3.2 Factors influencing infiltration rate
Four factors namely, natural recharge, tidal effects of North Sea,
pumping rate of the MAR facility and pondwater temperature have been
analyzed using single regression analysis and multivariate regression
analysis. Coefficient of determination (R2) indicated
the role of each parameter in the variation of infiltration rates in the
single variable simple regression approach and for multivariate
regression approach, p-value provided the sensitivities of the
parameters.
From the single linear regression analysis, it is observed that natural
recharge and tidal effect of the North Sea do not significantly affect
the infiltration rate (figures 14.a and 14.b). However, daily pumping
volume and water temperature show a positive correlation (figures 14.c,
14.d) with infiltration rate. Temperature shows the highest correlation
of 0.42 with infiltration rate whereas pumping rates have a correlation
coefficient of 0.23. From this test, it is inferred that temperature is
the most influencing factor in the seasonal variation of infiltration
rate through the pond bed.
Fig. 14 Linear regression plot for i) natural recharge vs
infiltration rate, ii) daily sea level vs infiltration rate, iii) daily
pumping rate vs infiltration rate, and iv) daily pondwater temperature
vs infiltration rate
On performing a multivariate analysis of the 4 factors, the following
relation (eq. 3) has been obtained:
\(y=0.1094+0.0035\ x_{1}+0.0255x_{2}+{5.41\times 10^{-6}x}_{3}+0.0053x_{4}\) (3)
Where y is predicted infiltration rate, x1 is natural recharge, x2 is daily sea level in the North Sea, x3 is daily pumping rate and x4 is mean daily pond water temperature.
Table 2 shows the statistics of the multivariate regression analysis and it is observed that the pond water temperature (variable x4) shows the least p-value of < 2E-16 and the highest coefficient among all other parameters. From fig. 15, it can be seen that the observed and predicted infiltration rate shows a fairly good match with a coefficient of determination of 0.4382. However, there are a few outliers in the observed infiltration rates, which may be attributed to human errors involved in the process of data collection for the parameters required for calculation of infiltration rates. Also, the outliers might have originated at the time of scheduled maintenance and cleaning of the infiltration ponds. It is conclusive from the tests that temperature is a dominant factor in influencing the infiltration rate across the pond bed.
Table 2. Components of multivariate linear regression to obtain infiltration rate
FIg. 15 Observed vs Predicted infiltration rate obtained after multivariate regression analysis
It was found that temperature has the most influence in the variation of infiltration rates across the pond bed. This can also be visually verified from fig 16. Temperature follows a sinusoidal pattern (Vandenbohede & Houtte, 2012) and infiltration rate is also seen to follow a cyclic pattern where the highest rates are observed in summer and lowest in winter. The R2 between temperature and infiltration rate is 0.424.
Viscosity and density of water are the two derivate properties of temperature. Sensitivities of density and viscosity on infiltration rate are checked by using linear regression. It is necessary to know which component of temperature is responsible for temperature to be the dominant factor controlling the variation of infiltration rate. From figures 17.a and 17.b and 18, it is seen that with an increase of both viscosity and density of pond water, the rate of infiltration through pond bed decreases. However, the R2 between viscosity and infiltration rate is higher than that of density and infiltration rate.
Fig. 16 Comparison of mean daily pond water temperature and infiltration rate through pond bed
Fig. 17 Regression analysis for density of water vs infiltration rate through pond bed
Following Muskat’s relation between hydraulic conductivity and intrinsic permeability (Muskat, 1937), hydraulic conductivity can be expressed as a function of temperature of water (eq, 4), assuming intrinsic permeability of the pond bed to be constant over time.
\(K\left(T\right)=K_{\text{ref}}\times\ \frac{f\left(T\right)}{f\left(T_{\text{ref}}\right)}\) (4)