The classical Darcy law is generalized by regarding the water flow as a function of a noninteger order derivative of the piezometric head. This generalized law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Two methods including Frobenius and Adomian decomposition method are used to obtain an asymptotic analytical solution to the generalized groundwater flow equation. The solution obtained via Frobenius method is valid in the vicinity of the borehole. This solution is in perfect agreement with the data observed from the pumping test performed by the institute for groundwater study on one of their boreholes settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rateQand monitoring the piezometric head for 350 minutes. Numerical solutions obtained via Adomian method are compared with the Barker generalized radial flow model for which a fractal dimension for the flow is assumed. Proposition for uncertainties in groundwater studies was given.

In 1934, Act No. 38 of 1938 was approved, providing permission to construct the Vaal Dam and develop the Vaalharts Irrigation Scheme There are currently 1 200 plots varying in size from 25 to -75 ha and covering a total area of 35 302 ha. Water logging and salinisation are being experienced, leading to research being initiated in the area. The area researched stretches from Jan Kempdorp in the south to Taung (the Dry Harts River) in the north. A sampling network of 246 piezometers was installed to monitor the water levels and electrical conductivity (EC) over a period of 1 year. It was found that the leaching requirement to ensure sustainable irrigation is 611.5 mm/a. According to the water balance this requirement is 562 mm/a. Salt deposited through irrigation water amounts to 4.65 t/ha per annum. The total dissolved salts (TDS) averaged 1 005 mg/ℓ in 1976 and 1 350 mg/ℓ in 2004, an average increase per annum of 13 mg/ℓ. At the time of this research TDS was 1 476 mg/ℓ, representing an increase of 96 mg/ℓ in 5 years, an average increase per annum of 19.25 mg/ℓ. Irrigated salt deposits not drained build up in the soil at a rate of 0.8 t/ha per annum. Results of this study suggest that upgrading of all infrastructure is essential. Suitable internal subsurface drainage should be cleaned, unsuitable drainage replaced and spacing decreased to drain the area more effectively. Effective drainage would minimise the salt build-up in the soil, have a positive influence on the sustainability of irrigation farming and improve crop yields and quality in the area. The drained water can be reticulated into an evaporation pond to confine the salt mass, thus preventing it from influencing the environment and other activities downstream.

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From South African and international experience, it is known that coal mining has a pronounced impact on surface and groundwater quality and quantity. The influx of water may be as low as 1% of rainfall for underground mines to as much as 20% for opencast mines. Such differences may influence the quantity and quality of surface water and groundwater resources at the local scale and further afield. The Waterberg coal reserves represent the only area with proven coal reserves which are still available for development in South Africa. These reserves are targeted for large-scale mining in the near future, and are situated in a relatively dry part of South Africa. In view of the low rainfall and limited surface water resources, the necessary level of safeguard measures to ensure the quantity and quality of existing water resources is unclear. Experience from other areas cannot necessarily be extrapolated directly. A scoping level study was performed to consolidate the existing information on the geohydrology and pre-mining water quantity and quality of water resources associated with the Waterberg coal reserves. New data regarding water quality and acid-base potential for the different geological areas (through field investigations) and geology and mining methods were obtained. Findings showed a significant likely impact on groundwater resources, with a potential for generation of acid mine drainage, although low transmissivities will in all probability prevent decant after back-filling is complete.

Freshwater shortage already affects large parts of the world, and is expected to increase rapidly over the coming decades as a result of increased water demands and the impacts of climate change. Global-scale water risk or stress maps are available online, but these lack quantitative information on local freshwater availability, rendering them unsuitable for water risk assessment from an operational perspective, i.e. when comparing water availability to a specific quantified water demand (in m 3 s −1 rather than generic risk indicators). Therefore, our main goal was to develop a rapid screening method to estimate current and future operational freshwater availability using global-scale models. Operational Freshwater Availability (OFWA) was computed using the PCR-GLOBWB global hydrology and water resources model, coupled to a global MODFLOW groundwater model. PCR-GLOBWB was forced with rainfall and temperature fields from the IPSL-CM5A-LR climate model under the RCP6.0 climate scenario, with water demands based on the SSP2 socio-economic scenario. Unique to our study are the downscaling of the coupled PCR-GLOBWB-MODFLOW model to 90 m resolution and the provision of quantitative estimates on long term trends in operational freshwater availability. Our results showed a high, i.e. operationally relevant, accuracy for operational surface water availability, while the uncertainty about operational groundwater availability remained high due to limited availability of subsurface data. With this method, we developed a modelling capacity for rapidly generating scenario-based water availability projections with operational relevance in a rigorous, systematic way, such that it Water Resour Manage (2016) 30:3013-3026 DOI 10.1007/s11269-016-1327-5 Electronic supplementary