AnAqSim River Element with Dry Up Feature

AnAqSim River Element is Different from a MODFLOW River Cell

AnAqSim has a River element that is similar in function to the MODFLOW River Package (or River cell). The AnAqSim River element has a “Dry Up” option that allows the River element to also behave like a MODFLOW Drain cell. We will discuss both modes of River element operation below.

[Note: The AnAqSim Drain/Fracture element is different from a MODFLOW Drain cell; but that is a story for another blog post. For example, the MODFLOW Drain cell has a lower threshold reference head - - an AnAqSim Drain element does not.]

How a River Element Behaves

When creating an AnAqSIm River element, the user specifies a Reference Stage (hydraulic head) in the river, a conductance for the river bed, and also the elevation of the bottom of the river bed (which comes into play in certain head conditions as described below). If the Aquifer Head is above the Reference Stage, groundwater discharges from the aquifer into the river (Figure 1). AnAqSim calculates the groundwater flux per length of river element into the river linesink based on 1) the head difference between the groundwater in the domain at the river location and the river reference stage, and 2) the conductance of the river bed using the following equation:

Q/L = C*(h - stage)                                           (Equation 1)

where conductance, C = (bed Kv * river width) / bed thickness.

Figure 1. Aquifer Head greater than river Reference Stage. Groundwater flows from the aquifer into the river (gaining river).

The greater the calculated Aquifer Head, the greater the groundwater discharge to the river per length of river, as shown by the red-blue dashed line in Figure 2 (see also AnAqSim User Guide):

Figure 2. River Discharge (Q/L) from the aquifer (positive Q/L) or to the aquifer (negative Q/L) per unit length of River element depending on relationship between calculated aquifer head and specified river reference stage.

 

When the Aquifer Head falls to an elevation equal to the Reference Stage, then flow in or out of the river is zero (as shown in Figure 2 at Aquifer Head equals 100, and in Figure 3).

Figure 3. Aquifer Head equal to river Reference Stage. No flow occurs between the aquifer and the river.

When the calculated Aquifer Head falls below the river Reference Stage (Aquifer Head = 100 in Figure 2), but is still above the bottom of the river bed material (“Base resisting layer” - - 98 in Figure 2), flow reverses and leakage goes from the river to the aquifer (losing river) (Figure 4). 

As Aquifer Head falls, AnAqSim continues to calculate flow per unit of line length using Equation 1 above, but at a continually decreasing rate (as shown in Figure 2 when Aquifer Head is between 100 and 98, and in Figure 4).

 

Figure 4. Aquifer Head falls below Reference Stage but remains above the bottom of the river bed. River leaks water through the bed to the aquifer (losing river).

This reduction in Aquifer Head values continues until the Aquifer Head falls below the base (bottom) of the river bed material (Figure 5).

At that point, and for any lower aquifer heads, the river element switches from Equation 1 to this equation:

Q/L = C*(base bed - stage)                                (Equation 2)

This means that the Aquifer Head no longer affects the river leakage rate through the bed, since the Aquifer Head is now below the bottom of the bed. Bed leakage is now solely a function of the head drop from the river stage to the elevation of the bottom of the bed, and the bed’s resistance (conductance). With “Dries up” unchecked AnAqSim assumes that there is enough of an upstream water source to keep the water elevation in the river constantly at the Reference Stage. This causes Q/L from Equation 2 to also be constant (flat horizontal line to the left of “Base resisting layer” - - 98 in Figure 2).

Figure 5. Aquifer Head below bottom of river bed (resisting layer). Leakage from river to aquifer is not influenced by Aquifer Head but is controlled by the head drop from the reference stage to the elevation of the river bed through the river bed conductance.

How a River Element Behaves with Dry Up Checked

The AnAqSim river element has a very useful user-selectable “Dry Up” feature. This feature allows a river linesink that is being used to represent a small stream to “dry up” - - i.e. stop accepting water from the aquifer into the river, and do not add water to the aquifer from the river - - when AnAqSim calculates that the Aquifer Head is lower than the river Reference Stage.

The underlying concept here is that the stream is not fed by a large enough upstream source to maintain the user-specified Reference Head. Instead, as groundwater falls below the Reference Head, so too does the stage in the stream. Under those conditions, the stream, which is experiencing zero head gradient between itself and the surrounding aquifer, neither receives nor gives water until the stream completely dries up (when the stage reaches the top of the bed material).

Thus the “Dry Up” condition is more properly understood not as an immediately “dried up” stream (i.e. stream stage at the top of the bed) as soon as the groundwater reaches the same elevation as the Reference Stage, but rather as a “no longer either receives nor gives water” from that reference elevation or lesser, with the stream stage matching the Aquifer Head and no water interchange occurring.

Just as happens for the “no-dry-up” river element, groundwater discharges into the “Dry Up” river element when Aquifer Head is greater than the river Reference Stage (Figure 6).

Figure 6. Aquifer Head greater than river Reference Stage. Groundwater flows from the aquifer into the river (gaining river).

And similar to the no-dry-up river, when the Aquifer Head falls to an elevation equal to the Reference Stage in the Dry-Up river element (Aquifer Head = 100 in Figure 2), flow in or out of the river is zero (see Figure 2 and Figure 7).

Figure 7. Aquifer Head equal to river Reference Stage. No flow occurs between the aquifer and the river.

But, differing from the no-dry-up river element, when Aquifer Head falls below the river Reference Stage (but remains above the bottom of the bed), the Dry-Up river element does not give leakage flow to the aquifer (i.e. it is not a losing river) (Figure 8).

Figure 8. Aquifer Head falls below Reference Stage but remains above the bottom of the river bed. Leakage into river remains at zero (because it is assumed that the stream stage cannot be maintained in the small stream and falls to coincide with the head in the aquifer).

Further, when the Aquifer Head falls below the stream bed bottom elevation, instead of the stream supplying water to the aquifer under Equation 2 above, it yields no water (“dries up”) (Figure 9).

Figure 9. Aquifer Head below bottom of river bed (resisting layer). No leakage occurs from the river to the aquifer because under this condition the river is assumed to be completely dried up.

What MODFLOW Does to Represent a River and a Drain

MODFLOW does not have this “Dry Up” capability in the River Package. Instead, MODFLOW handles this condition in two ways:

1.  If the user specifies the river using the River Package, and the groundwater head in a cell falls below the user-specified reference stage, the river continues to flow (does not dry up), and it infiltrates river water to groundwater at a rate determined by the head difference and the bed conductance. This is how the River Package functions, and there is no “Dry Up” option to turn off the infiltration of river water if calculated groundwater head falls below the specified reference stage.

OR

2.  If the user specifies a small river or stream using the Drain Package, and groundwater head in a cell falls below the user-specified reference stage, the stream (drain) dries up and does not infiltrate stream water to groundwater. This is inherently how the Drain functions; there is no checkbox for the user to turn this behavior on or off.

 Conclusion

Thus the AnAqSim River Element, with its “Dry Up” capability, functions as both a traditional MODFLOW River Package feature or a traditional MODFLOW Drain Package feature, depending on how the user sets the “Dries Up” checkbox setting.