The evaluation of groundwater resources in the crystalline basement of northern Nigeria

A methodology of assessment is presented of the groundwater resources available in fracture zones, within the weathered mantle of gneiss, migmatite and granite. A model of weathering is developed, and values of porosity, hydraulic conductivity and electrical resistivity assigned to the different grades of weathering. A geophysical technique is developed, based upon a combination of electrical resistivity profiling and sounding, which allows a volume estimate of the various weathering grades to be made. A finite difference algorithm is used for this estimate which enables the apparent resistivity response of an inhomogeneous resistivity distribution to be calculated. An iterative approach is then adopted, adjusting the resistivity model until the calculated response agrees with the field data. An analysis of recharge in a savanna climate is developed based upon the Monteith equation for predicting evapotranspiration, and upon a model of unsaturated zone soil moisture movement. The recharge function developed is included in a one dimensional catchment water balance model. The results from this model are compared with observed runoff and groundwater hydrographs. The estimate of recharge is combined with the estimate of aquifer storage to produce an assessment of available groundwater. Optimal methods for the development of the resource are discussed. While developed in Northern Nigeria, the methodology of assessment is applicable to any similar geological and climatological environment

Technical note: Disentangling the groundwater response to Earth and atmospheric tides to improve subsurface characterisation

The groundwater response to Earth tides and atmospheric pressure changes can be used to understand subsurface processes and estimate hydraulic and hydro-mechanical properties. We develop a generalised frequency domain approach to disentangle the impacts of Earth and atmospheric tides on groundwater level responses. By considering the complex harmonic properties of the signal, we improve upon a previous method for quantifying barometric efficiency (BE), while simultaneously assessing system confinement and estimating hydraulic conductivity and specific storage. We demonstrate and validate this novel approach using an example barometric and groundwater pressure record with strong Earth tide influences. Our method enables improved and rapid assessment of subsurface processes and properties using standard pressure measurements

Runoff and focused groundwater recharge response to flooding rains in the arid zone of Australia

A groundwater recharge investigation in the arid zone of Australia is presented. The investigation used a wide range of hydrogeological techniques including geological mapping, surface and borehole geophysics, groundwater hydraulics, streambed temperature and pressure monitoring, and hydrogeochemical and environmental tracer sampling, and it was complemented by analysis of rainfall intensity from 18 tipping-bucked rain gauges, climate data and stream runoff measurements. Run-off and recharge from a 200-mm rainfall event in January 2015, the largest daily rainfall in the local 50-year record, were investigated in detail. While this major storm provided substantial run-off as a potential source for focused, indirect recharge, it only produced enough actual recharge to the shallow aquifer to temporarily halt a long-term groundwater recession. A series of smaller rainfall-runoff events in 2016 produced a similar recharge response. The results suggest that the total magnitude of a flood event is not the main control on indirect groundwater recharge at this location. A deeper aquifer shows no hydraulic response to surface-water flow events and is isolated from the shallow system, consistent with its Pleistocene groundwater age. This supports a growing body of evidence indicating that attributing or predicting generalised changes in recharge to changes in climate in dryland environments should not be attempted without first unravelling the dynamic processes governing groundwater recharge in the locality of interest. The results should prompt more detailed and long-term field investigation in other arid zone locations to further understand the episodic and nonlinear nature of recharge in such environments

An objective frequency domain method for quantifying confined aquifer compressible storage using Earth and atmospheric tides

The groundwater hydraulic head response to the worldwide and ubiquitous atmospheric tide at 2 cycles per day (cpd) is a direct function of confined aquifer compressible storage. The ratio of the responses of hydraulic head to the atmospheric pressure change is a measure of aquifer barometric efficiency, from which formation compressibility and aquifer specific storage can be determined in situ rather than resorting to laboratory or aquifer pumping tests. The Earth tide also impacts the hydraulic head response at the same frequency, and a method is developed here to quantify and remove this interference. As a result, the barometric efficiency can be routinely calculated from 6-hourly hydraulic head, atmospheric pressure, and modeled Earth tide records where available for a minimum of 15 days duration. This new approach will be of critical importance in assessing worldwide problems of land subsidence or groundwater resource evaluation that both occur due to groundwater abstractio

Vertical hydraulic conductivity of a clayey-silt aquitard: accelerated fluid flow in a centrifuge permeameter compared with in situ conditions

This discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The revised manuscript was not accepted.Evaluating the possibility of leakage through low permeability geological strata is critically important for sustainable water supplies, extraction of fuels from strata such as coal beds, and confinement of waste within the earth. Characterizing low or negligible flow rates and transport of solutes can require impractically long periods of field or laboratory testing, but is necessary for evaluations over regional areas and over multi-decadal timescales. The current work reports a custom designed centrifuge permeameter (CP) system, which can provide relatively rapid and reliable hydraulic conductivity (K) measurement compared to column permeameter tests at standard gravity (1g). Linear fluid velocity through a low K porous sample is linearly related to g-level during a CP flight unless consolidation or geochemical reactions occur. The CP module is designed to fit within a standard 2 m diameter, geotechnical centrifuge with a capacity for sample dimensions of 30 to 100 mm diameter and 30 to 200 mm in length. At maximum RPM the resultant centrifugal force is equivalent to 550g at base of sample or a total stress of ~2 MPa. K is calculated by measuring influent and effluent volumes. A custom designed mounting system allows minimal disturbance of drill core samples and a centrifugal force that represents realistic in situ stress conditions is applied. Formation fluids were used as influent to limit any shrink-swell phenomena which may alter the resultant K value. Vertical hydraulic conductivity (Kv) results from CP testing of core from the sites in the same clayey silt formation varied (10−7 to 10−9 m s−1, n = 14) but higher than 1g column permeameter tests of adjacent core using deionized water (10−9 to 10−11 m s−1, n = 7). Results at one site were similar to in situ Kv values (3 × 10−9 m s−1) from pore pressure responses within a 30 m clayey sequence in a homogenous area of the formation. Kv sensitivity to sample heterogeneity was observed, and anomalous flow via preferential pathways could be readily identified. Results demonstrate the utility of centrifuge testing for measuring minimum K values that can contribute to assessments of geological formations at large scale. The importance of using realistic stress conditions and influent geochemistry during hydraulic testing is also demonstrated.Australian Research CouncilNational Water Commissio

Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations

In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and Kohatsu-Higa (2003). Efficient path-generation algorithms, such as Linear Transformation and Principal Component Analysis, exhibit a high computational cost in a market with time-dependent volatilities. We present a new and fast Cholesky algorithm for block matrices that makes the Linear Transformation even more convenient. Moreover, we propose a new-path generation technique based on a Kronecker Product Approximation. This construction returns the same accuracy of the Linear Transformation used for the computation of the deltas and the prices in the case of correlated asset returns while requiring a lower computational time. All these techniques can be easily employed for stochastic volatility models based on the mixture of multi-dimensional dynamics introduced by Brigo et al. (2004).Comment: 16 page

Future-proofing hydrogeology by revising groundwater monitoring practice

Groundwater is an important global resource and its sustainable use faces major challenges. New methods and advances in computational science could lead to much improved understanding of groundwater processes and subsurface properties. A closer look at current groundwater monitoring practice reveals the need for updates with a special focus on the benefits of high-frequency and high-resolution datasets. To future-proof hydrogeology, this paper raises awareness about the necessity for improvement, provides initial recommendations and advocates for the development of universal guide-lines

Technical Note: Disentangling the groundwater response to Earth and atmospheric tides to improve subsurface characterisation

The groundwater response to Earth tides and atmospheric pressure changes can be used to understand subsurface processes and estimate hydraulic and hydro-mechanical properties. We develop a generalised frequency domain approach to disentangle the impacts of Earth and atmospheric tides on groundwater level responses. By considering the complex harmonic properties of the signal, we improve upon a previous method for quantifying barometric efficiency (BE), while simultaneously assessing system confinement and estimating hydraulic conductivity and specific storage. We demonstrate and validate this novel approach using an example barometric and groundwater pressure record with strong Earth tide influences. Our method enables improved and rapid assessment of subsurface processes and properties using standard pressure measurements

Vertical groundwater storage properties and changes in confinement determined using hydraulic head response to atmospheric tides

Accurate determination of groundwater state of confinement and compressible storage properties at vertical resolution over depth is notoriously difficult. We use the hydraulic head response to atmospheric tides at 2 cpd frequency as a tracer to quantify barometric efficiency (BE) and specific storage (Ss) over depth. Records of synthesized Earth tides, atmospheric pressure, and hydraulic heads measured in nine piezometers completed at depths between 5 and 55 m into unconsolidated smectitic clay and silt, sand and gravel were examined in the frequency domain. The barometric efficiency increased over depth from ∼0.05 in silty clay to ∼0.15 in sands and gravels. BE for silty clay was confirmed by calculating the loading efficiency as 0.95 using rainfall at the surface. Specific storage was calculated using effective rather than total moisture. The differences in phase between atmospheric pressure and hydraulic heads at 2 cpd were ∼180° below 10 m indicating confined conditions despite the low BE. Heads in the sediment above a fine sand and silt layer at 12 m exhibited a time variable phase difference between 0° and 180° indicating varying confinement. Our results illustrate that the atmospheric tide at 2 cpd is a powerful natural tracer for quantifying groundwater state of confinement and compressible storage properties in layered formations from hydraulic heads and atmospheric pressure records without the need for externally induced hydraulic stress. This approach could significantly improve the development of conceptual hydrogeological model used for groundwater resource development and management