The study, conducted by Amaury de Souza of the Federal University of Mato Grosso do Sul and José Francisco de Oliveira Junior of Fluminense Federal University and the Federal University of Alagoas, focused on the capital cities of Midwest Brazil: Brasília, Goiânia, Cuiabá, and Campo Grande. The team drew on the TerraClimate dataset, a high-resolution global climate product with roughly four-kilometer spatial resolution, to extract monthly precipitation and actual evapotranspiration from 1958 to 2024. Crucially, the dataset contained no missing values, eliminating the need for gap-filling procedures that can introduce artificial structure into a time series. From these two variables, the researchers constructed what they call the Hydroclimatic Balance Index, or HBI — the difference between precipitation and actual evapotranspiration, accumulated over twelve months and standardized as a z-score.

The choice of actual evapotranspiration rather than potential evapotranspiration is what sets the HBI apart from its better-known cousin, the Standardized Precipitation Evapotranspiration Index, or SPEI. Potential evapotranspiration measures how much water the atmosphere would demand if supply were unlimited; actual evapotranspiration measures how much water is genuinely exchanged between the land surface and the atmosphere, constrained by soil moisture, vegetation dynamics, and land-surface feedbacks. In tropical continental environments where evapotranspiration is a major component of the hydrological cycle, that distinction matters. The authors stress that the HBI is not intended to replace established drought indices, but to complement them by capturing realized hydroclimatic conditions rather than atmospheric demand alone. As a benchmark, the team also computed the classic Standardized Precipitation Index at the twelve-month scale, SPI-12, which relies exclusively on rainfall.

Before turning to fractal analysis, the researchers established a rigorous statistical baseline. Linear regression of annual precipitation, evapotranspiration, and HBI series revealed only weak slopes with p-values all exceeding the five percent significance level and coefficients of determination that were vanishingly small. The non-parametric Mann-Kendall test, which operates on data ranks and is robust to the outliers that plague hydroclimatic records, told the same story: Kendall’s tau coefficients hovered near zero, confirming the absence of significant monotonic trends. The Pettitt change-point test, designed to detect abrupt structural shifts without assumptions of normality, found significant breakpoints only in the evapotranspiration series of Goiânia in 2001 and Cuiabá in 2009. By every conventional measure, the region’s climate looked stable — which is precisely what made the next set of results so striking.

That next step was Multifractal Detrended Fluctuation Analysis, or MFDFA, a technique developed by Kantelhardt and colleagues in 2002 that extends earlier methods for detecting long-range correlations in nonstationary signals. The procedure integrates the original series, divides it into segments of varying lengths, removes local polynomial trends from each segment, and then examines how fluctuation magnitudes scale with segment size. For a monofractal process, the generalized Hurst exponent h(q) remains constant regardless of the moment order q. For a multifractal process, h(q) varies systematically with q, revealing that small and large fluctuations obey different scaling rules — a hallmark of complex, intermittently organized systems. Rainfall, temperature, wind, and river flow have all been shown to behave this way, but multifractal assessments of drought indices in tropical continental settings have remained scarce.

The results were unambiguous. Across all four capitals, the generalized Hurst exponent declined systematically with increasing moment order, confirming genuine multifractal scaling in both SPI-12 and HBI-12 series. The Hurst exponent at q equals two ranged from approximately 0.87 to 1.11, values that indicate strong long-range dependence — a form of hydroclimatic memory in which wet and dry conditions cluster together rather than arriving randomly. Persistent systems of this kind are prone to drought clustering and prolonged anomalies, a property with direct implications for agriculture and hydropower in a region that anchors Brazil’s agricultural production and generates a substantial share of its electricity. The width of the singularity spectrum, denoted delta-alpha, served as the study’s measure of multifractal strength: values below 0.5 indicate weak multifractality, values between 0.5 and 1.0 moderate, and values above 1.0 strong.

The spatial patterns proved revealing. Brasília exhibited the weakest multifractality, with SPI-12 producing a narrow spectrum of just 0.194, though even there the HBI-12 spectrum widened to 0.517 when evapotranspiration entered the calculation. Goiânia showed strong multifractality for both indices, at 1.333 and 1.382 respectively, suggesting that rainfall variability alone already accounts for much of its complexity. The most dramatic contrasts emerged in Cuiabá and Campo Grande. Cuiabá jumped from weak multifractality under SPI-12 at 0.254 to strong multifractality under HBI-12 at 1.008, while Campo Grande surged from a moderate 0.755 to 1.488 — the strongest multifractal signature of any capital. In these locations, evapotranspiration processes, vegetation dynamics, soil moisture availability, and land-surface feedbacks amplify nonlinear fluctuations far beyond what precipitation alone can explain.

Perhaps the most consequential finding came from splitting the record into two sub-periods, 1958 to 1990 and 1991 to 2024. The recent period showed broader singularity spectra in several capitals, with Campo Grande reaching a delta-alpha of 1.938 and Cuiabá 1.341, indicating intensified intermittency and hydroclimatic heterogeneity in recent decades. Brasília, by contrast, showed a modest reduction, underscoring the spatially uneven character of the change. Spectral asymmetry values predominantly exceeded one, meaning that large-magnitude fluctuations — the extreme wet and dry events — contribute disproportionately to the multifractal organization. Yet throughout, generalized Hurst exponents remained above unity, confirming persistent long-range dependence across all cities and both periods. The intensification of variability, in other words, is happening within a persistently memory-laden system, a combination that favors clustering of extremes.

The contrast between the classical and fractal diagnoses carries a pointed message for drought monitoring. Linear regression, Mann-Kendall tests, and Pettitt analysis detected almost nothing, yet the multifractal framework revealed substantial structural variability, growing intermittency, and shifts in scaling behavior that no trend statistic could capture. The authors argue that hydroclimatic change in Central Brazil should not be judged solely by the presence or absence of monotonic trends; increasing persistence, enhanced intermittency, and greater scaling heterogeneity may be equally important indicators of environmental change. This resonates with a broader body of climate-complexity research showing that scaling diagnostics can expose structural variability invisible to conventional methods, particularly in regions governed by monsoon dynamics and land-atmosphere interactions.

The study’s implications extend beyond Brazil. The measured spectrum widths, ranging from roughly 0.19 to 1.94, are comparable to or exceed those reported for Mediterranean rainfall systems, Indian monsoon basins, African semi-arid regions, and East Asian monsoon domains — but the gap between precipitation-only and water-balance multifractality appears unusually large in Central Brazil, underscoring the outsized role of evapotranspiration in tropical continental hydroclimates. The authors acknowledge limitations: the analysis rests entirely on gridded TerraClimate data, which may smooth local extremes; only the twelve-month accumulation scale was evaluated; and causal attribution to land-use change, though plausible given the Cerrado’s rapid agricultural transformation, would require integration with remote sensing and land-cover datasets. Still, the core conclusion stands. Drought monitoring frameworks built on precipitation alone may systematically underestimate hydroclimatic complexity in monsoon-influenced tropical regions, and as warming and land-use change continue, complexity-based diagnostics may become essential tools for anticipating when quiet variability turns into visible crisis.

Subject of Research: Multifractal assessment of hydroclimatic variability and drought indices in Midwest Brazil

Article Title: Multifractal assessment of hydroclimatic variability in Midwest Brazil using the hydroclimatic balance index (HBI): a comparison with the standardized precipitation index (SPI)

Article References: de Souza, A., & de Oliveira Junior, J. F. (2026). Multifractal assessment of hydroclimatic variability in Midwest Brazil using the hydroclimatic balance index (HBI): a comparison with the standardized precipitation index (SPI). Theoretical and Applied Climatology, 157(10), Article 682. https://doi.org/10.1007/s00704-026-06467-6

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06467-6

Keywords: multifractal analysis, MFDFA, drought, hydroclimatic variability, Brazil, Cerrado, evapotranspiration, Standardized Precipitation Index, Hurst exponent, TerraClimate, South American Monsoon, water balance

The stakes of this kind of evaluation are far higher than an academic exercise in scorekeeping. Global climate models are the engines that generate the projections used by the Intergovernmental Panel on Climate Change, and they also supply the boundary conditions that drive regional climate models in so-called dynamical downscaling. If a global model misrepresents the circulation patterns, moisture transport or precipitation regimes of a particular region, every downstream projection inherits those errors. For South America, a continent that contains the Amazon rainforest, the vast wetlands of the La Plata Basin, the semiarid interior of northeastern Brazil and the dramatic seasonal reversal of the South American Monsoon, the choice of which model to trust is not a technical footnote. It shapes estimates of future water availability, agricultural viability, forest resilience and flood risk for hundreds of millions of people.

The research team framed their assessment around the historical period from 1979 to 2014, comparing each model’s simulations against ERA5, the state-of-the-art atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts. Reanalyses blend observations with numerical weather prediction to create a physically consistent record of the past climate, and ERA5 has become a standard benchmark for model evaluation worldwide. By measuring how closely each CMIP6 model tracks ERA5 across multiple atmospheric variables and vertical levels, the researchers could quantify not just whether a model gets surface temperature roughly right, but whether it captures the three-dimensional structure of the atmosphere—the winds aloft, the geopotential heights, the vertical distribution of moisture—that governs how weather systems actually form and evolve over the continent.

What makes the study genuinely distinctive is its multilevel design. Rather than confining the analysis to a single variable at the surface, the authors examined the atmosphere at different heights, recognizing that a model can simulate plausible surface conditions while simultaneously botching the upper-level circulation that steers storms and organizes convection. This vertical dimension matters enormously for South America, where the Bolivian High, an anticyclone that forms aloft during the austral summer, is intimately linked to the monsoon system and to deep convection over the Amazon. A model that fails to reproduce upper-level circulation may still appear competent in surface statistics while getting the fundamental dynamics wrong—a trap that single-variable evaluations routinely miss.

To make the comparison tractable, the researchers divided South America into five subdomains that capture the continent’s principal climatic regimes: the northern Amazon Basin, the southern Amazon Basin, the Northeast region of Brazil, the South American Monsoon domain, and the La Plata Basin. Each of these regions poses its own modeling challenge. The Amazon tests how well a model handles the coupling between forest, soil moisture and deep convection in a regime where precipitation is largely recycled from evapotranspiration. Northeast Brazil, with its semiarid climate punctuated by extreme droughts, probes the representation of the intertropical convergence zone and its seasonal migrations. The monsoon domain demands that a model capture a full seasonal cycle of onset, maturity and demise, while the La Plata Basin, one of the world’s great agricultural heartlands, is notorious for organized mesoscale convective systems that produce some of the most intense rainfall events on the planet.

Across these regions and variables, the team deployed a battery of statistical metrics—measures of bias, spatial pattern correlation, and the ability to reproduce observed variability—and then synthesized them through a comprehensive rating index, or CRI. This framework condenses many separate performance measures into a single score for each model in each region, allowing a consistent ranking that would otherwise be impossible when different metrics point in different directions. The approach addresses a long-standing problem in climate science: model evaluation often produces contradictory conclusions depending on which metric an analyst happens to emphasize, and a transparent, integrated index reduces the subjectivity inherent in model selection. It also echoes a broader movement in the field, reflected in recent benchmarking literature, toward systematic, multi-metric assessment rather than ad hoc comparisons.

The results reveal a striking geographic pattern. Model performance diverges most strongly in the tropical subdomains, where the interplay of convection, land surface feedbacks and large-scale circulation creates a punishing test for coarse-resolution global models. In the subtropical regions, by contrast, the models show considerably higher consistency with one another and with the reanalysis, suggesting that the large-scale dynamics there are more robustly captured. This dispersion in the tropics is a familiar refrain in climate modeling—convection remains one of the hardest processes to represent because it occurs at scales far smaller than a typical model grid cell and must be approximated through parameterizations—but the study quantifies just how much this limitation separates individual models from one another over South America.

At the top of the rankings, four models distinguish themselves. CNRM-CM6-1, developed by the French research community; GFDL-ESM4, from the United States Geophysical Fluid Dynamics Laboratory; MPI-ESM1-2-HR, the high-resolution configuration of the Max Planck Institute Earth System Model; and NorESM2-MM, the medium-resolution variant of the Norwegian Earth System Model, all deliver superior performance across multiple variables and multiple regions. Their common thread is instructive: several of these models incorporate relatively sophisticated atmospheric components or finer horizontal resolution, which helps them resolve the terrain, coastlines and circulation features that shape South American climate. At the other end of the spectrum, INM-CM4-8, KIOST and NESM3 show persistent limitations, particularly in simulating upper-level circulation and the precipitation processes that depend on it. The authors emphasize that these weaker models are not without value in a global context, but their specific failures over South America make them poor candidates for regional applications on this continent.

Perhaps the most practically important finding is that the best-ranked models also reproduce the observed monthly precipitation climatology and its variability more faithfully than their lower-ranked counterparts. Precipitation is the variable that matters most for water resources, hydropower and agriculture in South America, and it is notoriously difficult to simulate because it depends on the delicate interaction of moisture convergence, atmospheric stability and convection. The fact that the comprehensive rating index successfully identifies models that excel specifically in precipitation suggests that the framework captures something real about model quality rather than merely rewarding statistical conformity in easier variables. The authors explicitly position their ranking as a foundation for selecting boundary conditions for dynamical downscaling over South America, giving regional modeling groups a defensible, evidence-based starting point for their experiments.

The broader lesson of the study is one that climate scientists have been articulating with increasing urgency: there is no universally best climate model, and ensembles should not be treated as interchangeable collections of equals. A model that performs admirably over Europe or East Asia may stumble over the Amazon, and a model that excels at surface temperature may misrepresent the winds five kilometers above the surface. The authors’ central conclusion—that models should be chosen based on their demonstrated performance in the region of interest—represents a shift from the traditional practice of using all available models indiscriminately toward a more discriminating, regionally informed selection strategy. For a continent whose climate future hinges on the fate of the Amazon forest, the reliability of the monsoon and the behavior of the La Plata Basin’s rivers, knowing which models deserve a seat at the table is not a luxury. It is the difference between projections that inform sound adaptation policy and projections that quietly mislead it.

Subject of Research: Evaluation of CMIP6 global climate model performance over South America

Article Title: Assessment of CMIP6 models’ performance for South America: multilevel perspective

Article References: Assessment of CMIP6 models’ performance for South America: multilevel perspective. (n.d.). https://doi.org/10.1007/s00704-026-06585-1

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06585-1

Keywords: CMIP6, climate models, South America, ERA5, precipitation, Amazon Basin, South American Monsoon, La Plata Basin, model evaluation, dynamical downscaling, reanalysis, climate projections