126 / EDUCACIÓN PARA EL DESARROLLO

As shown in Eq. (5.2.13), the recharge parameter ß must be evaluated before the rising limb of the baseflow hydrograph can be calculated using this equation.

The processes of recharge to confined and unconfined aquifers are different. The difference as shown by Ishihara and Takagi (1965), however, is only in the magnitude of a recharge parameter ß, which is a measure of the rate at which recharging water enters the groundwater flow system.

Several kinds of recharge rates can be defined: the average recharge rate, maximum recharge rate, constant recharge rate or a variable recharge rate.

5 . 2 . 5 . 1 The Average and Maximum Recharge Rates

As stated earlier, the rainfall intensities in the Sherwood catchment are lower than the saturated hydraulic conductivities of the surface soil so that subsurface runoff originates from the recharged storm water while overland flow originates from the saturated surfaces only.

For analysis of recharge, it is reasonable to assume that the effective rainfall intensity is a direct measure of the recharge rate in this catchment. Several cases are then

discussed below.

For constant rainfall intensity, the recharge rate can be computed using Eq. (5.2.6). However, several options can be developed to derive recharge rates for varying rainfall intensities. The First option is to equate the maximum effective rainfall intensity to the recharge rate so that the maximum discharge of the stream flow is equal to or less than the maximum recharge rate from the particular rainfall event. The second option is to use an average recharge rate to derive the parameter ß.

For the maximum recharge rate, the relationship could be expressed as

R<m = rm - K r (5.2.14)

where

Ron is the maximum recharge rate;

rm is the maximum rainfall intensity during a rainfall event; and Kr is the average continuing loss rate.

For an average recharge rate during a particular storm event, this relationship could be expressed as

Rea = ra - Kr (5.2.15)

where

Rea is the average recharge rate; and ra is the average rainfall intensity.

The average rainfall intensity ra could be determined as

ra = H ^ rei (5-2.16)

1 = 1

where

rei is the effective rainfall intensity in the time interval i, determined using Eq. (5.2.6), and

m is the number of effective rainfalls at discrete time intervals.

It is clear that the former (Ron) overestimates the total recharge while the latter ( R ^ underestimates the peak of the baseflow discharge.

In the analysis both options above have been used to compute the recharge rates. The maximum and average recharge rates for different storms in 1990 and 1991 are listed in Table 5.2.4.

Table 5.2.4 shows that the maximum recharge rate is about 3 times the average recharge rate. The effect of the magnitude of recharge rates on the recharge parameter is discussed below.

5 . 2 . 5 . 2 The Recharge Parameter

There are several means available for evaluating the parameter ß. (1). For Constant Recharge Rate:

Table 5.2.4. The Maximum and Average Recharge Rate

Date Maximum Recharge Rates Average Recharge Rates (mmh’1) (mmh*1) 1990 11 April 4.44 1.97 13 April 3.55 2.23 18 April 5.44 1.53 20 April 7.62 2.55 22 May 3.94 1.46 24 May 3.23 2.50 30 May 6.24 1.78 26 June 3.81 1.57 1 July 3.35 1.10 4 July 7.36 1.28 18 July 0.82 1.26 5 Aug. 4.02 1.33 12 Sept. 4.41 1.64 ►91 7 June 7.02 2.06 9 June 9.02 1.65 11 June 2.84 0.96 12 June 2.30 0.90 8 July 3.91 1.28 9 July 2.45 1.55 10 July 1.28 1.21 11 July 2.48 1.28 5 Aug. 4.77 2.58 7 Aug. 4.88 1.26

If the effective rainfall intensity is greater than the saturated hydraulic conductivity of the surface soil, Ko, then it is reasonable to infer that the recharge rate, Re, can be set equal to the saturated hydraulic conductivity, that is

Ro = K0 Re >Ko (5.2.17)

where

Ro = Re, and is called the constant recharge rate. Then Eq. (5.2.13) can be written as

Qbu = 0.278K0[1- e-ß(t- V ] (5.2.18)

Equation (5.2.18) describes the rising limb of a baseflow hydrograph from time to time tpb (see Fig. 5.2.1).

If the only available reading on the rising limb of the baseflow hydrograph is discharge Qtpb at time tpb, as assumed, then Qbu in Eq. (5.2.18) can be replaced by Qtpb and t replaced with tpb. Substituting and rearranging Eq. (5.2.18) gives

Qtpb (5.2.19) ln[l 0.27 8K0 tpb - Tib If we substitute (cf. Fig. 5.2.1) te = tpb - Tib (5.2.20)

then, Eq. (5.2.19) finally can be written as

ß

ln[l - Qtpb 0.278KpJ

te (5.2.21)

In Eq. (5.2.21), ß can be evaluated as QtPb and te are known, and Ko can be measured. 0.6- ... ß = 0.001 - - - ß = 0.010 - - ß = 0.050 ß = 0.100 0.4 H

Time since recharge started, h.

This approach, which can only be used if the rainfall intensity is greater than the saturated hydraulic conductivity of the surface soil, yields the curves shown in Fig. 5.2.12 with different values of the parameter ß.

This figure shows that the larger is the value of ß, the shorter the time to equilibrium of baseflow discharge.

However, the duration-intensity-frequency analysis (Fig. 5.2.6) shows that the maximum rainfall intensity, within a one year return period, is 11.4 mmh'1 averaged over the period of 1 hour or 40.0 mmh"1 over a period of 6 minutes. It follows that rainfall intensity did not exceed the saturated hydraulic conductivity of the surface soil during the period of record. Therefore it is unreasonable to assume that the recharge rate is equal to the saturated hydraulic conductivity.

For this case, alternative approaches should be developed to evaluate ß. (2). For Average Recharge Rate:

One of these approaches is to assume the effective recharge rate to be the effective rainfall intensity, as mentioned earlier. This is equivalent to stating that for rainfall intensities less than the saturated hydraulic conductivity of the surface soil the recharge rate to the subsurface flow or the groundwater is equal to the effective rainfall intensity.

Then, the only change to be made in Eq. (5.2.21) is replacing Koby R^

ß where

ln[l - Qtpb 1 0.278R(aJ

te (5.2.22)

R ^is the average recharge rate determined by Eq. (5.2.15) (3). For Maximum Recharge Rate:

As mentioned earlier, the parameter ß can also be evaluated using the maximum recharge rate. Then we have

ß

where

ln[l - Q tp b n 0.2 7 8R qT1J

te (5.2.23)

R^mis the maximum recharge rate determined by Eq. (5.2.14)

Use of Eqs. (5.2.22) and (5.2.23) yields the values of ß for different storms as listed in Table 5.2.5.

It can be seen from this table that the values of ß are different depending on the recharge rates selected for the computations.

In Eq. (5.2.8), because ß is proportional to Ho, and VQo is also proportional to Ho as shown by Ishihara and Takagi (1965), then a linear relationship can be expected between ß and VQo.

The values of ß, evaluated from analysis of the data for the storms in 1990 and 1991 in the Sherwood catchment, are plotted in Figs. 5.2.13 and 5.2.14 showing the

Table 5.2.5. Recharge Parameter Determined from Maximum and Mean Recharge Rates

Date Values of ß

Based on

Maximum Recharge Rate (mmh_1)

Values of ß Based on Mean Recharge rate

(rnrnh-1) 1990 11 April 0.006111 0.014779 13 April 0.007960 0.013180 18 April 0.004685 0.019260 20April 0.012530 0.054470 22 April 0.004190 0.012460 24 April 0.031840 0.042890 30 may 0.007680 0.030900 26 June 0.001295 0.009665 01 July 0.003245 0.010900 04 July 0.008725 0.004593 05 Aug. 0.004000 0.001345 12 Sept. 0.001226 0.003380 1991 07 June 0.000990 0.005708 09 June 0.002382 0.007642 11 June 0.004850 0.014920 12 June 0.008155 0.022110 08 July 0.002480 0.008000 09 July 0.014660 0.027480 10 July 0.014080 0.058870 11 July 0.029120 0.069410 05 Aug. 0.0092800 0.019020 07 Aug. 0.0016050 0.006683 86

0.035 -I 0.03 - 0.025 - 0.02 - 0.015 - 0.01 - 0.005 -o 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Fig. 5.2.13. The relationship between recharge parameter and initial baseflow - The values o f ß are determined with a maximum recharge rate.

0.07 n 0.06 - 0.05 - 0.04 - 0.03 - 0.02 - 0.01 -

Fig. 5.2.14. The relationship between recharge parameter and initial baseflow - The values o f ß are determined with an average recharge rate.

dependence of the values of ß on the initial baseflow discharges before the storms.

The relationship between ß and the initial baseflow discharge can be represented by an equation of the form

ßi = 0.002167 + 0.03140*Vq0 (5.2.24)

for the parameter ß determined using the maximum recharge rate, and

ß2 = 0.00641 + 0.07457*Vq„ (5.2.25)

for ß determined using the mean recharge rate.