Fig. 1   The cybernetic hydrologic balance (L'vovich, 1979).


HOW TO CALCULATE ONLINE A SUSTAINABLE

GROUNDWATER RECHARGE COEFFICIENT?


Victor M. Ponce

Professor Emeritus of Civil and Environmental Engineering

San Diego State University, San Diego, California


10 September 2024

ABSTRACT.  Vertical recharge of groundwater, i.e., that originating in local precipitation, is ostensibly the only discharge that could be freely tapped for capture by groundwater to avoid encroachment on established rights (Ponce and Da Silva, 2018). This analysis leads to the concept of sustainable groundwater discharge. For a given year, with annual precipitation P, the sustainable groundwater recharge coefficient Kg is defined as the ratio U/P, wherein U = baseflow, is the fraction of wetting (L'vovivh, 1979) which exfiltrates as the dry-weather flow of streams and rivers. The calcuiation of Kg requires a thoughtful evaluation of U. In this article, we feature an online calculator to evaluate the annual groundwater recharge coefficient Kg based on relevant precipitation-runoff data.

1.  SUSTAINABLE USE OF GROUNDWATER

The issues regarding the sustainable use of groundwater were brought into sharp focus with the pioneering work of Sophocleus (1997) and Alley et al (1999). More recently, these issues have been extensibly treated by Ponce and Da Silva (2018). Their analysis is based on the seminal work of L'vovich (1979), who laid the foundations for the cybernetic hydrologic balance. The difference between conventional and cybernetic hydrologic balances has been described by Ponce (2018). For the sake of completeness, we reiterate herein the methodology to evaluate the groundwater recharge coefficient.

2.  GROUNDWATER RECHARGE COEFFICIENT

In L'vovich's approach, annual precipitation P is separated into two components (Fig. 1):

            
P  =  S  +  W
             		(1)

in which S = surface runoff, i.e., the fraction of runoff originating directly on the land surface, and W = catchment wetting, or simply, wetting, the fraction of precipitation not contributing to surface runoff.

L'vovich's water balance

Fig. 1  The cybernetic hydrologic balance (L'vovich, 1979).

In turn, wetting is separated into two components:

            
W  =  U  +  V
             		(2)

in which U = baseflow, i.e., the fraction of wetting which exfiltrates as the dry-weather flow of streams and rivers, and V = vaporization, i.e., the fraction of wetting returned to the atmosphere as water vapor.

Runoff (i.e., total runoff) is the sum of surface runoff and baseflow:

            
R  =  S  +  U
             		(3)

Combining Eqs. 1 to 3:

            
P  =  R  +  V
             		(4)

Equations 1 to 4 constitute a set of water balance equations. Four water balance coefficients may be defined: (1) runoff coefficient, (2) baseflow coefficient, (3) wetting coefficient, and (4) groundwater recharge coefficient.

The runoff coefficient is:


            R
Kr  =  _____
            P

(5)

The baseflow coefficient is:


             U
Ku  =  _____
            W

(6)

The wetting coefficient is:


             W
Kw  =  _____
             R

(7)

The groundwater recharge coefficient is:


             U
Kg  =  _____
             P

(8)

3.  THE ONLINE CALCULATOR

The online calculator ONLINEWATERBALANCE2 was developed at the Visualab, Department of Civil, Construction, and Environmental Engineering, at San Diego State University, San Diego, California. The calculator requires the following input data:

INPUT DATA

  1. System of units (either SI or U.S. Customary Units)

  2. Number of years of precipitation-runoff record: n

  3. n values of annual precipitation P (mm or in)

  4. n values of annual runoff R (mm or in)

  5. n values of annual surface runoff S (mm or in).

Precipitation P (mm or in) is the total amount of spatially weighted measured precipitation in a given catchment for the given year.

Runoff R is the total amount of runoff at the gaging station at the catchment mouth for the given year. It is obtained by integrating the measured annual runoff hydrograph Qr to calculate the total runoff volume Vr, and dividing this volume by the catchment drainage area Ac to obtain R (mm or in).

Surface runoff S is obtained by separating, using an appropriate baseflow separation technique, the measured annual runoff hydrograph Qr into its two components: (1) surface-runoff hydrograph, and (2) baseflow hydrograph (Ponce, 2014). The surface-runoff hydrograph is integrated to obtain the surface-runoff volume Vs; in turn, the latter is divided by the catchment drainage area to obtain S (mm or in).

A suitable input data file is shown in the following box. The data file was originally presented by Ponce and Da Silva (2018).

Example Input Data File

  • Units [Select one]:   

    		•
     SI Units (metric) 

  • Number of years of record n:   

    		•
     11

  • n values of P: 

    		•

     943, 1060, 1312, 824, 953, 1347, 1047, 1379, 856, 1090, 1521 

  • n values of R: 

    		•
     544, 458, 671, 275, 365, 511, 360, 586, 350, 471, 249  

  • n values of S: 

    		•
     506, 413, 564, 243, 346, 444, 319, 530, 325, 441, 111  

Figure 2 shows the results from the calculator. Columns 2, 3, and 4 echo the input data; Columns 4 to 10 show the indicated hydrologic variables and coefficients; and lastly, Column 11 shows the groundwater recharge coefficient Kg (Eq. 8). The average value of groundwater recharge coefficient for the tested period of record, shown in Col. 11 (in the line labeled Average and colored gray near the bottom of the table) is Kga = 0.045, This result means that the average value of local baseflow U (ie., that originating within the basin) amounts to 4.5% of precipitation.

Fig. 2  Sample output from ONLINEWATERBALANCE2.

4.  CLOSING STATEMENT

The calculated average value of Kg may be used as a reference to support the sustainable use of groundwater in the catchment/watershed/basin under consideration. For instance, given the average value of Kga = 0.045 for the catchment of the present example, an annual precipitation forecast Pi for the ith year and catchment/watershed/basin area Ac leads to the following volume Vi of sustainable annual groundwater pumping: Vi = Kga Pi Ac.

REFERENCES

Alley, W. M., T. E. Reilly, and O. E. Franke. 1999. Sustainability of groundwater resources. U.S. Geological Survey Circular 1186, Denver, Colorado, 79 p.

L'vovich, M. I. 1979. World water resources and their future. Translation from Russian by Raymond L. Nace, American Geophysical Union.

Ponce, V. M. 2014. Engineering Hydrology: Principles and Practices, Chapter 5, Section 5.3: Unit HYdrograph.

Ponce, V. M. . 2018. Why is the cybernetic hydrologic balance better suited for yield hydrology than the conventional approach? Online article.

Ponce, V. M. and J. Da Silva. 2018. How much water could be pumped from an aquifer and still remain sustainable? Online article.

Sophocleous, M. 1997. Managing water resources systems: Why "safe yield" is not sustainable? Editorial, Ground Water, Vol. 35, No. 4, July-August, 561.

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