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A mathematical model for efficient groundwater management

Groundwater reservoirs form one of the most important sources of water available for human consumption. In India, it is the most preferred source of water due to its widespread availability, dependability and relatively low capital cost. But indiscriminate extraction of groundwater in certain areas of the country is affecting the availability of our most basic resource. The brunt of this current crisis is mainly borne by farmers; almost 92% of all the groundwater extracted is for irrigation, making Indian agriculture very dependent on groundwater.

Researchers from the Department of Civil Engineering at the Indian Institute of Science have now developed a mathematical model that can be used to get optimum cost estimates for pumping out groundwater, while avoiding-over extraction.

“Efficient groundwater management is an important need in our country. All we need is the input data to start using this method and come up with effective estimates to efficiently manage groundwater in India” says Prof. D Nagesh Kumar, one of the authors of the paper.

Groundwater is the water present beneath the earth’s surface, in soil pores and rock fractures. Once extracted, it is recharged with water from the surface, mainly through rainfall, rivers and streams. When too much water is extracted from any one ground water source, it affects not just the level of water in a particular area, but also the purity of water in nearby sources. Low groundwater levels have found to cause excess salinity of river water sources close by. On the other hand, when groundwater is not adequately extracted, it could cause water logging and increased soil salinity. Pumping out optimal amounts of groundwater, while maintaining the cost at a minimum, is a priority for any nation.

Researchers from IISc, Bangalore and BITS Pilani, Hyderabad in collaboration with the Department of Geosciences and Environment at The Ecole Nationale Superieure des Mines de Saint-Etienne, France have developed a mathematical tool, Multi-Objective Fuzzy Optimization (MOFO), to estimate the amount of water that can be extracted at various groundwater sources. The tool also measures the effect extraction can have on nearby water sources, while also keeping other constraints, like cost, under check.

The study area chosen was the town of Thiers, a major town in the Loire region in France. The area contains two rivers, Allier and Dore, whose water levels, along with the water levels of other wells in the area, were constantly monitored. The team was then able, using the MOFO model, to come up with satisfactory estimates for costs and the maximum amount of groundwater that could be pumped out. The study was used in the establishment of new pumping wells in the Dore river catchment area to satisfy the growing water demand of the town of Thiers.

Three objectives were considered in the study: “maximum discharge” or the maximum amount of groundwater extractable without affecting other nearby sources considerably, minimizing the pumping cost, and minimizing the piping cost -- the cost of laying pipes to make the water ready for use. Currently popular methods focus on optimizing each of the objectives individually; but since the objectives could be interdependent, the estimates made using these methods aren’t quite effective. For example, if the pumping cost is reduced, it also reduces the maximum amount of extractable water.

The MOFO model requires a best value, maximum discharge or minimum costs, and a worst value, minimum discharge or maximum costs, for each of the objectives considered. These values were obtained using methods like Analytical Element Method (AEM) and Particle Swarm Optimization (PSO). Once the values are obtained, the MOFO method is applied to come up with an optimum value, close to the best value, for each of the objectives, providing estimates for maximum amount of extractable water, pumping cost and piping cost. These estimates were found to be efficient and more cost effective compared to current methods.

The successful use of this method depends on the amount of input data, like water level at various surface and ground-water sources, cost of digging wells, cost of pumping the groundwater out and other groundwater policies, that is available.

About the authors:

Prof. D Nagesh Kumar is a Professor at the Department of Civil Engineering, IISc.


Prof. K Srinivas Raju is a Professor at BITS Pilani, Hyderabad.


Shishir Gaur and Didier Graillot are researchers at the Department of Geosciences and Environment at The Ecole Nationale Superieure des Mines de Saint-Etienne, France.


About the paper:

The paper appeared in the journal Hydrological Processes last month.