Heterogeneity and non-stationary variance in hard rock hydrogeology

Extreme variability and its role in hydrogeology

Land and Water Resources EngineeringRobert Earon

• Changing Climate• Limited Storage• Increasing residency near coast• Heteroscedasticity

There is no annual shortage of water in Sweden.Problems arise due to temporal distribution of meteoric water and water storage.

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Grou

ndw

ater

Leve

l (m

und

er G

roun

d Su

rfac

e)

Glacial Till

Hard Rock

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Heterogeneity

Range

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Nugget

Sill

Spatial AnisotropyIntroduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Spatial AnisotropyIntroduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Spatial AnisotropyIntroduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Heterogeneity in spatial variance

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

• ANOVA, t-test both indicate samples significantly (sig.<0.000) different

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Heterogeneity in spatial variance

AreaMedian

Distance (m) n Mean Median Variance Skewness KurtosisNorth 1802 10264 1.04 0.39 3.18 3.92 23.43South 1930 14169 1.45 0.53 5.46 3.33 15.32

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Multivariate Approach to Groundwater Resources

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Multivariate Approach to Groundwater Resources

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Review

• Heterogeneity places a high burden on point estimates for regional or even local characterization

• Heterogenic, anisotropic variability implies caution should be taken when applying statistical tools

• From the standpoint of limited-resource hydrogeological investigation, plausibility of applying and developing other tools

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Questions?

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks