Significance
Society faces the multifaceted crossroads dilemma of sustainably balancing today’s livelihood with future resource needs. Currently, agriculture is tapping the High Plains Aquifer beyond natural replenishment rates to grow irrigated crops and livestock that augment global food stocks, and science-based information is needed to guide choices. We present new methods to project trends in groundwater pumping and irrigated corn and cattle production. Although production declines are inevitable, scenario analysis substantiates the impacts of increasing near-term water savings, which would extend the usable lifetime of the aquifer, increase net production, and generate a less dramatic production decline.
[1] In advective transport through weakly heterogeneous aquifers of random stationary and isotropic three-dimensional permeability distribution, transverse macrodispersivity a T is found to be zero. This was determined in the past by solving the transport equation at first order in the log conductivity variance s Y 2 . However, field findings indicate the presence of small but finite a T . The aim of the paper is to determine a T for highly heterogeneous formations using a model that contains inclusions of conductivity K, submerged in a matrix of conductivity K 0 , for large k = K/K 0 . In the dilute medium approximation, valid for small volume fraction n, but arbitrary k, and for spherical inclusions, it is found that a T = 0 because of the axisymmetry of flow past a sphere. A medium made up of rotational ellipsoids of arbitrary random orientation, macroscopically isotropic, and of the same k and n is devised as a counterexample. It is found that because of the intertwining of streamlines a T > 0, being of order (k À 1) 4 for k ! 1. These findings are confirmed by accurate numerical simulations of flow through a large number of interacting inclusions; for k = 10 and n = 0.2 (jamming limit), the large value a T /a L ' 0.15 is attained. The numerical simulations display the strong permanent deformation of stream tubes responsible for this phenomenon, coined as ''advective mixing.'' The two-point covariance, used in practice in order to characterize the aquifer structure, is not able to detect the structures that produce advective mixing. Nevertheless, the presence of high-conductivity lenses inclined with respect to the mean flow may explain the occurrence of finite a T in field applications.
Abstract. The flux along a horizontal well in uniform flow is examined using an analytic three-dimensional, steady model. Wells with uniform head and low pumping rates have gaining sections along which water enters the well and losing sections along which water exits. Such a well may provide a conduit for contaminated groundwater to be drawn into the well, conveyed a large distance, and injected into an uncontaminated region of an aquifer. Dimensionless ratios of the well's length L and radius R, aquifer thickness H, and uniform flow rate U are developed to quantify the minimum pumping rate Q min at which no losing section occurs. The ratio Qmin/(ULH) is presented as a nomograph using R/H and L/H for placement parallel to flow and is 6rrR/H for placement perpendicular to flow, and a parabolic relationship between these limiting cases is developed for placement oblique to flow. Capture zone geometry is quantified using Qmin/(ULH).
[1] An integrated foundation is presented to study the impacts of external forcings on irrigated agricultural systems. Individually, models are presented that simulate groundwater hydrogeology and econometric farm level crop choices and irrigated water use. The natural association between groundwater wells and agricultural parcels is employed to couple these models using geographic information science technology and open modeling interface protocols. This approach is used to study the collective action problem of the common pool. Three different policies (existing, regulation, and incentive based) are studied in the semiarid grasslands overlying the Ogallala Aquifer in the central United States. Results show that while regulation using the prior appropriation doctrine and incentives using a water buy-back program may each achieve the same level of water savings across the study region, each policy has a different impact on spatial patterns of groundwater declines and farm level economic activity. This represents the first time that groundwater and econometric models of irrigated agriculture have been integrated at the well-parcel level and provides methods for scientific investigation of this coupled natural-human system. Results are useful for science to inform decision making and public policy debate.
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