Markov chain modelling of meteorological drought return periods: A case of Mberengwa district, Zimbabwe

Abstract

This study applies a first-order Markov chain modelling approach to Standardised Precipitation Index data derived from 2011 to 2021 annual rainfall data collected across the 37 wards in Mberengwa District, Zimbabwe, to assess its meteorological drought return period patterns. The study aims to estimate the meteorological drought return periods using the steady-state probabilities and calculate multiple-year drought probabilities and the expected duration of drought, providing a probabilistic understanding of drought dynamics to support effective drought risk management and climate adaptation planning in the district and other arid areas. The Standardised Precipitation Index values were classified into drought, normal and wet states based on their magnitudes. The transition probabilities were used to calculate the steady-state probabilities, which were used to estimate the return periods. The Markov Chain Property (Memoryless Property) and stationarity assumptions were validated using the autocorrelation graph and chi-square distribution, respectively. Each validation resulted positively supported the Markov chain assumptions, suggesting that the local authorities could rely on the model’s predictions for planning and resource management. The findings indicated that drought conditions occur 23% of the time with a corresponding return period of approximately 4.35 years, normal conditions occur 59% of the time with a corresponding return period of approximately 1.69 years, and wet conditions occur 18% of the time with a corresponding return period of approximately 5.56 years. The probabilities of the multi-year droughts revealed a 24.7% chance of a drought lasting approximately 2 years, diminishing to 0.37% for five consecutive years. The expected length of drought was estimated to be 1.33 years, suggesting that while droughts are a concern, they often resolve relatively quickly. This study emphasises the need for local authorities to develop comprehensive emergency preparedness plans, invest in water conservation infrastructure and foster community engagement to enhance resilience against the impacts of climate variability.