Characterization of Spatially Heterogeneous Environmental Variables Through Multi‐Modal Generalized Sub‐Gaussian Distributions
Abstract We provide a sound theoretical framework for the characterization of randomly heterogeneous spatial fields exhibiting multi‐modal, long‐tailed probability densities. Multi‐modal distributions are at the core of conceptual models employed to represent heterogeneity of hydrogeological or geoc...
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| Format: | Article |
| Language: | English |
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Wiley
2025-03-01
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| Series: | Water Resources Research |
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| Online Access: | https://doi.org/10.1029/2024WR038487 |
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| author | Chiara Recalcati Alberto Guadagnini Monica Riva |
| author_facet | Chiara Recalcati Alberto Guadagnini Monica Riva |
| author_sort | Chiara Recalcati |
| collection | DOAJ |
| description | Abstract We provide a sound theoretical framework for the characterization of randomly heterogeneous spatial fields exhibiting multi‐modal, long‐tailed probability densities. Multi‐modal distributions are at the core of conceptual models employed to represent heterogeneity of hydrogeological or geochemical systems across which one can otherwise distinguish diverse regions whose location is uncertain. Within each region, the quantity of interest shows a distinct heterogeneous pattern that can be described through a generally non‐Gaussian distribution. Our analytical model embeds the joint formulation of the probability density of the target variable and its spatial increments. The distributions of the latter scale with separation distance between locations at which increments are evaluated. This feature is in line with documented experimental observations of a variety of Earth system quantities. Our stochastic modeling framework integrates approaches based on unimodal non‐Gaussian fields described through a Generalized Sub‐Gaussian model and (multi‐modal) distributions resulting from mixtures of Gaussian fields. These are recovered as specific instances within our comprehensive formulation. We apply this framework to an experimental data set consisting of a collection of dissolution rate fields obtained from high‐resolution nanoscale measurements acquired through Atomic Force Microscopy and documenting the dissolution behavior of a calcite sample under continuous flow conditions. Our findings demonstrate the capability of our stochastic approach to elucidate key statistical traits and scaling features inherent in the heterogeneous distributions of these types of environmental variables. |
| format | Article |
| id | doaj-art-d4e4fa7bdbfc40aa966e441725ea05d0 |
| institution | Kabale University |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-d4e4fa7bdbfc40aa966e441725ea05d02025-08-20T03:30:57ZengWileyWater Resources Research0043-13971944-79732025-03-01613n/an/a10.1029/2024WR038487Characterization of Spatially Heterogeneous Environmental Variables Through Multi‐Modal Generalized Sub‐Gaussian DistributionsChiara Recalcati0Alberto Guadagnini1Monica Riva2Department of Civil and Environmental Engineering Politecnico di Milano Milano ItalyDepartment of Civil and Environmental Engineering Politecnico di Milano Milano ItalyDepartment of Civil and Environmental Engineering Politecnico di Milano Milano ItalyAbstract We provide a sound theoretical framework for the characterization of randomly heterogeneous spatial fields exhibiting multi‐modal, long‐tailed probability densities. Multi‐modal distributions are at the core of conceptual models employed to represent heterogeneity of hydrogeological or geochemical systems across which one can otherwise distinguish diverse regions whose location is uncertain. Within each region, the quantity of interest shows a distinct heterogeneous pattern that can be described through a generally non‐Gaussian distribution. Our analytical model embeds the joint formulation of the probability density of the target variable and its spatial increments. The distributions of the latter scale with separation distance between locations at which increments are evaluated. This feature is in line with documented experimental observations of a variety of Earth system quantities. Our stochastic modeling framework integrates approaches based on unimodal non‐Gaussian fields described through a Generalized Sub‐Gaussian model and (multi‐modal) distributions resulting from mixtures of Gaussian fields. These are recovered as specific instances within our comprehensive formulation. We apply this framework to an experimental data set consisting of a collection of dissolution rate fields obtained from high‐resolution nanoscale measurements acquired through Atomic Force Microscopy and documenting the dissolution behavior of a calcite sample under continuous flow conditions. Our findings demonstrate the capability of our stochastic approach to elucidate key statistical traits and scaling features inherent in the heterogeneous distributions of these types of environmental variables.https://doi.org/10.1029/2024WR038487atomic force microscopynon Gaussian mixture modelstatistical scalingheavy‐tailed distributionsdissolution rate heterogeneitystochastic modeling |
| spellingShingle | Chiara Recalcati Alberto Guadagnini Monica Riva Characterization of Spatially Heterogeneous Environmental Variables Through Multi‐Modal Generalized Sub‐Gaussian Distributions Water Resources Research atomic force microscopy non Gaussian mixture model statistical scaling heavy‐tailed distributions dissolution rate heterogeneity stochastic modeling |
| title | Characterization of Spatially Heterogeneous Environmental Variables Through Multi‐Modal Generalized Sub‐Gaussian Distributions |
| title_full | Characterization of Spatially Heterogeneous Environmental Variables Through Multi‐Modal Generalized Sub‐Gaussian Distributions |
| title_fullStr | Characterization of Spatially Heterogeneous Environmental Variables Through Multi‐Modal Generalized Sub‐Gaussian Distributions |
| title_full_unstemmed | Characterization of Spatially Heterogeneous Environmental Variables Through Multi‐Modal Generalized Sub‐Gaussian Distributions |
| title_short | Characterization of Spatially Heterogeneous Environmental Variables Through Multi‐Modal Generalized Sub‐Gaussian Distributions |
| title_sort | characterization of spatially heterogeneous environmental variables through multi modal generalized sub gaussian distributions |
| topic | atomic force microscopy non Gaussian mixture model statistical scaling heavy‐tailed distributions dissolution rate heterogeneity stochastic modeling |
| url | https://doi.org/10.1029/2024WR038487 |
| work_keys_str_mv | AT chiararecalcati characterizationofspatiallyheterogeneousenvironmentalvariablesthroughmultimodalgeneralizedsubgaussiandistributions AT albertoguadagnini characterizationofspatiallyheterogeneousenvironmentalvariablesthroughmultimodalgeneralizedsubgaussiandistributions AT monicariva characterizationofspatiallyheterogeneousenvironmentalvariablesthroughmultimodalgeneralizedsubgaussiandistributions |