Kinematic Porosity and Heteroscedasticity in Hard Rock Terrains
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
Heterogeneity in spatial variance
Introduction 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
Multivariate Approach to Groundwater Resources
Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks
Multivariate Approach to Groundwater ResourcesGroup GRP Range Group Median1 -0.75>GRP 3.96 l/hr, m
2 -0.75<GRP<-0.5 4.09 l/hr, m
3 0.5<GRP<0 6.08 l/hr, m
4 0<GRP 6.36 l/hr, m
4
3
2
1
01 2 3 4
GRP Group
LN(S
C)
Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks
Kinematic Porosity
• Based on simple fracture geometry (Carlsson and Olsson, 1993)
• Relationship between fracture spacing, relation to measurement face, average angle between fractures, average estimated hydraulic aperture
• Relatively simple to collect data• Influenced by surficial physical factors (weathering)
Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks
Kinematic Porosity
Area Rock typeFracture frequencyNa (m-1) 𝜖 eg
(m)λ
Kinematic porositynk
Median capacity(lit/hr)
Älgö Granite 2.13 1.5 0.001 0.25 0.08 % 375
Älgö Gneiss-granite 1.87 1.75 0.001 0.2 0.065 % 200
Älgö Sedimentary gneiss 1.57 1.5 0.001 0.2 0.05 % 100
Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks
• Kinematic porosity maps correlated to specific capacity maps (sig. = 0.003) but have a very low correlation coefficient (0.2)
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
