A statistical makeover for soil data reshapes how scientists read pollution maps

A seemingly technical choice about how soil chemistry data are prepared before analysis can dramatically change what scientists conclude about pollution in urban landscapes, according to a new study of a peri-urban retention basin in Ljubljana, Slovenia. The research, published in Discover Soil, compared two standard ways of processing portable X-ray fluorescence (pXRF) measurements before a widely used statistical technique called principal component analysis, or PCA. The differences were striking: on identical soil samples, the two preprocessing methods assigned sharply different amounts of variance to the leading statistical axes, produced different elemental patterns, and even changed the outcome of formal group tests. Because such ordinations are often used to define geochemical zones, select follow-up sampling sites and explain regulatory exceedances, the finding carries a practical warning for environmental monitoring programmes far beyond one Slovenian basin.

The problem at the heart of the study is one that geochemists have wrestled with for four decades. Elemental concentrations measured in soil are compositional data: each element is reported as a part of a constrained whole, relative to a fixed total. When one part rises, the others must fall in relative terms, even if nothing has changed in absolute mass. Applying ordinary statistical tools designed for unconstrained variables to such closed data can generate spurious covariances and misleading gradients. The standard workaround, z-score standardisation, rescales each element to a common mean and spread but does nothing to remove this closure constraint. A z-scored calcium value is still calculated from a closed part of a composition, so the mathematical compensation among elements remains entangled with genuine geochemical signals.

The alternative tested by Nejc Golob and Vesna Zupanc is the centred log-ratio, or CLR, transformation. Rather than comparing elements through absolute magnitudes, CLR expresses each element as a logarithm of its ratio to the geometric mean of all measured elements in the sample. This moves the data into a space where Euclidean distances and PCA are mathematically meaningful for compositional data. The researchers applied both workflows to the same 17-element matrix from 61 georeferenced soil profiles sampled in two layers, using an Olympus Delta Premium 50 pXRF instrument operated in Soil mode with dual-beam excitation and calibration verified against certified reference materials. Every one of the 122 samples returned strictly positive readings for all 17 elements, a crucial requirement for log-ratio methods that cannot handle zeros.

The quantitative contrast between the two approaches was large. In the upper soil layer, conventional z-score PCA explained 26.1 percent of variance on the first principal component and 21.1 percent on the second, whereas CLR-PCA explained 44.8 percent and 33.7 percent respectively. In the lower layer the gap widened further: 31.5 and 21.7 percent for the z-score approach against 49.7 and 36.0 percent for CLR-PCA, pushing cumulative variance captured by the first two CLR axes to 85.7 percent. In other words, the log-ratio transformation condensed most of the compositional structure of the dataset into just two interpretable dimensions, while the conventional approach left that structure smeared across more axes.

The loading structures told an equally consequential story. Under z-score PCA, abundant lithogenic elements such as iron, chromium, zirconium and rubidium dominated the first axis together with trace metals, mixing dilution effects with enrichment signals of comparable magnitude. CLR-PCA instead resolved a clear carbonate-phosphate versus silicate contrast, led by calcium and phosphorus set against silicon, zirconium and aluminium. Crucially, lead, copper, zinc and arsenic did not appear among the largest loadings on either leading CLR axis in either layer. Correlating the axis scores with independent geoaccumulation indices, which benchmark measured concentrations against regional background values, showed only moderate associations for copper (r = 0.52) and zinc (r = 0.40) and weak ones for lead and arsenic (r below 0.15). The dominant CLR gradient is therefore a compositional balance, not a simple pollution map, and the authors caution explicitly against reading it as one.

The trace metals were not absent from the ordination, however. They formed a coherent signal on lower-variance axes: in the upper layer, the fourth component, carrying just 4.4 percent of variance, contrasted lead against nickel and correlated strongly with the lead geoaccumulation index (r = 0.82), while the third component captured arsenic (r = -0.71). Under z-score PCA these same metals had been folded into the first axis alongside lithogenic elements and could not be resolved separately at all. This matters because a routine two-component summary of the z-score ordination would miss the metal signal entirely, while a two-component summary of the CLR ordination would correctly reveal that metal enrichment, though present, is minor relative to the basin-wide carbonate-phosphate balance.

To test how sensitive the results were to a handful of unusual samples, the researchers also ran a robust PCA based on a minimum covariance determinant estimator. In the lower layer, the correlation between classical and robust first-axis scores was nearly perfect at r = 0.994, indicating that the main gradient there is stable and not an artefact of a few high-leverage observations. In the topsoil, by contrast, the correlation dropped to r = 0.787, showing that ordinary PCA in the upper layer is noticeably influenced by specific samples, most of them grassland, riverbed and forest points with unusual calcium-phosphorus versus silicate balances rather than contamination hotspots. Topsoil, which receives atmospheric deposition, flood sediment and accumulating organic matter, is simply more heterogeneous, and the robust analysis serves as a diagnostic of where caution is warranted rather than a reason to delete samples.

Preprocessing even changed the verdict of formal hypothesis tests. A PERMANOVA on the CLR distance matrix found significant land-use effects in both layers, whereas the same test on the z-score-standardised matrix produced a stronger result in the upper layer but a non-significant one in the lower layer. Because the land-use groups were strongly unbalanced, with only four forest points and a single riverbed site, the authors also ran a dispersion test, which suggested that part of the upper-layer signal reflected within-group spread rather than shifts in group means. An additional check with an isometric log-ratio transformation, grouping elements into silicate, carbonate-biogenic and metal-oxide balances, reproduced the leading CLR gradient with correlations of 0.96 in both layers, confirming that the calcium-phosphorus contrast was not an artefact of the specific transformation chosen. Notably, the depth contrast persisted even after excluding the 31 cultivated-field points where tillage might homogenise the profile.

The regulatory implications are subtle but important. Screening against Slovenian limit values revealed only rare, scattered, single-element exceedances, affecting 2 of 61 samples for lead and 1 to 2 for zinc, and geoaccumulation indices placed nearly all samples in the unpolluted to unpolluted-moderate classes. Neither ordination, in other words, should be mistaken for a contamination map, and only individual element concentrations can determine a legal exceedance. But when PCA is used to design follow-up sampling or explain exceedance patterns, the geometry underneath must be defensible. A z-score analysis that confounds carbonate dilution with metal enrichment could direct sampling to the wrong locations, while CLR scores should be reported as compositional tendencies rather than concentration classes.

The authors are careful to frame their conclusion as site-specific rather than universal. The Brdnikova basin, which covers roughly 42 hectares and receives runoff and sediment from the whole Glinščica catchment while remaining under active agricultural use, is a mosaic of alluvial deposits, sandstone-influenced margins, farmland and semi-natural vegetation, exactly the kind of mixed-source setting where compositional effects are strongest. In a mining district, a landfill margin or a volcanic soil, different elements would define the dominant balances and the calcium-phosphorus pattern would not necessarily recur. The methodological lesson, however, travels well: closed element compositions should be opened through log ratios before Euclidean multivariate methods are applied, non-detect replacement rules should be documented transparently, robust diagnostics should accompany ordinary ordinations, and broader validation across sites and element suites is needed before CLR-PCA becomes a default for pXRF-based soil monitoring everywhere.

Subject of Research: Comparison of centred log-ratio and z-score preprocessing for PCA of pXRF soil geochemistry in a peri-urban retention basin

Article Title: Comparing centred log ratio and conventional standardisation for principal component analysis of portable X ray fluorescence soil geochemistry in a peri urban retention basin

Article References: Golob, N., & Zupanc, V. (2026). Comparing centred log ratio and conventional standardisation for principal component analysis of portable X ray fluorescence soil geochemistry in a peri urban retention basin. Discover Soil, 3(1), Article 196. https://doi.org/10.1007/s44378-026-00338-2

Image Credits: AI Generated

DOI: 10.1007/s44378-026-00338-2

Keywords: pXRF, soil geochemistry, compositional data analysis, centred log-ratio, principal component analysis, robust PCA, retention basin, urban soil monitoring, geoaccumulation index, PERMANOVA, Slovenia, Comparing