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


XXX September 2024

ABSTRACT.  Vertical recharge of groundwater, i.e., that originating in local precipitation, os 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 leads to a sustainable grounwater recharge/discharge coefficient. For a given year, with annual precipitation P, the 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 paper, 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 have been described in a comprehensive manner by Ponce and Da Silva (2018). Their analysis is based on the pioneering work of L'vovich (1979), who laid the foundations for the cybernetic hydrologic balance. The difference between the conventional and cybernetic hydrologic balances have been elaborated by Ponce (2018). For the sake of completeness, we reiterate herein the methodology to evaluate the groundwater recharge coefficient.

2.  GROUNDWATER DISCHARGE 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 (in or mm)

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

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

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

Runoff R is the total amount of runoff at the gaging station of interest 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. The surface-runoff hydrograph is integrated to obtain the surface-runoff volume Vs; in turn, the latter is divided by the catchment area (Ac) to obtain S (mm or in).

A sample input data file is shown in the following box.

Sample Input Data File

  • Units [Select one]:   

    		•
     SI Units (metric) 

  • Number of years of record n:   

    		•
     8

  • n values of mean annual precipitation P:   

    		•
     920, 1016, 1251, 770, 915, 1235, 981, 1034 

  • n values of annual runoff R::   

    		•
     87, 141, 377, 71, 69, 281, 205, 187 

  • n values of annual surface runoff S::   

    		•
     61, 96, 266, 50, 53, 199, 134, 107 

Output from the calculator is shown below.

REFERENCES

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

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