Catchment Water Table Configuration and Baseflow Regression Problem
Consider the mounding of groundwater between two streams draining an unconfined aquifer (see Figure 1). A common practice is to analyze the flow in the system by assuming predominantly horizontal flow in the aquifer. The analysis may be further simplified by assuming that the change of the saturated thickness along the direction of flow (x-direction) of the aquifer is small compared to the average saturated thickness.
For the conditions indicated below, determine discuss the water level change DhL across the aquifer (x-direction) and an "effective" transmissivity for the overall aquifer system. Also determine the maximum mound height, hmax, and average head, have. Discuss how different parameters of the aquifer system (L, recharge, and transmissivity) impact DhL,, hmax, etc.
- Surface aquifer transmissivity = 1000 m2/day
- Bottom aquifer thickness = 2000 m2/day
- River depth = 10 m
- Recharge = 0.001 m/day
- Aquifer Horizontal extent = 1 km
Figure 1: Mounding of groundwater between two streams draining an unconfined aquifer.
Now consider the baseflow for one of the streams (see Figure 2). If the water table between the groundwater divide and the stream can be expressed as:
Derive an analytical expression that describes the water level recession process in a dry season (recharge = 0), i.e., the flux into the stream as a function of time. Given the derived flux equation, propose a regression procedure that can be used to estimate the aquifer transmissivity using stream base flow measurements.
Figure 2: Cross-section (left) and plan view (right) of the unconfined aquifer.