The use of a streamflow hydrograph to estimate ground-water recharge and discharge in humid settings By Al Rutledge U.S. Geological Survey Geological Society of America Annual Meeting, October 2005

“Hydrograph separation” is used in hydrologic settings where there is areal recharge to the water table and ground-water discharge to a gaining stream The idea is to quantify the portion of the streamflow hydrograph that comes from ground-water discharge.

Before the 1980’s hydrograph separation was performed manually. Computerized methods are advantageous because of speed and repeatability. Examples are HYSEP, BFI, and PART. The topic here is the analytical model PULSE. This is a hybrid between manual and computerized methods. The user designates model input (recharge and other variables), then the program generates the hydrograph of ground-water discharge. A calibration process is required. PULSE allows for monthly accounting of ground-water recharge and ground-water discharge.

PULSE is a computer implementation of the “Rorabaugh Model” of ground-water discharge to a stream. The Rorabaugh model (ref 1) is formulated for a cross-section of the aquifer of unit width. The flow in the section is a function of aquifer hydraulic properties, geometry, instantaneous water-level rise, etc. For PULSE, substitutions have been performed so that total ground-water discharge in the basin can be expressed as a function of drainage area, recession index (K), and recharge.

PULSE can allow for --- Instantaneous recharge Gradual recharge during storm events Gradual recharge over a long period (the month or season) Leakage to or from a deeper aquifer

To account for gradual recharge the model uses an equation derived from Daniel (ref 2). Gradual recharge is initiated and terminated using superposition. The following slide shows two simulations (instantaneous and gradual recharge).

Same recharge applied (1) as series of instantaneous recharge events and (2) as a gradual process

The calibration process ---- adjusting the estimate of recharge until there is a reasonable match between simulated ground-water discharge and streamflow on days that represent ground-water discharge. Total streamflow GWD

Some segments of the streamflow hydrograph are dominated by direct-surface runoff. These segments will not be matched in the calibration process. How do we determine duration of these segments? This will depend on drainage area, basin relief, and other factors. Reference 3 includes discussion of runoff.

Example application See reference 5 – Risser and others Streamflow station Wells (red)

A period of recharge is selected for analysis, which begins with low flow and ends with low flow. This way, total recharge should be roughly equal to total ground-water discharge. Sep Aug

Streamflow Simulated GWD Log Linear

The model can be applied if the streamflow record is the only data source. In this example, ground-water-level data are used to help verify the way the model is applied. In particular, GWL data are used to evaluate the timing of recharge. The rise for day i ….. Rise(i) = GWL(i) – GWL(i-1) (if less than zero it is designated zero)

Monthly GWL rise – five wells. Monthly Recharge Note months 7-11 (alternating highs and lows)

Monthly ground-water discharge Calculated by PULSE Automated base-flow- record estimation HYSEP PART

Observations from the example Timing of recharge specified in the model is similar to timing of GWL rises. Over the period of analysis, total recharge (R) is nearly identical to total discharge (D) (about 21 inches). On a small time scale such as the month, R and D can be quite different. Monthly fluctuations of R can be greater than monthly fluctuation of D. (Such as months 7-11)

Limits of GWL data In the preceding analysis, ground-water-level (GWL) data are only used to verify timing of recharge. GWL data might be used for other reasons, but there are limits…. There may not be a unique relation between GWL and ground- water discharge (D) (ref 4). Proportionality between GWL and D (flawed because of previous item) can only be approximated if GWL is expressed relative to the altitude of the outflow boundary. Care should be used when assessing the flow recession index on the basis of GWL recession (ref 4 and a future publication).

General comment about PULSE In regional studies that include many streamflow gaging stations, automated hydrograph separation will be the preferred method. Nonetheless, PULSE might have a role. The hydrologist might select a small subset of the data for detailed analysis. Results from PULSE for this subset should agree with results from automated hydrograph separation. The PULSE model can be used to (1) Incorporate results of GWL analysis. (2) Define temporal distribution of recharge and discharge.

Al Rutledge, U.S. Geological Survey References – (1) Rorabaugh, (2) Daniel, 1976, WRR, v. 12, no. 3. (3) Rutledge, 1997, USGS WRIR (4) Rutledge, 2002, USGS OFR (5) Risser and others, 2005, USGS SIR