in recent decades. The model ensemble realistically represents the regional climate reasonably well over the region. The projected change in near future drought shows more frequent events using both SPI and SPEI indices that are also detected in the observational analysis.

Research Highlights

• The Northern region of Bundelkhand is more prone to drought due to high temperature and low precipitation.

• The region receives most of its precipitation from Arabian Sea branch of monsoon winds that generally weakened in drought composite years.

• About 40% of drought variability is teleconnected with El–Nino years that has become more stronger in recent decades

• The ensemble of RCM simulations over CORDEX South–Asian domain indicates that the drought events are projected to be more frequent in near future.

Appendices

A. Appendix

A.1 SPI Calculation

SPI is derived by fitting gamma distribution function. It is then transformed into standard normal distribution where the mean value is zero and variance is one (McKee et al. 1993).

The gamma distribution is defined by probability density function (p.d.f.) as

$$ g\left( x \right) \, = \, [1/ \, \beta^{\alpha } \times \varGamma (\alpha )] \times \, x^{{\alpha {-}1}} \times e^{{{-}x/\beta }} $$

(A.1)

where α > 0, α is a shape parameter; β > 0, β is a scale parameter; x > 0, x is the precipitation amount.

$$(\alpha)=\int \nolimits_{0}^{\infty }y^{\alpha -1}e^{-y}{\text{d}}y, \quad(\alpha) \, {\text{is a gamma function}}.$$

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

$$ G\left( x \right) = \mathop \int \nolimits_{0}^{x} g\left( x \right)dx = \frac{1}{{\hat{\beta }^{{\hat{ \alpha }}} \varGamma \left( {\hat{ \alpha }} \right)}}\mathop \int \nolimits_{0}^{x} x^{{\hat{ \alpha} - 1}} e^{{ - x/\hat{\beta }}} dx $$

(A. 2)

where

$$ \hat{ \alpha } = \frac{1}{4A}\left( {1 + \sqrt {1 + \frac{4A}{3}} } \right) $$

$$ \hat{\beta } = \frac{{\overline{x}}}{{\hat{ \alpha }}} $$

$$ A = \, \text{ln} \, (\overline{x}) - \frac{{\sum {\text{ln}}\left( x \right)}}{n} $$

n is the number of precipitation observations.

Let t = x/$\hat{\beta }$, putting it in G(x)

$$ G\left( x \right) = \frac{1}{{\varGamma \left( {\hat{ \alpha }} \right)}}\mathop \int \nolimits_{0}^{x} t^{{\hat{ \alpha } - 1}} e^{ - t} dt. $$

(A. 3)

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

$$ H\left( x \right) \, = \, q \, + \, \left( {1{-}q} \right)G\left( x \right). $$

(A. 4)

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 normal cumulative distribution function having mean value zero and variance as one. Then SPI is calculated using Abramowitz and Stegun (1965) approximation as:

$$ SPI = - \left( {t - \frac{{C_{0} + C_{1} t + C_{2} t^{2} }}{{1 + d_{1} t + d_{2} t + d_{3} t^{3} }}} \right)\quad {\text{for}} \;0 < H(x) < 0.5\, , $$

(A. 5)

$$ SPI = + \left( {t - \frac{{C_{0} + C_{1} t + C_{2} t^{2} }}{{1 + d_{1} t + d_{2} t + d_{3} t^{3} }}} \right)\quad {\text{for}}\;0.5 < \, H(x) < \, 1.0 \, ,$$

(A. 6)

where

$$ t = \sqrt {{\text{ln}}\left( {\frac{1}{{\left( {H\left( x \right)} \right)^{2} }}} \right)} \quad \text{for}\;0 < H(x) < 0.5\, , $$

$$ t = \sqrt {{\text{ln}}\left( {\frac{1}{{\left( {1.0 - H\left( x \right)} \right)^{2} }}} \right)}\quad \text{for} \; 0.5 < H\left( x \right) < 1.0 $$

$C_{0} = 2.515517$, $C_{1} = 0.802853$, $C_{2} = 0.010328$, $d_{1} = 1.432788$, $d_{2} = 1.89269$ and $d_{3} = 0.001308$.

A.2 SPEI calculation

The SPEI is calculated as

$$ D_{i} = P_{i} - {\text{PETi}} \, ,$$

(A. 7)

where ${D}_{i}$ is aggregate at different time scale, P_i is monthly precipitation and PET is the monthly potential evapotranspiration.

The probability density function (for log logistic distributed variable) is given by

$$ f\left( x \right) = \frac{\beta }{\alpha }\left( {\frac{x - \gamma }{\alpha }} \right)^{\beta - 1} \left[ {1 + \left( {\frac{x - \gamma }{\alpha }} \right)^{\beta } } \right]^{ - 2} \, ,$$

(A. 8)

where α is a scale parameter for D values

$$ \alpha = \frac{{\left( {W_{0} - 2W_{1} } \right)\beta }}{{\varGamma \left( {1 + \frac{1}{\beta }} \right)\varGamma \left( {1 - \frac{1}{\beta }} \right)}}\, , $$

β is a shape parameter for D values

$$ \beta = \frac{{2W_{1} - W_{0} }}{{6W_{1} - W_{0} - 6W_{2} }} \, ,$$

$\gamma$ is an origin parameter for D values

$\gamma = W_{0} - \alpha {\varGamma }\left( {1 + \frac{1}{\beta }} \right){\varGamma }\left( {1 - \frac{1}{\beta }} \right)$.

Probability weighted moments (PWMs) calculated by

$$ \omega_{s} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \left( {1 - F_{i} } \right)^{S} D_{i}\, , $$

(A. 9)

where S is an order of PWMs, N is the number of data, F_i is the frequency estimator and can be expressed as:

$$ F_{i} = \frac{i - 0.35}{N}\, , $$

where i is a range of observations.

The unbiased PWMs calculated as:

$$ \omega_{s} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \frac{{\left( {\begin{array}{*{20}c} {N - i} \\ s \\ \end{array} } \right)D_{i} }}{{\left( {\begin{array}{*{20}c} {N - i} \\ s \\ \end{array} } \right)}}. $$

(A. 10)

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

$$ F\left( x \right) = \left[ {1 + \left( {\frac{\alpha }{x - \gamma }} \right)^{\beta } } \right]^{ - 1} . $$

(A. 11)

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

$$ SPEI = W{-} \frac{{C_{0} + C_{1} W + C_{2} W^{2} }}{{1 + d_{1} W + d_{2} W^{2} + d_{3} W^{3} }} $$

(A. 12)

where

$$ W = \sqrt { - 2\, {\text{ln}}\left( P \right){ }} \quad {\text{for}}\;P \le 0.5. $$

Constants hold the same value as in SPI for $C_{0} , C_{1} , C_{2}$ and $d_{1} , d_{2} , d_{3}$ mentioned above in SPI calculation section.