Statistical modelling of spatio-temporal rainfall trends, dependence, and extremes in Zimbabwe (1984–2024)

Abstract

Understanding the spatio-temporal variability of extreme rainfall is critical for climate adaptation and for informed water-resource planning in Zimbabwe. This study develops a unified statistical framework to:(1) characterize annual rainfall variability and detect monotonic trends;(2) model extreme rainfall events via block maxima and peaks-over-threshold methods and quantify their long-range dependence;(3) assess the spatial autocorrelation patterns of rainfall across provinces; and (4) explore inter-provincial rainfall dynamics using a Vector Autoregressive (VAR) model. Monthly rainfall totals for ten provinces (1984–2024) were retrieved from NASA POWER at provincial centroids. Descriptive statistics reveal a pronounced east–west gradient in mean annual rainfall (390.1 mm in Manicaland; 190.8 mm in Matabeleland South) and variability (Standard deviation up to 147 mm in Manicaland). The Mann–Kendall and block-bootstrap tests indicate no significant monotonic trends (all\(\varvec {p} _ {{\textbf {BBS}}}>\) 0.16), suggesting stationary annual totals over the study period. Extreme-value analysis shows uniformly positive Generalized Extreme Value (GEV) shape parameters (for example\(\varvec {\xi} _ {{\textbf {GEV}}}\varvec {= 0.05--0.38}\)) with anomalously large estimates in Harare and the Midlands; Generalized Pareto Distribution (GPD) fits yield moderate heavy-tails (\(\varvec {\xi} _ {{\textbf {GPD}}}\varvec {= 0.02-0.32}\)) and scale parameters of 5.6–9.9 mm. Detrended fluctuation analysis produces Hurst exponents\(\varvec {H< 0.5}\)(0.25–0.35), indicating anti-persistence and mean-reversion in extreme-rainfall maxima. Spatial autocorrelation metrics (Global Moran’s I= 0.266,\(\varvec {p= 0.018}\); Geary’s\(\varvec {C= 0.631, p= 0.007}\)) confirm significant clustering. Local Moran’s I identifies northeastern hot-spots and southwestern cold-spots. A VAR (2) model—selected via minimum Akaike Information Criterion/Bayesian Information Criterion (also known as the Schwarz Criterion)(AIC/BIC)—highlights significant two-month persistence in Manicaland (\(\varvec {L} _ {\varvec {2}}\varvec {= 0.916}\),\(\varvec {p= 0.033}\)) and one-month memory in Matabeleland North (\(\varvec {L} _ {\varvec {1}}\varvec {= 1.319}\),\(\varvec {p= 0.049}\)). These findings reveal heterogeneous heavy-tailed behaviour, mean-reversion, and spatial clustering in Zimbabwe’s rainfall extremes, underscoring the need for region-specific risk assessments and infrastructure design tailored to local hydro-climatic regimes.