The highest long-term values were concentrated in northern Kerala, while the smallest erosion-potential domain covered much of southern and parts of central Kerala. Rainfall erosivity describes the capacity of rainfall to detach and transport soil, while erosivity density expresses that erosive potential relative to the amount of rainfall. The two measures help distinguish the effect of how much rain falls from the effect of how intensely it falls.

For the analysis, the researchers converted daily gridded rainfall observations into monthly totals for each year and applied the Arnoldus empirical approach, a monthly-rainfall method widely used for long-term regional assessments. They calculated annual erosivity density as annual rainfall erosivity divided by annual rainfall. Trend significance was evaluated with the modified Mann–Kendall test, which adjusts for serial correlation, and trend magnitude was estimated with Sen’s slope method.

Agglomerative hierarchical clustering with Ward’s linkage then grouped grid cells with similar 120-year mean rainfall erosivity and erosivity density. The analysis identified a pronounced north–south gradient. Northern Kerala contained the highest minimum, maximum and mean rainfall erosivity, as well as the highest erosivity-density values.

The largest values occurred in and around Kasaragod, Kannur, Wayanad, Kozhikode and parts of eastern Palakkad, with additional high-erosivity areas in parts of Thrissur, Ernakulam and Kottayam. Most of central and southern Kerala had low to moderate values. The mapped patterns broadly followed rainfall totals, but rainfall erosivity had a higher coefficient of variation than rainfall, indicating that the erosive potential of Kerala’s rainfall was more variable across space and time than precipitation amount alone.

Four statistically distinct erosivity domains emerged from the clustering. The largest, C1, contained 23 cells and represented comparatively low conditions, mainly across southern and parts of central Kerala. Its mean rainfall erosivity ranged from 1,291 to 7,044 MJ mm ha⁻¹ h⁻¹ y⁻¹, and its erosivity density ranged from 1.34 to 3.38 MJ ha⁻¹ h⁻¹.

The intermediate C2 domain comprised 17 cells across much of central Kerala, with rainfall erosivity from 8,375 to 12,685 MJ mm ha⁻¹ h⁻¹ y⁻¹ and erosivity density from 2.45 to 3.99 MJ ha⁻¹ h⁻¹. Eight northern cells formed the high-erosivity C3 domain, reaching 21,643 MJ mm ha⁻¹ h⁻¹ y⁻¹ for rainfall erosivity and 5.76 MJ ha⁻¹ h⁻¹ for erosivity density. Two northern cells formed C4, the extreme domain, with rainfall erosivity of 26,974 to 29,987 MJ mm ha⁻¹ h⁻¹ y⁻¹ and erosivity density of 6.54 to 7.38 MJ ha⁻¹ h⁻¹.

Long-term averages nevertheless concealed substantial temporal variability. The 1991–2000 decade showed the widest spread in rainfall erosivity, from 1,269 to 38,824 MJ mm ha⁻¹ h⁻¹ y⁻¹, and the widest spread in erosivity density, from 1.26 to 10.53 MJ ha⁻¹ h⁻¹. Those ranges did not coincide with the highest average values: the decade with the greatest mean rainfall erosivity was 1921–1930, at 12,224 MJ mm ha⁻¹ h⁻¹ y⁻¹, and the highest mean erosivity density was 3.74 MJ ha⁻¹ h⁻¹.

Inter-decadal comparisons showed alternating periods of increase and decrease rather than a smooth progression. Rainfall erosivity rose most strongly between the second and third decades, while pronounced decreases occurred in several later transitions, particularly between 1991–2000 and 2001–2010. Comparing the first and last decades likewise showed that declines predominated statewide.

Statewide linear analysis confirmed the general direction of change. Mean annual rainfall decreased at a rate of 3.53 mm per year, with an R² of 0.1119. Mean rainfall erosivity declined by 34.34 MJ mm ha⁻¹ h⁻¹ y⁻¹ per year, with an R² of 0.1302, while erosivity density fell by 0.0074 MJ ha⁻¹ h⁻¹ per year, with an R² of 0.0947.

Grid-level results were more varied. For rainfall erosivity, 39 of 50 cells showed decreasing trends, including 33 statistically significant declines; 10 showed increases, five of them significant, and one showed no trend. Sen’s slopes ranged from −171.72 to 38.79 MJ mm ha⁻¹ h⁻¹ y⁻¹ per year.

For erosivity density, 40 cells declined, including 34 significant decreases, nine increased, including four significant increases, and one showed no trend. The strongest declines occurred in northern districts, whereas increases were confined to a few eastern highland locations. Elevation did not explain the regional pattern by itself.

In an analysis using 300 spatially distributed points sampled from interpolated surfaces, elevation had a moderate negative relationship with mean rainfall, with r = −0.49 and R² = 0.2418. Its relationships with rainfall erosivity and erosivity density were much weaker: r = −0.24 and R² = 0.0589 for erosivity, and r = −0.18 and R² = 0.0325 for erosivity density. Low-elevation locations generally received more than 3,000 mm of annual rainfall and often had greater erosivity, whereas high-elevation sites commonly received 1,000–1,500 mm, but considerable variation occurred within every elevation band.

The results indicate that monsoon circulation, rainfall intensity, seasonal distribution, topographic position and local atmospheric conditions jointly shaped erosivity rather than altitude acting as a simple control. The coexistence of declining long-term averages and episodic high-erosivity periods is an important feature of the record. A reduction in mean rainfall erosivity does not necessarily imply a proportional reduction in erosion hazard, because average conditions and extreme events represent different parts of the rainfall regime.

The monthly-rainfall method also cannot resolve the kinetic energy, duration or within-storm intensity of individual short-duration storms. Although this approach provides a consistent century-scale comparison, it may under- or overestimate local annual erosivity where extreme storms make a disproportionate contribution. The estimates describe climatic potential for soil detachment, not observed soil loss, which also depends on soil properties, vegetation, land use, slope, infiltration and sediment connectivity.

Likewise, the annual erosivity-density calculation describes long-term rainfall aggressiveness per unit rainfall rather than seasonal concentration or event-scale behavior. The spatial divergence also carries implications for erosion modelling. Because Kerala’s rainfall erosivity varies sharply over a comparatively small and topographically diverse area, applying one statewide R-factor could obscure localized high-erosivity conditions.

The four-domain classification provides an alternative framework for parameterizing Revised Universal Soil Loss Equation models, prioritizing watersheds and supporting spatially differentiated conservation planning. It does not by itself establish current erosion rates, however, and the four-cluster solution was selected through dendrogram interpretation rather than quantitative validation with indices such as silhouette width. High-temporal-resolution rainfall observations, climate projections and further analysis of extreme events will be needed to clarify future erosion susceptibility, but the current evidence shows that Kerala’s erosive rainfall has been highly variable despite its broad long-term decline.

Subject of Research: Century-scale analysis of rainfall erosivity and erosivity density across Kerala, India

Article Title: Century-scale spatiotemporal variability and trends of rainfall erosivity and erosivity density in an ecologically sensitive tropical monsoon region of India (1901–2020)

Article References: Valappil, N. K. M., Yusup, Y., Dewi, J. R., Huda, N., & Hamza, V. (2026). Century-scale spatiotemporal variability and trends of rainfall erosivity and erosivity density in an ecologically sensitive tropical monsoon region of India (1901–2020). Environmental Earth Sciences, 85(17), Article 437. https://doi.org/10.1007/s12665-026-13119-5

Image Credits: AI Generated

DOI: 10.1007/s12665-026-13119-5

Keywords: rainfall erosivity, erosivity density, Kerala, monsoon rainfall, soil erosion, Western Ghats, climate variability, Mann–Kendall test, hydroclimatology, RUSLE, spatial analysis, long-term trends

The mathematical foundation of the study lies in extreme value theory, a branch of statistics developed specifically to model the behavior of rare events rather than averages. The Generalized Extreme Value, or GEV, distribution works by taking the single largest daily rainfall value from each year and fitting a flexible probability curve to those annual maxima. That curve has three variants named after their discoverers: the Gumbel family, with a moderately heavy tail; the Fréchet family, whose unbounded tail allows for extraordinarily large extremes; and the Weibull family, whose tail is bounded, meaning there is a physical ceiling on how extreme an event can become. Which variant applies in a given region is governed by the shape parameter, and estimating it correctly is the crux of any return-period calculation, because the tail behavior determines how quickly probabilities decay as you project toward rarer and rarer storms.

The Peak Over Threshold, or POT, approach takes a fundamentally different view of the data. Instead of discarding all but one value per year, it captures every daily rainfall that exceeds a chosen high threshold, thereby using far more information about the upper tail of the distribution. The exceedances are then modeled with the Generalized Pareto distribution, a technique rooted in Picklands’ foundational 1975 work on extreme order statistics. The trade-off is well known among hydrologists: POT extracts more signal from limited records and typically yields narrower uncertainty intervals, but its results are sensitive to how the threshold is selected, whereas GEV discards potentially useful secondary storms within a single year yet is simpler and more standardized in practice.

To capture India’s enormous climatic diversity, the authors divided the country into six homogeneous regions: north, northeast, west, east, central, and peninsular India. This regional partition matters because the drivers of extreme rainfall differ dramatically across the subcontinent, from the orographic uplift along the Western Ghats and the Himalayan foothills to the depression-driven systems that sweep across the Gangetic plains. The rainfall data came from the gridded daily product maintained by the India Meteorological Department, providing a spatially consistent record spanning nine decades, a period during which global warming, rapid urbanization, and land-use change have all reshaped the hydrological cycle.

The shape parameter results reveal a striking geographic split. In Northeast India, one of the wettest places on the planet, the fitted GEV shape parameter was approximately zero, which corresponds to an effectively Gumbel-type tail: extremes grow with rainfall intensity but without the explosive amplification of a heavy-tailed Fréchet distribution. In the other five regions, the shape parameter was negative, indicating bounded Weibull-type tails in which the largest conceivable daily rainfall approaches a finite upper limit. For flood engineers, this distinction is far from academic. A bounded tail implies that 100-year and 1000-year return levels converge toward a ceiling, while a heavier tail keeps pushing design storms upward as the return period lengthens, with direct consequences for the safety margins built into critical infrastructure.

The estimated 100-year return levels quantify just how uneven India’s extreme rainfall landscape is. In western India, the GEV-based 100-year daily rainfall came out at roughly 358 millimeters, with a 95 percent bootstrap confidence interval spanning 308 to 409 millimeters. In northeastern India, the corresponding figure soared to about 1107 millimeters, with an interval of 923 to 1353 millimeters, meaning that in the worst plausible case a single day’s rain in the northeast could exceed the entire annual rainfall of many semi-arid regions. These numbers translate directly into design guidance: a culvert sized for western Indian extremes would be dangerously undersized if transplanted to the Brahmaputra valley, and the wide confidence intervals in the northeast underscore how much statistical uncertainty remains even with ninety years of data.

When the two modeling philosophies were compared directly, the POT method emerged as the more accurate fit in every one of the six regions. Its 100-year return level estimates ranged from about 357 millimeters to 1045 millimeters, closely tracking the GEV values but generally with tighter precision, a benefit attributable to its richer use of threshold exceedances. This finding aligns with a growing body of international literature suggesting that threshold-based models, when their thresholds are chosen carefully, offer the best of both worlds: the theoretical rigor of extreme value theory combined with the statistical efficiency of using multiple extreme events per year rather than just the annual maximum.

Perhaps the most methodologically important contribution of the study is its insistence on out-of-sample validation. The authors split the record into a training period from 1930 to 1999 and a testing period from 2000 to 2019, then evaluated how well models calibrated on the historical data predicted the extremes of the most recent two decades, using the negative log-likelihood as the scoring metric. The results exposed regional differences in predictive calibration that would have remained invisible under conventional in-sample goodness-of-fit testing. A model can fit the data it was trained on beautifully and still misjudge the tail behavior of the future, and the study demonstrates that out-of-sample evaluation is a genuinely better guide to real-world flood risk than fit statistics computed on the same data used for estimation.

The practical stakes of this work are considerable. Floods rank among the most frequent and destructive natural hazards worldwide, threatening lives, ecosystems, infrastructure, and economic stability, and their severity is being amplified by climate change, urbanization, and hydrological variability. Previous research, including landmark analyses of increasing extreme rain events over India in a warming environment, has documented that the character of Indian rainfall extremes has been shifting, which makes the choice of statistical model even more consequential: an outdated or poorly validated tail model can silently understate the risk that a dam, levee, or urban drainage network will be overwhelmed. By providing a regionally consistent assessment that explicitly separates model fit from predictive skill, the study gives Indian water managers a clearer map of where each tool can be trusted.

The research also opens doors for future refinement. The analysis assumes stationarity, treating the 1930 to 2019 record as drawn from an unchanging climate, whereas a growing literature on non-stationary extreme rainfall over Indian cities suggests that allowing distribution parameters to evolve with time or with climate covariates could sharpen return-level estimates further. Extending the out-of-sample framework to non-stationary models, to finer spatial resolutions, and to sub-seasonal extremes would be natural next steps. For now, the message of this study is clear and actionable: for diagnosing extreme precipitation across India, the Peak Over Threshold method offers the most accurate regional fits, the northeast demands special caution because of its extraordinary rainfall magnitudes and wide uncertainty bands, and no flood risk assessment should rely on in-sample fit alone when the true test is how well a model anticipates the storms of the next twenty years.

Subject of Research: Extreme value analysis of extreme precipitation and return levels across India using GEV and POT methods

Article Title: Assessing the suitability of GEV and POT for extreme precipitation diagnostics over India

Article References: Jain, J., Muñoz-Arriola, F., & Khare, D. (2026). Assessing the suitability of GEV and POT for extreme precipitation diagnostics over India. Theoretical and Applied Climatology, 157(11), Article 693. https://doi.org/10.1007/s00704-026-06643-8

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06643-8

Keywords: extreme precipitation, extreme value theory, Generalized Extreme Value distribution, Peak Over Threshold, return levels, flood risk, India, monsoon, Generalized Pareto distribution, out-of-sample validation, hydroclimatology, Theoretical and Applied Climatology

The target of the new model is the Soil Moisture Condition Index, or SMCI, a measure that captures how wet or dry the land surface actually is and therefore how much stress crops are under. Unlike meteorological drought, which is defined by rainfall deficits, agricultural drought reflects the moisture available in the soil profile, where the memory of past weather lingers for weeks or months. Predicting this quantity is notoriously difficult because it depends on a tangled web of interacting variables: temperature drives evaporation, precipitation replenishes the soil, radiation and humidity control how fast water leaves the surface, and wind modulates all of these exchanges. The team selected eleven hydroclimatological predictors from the ERA5-Land reanalysis dataset, a long-term, high-resolution record of land surface conditions produced by the Copernicus Climate Change Service and freely available under a CC-BY 4.0 license.

Those eleven variables read like a physical checklist of the land-atmosphere water balance. They include two-meter air temperature, the east-west and north-south components of ten-meter wind, precipitation, surface pressure, specific humidity, surface downward solar radiation, surface downward thermal radiation, the temperature of the topsoil layer, total evaporation, and soil water capacity. Each of these quantities carries information relevant to soil moisture, but each also carries noise, measurement artifacts, and complex non-linear relationships with the target. The authors point out that existing deep learning methodologies frequently overlook the inherent stochastic noise in multi-source datasets and the often non-positive, non-linear correlations between hydroclimatological predictors and the variables they are meant to predict. A model that treats every input as equally trustworthy, or that assumes simple linear linkages, leaves predictive skill on the table.

The heart of FAELSTM is a dual-attention module the authors call FAE, which adaptively reweights the hydroclimatological input variables before they reach the forecasting engine. In practical terms, the network learns to amplify the signals that matter for a given prediction and to suppress the ones that are noisy or redundant at that moment. This is a direct answer to the data-quality problem: rather than cleaning every dataset by hand, the model performs a kind of learned filtering, continuously deciding which features deserve emphasis. The second half of the attention pair operates on time. Because drought unfolds over seasons, the architecture pairs the feature attention with a bidirectional long short-term memory backbone, or BiLSTM, a recurrent neural network design that can capture long-range temporal dependencies by processing sequences in both forward and backward directions.

Long short-term memory networks, first introduced by Sepp Hochreiter and Jürgen Schmidhuber in 1997, solved a fundamental weakness of earlier recurrent networks by using gated cells that preserve information across long time lags. That property makes them natural candidates for drought forecasting, where the state of the soil today reflects rainfall from months ago. The bidirectional variant strengthens this by letting the model contextualize each time step with information from both its past and its future within the training sequence, producing richer representations of how drought conditions build and decay. Previous studies have applied attention-augmented LSTM architectures to streamflow prediction, water level forecasting and soil moisture estimation, and the new work builds on that lineage while pushing the attention mechanism to operate on the input features themselves rather than only on hidden states.

The experimental results carry the argument. Across benchmarks, FAELSTM consistently outperformed a range of state-of-the-art baseline models, exhibiting enhanced predictive precision and superior robustness. Particularly striking is the model’s performance on the cases that matter most: severe and extreme drought stages. Forecasting problems in hydrology are plagued by class imbalance and data skewness, because genuinely extreme droughts are rare compared with normal conditions, and standard models trained on such data tend to gravitate toward the common case and miss the rare one. The authors report that their framework navigates this imbalance to accurately identify the severe and extreme stages where traditional architectures often falter, precisely the failures that translate into unprepared farmers and unmitigated losses.

Just as important as raw accuracy is what the model learned about physics. A feature interpretability analysis confirmed that FAELSTM autonomously prioritizes key physical drivers of soil moisture, and that the priorities it discovered align with established hydrological water balance principles. In other words, the attention mechanism did not latch onto statistical quirks of the dataset; it converged on the same variables a hydrologist would nominate, such as precipitation, evaporation and temperature, as the dominant controls on soil moisture. This kind of agreement between learned attention and domain theory matters for trust. A black box that happens to be accurate is hard to deploy in operational water management, but a model whose internal weighting can be read and validated against physical understanding offers forecasters a defensible basis for action.

The study’s geographic scope is one of its most ambitious features. China spans humid subtropical rice belts in the south, semi-arid wheat and maize regions in the north, and high-altitude grasslands in the west, each with distinct soil properties, radiation regimes and drought dynamics. By training and evaluating on a national-scale ERA5-Land record, the authors tested whether a single architecture could generalize across this diversity, and their results suggest it can. The choice of ERA5-Land also matters for reproducibility: the reanalysis data are publicly available from the Copernicus Climate Data Store, and the team has released the complete source code for preprocessing, model training, evaluation and visualization on GitHub, with a permanent backup deposited on Zenodo for long-term citability. The derived dataset can be regenerated with the provided scripts, an increasingly important standard for machine learning studies in the geosciences.

The practical payoff the authors envision is a reliable decision-support tool for proactive agricultural water management and disaster mitigation. A forecast that flags emerging severe drought weeks in advance gives irrigation districts time to allocate scarce water, gives insurers time to prepare for claims, and gives governments time to mobilize relief before crop failure hardens into famine risk. The work was partially supported by the Natural Science Foundation of China and by several Jilin Province science and technology programs, reflecting the institutional priority that Chinese authorities have placed on drought preparedness after a series of costly events in recent decades, including the severe winter-spring drought of 2011 in East China and the intense 2019 drought linked to warm equatorial Pacific sea surface temperatures.

More broadly, the study validates the effectiveness of attention-based deep learning in processing complex land-atmosphere coupled systems, a class of problems where the signal is buried in noise, the relationships are non-linear, and the extremes matter more than the averages. As warming shifts precipitation patterns and accelerates evaporation across much of the world, the gap between meteorological and agricultural drought is likely to widen, and models that can read the soil directly, weigh their inputs intelligently, and explain what they learned will be at a premium. FAELSTM is a step in that direction: a demonstration that when a neural network is built to pay attention, both to its features and to its history, it can see a drought coming more clearly than the architectures that came before it.

Subject of Research: Deep learning-based agricultural drought prediction using attention-enhanced LSTM networks in China

Article Title: Based on improved long short-term memory network feature attention extraction for china drought prediction

Article References: Lv, W., Wang, D., Ji, Y., Xue, B., & Yang, S. (2026). Based on improved long short-term memory network feature attention extraction for china drought prediction. Theoretical and Applied Climatology, 157(9), Article 597. https://doi.org/10.1007/s00704-026-06534-y

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06534-y

Keywords: agricultural drought, deep learning, LSTM, attention mechanism, soil moisture, ERA5-Land, China, hydroclimatology, forecasting, food security, machine learning, water management

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

The research, led by Ali Haji Elyasi together with Mohsen Nasseri and Peyman Badiei of the School of Civil Engineering at the University of Tehran, set out to quantify how two large-scale teleconnections, the El Niño–Southern Oscillation (ENSO) and the North Sea–Caspian Pattern (NCP), shape the hydrological behavior of the Anzali Wetland over the period 2000 to 2024. Teleconnections are recurring patterns of atmospheric pressure and circulation that link weather in one part of the world to conditions in another. While their influence on regional temperature and rainfall is well documented, their connection to the dynamics of individual wetland ecosystems has remained largely unquantified, a gap the authors describe as a missing link.

To close that gap, the team assembled a suite of hydroclimatic variables, including precipitation, drought indices, minimum and maximum temperature, Caspian Sea level, and the surface area of the wetland itself, which they derived from satellite observations. All variables were standardized on a bi-monthly time scale, allowing the researchers to compare signals that are normally expressed in very different units. Before any correlation was computed, the series underwent rigorous quality control and pre-whitening using ARIMA and seasonal ARIMA models, a statistical step that strips out autocorrelation and seasonal structure so that apparent relationships between climate indices and wetland behavior cannot arise as artifacts of shared trends or persistence.

With the cleaned series in hand, the researchers deployed three complementary analytical tools. Cross-correlation functions measured the strength of the relationship between each teleconnection index and each hydroclimatic variable at different time lags. Wavelet coherence analysis, a technique borrowed from signal processing, revealed how strongly two time series are synchronized across different frequencies and how that synchronization evolves through time. Finally, structural equation modeling (SEM) allowed the team to test whether the teleconnections act on the wetland directly or through intermediate climatic pathways, effectively disentangling cause-like chains of influence that simpler correlation analysis cannot resolve.

The results reveal two strikingly different styles of influence. The ENSO index showed lagged relationships of roughly six months with precipitation, drought, and wetland extent, meaning that a shift in the tropical Pacific today echoes in the Caspian lowlands half a year later. This delay is physically plausible: ENSO anomalies propagate through the atmosphere and ocean over months, and their downstream effects on Middle Eastern circulation build gradually. The North Sea–Caspian Pattern, by contrast, acted almost immediately, with relationships appearing at lags of zero to two months and often in synchrony with the hydroclimatic variables themselves. NCP phases also aligned strongly with wetland area on sub-annual to annual scales, whereas ENSO’s fingerprint was episodic and event-driven, surfacing mainly during major El Niño and La Niña episodes.

Perhaps the most consequential finding came from the structural equation models. Both teleconnections were linked to the wetland primarily through indirect climatic mediation, with indirect pathways accounting for more than 72 percent of the NCP effect and more than 61 percent of the ENSO effect. In other words, these oscillations do not act on the wetland like a tap; instead, they reshape the regional climate, altering rainfall, drought severity, and temperature, and the wetland responds to those reshaped conditions. The models also found no significant synergistic interaction between the two patterns, indicating that ENSO and NCP operate as distinct yet complementary components of the atmospheric machinery governing the region.

The historical record makes the stakes vivid. Positive NCP phases coincided with wetland expansion during the decade from 2000 to 2009, while a 30 percent reduction in wetland area between 2020 and 2024 unfolded in step with persistently negative NCP conditions. That temporal alignment does not prove the atmosphere alone caused the shrinkage, and the authors are careful to frame teleconnections as contributing factors rather than sole drivers. Still, the correspondence suggests that a substantial portion of the wetland’s recent decline may reflect a climatic backdrop that local management cannot control, even as local stressors such as land conversion and sediment loading continue to erode the ecosystem’s resilience.

Methodologically, the study is notable for the care taken to avoid the classic pitfalls of lag-based climate analysis. Spurious cross-correlations are a well-known hazard when two autocorrelated series share a trend, and the pre-whitening procedure directly addresses this. The wavelet approach adds a second layer of protection by showing where in the time-frequency domain coherence genuinely exists, distinguishing persistent phase-aligned coupling from coincidental overlap. The SEM framework, increasingly popular in ecology and hydrology, then converts these pairwise associations into a network of direct and indirect pathways, quantified with standard goodness-of-fit measures. Together, the three methods triangulate a conclusion that any single technique alone could not support with confidence.

The study also claims a first: the earliest quantitative evidence of a linkage between the North Sea–Caspian Pattern and wetland dynamics. The NCP, identified in the early 2000s as an upper-level atmospheric pattern affecting the eastern Mediterranean and the Caspian region, has been linked to winter temperatures in Iran and to drought and vegetation responses across western Eurasia, but its role in wetland hydrology had not previously been pinned down. By demonstrating that NCP exerts a fast, phase-aligned influence on the Anzali system, the researchers effectively add a new, regionally tuned predictor to the toolkit available for wetland monitoring in the Caspian basin.

The practical implications extend well beyond one Iranian wetland. If NCP conditions can foreshadow wetland expansion or contraction within weeks to months, and ENSO can foreshadow them half a year ahead, then managers gain something they have historically lacked: a leading indicator. Anticipating a drying phase could inform decisions about water allocation, dredging, and habitat protection before crisis points are reached, while a forecast of favorable phases could guide restoration timing. More broadly, the work signals a shift in how wetland science accounts for climate variability, treating these ecosystems not as isolated victims of local exploitation but as sensitive recorders of planetary-scale atmospheric rhythms. As climate change alters both the background hydrology and potentially the behavior of the teleconnections themselves, understanding these distant controls will become essential for anyone hoping to keep the world’s wetlands, and the communities that depend on them, above water.

Subject of Research: Teleconnection influences on the spatiotemporal hydrological dynamics of the Anzali Wetland

Article Title: Unraveling a missing link: What role do teleconnections play as contributing factors in spatiotemporal wetland dynamics?

Article References: Elyasi, A. H., Nasseri, M., & Badiei, P. (2026). Unraveling a missing link: What role do teleconnections play as contributing factors in spatiotemporal wetland dynamics?. Theoretical and Applied Climatology, 157(10), Article 640. https://doi.org/10.1007/s00704-026-06565-5

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06565-5

Keywords: teleconnections, ENSO, North Sea–Caspian Pattern, Anzali Wetland, wetland dynamics, wavelet coherence, structural equation modeling, drought, Caspian Sea, hydroclimatology, remote sensing, Iran