Characterization of drought over Botswana using multivariate statistics

Droughts pose a significant challenge to water resources, causing several socio-economic

consequences. The growing economy requires improved assessments of drought-related

impacts in the water sector, particularly under semi-arid environments where its climate is

getting drier and warmer. This study proposes a probabilistic model (copula approach) that

is intended to contribute to the drought risk assessment by providing an essential information

in drought prediction, decision making and management of the limited water resources

available during drought events. The three key pillars (i. Drought monitoring and early

warning systems, ii.vulnerability, and impact assessments, and iii. mitigation and response

measures) are recommended as the basis of national drought policy and management plans,

providing a practical way to organize multiple actions and activities that the country need to

implement to better prepare and respond to drought. In the study, drought events are

characterized by duration, severity and intensity, and the Standardized Precipitation Index

(SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI) were used to

analyse hydrological drought based on gridded rain gauge and potential evapotranspiration

data referred to as Climatic Research Unit (CRU) covering a period of 1901-2018 at a time

scale of 12 months. Both SPI and SPEI were able to detect the spatial and temporal variation

of drought. But SPEI was able to identify more droughts in the severe to moderate categories

over wider areas in the country than SPI did. A set of seven homogeneous drought regimes

based on spatial characteristics of SPEI were obtained. Region 1 and 7 are relatively wet

regions, followed by region 2 and 6, while region 2 and 4 are relatively dry regions which

borders the Kgalagadi Basin. The optimal marginal distribution for drought duration,

severity and intensity were identified by employing the Akaike Information Criterion (AIC).

The drought duration was best described by the Generalized Extreme Value distribution

while the drought severity and intensity were both found to optimally fit with Weibull

distribution. Nine copula distributions, namely-Normal, Student’s t, Gumbel-Hougaard,

Rotated Gumbel, Clayton, Rotated Clayton, Joe Clayton, Frank, and Plackett copula

distributions were applied to construct the bivariate and trivariate distributions. The most

appropriate copula functions were determined also based on AIC. The joint distribution of

the best marginal cumulative density functions of duration and severity is found to optimally

fit Normal copula while Clayton copula distribution is the best copula function that describes

joint distribution of duration and intensity as well as the joint distribution of severity and

intensity over most grids in Botswana. The trivariate distribution of the univariate marginals

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of duration, severity and intensity is best fitted by Normal copula. The conditional return

period of drought of different categories was also determined in a multivariate context by

coupling duration, severity, intensity of drought based on copula distribution and cumulative

density functions. Most of the historical drought events over homogenous drought regimes

in Botswana have short duration, low severity, low intensity and short return period, with

drought regimes 1, 3, 4 and 7 having longer drought return periods than the other three zones

(2, 5 and 6). The risk of having long and severe droughts within the 10-year design lifetime

of any hydrological system was low in drought events with longer duration and high severity

across all the regions in Botswana. Improved information on drought characterization can

be useful in evaluating the water-supply capability and the needed supplementary water

resources during severe drought conditions for a specific water-supply system.