Century-Long Rainfall Records Reveal Hidden Memory in Africa’s Drylands

Across the arid and semi-arid belt of Africa, where the Sahara, the Sahel, the Namib and the Kalahari impose some of the harshest living conditions on Earth, rainfall is everything. A new statistical study spanning more than a century of monthly observations suggests that the way rainfall anomalies linger in these regions is far more varied than scientists had assumed, with profound consequences for how droughts and flash floods should be managed. The research, published in Theoretical and Applied Climatology, applied a sophisticated seasonal fractional model to rainfall data from 17 African countries prone to aridity, using records that stretch continuously from January 1901 to December 2024.

The team, led by Luis A. Gil-Alana of the University of Navarra in Spain together with OlaOluwa S. Yaya of the University of Ibadan in Nigeria, Ramiro Gil-Serrate of Universidad Antonio de Nebrija and Peter O. Ohue of Queens University, set out to answer a deceptively simple question: when a wet or dry month arrives in these drylands, how long does its influence persist? The answer matters enormously for the hundreds of millions of people whose agriculture, livestock and water supplies depend almost entirely on rain-fed systems. If rainfall shocks fade quickly, droughts are transient annoyances; if they persist, a single bad season can cascade into years of hardship.

To quantify persistence, the researchers turned to the econometric concept of fractional integration. In classical time-series analysis, a series is either stationary, meaning shocks die out quickly, or nonstationary, meaning shocks accumulate indefinitely and require full differencing to stabilise. Fractional models allow an intermediate possibility: a differencing parameter d that can take any real value. When d lies between zero and 0.5, the series displays long memory, with autocorrelations that decay hyperbolically slowly rather than exponentially fast, so disturbances echo through the record for a very long time even though the series ultimately reverts to its mean. When d reaches or exceeds 0.5, the series becomes nonstationary and shocks become effectively permanent in statistical terms.

The innovation in this study lies in extending that framework to seasonality. Monthly rainfall is dominated by an annual cycle, and standard seasonal unit root tests such as the HEGY procedure assume that the seasonal pattern can be removed by differencing the data twelve months apart. Preliminary HEGY tests on the African data rejected both non-seasonal and seasonal unit roots, but the authors argue that such tests are too restrictive: forcing d to equal exactly one risks overdifferencing, which can manufacture spurious conclusions. Their seasonal fractional model instead treats the operator (1 minus L to the twelfth power) raised to the power d, where L is the lag operator and d is estimated freely from the data. This allows the seasonal memory of rainfall to be measured on a continuum rather than forced into a binary stationary-or-not verdict.

The data came from the Climatic Research Unit Time Series dataset hosted on the World Bank Climate Change Knowledge Portal, a globally gridded observational product built by interpolating station measurements onto a regular 0.5-degree grid. Each country series contained 1,488 monthly observations. The descriptive statistics alone tell a story of extremes: mean monthly rainfall ranges from a mere 1.8 millimetres in Egypt and 3.4 millimetres in Libya to more than 70 millimetres in Ethiopia and 83 millimetres in South Sudan. Coefficients of variation frequently exceed 100 percent in countries such as Niger, Mauritania and Namibia, and every series is positively skewed, reflecting long stretches of near-zero rainfall punctuated by occasional torrential events.

The headline finding is that all estimated fractional parameters fall strictly between zero and one, confirming genuine fractional integration in every country examined. But the values split the continent into two hydroclimatic camps. In one group, the estimates are low enough to guarantee stationarity: Somalia records the lowest value at 0.25, followed by Algeria, Tunisia and Kenya at 0.27, Morocco and Egypt at 0.32, and Botswana, Libya, South Africa and Namibia in the 0.36 to 0.40 range. In these countries, rainfall deviations from the long-term mean are corrected relatively quickly, and the confidence intervals rule out nonstationarity. At the other extreme, Mauritania (0.54), Niger (0.56), Sudan and South Sudan (0.60), Chad (0.66) and Mali (0.67) all show estimates at or above the 0.5 threshold, meaning rainfall anomalies there are highly enduring and revert only slowly. Ethiopia sits almost exactly on the boundary at 0.49.

The geography of these results is not accidental. The high-persistence countries are concentrated in the Sahelian belt, where rainfall arrives in a single monsoonal wet season governed by the annual migration of the Intertropical Convergence Zone and the West African Monsoon. Rainfall events in these regions occur in coherent seasonal sequences, and prolonged dry seasons with relatively low intra-seasonal variability enhance temporal persistence. By contrast, the low-persistence countries experience climatically noisy regimes. Kenya and Somalia are shaped by two distinct rainy seasons, the so-called long rains and short rains, modulated strongly by the El Niño-Southern Oscillation and the Indian Ocean Dipole, while Algeria and Tunisia receive episodic precipitation from Mediterranean cyclones and mid-latitude weather systems. Multiple, interacting rainfall-generating mechanisms fragment the seasonal signal and weaken long memory.

The study also detected statistically significant positive time trends in 10 of the 17 countries, with the steepest increases in Ethiopia and Kenya, equivalent to roughly 0.20 and 0.34 millimetres per year respectively under the white-noise specification. To check robustness, the authors repeated the analysis allowing for weakly dependent errors using the non-parametric Bloomfield approach, which approximates the spectrum of autoregressive moving average processes with far fewer parameters, and by aggregating the monthly data to quarterly series. The broad picture held: under the Bloomfield specification, stationarity was confirmed in the same ten countries plus Ethiopia, with only South Sudan, Chad and Mali remaining nonstationary, while the quarterly analysis pushed estimates slightly higher, leaving nine countries in the nonstationary camp, with Chad reaching 0.89 and Mali 0.84. Across all specifications, six countries, Somalia, Algeria, Kenya, Tunisia, Egypt and Morocco, showed consistent evidence of stationary rainfall.

For drought managers and agricultural planners, the implications are stark. In Mali, Chad and South Sudan, a drought year is not simply a bad year that the climate forgets; the statistical signature suggests its effects linger, compounding food insecurity and water stress over successive seasons. Conversely, in the Mediterranean-influenced north and the dual-season east, rainfall anomalies wash out faster, but the very variability that produces this rapid mean reversion also makes rainfall harder to forecast from one season to the next. The authors note that countries with higher seasonal persistence may require fundamentally different drought-monitoring and agricultural-planning strategies than those where anomalies revert quickly, and the findings underscore sharply differing levels of hydroclimatic resilience across the continent.

The authors are candid about limitations. Country-level averages can mask enormous sub-national diversity, particularly in climatically heterogeneous nations such as Kenya, Ethiopia, South Africa and Sudan, where distinct regional rainfall regimes coexist within national borders. Future work, they suggest, will examine monthly rainfall totals, anomalies relative to the 1991 to 2020 climate baseline, standardised precipitation indices and log-transformed series, as well as non-linear trends built from Chebyshev polynomials, Fourier functions or neural networks, and the possible role of structural breaks in creating spurious long memory. Even with these caveats, the study delivers a rare century-scale, statistically rigorous portrait of rainfall behaviour in some of the world’s most vulnerable drylands, and it offers a quantitative foundation for anticipating which regions will recover from climate shocks and which will carry them forward.

Subject of Research: Seasonal persistence and long-memory dynamics of rainfall in arid and semi-arid African climatic zones

Article Title: Testing seasonal persistence of rainfall in arid and semi-arid african climatic zones using a seasonal fractional model

Article References: Gil-Alana, L. A., Yaya, O. S., Gil-Serrate, R., & Ohue, P. O. (2026). Testing seasonal persistence of rainfall in arid and semi-arid african climatic zones using a seasonal fractional model. Theoretical and Applied Climatology, 157(10), Article 628. https://doi.org/10.1007/s00704-026-06551-x

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06551-x

Keywords: rainfall persistence, fractional integration, long memory, Sahel, drought, arid climates, seasonality, Africa, time series analysis, HEGY test, Intertropical Convergence Zone, hydroclimatology