Growth of groundwater mounds affected by in‐transit water

Abstract

We appreciate R. Brock's interest and comments on our paper but are unsure about the meaning of his comment 'although a nonuniform porosity can lead to significantly larger mound heights, this will not always be the case.' Certainly, we agree that the increase in mound height caused by a reduced specific yield beneath the recharge area is small when the reduced specific yield is nearly the same as the specific yield external to the recharge area. This is clearly shown in our Figure 4 [Ortiz et al., 1978]. Nearly uniform specific yields result when the recharge rate is small in comparison to the hydraulic conductivity as shown by (6). Calculations of mound height from Figure 4 will show that the ratio of the mound height with nonuniform specific yields to the mound height with uniform specific yield decreases as time increases, in agreement with Brock. The difference between the mound heights, calculated with and without reduced specific yield, increases, however. It is the relative error that decreases as was mentioned in our discussion of Figure 2. We are also aware that the effect on nonlinearity tends to offset the increase • Now with the Colorado-Wyoming Area, USDA, Science and Education Administration, Fort Collins, Colorado 80523.caused by a reduced specific yield. Brock provides a method for quantifying the effects of nonlinearity.It seems worth emphasizing that our procedures provide a means of relating the reduced specific yield to the recharge rate and, thereby, an improved way of relating mound growth to recharge rate. However, our equation (6) does not apply for the case where recharge has ceased and the mound is receding. The mound will not necessarily begin to recede at the moment recharge ceases, however, because drainage of the in-transit water will continue for some time after the flux at the ground surface becomes zero. The rate of drainage of in-transit water will decrease with time, and eventually, the mound will begin to recede. An appropriate expression for the effective specific yield during drainage of in-transit water and the subsequent recession of the mound has not been established. It seems reasonable that Brock's assertion of uniform specific yield during mound recession would be true in the later stages of recession, at least. We are currently investigating this problem. REFERENCE

Evaluation of the response of a water table to a variable recharge rate

“…In the Ghazvin Plain, the aquifer is very thick and the effect of capillarity may be safely disregarded. Ortiz et al (1978b) also studied the effect of in-transit water under a recharge basin. They stated that beneath the recharge area, the percolating water occupies a substantial volume of the otherwise tillable pore space and causes the effective specific yield to be less than the drainable porosity.…”

Groundwater recharge estimation from ephemeral streams. Case study: Wadi Tabalah, Saudi Arabia

“…The typical spreading of a groundwater mound after recharge has stopped is expressed by Ortiz et al (1978) analytically using half width, w, and height, h, at time, t. The hydraulic conductivity, K, is assumed to be uniform, homogeneous and isotropic.…”

“…The results from the analytical solution (Ortiz et al, 1978) were presented as dimensionless curves at the centre of the mound, and water table pro®les were generated by the solutions and represented by ®gures, which may be used to estimate the height of the mound or to determine the aquifer properties from observed data. The case when the ratio of the speci®c yield in the zone remote from the recharge region to the speci®c yield in the recharge zone is one which is identical to the previous analytical solutions obtained by Glover (1961) and Hantush (1964), where the reduction in storage capacity beneath the recharge area is not considered.…”

“…Groundwater table¯uctuations calculated by a model of the process in discrete numerical form are compared with observations in a well located at the edge of the recharge area. However, because there are assumptions in the theory on which this model is based, the model is validated by comparing its results with the analytical solution of Ortiz et al (1978). Then, a numerical approach is applied which is an extension and numerical form of an integral formulation .…”

“…Both methodologies are simple to apply and relevant to the unsaturated¯ow problems faced in recharge basins. Ortiz et al (1978) developed an analytical solution to account for the reduction in storage capacity in the growth of groundwater mounds in an uncon®ned aquifer in response to uniform and steady percolation from a recharge strip of in®nite length in the longitudinal (down-channel) direction but ®nite width across the channel bed. Beyond the boundaries of the in®ltration area, the ®llable pore space is considered equal to the drainable porosity.…”