Estimation of the groundwater recharge coefficient by minimizing the sum total error of a regional water balance

Abstract

The sustainable use of groundwater resources requires that the components of a regional water balance are understood with a high degree of accuracy, especially in arid and semi-arid regions. Although groundwater recharge is one of the most important components of a groundwater balance, its rate is one of the most uncertain components. Despite the simplicity and widespread use of water balance method (WB) for estimating groundwater recharge in arid and semi-arid regions, the accuracy of the groundwater recharge estimation depends on the accuracy of the other components in this method, so a reduction in errors that are associated with measuring these can improve the accuracy of recharge estimation. Therefore, the main objective of the current paper was to present a method for estimating groundwater recharge based on minimization of the sum total error of the system water and groundwater balance equations simultaneously. A set of correction coefficients that reflect the error in estimation of each component of balance equations, were applied to different components in annual scale. Reasonable ranges, obtained from error analysis, were considered for the correction coefficients and the sum of absolute errors in the overall system water balance and groundwater balance equations was minimized for the period of study. The proposed method was used to estimate groundwater recharge in Mahvelat basin in Khorasan Razavi province of Iran, as a case study. The minimization process used in this research reduced the error of system water and groundwater balance equations by 55% and 65%, respectively. Moreover, as the results of optimization process on the correction coefficients, the recharge coefficients due to precipitation and irrigation return flow were estimated to be 2% and 16.5%, respectively.

Appendix

As mentioned in “Evapotranspiration” section, the Turc equation was used to estimate evapotranspiration in the study area. To calculate the error of estimating evapotranspiration by the Turc method, the error of estimating precipitation and temperature must be combined with each other, according to the following equation (Eq. 20 in the text of the article).

$${Error(}{{ET}}_{{\rm a}}{) = }\left|\frac{{{\partial}}{{ET}}_{{\rm a}}}{{{\partial}}{{T}}}{\cdot Error(T)}\right|{+}\left|\frac{{{\partial}}{{ET}}_{{a}}}{{{\partial}}{{P}}}{\cdot Error(P)}\right|$$

(32)

The mean absolute of temperature and precipitation interpolation error in each year was calculated by cross-validation procedure in Arc GIS geostatistical analyser. In addition to the interpolation error, the error of the measuring devices was also included in the calculation of the precipitation and temperature estimation error. Then, the temperature estimation error in each year was combined with the precipitation estimation error according to Eq. (32) using Microsoft Mathematics software.

According to Ekern and Chang (1985) and Gurney and Camillo (1984), there is a 10% error in estimating evapotranspiration using empirical relationships to direct measurement methods. Therefore, 10% should be added to the error calculated from the combination of temperature and precipitation error to calculate the error of estimating evapotranspiration using the Turc equation. The results of calculating the error of estimating the evapotranspiration are presented in the Table 8.

Table 8 Evapotranspiration estimation error

After calculating the estimation error in each year, the range of correction coefficient of evapotranspiration was calculated by Eq. (33) (Eq. (27) in the text of the article).

$$\left( {\overline{x}_{j} - 2\sigma_{j} } \right) \le |x_{j} | \le \left( {\overline{x}_{j} + 2\sigma_{j} } \right)$$

(33)

where $\overline{x}_{j}$ and σ_j are the average and standard deviation of the evapotranspiration estimation error for a j-year (12 year). The result of calculation of the range of correction coefficient of evapotranspiration is presented in below.

$$1 - (12.54 + 2 \times 3.4)/100 < c_{{ET_{a} }} < 1 + (12.54 + 2 \times 3.4)/100 \to 0.81 < c_{{ET_{a} }} < 1.19$$

(34)